Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [506,2,Mod(47,506)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(506, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("506.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 506 = 2 \cdot 11 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 506.e (of order \(5\), degree \(4\), 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: | \(4.04043034228\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 13 x^{18} - 32 x^{17} + 171 x^{16} + 76 x^{15} + 1273 x^{14} + 1050 x^{13} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(-0.658008 + 2.02514i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 506.47 |
Dual form | 506.2.e.h.323.2 |
$q$-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 \(\left(\mathbb{Z}/506\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(419\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | −0.348991 | − | 1.07408i | −0.201490 | − | 0.620122i | −0.999839 | − | 0.0179275i | \(-0.994293\pi\) |
0.798349 | − | 0.602194i | \(-0.205707\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 2.43018 | + | 1.76563i | 1.08681 | + | 0.789613i | 0.978858 | − | 0.204543i | \(-0.0655708\pi\) |
0.107952 | + | 0.994156i | \(0.465571\pi\) | |||||||
\(6\) | 0.913669 | + | 0.663820i | 0.373004 | + | 0.271003i | ||||
\(7\) | 0.436107 | − | 1.34220i | 0.164833 | − | 0.507304i | −0.834191 | − | 0.551476i | \(-0.814065\pi\) |
0.999024 | + | 0.0441719i | \(0.0140649\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 1.39519 | − | 1.01367i | 0.465064 | − | 0.337889i | ||||
\(10\) | −3.00387 | −0.949906 | ||||||||
\(11\) | −0.516825 | + | 3.27611i | −0.155829 | + | 0.987784i | ||||
\(12\) | −1.12936 | −0.326017 | ||||||||
\(13\) | 0.705636 | − | 0.512675i | 0.195708 | − | 0.142190i | −0.485616 | − | 0.874172i | \(-0.661405\pi\) |
0.681324 | + | 0.731982i | \(0.261405\pi\) | |||||||
\(14\) | 0.436107 | + | 1.34220i | 0.116555 | + | 0.358718i | ||||
\(15\) | 1.04832 | − | 3.22640i | 0.270675 | − | 0.833053i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 1.93934 | + | 1.40901i | 0.470359 | + | 0.341736i | 0.797581 | − | 0.603211i | \(-0.206113\pi\) |
−0.327222 | + | 0.944947i | \(0.606113\pi\) | |||||||
\(18\) | −0.532916 | + | 1.64015i | −0.125609 | + | 0.386586i | ||||
\(19\) | −0.237518 | − | 0.731004i | −0.0544903 | − | 0.167704i | 0.920108 | − | 0.391665i | \(-0.128101\pi\) |
−0.974598 | + | 0.223962i | \(0.928101\pi\) | |||||||
\(20\) | 2.43018 | − | 1.76563i | 0.543405 | − | 0.394807i | ||||
\(21\) | −1.59383 | −0.347802 | ||||||||
\(22\) | −1.50753 | − | 2.95421i | −0.321406 | − | 0.629840i | ||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.913669 | − | 0.663820i | 0.186502 | − | 0.135502i | ||||
\(25\) | 1.24324 | + | 3.82631i | 0.248648 | + | 0.765261i | ||||
\(26\) | −0.269529 | + | 0.829525i | −0.0528590 | + | 0.162683i | ||||
\(27\) | −4.31668 | − | 3.13625i | −0.830745 | − | 0.603572i | ||||
\(28\) | −1.14174 | − | 0.829525i | −0.215769 | − | 0.156766i | ||||
\(29\) | −0.719336 | + | 2.21389i | −0.133577 | + | 0.411109i | −0.995366 | − | 0.0961587i | \(-0.969344\pi\) |
0.861789 | + | 0.507267i | \(0.169344\pi\) | |||||||
\(30\) | 1.04832 | + | 3.22640i | 0.191396 | + | 0.589058i | ||||
\(31\) | 7.52285 | − | 5.46567i | 1.35114 | − | 0.981663i | 0.352189 | − | 0.935929i | \(-0.385437\pi\) |
0.998954 | − | 0.0457342i | \(-0.0145627\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.69918 | − | 0.588218i | 0.643944 | − | 0.102396i | ||||
\(34\) | −2.39716 | −0.411109 | ||||||||
\(35\) | 3.42965 | − | 2.49178i | 0.579716 | − | 0.421188i | ||||
\(36\) | −0.532916 | − | 1.64015i | −0.0888193 | − | 0.273358i | ||||
\(37\) | 0.873579 | − | 2.68860i | 0.143616 | − | 0.442003i | −0.853215 | − | 0.521560i | \(-0.825350\pi\) |
0.996830 | + | 0.0795565i | \(0.0253504\pi\) | |||||||
\(38\) | 0.621829 | + | 0.451785i | 0.100874 | + | 0.0732892i | ||||
\(39\) | −0.796915 | − | 0.578993i | −0.127609 | − | 0.0927131i | ||||
\(40\) | −0.928246 | + | 2.85685i | −0.146769 | + | 0.451707i | ||||
\(41\) | 3.09048 | + | 9.51152i | 0.482652 | + | 1.48545i | 0.835353 | + | 0.549714i | \(0.185263\pi\) |
−0.352701 | + | 0.935736i | \(0.614737\pi\) | |||||||
\(42\) | 1.28944 | − | 0.936830i | 0.198964 | − | 0.144556i | ||||
\(43\) | 6.13188 | 0.935103 | 0.467552 | − | 0.883966i | \(-0.345136\pi\) | ||||
0.467552 | + | 0.883966i | \(0.345136\pi\) | |||||||
\(44\) | 2.95606 | + | 1.50390i | 0.445642 | + | 0.226722i | ||||
\(45\) | 5.18033 | 0.772237 | ||||||||
\(46\) | 0.809017 | − | 0.587785i | 0.119283 | − | 0.0866642i | ||||
\(47\) | 0.788149 | + | 2.42567i | 0.114963 | + | 0.353821i | 0.991939 | − | 0.126713i | \(-0.0404428\pi\) |
−0.876976 | + | 0.480534i | \(0.840443\pi\) | |||||||
\(48\) | −0.348991 | + | 1.07408i | −0.0503725 | + | 0.155030i | ||||
\(49\) | 4.05181 | + | 2.94381i | 0.578830 | + | 0.420544i | ||||
\(50\) | −3.25485 | − | 2.36479i | −0.460305 | − | 0.334431i | ||||
\(51\) | 0.836585 | − | 2.57474i | 0.117145 | − | 0.360536i | ||||
\(52\) | −0.269529 | − | 0.829525i | −0.0373770 | − | 0.115034i | ||||
\(53\) | 9.60192 | − | 6.97621i | 1.31893 | − | 0.958256i | 0.318981 | − | 0.947761i | \(-0.396659\pi\) |
0.999945 | − | 0.0104945i | \(-0.00334056\pi\) | |||||||
\(54\) | 5.33571 | 0.726098 | ||||||||
\(55\) | −7.04037 | + | 7.04901i | −0.949323 | + | 0.950488i | ||||
\(56\) | 1.41127 | 0.188589 | ||||||||
\(57\) | −0.702267 | + | 0.510227i | −0.0930175 | + | 0.0675812i | ||||
\(58\) | −0.719336 | − | 2.21389i | −0.0944534 | − | 0.290698i | ||||
\(59\) | 1.83699 | − | 5.65368i | 0.239156 | − | 0.736047i | −0.757387 | − | 0.652966i | \(-0.773524\pi\) |
0.996543 | − | 0.0830802i | \(-0.0264758\pi\) | |||||||
\(60\) | −2.74454 | − | 1.99403i | −0.354319 | − | 0.257428i | ||||
\(61\) | −6.29515 | − | 4.57370i | −0.806012 | − | 0.585602i | 0.106660 | − | 0.994296i | \(-0.465984\pi\) |
−0.912672 | + | 0.408694i | \(0.865984\pi\) | |||||||
\(62\) | −2.87347 | + | 8.84364i | −0.364931 | + | 1.12314i | ||||
\(63\) | −0.752090 | − | 2.31469i | −0.0947544 | − | 0.291624i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 2.62002 | 0.324973 | ||||||||
\(66\) | −2.64695 | + | 2.65020i | −0.325817 | + | 0.326217i | ||||
\(67\) | −13.4543 | −1.64370 | −0.821851 | − | 0.569703i | \(-0.807058\pi\) | ||||
−0.821851 | + | 0.569703i | \(0.807058\pi\) | |||||||
\(68\) | 1.93934 | − | 1.40901i | 0.235180 | − | 0.170868i | ||||
\(69\) | 0.348991 | + | 1.07408i | 0.0420135 | + | 0.129304i | ||||
\(70\) | −1.31001 | + | 4.03179i | −0.156576 | + | 0.481891i | ||||
\(71\) | 0.244235 | + | 0.177447i | 0.0289853 | + | 0.0210591i | 0.602184 | − | 0.798358i | \(-0.294298\pi\) |
−0.573198 | + | 0.819417i | \(0.694298\pi\) | |||||||
\(72\) | 1.39519 | + | 1.01367i | 0.164425 | + | 0.119462i | ||||
\(73\) | −1.53573 | + | 4.72648i | −0.179743 | + | 0.553192i | −0.999818 | − | 0.0190634i | \(-0.993932\pi\) |
0.820075 | + | 0.572256i | \(0.193932\pi\) | |||||||
\(74\) | 0.873579 | + | 2.68860i | 0.101552 | + | 0.312543i | ||||
\(75\) | 3.67589 | − | 2.67069i | 0.424455 | − | 0.308385i | ||||
\(76\) | −0.768623 | −0.0881671 | ||||||||
\(77\) | 4.17180 | + | 2.12242i | 0.475421 | + | 0.241872i | ||||
\(78\) | 0.985042 | 0.111534 | ||||||||
\(79\) | −10.1724 | + | 7.39067i | −1.14448 | + | 0.831515i | −0.987737 | − | 0.156124i | \(-0.950100\pi\) |
−0.156745 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(80\) | −0.928246 | − | 2.85685i | −0.103781 | − | 0.319405i | ||||
\(81\) | −0.263364 | + | 0.810550i | −0.0292626 | + | 0.0900611i | ||||
\(82\) | −8.09098 | − | 5.87844i | −0.893500 | − | 0.649166i | ||||
\(83\) | −9.60819 | − | 6.98076i | −1.05464 | − | 0.766238i | −0.0815475 | − | 0.996669i | \(-0.525986\pi\) |
−0.973089 | + | 0.230432i | \(0.925986\pi\) | |||||||
\(84\) | −0.492521 | + | 1.51582i | −0.0537384 | + | 0.165390i | ||||
\(85\) | 2.22515 | + | 6.84831i | 0.241352 | + | 0.742804i | ||||
\(86\) | −4.96080 | + | 3.60423i | −0.534936 | + | 0.388654i | ||||
\(87\) | 2.62894 | 0.281852 | ||||||||
\(88\) | −3.27547 | + | 0.520843i | −0.349167 | + | 0.0555221i | ||||
\(89\) | 7.28452 | 0.772158 | 0.386079 | − | 0.922466i | \(-0.373829\pi\) | ||||
0.386079 | + | 0.922466i | \(0.373829\pi\) | |||||||
\(90\) | −4.19097 | + | 3.04492i | −0.441767 | + | 0.320963i | ||||
\(91\) | −0.380379 | − | 1.17069i | −0.0398745 | − | 0.122721i | ||||
\(92\) | −0.309017 | + | 0.951057i | −0.0322172 | + | 0.0991545i | ||||
\(93\) | −8.49598 | − | 6.17269i | −0.880992 | − | 0.640078i | ||||
\(94\) | −2.06340 | − | 1.49915i | −0.212824 | − | 0.154625i | ||||
\(95\) | 0.713471 | − | 2.19584i | 0.0732006 | − | 0.225288i | ||||
\(96\) | −0.348991 | − | 1.07408i | −0.0356187 | − | 0.109623i | ||||
\(97\) | 2.90613 | − | 2.11143i | 0.295073 | − | 0.214383i | −0.430392 | − | 0.902642i | \(-0.641625\pi\) |
0.725465 | + | 0.688259i | \(0.241625\pi\) | |||||||
\(98\) | −5.00831 | −0.505916 | ||||||||
\(99\) | 2.59981 | + | 5.09469i | 0.261291 | + | 0.512036i | ||||
\(100\) | 4.02322 | 0.402322 | ||||||||
\(101\) | −15.2215 | + | 11.0591i | −1.51459 | + | 1.10042i | −0.550508 | + | 0.834830i | \(0.685566\pi\) |
−0.964087 | + | 0.265587i | \(0.914434\pi\) | |||||||
\(102\) | 0.836585 | + | 2.57474i | 0.0828343 | + | 0.254938i | ||||
\(103\) | −2.09133 | + | 6.43644i | −0.206065 | + | 0.634201i | 0.793603 | + | 0.608435i | \(0.208202\pi\) |
−0.999668 | + | 0.0257661i | \(0.991798\pi\) | |||||||
\(104\) | 0.705636 | + | 0.512675i | 0.0691933 | + | 0.0502719i | ||||
\(105\) | −3.87329 | − | 2.81411i | −0.377995 | − | 0.274629i | ||||
\(106\) | −3.66761 | + | 11.2877i | −0.356230 | + | 1.09636i | ||||
\(107\) | −5.11821 | − | 15.7522i | −0.494796 | − | 1.52282i | −0.817275 | − | 0.576248i | \(-0.804516\pi\) |
0.322479 | − | 0.946577i | \(-0.395484\pi\) | |||||||
\(108\) | −4.31668 | + | 3.13625i | −0.415373 | + | 0.301786i | ||||
\(109\) | −0.214079 | −0.0205050 | −0.0102525 | − | 0.999947i | \(-0.503264\pi\) | ||||
−0.0102525 | + | 0.999947i | \(0.503264\pi\) | |||||||
\(110\) | 1.55247 | − | 9.84100i | 0.148023 | − | 0.938302i | ||||
\(111\) | −3.19265 | −0.303033 | ||||||||
\(112\) | −1.14174 | + | 0.829525i | −0.107885 | + | 0.0783828i | ||||
\(113\) | 2.27533 | + | 7.00274i | 0.214045 | + | 0.658762i | 0.999220 | + | 0.0394886i | \(0.0125729\pi\) |
−0.785175 | + | 0.619274i | \(0.787427\pi\) | |||||||
\(114\) | 0.268242 | − | 0.825564i | 0.0251232 | − | 0.0773212i | ||||
\(115\) | −2.43018 | − | 1.76563i | −0.226615 | − | 0.164646i | ||||
\(116\) | 1.88325 | + | 1.36826i | 0.174855 | + | 0.127040i | ||||
\(117\) | 0.464817 | − | 1.43056i | 0.0429723 | − | 0.132255i | ||||
\(118\) | 1.83699 | + | 5.65368i | 0.169109 | + | 0.520464i | ||||
\(119\) | 2.73694 | − | 1.98850i | 0.250895 | − | 0.182286i | ||||
\(120\) | 3.39244 | 0.309686 | ||||||||
\(121\) | −10.4658 | − | 3.38635i | −0.951435 | − | 0.307850i | ||||
\(122\) | 7.78124 | 0.704480 | ||||||||
\(123\) | 9.13761 | − | 6.63886i | 0.823911 | − | 0.598606i | ||||
\(124\) | −2.87347 | − | 8.84364i | −0.258045 | − | 0.794182i | ||||
\(125\) | 0.906696 | − | 2.79052i | 0.0810974 | − | 0.249592i | ||||
\(126\) | 1.96900 | + | 1.43056i | 0.175412 | + | 0.127444i | ||||
\(127\) | −6.16987 | − | 4.48267i | −0.547487 | − | 0.397773i | 0.279371 | − | 0.960183i | \(-0.409874\pi\) |
−0.826858 | + | 0.562410i | \(0.809874\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | −2.13997 | − | 6.58615i | −0.188414 | − | 0.579878i | ||||
\(130\) | −2.11964 | + | 1.54001i | −0.185904 | + | 0.135068i | ||||
\(131\) | −10.9427 | −0.956067 | −0.478033 | − | 0.878342i | \(-0.658650\pi\) | ||||
−0.478033 | + | 0.878342i | \(0.658650\pi\) | |||||||
\(132\) | 0.583680 | − | 3.69990i | 0.0508029 | − | 0.322035i | ||||
\(133\) | −1.08474 | −0.0940586 | ||||||||
\(134\) | 10.8847 | − | 7.90823i | 0.940298 | − | 0.683167i | ||||
\(135\) | −4.95285 | − | 15.2433i | −0.426273 | − | 1.31193i | ||||
\(136\) | −0.740762 | + | 2.27983i | −0.0635198 | + | 0.195494i | ||||
\(137\) | −16.7529 | − | 12.1717i | −1.43130 | − | 1.03990i | −0.989773 | − | 0.142651i | \(-0.954437\pi\) |
−0.441526 | − | 0.897248i | \(-0.645563\pi\) | |||||||
\(138\) | −0.913669 | − | 0.663820i | −0.0777767 | − | 0.0565081i | ||||
\(139\) | −1.07643 | + | 3.31293i | −0.0913020 | + | 0.280999i | −0.986272 | − | 0.165127i | \(-0.947197\pi\) |
0.894970 | + | 0.446126i | \(0.147197\pi\) | |||||||
\(140\) | −1.31001 | − | 4.03179i | −0.110716 | − | 0.340748i | ||||
\(141\) | 2.33032 | − | 1.69307i | 0.196248 | − | 0.142583i | ||||
\(142\) | −0.301890 | −0.0253341 | ||||||||
\(143\) | 1.31489 | + | 2.57670i | 0.109956 | + | 0.215475i | ||||
\(144\) | −1.72455 | −0.143713 | ||||||||
\(145\) | −5.65702 | + | 4.11007i | −0.469790 | + | 0.341322i | ||||
\(146\) | −1.53573 | − | 4.72648i | −0.127098 | − | 0.391166i | ||||
\(147\) | 1.74785 | − | 5.37934i | 0.144160 | − | 0.443680i | ||||
\(148\) | −2.28706 | − | 1.66165i | −0.187995 | − | 0.136586i | ||||
\(149\) | −0.189431 | − | 0.137630i | −0.0155188 | − | 0.0112751i | 0.579999 | − | 0.814617i | \(-0.303053\pi\) |
−0.595518 | + | 0.803342i | \(0.703053\pi\) | |||||||
\(150\) | −1.40406 | + | 4.32127i | −0.114641 | + | 0.352830i | ||||
\(151\) | 0.721536 | + | 2.22066i | 0.0587178 | + | 0.180715i | 0.976113 | − | 0.217262i | \(-0.0697125\pi\) |
−0.917396 | + | 0.397977i | \(0.869713\pi\) | |||||||
\(152\) | 0.621829 | − | 0.451785i | 0.0504370 | − | 0.0366446i | ||||
\(153\) | 4.13402 | 0.334216 | ||||||||
\(154\) | −4.62258 | + | 0.735052i | −0.372498 | + | 0.0592322i | ||||
\(155\) | 27.9322 | 2.24357 | ||||||||
\(156\) | −0.796915 | + | 0.578993i | −0.0638043 | + | 0.0463565i | ||||
\(157\) | 0.577593 | + | 1.77765i | 0.0460970 | + | 0.141872i | 0.971456 | − | 0.237220i | \(-0.0762363\pi\) |
−0.925359 | + | 0.379092i | \(0.876236\pi\) | |||||||
\(158\) | 3.88551 | − | 11.9584i | 0.309114 | − | 0.951356i | ||||
\(159\) | −10.8440 | − | 7.87863i | −0.859985 | − | 0.624816i | ||||
\(160\) | 2.43018 | + | 1.76563i | 0.192123 | + | 0.139585i | ||||
\(161\) | −0.436107 | + | 1.34220i | −0.0343701 | + | 0.105780i | ||||
\(162\) | −0.263364 | − | 0.810550i | −0.0206918 | − | 0.0636828i | ||||
\(163\) | −0.166490 | + | 0.120962i | −0.0130405 | + | 0.00947450i | −0.594286 | − | 0.804253i | \(-0.702565\pi\) |
0.581246 | + | 0.813728i | \(0.302565\pi\) | |||||||
\(164\) | 10.0010 | 0.780947 | ||||||||
\(165\) | 10.0282 | + | 5.10190i | 0.780698 | + | 0.397182i | ||||
\(166\) | 11.8764 | 0.921786 | ||||||||
\(167\) | −3.58189 | + | 2.60240i | −0.277175 | + | 0.201379i | −0.717684 | − | 0.696369i | \(-0.754798\pi\) |
0.440509 | + | 0.897748i | \(0.354798\pi\) | |||||||
\(168\) | −0.492521 | − | 1.51582i | −0.0379988 | − | 0.116948i | ||||
\(169\) | −3.78213 | + | 11.6402i | −0.290933 | + | 0.895401i | ||||
\(170\) | −5.82552 | − | 4.23249i | −0.446797 | − | 0.324617i | ||||
\(171\) | −1.07238 | − | 0.779127i | −0.0820067 | − | 0.0595813i | ||||
\(172\) | 1.89486 | − | 5.83177i | 0.144481 | − | 0.444668i | ||||
\(173\) | 3.57710 | + | 11.0092i | 0.271962 | + | 0.837013i | 0.990007 | + | 0.141017i | \(0.0450371\pi\) |
−0.718045 | + | 0.695996i | \(0.754963\pi\) | |||||||
\(174\) | −2.12686 | + | 1.54525i | −0.161237 | + | 0.117145i | ||||
\(175\) | 5.67785 | 0.429205 | ||||||||
\(176\) | 2.34377 | − | 2.34665i | 0.176668 | − | 0.176885i | ||||
\(177\) | −6.71361 | −0.504626 | ||||||||
\(178\) | −5.89330 | + | 4.28173i | −0.441722 | + | 0.320929i | ||||
\(179\) | 7.46462 | + | 22.9737i | 0.557932 | + | 1.71714i | 0.688072 | + | 0.725642i | \(0.258457\pi\) |
−0.130140 | + | 0.991496i | \(0.541543\pi\) | |||||||
\(180\) | 1.60081 | − | 4.92678i | 0.119317 | − | 0.367221i | ||||
\(181\) | −8.97707 | − | 6.52222i | −0.667260 | − | 0.484793i | 0.201847 | − | 0.979417i | \(-0.435306\pi\) |
−0.869107 | + | 0.494624i | \(0.835306\pi\) | |||||||
\(182\) | 0.995845 | + | 0.723524i | 0.0738169 | + | 0.0536311i | ||||
\(183\) | −2.71558 | + | 8.35769i | −0.200741 | + | 0.617818i | ||||
\(184\) | −0.309017 | − | 0.951057i | −0.0227810 | − | 0.0701128i | ||||
\(185\) | 6.87002 | − | 4.99136i | 0.505094 | − | 0.366972i | ||||
\(186\) | 10.5016 | 0.770015 | ||||||||
\(187\) | −5.61838 | + | 5.62528i | −0.410857 | + | 0.411361i | ||||
\(188\) | 2.55050 | 0.186015 | ||||||||
\(189\) | −6.09201 | + | 4.42610i | −0.443128 | + | 0.321952i | ||||
\(190\) | 0.713471 | + | 2.19584i | 0.0517606 | + | 0.159303i | ||||
\(191\) | −1.46123 | + | 4.49722i | −0.105731 | + | 0.325407i | −0.989901 | − | 0.141758i | \(-0.954725\pi\) |
0.884170 | + | 0.467165i | \(0.154725\pi\) | |||||||
\(192\) | 0.913669 | + | 0.663820i | 0.0659384 | + | 0.0479070i | ||||
\(193\) | −7.10387 | − | 5.16127i | −0.511348 | − | 0.371516i | 0.301987 | − | 0.953312i | \(-0.402350\pi\) |
−0.813335 | + | 0.581796i | \(0.802350\pi\) | |||||||
\(194\) | −1.11004 | + | 3.41636i | −0.0796965 | + | 0.245281i | ||||
\(195\) | −0.914361 | − | 2.81411i | −0.0654787 | − | 0.201523i | ||||
\(196\) | 4.05181 | − | 2.94381i | 0.289415 | − | 0.210272i | ||||
\(197\) | 0.205305 | 0.0146274 | 0.00731369 | − | 0.999973i | \(-0.497672\pi\) | ||||
0.00731369 | + | 0.999973i | \(0.497672\pi\) | |||||||
\(198\) | −5.09788 | − | 2.59356i | −0.362290 | − | 0.184316i | ||||
\(199\) | 16.3140 | 1.15647 | 0.578235 | − | 0.815871i | \(-0.303742\pi\) | ||||
0.578235 | + | 0.815871i | \(0.303742\pi\) | |||||||
\(200\) | −3.25485 | + | 2.36479i | −0.230153 | + | 0.167216i | ||||
\(201\) | 4.69542 | + | 14.4510i | 0.331189 | + | 1.01930i | ||||
\(202\) | 5.81409 | − | 17.8939i | 0.409078 | − | 1.25901i | ||||
\(203\) | 2.65777 | + | 1.93099i | 0.186539 | + | 0.135529i | ||||
\(204\) | −2.19021 | − | 1.59128i | −0.153345 | − | 0.111412i | ||||
\(205\) | −9.28339 | + | 28.5713i | −0.648380 | + | 1.99551i | ||||
\(206\) | −2.09133 | − | 6.43644i | −0.145710 | − | 0.448448i | ||||
\(207\) | −1.39519 | + | 1.01367i | −0.0969726 | + | 0.0704547i | ||||
\(208\) | −0.872214 | −0.0604772 | ||||||||
\(209\) | 2.51760 | − | 0.400332i | 0.174146 | − | 0.0276916i | ||||
\(210\) | 4.78766 | 0.330380 | ||||||||
\(211\) | −1.75748 | + | 1.27688i | −0.120990 | + | 0.0879043i | −0.646635 | − | 0.762800i | \(-0.723824\pi\) |
0.525645 | + | 0.850704i | \(0.323824\pi\) | |||||||
\(212\) | −3.66761 | − | 11.2877i | −0.251892 | − | 0.775245i | ||||
\(213\) | 0.105357 | − | 0.324255i | 0.00721894 | − | 0.0222176i | ||||
\(214\) | 13.3996 | + | 9.73541i | 0.915981 | + | 0.665499i | ||||
\(215\) | 14.9016 | + | 10.8266i | 1.01628 | + | 0.738370i | ||||
\(216\) | 1.64882 | − | 5.07456i | 0.112188 | − | 0.345280i | ||||
\(217\) | −4.05525 | − | 12.4808i | −0.275288 | − | 0.847251i | ||||
\(218\) | 0.173193 | − | 0.125832i | 0.0117301 | − | 0.00852244i | ||||
\(219\) | 5.61258 | 0.379263 | ||||||||
\(220\) | 4.52841 | + | 8.87405i | 0.305306 | + | 0.598289i | ||||
\(221\) | 2.09083 | 0.140645 | ||||||||
\(222\) | 2.58291 | − | 1.87659i | 0.173353 | − | 0.125949i | ||||
\(223\) | 1.35482 | + | 4.16970i | 0.0907252 | + | 0.279224i | 0.986116 | − | 0.166058i | \(-0.0531037\pi\) |
−0.895391 | + | 0.445281i | \(0.853104\pi\) | |||||||
\(224\) | 0.436107 | − | 1.34220i | 0.0291386 | − | 0.0896795i | ||||
\(225\) | 5.61316 | + | 4.07820i | 0.374211 | + | 0.271880i | ||||
\(226\) | −5.95689 | − | 4.32793i | −0.396246 | − | 0.287890i | ||||
\(227\) | 8.57530 | − | 26.3921i | 0.569163 | − | 1.75170i | −0.0860840 | − | 0.996288i | \(-0.527435\pi\) |
0.655247 | − | 0.755415i | \(-0.272565\pi\) | |||||||
\(228\) | 0.268242 | + | 0.825564i | 0.0177648 | + | 0.0546743i | ||||
\(229\) | −17.7182 | + | 12.8730i | −1.17085 | + | 0.850671i | −0.991110 | − | 0.133043i | \(-0.957525\pi\) |
−0.179738 | + | 0.983714i | \(0.557525\pi\) | |||||||
\(230\) | 3.00387 | 0.198069 | ||||||||
\(231\) | 0.823732 | − | 5.22156i | 0.0541976 | − | 0.343554i | ||||
\(232\) | −2.32782 | −0.152829 | ||||||||
\(233\) | −10.0523 | + | 7.30344i | −0.658550 | + | 0.478464i | −0.866173 | − | 0.499745i | \(-0.833427\pi\) |
0.207623 | + | 0.978209i | \(0.433427\pi\) | |||||||
\(234\) | 0.464817 | + | 1.43056i | 0.0303860 | + | 0.0935186i | ||||
\(235\) | −2.36749 | + | 7.28640i | −0.154438 | + | 0.475312i | ||||
\(236\) | −4.80931 | − | 3.49417i | −0.313059 | − | 0.227451i | ||||
\(237\) | 11.4883 | + | 8.34671i | 0.746242 | + | 0.542177i | ||||
\(238\) | −1.04542 | + | 3.21746i | −0.0677644 | + | 0.208557i | ||||
\(239\) | 1.69777 | + | 5.22519i | 0.109819 | + | 0.337990i | 0.990831 | − | 0.135105i | \(-0.0431370\pi\) |
−0.881012 | + | 0.473094i | \(0.843137\pi\) | |||||||
\(240\) | −2.74454 | + | 1.99403i | −0.177159 | + | 0.128714i | ||||
\(241\) | −10.0588 | −0.647946 | −0.323973 | − | 0.946066i | \(-0.605019\pi\) | ||||
−0.323973 | + | 0.946066i | \(0.605019\pi\) | |||||||
\(242\) | 10.4574 | − | 3.41202i | 0.672230 | − | 0.219333i | ||||
\(243\) | −15.0446 | −0.965112 | ||||||||
\(244\) | −6.29515 | + | 4.57370i | −0.403006 | + | 0.292801i | ||||
\(245\) | 4.64894 | + | 14.3080i | 0.297010 | + | 0.914103i | ||||
\(246\) | −3.49026 | + | 10.7419i | −0.222531 | + | 0.684879i | ||||
\(247\) | −0.542368 | − | 0.394054i | −0.0345101 | − | 0.0250730i | ||||
\(248\) | 7.52285 | + | 5.46567i | 0.477701 | + | 0.347070i | ||||
\(249\) | −4.14474 | + | 12.7562i | −0.262662 | + | 0.808392i | ||||
\(250\) | 0.906696 | + | 2.79052i | 0.0573445 | + | 0.176488i | ||||
\(251\) | 1.46478 | − | 1.06422i | 0.0924561 | − | 0.0671733i | −0.540597 | − | 0.841282i | \(-0.681802\pi\) |
0.633053 | + | 0.774109i | \(0.281802\pi\) | |||||||
\(252\) | −2.43381 | −0.153316 | ||||||||
\(253\) | 0.516825 | − | 3.27611i | 0.0324925 | − | 0.205967i | ||||
\(254\) | 7.62638 | 0.478521 | ||||||||
\(255\) | 6.57910 | − | 4.77999i | 0.411999 | − | 0.299335i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 4.34144 | − | 13.3616i | 0.270812 | − | 0.833472i | −0.719486 | − | 0.694507i | \(-0.755622\pi\) |
0.990297 | − | 0.138965i | \(-0.0443776\pi\) | |||||||
\(258\) | 5.60251 | + | 4.07046i | 0.348797 | + | 0.253416i | ||||
\(259\) | −3.22766 | − | 2.34504i | −0.200557 | − | 0.145713i | ||||
\(260\) | 0.809629 | − | 2.49178i | 0.0502111 | − | 0.154534i | ||||
\(261\) | 1.24053 | + | 3.81797i | 0.0767870 | + | 0.236326i | ||||
\(262\) | 8.85282 | − | 6.43195i | 0.546929 | − | 0.397367i | ||||
\(263\) | 3.63063 | 0.223874 | 0.111937 | − | 0.993715i | \(-0.464294\pi\) | ||||
0.111937 | + | 0.993715i | \(0.464294\pi\) | |||||||
\(264\) | 1.70254 | + | 3.33636i | 0.104784 | + | 0.205339i | ||||
\(265\) | 35.6518 | 2.19007 | ||||||||
\(266\) | 0.877570 | − | 0.637592i | 0.0538073 | − | 0.0390933i | ||||
\(267\) | −2.54223 | − | 7.82418i | −0.155582 | − | 0.478832i | ||||
\(268\) | −4.15760 | + | 12.7958i | −0.253966 | + | 0.781627i | ||||
\(269\) | −10.0205 | − | 7.28035i | −0.610963 | − | 0.443891i | 0.238790 | − | 0.971071i | \(-0.423249\pi\) |
−0.849753 | + | 0.527181i | \(0.823249\pi\) | |||||||
\(270\) | 12.9667 | + | 9.42088i | 0.789130 | + | 0.573336i | ||||
\(271\) | −2.63957 | + | 8.12375i | −0.160342 | + | 0.493483i | −0.998663 | − | 0.0516948i | \(-0.983538\pi\) |
0.838321 | + | 0.545177i | \(0.183538\pi\) | |||||||
\(272\) | −0.740762 | − | 2.27983i | −0.0449153 | − | 0.138235i | ||||
\(273\) | −1.12466 | + | 0.817117i | −0.0680678 | + | 0.0494542i | ||||
\(274\) | 20.7078 | 1.25100 | ||||||||
\(275\) | −13.1779 | + | 2.09547i | −0.794659 | + | 0.126361i | ||||
\(276\) | 1.12936 | 0.0679793 | ||||||||
\(277\) | −6.82700 | + | 4.96010i | −0.410194 | + | 0.298024i | −0.773681 | − | 0.633576i | \(-0.781586\pi\) |
0.363486 | + | 0.931600i | \(0.381586\pi\) | |||||||
\(278\) | −1.07643 | − | 3.31293i | −0.0645603 | − | 0.198696i | ||||
\(279\) | 4.95545 | − | 15.2513i | 0.296675 | − | 0.913072i | ||||
\(280\) | 3.42965 | + | 2.49178i | 0.204961 | + | 0.148913i | ||||
\(281\) | 18.9199 | + | 13.7461i | 1.12867 | + | 0.820025i | 0.985500 | − | 0.169673i | \(-0.0542712\pi\) |
0.143168 | + | 0.989698i | \(0.454271\pi\) | |||||||
\(282\) | −0.890102 | + | 2.73945i | −0.0530048 | + | 0.163132i | ||||
\(283\) | −3.47848 | − | 10.7057i | −0.206774 | − | 0.636385i | −0.999636 | − | 0.0269836i | \(-0.991410\pi\) |
0.792862 | − | 0.609401i | \(-0.208590\pi\) | |||||||
\(284\) | 0.244235 | − | 0.177447i | 0.0144927 | − | 0.0105295i | ||||
\(285\) | −2.60751 | −0.154455 | ||||||||
\(286\) | −2.57832 | − | 1.31173i | −0.152459 | − | 0.0775640i | ||||
\(287\) | 14.1141 | 0.833132 | ||||||||
\(288\) | 1.39519 | − | 1.01367i | 0.0822125 | − | 0.0597309i | ||||
\(289\) | −3.47757 | − | 10.7028i | −0.204563 | − | 0.629579i | ||||
\(290\) | 2.16079 | − | 6.65023i | 0.126886 | − | 0.390515i | ||||
\(291\) | −3.28206 | − | 2.38456i | −0.192398 | − | 0.139785i | ||||
\(292\) | 4.02058 | + | 2.92112i | 0.235287 | + | 0.170946i | ||||
\(293\) | 5.51320 | − | 16.9679i | 0.322085 | − | 0.991275i | −0.650654 | − | 0.759374i | \(-0.725505\pi\) |
0.972739 | − | 0.231901i | \(-0.0744946\pi\) | |||||||
\(294\) | 1.74785 | + | 5.37934i | 0.101937 | + | 0.313729i | ||||
\(295\) | 14.4465 | − | 10.4960i | 0.841109 | − | 0.611102i | ||||
\(296\) | 2.82696 | 0.164314 | ||||||||
\(297\) | 12.5057 | − | 12.5210i | 0.725652 | − | 0.726543i | ||||
\(298\) | 0.234149 | 0.0135639 | ||||||||
\(299\) | −0.705636 | + | 0.512675i | −0.0408080 | + | 0.0296487i | ||||
\(300\) | −1.40406 | − | 4.32127i | −0.0810637 | − | 0.249488i | ||||
\(301\) | 2.67416 | − | 8.23021i | 0.154136 | − | 0.474381i | ||||
\(302\) | −1.88901 | − | 1.37244i | −0.108700 | − | 0.0789752i | ||||
\(303\) | 17.1905 | + | 12.4896i | 0.987568 | + | 0.717510i | ||||
\(304\) | −0.237518 | + | 0.731004i | −0.0136226 | + | 0.0419259i | ||||
\(305\) | −7.22290 | − | 22.2298i | −0.413582 | − | 1.27287i | ||||
\(306\) | −3.34449 | + | 2.42992i | −0.191192 | + | 0.138909i | ||||
\(307\) | 19.7390 | 1.12657 | 0.563283 | − | 0.826264i | \(-0.309538\pi\) | ||||
0.563283 | + | 0.826264i | \(0.309538\pi\) | |||||||
\(308\) | 3.30770 | − | 3.31176i | 0.188474 | − | 0.188705i | ||||
\(309\) | 7.64312 | 0.434802 | ||||||||
\(310\) | −22.5976 | + | 16.4181i | −1.28346 | + | 0.932488i | ||||
\(311\) | 3.01540 | + | 9.28044i | 0.170987 | + | 0.526245i | 0.999428 | − | 0.0338324i | \(-0.0107713\pi\) |
−0.828440 | + | 0.560078i | \(0.810771\pi\) | |||||||
\(312\) | 0.304395 | − | 0.936830i | 0.0172330 | − | 0.0530376i | ||||
\(313\) | 3.10134 | + | 2.25325i | 0.175298 | + | 0.127361i | 0.671974 | − | 0.740574i | \(-0.265446\pi\) |
−0.496677 | + | 0.867936i | \(0.665446\pi\) | |||||||
\(314\) | −1.51216 | − | 1.09865i | −0.0853361 | − | 0.0620003i | ||||
\(315\) | 2.25918 | − | 6.95303i | 0.127290 | − | 0.391759i | ||||
\(316\) | 3.88551 | + | 11.9584i | 0.218577 | + | 0.672710i | ||||
\(317\) | −3.51695 | + | 2.55522i | −0.197532 | + | 0.143515i | −0.682155 | − | 0.731208i | \(-0.738957\pi\) |
0.484623 | + | 0.874723i | \(0.338957\pi\) | |||||||
\(318\) | 13.4039 | 0.751655 | ||||||||
\(319\) | −6.88117 | − | 3.50082i | −0.385272 | − | 0.196008i | ||||
\(320\) | −3.00387 | −0.167921 | ||||||||
\(321\) | −15.1330 | + | 10.9948i | −0.844641 | + | 0.613667i | ||||
\(322\) | −0.436107 | − | 1.34220i | −0.0243033 | − | 0.0747979i | ||||
\(323\) | 0.569367 | − | 1.75233i | 0.0316804 | − | 0.0975023i | ||||
\(324\) | 0.689495 | + | 0.500948i | 0.0383053 | + | 0.0278304i | ||||
\(325\) | 2.83893 | + | 2.06260i | 0.157475 | + | 0.114413i | ||||
\(326\) | 0.0635937 | − | 0.195721i | 0.00352213 | − | 0.0108400i | ||||
\(327\) | 0.0747115 | + | 0.229938i | 0.00413155 | + | 0.0127156i | ||||
\(328\) | −8.09098 | + | 5.87844i | −0.446750 | + | 0.324583i | ||||
\(329\) | 3.59946 | 0.198444 | ||||||||
\(330\) | −11.1118 | + | 1.76693i | −0.611687 | + | 0.0972662i | ||||
\(331\) | −30.0198 | −1.65004 | −0.825019 | − | 0.565104i | \(-0.808836\pi\) | ||||
−0.825019 | + | 0.565104i | \(0.808836\pi\) | |||||||
\(332\) | −9.60819 | + | 6.98076i | −0.527318 | + | 0.383119i | ||||
\(333\) | −1.50653 | − | 4.63663i | −0.0825575 | − | 0.254086i | ||||
\(334\) | 1.36816 | − | 4.21076i | 0.0748624 | − | 0.230403i | ||||
\(335\) | −32.6963 | − | 23.7553i | −1.78639 | − | 1.29789i | ||||
\(336\) | 1.28944 | + | 0.936830i | 0.0703445 | + | 0.0511083i | ||||
\(337\) | 9.63992 | − | 29.6686i | 0.525120 | − | 1.61615i | −0.238959 | − | 0.971030i | \(-0.576806\pi\) |
0.764079 | − | 0.645123i | \(-0.223194\pi\) | |||||||
\(338\) | −3.78213 | − | 11.6402i | −0.205721 | − | 0.633144i | ||||
\(339\) | 6.72745 | − | 4.88778i | 0.365385 | − | 0.265468i | ||||
\(340\) | 7.20074 | 0.390515 | ||||||||
\(341\) | 14.0181 | + | 27.4705i | 0.759124 | + | 1.48761i | ||||
\(342\) | 1.32553 | 0.0716765 | ||||||||
\(343\) | 13.7104 | − | 9.96120i | 0.740293 | − | 0.537854i | ||||
\(344\) | 1.89486 | + | 5.83177i | 0.102164 | + | 0.314428i | ||||
\(345\) | −1.04832 | + | 3.22640i | −0.0564397 | + | 0.173704i | ||||
\(346\) | −9.36497 | − | 6.80405i | −0.503464 | − | 0.365788i | ||||
\(347\) | 10.2279 | + | 7.43101i | 0.549063 | + | 0.398918i | 0.827440 | − | 0.561554i | \(-0.189796\pi\) |
−0.278377 | + | 0.960472i | \(0.589796\pi\) | |||||||
\(348\) | 0.812387 | − | 2.50027i | 0.0435485 | − | 0.134029i | ||||
\(349\) | −1.28116 | − | 3.94302i | −0.0685792 | − | 0.211065i | 0.910894 | − | 0.412641i | \(-0.135394\pi\) |
−0.979473 | + | 0.201576i | \(0.935394\pi\) | |||||||
\(350\) | −4.59348 | + | 3.33736i | −0.245532 | + | 0.178389i | ||||
\(351\) | −4.65388 | −0.248406 | ||||||||
\(352\) | −0.516825 | + | 3.27611i | −0.0275469 | + | 0.174617i | ||||
\(353\) | −10.9557 | −0.583114 | −0.291557 | − | 0.956554i | \(-0.594173\pi\) | ||||
−0.291557 | + | 0.956554i | \(0.594173\pi\) | |||||||
\(354\) | 5.43143 | − | 3.94616i | 0.288677 | − | 0.209736i | ||||
\(355\) | 0.280229 | + | 0.862455i | 0.0148730 | + | 0.0457744i | ||||
\(356\) | 2.25104 | − | 6.92799i | 0.119305 | − | 0.367183i | ||||
\(357\) | −3.09098 | − | 2.24573i | −0.163592 | − | 0.118857i | ||||
\(358\) | −19.5426 | − | 14.1986i | −1.03286 | − | 0.750417i | ||||
\(359\) | −6.29437 | + | 19.3721i | −0.332204 | + | 1.02242i | 0.635879 | + | 0.771789i | \(0.280638\pi\) |
−0.968083 | + | 0.250630i | \(0.919362\pi\) | |||||||
\(360\) | 1.60081 | + | 4.92678i | 0.0843700 | + | 0.259664i | ||||
\(361\) | 14.8934 | − | 10.8207i | 0.783862 | − | 0.569509i | ||||
\(362\) | 11.0963 | 0.583207 | ||||||||
\(363\) | 0.0152379 | + | 12.4229i | 0.000799781 | + | 0.652034i | ||||
\(364\) | −1.23093 | −0.0645184 | ||||||||
\(365\) | −12.0773 | + | 8.77467i | −0.632154 | + | 0.459287i | ||||
\(366\) | −2.71558 | − | 8.35769i | −0.141946 | − | 0.436864i | ||||
\(367\) | −2.06048 | + | 6.34150i | −0.107556 | + | 0.331024i | −0.990322 | − | 0.138790i | \(-0.955679\pi\) |
0.882766 | + | 0.469813i | \(0.155679\pi\) | |||||||
\(368\) | 0.809017 | + | 0.587785i | 0.0421729 | + | 0.0306404i | ||||
\(369\) | 13.9533 | + | 10.1377i | 0.726381 | + | 0.527747i | ||||
\(370\) | −2.62412 | + | 8.07620i | −0.136421 | + | 0.419862i | ||||
\(371\) | −5.17600 | − | 15.9301i | −0.268724 | − | 0.827048i | ||||
\(372\) | −8.49598 | + | 6.17269i | −0.440496 | + | 0.320039i | ||||
\(373\) | −1.72565 | −0.0893508 | −0.0446754 | − | 0.999002i | \(-0.514225\pi\) | ||||
−0.0446754 | + | 0.999002i | \(0.514225\pi\) | |||||||
\(374\) | 1.23891 | − | 7.85335i | 0.0640626 | − | 0.406087i | ||||
\(375\) | −3.31368 | −0.171118 | ||||||||
\(376\) | −2.06340 | + | 1.49915i | −0.106412 | + | 0.0773127i | ||||
\(377\) | 0.627415 | + | 1.93099i | 0.0323135 | + | 0.0994508i | ||||
\(378\) | 2.32694 | − | 7.16159i | 0.119685 | − | 0.368352i | ||||
\(379\) | −8.95379 | − | 6.50531i | −0.459925 | − | 0.334155i | 0.333577 | − | 0.942723i | \(-0.391744\pi\) |
−0.793502 | + | 0.608568i | \(0.791744\pi\) | |||||||
\(380\) | −1.86789 | − | 1.35710i | −0.0958208 | − | 0.0696179i | ||||
\(381\) | −2.66153 | + | 8.19136i | −0.136355 | + | 0.419656i | ||||
\(382\) | −1.46123 | − | 4.49722i | −0.0747633 | − | 0.230098i | ||||
\(383\) | −12.2053 | + | 8.86770i | −0.623664 | + | 0.453118i | −0.854199 | − | 0.519946i | \(-0.825952\pi\) |
0.230536 | + | 0.973064i | \(0.425952\pi\) | |||||||
\(384\) | −1.12936 | −0.0576323 | ||||||||
\(385\) | 6.39083 | + | 12.5237i | 0.325707 | + | 0.638267i | ||||
\(386\) | 8.78087 | 0.446935 | ||||||||
\(387\) | 8.55515 | − | 6.21568i | 0.434883 | − | 0.315961i | ||||
\(388\) | −1.11004 | − | 3.41636i | −0.0563539 | − | 0.173440i | ||||
\(389\) | 0.883432 | − | 2.71892i | 0.0447918 | − | 0.137855i | −0.926160 | − | 0.377132i | \(-0.876910\pi\) |
0.970951 | + | 0.239277i | \(0.0769104\pi\) | |||||||
\(390\) | 2.39383 | + | 1.73922i | 0.121216 | + | 0.0880687i | ||||
\(391\) | −1.93934 | − | 1.40901i | −0.0980767 | − | 0.0712569i | ||||
\(392\) | −1.54765 | + | 4.76319i | −0.0781683 | + | 0.240577i | ||||
\(393\) | 3.81889 | + | 11.7533i | 0.192638 | + | 0.592878i | ||||
\(394\) | −0.166095 | + | 0.120675i | −0.00836776 | + | 0.00607954i | ||||
\(395\) | −37.7699 | −1.90041 | ||||||||
\(396\) | 5.64872 | − | 0.898222i | 0.283859 | − | 0.0451373i | ||||
\(397\) | −15.7519 | −0.790563 | −0.395281 | − | 0.918560i | \(-0.629353\pi\) | ||||
−0.395281 | + | 0.918560i | \(0.629353\pi\) | |||||||
\(398\) | −13.1983 | + | 9.58913i | −0.661571 | + | 0.480660i | ||||
\(399\) | 0.378563 | + | 1.16510i | 0.0189518 | + | 0.0583278i | ||||
\(400\) | 1.24324 | − | 3.82631i | 0.0621621 | − | 0.191315i | ||||
\(401\) | −28.6408 | − | 20.8088i | −1.43025 | − | 1.03914i | −0.989969 | − | 0.141283i | \(-0.954877\pi\) |
−0.440285 | − | 0.897858i | \(-0.645123\pi\) | |||||||
\(402\) | −12.2928 | − | 8.93121i | −0.613107 | − | 0.445448i | ||||
\(403\) | 2.50628 | − | 7.71355i | 0.124847 | − | 0.384239i | ||||
\(404\) | 5.81409 | + | 17.8939i | 0.289262 | + | 0.890256i | ||||
\(405\) | −2.07115 | + | 1.50478i | −0.102916 | + | 0.0747731i | ||||
\(406\) | −3.28519 | −0.163041 | ||||||||
\(407\) | 8.35666 | + | 4.25148i | 0.414224 | + | 0.210738i | ||||
\(408\) | 2.70725 | 0.134029 | ||||||||
\(409\) | 14.4812 | − | 10.5212i | 0.716048 | − | 0.520239i | −0.169071 | − | 0.985604i | \(-0.554077\pi\) |
0.885119 | + | 0.465365i | \(0.154077\pi\) | |||||||
\(410\) | −9.28339 | − | 28.5713i | −0.458474 | − | 1.41104i | ||||
\(411\) | −7.22681 | + | 22.2418i | −0.356472 | + | 1.09711i | ||||
\(412\) | 5.47516 | + | 3.97794i | 0.269742 | + | 0.195979i | ||||
\(413\) | −6.78725 | − | 4.93122i | −0.333979 | − | 0.242650i | ||||
\(414\) | 0.532916 | − | 1.64015i | 0.0261914 | − | 0.0806088i | ||||
\(415\) | −11.0242 | − | 33.9290i | −0.541157 | − | 1.66551i | ||||
\(416\) | 0.705636 | − | 0.512675i | 0.0345967 | − | 0.0251359i | ||||
\(417\) | 3.93402 | 0.192650 | ||||||||
\(418\) | −1.80147 | + | 1.80369i | −0.0881130 | + | 0.0882212i | ||||
\(419\) | −32.7237 | −1.59866 | −0.799329 | − | 0.600893i | \(-0.794812\pi\) | ||||
−0.799329 | + | 0.600893i | \(0.794812\pi\) | |||||||
\(420\) | −3.87329 | + | 2.81411i | −0.188997 | + | 0.137315i | ||||
\(421\) | 3.94668 | + | 12.1466i | 0.192349 | + | 0.591991i | 0.999997 | + | 0.00232562i | \(0.000740269\pi\) |
−0.807648 | + | 0.589665i | \(0.799260\pi\) | |||||||
\(422\) | 0.671298 | − | 2.06604i | 0.0326783 | − | 0.100573i | ||||
\(423\) | 3.55844 | + | 2.58536i | 0.173017 | + | 0.125704i | ||||
\(424\) | 9.60192 | + | 6.97621i | 0.466311 | + | 0.338795i | ||||
\(425\) | −2.98025 | + | 9.17226i | −0.144563 | + | 0.444920i | ||||
\(426\) | 0.105357 | + | 0.324255i | 0.00510456 | + | 0.0157102i | ||||
\(427\) | −8.88418 | + | 6.45473i | −0.429935 | + | 0.312366i | ||||
\(428\) | −16.5629 | −0.800596 | ||||||||
\(429\) | 2.30871 | − | 2.31154i | 0.111466 | − | 0.111602i | ||||
\(430\) | −18.4194 | −0.888260 | ||||||||
\(431\) | 21.0798 | − | 15.3154i | 1.01538 | − | 0.737715i | 0.0500469 | − | 0.998747i | \(-0.484063\pi\) |
0.965330 | + | 0.261032i | \(0.0840629\pi\) | |||||||
\(432\) | 1.64882 | + | 5.07456i | 0.0793291 | + | 0.244150i | ||||
\(433\) | 0.632113 | − | 1.94544i | 0.0303774 | − | 0.0934920i | −0.934718 | − | 0.355389i | \(-0.884348\pi\) |
0.965096 | + | 0.261897i | \(0.0843482\pi\) | |||||||
\(434\) | 10.6168 | + | 7.71355i | 0.509622 | + | 0.370262i | ||||
\(435\) | 6.38880 | + | 4.64173i | 0.306319 | + | 0.222554i | ||||
\(436\) | −0.0661540 | + | 0.203601i | −0.00316820 | + | 0.00975072i | ||||
\(437\) | 0.237518 | + | 0.731004i | 0.0113620 | + | 0.0349687i | ||||
\(438\) | −4.54067 | + | 3.29899i | −0.216962 | + | 0.157632i | ||||
\(439\) | 20.0406 | 0.956485 | 0.478243 | − | 0.878228i | \(-0.341274\pi\) | ||||
0.478243 | + | 0.878228i | \(0.341274\pi\) | |||||||
\(440\) | −8.87960 | − | 4.51753i | −0.423318 | − | 0.215365i | ||||
\(441\) | 8.63709 | 0.411290 | ||||||||
\(442\) | −1.69152 | + | 1.22896i | −0.0804575 | + | 0.0584558i | ||||
\(443\) | 8.80211 | + | 27.0901i | 0.418201 | + | 1.28709i | 0.909357 | + | 0.416018i | \(0.136575\pi\) |
−0.491156 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(444\) | −0.986583 | + | 3.03639i | −0.0468212 | + | 0.144101i | ||||
\(445\) | 17.7027 | + | 12.8618i | 0.839188 | + | 0.609706i | ||||
\(446\) | −3.54696 | − | 2.57701i | −0.167953 | − | 0.122025i | ||||
\(447\) | −0.0817159 | + | 0.251496i | −0.00386503 | + | 0.0118953i | ||||
\(448\) | 0.436107 | + | 1.34220i | 0.0206041 | + | 0.0634130i | ||||
\(449\) | 14.2179 | − | 10.3299i | 0.670984 | − | 0.487498i | −0.199370 | − | 0.979924i | \(-0.563890\pi\) |
0.870354 | + | 0.492426i | \(0.163890\pi\) | |||||||
\(450\) | −6.93825 | −0.327072 | ||||||||
\(451\) | −32.7580 | + | 5.20896i | −1.54252 | + | 0.245280i | ||||
\(452\) | 7.36312 | 0.346332 | ||||||||
\(453\) | 2.13336 | − | 1.54998i | 0.100234 | − | 0.0728243i | ||||
\(454\) | 8.57530 | + | 26.3921i | 0.402459 | + | 1.23864i | ||||
\(455\) | 1.14261 | − | 3.51658i | 0.0535663 | − | 0.164860i | ||||
\(456\) | −0.702267 | − | 0.510227i | −0.0328867 | − | 0.0238936i | ||||
\(457\) | −17.3242 | − | 12.5868i | −0.810391 | − | 0.588784i | 0.103553 | − | 0.994624i | \(-0.466979\pi\) |
−0.913944 | + | 0.405840i | \(0.866979\pi\) | |||||||
\(458\) | 6.76773 | − | 20.8289i | 0.316235 | − | 0.973272i | ||||
\(459\) | −3.95249 | − | 12.1645i | −0.184486 | − | 0.567791i | ||||
\(460\) | −2.43018 | + | 1.76563i | −0.113308 | + | 0.0823229i | ||||
\(461\) | 17.8109 | 0.829538 | 0.414769 | − | 0.909927i | \(-0.363862\pi\) | ||||
0.414769 | + | 0.909927i | \(0.363862\pi\) | |||||||
\(462\) | 2.40274 | + | 4.70851i | 0.111786 | + | 0.219060i | ||||
\(463\) | 10.6864 | 0.496639 | 0.248320 | − | 0.968678i | \(-0.420122\pi\) | ||||
0.248320 | + | 0.968678i | \(0.420122\pi\) | |||||||
\(464\) | 1.88325 | − | 1.36826i | 0.0874275 | − | 0.0635198i | ||||
\(465\) | −9.74808 | − | 30.0015i | −0.452056 | − | 1.39129i | ||||
\(466\) | 3.83965 | − | 11.8172i | 0.177868 | − | 0.547422i | ||||
\(467\) | −18.0177 | − | 13.0906i | −0.833759 | − | 0.605761i | 0.0868614 | − | 0.996220i | \(-0.472316\pi\) |
−0.920620 | + | 0.390459i | \(0.872316\pi\) | |||||||
\(468\) | −1.21691 | − | 0.884134i | −0.0562515 | − | 0.0408691i | ||||
\(469\) | −5.86751 | + | 18.0583i | −0.270936 | + | 0.833856i | ||||
\(470\) | −2.36749 | − | 7.28640i | −0.109204 | − | 0.336096i | ||||
\(471\) | 1.70777 | − | 1.24077i | 0.0786898 | − | 0.0571715i | ||||
\(472\) | 5.94463 | 0.273624 | ||||||||
\(473\) | −3.16911 | + | 20.0887i | −0.145716 | + | 0.923680i | ||||
\(474\) | −14.2003 | −0.652240 | ||||||||
\(475\) | 2.50175 | − | 1.81763i | 0.114788 | − | 0.0833986i | ||||
\(476\) | −1.04542 | − | 3.21746i | −0.0479166 | − | 0.147472i | ||||
\(477\) | 6.32498 | − | 19.4663i | 0.289601 | − | 0.891300i | ||||
\(478\) | −4.44481 | − | 3.22935i | −0.203301 | − | 0.147707i | ||||
\(479\) | −15.5731 | − | 11.3145i | −0.711555 | − | 0.516975i | 0.172120 | − | 0.985076i | \(-0.444938\pi\) |
−0.883675 | + | 0.468101i | \(0.844938\pi\) | |||||||
\(480\) | 1.04832 | − | 3.22640i | 0.0478491 | − | 0.147264i | ||||
\(481\) | −0.761948 | − | 2.34504i | −0.0347419 | − | 0.106924i | ||||
\(482\) | 8.13777 | − | 5.91243i | 0.370665 | − | 0.269304i | ||||
\(483\) | 1.59383 | 0.0725218 | ||||||||
\(484\) | −6.45472 | + | 8.90711i | −0.293396 | + | 0.404869i | ||||
\(485\) | 10.7904 | 0.489968 | ||||||||
\(486\) | 12.1713 | − | 8.84300i | 0.552104 | − | 0.401127i | ||||
\(487\) | −7.14423 | − | 21.9877i | −0.323736 | − | 0.996357i | −0.972008 | − | 0.234948i | \(-0.924508\pi\) |
0.648272 | − | 0.761409i | \(-0.275492\pi\) | |||||||
\(488\) | 2.40453 | − | 7.40040i | 0.108848 | − | 0.335000i | ||||
\(489\) | 0.188027 | + | 0.136610i | 0.00850288 | + | 0.00617770i | ||||
\(490\) | −12.1711 | − | 8.84282i | −0.549834 | − | 0.399478i | ||||
\(491\) | −6.23241 | + | 19.1814i | −0.281265 | + | 0.865643i | 0.706229 | + | 0.707984i | \(0.250395\pi\) |
−0.987493 | + | 0.157660i | \(0.949605\pi\) | |||||||
\(492\) | −3.49026 | − | 10.7419i | −0.157353 | − | 0.484283i | ||||
\(493\) | −4.51444 | + | 3.27993i | −0.203320 | + | 0.147721i | ||||
\(494\) | 0.670404 | 0.0301629 | ||||||||
\(495\) | −2.67732 | + | 16.9713i | −0.120337 | + | 0.762804i | ||||
\(496\) | −9.29875 | −0.417526 | ||||||||
\(497\) | 0.344681 | − | 0.250426i | 0.0154611 | − | 0.0112331i | ||||
\(498\) | −4.14474 | − | 12.7562i | −0.185730 | − | 0.571619i | ||||
\(499\) | 10.2945 | − | 31.6834i | 0.460847 | − | 1.41834i | −0.403284 | − | 0.915075i | \(-0.632131\pi\) |
0.864131 | − | 0.503267i | \(-0.167869\pi\) | |||||||
\(500\) | −2.37376 | − | 1.72464i | −0.106158 | − | 0.0771282i | ||||
\(501\) | 4.04523 | + | 2.93903i | 0.180728 | + | 0.131306i | ||||
\(502\) | −0.559496 | + | 1.72195i | −0.0249715 | + | 0.0768545i | ||||
\(503\) | 10.5846 | + | 32.5759i | 0.471942 | + | 1.45249i | 0.850037 | + | 0.526722i | \(0.176579\pi\) |
−0.378095 | + | 0.925767i | \(0.623421\pi\) | |||||||
\(504\) | 1.96900 | − | 1.43056i | 0.0877061 | − | 0.0637222i | ||||
\(505\) | −56.5171 | −2.51498 | ||||||||
\(506\) | 1.50753 | + | 2.95421i | 0.0670178 | + | 0.131331i | ||||
\(507\) | 13.8225 | 0.613878 | ||||||||
\(508\) | −6.16987 | + | 4.48267i | −0.273744 | + | 0.198886i | ||||
\(509\) | 3.96884 | + | 12.2148i | 0.175916 | + | 0.541413i | 0.999674 | − | 0.0255283i | \(-0.00812679\pi\) |
−0.823758 | + | 0.566941i | \(0.808127\pi\) | |||||||
\(510\) | −2.51299 | + | 7.73419i | −0.111277 | + | 0.342476i | ||||
\(511\) | 5.67414 | + | 4.12250i | 0.251009 | + | 0.182369i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −1.26732 | + | 3.90042i | −0.0559537 | + | 0.172208i | ||||
\(514\) | 4.34144 | + | 13.3616i | 0.191493 | + | 0.589354i | ||||
\(515\) | −16.4467 | + | 11.9492i | −0.724727 | + | 0.526545i | ||||
\(516\) | −6.92509 | −0.304860 | ||||||||
\(517\) | −8.35410 | + | 1.32841i | −0.367413 | + | 0.0584235i | ||||
\(518\) | 3.98961 | 0.175294 | ||||||||
\(519\) | 10.5764 | − | 7.68421i | 0.464253 | − | 0.337299i | ||||
\(520\) | 0.809629 | + | 2.49178i | 0.0355046 | + | 0.109272i | ||||
\(521\) | −12.2612 | + | 37.7360i | −0.537171 | + | 1.65324i | 0.201739 | + | 0.979439i | \(0.435341\pi\) |
−0.738911 | + | 0.673803i | \(0.764659\pi\) | |||||||
\(522\) | −3.24776 | − | 2.35963i | −0.142150 | − | 0.103278i | ||||
\(523\) | 11.4201 | + | 8.29716i | 0.499364 | + | 0.362809i | 0.808774 | − | 0.588119i | \(-0.200132\pi\) |
−0.309410 | + | 0.950929i | \(0.600132\pi\) | |||||||
\(524\) | −3.38148 | + | 10.4071i | −0.147720 | + | 0.454637i | ||||
\(525\) | −1.98152 | − | 6.09848i | −0.0864805 | − | 0.266160i | ||||
\(526\) | −2.93724 | + | 2.13403i | −0.128070 | + | 0.0930482i | ||||
\(527\) | 22.2906 | 0.970992 | ||||||||
\(528\) | −3.33844 | − | 1.69844i | −0.145287 | − | 0.0739153i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −28.8429 | + | 20.9556i | −1.25286 | + | 0.910253i | ||||
\(531\) | −3.16799 | − | 9.75007i | −0.137479 | − | 0.423117i | ||||
\(532\) | −0.335202 | + | 1.03165i | −0.0145328 | + | 0.0447275i | ||||
\(533\) | 7.05707 | + | 5.12726i | 0.305676 | + | 0.222086i | ||||
\(534\) | 6.65564 | + | 4.83561i | 0.288018 | + | 0.209257i | ||||
\(535\) | 15.3744 | − | 47.3176i | 0.664694 | − | 2.04572i | ||||
\(536\) | −4.15760 | − | 12.7958i | −0.179581 | − | 0.552694i | ||||
\(537\) | 22.0706 | − | 16.0352i | 0.952417 | − | 0.691971i | ||||
\(538\) | 12.3861 | 0.534001 | ||||||||
\(539\) | −11.7383 | + | 11.7527i | −0.505605 | + | 0.506226i | ||||
\(540\) | −16.0278 | −0.689725 | ||||||||
\(541\) | 36.8141 | − | 26.7470i | 1.58276 | − | 1.14994i | 0.669316 | − | 0.742978i | \(-0.266587\pi\) |
0.913444 | − | 0.406964i | \(-0.133413\pi\) | |||||||
\(542\) | −2.63957 | − | 8.12375i | −0.113379 | − | 0.348945i | ||||
\(543\) | −3.87249 | + | 11.9183i | −0.166185 | + | 0.511464i | ||||
\(544\) | 1.93934 | + | 1.40901i | 0.0831486 | + | 0.0604110i | ||||
\(545\) | −0.520250 | − | 0.377984i | −0.0222851 | − | 0.0161910i | ||||
\(546\) | 0.429584 | − | 1.32212i | 0.0183845 | − | 0.0565816i | ||||
\(547\) | 11.0719 | + | 34.0757i | 0.473399 | + | 1.45697i | 0.848105 | + | 0.529829i | \(0.177744\pi\) |
−0.374705 | + | 0.927144i | \(0.622256\pi\) | |||||||
\(548\) | −16.7529 | + | 12.1717i | −0.715650 | + | 0.519950i | ||||
\(549\) | −13.4192 | −0.572715 | ||||||||
\(550\) | 9.42949 | − | 9.44106i | 0.402075 | − | 0.402568i | ||||
\(551\) | 1.78922 | 0.0762232 | ||||||||
\(552\) | −0.913669 | + | 0.663820i | −0.0388883 | + | 0.0282540i | ||||
\(553\) | 5.48351 | + | 16.8765i | 0.233182 | + | 0.717662i | ||||
\(554\) | 2.60768 | − | 8.02562i | 0.110790 | − | 0.340976i | ||||
\(555\) | −7.75871 | − | 5.63703i | −0.329339 | − | 0.239279i | ||||
\(556\) | 2.81814 | + | 2.04750i | 0.119516 | + | 0.0868334i | ||||
\(557\) | −3.65806 | + | 11.2583i | −0.154997 | + | 0.477031i | −0.998161 | − | 0.0606257i | \(-0.980690\pi\) |
0.843164 | + | 0.537657i | \(0.180690\pi\) | |||||||
\(558\) | 4.95545 | + | 15.2513i | 0.209781 | + | 0.645640i | ||||
\(559\) | 4.32688 | − | 3.14366i | 0.183007 | − | 0.132963i | ||||
\(560\) | −4.23927 | −0.179142 | ||||||||
\(561\) | 8.00278 | + | 4.07144i | 0.337877 | + | 0.171896i | ||||
\(562\) | −23.3863 | −0.986492 | ||||||||
\(563\) | 20.1974 | − | 14.6742i | 0.851217 | − | 0.618445i | −0.0742644 | − | 0.997239i | \(-0.523661\pi\) |
0.925481 | + | 0.378793i | \(0.123661\pi\) | |||||||
\(564\) | −0.890102 | − | 2.73945i | −0.0374800 | − | 0.115352i | ||||
\(565\) | −6.83478 | + | 21.0353i | −0.287541 | + | 0.884962i | ||||
\(566\) | 9.10677 | + | 6.61646i | 0.382786 | + | 0.278110i | ||||
\(567\) | 0.973066 | + | 0.706974i | 0.0408649 | + | 0.0296901i | ||||
\(568\) | −0.0932893 | + | 0.287115i | −0.00391433 | + | 0.0120471i | ||||
\(569\) | −4.86692 | − | 14.9788i | −0.204032 | − | 0.627945i | −0.999752 | − | 0.0222807i | \(-0.992907\pi\) |
0.795720 | − | 0.605665i | \(-0.207093\pi\) | |||||||
\(570\) | 2.10952 | − | 1.53265i | 0.0883579 | − | 0.0641958i | ||||
\(571\) | 8.20461 | 0.343352 | 0.171676 | − | 0.985153i | \(-0.445082\pi\) | ||||
0.171676 | + | 0.985153i | \(0.445082\pi\) | |||||||
\(572\) | 2.85691 | − | 0.454287i | 0.119454 | − | 0.0189947i | ||||
\(573\) | 5.34034 | 0.223096 | ||||||||
\(574\) | −11.4186 | + | 8.29609i | −0.476602 | + | 0.346272i | ||||
\(575\) | −1.24324 | − | 3.82631i | −0.0518468 | − | 0.159568i | ||||
\(576\) | −0.532916 | + | 1.64015i | −0.0222048 | + | 0.0683394i | ||||
\(577\) | −15.4685 | − | 11.2385i | −0.643963 | − | 0.467867i | 0.217246 | − | 0.976117i | \(-0.430293\pi\) |
−0.861210 | + | 0.508250i | \(0.830293\pi\) | |||||||
\(578\) | 9.10438 | + | 6.61472i | 0.378692 | + | 0.275136i | ||||
\(579\) | −3.06444 | + | 9.43138i | −0.127354 | + | 0.391955i | ||||
\(580\) | 2.16079 | + | 6.65023i | 0.0897219 | + | 0.276136i | ||||
\(581\) | −13.5598 | + | 9.85175i | −0.562554 | + | 0.408720i | ||||
\(582\) | 4.05685 | 0.168162 | ||||||||
\(583\) | 17.8923 | + | 35.0624i | 0.741023 | + | 1.45214i | ||||
\(584\) | −4.96971 | −0.205648 | ||||||||
\(585\) | 3.65543 | − | 2.65582i | 0.151133 | − | 0.109805i | ||||
\(586\) | 5.51320 | + | 16.9679i | 0.227748 | + | 0.700937i | ||||
\(587\) | −0.131011 | + | 0.403211i | −0.00540740 | + | 0.0166423i | −0.953724 | − | 0.300684i | \(-0.902785\pi\) |
0.948316 | + | 0.317326i | \(0.102785\pi\) | |||||||
\(588\) | −4.57594 | − | 3.32461i | −0.188709 | − | 0.137105i | ||||
\(589\) | −5.78223 | − | 4.20104i | −0.238253 | − | 0.173101i | ||||
\(590\) | −5.51808 | + | 16.9829i | −0.227176 | + | 0.699175i | ||||
\(591\) | −0.0716496 | − | 0.220515i | −0.00294727 | − | 0.00907076i | ||||
\(592\) | −2.28706 | + | 1.66165i | −0.0939976 | + | 0.0682932i | ||||
\(593\) | −24.2623 | −0.996334 | −0.498167 | − | 0.867081i | \(-0.665993\pi\) | ||||
−0.498167 | + | 0.867081i | \(0.665993\pi\) | |||||||
\(594\) | −2.75763 | + | 17.4804i | −0.113147 | + | 0.717228i | ||||
\(595\) | 10.1622 | 0.416610 | ||||||||
\(596\) | −0.189431 | + | 0.137630i | −0.00775939 | + | 0.00563753i | ||||
\(597\) | −5.69343 | − | 17.5226i | −0.233017 | − | 0.717152i | ||||
\(598\) | 0.269529 | − | 0.829525i | 0.0110219 | − | 0.0339218i | ||||
\(599\) | 26.4281 | + | 19.2012i | 1.07982 | + | 0.784538i | 0.977652 | − | 0.210228i | \(-0.0674208\pi\) |
0.102172 | + | 0.994767i | \(0.467421\pi\) | |||||||
\(600\) | 3.67589 | + | 2.67069i | 0.150068 | + | 0.109030i | ||||
\(601\) | −5.73676 | + | 17.6559i | −0.234007 | + | 0.720200i | 0.763244 | + | 0.646110i | \(0.223605\pi\) |
−0.997252 | + | 0.0740902i | \(0.976395\pi\) | |||||||
\(602\) | 2.67416 | + | 8.23021i | 0.108991 | + | 0.335438i | ||||
\(603\) | −18.7713 | + | 13.6382i | −0.764427 | + | 0.555388i | ||||
\(604\) | 2.33494 | 0.0950073 | ||||||||
\(605\) | −19.4547 | − | 26.7081i | −0.790946 | − | 1.08584i | ||||
\(606\) | −21.2486 | −0.863166 | ||||||||
\(607\) | 34.6864 | − | 25.2012i | 1.40788 | − | 1.02288i | 0.414252 | − | 0.910162i | \(-0.364043\pi\) |
0.993627 | − | 0.112722i | \(-0.0359568\pi\) | |||||||
\(608\) | −0.237518 | − | 0.731004i | −0.00963261 | − | 0.0296461i | ||||
\(609\) | 1.14650 | − | 3.52856i | 0.0464585 | − | 0.142985i | ||||
\(610\) | 18.9098 | + | 13.7388i | 0.765636 | + | 0.556267i | ||||
\(611\) | 1.79973 | + | 1.30758i | 0.0728092 | + | 0.0528990i | ||||
\(612\) | 1.27748 | − | 3.93169i | 0.0516392 | − | 0.158929i | ||||
\(613\) | −5.78813 | − | 17.8140i | −0.233780 | − | 0.719502i | −0.997281 | − | 0.0736945i | \(-0.976521\pi\) |
0.763501 | − | 0.645807i | \(-0.223479\pi\) | |||||||
\(614\) | −15.9692 | + | 11.6023i | −0.644465 | + | 0.468231i | ||||
\(615\) | 33.9278 | 1.36810 | ||||||||
\(616\) | −0.729381 | + | 4.62348i | −0.0293876 | + | 0.186285i | ||||
\(617\) | −4.45081 | −0.179183 | −0.0895914 | − | 0.995979i | \(-0.528556\pi\) | ||||
−0.0895914 | + | 0.995979i | \(0.528556\pi\) | |||||||
\(618\) | −6.18342 | + | 4.49251i | −0.248733 | + | 0.180715i | ||||
\(619\) | 2.95779 | + | 9.10313i | 0.118884 | + | 0.365886i | 0.992737 | − | 0.120303i | \(-0.0383867\pi\) |
−0.873854 | + | 0.486189i | \(0.838387\pi\) | |||||||
\(620\) | 8.63153 | − | 26.5651i | 0.346650 | − | 1.06688i | ||||
\(621\) | 4.31668 | + | 3.13625i | 0.173222 | + | 0.125853i | ||||
\(622\) | −7.89441 | − | 5.73563i | −0.316537 | − | 0.229978i | ||||
\(623\) | 3.17683 | − | 9.77728i | 0.127277 | − | 0.391719i | ||||
\(624\) | 0.304395 | + | 0.936830i | 0.0121855 | + | 0.0375032i | ||||
\(625\) | 23.4047 | − | 17.0045i | 0.936188 | − | 0.680181i | ||||
\(626\) | −3.83346 | −0.153216 | ||||||||
\(627\) | −1.30861 | − | 2.56440i | −0.0522608 | − | 0.102412i | ||||
\(628\) | 1.86913 | 0.0745864 | ||||||||
\(629\) | 5.48244 | − | 3.98323i | 0.218599 | − | 0.158822i | ||||
\(630\) | 2.25918 | + | 6.95303i | 0.0900078 | + | 0.277015i | ||||
\(631\) | 0.199052 | − | 0.612620i | 0.00792415 | − | 0.0243880i | −0.947016 | − | 0.321186i | \(-0.895919\pi\) |
0.954940 | + | 0.296798i | \(0.0959187\pi\) | |||||||
\(632\) | −10.1724 | − | 7.39067i | −0.404636 | − | 0.293985i | ||||
\(633\) | 1.98482 | + | 1.44206i | 0.0788896 | + | 0.0573167i | ||||
\(634\) | 1.34336 | − | 4.13443i | 0.0533515 | − | 0.164199i | ||||
\(635\) | −7.07915 | − | 21.7874i | −0.280928 | − | 0.864606i | ||||
\(636\) | −10.8440 | + | 7.87863i | −0.429993 | + | 0.312408i | ||||
\(637\) | 4.36832 | 0.173079 | ||||||||
\(638\) | 7.62471 | − | 1.21243i | 0.301865 | − | 0.0480006i | ||||
\(639\) | 0.520626 | 0.0205956 | ||||||||
\(640\) | 2.43018 | − | 1.76563i | 0.0960613 | − | 0.0697926i | ||||
\(641\) | 7.19878 | + | 22.1556i | 0.284335 | + | 0.875092i | 0.986597 | + | 0.163174i | \(0.0521732\pi\) |
−0.702263 | + | 0.711918i | \(0.747827\pi\) | |||||||
\(642\) | 5.78028 | − | 17.7899i | 0.228130 | − | 0.702111i | ||||
\(643\) | −9.51391 | − | 6.91226i | −0.375192 | − | 0.272593i | 0.384169 | − | 0.923263i | \(-0.374488\pi\) |
−0.759361 | + | 0.650670i | \(0.774488\pi\) | |||||||
\(644\) | 1.14174 | + | 0.829525i | 0.0449910 | + | 0.0326879i | ||||
\(645\) | 6.42818 | − | 19.7839i | 0.253109 | − | 0.778991i | ||||
\(646\) | 0.569367 | + | 1.75233i | 0.0224014 | + | 0.0689445i | ||||
\(647\) | −30.1832 | + | 21.9294i | −1.18662 | + | 0.862132i | −0.992903 | − | 0.118925i | \(-0.962055\pi\) |
−0.193720 | + | 0.981057i | \(0.562055\pi\) | |||||||
\(648\) | −0.852263 | −0.0334801 | ||||||||
\(649\) | 17.5727 | + | 8.94015i | 0.689788 | + | 0.350932i | ||||
\(650\) | −3.50911 | −0.137638 | ||||||||
\(651\) | −11.9901 | + | 8.71135i | −0.469931 | + | 0.341425i | ||||
\(652\) | 0.0635937 | + | 0.195721i | 0.00249052 | + | 0.00766503i | ||||
\(653\) | 9.94077 | − | 30.5946i | 0.389013 | − | 1.19726i | −0.544515 | − | 0.838751i | \(-0.683286\pi\) |
0.933527 | − | 0.358506i | \(-0.116714\pi\) | |||||||
\(654\) | −0.195597 | − | 0.142110i | −0.00764846 | − | 0.00555693i | ||||
\(655\) | −26.5927 | − | 19.3207i | −1.03906 | − | 0.754923i | ||||
\(656\) | 3.09048 | − | 9.51152i | 0.120663 | − | 0.371363i | ||||
\(657\) | 2.64844 | + | 8.15106i | 0.103325 | + | 0.318003i | ||||
\(658\) | −2.91202 | + | 2.11571i | −0.113522 | + | 0.0824788i | ||||
\(659\) | −1.34581 | −0.0524251 | −0.0262126 | − | 0.999656i | \(-0.508345\pi\) | ||||
−0.0262126 | + | 0.999656i | \(0.508345\pi\) | |||||||
\(660\) | 7.95109 | − | 7.96085i | 0.309496 | − | 0.309876i | ||||
\(661\) | 43.9478 | 1.70937 | 0.854685 | − | 0.519147i | \(-0.173750\pi\) | ||||
0.854685 | + | 0.519147i | \(0.173750\pi\) | |||||||
\(662\) | 24.2866 | − | 17.6452i | 0.943924 | − | 0.685801i | ||||
\(663\) | −0.729682 | − | 2.24573i | −0.0283385 | − | 0.0872169i | ||||
\(664\) | 3.67000 | − | 11.2951i | 0.142424 | − | 0.438335i | ||||
\(665\) | −2.63610 | − | 1.91524i | −0.102224 | − | 0.0742699i | ||||
\(666\) | 3.94415 | + | 2.86560i | 0.152833 | + | 0.111040i | ||||
\(667\) | 0.719336 | − | 2.21389i | 0.0278528 | − | 0.0857221i | ||||
\(668\) | 1.36816 | + | 4.21076i | 0.0529357 | + | 0.162919i | ||||
\(669\) | 4.00578 | − | 2.91037i | 0.154872 | − | 0.112521i | ||||
\(670\) | 40.4149 | 1.56136 | ||||||||
\(671\) | 18.2374 | − | 18.2598i | 0.704048 | − | 0.704912i | ||||
\(672\) | −1.59383 | −0.0614834 | ||||||||
\(673\) | 38.1853 | − | 27.7432i | 1.47193 | − | 1.06942i | 0.491887 | − | 0.870659i | \(-0.336307\pi\) |
0.980047 | − | 0.198764i | \(-0.0636927\pi\) | |||||||
\(674\) | 9.63992 | + | 29.6686i | 0.371316 | + | 1.14279i | ||||
\(675\) | 6.63358 | − | 20.4160i | 0.255326 | − | 0.785814i | ||||
\(676\) | 9.90175 | + | 7.19405i | 0.380837 | + | 0.276694i | ||||
\(677\) | −34.4754 | − | 25.0478i | −1.32500 | − | 0.962666i | −0.999855 | − | 0.0170010i | \(-0.994588\pi\) |
−0.325141 | − | 0.945665i | \(-0.605412\pi\) | |||||||
\(678\) | −2.56966 | + | 7.90860i | −0.0986871 | + | 0.303728i | ||||
\(679\) | −1.56657 | − | 4.82142i | −0.0601196 | − | 0.185029i | ||||
\(680\) | −5.82552 | + | 4.23249i | −0.223399 | + | 0.162309i | ||||
\(681\) | −31.3400 | −1.20095 | ||||||||
\(682\) | −27.4876 | − | 13.9844i | −1.05256 | − | 0.535491i | ||||
\(683\) | −33.8626 | −1.29571 | −0.647857 | − | 0.761762i | \(-0.724335\pi\) | ||||
−0.647857 | + | 0.761762i | \(0.724335\pi\) | |||||||
\(684\) | −1.07238 | + | 0.779127i | −0.0410033 | + | 0.0297907i | ||||
\(685\) | −19.2219 | − | 59.1589i | −0.734431 | − | 2.26034i | ||||
\(686\) | −5.23691 | + | 16.1176i | −0.199946 | + | 0.615371i | ||||
\(687\) | 20.0101 | + | 14.5382i | 0.763434 | + | 0.554667i | ||||
\(688\) | −4.96080 | − | 3.60423i | −0.189129 | − | 0.137410i | ||||
\(689\) | 3.19894 | − | 9.84533i | 0.121870 | − | 0.375077i | ||||
\(690\) | −1.04832 | − | 3.22640i | −0.0399089 | − | 0.122827i | ||||
\(691\) | −2.92103 | + | 2.12226i | −0.111121 | + | 0.0807344i | −0.641958 | − | 0.766740i | \(-0.721878\pi\) |
0.530837 | + | 0.847474i | \(0.321878\pi\) | |||||||
\(692\) | 11.5757 | 0.440044 | ||||||||
\(693\) | 7.97189 | − | 1.26764i | 0.302827 | − | 0.0481535i | ||||
\(694\) | −12.6424 | −0.479899 | ||||||||
\(695\) | −8.46532 | + | 6.15042i | −0.321108 | + | 0.233299i | ||||
\(696\) | 0.812387 | + | 2.50027i | 0.0307935 | + | 0.0947725i | ||||
\(697\) | −7.40837 | + | 22.8006i | −0.280612 | + | 0.863635i | ||||
\(698\) | 3.35413 | + | 2.43692i | 0.126956 | + | 0.0922388i | ||||
\(699\) | 11.3527 | + | 8.24819i | 0.429397 | + | 0.311975i | ||||
\(700\) | 1.75455 | − | 5.39996i | 0.0663159 | − | 0.204099i | ||||
\(701\) | 2.32272 | + | 7.14859i | 0.0877279 | + | 0.269999i | 0.985290 | − | 0.170889i | \(-0.0546639\pi\) |
−0.897562 | + | 0.440887i | \(0.854664\pi\) | |||||||
\(702\) | 3.76507 | − | 2.73548i | 0.142103 | − | 0.103244i | ||||
\(703\) | −2.17287 | −0.0819513 | ||||||||
\(704\) | −1.50753 | − | 2.95421i | −0.0568171 | − | 0.111341i | ||||
\(705\) | 8.65243 | 0.325869 | ||||||||
\(706\) | 8.86336 | − | 6.43961i | 0.333577 | − | 0.242358i | ||||
\(707\) | 8.20527 | + | 25.2532i | 0.308591 | + | 0.949745i | ||||
\(708\) | −2.07462 | + | 6.38503i | −0.0779690 | + | 0.239964i | ||||
\(709\) | 18.6950 | + | 13.5827i | 0.702107 | + | 0.510111i | 0.880618 | − | 0.473827i | \(-0.157128\pi\) |
−0.178511 | + | 0.983938i | \(0.557128\pi\) | |||||||
\(710\) | −0.733648 | − | 0.533026i | −0.0275333 | − | 0.0200041i | ||||
\(711\) | −6.70076 | + | 20.6228i | −0.251298 | + | 0.773416i | ||||
\(712\) | 2.25104 | + | 6.92799i | 0.0843613 | + | 0.259637i | ||||
\(713\) | −7.52285 | + | 5.46567i | −0.281733 | + | 0.204691i | ||||
\(714\) | 3.82066 | 0.142985 | ||||||||
\(715\) | −1.35409 | + | 8.58346i | −0.0506401 | + | 0.321003i | ||||
\(716\) | 24.1560 | 0.902753 | ||||||||
\(717\) | 5.01978 | − | 3.64709i | 0.187467 | − | 0.136203i | ||||
\(718\) | −6.29437 | − | 19.3721i | −0.234904 | − | 0.722959i | ||||
\(719\) | −1.16462 | + | 3.58434i | −0.0434331 | + | 0.133673i | −0.970422 | − | 0.241416i | \(-0.922388\pi\) |
0.926989 | + | 0.375090i | \(0.122388\pi\) | |||||||
\(720\) | −4.19097 | − | 3.04492i | −0.156188 | − | 0.113477i | ||||
\(721\) | 7.72695 | + | 5.61396i | 0.287767 | + | 0.209075i | ||||
\(722\) | −5.68876 | + | 17.5082i | −0.211714 | + | 0.651588i | ||||
\(723\) | 3.51044 | + | 10.8040i | 0.130555 | + | 0.401806i | ||||
\(724\) | −8.97707 | + | 6.52222i | −0.333630 | + | 0.242397i | ||||
\(725\) | −9.36532 | −0.347819 | ||||||||
\(726\) | −7.31434 | − | 10.0414i | −0.271461 | − | 0.372671i | ||||
\(727\) | 0.902406 | 0.0334684 | 0.0167342 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167342 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(728\) | 0.995845 | − | 0.723524i | 0.0369085 | − | 0.0268156i | ||||
\(729\) | 6.04052 | + | 18.5908i | 0.223723 | + | 0.688548i | ||||
\(730\) | 4.61312 | − | 14.1977i | 0.170739 | − | 0.525481i | ||||
\(731\) | 11.8918 | + | 8.63991i | 0.439834 | + | 0.319558i | ||||
\(732\) | 7.10948 | + | 5.16534i | 0.262774 | + | 0.190916i | ||||
\(733\) | −11.5170 | + | 35.4457i | −0.425390 | + | 1.30922i | 0.477231 | + | 0.878778i | \(0.341641\pi\) |
−0.902621 | + | 0.430437i | \(0.858359\pi\) | |||||||
\(734\) | −2.06048 | − | 6.34150i | −0.0760536 | − | 0.234069i | ||||
\(735\) | 13.7455 | − | 9.98670i | 0.507011 | − | 0.368365i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 6.95351 | − | 44.0777i | 0.256136 | − | 1.62362i | ||||
\(738\) | −17.2473 | −0.634880 | ||||||||
\(739\) | −31.1727 | + | 22.6483i | −1.14671 | + | 0.833131i | −0.988039 | − | 0.154202i | \(-0.950719\pi\) |
−0.158666 | + | 0.987332i | \(0.550719\pi\) | |||||||
\(740\) | −2.62412 | − | 8.07620i | −0.0964644 | − | 0.296887i | ||||
\(741\) | −0.233965 | + | 0.720069i | −0.00859491 | + | 0.0264524i | ||||
\(742\) | 13.5509 | + | 9.84533i | 0.497470 | + | 0.361433i | ||||
\(743\) | 39.7928 | + | 28.9112i | 1.45986 | + | 1.06065i | 0.983400 | + | 0.181452i | \(0.0580796\pi\) |
0.476458 | + | 0.879197i | \(0.341920\pi\) | |||||||
\(744\) | 3.24518 | − | 9.98762i | 0.118974 | − | 0.366164i | ||||
\(745\) | −0.217348 | − | 0.668929i | −0.00796302 | − | 0.0245077i | ||||
\(746\) | 1.39608 | − | 1.01431i | 0.0511141 | − | 0.0371366i | ||||
\(747\) | −20.4814 | −0.749376 | ||||||||
\(748\) | 3.61378 | + | 7.08171i | 0.132133 | + | 0.258933i | ||||
\(749\) | −23.3747 | −0.854094 | ||||||||
\(750\) | 2.68082 | − | 1.94773i | 0.0978899 | − | 0.0711211i | ||||
\(751\) | 3.45334 | + | 10.6283i | 0.126014 | + | 0.387832i | 0.994085 | − | 0.108609i | \(-0.0346398\pi\) |
−0.868070 | + | 0.496441i | \(0.834640\pi\) | |||||||
\(752\) | 0.788149 | − | 2.42567i | 0.0287408 | − | 0.0884552i | ||||
\(753\) | −1.65426 | − | 1.20189i | −0.0602846 | − | 0.0437993i | ||||
\(754\) | −1.64259 | − | 1.19341i | −0.0598198 | − | 0.0434616i | ||||
\(755\) | −2.16740 | + | 6.67056i | −0.0788797 | + | 0.242767i | ||||
\(756\) | 2.32694 | + | 7.16159i | 0.0846300 | + | 0.260464i | ||||
\(757\) | 35.4824 | − | 25.7795i | 1.28963 | − | 0.936971i | 0.289832 | − | 0.957077i | \(-0.406400\pi\) |
0.999798 | + | 0.0201061i | \(0.00640042\pi\) | |||||||
\(758\) | 11.0675 | 0.401989 | ||||||||
\(759\) | −3.69918 | + | 0.588218i | −0.134272 | + | 0.0213510i | ||||
\(760\) | 2.30884 | 0.0837505 | ||||||||
\(761\) | 41.5568 | − | 30.1928i | 1.50643 | − | 1.09449i | 0.538706 | − | 0.842494i | \(-0.318913\pi\) |
0.967729 | − | 0.251995i | \(-0.0810866\pi\) | |||||||
\(762\) | −2.66153 | − | 8.19136i | −0.0964172 | − | 0.296742i | ||||
\(763\) | −0.0933613 | + | 0.287337i | −0.00337991 | + | 0.0104023i | ||||
\(764\) | 3.82556 | + | 2.77943i | 0.138404 | + | 0.100556i | ||||
\(765\) | 10.0464 | + | 7.29915i | 0.363229 | + | 0.263901i | ||||
\(766\) | 4.66202 | − | 14.3482i | 0.168446 | − | 0.518423i | ||||
\(767\) | −1.60225 | − | 4.93122i | −0.0578539 | − | 0.178056i | ||||
\(768\) | 0.913669 | − | 0.663820i | 0.0329692 | − | 0.0239535i | ||||
\(769\) | −23.3690 | −0.842707 | −0.421353 | − | 0.906897i | \(-0.638445\pi\) | ||||
−0.421353 | + | 0.906897i | \(0.638445\pi\) | |||||||
\(770\) | −12.5315 | − | 6.37546i | −0.451605 | − | 0.229756i | ||||
\(771\) | −15.8666 | −0.571420 | ||||||||
\(772\) | −7.10387 | + | 5.16127i | −0.255674 | + | 0.185758i | ||||
\(773\) | −5.26289 | − | 16.1975i | −0.189293 | − | 0.582584i | 0.810703 | − | 0.585458i | \(-0.199085\pi\) |
−0.999996 | + | 0.00287391i | \(0.999085\pi\) | |||||||
\(774\) | −3.26778 | + | 10.0572i | −0.117458 | + | 0.361498i | ||||
\(775\) | 30.2660 | + | 21.9896i | 1.08719 | + | 0.789888i | ||||
\(776\) | 2.90613 | + | 2.11143i | 0.104324 | + | 0.0757959i | ||||
\(777\) | −1.39234 | + | 4.28517i | −0.0499498 | + | 0.153730i | ||||
\(778\) | 0.883432 | + | 2.71892i | 0.0316726 | + | 0.0974782i | ||||
\(779\) | 6.21892 | − | 4.51831i | 0.222816 | − | 0.161885i | ||||
\(780\) | −2.95893 | −0.105947 | ||||||||
\(781\) | −0.707562 | + | 0.708430i | −0.0253185 | + | 0.0253496i | ||||
\(782\) | 2.39716 | 0.0857222 | ||||||||
\(783\) | 10.0485 | − | 7.30063i | 0.359102 | − | 0.260903i | ||||
\(784\) | −1.54765 | − | 4.76319i | −0.0552733 | − | 0.170114i | ||||
\(785\) | −1.73501 | + | 5.33982i | −0.0619253 | + | 0.190586i | ||||
\(786\) | −9.99799 | − | 7.26397i | −0.356617 | − | 0.259097i | ||||
\(787\) | −30.7396 | − | 22.3336i | −1.09575 | − | 0.796108i | −0.115388 | − | 0.993321i | \(-0.536811\pi\) |
−0.980361 | + | 0.197213i | \(0.936811\pi\) | |||||||
\(788\) | 0.0634428 | − | 0.195257i | 0.00226006 | − | 0.00695574i | ||||
\(789\) | −1.26706 | − | 3.89960i | −0.0451084 | − | 0.138829i | ||||
\(790\) | 30.5565 | − | 22.2006i | 1.08715 | − | 0.789861i | ||||
\(791\) | 10.3914 | 0.369474 | ||||||||
\(792\) | −4.04195 | + | 4.04691i | −0.143625 | + | 0.143801i | ||||
\(793\) | −6.78691 | −0.241010 | ||||||||
\(794\) | 12.7435 | − | 9.25871i | 0.452251 | − | 0.328579i | ||||
\(795\) | −12.4421 | − | 38.2930i | −0.441277 | − | 1.35811i | ||||
\(796\) | 5.04130 | − | 15.5155i | 0.178684 | − | 0.549934i | ||||
\(797\) | 16.4585 | + | 11.9578i | 0.582990 | + | 0.423567i | 0.839801 | − | 0.542895i | \(-0.182672\pi\) |
−0.256811 | + | 0.966462i | \(0.582672\pi\) | |||||||
\(798\) | −0.991090 | − | 0.720069i | −0.0350842 | − | 0.0254902i | ||||
\(799\) | −1.88932 | + | 5.81472i | −0.0668392 | + | 0.205710i | ||||
\(800\) | 1.24324 | + | 3.82631i | 0.0439552 | + | 0.135280i | ||||
\(801\) | 10.1633 | − | 7.38407i | 0.359103 | − | 0.260903i | ||||
\(802\) | 35.4020 | 1.25009 | ||||||||
\(803\) | −14.6908 | − | 7.47397i | −0.518426 | − | 0.263751i | ||||
\(804\) | 15.1947 | 0.535875 | ||||||||
\(805\) | −3.42965 | + | 2.49178i | −0.120879 | + | 0.0878238i | ||||
\(806\) | 2.50628 | + | 7.71355i | 0.0882801 | + | 0.271698i | ||||
\(807\) | −4.32262 | + | 13.3037i | −0.152163 | + | 0.468311i | ||||
\(808\) | −15.2215 | − | 11.0591i | −0.535490 | − | 0.389056i | ||||
\(809\) | 34.0565 | + | 24.7435i | 1.19736 | + | 0.869936i | 0.994023 | − | 0.109172i | \(-0.0348198\pi\) |
0.203342 | + | 0.979108i | \(0.434820\pi\) | |||||||
\(810\) | 0.791110 | − | 2.43478i | 0.0277968 | − | 0.0855496i | ||||
\(811\) | 4.25441 | + | 13.0937i | 0.149393 | + | 0.459783i | 0.997550 | − | 0.0699615i | \(-0.0222876\pi\) |
−0.848157 | + | 0.529745i | \(0.822288\pi\) | |||||||
\(812\) | 2.65777 | − | 1.93099i | 0.0932696 | − | 0.0677643i | ||||
\(813\) | 9.64676 | 0.338327 | ||||||||
\(814\) | −9.25964 | + | 1.47240i | −0.324550 | + | 0.0516077i | ||||
\(815\) | −0.618176 | −0.0216538 | ||||||||
\(816\) | −2.19021 | + | 1.59128i | −0.0766726 | + | 0.0557059i | ||||
\(817\) | −1.45643 | − | 4.48243i | −0.0509540 | − | 0.156820i | ||||
\(818\) | −5.53132 | + | 17.0236i | −0.193398 | + | 0.595218i | ||||
\(819\) | −1.71739 | − | 1.24775i | −0.0600104 | − | 0.0436001i | ||||
\(820\) | 24.3042 | + | 17.6581i | 0.848741 | + | 0.616646i | ||||
\(821\) | 8.06946 | − | 24.8353i | 0.281626 | − | 0.866756i | −0.705763 | − | 0.708448i | \(-0.749396\pi\) |
0.987390 | − | 0.158309i | \(-0.0506041\pi\) | |||||||
\(822\) | −7.22681 | − | 22.2418i | −0.252064 | − | 0.775773i | ||||
\(823\) | 36.9759 | − | 26.8646i | 1.28890 | − | 0.936440i | 0.289117 | − | 0.957294i | \(-0.406638\pi\) |
0.999783 | + | 0.0208535i | \(0.00663836\pi\) | |||||||
\(824\) | −6.76767 | −0.235763 | ||||||||
\(825\) | 6.84968 | + | 13.4229i | 0.238475 | + | 0.467325i | ||||
\(826\) | 8.38950 | 0.291908 | ||||||||
\(827\) | −35.6353 | + | 25.8906i | −1.23916 | + | 0.900304i | −0.997542 | − | 0.0700675i | \(-0.977679\pi\) |
−0.241619 | + | 0.970371i | \(0.577679\pi\) | |||||||
\(828\) | 0.532916 | + | 1.64015i | 0.0185201 | + | 0.0569990i | ||||
\(829\) | 4.35190 | − | 13.3938i | 0.151148 | − | 0.465185i | −0.846602 | − | 0.532226i | \(-0.821356\pi\) |
0.997750 | + | 0.0670406i | \(0.0213557\pi\) | |||||||
\(830\) | 28.8617 | + | 20.9693i | 1.00181 | + | 0.727854i | ||||
\(831\) | 7.71012 | + | 5.60173i | 0.267461 | + | 0.194322i | ||||
\(832\) | −0.269529 | + | 0.829525i | −0.00934424 | + | 0.0287586i | ||||
\(833\) | 3.70997 | + | 11.4181i | 0.128543 | + | 0.395614i | ||||
\(834\) | −3.18269 | + | 2.31236i | −0.110208 | + | 0.0800705i | ||||
\(835\) | −13.2995 | −0.460248 | ||||||||
\(836\) | 0.397244 | − | 2.51809i | 0.0137390 | − | 0.0870901i | ||||
\(837\) | −49.6154 | −1.71496 | ||||||||
\(838\) | 26.4741 | − | 19.2345i | 0.914531 | − | 0.664446i | ||||
\(839\) | 3.34094 | + | 10.2823i | 0.115342 | + | 0.354986i | 0.992018 | − | 0.126095i | \(-0.0402444\pi\) |
−0.876676 | + | 0.481081i | \(0.840244\pi\) | |||||||
\(840\) | 1.47947 | − | 4.55333i | 0.0510465 | − | 0.157105i | ||||
\(841\) | 19.0776 | + | 13.8607i | 0.657849 | + | 0.477956i | ||||
\(842\) | −10.3325 | − | 7.50703i | −0.356083 | − | 0.258709i | ||||
\(843\) | 8.16160 | − | 25.1188i | 0.281101 | − | 0.865139i | ||||
\(844\) | 0.671298 | + | 2.06604i | 0.0231070 | + | 0.0711161i | ||||
\(845\) | −29.7436 | + | 21.6100i | −1.02321 | + | 0.743405i | ||||
\(846\) | −4.39848 | −0.151223 | ||||||||
\(847\) | −9.10936 | + | 12.5704i | −0.313001 | + | 0.431923i | ||||
\(848\) | −11.8686 | −0.407570 | ||||||||
\(849\) | −10.2848 | + | 7.47234i | −0.352973 | + | 0.256450i | ||||
\(850\) | −2.98025 | − | 9.17226i | −0.102222 | − | 0.314606i | ||||
\(851\) | −0.873579 | + | 2.68860i | −0.0299459 | + | 0.0921640i | ||||
\(852\) | −0.275828 | − | 0.200401i | −0.00944971 | − | 0.00686562i | ||||
\(853\) | 25.5500 | + | 18.5631i | 0.874815 | + | 0.635590i | 0.931875 | − | 0.362781i | \(-0.118173\pi\) |
−0.0570599 | + | 0.998371i | \(0.518173\pi\) | |||||||
\(854\) | 3.39345 | − | 10.4440i | 0.116122 | − | 0.357386i | ||||
\(855\) | −1.23042 | − | 3.78684i | −0.0420794 | − | 0.129507i | ||||
\(856\) | 13.3996 | − | 9.73541i | 0.457990 | − | 0.332749i | ||||
\(857\) | −44.5969 | −1.52340 | −0.761701 | − | 0.647929i | \(-0.775635\pi\) | ||||
−0.761701 | + | 0.647929i | \(0.775635\pi\) | |||||||
\(858\) | −0.509094 | + | 3.22710i | −0.0173802 | + | 0.110172i | ||||
\(859\) | −22.3644 | −0.763064 | −0.381532 | − | 0.924356i | \(-0.624603\pi\) | ||||
−0.381532 | + | 0.924356i | \(0.624603\pi\) | |||||||
\(860\) | 14.9016 | − | 10.8266i | 0.508139 | − | 0.369185i | ||||
\(861\) | −4.92570 | − | 15.1598i | −0.167868 | − | 0.516643i | ||||
\(862\) | −8.05176 | + | 24.7808i | −0.274244 | + | 0.844036i | ||||
\(863\) | 45.9232 | + | 33.3652i | 1.56325 | + | 1.13576i | 0.933285 | + | 0.359136i | \(0.116929\pi\) |
0.629960 | + | 0.776628i | \(0.283071\pi\) | |||||||
\(864\) | −4.31668 | − | 3.13625i | −0.146856 | − | 0.106697i | ||||
\(865\) | −10.7451 | + | 33.0701i | −0.365346 | + | 1.12442i | ||||
\(866\) | 0.632113 | + | 1.94544i | 0.0214801 | + | 0.0661088i | ||||
\(867\) | −10.2821 | + | 7.47038i | −0.349198 | + | 0.253708i | ||||
\(868\) | −13.1231 | −0.445426 | ||||||||
\(869\) | −18.9553 | − | 37.1455i | −0.643014 | − | 1.26008i | ||||
\(870\) | −7.89699 | −0.267733 | ||||||||
\(871\) | −9.49383 | + | 6.89767i | −0.321686 | + | 0.233719i | ||||
\(872\) | −0.0661540 | − | 0.203601i | −0.00224026 | − | 0.00689480i | ||||
\(873\) | 1.91433 | − | 5.89170i | 0.0647902 | − | 0.199404i | ||||
\(874\) | −0.621829 | − | 0.451785i | −0.0210337 | − | 0.0152819i | ||||
\(875\) | −3.35002 | − | 2.43393i | −0.113251 | − | 0.0822820i | ||||
\(876\) | 1.73438 | − | 5.33788i | 0.0585994 | − | 0.180350i | ||||
\(877\) | −14.0889 | − | 43.3613i | −0.475749 | − | 1.46421i | −0.844945 | − | 0.534854i | \(-0.820367\pi\) |
0.369196 | − | 0.929352i | \(-0.379633\pi\) | |||||||
\(878\) | −16.2132 | + | 11.7796i | −0.547168 | + | 0.397541i | ||||
\(879\) | −20.1490 | −0.679608 | ||||||||
\(880\) | 9.83908 | − | 1.56454i | 0.331675 | − | 0.0527408i | ||||
\(881\) | 39.8248 | 1.34173 | 0.670866 | − | 0.741579i | \(-0.265923\pi\) | ||||
0.670866 | + | 0.741579i | \(0.265923\pi\) | |||||||
\(882\) | −6.98755 | + | 5.07676i | −0.235283 | + | 0.170943i | ||||
\(883\) | 10.4878 | + | 32.2781i | 0.352943 | + | 1.08625i | 0.957193 | + | 0.289451i | \(0.0934728\pi\) |
−0.604250 | + | 0.796795i | \(0.706527\pi\) | |||||||
\(884\) | 0.646104 | − | 1.98850i | 0.0217308 | − | 0.0668806i | ||||
\(885\) | −16.3153 | − | 11.8537i | −0.548432 | − | 0.398459i | ||||
\(886\) | −23.0442 | − | 16.7426i | −0.774185 | − | 0.562479i | ||||
\(887\) | 5.59307 | − | 17.2137i | 0.187797 | − | 0.577979i | −0.812189 | − | 0.583395i | \(-0.801724\pi\) |
0.999985 | + | 0.00541602i | \(0.00172398\pi\) | |||||||
\(888\) | −0.986583 | − | 3.03639i | −0.0331076 | − | 0.101895i | ||||
\(889\) | −8.70737 | + | 6.32627i | −0.292036 | + | 0.212176i | ||||
\(890\) | −21.8817 | −0.733477 | ||||||||
\(891\) | −2.51934 | − | 1.28172i | −0.0844010 | − | 0.0429393i | ||||
\(892\) | 4.38428 | 0.146797 | ||||||||
\(893\) | 1.58598 | − | 1.15228i | 0.0530727 | − | 0.0385596i | ||||
\(894\) | −0.0817159 | − | 0.251496i | −0.00273299 | − | 0.00841128i | ||||
\(895\) | −22.4227 | + | 69.0100i | −0.749509 | + | 2.30675i | ||||
\(896\) | −1.14174 | − | 0.829525i | −0.0381430 | − | 0.0277125i | ||||
\(897\) | 0.796915 | + | 0.578993i | 0.0266082 | + | 0.0193320i | ||||
\(898\) | −5.43075 | + | 16.7141i | −0.181227 | + | 0.557758i | ||||
\(899\) | 6.68893 | + | 20.5864i | 0.223088 | + | 0.686595i | ||||
\(900\) | 5.61316 | − | 4.07820i | 0.187105 | − | 0.135940i | ||||
\(901\) | 28.4510 | 0.947839 | ||||||||
\(902\) | 23.4401 | − | 23.4688i | 0.780468 | − | 0.781426i | ||||
\(903\) | −9.77318 | −0.325231 | ||||||||
\(904\) | −5.95689 | + | 4.32793i | −0.198123 | + | 0.143945i | ||||
\(905\) | −10.3001 | − | 31.7003i | −0.342386 | − | 1.05376i | ||||
\(906\) | −0.814872 | + | 2.50792i | −0.0270723 | + | 0.0833200i | ||||
\(907\) | 29.3444 | + | 21.3200i | 0.974366 | + | 0.707918i | 0.956442 | − | 0.291921i | \(-0.0942945\pi\) |
0.0179234 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(908\) | −22.4504 | − | 16.3112i | −0.745044 | − | 0.541306i | ||||
\(909\) | −10.0267 | + | 30.8590i | −0.332565 | + | 1.02353i | ||||
\(910\) | 1.14261 | + | 3.51658i | 0.0378771 | + | 0.116574i | ||||
\(911\) | −11.2078 | + | 8.14294i | −0.371331 | + | 0.269788i | −0.757763 | − | 0.652530i | \(-0.773707\pi\) |
0.386432 | + | 0.922318i | \(0.373707\pi\) | |||||||
\(912\) | 0.868050 | 0.0287440 | ||||||||
\(913\) | 27.8355 | − | 27.8697i | 0.921220 | − | 0.922351i | ||||
\(914\) | 21.4139 | 0.708308 | ||||||||
\(915\) | −21.3559 | + | 15.5160i | −0.706005 | + | 0.512943i | ||||
\(916\) | 6.76773 | + | 20.8289i | 0.223612 | + | 0.688208i | ||||
\(917\) | −4.77218 | + | 14.6873i | −0.157591 | + | 0.485016i | ||||
\(918\) | 10.3478 | + | 7.51808i | 0.341527 | + | 0.248134i | ||||
\(919\) | 2.68224 | + | 1.94876i | 0.0884790 | + | 0.0642838i | 0.631145 | − | 0.775665i | \(-0.282585\pi\) |
−0.542666 | + | 0.839948i | \(0.682585\pi\) | |||||||
\(920\) | 0.928246 | − | 2.85685i | 0.0306034 | − | 0.0941875i | ||||
\(921\) | −6.88874 | − | 21.2014i | −0.226992 | − | 0.698608i | ||||
\(922\) | −14.4093 | + | 10.4690i | −0.474547 | + | 0.344778i | ||||
\(923\) | 0.263313 | 0.00866706 | ||||||||
\(924\) | −4.71146 | − | 2.39697i | −0.154995 | − | 0.0788544i | ||||
\(925\) | 11.3735 | 0.373958 | ||||||||
\(926\) | −8.64548 | + | 6.28131i | −0.284108 | + | 0.206417i | ||||
\(927\) | 3.60660 | + | 11.1000i | 0.118456 | + | 0.364571i | ||||
\(928\) | −0.719336 | + | 2.21389i | −0.0236134 | + | 0.0726745i | ||||
\(929\) | −38.8077 | − | 28.1954i | −1.27324 | − | 0.925062i | −0.273912 | − | 0.961755i | \(-0.588318\pi\) |
−0.999327 | + | 0.0366933i | \(0.988318\pi\) | |||||||
\(930\) | 25.5208 | + | 18.5419i | 0.836860 | + | 0.608014i | ||||
\(931\) | 1.18956 | − | 3.66109i | 0.0389863 | − | 0.119988i | ||||
\(932\) | 3.83965 | + | 11.8172i | 0.125772 | + | 0.387086i | ||||
\(933\) | 8.91561 | − | 6.47757i | 0.291884 | − | 0.212066i | ||||
\(934\) | 22.2711 | 0.728732 | ||||||||
\(935\) | −23.5858 | + | 3.75046i | −0.771339 | + | 0.122653i | ||||
\(936\) | 1.50418 | 0.0491656 | ||||||||
\(937\) | −48.5808 | + | 35.2960i | −1.58707 | + | 1.15307i | −0.679086 | + | 0.734059i | \(0.737624\pi\) |
−0.907981 | + | 0.419012i | \(0.862376\pi\) | |||||||
\(938\) | −5.86751 | − | 18.0583i | −0.191581 | − | 0.589626i | ||||
\(939\) | 1.33784 | − | 4.11746i | 0.0436588 | − | 0.134368i | ||||
\(940\) | 6.19818 | + | 4.50324i | 0.202162 | + | 0.146880i | ||||
\(941\) | −30.3475 | − | 22.0488i | −0.989301 | − | 0.718769i | −0.0295327 | − | 0.999564i | \(-0.509402\pi\) |
−0.959768 | + | 0.280795i | \(0.909402\pi\) | |||||||
\(942\) | −0.652309 | + | 2.00760i | −0.0212534 | + | 0.0654112i | ||||
\(943\) | −3.09048 | − | 9.51152i | −0.100640 | − | 0.309738i | ||||
\(944\) | −4.80931 | + | 3.49417i | −0.156530 | + | 0.113725i | ||||
\(945\) | −22.6195 | −0.735813 | ||||||||
\(946\) | −9.24399 | − | 18.1149i | −0.300548 | − | 0.588965i | ||||
\(947\) | 28.6387 | 0.930634 | 0.465317 | − | 0.885144i | \(-0.345940\pi\) | ||||
0.465317 | + | 0.885144i | \(0.345940\pi\) | |||||||
\(948\) | 11.4883 | − | 8.34671i | 0.373121 | − | 0.271088i | ||||
\(949\) | 1.33948 | + | 4.12250i | 0.0434814 | + | 0.133822i | ||||
\(950\) | −0.955584 | + | 2.94099i | −0.0310032 | + | 0.0954182i | ||||
\(951\) | 3.97190 | + | 2.88575i | 0.128798 | + | 0.0935769i | ||||
\(952\) | 2.73694 | + | 1.98850i | 0.0887047 | + | 0.0644477i | ||||
\(953\) | −4.57146 | + | 14.0695i | −0.148084 | + | 0.455757i | −0.997395 | − | 0.0721372i | \(-0.977018\pi\) |
0.849310 | + | 0.527894i | \(0.177018\pi\) | |||||||
\(954\) | 6.32498 | + | 19.4663i | 0.204779 | + | 0.630245i | ||||
\(955\) | −11.4915 | + | 8.34905i | −0.371855 | + | 0.270169i | ||||
\(956\) | 5.49409 | 0.177692 | ||||||||
\(957\) | −1.35870 | + | 8.61270i | −0.0439206 | + | 0.278409i | ||||
\(958\) | 19.2495 | 0.621922 | ||||||||
\(959\) | −23.6429 | + | 17.1776i | −0.763470 | + | 0.554694i | ||||
\(960\) | 1.04832 | + | 3.22640i | 0.0338344 | + | 0.104132i | ||||
\(961\) | 17.1402 | − | 52.7520i | 0.552909 | − | 1.70168i | ||||
\(962\) | 1.99481 | + | 1.44931i | 0.0643151 | + | 0.0467277i | ||||
\(963\) | −23.1084 | − | 16.7892i | −0.744657 | − | 0.541025i | ||||
\(964\) | −3.10835 | + | 9.56652i | −0.100113 | + | 0.308117i | ||||
\(965\) | −8.15081 | − | 25.0856i | −0.262384 | − | 0.807534i | ||||
\(966\) | −1.28944 | + | 0.936830i | −0.0414869 | + | 0.0301420i | ||||
\(967\) | 31.4447 | 1.01119 | 0.505596 | − | 0.862770i | \(-0.331272\pi\) | ||||
0.505596 | + | 0.862770i | \(0.331272\pi\) | |||||||
\(968\) | −0.0134925 | − | 11.0000i | −0.000433666 | − | 0.353553i | ||||
\(969\) | −2.08085 | −0.0668466 | ||||||||
\(970\) | −8.72963 | + | 6.34245i | −0.280292 | + | 0.203644i | ||||
\(971\) | 15.8637 | + | 48.8236i | 0.509091 | + | 1.56682i | 0.793782 | + | 0.608203i | \(0.208109\pi\) |
−0.284690 | + | 0.958620i | \(0.591891\pi\) | |||||||
\(972\) | −4.64904 | + | 14.3083i | −0.149118 | + | 0.458938i | ||||
\(973\) | 3.97717 | + | 2.88958i | 0.127502 | + | 0.0926357i | ||||
\(974\) | 18.7038 | + | 13.5891i | 0.599309 | + | 0.435424i | ||||
\(975\) | 1.22465 | − | 3.76907i | 0.0392200 | − | 0.120707i | ||||
\(976\) | 2.40453 | + | 7.40040i | 0.0769673 | + | 0.236881i | ||||
\(977\) | 21.1206 | − | 15.3450i | 0.675708 | − | 0.490931i | −0.196223 | − | 0.980559i | \(-0.562868\pi\) |
0.871931 | + | 0.489629i | \(0.162868\pi\) | |||||||
\(978\) | −0.232414 | −0.00743179 | ||||||||
\(979\) | −3.76482 | + | 23.8649i | −0.120324 | + | 0.762725i | ||||
\(980\) | 15.0443 | 0.480572 | ||||||||
\(981\) | −0.298681 | + | 0.217004i | −0.00953615 | + | 0.00692842i | ||||
\(982\) | −6.23241 | − | 19.1814i | −0.198884 | − | 0.612102i | ||||
\(983\) | −0.715813 | + | 2.20305i | −0.0228309 | + | 0.0702663i | −0.961823 | − | 0.273673i | \(-0.911761\pi\) |
0.938992 | + | 0.343939i | \(0.111761\pi\) | |||||||
\(984\) | 9.13761 | + | 6.63886i | 0.291296 | + | 0.211639i | ||||
\(985\) | 0.498928 | + | 0.362493i | 0.0158972 | + | 0.0115500i | ||||
\(986\) | 1.72436 | − | 5.30704i | 0.0549149 | − | 0.169011i | ||||
\(987\) | −1.25618 | − | 3.86611i | −0.0399845 | − | 0.123060i | ||||
\(988\) | −0.542368 | + | 0.394054i | −0.0172550 | + | 0.0125365i | ||||
\(989\) | −6.13188 | −0.194983 | ||||||||
\(990\) | −7.80949 | − | 15.3038i | −0.248202 | − | 0.486386i | ||||
\(991\) | 24.4932 | 0.778053 | 0.389026 | − | 0.921227i | \(-0.372812\pi\) | ||||
0.389026 | + | 0.921227i | \(0.372812\pi\) | |||||||
\(992\) | 7.52285 | − | 5.46567i | 0.238851 | − | 0.173535i | ||||
\(993\) | 10.4766 | + | 32.2438i | 0.332466 | + | 1.02323i | ||||
\(994\) | −0.131657 | + | 0.405197i | −0.00417589 | + | 0.0128521i | ||||
\(995\) | 39.6460 | + | 28.8045i | 1.25686 | + | 0.913163i | ||||
\(996\) | 10.8511 | + | 7.88377i | 0.343830 | + | 0.249807i | ||||
\(997\) | 2.51361 | − | 7.73610i | 0.0796069 | − | 0.245005i | −0.903331 | − | 0.428945i | \(-0.858885\pi\) |
0.982937 | + | 0.183940i | \(0.0588853\pi\) | |||||||
\(998\) | 10.2945 | + | 31.6834i | 0.325868 | + | 1.00292i | ||||
\(999\) | −12.2031 | + | 8.86606i | −0.386088 | + | 0.280510i |
(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 | 506.2.e.h.47.2 | ✓ | 20 | |
11.2 | odd | 10 | 5566.2.a.bt.1.3 | 10 | |||
11.4 | even | 5 | inner | 506.2.e.h.323.2 | yes | 20 | |
11.9 | even | 5 | 5566.2.a.bu.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
506.2.e.h.47.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
506.2.e.h.323.2 | yes | 20 | 11.4 | even | 5 | inner | |
5566.2.a.bt.1.3 | 10 | 11.2 | odd | 10 | |||
5566.2.a.bu.1.3 | 10 | 11.9 | even | 5 |