Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.1 | ||
Root | \(1.43801 - 1.04478i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.q.372.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.549273 | − | 1.69049i | −0.388395 | − | 1.19536i | −0.933988 | − | 0.357305i | \(-0.883696\pi\) |
0.545593 | − | 0.838050i | \(-0.316304\pi\) | |||||||
\(3\) | −0.500000 | − | 0.363271i | −0.288675 | − | 0.209735i | 0.434017 | − | 0.900905i | \(-0.357096\pi\) |
−0.722692 | + | 0.691170i | \(0.757096\pi\) | |||||||
\(4\) | −0.938015 | + | 0.681508i | −0.469007 | + | 0.340754i | ||||
\(5\) | −0.858290 | + | 2.64154i | −0.383839 | + | 1.18133i | 0.553480 | + | 0.832862i | \(0.313299\pi\) |
−0.937319 | + | 0.348472i | \(0.886701\pi\) | |||||||
\(6\) | −0.339469 | + | 1.04478i | −0.138588 | + | 0.426529i | ||||
\(7\) | −0.809017 | + | 0.587785i | −0.305780 | + | 0.222162i | ||||
\(8\) | −1.20872 | − | 0.878189i | −0.427348 | − | 0.310487i | ||||
\(9\) | −0.809017 | − | 2.48990i | −0.269672 | − | 0.829966i | ||||
\(10\) | 4.93693 | 1.56120 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.716580 | 0.206859 | ||||||||
\(13\) | 1.32676 | + | 4.08334i | 0.367976 | + | 1.13251i | 0.948096 | + | 0.317983i | \(0.103006\pi\) |
−0.580120 | + | 0.814531i | \(0.696994\pi\) | |||||||
\(14\) | 1.43801 | + | 1.04478i | 0.384326 | + | 0.279229i | ||||
\(15\) | 1.38874 | − | 1.00898i | 0.358572 | − | 0.260518i | ||||
\(16\) | −1.53723 | + | 4.73110i | −0.384307 | + | 1.18278i | ||||
\(17\) | 0.851514 | − | 2.62069i | 0.206522 | − | 0.635611i | −0.793125 | − | 0.609059i | \(-0.791547\pi\) |
0.999647 | − | 0.0265518i | \(-0.00845268\pi\) | |||||||
\(18\) | −3.76477 | + | 2.73527i | −0.887365 | + | 0.644709i | ||||
\(19\) | 1.56876 | + | 1.13977i | 0.359898 | + | 0.261482i | 0.753010 | − | 0.658009i | \(-0.228601\pi\) |
−0.393111 | + | 0.919491i | \(0.628601\pi\) | |||||||
\(20\) | −0.995144 | − | 3.06274i | −0.222521 | − | 0.684849i | ||||
\(21\) | 0.618034 | 0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.37009 | 0.911228 | 0.455614 | − | 0.890178i | \(-0.349420\pi\) | ||||
0.455614 | + | 0.890178i | \(0.349420\pi\) | |||||||
\(24\) | 0.285341 | + | 0.878189i | 0.0582450 | + | 0.179260i | ||||
\(25\) | −2.19601 | − | 1.59550i | −0.439202 | − | 0.319099i | ||||
\(26\) | 6.17408 | − | 4.48573i | 1.21084 | − | 0.879725i | ||||
\(27\) | −1.07295 | + | 3.30220i | −0.206489 | + | 0.635508i | ||||
\(28\) | 0.358290 | − | 1.10270i | 0.0677104 | − | 0.208391i | ||||
\(29\) | 6.98027 | − | 5.07146i | 1.29620 | − | 0.941747i | 0.296293 | − | 0.955097i | \(-0.404250\pi\) |
0.999911 | + | 0.0133499i | \(0.00424953\pi\) | |||||||
\(30\) | −2.46847 | − | 1.79345i | −0.450678 | − | 0.327437i | ||||
\(31\) | −0.0619850 | − | 0.190770i | −0.0111328 | − | 0.0342634i | 0.945336 | − | 0.326099i | \(-0.105734\pi\) |
−0.956469 | + | 0.291835i | \(0.905734\pi\) | |||||||
\(32\) | 5.85410 | 1.03487 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.89796 | −0.839993 | ||||||||
\(35\) | −0.858290 | − | 2.64154i | −0.145077 | − | 0.446503i | ||||
\(36\) | 2.45576 | + | 1.78421i | 0.409293 | + | 0.297368i | ||||
\(37\) | −0.837721 | + | 0.608640i | −0.137720 | + | 0.100060i | −0.654512 | − | 0.756051i | \(-0.727126\pi\) |
0.516792 | + | 0.856111i | \(0.327126\pi\) | |||||||
\(38\) | 1.06509 | − | 3.27802i | 0.172781 | − | 0.531765i | ||||
\(39\) | 0.819981 | − | 2.52364i | 0.131302 | − | 0.404106i | ||||
\(40\) | 3.35721 | − | 2.43916i | 0.530821 | − | 0.385664i | ||||
\(41\) | 7.77155 | + | 5.64636i | 1.21371 | + | 0.881813i | 0.995563 | − | 0.0941021i | \(-0.0299980\pi\) |
0.218149 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(42\) | −0.339469 | − | 1.04478i | −0.0523812 | − | 0.161213i | ||||
\(43\) | 4.70820 | 0.717994 | 0.358997 | − | 0.933339i | \(-0.383119\pi\) | ||||
0.358997 | + | 0.933339i | \(0.383119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.27155 | 1.08398 | ||||||||
\(46\) | −2.40037 | − | 7.38759i | −0.353916 | − | 1.08924i | ||||
\(47\) | 10.5541 | + | 7.66797i | 1.53947 | + | 1.11849i | 0.950668 | + | 0.310210i | \(0.100399\pi\) |
0.588800 | + | 0.808279i | \(0.299601\pi\) | |||||||
\(48\) | 2.48729 | − | 1.80712i | 0.359009 | − | 0.260835i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | −1.49096 | + | 4.58869i | −0.210853 | + | 0.648939i | ||||
\(51\) | −1.37778 | + | 1.00101i | −0.192928 | + | 0.140170i | ||||
\(52\) | −4.02734 | − | 2.92604i | −0.558492 | − | 0.405768i | ||||
\(53\) | −1.20520 | − | 3.70923i | −0.165547 | − | 0.509502i | 0.833529 | − | 0.552476i | \(-0.186317\pi\) |
−0.999076 | + | 0.0429735i | \(0.986317\pi\) | |||||||
\(54\) | 6.17167 | 0.839857 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.49406 | 0.199653 | ||||||||
\(57\) | −0.370334 | − | 1.13977i | −0.0490520 | − | 0.150966i | ||||
\(58\) | −12.4073 | − | 9.01445i | −1.62916 | − | 1.18365i | ||||
\(59\) | 6.92286 | − | 5.02975i | 0.901280 | − | 0.654818i | −0.0375144 | − | 0.999296i | \(-0.511944\pi\) |
0.938794 | + | 0.344478i | \(0.111944\pi\) | |||||||
\(60\) | −0.615033 | + | 1.89288i | −0.0794004 | + | 0.244369i | ||||
\(61\) | 0.305497 | − | 0.940223i | 0.0391149 | − | 0.120383i | −0.929592 | − | 0.368589i | \(-0.879841\pi\) |
0.968707 | + | 0.248206i | \(0.0798410\pi\) | |||||||
\(62\) | −0.288448 | + | 0.209570i | −0.0366330 | + | 0.0266154i | ||||
\(63\) | 2.11803 | + | 1.53884i | 0.266847 | + | 0.193876i | ||||
\(64\) | −0.141042 | − | 0.434084i | −0.0176303 | − | 0.0542605i | ||||
\(65\) | −11.9251 | −1.47912 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.41745 | −0.661846 | −0.330923 | − | 0.943658i | \(-0.607360\pi\) | ||||
−0.330923 | + | 0.943658i | \(0.607360\pi\) | |||||||
\(68\) | 0.987288 | + | 3.03856i | 0.119726 | + | 0.368479i | ||||
\(69\) | −2.18505 | − | 1.58753i | −0.263049 | − | 0.191116i | ||||
\(70\) | −3.99406 | + | 2.90186i | −0.477382 | + | 0.346838i | ||||
\(71\) | −0.623302 | + | 1.91833i | −0.0739724 | + | 0.227664i | −0.981206 | − | 0.192964i | \(-0.938190\pi\) |
0.907234 | + | 0.420627i | \(0.138190\pi\) | |||||||
\(72\) | −1.20872 | + | 3.72007i | −0.142449 | + | 0.438414i | ||||
\(73\) | −8.06677 | + | 5.86085i | −0.944144 | + | 0.685961i | −0.949415 | − | 0.314025i | \(-0.898322\pi\) |
0.00527037 | + | 0.999986i | \(0.498322\pi\) | |||||||
\(74\) | 1.48904 | + | 1.08185i | 0.173097 | + | 0.125762i | ||||
\(75\) | 0.518408 | + | 1.59550i | 0.0598606 | + | 0.184232i | ||||
\(76\) | −2.24828 | −0.257896 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.71658 | −0.534047 | ||||||||
\(79\) | −1.94479 | − | 5.98545i | −0.218806 | − | 0.673416i | −0.998861 | − | 0.0477054i | \(-0.984809\pi\) |
0.780055 | − | 0.625711i | \(-0.215191\pi\) | |||||||
\(80\) | −11.1780 | − | 8.12131i | −1.24974 | − | 0.907991i | ||||
\(81\) | −4.61803 | + | 3.35520i | −0.513115 | + | 0.372800i | ||||
\(82\) | 5.27640 | − | 16.2391i | 0.582681 | − | 1.79331i | ||||
\(83\) | 0.531960 | − | 1.63720i | 0.0583902 | − | 0.179707i | −0.917607 | − | 0.397488i | \(-0.869882\pi\) |
0.975998 | + | 0.217781i | \(0.0698820\pi\) | |||||||
\(84\) | −0.579725 | + | 0.421195i | −0.0632532 | + | 0.0459561i | ||||
\(85\) | 6.19182 | + | 4.49862i | 0.671598 | + | 0.487944i | ||||
\(86\) | −2.58609 | − | 7.95916i | −0.278865 | − | 0.858259i | ||||
\(87\) | −5.33245 | −0.571699 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3035 | −1.62217 | −0.811086 | − | 0.584928i | \(-0.801123\pi\) | ||||
−0.811086 | + | 0.584928i | \(0.801123\pi\) | |||||||
\(90\) | −3.99406 | − | 12.2925i | −0.421011 | − | 1.29574i | ||||
\(91\) | −3.47350 | − | 2.52364i | −0.364121 | − | 0.264550i | ||||
\(92\) | −4.09921 | + | 2.97825i | −0.427373 | + | 0.310504i | ||||
\(93\) | −0.0383089 | + | 0.117903i | −0.00397244 | + | 0.0122259i | ||||
\(94\) | 7.16556 | − | 22.0533i | 0.739071 | − | 2.27463i | ||||
\(95\) | −4.35721 | + | 3.16570i | −0.447040 | + | 0.324794i | ||||
\(96\) | −2.92705 | − | 2.12663i | −0.298741 | − | 0.217048i | ||||
\(97\) | 3.58961 | + | 11.0477i | 0.364470 | + | 1.12172i | 0.950313 | + | 0.311297i | \(0.100764\pi\) |
−0.585843 | + | 0.810425i | \(0.699236\pi\) | |||||||
\(98\) | −1.77748 | −0.179553 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.14723 | 0.314723 | ||||||||
\(101\) | −1.05430 | − | 3.24480i | −0.104907 | − | 0.322870i | 0.884802 | − | 0.465968i | \(-0.154294\pi\) |
−0.989709 | + | 0.143098i | \(0.954294\pi\) | |||||||
\(102\) | 2.44898 | + | 1.77929i | 0.242485 | + | 0.176176i | ||||
\(103\) | 14.7100 | − | 10.6875i | 1.44942 | − | 1.05307i | 0.463455 | − | 0.886121i | \(-0.346610\pi\) |
0.985966 | − | 0.166945i | \(-0.0533903\pi\) | |||||||
\(104\) | 1.98226 | − | 6.10077i | 0.194377 | − | 0.598230i | ||||
\(105\) | −0.530452 | + | 1.63256i | −0.0517668 | + | 0.159322i | ||||
\(106\) | −5.60843 | + | 4.07476i | −0.544739 | + | 0.395776i | ||||
\(107\) | 2.62725 | + | 1.90881i | 0.253986 | + | 0.184532i | 0.707491 | − | 0.706722i | \(-0.249827\pi\) |
−0.453506 | + | 0.891253i | \(0.649827\pi\) | |||||||
\(108\) | −1.24403 | − | 3.82873i | −0.119707 | − | 0.368420i | ||||
\(109\) | −12.6912 | −1.21559 | −0.607796 | − | 0.794093i | \(-0.707946\pi\) | ||||
−0.607796 | + | 0.794093i | \(0.707946\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.639962 | 0.0607425 | ||||||||
\(112\) | −1.53723 | − | 4.73110i | −0.145254 | − | 0.447047i | ||||
\(113\) | 14.9248 | + | 10.8435i | 1.40401 | + | 1.02007i | 0.994160 | + | 0.107915i | \(0.0344173\pi\) |
0.409845 | + | 0.912155i | \(0.365583\pi\) | |||||||
\(114\) | −1.72336 | + | 1.25209i | −0.161407 | + | 0.117269i | ||||
\(115\) | −3.75081 | + | 11.5438i | −0.349765 | + | 1.07646i | ||||
\(116\) | −3.09136 | + | 9.51422i | −0.287025 | + | 0.883373i | ||||
\(117\) | 9.09373 | − | 6.60698i | 0.840715 | − | 0.610816i | ||||
\(118\) | −12.3053 | − | 8.94031i | −1.13279 | − | 0.823022i | ||||
\(119\) | 0.851514 | + | 2.62069i | 0.0780581 | + | 0.240238i | ||||
\(120\) | −2.56468 | −0.234122 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.75724 | −0.159093 | ||||||||
\(123\) | −1.83461 | − | 5.64636i | −0.165422 | − | 0.509115i | ||||
\(124\) | 0.188154 | + | 0.136702i | 0.0168968 | + | 0.0122762i | ||||
\(125\) | −5.13577 | + | 3.73136i | −0.459358 | + | 0.333743i | ||||
\(126\) | 1.43801 | − | 4.42575i | 0.128109 | − | 0.394278i | ||||
\(127\) | −6.02870 | + | 18.5544i | −0.534961 | + | 1.64644i | 0.208772 | + | 0.977964i | \(0.433053\pi\) |
−0.743733 | + | 0.668476i | \(0.766947\pi\) | |||||||
\(128\) | 8.81579 | − | 6.40505i | 0.779213 | − | 0.566132i | ||||
\(129\) | −2.35410 | − | 1.71036i | −0.207267 | − | 0.150588i | ||||
\(130\) | 6.55011 | + | 20.1592i | 0.574483 | + | 1.76808i | ||||
\(131\) | 6.89796 | 0.602677 | 0.301339 | − | 0.953517i | \(-0.402567\pi\) | ||||
0.301339 | + | 0.953517i | \(0.402567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93910 | −0.168141 | ||||||||
\(134\) | 2.97566 | + | 9.15813i | 0.257058 | + | 0.791142i | ||||
\(135\) | −7.80200 | − | 5.66849i | −0.671489 | − | 0.487866i | ||||
\(136\) | −3.33070 | + | 2.41990i | −0.285606 | + | 0.207505i | ||||
\(137\) | −0.806750 | + | 2.48292i | −0.0689253 | + | 0.212130i | −0.979586 | − | 0.201024i | \(-0.935573\pi\) |
0.910661 | + | 0.413154i | \(0.135573\pi\) | |||||||
\(138\) | −1.48351 | + | 4.56578i | −0.126285 | + | 0.388665i | ||||
\(139\) | −0.810097 | + | 0.588570i | −0.0687116 | + | 0.0499219i | −0.621611 | − | 0.783326i | \(-0.713521\pi\) |
0.552899 | + | 0.833248i | \(0.313521\pi\) | |||||||
\(140\) | 2.60532 | + | 1.89288i | 0.220190 | + | 0.159977i | ||||
\(141\) | −2.49148 | − | 7.66797i | −0.209820 | − | 0.645760i | ||||
\(142\) | 3.58527 | 0.300869 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.0236 | 1.08530 | ||||||||
\(145\) | 7.40540 | + | 22.7915i | 0.614985 | + | 1.89273i | ||||
\(146\) | 14.3386 | + | 10.4176i | 1.18667 | + | 0.862165i | ||||
\(147\) | −0.500000 | + | 0.363271i | −0.0412393 | + | 0.0299621i | ||||
\(148\) | 0.371002 | − | 1.14183i | 0.0304962 | − | 0.0938576i | ||||
\(149\) | 4.60273 | − | 14.1658i | 0.377071 | − | 1.16050i | −0.565000 | − | 0.825091i | \(-0.691124\pi\) |
0.942071 | − | 0.335413i | \(-0.108876\pi\) | |||||||
\(150\) | 2.41242 | − | 1.75272i | 0.196973 | − | 0.143109i | ||||
\(151\) | 12.7862 | + | 9.28970i | 1.04052 | + | 0.755985i | 0.970388 | − | 0.241552i | \(-0.0776564\pi\) |
0.0701368 | + | 0.997537i | \(0.477656\pi\) | |||||||
\(152\) | −0.895263 | − | 2.75534i | −0.0726154 | − | 0.223487i | ||||
\(153\) | −7.21414 | −0.583229 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.557129 | 0.0447497 | ||||||||
\(156\) | 0.950727 | + | 2.92604i | 0.0761191 | + | 0.234270i | ||||
\(157\) | −3.71438 | − | 2.69866i | −0.296440 | − | 0.215376i | 0.429616 | − | 0.903011i | \(-0.358649\pi\) |
−0.726056 | + | 0.687635i | \(0.758649\pi\) | |||||||
\(158\) | −9.05011 | + | 6.57529i | −0.719988 | + | 0.523102i | ||||
\(159\) | −0.744856 | + | 2.29243i | −0.0590710 | + | 0.181802i | ||||
\(160\) | −5.02452 | + | 15.4639i | −0.397223 | + | 1.22253i | ||||
\(161\) | −3.53548 | + | 2.56868i | −0.278635 | + | 0.202440i | ||||
\(162\) | 8.20848 | + | 5.96381i | 0.644919 | + | 0.468561i | ||||
\(163\) | 2.48377 | + | 7.64425i | 0.194544 | + | 0.598744i | 0.999982 | + | 0.00606379i | \(0.00193018\pi\) |
−0.805438 | + | 0.592680i | \(0.798070\pi\) | |||||||
\(164\) | −11.1379 | −0.869721 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.05987 | −0.237492 | ||||||||
\(167\) | 4.14296 | + | 12.7507i | 0.320592 | + | 0.986681i | 0.973391 | + | 0.229150i | \(0.0735946\pi\) |
−0.652799 | + | 0.757531i | \(0.726405\pi\) | |||||||
\(168\) | −0.747032 | − | 0.542750i | −0.0576348 | − | 0.0418741i | ||||
\(169\) | −4.39615 | + | 3.19399i | −0.338165 | + | 0.245691i | ||||
\(170\) | 4.20387 | − | 12.9382i | 0.322422 | − | 0.992313i | ||||
\(171\) | 1.56876 | − | 4.82815i | 0.119966 | − | 0.369218i | ||||
\(172\) | −4.41637 | + | 3.20868i | −0.336745 | + | 0.244659i | ||||
\(173\) | −16.6512 | − | 12.0978i | −1.26597 | − | 0.919782i | −0.266936 | − | 0.963714i | \(-0.586011\pi\) |
−0.999035 | + | 0.0439325i | \(0.986011\pi\) | |||||||
\(174\) | 2.92897 | + | 9.01445i | 0.222045 | + | 0.683383i | ||||
\(175\) | 2.71442 | 0.205191 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.28860 | −0.397515 | ||||||||
\(178\) | 8.40581 | + | 25.8704i | 0.630042 | + | 1.93907i | ||||
\(179\) | 3.00566 | + | 2.18374i | 0.224653 | + | 0.163220i | 0.694419 | − | 0.719571i | \(-0.255662\pi\) |
−0.469765 | + | 0.882791i | \(0.655662\pi\) | |||||||
\(180\) | −6.82082 | + | 4.95562i | −0.508394 | + | 0.369370i | ||||
\(181\) | 1.47458 | − | 4.53828i | 0.109604 | − | 0.337327i | −0.881179 | − | 0.472783i | \(-0.843250\pi\) |
0.990783 | + | 0.135455i | \(0.0432496\pi\) | |||||||
\(182\) | −2.35829 | + | 7.25807i | −0.174808 | + | 0.538004i | ||||
\(183\) | −0.494304 | + | 0.359133i | −0.0365400 | + | 0.0265479i | ||||
\(184\) | −5.28223 | − | 3.83777i | −0.389411 | − | 0.282924i | ||||
\(185\) | −0.888742 | − | 2.73527i | −0.0653416 | − | 0.201101i | ||||
\(186\) | 0.220355 | 0.0161572 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −15.1257 | −1.10315 | ||||||||
\(189\) | −1.07295 | − | 3.30220i | −0.0780456 | − | 0.240200i | ||||
\(190\) | 7.74487 | + | 5.62698i | 0.561872 | + | 0.408224i | ||||
\(191\) | 0.670803 | − | 0.487367i | 0.0485376 | − | 0.0352646i | −0.563252 | − | 0.826285i | \(-0.690450\pi\) |
0.611790 | + | 0.791021i | \(0.290450\pi\) | |||||||
\(192\) | −0.0871690 | + | 0.268279i | −0.00629088 | + | 0.0193613i | ||||
\(193\) | 2.08216 | − | 6.40824i | 0.149878 | − | 0.461276i | −0.847728 | − | 0.530430i | \(-0.822030\pi\) |
0.997606 | + | 0.0691550i | \(0.0220303\pi\) | |||||||
\(194\) | 16.7043 | − | 12.1364i | 1.19930 | − | 0.871341i | ||||
\(195\) | 5.96253 | + | 4.33203i | 0.426986 | + | 0.310223i | ||||
\(196\) | 0.358290 | + | 1.10270i | 0.0255921 | + | 0.0787645i | ||||
\(197\) | 10.9216 | 0.778129 | 0.389065 | − | 0.921210i | \(-0.372798\pi\) | ||||
0.389065 | + | 0.921210i | \(0.372798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9746 | 1.48685 | 0.743424 | − | 0.668820i | \(-0.233200\pi\) | ||||
0.743424 | + | 0.668820i | \(0.233200\pi\) | |||||||
\(200\) | 1.25322 | + | 3.85702i | 0.0886163 | + | 0.272733i | ||||
\(201\) | 2.70872 | + | 1.96800i | 0.191059 | + | 0.138812i | ||||
\(202\) | −4.90620 | + | 3.56457i | −0.345199 | + | 0.250802i | ||||
\(203\) | −2.66623 | + | 8.20580i | −0.187132 | + | 0.575934i | ||||
\(204\) | 0.610177 | − | 1.87793i | 0.0427210 | − | 0.131482i | ||||
\(205\) | −21.5854 | + | 15.6827i | −1.50759 | + | 1.09533i | ||||
\(206\) | −26.1468 | − | 18.9968i | −1.82174 | − | 1.32357i | ||||
\(207\) | −3.53548 | − | 10.8811i | −0.245733 | − | 0.756288i | ||||
\(208\) | −21.3582 | −1.48093 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.05119 | 0.210552 | ||||||||
\(211\) | 1.86140 | + | 5.72879i | 0.128144 | + | 0.394386i | 0.994461 | − | 0.105109i | \(-0.0335190\pi\) |
−0.866317 | + | 0.499495i | \(0.833519\pi\) | |||||||
\(212\) | 3.65837 | + | 2.65796i | 0.251258 | + | 0.182550i | ||||
\(213\) | 1.00852 | − | 0.732736i | 0.0691029 | − | 0.0502062i | ||||
\(214\) | 1.78374 | − | 5.48979i | 0.121934 | − | 0.375274i | ||||
\(215\) | −4.04100 | + | 12.4369i | −0.275594 | + | 0.848192i | ||||
\(216\) | 4.19685 | − | 3.04919i | 0.285560 | − | 0.207471i | ||||
\(217\) | 0.162279 | + | 0.117903i | 0.0110162 | + | 0.00800375i | ||||
\(218\) | 6.97091 | + | 21.4542i | 0.472129 | + | 1.45306i | ||||
\(219\) | 6.16247 | 0.416421 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.8309 | 0.795833 | ||||||||
\(222\) | −0.351514 | − | 1.08185i | −0.0235921 | − | 0.0726089i | ||||
\(223\) | 3.74176 | + | 2.71855i | 0.250567 | + | 0.182048i | 0.705978 | − | 0.708234i | \(-0.250508\pi\) |
−0.455411 | + | 0.890281i | \(0.650508\pi\) | |||||||
\(224\) | −4.73607 | + | 3.44095i | −0.316442 | + | 0.229908i | ||||
\(225\) | −2.19601 | + | 6.75863i | −0.146401 | + | 0.450575i | ||||
\(226\) | 10.1330 | − | 31.1862i | 0.674038 | − | 2.07448i | ||||
\(227\) | 13.9963 | − | 10.1689i | 0.928965 | − | 0.674932i | −0.0167745 | − | 0.999859i | \(-0.505340\pi\) |
0.945739 | + | 0.324927i | \(0.105340\pi\) | |||||||
\(228\) | 1.12414 | + | 0.816737i | 0.0744481 | + | 0.0540897i | ||||
\(229\) | −1.36775 | − | 4.20949i | −0.0903832 | − | 0.278171i | 0.895640 | − | 0.444780i | \(-0.146718\pi\) |
−0.986023 | + | 0.166609i | \(0.946718\pi\) | |||||||
\(230\) | 21.5749 | 1.42260 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.8909 | −0.846330 | ||||||||
\(233\) | 3.25489 | + | 10.0175i | 0.213235 | + | 0.656269i | 0.999274 | + | 0.0380929i | \(0.0121283\pi\) |
−0.786039 | + | 0.618176i | \(0.787872\pi\) | |||||||
\(234\) | −16.1640 | − | 11.7438i | −1.05667 | − | 0.767716i | ||||
\(235\) | −29.3137 | + | 21.2977i | −1.91222 | + | 1.38931i | ||||
\(236\) | −3.06593 | + | 9.43597i | −0.199575 | + | 0.614229i | ||||
\(237\) | −1.20195 | + | 3.69921i | −0.0780748 | + | 0.240290i | ||||
\(238\) | 3.96253 | − | 2.87895i | 0.256853 | − | 0.186614i | ||||
\(239\) | −7.89314 | − | 5.73470i | −0.510565 | − | 0.370947i | 0.302473 | − | 0.953158i | \(-0.402188\pi\) |
−0.813038 | + | 0.582211i | \(0.802188\pi\) | |||||||
\(240\) | 2.63878 | + | 8.12131i | 0.170332 | + | 0.524229i | ||||
\(241\) | −12.5501 | −0.808422 | −0.404211 | − | 0.914666i | \(-0.632454\pi\) | ||||
−0.404211 | + | 0.914666i | \(0.632454\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 0.354208 | + | 1.09014i | 0.0226759 | + | 0.0697892i | ||||
\(245\) | 2.24703 | + | 1.63256i | 0.143558 | + | 0.104301i | ||||
\(246\) | −8.53740 | + | 6.20278i | −0.544325 | + | 0.395475i | ||||
\(247\) | −2.57271 | + | 7.91798i | −0.163698 | + | 0.503809i | ||||
\(248\) | −0.0926096 | + | 0.285023i | −0.00588072 | + | 0.0180990i | ||||
\(249\) | −0.860729 | + | 0.625357i | −0.0545465 | + | 0.0396304i | ||||
\(250\) | 9.12876 | + | 6.63243i | 0.577353 | + | 0.419472i | ||||
\(251\) | −3.39646 | − | 10.4532i | −0.214383 | − | 0.659803i | −0.999197 | − | 0.0400713i | \(-0.987241\pi\) |
0.784814 | − | 0.619732i | \(-0.212759\pi\) | |||||||
\(252\) | −3.03548 | −0.191217 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 34.6775 | 2.17586 | ||||||||
\(255\) | −1.46169 | − | 4.49862i | −0.0915346 | − | 0.281715i | ||||
\(256\) | −16.4084 | − | 11.9214i | −1.02553 | − | 0.745089i | ||||
\(257\) | −4.31432 | + | 3.13454i | −0.269120 | + | 0.195527i | −0.714158 | − | 0.699985i | \(-0.753190\pi\) |
0.445038 | + | 0.895512i | \(0.353190\pi\) | |||||||
\(258\) | −1.59829 | + | 4.91903i | −0.0995052 | + | 0.306246i | ||||
\(259\) | 0.319981 | − | 0.984800i | 0.0198827 | − | 0.0611925i | ||||
\(260\) | 11.1859 | − | 8.12702i | 0.693719 | − | 0.504017i | ||||
\(261\) | −18.2746 | − | 13.2773i | −1.13117 | − | 0.821842i | ||||
\(262\) | −3.78886 | − | 11.6609i | −0.234077 | − | 0.720414i | ||||
\(263\) | 8.18034 | 0.504421 | 0.252211 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252211 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8325 | 0.665436 | ||||||||
\(266\) | 1.06509 | + | 3.27802i | 0.0653050 | + | 0.200988i | ||||
\(267\) | 7.65177 | + | 5.55933i | 0.468280 | + | 0.340226i | ||||
\(268\) | 5.08165 | − | 3.69203i | 0.310411 | − | 0.225527i | ||||
\(269\) | 3.96899 | − | 12.2153i | 0.241993 | − | 0.744779i | −0.754123 | − | 0.656733i | \(-0.771938\pi\) |
0.996116 | − | 0.0880459i | \(-0.0280622\pi\) | |||||||
\(270\) | −5.29708 | + | 16.3027i | −0.322370 | + | 0.992153i | ||||
\(271\) | −17.8366 | + | 12.9590i | −1.08349 | + | 0.787205i | −0.978289 | − | 0.207246i | \(-0.933550\pi\) |
−0.105206 | + | 0.994450i | \(0.533550\pi\) | |||||||
\(272\) | 11.0898 | + | 8.05720i | 0.672417 | + | 0.488539i | ||||
\(273\) | 0.819981 | + | 2.52364i | 0.0496275 | + | 0.152738i | ||||
\(274\) | 4.64047 | 0.280341 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.13152 | 0.188495 | ||||||||
\(277\) | −7.44019 | − | 22.8986i | −0.447038 | − | 1.37584i | −0.880234 | − | 0.474541i | \(-0.842614\pi\) |
0.433196 | − | 0.901300i | \(-0.357386\pi\) | |||||||
\(278\) | 1.43994 | + | 1.04617i | 0.0863616 | + | 0.0627454i | ||||
\(279\) | −0.424852 | + | 0.308673i | −0.0254352 | + | 0.0184798i | ||||
\(280\) | −1.28234 | + | 3.94664i | −0.0766345 | + | 0.235857i | ||||
\(281\) | −4.77179 | + | 14.6861i | −0.284661 | + | 0.876097i | 0.701839 | + | 0.712336i | \(0.252363\pi\) |
−0.986500 | + | 0.163761i | \(0.947637\pi\) | |||||||
\(282\) | −11.5941 | + | 8.42362i | −0.690420 | + | 0.501619i | ||||
\(283\) | −2.71613 | − | 1.97338i | −0.161457 | − | 0.117305i | 0.504123 | − | 0.863632i | \(-0.331816\pi\) |
−0.665580 | + | 0.746326i | \(0.731816\pi\) | |||||||
\(284\) | −0.722688 | − | 2.22421i | −0.0428836 | − | 0.131982i | ||||
\(285\) | 3.32861 | 0.197170 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.60616 | −0.567034 | ||||||||
\(288\) | −4.73607 | − | 14.5761i | −0.279075 | − | 0.858906i | ||||
\(289\) | 7.61035 | + | 5.52924i | 0.447668 | + | 0.325250i | ||||
\(290\) | 34.4611 | − | 25.0375i | 2.02363 | − | 1.47025i | ||||
\(291\) | 2.21850 | − | 6.82784i | 0.130051 | − | 0.400255i | ||||
\(292\) | 3.57254 | − | 10.9951i | 0.209067 | − | 0.643442i | ||||
\(293\) | 5.53129 | − | 4.01872i | 0.323142 | − | 0.234776i | −0.414373 | − | 0.910107i | \(-0.635999\pi\) |
0.737515 | + | 0.675331i | \(0.235999\pi\) | |||||||
\(294\) | 0.888742 | + | 0.645709i | 0.0518325 | + | 0.0376585i | ||||
\(295\) | 7.34450 | + | 22.6040i | 0.427613 | + | 1.31606i | ||||
\(296\) | 1.54707 | 0.0899218 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.4752 | −1.53367 | ||||||||
\(299\) | 5.79805 | + | 17.8446i | 0.335310 | + | 1.03198i | ||||
\(300\) | −1.57362 | − | 1.14330i | −0.0908528 | − | 0.0660084i | ||||
\(301\) | −3.80902 | + | 2.76741i | −0.219548 | + | 0.159511i | ||||
\(302\) | 8.68103 | − | 26.7175i | 0.499537 | − | 1.53742i | ||||
\(303\) | −0.651594 | + | 2.00540i | −0.0374331 | + | 0.115207i | ||||
\(304\) | −7.80392 | + | 5.66988i | −0.447586 | + | 0.325190i | ||||
\(305\) | 2.22144 | + | 1.61397i | 0.127199 | + | 0.0924155i | ||||
\(306\) | 3.96253 | + | 12.1954i | 0.226523 | + | 0.697166i | ||||
\(307\) | 11.7970 | 0.673293 | 0.336646 | − | 0.941631i | \(-0.390707\pi\) | ||||
0.336646 | + | 0.941631i | \(0.390707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2375 | −0.639276 | ||||||||
\(310\) | −0.306016 | − | 0.941821i | −0.0173805 | − | 0.0534918i | ||||
\(311\) | −20.4794 | − | 14.8791i | −1.16128 | − | 0.843718i | −0.171339 | − | 0.985212i | \(-0.554809\pi\) |
−0.989939 | + | 0.141494i | \(0.954809\pi\) | |||||||
\(312\) | −3.20736 | + | 2.33029i | −0.181581 | + | 0.131926i | ||||
\(313\) | −6.07352 | + | 18.6924i | −0.343296 | + | 1.05656i | 0.619194 | + | 0.785238i | \(0.287460\pi\) |
−0.962490 | + | 0.271318i | \(0.912540\pi\) | |||||||
\(314\) | −2.52184 | + | 7.76141i | −0.142315 | + | 0.438002i | ||||
\(315\) | −5.88281 | + | 4.27411i | −0.331459 | + | 0.240819i | ||||
\(316\) | 5.90337 | + | 4.28905i | 0.332091 | + | 0.241278i | ||||
\(317\) | 1.11572 | + | 3.43385i | 0.0626653 | + | 0.192864i | 0.977488 | − | 0.210992i | \(-0.0676695\pi\) |
−0.914822 | + | 0.403856i | \(0.867670\pi\) | |||||||
\(318\) | 4.28446 | 0.240261 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.26771 | 0.0708670 | ||||||||
\(321\) | −0.620210 | − | 1.90881i | −0.0346167 | − | 0.106539i | ||||
\(322\) | 6.28426 | + | 4.56578i | 0.350208 | + | 0.254441i | ||||
\(323\) | 4.32281 | − | 3.14071i | 0.240528 | − | 0.174754i | ||||
\(324\) | 2.04519 | − | 6.29445i | 0.113622 | − | 0.349692i | ||||
\(325\) | 3.60137 | − | 11.0839i | 0.199768 | − | 0.614824i | ||||
\(326\) | 11.5582 | − | 8.39756i | 0.640152 | − | 0.465098i | ||||
\(327\) | 6.34558 | + | 4.61033i | 0.350911 | + | 0.254952i | ||||
\(328\) | −4.43508 | − | 13.6498i | −0.244886 | − | 0.753683i | ||||
\(329\) | −13.0455 | −0.719224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.5335 | −1.45841 | −0.729205 | − | 0.684295i | \(-0.760110\pi\) | ||||
−0.729205 | + | 0.684295i | \(0.760110\pi\) | |||||||
\(332\) | 0.616781 | + | 1.89826i | 0.0338503 | + | 0.104180i | ||||
\(333\) | 2.19318 | + | 1.59344i | 0.120186 | + | 0.0873200i | ||||
\(334\) | 19.2793 | − | 14.0073i | 1.05492 | − | 0.766443i | ||||
\(335\) | 4.64974 | − | 14.3104i | 0.254042 | − | 0.781862i | ||||
\(336\) | −0.950059 | + | 2.92398i | −0.0518300 | + | 0.159516i | ||||
\(337\) | −0.554969 | + | 0.403208i | −0.0302311 | + | 0.0219642i | −0.602798 | − | 0.797894i | \(-0.705948\pi\) |
0.572567 | + | 0.819858i | \(0.305948\pi\) | |||||||
\(338\) | 7.81408 | + | 5.67726i | 0.425030 | + | 0.308802i | ||||
\(339\) | −3.52326 | − | 10.8435i | −0.191357 | − | 0.588938i | ||||
\(340\) | −8.87387 | −0.481253 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.02361 | −0.487941 | ||||||||
\(343\) | 0.309017 | + | 0.951057i | 0.0166853 | + | 0.0513522i | ||||
\(344\) | −5.69091 | − | 4.13469i | −0.306834 | − | 0.222928i | ||||
\(345\) | 6.06893 | − | 4.40934i | 0.326740 | − | 0.237391i | ||||
\(346\) | −11.3052 | + | 34.7937i | −0.607770 | + | 1.87052i | ||||
\(347\) | −6.64555 | + | 20.4529i | −0.356752 | + | 1.09797i | 0.598235 | + | 0.801321i | \(0.295869\pi\) |
−0.954987 | + | 0.296649i | \(0.904131\pi\) | |||||||
\(348\) | 5.00192 | − | 3.63411i | 0.268131 | − | 0.194809i | ||||
\(349\) | 15.7296 | + | 11.4282i | 0.841987 | + | 0.611739i | 0.922925 | − | 0.384980i | \(-0.125792\pi\) |
−0.0809381 | + | 0.996719i | \(0.525792\pi\) | |||||||
\(350\) | −1.49096 | − | 4.58869i | −0.0796950 | − | 0.245276i | ||||
\(351\) | −14.9075 | −0.795705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.9307 | −1.11403 | −0.557015 | − | 0.830502i | \(-0.688053\pi\) | ||||
−0.557015 | + | 0.830502i | \(0.688053\pi\) | |||||||
\(354\) | 2.90488 | + | 8.94031i | 0.154393 | + | 0.475172i | ||||
\(355\) | −4.53237 | − | 3.29296i | −0.240553 | − | 0.174772i | ||||
\(356\) | 14.3549 | − | 10.4295i | 0.760810 | − | 0.552761i | ||||
\(357\) | 0.526264 | − | 1.61968i | 0.0278529 | − | 0.0857223i | ||||
\(358\) | 2.04066 | − | 6.28050i | 0.107852 | − | 0.331935i | ||||
\(359\) | 7.90512 | − | 5.74341i | 0.417216 | − | 0.303125i | −0.359300 | − | 0.933222i | \(-0.616985\pi\) |
0.776517 | + | 0.630096i | \(0.216985\pi\) | |||||||
\(360\) | −8.78929 | − | 6.38579i | −0.463236 | − | 0.336561i | ||||
\(361\) | −4.70939 | − | 14.4940i | −0.247863 | − | 0.762843i | ||||
\(362\) | −8.48185 | −0.445796 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.97807 | 0.260922 | ||||||||
\(365\) | −8.55808 | − | 26.3390i | −0.447950 | − | 1.37865i | ||||
\(366\) | 0.878618 | + | 0.638353i | 0.0459261 | + | 0.0333673i | ||||
\(367\) | −8.00901 | + | 5.81889i | −0.418067 | + | 0.303744i | −0.776860 | − | 0.629674i | \(-0.783189\pi\) |
0.358793 | + | 0.933417i | \(0.383189\pi\) | |||||||
\(368\) | −6.71783 | + | 20.6754i | −0.350191 | + | 1.07778i | ||||
\(369\) | 7.77155 | − | 23.9184i | 0.404571 | − | 1.24514i | ||||
\(370\) | −4.13577 | + | 3.00482i | −0.215009 | + | 0.156213i | ||||
\(371\) | 3.15526 | + | 2.29243i | 0.163813 | + | 0.119017i | ||||
\(372\) | −0.0444172 | − | 0.136702i | −0.00230293 | − | 0.00708768i | ||||
\(373\) | 4.27475 | 0.221338 | 0.110669 | − | 0.993857i | \(-0.464701\pi\) | ||||
0.110669 | + | 0.993857i | \(0.464701\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.92338 | 0.202603 | ||||||||
\(376\) | −6.02301 | − | 18.5369i | −0.310613 | − | 0.955968i | ||||
\(377\) | 29.9696 | + | 21.7742i | 1.54351 | + | 1.12143i | ||||
\(378\) | −4.99298 | + | 3.62761i | −0.256811 | + | 0.186584i | ||||
\(379\) | 1.33679 | − | 4.11421i | 0.0686662 | − | 0.211333i | −0.910835 | − | 0.412770i | \(-0.864561\pi\) |
0.979501 | + | 0.201437i | \(0.0645612\pi\) | |||||||
\(380\) | 1.92968 | − | 5.93894i | 0.0989905 | − | 0.304661i | ||||
\(381\) | 9.75465 | − | 7.08717i | 0.499746 | − | 0.363087i | ||||
\(382\) | −1.19234 | − | 0.866287i | −0.0610055 | − | 0.0443231i | ||||
\(383\) | −0.408551 | − | 1.25739i | −0.0208760 | − | 0.0642497i | 0.940076 | − | 0.340966i | \(-0.110754\pi\) |
−0.960952 | + | 0.276716i | \(0.910754\pi\) | |||||||
\(384\) | −6.73467 | −0.343677 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.9767 | −0.609600 | ||||||||
\(387\) | −3.80902 | − | 11.7229i | −0.193623 | − | 0.595911i | ||||
\(388\) | −10.8962 | − | 7.91654i | −0.553170 | − | 0.401902i | ||||
\(389\) | 31.1546 | − | 22.6351i | 1.57960 | − | 1.14765i | 0.662447 | − | 0.749109i | \(-0.269518\pi\) |
0.917152 | − | 0.398537i | \(-0.130482\pi\) | |||||||
\(390\) | 4.04819 | − | 12.4591i | 0.204988 | − | 0.630889i | ||||
\(391\) | 3.72119 | − | 11.4527i | 0.188189 | − | 0.579186i | ||||
\(392\) | −1.20872 | + | 0.878189i | −0.0610497 | + | 0.0443552i | ||||
\(393\) | −3.44898 | − | 2.50583i | −0.173978 | − | 0.126402i | ||||
\(394\) | −5.99892 | − | 18.4628i | −0.302221 | − | 0.930141i | ||||
\(395\) | 17.4800 | 0.879516 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.410109 | −0.0205828 | −0.0102914 | − | 0.999947i | \(-0.503276\pi\) | ||||
−0.0102914 | + | 0.999947i | \(0.503276\pi\) | |||||||
\(398\) | −11.5208 | − | 35.4573i | −0.577484 | − | 1.77731i | ||||
\(399\) | 0.969548 | + | 0.704418i | 0.0485381 | + | 0.0352650i | ||||
\(400\) | 10.9242 | − | 7.93691i | 0.546211 | − | 0.396846i | ||||
\(401\) | −0.484180 | + | 1.49015i | −0.0241788 | + | 0.0744147i | −0.962418 | − | 0.271573i | \(-0.912456\pi\) |
0.938239 | + | 0.345988i | \(0.112456\pi\) | |||||||
\(402\) | 1.83906 | − | 5.66003i | 0.0917238 | − | 0.282297i | ||||
\(403\) | 0.696741 | − | 0.506212i | 0.0347071 | − | 0.0252162i | ||||
\(404\) | 3.20031 | + | 2.32516i | 0.159221 | + | 0.115681i | ||||
\(405\) | −4.89929 | − | 15.0785i | −0.243448 | − | 0.749255i | ||||
\(406\) | 15.3363 | 0.761127 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.54443 | 0.125968 | ||||||||
\(409\) | 2.09468 | + | 6.44676i | 0.103575 | + | 0.318772i | 0.989393 | − | 0.145261i | \(-0.0464021\pi\) |
−0.885818 | + | 0.464032i | \(0.846402\pi\) | |||||||
\(410\) | 38.3676 | + | 27.8757i | 1.89484 | + | 1.37668i | ||||
\(411\) | 1.30535 | − | 0.948391i | 0.0643881 | − | 0.0467807i | ||||
\(412\) | −6.51463 | + | 20.0500i | −0.320953 | + | 0.987792i | ||||
\(413\) | −2.64430 | + | 8.13831i | −0.130117 | + | 0.400460i | ||||
\(414\) | −16.4524 | + | 11.9534i | −0.808592 | + | 0.587476i | ||||
\(415\) | 3.86817 | + | 2.81039i | 0.189881 | + | 0.137957i | ||||
\(416\) | 7.76697 | + | 23.9043i | 0.380807 | + | 1.17200i | ||||
\(417\) | 0.618859 | 0.0303057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.7218 | 1.40315 | 0.701577 | − | 0.712594i | \(-0.252480\pi\) | ||||
0.701577 | + | 0.712594i | \(0.252480\pi\) | |||||||
\(420\) | −0.615033 | − | 1.89288i | −0.0300105 | − | 0.0923629i | ||||
\(421\) | −9.89070 | − | 7.18601i | −0.482043 | − | 0.350225i | 0.320073 | − | 0.947393i | \(-0.396293\pi\) |
−0.802116 | + | 0.597168i | \(0.796293\pi\) | |||||||
\(422\) | 8.66204 | − | 6.29334i | 0.421661 | − | 0.306355i | ||||
\(423\) | 10.5541 | − | 32.4821i | 0.513156 | − | 1.57933i | ||||
\(424\) | −1.80065 | + | 5.54183i | −0.0874473 | + | 0.269135i | ||||
\(425\) | −6.05123 | + | 4.39648i | −0.293528 | + | 0.213260i | ||||
\(426\) | −1.79264 | − | 1.30243i | −0.0868535 | − | 0.0631028i | ||||
\(427\) | 0.305497 | + | 0.940223i | 0.0147840 | + | 0.0455006i | ||||
\(428\) | −3.76527 | −0.182001 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.2441 | 1.12093 | ||||||||
\(431\) | −1.14067 | − | 3.51063i | −0.0549442 | − | 0.169101i | 0.919819 | − | 0.392344i | \(-0.128336\pi\) |
−0.974763 | + | 0.223243i | \(0.928336\pi\) | |||||||
\(432\) | −13.9737 | − | 10.1525i | −0.672308 | − | 0.488461i | ||||
\(433\) | −23.5221 | + | 17.0898i | −1.13040 | + | 0.821283i | −0.985753 | − | 0.168201i | \(-0.946204\pi\) |
−0.144646 | + | 0.989483i | \(0.546204\pi\) | |||||||
\(434\) | 0.110177 | − | 0.339091i | 0.00528869 | − | 0.0162769i | ||||
\(435\) | 4.57679 | − | 14.0859i | 0.219440 | − | 0.675368i | ||||
\(436\) | 11.9045 | − | 8.64912i | 0.570122 | − | 0.414218i | ||||
\(437\) | 6.85563 | + | 4.98091i | 0.327949 | + | 0.238269i | ||||
\(438\) | −3.38488 | − | 10.4176i | −0.161736 | − | 0.497771i | ||||
\(439\) | 14.2017 | 0.677811 | 0.338905 | − | 0.940820i | \(-0.389943\pi\) | ||||
0.338905 | + | 0.940820i | \(0.389943\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | −6.49840 | − | 20.0000i | −0.309097 | − | 0.951304i | ||||
\(443\) | −22.0341 | − | 16.0087i | −1.04687 | − | 0.760595i | −0.0752548 | − | 0.997164i | \(-0.523977\pi\) |
−0.971615 | + | 0.236569i | \(0.923977\pi\) | |||||||
\(444\) | −0.600294 | + | 0.436139i | −0.0284887 | + | 0.0206982i | ||||
\(445\) | 13.1349 | − | 40.4250i | 0.622652 | − | 1.91633i | ||||
\(446\) | 2.54043 | − | 7.81863i | 0.120293 | − | 0.370223i | ||||
\(447\) | −7.44738 | + | 5.41084i | −0.352249 | + | 0.255924i | ||||
\(448\) | 0.369254 | + | 0.268279i | 0.0174456 | + | 0.0126750i | ||||
\(449\) | −12.9527 | − | 39.8644i | −0.611277 | − | 1.88132i | −0.445888 | − | 0.895089i | \(-0.647112\pi\) |
−0.165389 | − | 0.986228i | \(-0.552888\pi\) | |||||||
\(450\) | 12.6316 | 0.595459 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −21.3896 | −1.00608 | ||||||||
\(453\) | −3.01841 | − | 9.28970i | −0.141817 | − | 0.436468i | ||||
\(454\) | −24.8781 | − | 18.0750i | −1.16759 | − | 0.848303i | ||||
\(455\) | 9.64758 | − | 7.00938i | 0.452285 | − | 0.328605i | ||||
\(456\) | −0.553303 | + | 1.70289i | −0.0259108 | + | 0.0797452i | ||||
\(457\) | −6.02512 | + | 18.5434i | −0.281843 | + | 0.867424i | 0.705484 | + | 0.708726i | \(0.250730\pi\) |
−0.987327 | + | 0.158698i | \(0.949270\pi\) | |||||||
\(458\) | −6.36483 | + | 4.62432i | −0.297409 | + | 0.216080i | ||||
\(459\) | 7.74040 | + | 5.62373i | 0.361291 | + | 0.262493i | ||||
\(460\) | −4.34887 | − | 13.3845i | −0.202767 | − | 0.624054i | ||||
\(461\) | −12.2251 | −0.569380 | −0.284690 | − | 0.958620i | \(-0.591891\pi\) | ||||
−0.284690 | + | 0.958620i | \(0.591891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8550 | 0.643894 | 0.321947 | − | 0.946758i | \(-0.395663\pi\) | ||||
0.321947 | + | 0.946758i | \(0.395663\pi\) | |||||||
\(464\) | 13.2633 | + | 40.8204i | 0.615735 | + | 1.89504i | ||||
\(465\) | −0.278565 | − | 0.202389i | −0.0129181 | − | 0.00938557i | ||||
\(466\) | 15.1467 | − | 11.0047i | 0.701656 | − | 0.509783i | ||||
\(467\) | −5.07428 | + | 15.6170i | −0.234810 | + | 0.722671i | 0.762337 | + | 0.647181i | \(0.224052\pi\) |
−0.997147 | + | 0.0754899i | \(0.975948\pi\) | |||||||
\(468\) | −4.02734 | + | 12.3949i | −0.186164 | + | 0.572954i | ||||
\(469\) | 4.38281 | − | 3.18429i | 0.202379 | − | 0.147037i | ||||
\(470\) | 52.1047 | + | 37.8563i | 2.40341 | + | 1.74618i | ||||
\(471\) | 0.876846 | + | 2.69866i | 0.0404029 | + | 0.124347i | ||||
\(472\) | −12.7849 | −0.588473 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.91367 | 0.317555 | ||||||||
\(475\) | −1.62652 | − | 5.00590i | −0.0746297 | − | 0.229687i | ||||
\(476\) | −2.58475 | − | 1.87793i | −0.118472 | − | 0.0860749i | ||||
\(477\) | −8.26058 | + | 6.00167i | −0.378226 | + | 0.274797i | ||||
\(478\) | −5.35896 | + | 16.4932i | −0.245113 | + | 0.754380i | ||||
\(479\) | 7.66096 | − | 23.5780i | 0.350038 | − | 1.07731i | −0.608793 | − | 0.793329i | \(-0.708346\pi\) |
0.958831 | − | 0.283977i | \(-0.0916540\pi\) | |||||||
\(480\) | 8.12984 | − | 5.90667i | 0.371075 | − | 0.269602i | ||||
\(481\) | −3.59674 | − | 2.61318i | −0.163997 | − | 0.119151i | ||||
\(482\) | 6.89342 | + | 21.2158i | 0.313987 | + | 0.966352i | ||||
\(483\) | 2.70087 | 0.122894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32.2639 | −1.46503 | ||||||||
\(486\) | −7.65921 | − | 23.5726i | −0.347429 | − | 1.06928i | ||||
\(487\) | 11.5966 | + | 8.42542i | 0.525492 | + | 0.381792i | 0.818669 | − | 0.574266i | \(-0.194712\pi\) |
−0.293177 | + | 0.956058i | \(0.594712\pi\) | |||||||
\(488\) | −1.19495 | + | 0.868185i | −0.0540930 | + | 0.0393009i | ||||
\(489\) | 1.53505 | − | 4.72441i | 0.0694175 | − | 0.213645i | ||||
\(490\) | 1.52560 | − | 4.69530i | 0.0689194 | − | 0.212112i | ||||
\(491\) | −17.8140 | + | 12.9426i | −0.803935 | + | 0.584093i | −0.912066 | − | 0.410044i | \(-0.865514\pi\) |
0.108131 | + | 0.994137i | \(0.465514\pi\) | |||||||
\(492\) | 5.56893 | + | 4.04607i | 0.251067 | + | 0.182411i | ||||
\(493\) | −7.34694 | − | 22.6115i | −0.330889 | − | 1.01837i | ||||
\(494\) | 14.7984 | 0.665810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.997839 | 0.0448043 | ||||||||
\(497\) | −0.623302 | − | 1.91833i | −0.0279589 | − | 0.0860487i | ||||
\(498\) | 1.52993 | + | 1.11156i | 0.0685579 | + | 0.0498103i | ||||
\(499\) | 20.4776 | − | 14.8779i | 0.916704 | − | 0.666024i | −0.0259975 | − | 0.999662i | \(-0.508276\pi\) |
0.942701 | + | 0.333638i | \(0.108276\pi\) | |||||||
\(500\) | 2.27448 | − | 7.00014i | 0.101718 | − | 0.313056i | ||||
\(501\) | 2.56049 | − | 7.88038i | 0.114394 | − | 0.352070i | ||||
\(502\) | −15.8055 | + | 11.4834i | −0.705434 | + | 0.512528i | ||||
\(503\) | −21.0518 | − | 15.2950i | −0.938653 | − | 0.681971i | 0.00944301 | − | 0.999955i | \(-0.496994\pi\) |
−0.948096 | + | 0.317984i | \(0.896994\pi\) | |||||||
\(504\) | −1.20872 | − | 3.72007i | −0.0538408 | − | 0.165705i | ||||
\(505\) | 9.47619 | 0.421685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.35836 | 0.149150 | ||||||||
\(508\) | −6.98998 | − | 21.5130i | −0.310130 | − | 0.954483i | ||||
\(509\) | −30.8453 | − | 22.4104i | −1.36719 | − | 0.993325i | −0.997950 | − | 0.0639922i | \(-0.979617\pi\) |
−0.369244 | − | 0.929333i | \(-0.620383\pi\) | |||||||
\(510\) | −6.80200 | + | 4.94194i | −0.301198 | + | 0.218833i | ||||
\(511\) | 3.08123 | − | 9.48306i | 0.136306 | − | 0.419506i | ||||
\(512\) | −4.40566 | + | 13.5592i | −0.194704 | + | 0.599238i | ||||
\(513\) | −5.44695 | + | 3.95744i | −0.240489 | + | 0.174725i | ||||
\(514\) | 7.66864 | + | 5.57159i | 0.338249 | + | 0.245753i | ||||
\(515\) | 15.6059 | + | 48.0301i | 0.687679 | + | 2.11646i | ||||
\(516\) | 3.37380 | 0.148523 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.84055 | −0.0808691 | ||||||||
\(519\) | 3.93083 | + | 12.0978i | 0.172544 | + | 0.531036i | ||||
\(520\) | 14.4141 | + | 10.4725i | 0.632100 | + | 0.459248i | ||||
\(521\) | 21.0684 | − | 15.3071i | 0.923024 | − | 0.670616i | −0.0212509 | − | 0.999774i | \(-0.506765\pi\) |
0.944275 | + | 0.329158i | \(0.106765\pi\) | |||||||
\(522\) | −12.4073 | + | 38.1858i | −0.543054 | + | 1.67135i | ||||
\(523\) | −5.90933 | + | 18.1870i | −0.258397 | + | 0.795263i | 0.734745 | + | 0.678344i | \(0.237302\pi\) |
−0.993141 | + | 0.116920i | \(0.962698\pi\) | |||||||
\(524\) | −6.47039 | + | 4.70101i | −0.282660 | + | 0.205365i | ||||
\(525\) | −1.35721 | − | 0.986070i | −0.0592335 | − | 0.0430356i | ||||
\(526\) | −4.49324 | − | 13.8288i | −0.195915 | − | 0.602963i | ||||
\(527\) | −0.552731 | −0.0240773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.90228 | −0.169664 | ||||||||
\(530\) | −5.95001 | − | 18.3122i | −0.258452 | − | 0.795433i | ||||
\(531\) | −18.1243 | − | 13.1681i | −0.786527 | − | 0.571445i | ||||
\(532\) | 1.81890 | − | 1.32151i | 0.0788593 | − | 0.0572947i | ||||
\(533\) | −12.7450 | + | 39.2252i | −0.552049 | + | 1.69903i | ||||
\(534\) | 5.19508 | − | 15.9888i | 0.224813 | − | 0.691903i | ||||
\(535\) | −7.29714 | + | 5.30169i | −0.315483 | + | 0.229212i | ||||
\(536\) | 6.54819 | + | 4.75754i | 0.282839 | + | 0.205494i | ||||
\(537\) | −0.709539 | − | 2.18374i | −0.0306189 | − | 0.0942352i | ||||
\(538\) | −22.8298 | −0.984265 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.1815 | 0.481176 | ||||||||
\(541\) | −3.36397 | − | 10.3532i | −0.144628 | − | 0.445120i | 0.852335 | − | 0.522997i | \(-0.175186\pi\) |
−0.996963 | + | 0.0778764i | \(0.975186\pi\) | |||||||
\(542\) | 31.7042 | + | 23.0345i | 1.36181 | + | 0.989415i | ||||
\(543\) | −2.38591 | + | 1.73347i | −0.102389 | + | 0.0743902i | ||||
\(544\) | 4.98485 | − | 15.3418i | 0.213724 | − | 0.657774i | ||||
\(545\) | 10.8927 | − | 33.5243i | 0.466592 | − | 1.43602i | ||||
\(546\) | 3.81579 | − | 2.77234i | 0.163301 | − | 0.118645i | ||||
\(547\) | −10.4436 | − | 7.58775i | −0.446538 | − | 0.324429i | 0.341689 | − | 0.939813i | \(-0.389001\pi\) |
−0.788227 | + | 0.615384i | \(0.789001\pi\) | |||||||
\(548\) | −0.935386 | − | 2.87882i | −0.0399577 | − | 0.122977i | ||||
\(549\) | −2.58821 | −0.110462 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.7307 | 0.712751 | ||||||||
\(552\) | 1.24697 | + | 3.83777i | 0.0530744 | + | 0.163346i | ||||
\(553\) | 5.09153 | + | 3.69921i | 0.216514 | + | 0.157307i | ||||
\(554\) | −34.6230 | + | 25.1551i | −1.47099 | + | 1.06874i | ||||
\(555\) | −0.549273 | + | 1.69049i | −0.0233153 | + | 0.0717572i | ||||
\(556\) | 0.358768 | − | 1.10418i | 0.0152152 | − | 0.0468275i | ||||
\(557\) | −0.616977 | + | 0.448260i | −0.0261422 | + | 0.0189934i | −0.600780 | − | 0.799415i | \(-0.705143\pi\) |
0.574637 | + | 0.818408i | \(0.305143\pi\) | |||||||
\(558\) | 0.755167 | + | 0.548661i | 0.0319688 | + | 0.0232267i | ||||
\(559\) | 6.24664 | + | 19.2252i | 0.264205 | + | 0.813139i | ||||
\(560\) | 13.8168 | 0.583867 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.4476 | 1.15781 | ||||||||
\(563\) | 6.86886 | + | 21.1402i | 0.289488 | + | 0.890953i | 0.985017 | + | 0.172455i | \(0.0551700\pi\) |
−0.695529 | + | 0.718498i | \(0.744830\pi\) | |||||||
\(564\) | 7.56283 | + | 5.49471i | 0.318452 | + | 0.231369i | ||||
\(565\) | −41.4534 | + | 30.1176i | −1.74396 | + | 1.26706i | ||||
\(566\) | −1.84408 | + | 5.67551i | −0.0775127 | + | 0.238559i | ||||
\(567\) | 1.76393 | − | 5.42882i | 0.0740782 | − | 0.227989i | ||||
\(568\) | 2.43805 | − | 1.77135i | 0.102298 | − | 0.0743242i | ||||
\(569\) | −16.5955 | − | 12.0573i | −0.695719 | − | 0.505469i | 0.182816 | − | 0.983147i | \(-0.441479\pi\) |
−0.878535 | + | 0.477678i | \(0.841479\pi\) | |||||||
\(570\) | −1.82832 | − | 5.62698i | −0.0765797 | − | 0.235688i | ||||
\(571\) | 19.5654 | 0.818785 | 0.409393 | − | 0.912358i | \(-0.365741\pi\) | ||||
0.409393 | + | 0.912358i | \(0.365741\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.512448 | −0.0214078 | ||||||||
\(574\) | 5.27640 | + | 16.2391i | 0.220233 | + | 0.677807i | ||||
\(575\) | −9.59677 | − | 6.97246i | −0.400213 | − | 0.290772i | ||||
\(576\) | −0.966719 | + | 0.702362i | −0.0402800 | + | 0.0292651i | ||||
\(577\) | −6.04795 | + | 18.6137i | −0.251780 | + | 0.774898i | 0.742668 | + | 0.669660i | \(0.233560\pi\) |
−0.994447 | + | 0.105237i | \(0.966440\pi\) | |||||||
\(578\) | 5.16696 | − | 15.9023i | 0.214917 | − | 0.661447i | ||||
\(579\) | −3.36901 | + | 2.44773i | −0.140011 | + | 0.101724i | ||||
\(580\) | −22.4790 | − | 16.3319i | −0.933388 | − | 0.678146i | ||||
\(581\) | 0.531960 | + | 1.63720i | 0.0220694 | + | 0.0679227i | ||||
\(582\) | −12.7609 | −0.528958 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.8974 | 0.616460 | ||||||||
\(585\) | 9.64758 | + | 29.6922i | 0.398878 | + | 1.22762i | ||||
\(586\) | −9.83178 | − | 7.14321i | −0.406147 | − | 0.295083i | ||||
\(587\) | −1.27071 | + | 0.923224i | −0.0524477 | + | 0.0381055i | −0.613700 | − | 0.789539i | \(-0.710320\pi\) |
0.561253 | + | 0.827645i | \(0.310320\pi\) | |||||||
\(588\) | 0.221435 | − | 0.681508i | 0.00913184 | − | 0.0281049i | ||||
\(589\) | 0.120195 | − | 0.369922i | 0.00495254 | − | 0.0152424i | ||||
\(590\) | 34.1777 | − | 24.8316i | 1.40707 | − | 1.02230i | ||||
\(591\) | −5.46078 | − | 3.96749i | −0.224627 | − | 0.163201i | ||||
\(592\) | −1.59177 | − | 4.89896i | −0.0654213 | − | 0.201346i | ||||
\(593\) | 30.1230 | 1.23700 | 0.618502 | − | 0.785783i | \(-0.287740\pi\) | ||||
0.618502 | + | 0.785783i | \(0.287740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.65351 | −0.313763 | ||||||||
\(596\) | 5.33664 | + | 16.4245i | 0.218597 | + | 0.672773i | ||||
\(597\) | −10.4873 | − | 7.61946i | −0.429216 | − | 0.311844i | ||||
\(598\) | 26.9813 | − | 19.6031i | 1.10335 | − | 0.801629i | ||||
\(599\) | 1.78547 | − | 5.49513i | 0.0729525 | − | 0.224525i | −0.907931 | − | 0.419119i | \(-0.862339\pi\) |
0.980884 | + | 0.194594i | \(0.0623390\pi\) | |||||||
\(600\) | 0.774534 | − | 2.38377i | 0.0316202 | − | 0.0973171i | ||||
\(601\) | 36.8625 | − | 26.7822i | 1.50365 | − | 1.09247i | 0.534754 | − | 0.845008i | \(-0.320404\pi\) |
0.968898 | − | 0.247460i | \(-0.0795958\pi\) | |||||||
\(602\) | 6.77047 | + | 4.91903i | 0.275944 | + | 0.200485i | ||||
\(603\) | 4.38281 | + | 13.4889i | 0.178482 | + | 0.549310i | ||||
\(604\) | −18.3246 | −0.745619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.74801 | 0.152252 | ||||||||
\(607\) | −10.7294 | − | 33.0217i | −0.435493 | − | 1.34031i | −0.892581 | − | 0.450887i | \(-0.851108\pi\) |
0.457088 | − | 0.889421i | \(-0.348892\pi\) | |||||||
\(608\) | 9.18369 | + | 6.67234i | 0.372448 | + | 0.270599i | ||||
\(609\) | 4.31404 | − | 3.13434i | 0.174814 | − | 0.127010i | ||||
\(610\) | 1.50822 | − | 4.64182i | 0.0610660 | − | 0.187942i | ||||
\(611\) | −17.3083 | + | 53.2693i | −0.700217 | + | 2.15505i | ||||
\(612\) | 6.76697 | − | 4.91649i | 0.273539 | − | 0.198737i | ||||
\(613\) | −19.5315 | − | 14.1905i | −0.788870 | − | 0.573148i | 0.118758 | − | 0.992923i | \(-0.462109\pi\) |
−0.907628 | + | 0.419776i | \(0.862109\pi\) | |||||||
\(614\) | −6.47979 | − | 19.9428i | −0.261503 | − | 0.804824i | ||||
\(615\) | 16.4897 | 0.664931 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.4967 | −0.543358 | −0.271679 | − | 0.962388i | \(-0.587579\pi\) | ||||
−0.271679 | + | 0.962388i | \(0.587579\pi\) | |||||||
\(618\) | 6.17243 | + | 18.9968i | 0.248291 | + | 0.764162i | ||||
\(619\) | 35.1806 | + | 25.5602i | 1.41403 | + | 1.02735i | 0.992721 | + | 0.120433i | \(0.0384284\pi\) |
0.421307 | + | 0.906918i | \(0.361572\pi\) | |||||||
\(620\) | −0.522596 | + | 0.379688i | −0.0209879 | + | 0.0152486i | ||||
\(621\) | −4.68889 | + | 14.4309i | −0.188159 | + | 0.579093i | ||||
\(622\) | −13.9042 | + | 42.7928i | −0.557509 | + | 1.71584i | ||||
\(623\) | 12.3808 | − | 8.99519i | 0.496027 | − | 0.360385i | ||||
\(624\) | 10.6791 | + | 7.75883i | 0.427507 | + | 0.310602i | ||||
\(625\) | −9.64257 | − | 29.6768i | −0.385703 | − | 1.18707i | ||||
\(626\) | 34.9353 | 1.39629 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.32330 | 0.212423 | ||||||||
\(629\) | 0.881726 | + | 2.71367i | 0.0351567 | + | 0.108201i | ||||
\(630\) | 10.4566 | + | 7.59716i | 0.416601 | + | 0.302678i | ||||
\(631\) | −5.19398 | + | 3.77365i | −0.206769 | + | 0.150227i | −0.686351 | − | 0.727271i | \(-0.740788\pi\) |
0.479581 | + | 0.877497i | \(0.340788\pi\) | |||||||
\(632\) | −2.90564 | + | 8.94265i | −0.115580 | + | 0.355719i | ||||
\(633\) | 1.15041 | − | 3.54059i | 0.0457246 | − | 0.140726i | ||||
\(634\) | 5.19204 | − | 3.77224i | 0.206202 | − | 0.149815i | ||||
\(635\) | −43.8380 | − | 31.8502i | −1.73966 | − | 1.26394i | ||||
\(636\) | −0.863624 | − | 2.65796i | −0.0342449 | − | 0.105395i | ||||
\(637\) | 4.29348 | 0.170114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.28070 | 0.208901 | ||||||||
\(640\) | 9.35272 | + | 28.7847i | 0.369699 | + | 1.13782i | ||||
\(641\) | 5.17447 | + | 3.75947i | 0.204379 | + | 0.148490i | 0.685267 | − | 0.728292i | \(-0.259686\pi\) |
−0.480888 | + | 0.876782i | \(0.659686\pi\) | |||||||
\(642\) | −2.88615 | + | 2.09691i | −0.113907 | + | 0.0827586i | ||||
\(643\) | 0.201683 | − | 0.620716i | 0.00795360 | − | 0.0244787i | −0.947001 | − | 0.321231i | \(-0.895903\pi\) |
0.954955 | + | 0.296752i | \(0.0959035\pi\) | |||||||
\(644\) | 1.56576 | − | 4.81891i | 0.0616996 | − | 0.189892i | ||||
\(645\) | 6.53848 | − | 4.75048i | 0.257452 | − | 0.187050i | ||||
\(646\) | −7.68373 | − | 5.58255i | −0.302312 | − | 0.219643i | ||||
\(647\) | 5.55061 | + | 17.0830i | 0.218217 | + | 0.671603i | 0.998910 | + | 0.0466874i | \(0.0148665\pi\) |
−0.780693 | + | 0.624915i | \(0.785134\pi\) | |||||||
\(648\) | 8.52842 | 0.335028 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −20.7153 | −0.812522 | ||||||||
\(651\) | −0.0383089 | − | 0.117903i | −0.00150144 | − | 0.00462096i | ||||
\(652\) | −7.53943 | − | 5.47771i | −0.295267 | − | 0.214524i | ||||
\(653\) | 13.6870 | − | 9.94419i | 0.535614 | − | 0.389146i | −0.286840 | − | 0.957979i | \(-0.592605\pi\) |
0.822454 | + | 0.568832i | \(0.192605\pi\) | |||||||
\(654\) | 4.30826 | − | 13.2595i | 0.168466 | − | 0.518486i | ||||
\(655\) | −5.92045 | + | 18.2213i | −0.231331 | + | 0.711964i | ||||
\(656\) | −38.6602 | + | 28.0882i | −1.50943 | + | 1.09666i | ||||
\(657\) | 21.1191 | + | 15.3439i | 0.823934 | + | 0.598623i | ||||
\(658\) | 7.16556 | + | 22.0533i | 0.279343 | + | 0.859728i | ||||
\(659\) | −23.6249 | −0.920297 | −0.460148 | − | 0.887842i | \(-0.652204\pi\) | ||||
−0.460148 | + | 0.887842i | \(0.652204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.9819 | −0.816103 | −0.408051 | − | 0.912959i | \(-0.633792\pi\) | ||||
−0.408051 | + | 0.912959i | \(0.633792\pi\) | |||||||
\(662\) | 14.5741 | + | 44.8545i | 0.566439 | + | 1.74332i | ||||
\(663\) | −5.91546 | − | 4.29783i | −0.229737 | − | 0.166914i | ||||
\(664\) | −2.08077 | + | 1.51177i | −0.0807494 | + | 0.0586679i | ||||
\(665\) | 1.66431 | − | 5.12221i | 0.0645390 | − | 0.198631i | ||||
\(666\) | 1.48904 | − | 4.58278i | 0.0576990 | − | 0.177579i | ||||
\(667\) | 30.5044 | − | 22.1628i | 1.18114 | − | 0.858146i | ||||
\(668\) | −12.5759 | − | 9.13691i | −0.486575 | − | 0.353518i | ||||
\(669\) | −0.883311 | − | 2.71855i | −0.0341508 | − | 0.105105i | ||||
\(670\) | −26.7456 | −1.03327 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.61803 | 0.139569 | ||||||||
\(673\) | −3.73868 | − | 11.5065i | −0.144116 | − | 0.443542i | 0.852781 | − | 0.522269i | \(-0.174914\pi\) |
−0.996896 | + | 0.0787272i | \(0.974914\pi\) | |||||||
\(674\) | 0.986448 | + | 0.716696i | 0.0379965 | + | 0.0276061i | ||||
\(675\) | 7.62485 | − | 5.53978i | 0.293481 | − | 0.213226i | ||||
\(676\) | 1.94692 | − | 5.99202i | 0.0748817 | − | 0.230462i | ||||
\(677\) | 2.91399 | − | 8.96834i | 0.111994 | − | 0.344681i | −0.879314 | − | 0.476242i | \(-0.841999\pi\) |
0.991308 | + | 0.131560i | \(0.0419987\pi\) | |||||||
\(678\) | −16.3956 | + | 11.9121i | −0.629668 | + | 0.457480i | ||||
\(679\) | −9.39772 | − | 6.82784i | −0.360651 | − | 0.262029i | ||||
\(680\) | −3.53356 | − | 10.8752i | −0.135506 | − | 0.417044i | ||||
\(681\) | −10.6922 | −0.409726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.2986 | −0.585385 | −0.292692 | − | 0.956207i | \(-0.594551\pi\) | ||||
−0.292692 | + | 0.956207i | \(0.594551\pi\) | |||||||
\(684\) | 1.81890 | + | 5.59800i | 0.0695474 | + | 0.214045i | ||||
\(685\) | −5.86632 | − | 4.26213i | −0.224141 | − | 0.162848i | ||||
\(686\) | 1.43801 | − | 1.04478i | 0.0549037 | − | 0.0398898i | ||||
\(687\) | −0.845314 | + | 2.60161i | −0.0322507 | + | 0.0992575i | ||||
\(688\) | −7.23758 | + | 22.2750i | −0.275930 | + | 0.849226i | ||||
\(689\) | 13.5470 | − | 9.84250i | 0.516101 | − | 0.374970i | ||||
\(690\) | −10.7874 | − | 7.83753i | −0.410671 | − | 0.298370i | ||||
\(691\) | 7.05154 | + | 21.7024i | 0.268253 | + | 0.825599i | 0.990926 | + | 0.134408i | \(0.0429134\pi\) |
−0.722673 | + | 0.691190i | \(0.757087\pi\) | |||||||
\(692\) | 23.8639 | 0.907169 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.2256 | 1.45102 | ||||||||
\(695\) | −0.859436 | − | 2.64507i | −0.0326003 | − | 0.100333i | ||||
\(696\) | 6.44546 | + | 4.68290i | 0.244314 | + | 0.177505i | ||||
\(697\) | 21.4149 | − | 15.5589i | 0.811149 | − | 0.589334i | ||||
\(698\) | 10.6794 | − | 32.8679i | 0.404223 | − | 1.24407i | ||||
\(699\) | 2.01163 | − | 6.19117i | 0.0760869 | − | 0.234171i | ||||
\(700\) | −2.54617 | + | 1.84990i | −0.0962360 | + | 0.0699196i | ||||
\(701\) | −26.1508 | − | 18.9997i | −0.987702 | − | 0.717607i | −0.0282853 | − | 0.999600i | \(-0.509005\pi\) |
−0.959417 | + | 0.281992i | \(0.909005\pi\) | |||||||
\(702\) | 8.18830 | + | 25.2010i | 0.309048 | + | 0.951151i | ||||
\(703\) | −2.00789 | −0.0757292 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.3937 | 0.843396 | ||||||||
\(706\) | 11.4967 | + | 35.3831i | 0.432683 | + | 1.33166i | ||||
\(707\) | 2.76020 | + | 2.00540i | 0.103808 | + | 0.0754208i | ||||
\(708\) | 4.96078 | − | 3.60422i | 0.186438 | − | 0.135455i | ||||
\(709\) | 4.49922 | − | 13.8472i | 0.168972 | − | 0.520041i | −0.830335 | − | 0.557264i | \(-0.811851\pi\) |
0.999307 | + | 0.0372228i | \(0.0118511\pi\) | |||||||
\(710\) | −3.07720 | + | 9.47066i | −0.115485 | + | 0.355427i | ||||
\(711\) | −13.3298 | + | 9.68466i | −0.499906 | + | 0.363203i | ||||
\(712\) | 18.4977 | + | 13.4394i | 0.693232 | + | 0.503662i | ||||
\(713\) | −0.270880 | − | 0.833684i | −0.0101446 | − | 0.0312217i | ||||
\(714\) | −3.02710 | −0.113287 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.30759 | −0.160982 | ||||||||
\(717\) | 1.86332 | + | 5.73470i | 0.0695869 | + | 0.214166i | ||||
\(718\) | −14.0512 | − | 10.2088i | −0.524387 | − | 0.380990i | ||||
\(719\) | −36.2926 | + | 26.3682i | −1.35349 | + | 0.983366i | −0.354658 | + | 0.934996i | \(0.615403\pi\) |
−0.998829 | + | 0.0483700i | \(0.984597\pi\) | |||||||
\(720\) | −11.1780 | + | 34.4024i | −0.416581 | + | 1.28210i | ||||
\(721\) | −5.61873 | + | 17.2927i | −0.209252 | + | 0.644012i | ||||
\(722\) | −21.9152 | + | 15.9223i | −0.815600 | + | 0.592568i | ||||
\(723\) | 6.27504 | + | 4.55909i | 0.233371 | + | 0.169554i | ||||
\(724\) | 1.70970 | + | 5.26191i | 0.0635404 | + | 0.195557i | ||||
\(725\) | −23.4202 | −0.869806 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3582 | 1.05175 | 0.525874 | − | 0.850562i | \(-0.323738\pi\) | ||||
0.525874 | + | 0.850562i | \(0.323738\pi\) | |||||||
\(728\) | 1.98226 | + | 6.10077i | 0.0734674 | + | 0.226110i | ||||
\(729\) | 6.88197 | + | 5.00004i | 0.254888 | + | 0.185187i | ||||
\(730\) | −39.8251 | + | 28.9346i | −1.47399 | + | 1.07092i | ||||
\(731\) | 4.00910 | − | 12.3387i | 0.148282 | − | 0.456365i | ||||
\(732\) | 0.218913 | − | 0.673744i | 0.00809125 | − | 0.0249023i | ||||
\(733\) | 5.06199 | − | 3.67775i | 0.186969 | − | 0.135841i | −0.490364 | − | 0.871518i | \(-0.663136\pi\) |
0.677332 | + | 0.735677i | \(0.263136\pi\) | |||||||
\(734\) | 14.2359 | + | 10.3430i | 0.525456 | + | 0.381766i | ||||
\(735\) | −0.530452 | − | 1.63256i | −0.0195660 | − | 0.0602180i | ||||
\(736\) | 25.5830 | 0.943001 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −44.7024 | −1.64552 | ||||||||
\(739\) | −2.88993 | − | 8.89429i | −0.106308 | − | 0.327182i | 0.883727 | − | 0.468002i | \(-0.155026\pi\) |
−0.990035 | + | 0.140820i | \(0.955026\pi\) | |||||||
\(740\) | 2.69776 | + | 1.96004i | 0.0991716 | + | 0.0720524i | ||||
\(741\) | 4.16273 | − | 3.02440i | 0.152922 | − | 0.111104i | ||||
\(742\) | 2.14223 | − | 6.59310i | 0.0786437 | − | 0.242040i | ||||
\(743\) | −7.78926 | + | 23.9729i | −0.285760 | + | 0.879480i | 0.700409 | + | 0.713741i | \(0.253001\pi\) |
−0.986170 | + | 0.165739i | \(0.946999\pi\) | |||||||
\(744\) | 0.149845 | − | 0.108869i | 0.00549360 | − | 0.00399134i | ||||
\(745\) | 33.4690 | + | 24.3167i | 1.22621 | + | 0.890893i | ||||
\(746\) | −2.34800 | − | 7.22641i | −0.0859665 | − | 0.264578i | ||||
\(747\) | −4.50684 | −0.164897 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.24746 | −0.118660 | ||||||||
\(750\) | −2.15501 | − | 6.63243i | −0.0786897 | − | 0.242182i | ||||
\(751\) | 28.1128 | + | 20.4251i | 1.02585 | + | 0.745323i | 0.967474 | − | 0.252972i | \(-0.0814079\pi\) |
0.0583755 | + | 0.998295i | \(0.481408\pi\) | |||||||
\(752\) | −52.5020 | + | 38.1449i | −1.91455 | + | 1.39100i | ||||
\(753\) | −2.09913 | + | 6.46046i | −0.0764966 | + | 0.235432i | ||||
\(754\) | 20.3475 | − | 62.6233i | 0.741014 | − | 2.28061i | ||||
\(755\) | −35.5134 | + | 25.8020i | −1.29247 | + | 0.939031i | ||||
\(756\) | 3.25692 | + | 2.36629i | 0.118453 | + | 0.0860610i | ||||
\(757\) | 10.7526 | + | 33.0930i | 0.390808 | + | 1.20278i | 0.932178 | + | 0.362000i | \(0.117906\pi\) |
−0.541370 | + | 0.840784i | \(0.682094\pi\) | |||||||
\(758\) | −7.68929 | −0.279288 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.04674 | 0.291886 | ||||||||
\(761\) | 3.77787 | + | 11.6271i | 0.136948 | + | 0.421482i | 0.995888 | − | 0.0905941i | \(-0.0288766\pi\) |
−0.858940 | + | 0.512076i | \(0.828877\pi\) | |||||||
\(762\) | −17.3387 | − | 12.5973i | −0.628116 | − | 0.456353i | ||||
\(763\) | 10.2674 | − | 7.45967i | 0.371703 | − | 0.270058i | ||||
\(764\) | −0.297079 | + | 0.914315i | −0.0107479 | + | 0.0330788i | ||||
\(765\) | 6.19182 | − | 19.0565i | 0.223866 | − | 0.688988i | ||||
\(766\) | −1.90120 | + | 1.38130i | −0.0686931 | + | 0.0499085i | ||||
\(767\) | 29.7231 | + | 21.5951i | 1.07324 | + | 0.779755i | ||||
\(768\) | 3.87351 | + | 11.9214i | 0.139773 | + | 0.430178i | ||||
\(769\) | 2.61946 | 0.0944603 | 0.0472301 | − | 0.998884i | \(-0.484961\pi\) | ||||
0.0472301 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.29585 | 0.118697 | ||||||||
\(772\) | 2.41417 | + | 7.43004i | 0.0868878 | + | 0.267413i | ||||
\(773\) | 0.172162 | + | 0.125083i | 0.00619225 | + | 0.00449894i | 0.590877 | − | 0.806762i | \(-0.298782\pi\) |
−0.584685 | + | 0.811261i | \(0.698782\pi\) | |||||||
\(774\) | −17.7253 | + | 12.8782i | −0.637123 | + | 0.462897i | ||||
\(775\) | −0.168253 | + | 0.517831i | −0.00604384 | + | 0.0186010i | ||||
\(776\) | 5.36310 | − | 16.5059i | 0.192524 | − | 0.592529i | ||||
\(777\) | −0.517740 | + | 0.376160i | −0.0185738 | + | 0.0134947i | ||||
\(778\) | −55.3767 | − | 40.2336i | −1.98535 | − | 1.44244i | ||||
\(779\) | 5.75614 | + | 17.7156i | 0.206235 | + | 0.634727i | ||||
\(780\) | −8.54526 | −0.305969 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −21.4045 | −0.765425 | ||||||||
\(783\) | 9.25750 | + | 28.4917i | 0.330836 | + | 1.01821i | ||||
\(784\) | 4.02452 | + | 2.92398i | 0.143733 | + | 0.104428i | ||||
\(785\) | 10.3166 | − | 7.49547i | 0.368216 | − | 0.267525i | ||||
\(786\) | −2.34164 | + | 7.20684i | −0.0835237 | + | 0.257060i | ||||
\(787\) | −9.00399 | + | 27.7114i | −0.320958 | + | 0.987806i | 0.652275 | + | 0.757983i | \(0.273815\pi\) |
−0.973232 | + | 0.229823i | \(0.926185\pi\) | |||||||
\(788\) | −10.2446 | + | 7.44313i | −0.364948 | + | 0.265151i | ||||
\(789\) | −4.09017 | − | 2.97168i | −0.145614 | − | 0.105795i | ||||
\(790\) | −9.60131 | − | 29.5498i | −0.341599 | − | 1.05133i | ||||
\(791\) | −18.4480 | −0.655937 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.24457 | 0.150729 | ||||||||
\(794\) | 0.225262 | + | 0.693284i | 0.00799424 | + | 0.0246037i | ||||
\(795\) | −5.41626 | − | 3.93514i | −0.192095 | − | 0.139565i | ||||
\(796\) | −19.6745 | + | 14.2943i | −0.697343 | + | 0.506649i | ||||
\(797\) | 9.95913 | − | 30.6510i | 0.352770 | − | 1.08572i | −0.604521 | − | 0.796589i | \(-0.706635\pi\) |
0.957291 | − | 0.289126i | \(-0.0933647\pi\) | |||||||
\(798\) | 0.658263 | − | 2.02593i | 0.0233023 | − | 0.0717170i | ||||
\(799\) | 29.0823 | − | 21.1295i | 1.02886 | − | 0.747509i | ||||
\(800\) | −12.8557 | − | 9.34019i | −0.454517 | − | 0.330226i | ||||
\(801\) | 12.3808 | + | 38.1042i | 0.437455 | + | 1.34635i | ||||
\(802\) | 2.78503 | 0.0983430 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −3.88203 | −0.136909 | ||||||||
\(805\) | −3.75081 | − | 11.5438i | −0.132199 | − | 0.406865i | ||||
\(806\) | −1.23845 | − | 0.899783i | −0.0436224 | − | 0.0316935i | ||||
\(807\) | −6.42195 | + | 4.66582i | −0.226064 | + | 0.164245i | ||||
\(808\) | −1.57519 | + | 4.84794i | −0.0554151 | + | 0.170550i | ||||
\(809\) | 9.06844 | − | 27.9098i | 0.318829 | − | 0.981256i | −0.655320 | − | 0.755351i | \(-0.727466\pi\) |
0.974149 | − | 0.225905i | \(-0.0725338\pi\) | |||||||
\(810\) | −22.7989 | + | 16.5644i | −0.801073 | + | 0.582013i | ||||
\(811\) | 0.840891 | + | 0.610943i | 0.0295277 | + | 0.0214531i | 0.602451 | − | 0.798156i | \(-0.294191\pi\) |
−0.572924 | + | 0.819609i | \(0.694191\pi\) | |||||||
\(812\) | −3.09136 | − | 9.51422i | −0.108485 | − | 0.333884i | ||||
\(813\) | 13.6259 | 0.477882 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.3244 | −0.781990 | ||||||||
\(816\) | −2.61794 | − | 8.05720i | −0.0916463 | − | 0.282058i | ||||
\(817\) | 7.38605 | + | 5.36628i | 0.258405 | + | 0.187742i | ||||
\(818\) | 9.74762 | − | 7.08206i | 0.340817 | − | 0.247618i | ||||
\(819\) | −3.47350 | + | 10.6903i | −0.121374 | + | 0.373550i | ||||
\(820\) | 9.55952 | − | 29.4212i | 0.333833 | − | 1.02743i | ||||
\(821\) | 23.0831 | − | 16.7709i | 0.805607 | − | 0.585308i | −0.106946 | − | 0.994265i | \(-0.534107\pi\) |
0.912554 | + | 0.408957i | \(0.134107\pi\) | |||||||
\(822\) | −2.32024 | − | 1.68575i | −0.0809275 | − | 0.0587973i | ||||
\(823\) | 8.23767 | + | 25.3529i | 0.287147 | + | 0.883748i | 0.985747 | + | 0.168235i | \(0.0538068\pi\) |
−0.698600 | + | 0.715513i | \(0.746193\pi\) | |||||||
\(824\) | −27.1659 | −0.946370 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.2102 | 0.529229 | ||||||||
\(827\) | −0.531399 | − | 1.63548i | −0.0184785 | − | 0.0568711i | 0.941392 | − | 0.337314i | \(-0.109519\pi\) |
−0.959871 | + | 0.280443i | \(0.909519\pi\) | |||||||
\(828\) | 10.7319 | + | 7.79717i | 0.372959 | + | 0.270970i | ||||
\(829\) | −22.6205 | + | 16.4347i | −0.785642 | + | 0.570802i | −0.906667 | − | 0.421847i | \(-0.861382\pi\) |
0.121025 | + | 0.992649i | \(0.461382\pi\) | |||||||
\(830\) | 2.62625 | − | 8.08277i | 0.0911585 | − | 0.280557i | ||||
\(831\) | −4.59829 | + | 14.1521i | −0.159513 | + | 0.490930i | ||||
\(832\) | 1.58538 | − | 1.15185i | 0.0549632 | − | 0.0399331i | ||||
\(833\) | −2.22929 | − | 1.61968i | −0.0772404 | − | 0.0561184i | ||||
\(834\) | −0.339923 | − | 1.04617i | −0.0117706 | − | 0.0362261i | ||||
\(835\) | −37.2375 | −1.28866 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.696468 | 0.0240735 | ||||||||
\(838\) | −15.7761 | − | 48.5539i | −0.544977 | − | 1.67727i | ||||
\(839\) | −29.0133 | − | 21.0794i | −1.00165 | − | 0.727742i | −0.0392091 | − | 0.999231i | \(-0.512484\pi\) |
−0.962441 | + | 0.271489i | \(0.912484\pi\) | |||||||
\(840\) | 2.07487 | − | 1.50748i | 0.0715898 | − | 0.0520130i | ||||
\(841\) | 14.0429 | − | 43.2197i | 0.484240 | − | 1.49034i | ||||
\(842\) | −6.71518 | + | 20.6672i | −0.231420 | + | 0.712239i | ||||
\(843\) | 7.72092 | − | 5.60957i | 0.265922 | − | 0.193204i | ||||
\(844\) | −5.65023 | − | 4.10514i | −0.194489 | − | 0.141305i | ||||
\(845\) | −4.66389 | − | 14.3540i | −0.160443 | − | 0.493792i | ||||
\(846\) | −60.7076 | −2.08717 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.4014 | 0.666248 | ||||||||
\(849\) | 0.641191 | + | 1.97338i | 0.0220056 | + | 0.0677263i | ||||
\(850\) | 10.7560 | + | 7.81467i | 0.368927 | + | 0.268041i | ||||
\(851\) | −3.66092 | + | 2.65981i | −0.125495 | + | 0.0911772i | ||||
\(852\) | −0.446646 | + | 1.37463i | −0.0153018 | + | 0.0470942i | ||||
\(853\) | 4.67937 | − | 14.4016i | 0.160218 | − | 0.493102i | −0.838434 | − | 0.545004i | \(-0.816528\pi\) |
0.998652 | + | 0.0519019i | \(0.0165283\pi\) | |||||||
\(854\) | 1.42163 | − | 1.03288i | 0.0486473 | − | 0.0353443i | ||||
\(855\) | 11.4073 | + | 8.28790i | 0.390122 | + | 0.283440i | ||||
\(856\) | −1.49932 | − | 4.61444i | −0.0512458 | − | 0.157718i | ||||
\(857\) | −25.3267 | −0.865142 | −0.432571 | − | 0.901600i | \(-0.642394\pi\) | ||||
−0.432571 | + | 0.901600i | \(0.642394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.5291 | 1.41696 | 0.708478 | − | 0.705733i | \(-0.249382\pi\) | ||||
0.708478 | + | 0.705733i | \(0.249382\pi\) | |||||||
\(860\) | −4.68534 | − | 14.4200i | −0.159769 | − | 0.491718i | ||||
\(861\) | 4.80308 | + | 3.48964i | 0.163689 | + | 0.118927i | ||||
\(862\) | −5.30813 | + | 3.85658i | −0.180796 | + | 0.131356i | ||||
\(863\) | −7.43197 | + | 22.8733i | −0.252987 | + | 0.778615i | 0.741232 | + | 0.671249i | \(0.234242\pi\) |
−0.994220 | + | 0.107366i | \(0.965758\pi\) | |||||||
\(864\) | −6.28115 | + | 19.3314i | −0.213689 | + | 0.657668i | ||||
\(865\) | 46.2486 | − | 33.6016i | 1.57250 | − | 1.14249i | ||||
\(866\) | 41.8101 | + | 30.3768i | 1.42077 | + | 1.03225i | ||||
\(867\) | −1.79656 | − | 5.52924i | −0.0610144 | − | 0.187783i | ||||
\(868\) | −0.232572 | −0.00789399 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −26.3260 | −0.892534 | ||||||||
\(871\) | −7.18764 | − | 22.1213i | −0.243544 | − | 0.749551i | ||||
\(872\) | 15.3401 | + | 11.1452i | 0.519481 | + | 0.377425i | ||||
\(873\) | 24.6035 | − | 17.8755i | 0.832704 | − | 0.604995i | ||||
\(874\) | 4.65455 | − | 14.3252i | 0.157443 | − | 0.484559i | ||||
\(875\) | 1.96169 | − | 6.03746i | 0.0663173 | − | 0.204104i | ||||
\(876\) | −5.78049 | + | 4.19977i | −0.195304 | + | 0.141897i | ||||
\(877\) | 27.3490 | + | 19.8702i | 0.923509 | + | 0.670969i | 0.944395 | − | 0.328813i | \(-0.106649\pi\) |
−0.0208857 | + | 0.999782i | \(0.506649\pi\) | |||||||
\(878\) | −7.80061 | − | 24.0078i | −0.263258 | − | 0.810225i | ||||
\(879\) | −4.22553 | −0.142524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.8296 | −1.24082 | −0.620410 | − | 0.784278i | \(-0.713034\pi\) | ||||
−0.620410 | + | 0.784278i | \(0.713034\pi\) | |||||||
\(882\) | 1.43801 | + | 4.42575i | 0.0484205 | + | 0.149023i | ||||
\(883\) | −43.2099 | − | 31.3938i | −1.45413 | − | 1.05649i | −0.984845 | − | 0.173438i | \(-0.944512\pi\) |
−0.469283 | − | 0.883048i | \(-0.655488\pi\) | |||||||
\(884\) | −11.0976 | + | 8.06286i | −0.373252 | + | 0.271183i | ||||
\(885\) | 4.53915 | − | 13.9701i | 0.152582 | − | 0.469599i | ||||
\(886\) | −14.9598 | + | 46.0414i | −0.502583 | + | 1.54679i | ||||
\(887\) | 9.27263 | − | 6.73696i | 0.311344 | − | 0.226205i | −0.421129 | − | 0.907001i | \(-0.638366\pi\) |
0.732473 | + | 0.680796i | \(0.238366\pi\) | |||||||
\(888\) | −0.773537 | − | 0.562007i | −0.0259582 | − | 0.0188597i | ||||
\(889\) | −6.02870 | − | 18.5544i | −0.202196 | − | 0.622296i | ||||
\(890\) | −75.5525 | −2.53253 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.36254 | −0.179551 | ||||||||
\(893\) | 7.81706 | + | 24.0584i | 0.261588 | + | 0.805085i | ||||
\(894\) | 13.2376 | + | 9.61768i | 0.442732 | + | 0.321663i | ||||
\(895\) | −8.34817 | + | 6.06530i | −0.279048 | + | 0.202741i | ||||
\(896\) | −3.36733 | + | 10.3636i | −0.112495 | + | 0.346223i | ||||
\(897\) | 3.58339 | − | 11.0286i | 0.119646 | − | 0.368233i | ||||
\(898\) | −60.2757 | + | 43.7929i | −2.01143 | + | 1.46139i | ||||
\(899\) | −1.40016 | − | 1.01727i | −0.0466979 | − | 0.0339280i | ||||
\(900\) | −2.54617 | − | 7.83629i | −0.0848722 | − | 0.261210i | ||||
\(901\) | −10.7470 | −0.358034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90983 | 0.0968331 | ||||||||
\(904\) | −8.51730 | − | 26.2136i | −0.283281 | − | 0.871850i | ||||
\(905\) | 10.7224 | + | 7.79031i | 0.356426 | + | 0.258959i | ||||
\(906\) | −14.0462 | + | 10.2052i | −0.466654 | + | 0.339044i | ||||
\(907\) | 17.6319 | − | 54.2655i | 0.585459 | − | 1.80186i | −0.0119596 | − | 0.999928i | \(-0.503807\pi\) |
0.597419 | − | 0.801929i | \(-0.296193\pi\) | |||||||
\(908\) | −6.19853 | + | 19.0771i | −0.205706 | + | 0.633097i | ||||
\(909\) | −7.22628 | + | 5.25020i | −0.239681 | + | 0.174138i | ||||
\(910\) | −17.1484 | − | 12.4591i | −0.568465 | − | 0.413014i | ||||
\(911\) | 2.06289 | + | 6.34893i | 0.0683467 | + | 0.210350i | 0.979396 | − | 0.201947i | \(-0.0647268\pi\) |
−0.911050 | + | 0.412296i | \(0.864727\pi\) | |||||||
\(912\) | 5.96167 | 0.197410 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 34.6568 | 1.14635 | ||||||||
\(915\) | −0.524410 | − | 1.61397i | −0.0173365 | − | 0.0533561i | ||||
\(916\) | 4.15177 | + | 3.01643i | 0.137178 | + | 0.0996658i | ||||
\(917\) | −5.58057 | + | 4.05452i | −0.184286 | + | 0.133892i | ||||
\(918\) | 5.25526 | − | 16.1740i | 0.173449 | − | 0.533822i | ||||
\(919\) | 9.00287 | − | 27.7080i | 0.296977 | − | 0.914002i | −0.685573 | − | 0.728004i | \(-0.740448\pi\) |
0.982550 | − | 0.185998i | \(-0.0595518\pi\) | |||||||
\(920\) | 14.6713 | − | 10.6593i | 0.483699 | − | 0.351428i | ||||
\(921\) | −5.89852 | − | 4.28553i | −0.194363 | − | 0.141213i | ||||
\(922\) | 6.71491 | + | 20.6664i | 0.221144 | + | 0.680611i | ||||
\(923\) | −8.66015 | −0.285052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.81073 | 0.0924161 | ||||||||
\(926\) | −7.61015 | − | 23.4216i | −0.250085 | − | 0.769683i | ||||
\(927\) | −38.5113 | − | 27.9801i | −1.26488 | − | 0.918987i | ||||
\(928\) | 40.8632 | − | 29.6889i | 1.34140 | − | 0.974585i | ||||
\(929\) | 0.724557 | − | 2.22996i | 0.0237720 | − | 0.0731626i | −0.938467 | − | 0.345370i | \(-0.887754\pi\) |
0.962239 | + | 0.272207i | \(0.0877536\pi\) | |||||||
\(930\) | −0.189128 | + | 0.582077i | −0.00620176 | + | 0.0190871i | ||||
\(931\) | 1.56876 | − | 1.13977i | 0.0514141 | − | 0.0373545i | ||||
\(932\) | −9.88015 | − | 7.17835i | −0.323635 | − | 0.235135i | ||||
\(933\) | 4.83452 | + | 14.8791i | 0.158275 | + | 0.487121i | ||||
\(934\) | 29.1876 | 0.955047 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.7940 | −0.548928 | ||||||||
\(937\) | −2.71558 | − | 8.35769i | −0.0887141 | − | 0.273034i | 0.896850 | − | 0.442334i | \(-0.145849\pi\) |
−0.985565 | + | 0.169300i | \(0.945849\pi\) | |||||||
\(938\) | −7.79037 | − | 5.66003i | −0.254365 | − | 0.184807i | ||||
\(939\) | 9.82717 | − | 7.13986i | 0.320698 | − | 0.233000i | ||||
\(940\) | 12.9822 | − | 39.9551i | 0.423432 | − | 1.30319i | ||||
\(941\) | −2.74676 | + | 8.45366i | −0.0895419 | + | 0.275582i | −0.985793 | − | 0.167966i | \(-0.946280\pi\) |
0.896251 | + | 0.443547i | \(0.146280\pi\) | |||||||
\(942\) | 4.08042 | − | 2.96460i | 0.132947 | − | 0.0965918i | ||||
\(943\) | 33.9624 | + | 24.6751i | 1.10597 | + | 0.803533i | ||||
\(944\) | 13.1543 | + | 40.4847i | 0.428135 | + | 1.31766i | ||||
\(945\) | 9.64380 | 0.313713 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.86275 | −0.255505 | −0.127752 | − | 0.991806i | \(-0.540776\pi\) | ||||
−0.127752 | + | 0.991806i | \(0.540776\pi\) | |||||||
\(948\) | −1.39360 | − | 4.28905i | −0.0452620 | − | 0.139302i | ||||
\(949\) | −34.6345 | − | 25.1634i | −1.12428 | − | 0.816840i | ||||
\(950\) | −7.56902 | + | 5.49921i | −0.245571 | + | 0.178418i | ||||
\(951\) | 0.689556 | − | 2.12223i | 0.0223604 | − | 0.0688182i | ||||
\(952\) | 1.27222 | − | 3.91548i | 0.0412328 | − | 0.126901i | ||||
\(953\) | −14.1290 | + | 10.2653i | −0.457683 | + | 0.332526i | −0.792622 | − | 0.609714i | \(-0.791284\pi\) |
0.334939 | + | 0.942240i | \(0.391284\pi\) | |||||||
\(954\) | 14.6831 | + | 10.6679i | 0.475382 | + | 0.345385i | ||||
\(955\) | 0.711658 | + | 2.19026i | 0.0230287 | + | 0.0708751i | ||||
\(956\) | 11.3121 | 0.365860 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −44.0663 | −1.42372 | ||||||||
\(959\) | −0.806750 | − | 2.48292i | −0.0260513 | − | 0.0801777i | ||||
\(960\) | −0.633854 | − | 0.460522i | −0.0204575 | − | 0.0148633i | ||||
\(961\) | 25.0470 | − | 18.1977i | 0.807967 | − | 0.587022i | ||||
\(962\) | −2.44196 | + | 7.51559i | −0.0787320 | + | 0.242312i | ||||
\(963\) | 2.62725 | − | 8.08584i | 0.0846619 | − | 0.260563i | ||||
\(964\) | 11.7722 | − | 8.55298i | 0.379156 | − | 0.275473i | ||||
\(965\) | 15.1406 | + | 11.0003i | 0.487392 | + | 0.354111i | ||||
\(966\) | −1.48351 | − | 4.56578i | −0.0477312 | − | 0.146902i | ||||
\(967\) | 45.6122 | 1.46679 | 0.733395 | − | 0.679802i | \(-0.237934\pi\) | ||||
0.733395 | + | 0.679802i | \(0.237934\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.30233 | −0.106086 | ||||||||
\(970\) | 17.7217 | + | 54.5417i | 0.569008 | + | 1.75123i | ||||
\(971\) | −1.92852 | − | 1.40115i | −0.0618892 | − | 0.0449651i | 0.556411 | − | 0.830908i | \(-0.312178\pi\) |
−0.618300 | + | 0.785942i | \(0.712178\pi\) | |||||||
\(972\) | −13.0799 | + | 9.50313i | −0.419539 | + | 0.304813i | ||||
\(973\) | 0.309430 | − | 0.952327i | 0.00991986 | − | 0.0305302i | ||||
\(974\) | 7.87338 | − | 24.2318i | 0.252279 | − | 0.776436i | ||||
\(975\) | −5.82715 | + | 4.23367i | −0.186618 | + | 0.135586i | ||||
\(976\) | 3.97867 | + | 2.89067i | 0.127354 | + | 0.0925282i | ||||
\(977\) | −5.95358 | − | 18.3232i | −0.190472 | − | 0.586212i | 0.809528 | − | 0.587082i | \(-0.199723\pi\) |
−1.00000 | 0.000869450i | \(0.999723\pi\) | ||||||||
\(978\) | −8.82972 | −0.282343 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.22035 | −0.102870 | ||||||||
\(981\) | 10.2674 | + | 31.5997i | 0.327812 | + | 1.00890i | ||||
\(982\) | 31.6641 | + | 23.0053i | 1.01044 | + | 0.734130i | ||||
\(983\) | 13.1268 | − | 9.53718i | 0.418680 | − | 0.304189i | −0.358426 | − | 0.933558i | \(-0.616687\pi\) |
0.777107 | + | 0.629369i | \(0.216687\pi\) | |||||||
\(984\) | −2.74103 | + | 8.43602i | −0.0873808 | + | 0.268931i | ||||
\(985\) | −9.37387 | + | 28.8498i | −0.298676 | + | 0.919231i | ||||
\(986\) | −34.1891 | + | 24.8398i | −1.08880 | + | 0.791061i | ||||
\(987\) | 6.52277 | + | 4.73907i | 0.207622 | + | 0.150846i | ||||
\(988\) | −2.98293 | − | 9.18051i | −0.0948996 | − | 0.292071i | ||||
\(989\) | 20.5753 | 0.654256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5214 | −1.60487 | −0.802433 | − | 0.596743i | \(-0.796461\pi\) | ||||
−0.802433 | + | 0.596743i | \(0.796461\pi\) | |||||||
\(992\) | −0.362867 | − | 1.11679i | −0.0115210 | − | 0.0354581i | ||||
\(993\) | 13.2667 | + | 9.63884i | 0.421007 | + | 0.305879i | ||||
\(994\) | −2.90055 | + | 2.10737i | −0.0919997 | + | 0.0668417i | ||||
\(995\) | −18.0023 | + | 55.4053i | −0.570710 | + | 1.75647i | ||||
\(996\) | 0.381192 | − | 1.17319i | 0.0120785 | − | 0.0371739i | ||||
\(997\) | −36.4224 | + | 26.4625i | −1.15351 | + | 0.838074i | −0.988944 | − | 0.148292i | \(-0.952623\pi\) |
−0.164567 | + | 0.986366i | \(0.552623\pi\) | |||||||
\(998\) | −36.3986 | − | 26.4452i | −1.15218 | − | 0.837107i | ||||
\(999\) | −1.11102 | − | 3.41936i | −0.0351510 | − | 0.108184i |
(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 | 847.2.f.q.148.1 | 8 | ||
11.2 | odd | 10 | 77.2.f.a.64.2 | ✓ | 8 | ||
11.3 | even | 5 | 847.2.a.k.1.2 | 4 | |||
11.4 | even | 5 | 847.2.f.s.729.2 | 8 | |||
11.5 | even | 5 | 847.2.f.s.323.2 | 8 | |||
11.6 | odd | 10 | 847.2.f.p.323.1 | 8 | |||
11.7 | odd | 10 | 847.2.f.p.729.1 | 8 | |||
11.8 | odd | 10 | 847.2.a.l.1.3 | 4 | |||
11.9 | even | 5 | inner | 847.2.f.q.372.1 | 8 | ||
11.10 | odd | 2 | 77.2.f.a.71.2 | yes | 8 | ||
33.2 | even | 10 | 693.2.m.g.64.1 | 8 | |||
33.8 | even | 10 | 7623.2.a.ch.1.2 | 4 | |||
33.14 | odd | 10 | 7623.2.a.co.1.3 | 4 | |||
33.32 | even | 2 | 693.2.m.g.379.1 | 8 | |||
77.2 | odd | 30 | 539.2.q.c.361.1 | 16 | |||
77.10 | even | 6 | 539.2.q.b.324.1 | 16 | |||
77.13 | even | 10 | 539.2.f.d.295.2 | 8 | |||
77.24 | even | 30 | 539.2.q.b.471.2 | 16 | |||
77.32 | odd | 6 | 539.2.q.c.324.1 | 16 | |||
77.41 | even | 10 | 5929.2.a.bi.1.3 | 4 | |||
77.46 | odd | 30 | 539.2.q.c.471.2 | 16 | |||
77.54 | even | 6 | 539.2.q.b.214.2 | 16 | |||
77.65 | odd | 6 | 539.2.q.c.214.2 | 16 | |||
77.68 | even | 30 | 539.2.q.b.361.1 | 16 | |||
77.69 | odd | 10 | 5929.2.a.bb.1.2 | 4 | |||
77.76 | even | 2 | 539.2.f.d.148.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.64.2 | ✓ | 8 | 11.2 | odd | 10 | ||
77.2.f.a.71.2 | yes | 8 | 11.10 | odd | 2 | ||
539.2.f.d.148.2 | 8 | 77.76 | even | 2 | |||
539.2.f.d.295.2 | 8 | 77.13 | even | 10 | |||
539.2.q.b.214.2 | 16 | 77.54 | even | 6 | |||
539.2.q.b.324.1 | 16 | 77.10 | even | 6 | |||
539.2.q.b.361.1 | 16 | 77.68 | even | 30 | |||
539.2.q.b.471.2 | 16 | 77.24 | even | 30 | |||
539.2.q.c.214.2 | 16 | 77.65 | odd | 6 | |||
539.2.q.c.324.1 | 16 | 77.32 | odd | 6 | |||
539.2.q.c.361.1 | 16 | 77.2 | odd | 30 | |||
539.2.q.c.471.2 | 16 | 77.46 | odd | 30 | |||
693.2.m.g.64.1 | 8 | 33.2 | even | 10 | |||
693.2.m.g.379.1 | 8 | 33.32 | even | 2 | |||
847.2.a.k.1.2 | 4 | 11.3 | even | 5 | |||
847.2.a.l.1.3 | 4 | 11.8 | odd | 10 | |||
847.2.f.p.323.1 | 8 | 11.6 | odd | 10 | |||
847.2.f.p.729.1 | 8 | 11.7 | odd | 10 | |||
847.2.f.q.148.1 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.q.372.1 | 8 | 11.9 | even | 5 | inner | ||
847.2.f.s.323.2 | 8 | 11.5 | even | 5 | |||
847.2.f.s.729.2 | 8 | 11.4 | even | 5 | |||
5929.2.a.bb.1.2 | 4 | 77.69 | odd | 10 | |||
5929.2.a.bi.1.3 | 4 | 77.41 | even | 10 | |||
7623.2.a.ch.1.2 | 4 | 33.8 | even | 10 | |||
7623.2.a.co.1.3 | 4 | 33.14 | odd | 10 |