Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(341,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.7278137344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 6x^{5} - 20x^{4} + 18x^{3} + 9x^{2} - 54x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 341.2 | ||
Root | \(1.67936 - 0.423958i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.341 |
Dual form | 570.2.f.d.341.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.67936 | + | 0.423958i | −0.969581 | + | 0.244772i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −1.67936 | + | 0.423958i | −0.685597 | + | 0.173080i | ||||
\(7\) | −2.47197 | −0.934316 | −0.467158 | − | 0.884174i | \(-0.654722\pi\) | ||||
−0.467158 | + | 0.884174i | \(0.654722\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.64052 | − | 1.42396i | 0.880173 | − | 0.474653i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | −1.67936 | + | 0.423958i | −0.484790 | + | 0.122386i | ||||
\(13\) | − | 1.15208i | − | 0.319531i | −0.987155 | − | 0.159765i | \(-0.948926\pi\) | ||
0.987155 | − | 0.159765i | \(-0.0510738\pi\) | |||||||
\(14\) | −2.47197 | −0.660661 | ||||||||
\(15\) | 0.423958 | + | 1.67936i | 0.109465 | + | 0.433610i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.67861i | − | 1.61980i | −0.586568 | − | 0.809900i | \(-0.699521\pi\) | ||
0.586568 | − | 0.809900i | \(-0.300479\pi\) | |||||||
\(18\) | 2.64052 | − | 1.42396i | 0.622376 | − | 0.335630i | ||||
\(19\) | 4.35873 | − | 0.0388432i | 0.999960 | − | 0.00891124i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 4.15133 | − | 1.04801i | 0.905895 | − | 0.228694i | ||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | − | 5.79185i | − | 1.20768i | −0.797104 | − | 0.603842i | \(-0.793636\pi\) | ||
0.797104 | − | 0.603842i | \(-0.206364\pi\) | |||||||
\(24\) | −1.67936 | + | 0.423958i | −0.342799 | + | 0.0865400i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 1.15208i | − | 0.225942i | ||||||
\(27\) | −3.83069 | + | 3.51081i | −0.737217 | + | 0.675656i | ||||
\(28\) | −2.47197 | −0.467158 | ||||||||
\(29\) | −3.35873 | −0.623700 | −0.311850 | − | 0.950131i | \(-0.600949\pi\) | ||||
−0.311850 | + | 0.950131i | \(0.600949\pi\) | |||||||
\(30\) | 0.423958 | + | 1.67936i | 0.0774037 | + | 0.306608i | ||||
\(31\) | 4.80907i | 0.863735i | 0.901937 | + | 0.431867i | \(0.142145\pi\) | ||||
−0.901937 | + | 0.431867i | \(0.857855\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.847915 | + | 3.35873i | 0.147603 | + | 0.584679i | ||||
\(34\) | − | 6.67861i | − | 1.14537i | ||||||
\(35\) | 2.47197i | 0.417839i | ||||||||
\(36\) | 2.64052 | − | 1.42396i | 0.440087 | − | 0.237326i | ||||
\(37\) | − | 11.6614i | − | 1.91712i | −0.284891 | − | 0.958560i | \(-0.591957\pi\) | ||
0.284891 | − | 0.958560i | \(-0.408043\pi\) | |||||||
\(38\) | 4.35873 | − | 0.0388432i | 0.707079 | − | 0.00630120i | ||||
\(39\) | 0.488435 | + | 1.93477i | 0.0782122 | + | 0.309811i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 7.83069 | 1.22295 | 0.611474 | − | 0.791264i | \(-0.290577\pi\) | ||||
0.611474 | + | 0.791264i | \(0.290577\pi\) | |||||||
\(42\) | 4.15133 | − | 1.04801i | 0.640564 | − | 0.161711i | ||||
\(43\) | −0.978379 | −0.149201 | −0.0746007 | − | 0.997213i | \(-0.523768\pi\) | ||||
−0.0746007 | + | 0.997213i | \(0.523768\pi\) | |||||||
\(44\) | − | 2.00000i | − | 0.301511i | ||||||
\(45\) | −1.42396 | − | 2.64052i | −0.212271 | − | 0.393625i | ||||
\(46\) | − | 5.79185i | − | 0.853962i | ||||||
\(47\) | 3.02162i | 0.440749i | 0.975415 | + | 0.220374i | \(0.0707279\pi\) | ||||
−0.975415 | + | 0.220374i | \(0.929272\pi\) | |||||||
\(48\) | −1.67936 | + | 0.423958i | −0.242395 | + | 0.0611930i | ||||
\(49\) | −0.889378 | −0.127054 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 2.83145 | + | 11.2158i | 0.396482 | + | 1.57053i | ||||
\(52\) | − | 1.15208i | − | 0.159765i | ||||||
\(53\) | 2.33710 | 0.321026 | 0.160513 | − | 0.987034i | \(-0.448685\pi\) | ||||
0.160513 | + | 0.987034i | \(0.448685\pi\) | |||||||
\(54\) | −3.83069 | + | 3.51081i | −0.521291 | + | 0.477761i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | −2.47197 | −0.330331 | ||||||||
\(57\) | −7.30341 | + | 1.91315i | −0.967361 | + | 0.253403i | ||||
\(58\) | −3.35873 | −0.441022 | ||||||||
\(59\) | −12.8076 | −1.66740 | −0.833701 | − | 0.552216i | \(-0.813783\pi\) | ||||
−0.833701 | + | 0.552216i | \(0.813783\pi\) | |||||||
\(60\) | 0.423958 | + | 1.67936i | 0.0547327 | + | 0.216805i | ||||
\(61\) | 11.9656 | 1.53203 | 0.766016 | − | 0.642821i | \(-0.222236\pi\) | ||||
0.766016 | + | 0.642821i | \(0.222236\pi\) | |||||||
\(62\) | 4.80907i | 0.610753i | ||||||||
\(63\) | −6.52728 | + | 3.51998i | −0.822360 | + | 0.443475i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.15208 | −0.142899 | ||||||||
\(66\) | 0.847915 | + | 3.35873i | 0.104371 | + | 0.413431i | ||||
\(67\) | 10.0183i | 1.22393i | 0.790883 | + | 0.611967i | \(0.209622\pi\) | ||||
−0.790883 | + | 0.611967i | \(0.790378\pi\) | |||||||
\(68\) | − | 6.67861i | − | 0.809900i | ||||||
\(69\) | 2.45550 | + | 9.72662i | 0.295607 | + | 1.17095i | ||||
\(70\) | 2.47197i | 0.295457i | ||||||||
\(71\) | 7.24810 | 0.860192 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(72\) | 2.64052 | − | 1.42396i | 0.311188 | − | 0.167815i | ||||
\(73\) | −6.97687 | −0.816581 | −0.408290 | − | 0.912852i | \(-0.633875\pi\) | ||||
−0.408290 | + | 0.912852i | \(0.633875\pi\) | |||||||
\(74\) | − | 11.6614i | − | 1.35561i | ||||||
\(75\) | 1.67936 | − | 0.423958i | 0.193916 | − | 0.0489544i | ||||
\(76\) | 4.35873 | − | 0.0388432i | 0.499980 | − | 0.00445562i | ||||
\(77\) | 4.94393i | 0.563414i | ||||||||
\(78\) | 0.488435 | + | 1.93477i | 0.0553044 | + | 0.219069i | ||||
\(79\) | − | 5.75301i | − | 0.647264i | −0.946183 | − | 0.323632i | \(-0.895096\pi\) | ||
0.946183 | − | 0.323632i | \(-0.104904\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 4.94469 | − | 7.51998i | 0.549410 | − | 0.835553i | ||||
\(82\) | 7.83069 | 0.864755 | ||||||||
\(83\) | 11.1565i | 1.22458i | 0.790632 | + | 0.612292i | \(0.209752\pi\) | ||||
−0.790632 | + | 0.612292i | \(0.790248\pi\) | |||||||
\(84\) | 4.15133 | − | 1.04801i | 0.452947 | − | 0.114347i | ||||
\(85\) | −6.67861 | −0.724397 | ||||||||
\(86\) | −0.978379 | −0.105501 | ||||||||
\(87\) | 5.64052 | − | 1.42396i | 0.604727 | − | 0.152664i | ||||
\(88\) | − | 2.00000i | − | 0.213201i | ||||||
\(89\) | −10.8868 | −1.15399 | −0.576997 | − | 0.816746i | \(-0.695776\pi\) | ||||
−0.576997 | + | 0.816746i | \(0.695776\pi\) | |||||||
\(90\) | −1.42396 | − | 2.64052i | −0.150098 | − | 0.278335i | ||||
\(91\) | 2.84792i | 0.298543i | ||||||||
\(92\) | − | 5.79185i | − | 0.603842i | ||||||
\(93\) | −2.03884 | − | 8.07618i | −0.211418 | − | 0.837461i | ||||
\(94\) | 3.02162i | 0.311656i | ||||||||
\(95\) | −0.0388432 | − | 4.35873i | −0.00398523 | − | 0.447196i | ||||
\(96\) | −1.67936 | + | 0.423958i | −0.171399 | + | 0.0432700i | ||||
\(97\) | 6.94393i | 0.705050i | 0.935802 | + | 0.352525i | \(0.114677\pi\) | ||||
−0.935802 | + | 0.352525i | \(0.885323\pi\) | |||||||
\(98\) | −0.889378 | −0.0898407 | ||||||||
\(99\) | −2.84792 | − | 5.28104i | −0.286226 | − | 0.530764i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 16.3356i | 1.62545i | 0.582646 | + | 0.812726i | \(0.302018\pi\) | ||||
−0.582646 | + | 0.812726i | \(0.697982\pi\) | |||||||
\(102\) | 2.83145 | + | 11.2158i | 0.280355 | + | 1.11053i | ||||
\(103\) | 4.04324i | 0.398392i | 0.979960 | + | 0.199196i | \(0.0638331\pi\) | ||||
−0.979960 | + | 0.199196i | \(0.936167\pi\) | |||||||
\(104\) | − | 1.15208i | − | 0.112971i | ||||||
\(105\) | −1.04801 | − | 4.15133i | −0.102275 | − | 0.405128i | ||||
\(106\) | 2.33710 | 0.227000 | ||||||||
\(107\) | −4.03294 | −0.389879 | −0.194939 | − | 0.980815i | \(-0.562451\pi\) | ||||
−0.194939 | + | 0.980815i | \(0.562451\pi\) | |||||||
\(108\) | −3.83069 | + | 3.51081i | −0.368609 | + | 0.337828i | ||||
\(109\) | − | 7.65699i | − | 0.733406i | −0.930338 | − | 0.366703i | \(-0.880486\pi\) | ||
0.930338 | − | 0.366703i | \(-0.119514\pi\) | |||||||
\(110\) | −2.00000 | −0.190693 | ||||||||
\(111\) | 4.94393 | + | 19.5837i | 0.469257 | + | 1.85880i | ||||
\(112\) | −2.47197 | −0.233579 | ||||||||
\(113\) | 7.08749 | 0.666735 | 0.333368 | − | 0.942797i | \(-0.391815\pi\) | ||||
0.333368 | + | 0.942797i | \(0.391815\pi\) | |||||||
\(114\) | −7.30341 | + | 1.91315i | −0.684027 | + | 0.179183i | ||||
\(115\) | −5.79185 | −0.540093 | ||||||||
\(116\) | −3.35873 | −0.311850 | ||||||||
\(117\) | −1.64052 | − | 3.04210i | −0.151666 | − | 0.281242i | ||||
\(118\) | −12.8076 | −1.17903 | ||||||||
\(119\) | 16.5093i | 1.51341i | ||||||||
\(120\) | 0.423958 | + | 1.67936i | 0.0387019 | + | 0.153304i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 11.9656 | 1.08331 | ||||||||
\(123\) | −13.1506 | + | 3.31988i | −1.18575 | + | 0.299344i | ||||
\(124\) | 4.80907i | 0.431867i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −6.52728 | + | 3.51998i | −0.581496 | + | 0.313584i | ||||
\(127\) | − | 8.71745i | − | 0.773549i | −0.922174 | − | 0.386774i | \(-0.873589\pi\) | ||
0.922174 | − | 0.386774i | \(-0.126411\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.64305 | − | 0.414791i | 0.144663 | − | 0.0365203i | ||||
\(130\) | −1.15208 | −0.101045 | ||||||||
\(131\) | − | 0.795138i | − | 0.0694715i | −0.999397 | − | 0.0347358i | \(-0.988941\pi\) | ||
0.999397 | − | 0.0347358i | \(-0.0110590\pi\) | |||||||
\(132\) | 0.847915 | + | 3.35873i | 0.0738016 | + | 0.292340i | ||||
\(133\) | −10.7746 | + | 0.0960191i | −0.934279 | + | 0.00832591i | ||||
\(134\) | 10.0183i | 0.865452i | ||||||||
\(135\) | 3.51081 | + | 3.83069i | 0.302162 | + | 0.329694i | ||||
\(136\) | − | 6.67861i | − | 0.572686i | ||||||
\(137\) | 14.1480i | 1.20874i | 0.796703 | + | 0.604371i | \(0.206575\pi\) | ||||
−0.796703 | + | 0.604371i | \(0.793425\pi\) | |||||||
\(138\) | 2.45550 | + | 9.72662i | 0.209026 | + | 0.827985i | ||||
\(139\) | −5.39166 | −0.457315 | −0.228657 | − | 0.973507i | \(-0.573434\pi\) | ||||
−0.228657 | + | 0.973507i | \(0.573434\pi\) | |||||||
\(140\) | 2.47197i | 0.208919i | ||||||||
\(141\) | −1.28104 | − | 5.07440i | −0.107883 | − | 0.427341i | ||||
\(142\) | 7.24810 | 0.608247 | ||||||||
\(143\) | −2.30417 | −0.192684 | ||||||||
\(144\) | 2.64052 | − | 1.42396i | 0.220043 | − | 0.118663i | ||||
\(145\) | 3.35873i | 0.278927i | ||||||||
\(146\) | −6.97687 | −0.577410 | ||||||||
\(147\) | 1.49359 | − | 0.377059i | 0.123189 | − | 0.0310993i | ||||
\(148\) | − | 11.6614i | − | 0.958560i | ||||||
\(149\) | 11.0530i | 0.905501i | 0.891637 | + | 0.452750i | \(0.149557\pi\) | ||||
−0.891637 | + | 0.452750i | \(0.850443\pi\) | |||||||
\(150\) | 1.67936 | − | 0.423958i | 0.137119 | − | 0.0346160i | ||||
\(151\) | − | 20.8837i | − | 1.69949i | −0.527190 | − | 0.849747i | \(-0.676754\pi\) | ||
0.527190 | − | 0.849747i | \(-0.323246\pi\) | |||||||
\(152\) | 4.35873 | − | 0.0388432i | 0.353539 | − | 0.00315060i | ||||
\(153\) | −9.51006 | − | 17.6350i | −0.768842 | − | 1.42571i | ||||
\(154\) | 4.94393i | 0.398394i | ||||||||
\(155\) | 4.80907 | 0.386274 | ||||||||
\(156\) | 0.488435 | + | 1.93477i | 0.0391061 | + | 0.154905i | ||||
\(157\) | −1.90838 | −0.152305 | −0.0761526 | − | 0.997096i | \(-0.524264\pi\) | ||||
−0.0761526 | + | 0.997096i | \(0.524264\pi\) | |||||||
\(158\) | − | 5.75301i | − | 0.457685i | ||||||
\(159\) | −3.92485 | + | 0.990834i | −0.311261 | + | 0.0785782i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 14.3173i | 1.12836i | ||||||||
\(162\) | 4.94469 | − | 7.51998i | 0.388491 | − | 0.590825i | ||||
\(163\) | 14.0747 | 1.10241 | 0.551207 | − | 0.834369i | \(-0.314168\pi\) | ||||
0.551207 | + | 0.834369i | \(0.314168\pi\) | |||||||
\(164\) | 7.83069 | 0.611474 | ||||||||
\(165\) | 3.35873 | − | 0.847915i | 0.261476 | − | 0.0660101i | ||||
\(166\) | 11.1565i | 0.865911i | ||||||||
\(167\) | −1.92231 | −0.148753 | −0.0743765 | − | 0.997230i | \(-0.523697\pi\) | ||||
−0.0743765 | + | 0.997230i | \(0.523697\pi\) | |||||||
\(168\) | 4.15133 | − | 1.04801i | 0.320282 | − | 0.0808557i | ||||
\(169\) | 11.6727 | 0.897900 | ||||||||
\(170\) | −6.67861 | −0.512226 | ||||||||
\(171\) | 11.4540 | − | 6.30921i | 0.875909 | − | 0.482477i | ||||
\(172\) | −0.978379 | −0.0746007 | ||||||||
\(173\) | 18.2235 | 1.38550 | 0.692752 | − | 0.721176i | \(-0.256398\pi\) | ||||
0.692752 | + | 0.721176i | \(0.256398\pi\) | |||||||
\(174\) | 5.64052 | − | 1.42396i | 0.427607 | − | 0.107950i | ||||
\(175\) | 2.47197 | 0.186863 | ||||||||
\(176\) | − | 2.00000i | − | 0.150756i | ||||||
\(177\) | 21.5085 | − | 5.42987i | 1.61668 | − | 0.408134i | ||||
\(178\) | −10.8868 | −0.815997 | ||||||||
\(179\) | 4.42722 | 0.330906 | 0.165453 | − | 0.986218i | \(-0.447091\pi\) | ||||
0.165453 | + | 0.986218i | \(0.447091\pi\) | |||||||
\(180\) | −1.42396 | − | 2.64052i | −0.106136 | − | 0.196813i | ||||
\(181\) | − | 7.68190i | − | 0.570991i | −0.958380 | − | 0.285495i | \(-0.907842\pi\) | ||
0.958380 | − | 0.285495i | \(-0.0921581\pi\) | |||||||
\(182\) | 2.84792i | 0.211102i | ||||||||
\(183\) | −20.0945 | + | 5.07289i | −1.48543 | + | 0.374999i | ||||
\(184\) | − | 5.79185i | − | 0.426981i | ||||||
\(185\) | −11.6614 | −0.857362 | ||||||||
\(186\) | −2.03884 | − | 8.07618i | −0.149495 | − | 0.592174i | ||||
\(187\) | −13.3572 | −0.976776 | ||||||||
\(188\) | 3.02162i | 0.220374i | ||||||||
\(189\) | 9.46935 | − | 8.67861i | 0.688794 | − | 0.631276i | ||||
\(190\) | −0.0388432 | − | 4.35873i | −0.00281798 | − | 0.316215i | ||||
\(191\) | − | 24.0153i | − | 1.73769i | −0.495087 | − | 0.868844i | \(-0.664864\pi\) | ||
0.495087 | − | 0.868844i | \(-0.335136\pi\) | |||||||
\(192\) | −1.67936 | + | 0.423958i | −0.121198 | + | 0.0305965i | ||||
\(193\) | − | 21.2018i | − | 1.52614i | −0.646315 | − | 0.763071i | \(-0.723691\pi\) | ||
0.646315 | − | 0.763071i | \(-0.276309\pi\) | |||||||
\(194\) | 6.94393i | 0.498545i | ||||||||
\(195\) | 1.93477 | − | 0.488435i | 0.138552 | − | 0.0349776i | ||||
\(196\) | −0.889378 | −0.0635270 | ||||||||
\(197\) | − | 6.53065i | − | 0.465290i | −0.972562 | − | 0.232645i | \(-0.925262\pi\) | ||
0.972562 | − | 0.232645i | \(-0.0747380\pi\) | |||||||
\(198\) | −2.84792 | − | 5.28104i | −0.202393 | − | 0.375307i | ||||
\(199\) | 13.4020 | 0.950040 | 0.475020 | − | 0.879975i | \(-0.342441\pi\) | ||||
0.475020 | + | 0.879975i | \(0.342441\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.24735 | − | 16.8244i | −0.299585 | − | 1.18670i | ||||
\(202\) | 16.3356i | 1.14937i | ||||||||
\(203\) | 8.30266 | 0.582733 | ||||||||
\(204\) | 2.83145 | + | 11.2158i | 0.198241 | + | 0.785264i | ||||
\(205\) | − | 7.83069i | − | 0.546919i | ||||||
\(206\) | 4.04324i | 0.281706i | ||||||||
\(207\) | −8.24735 | − | 15.2935i | −0.573230 | − | 1.06297i | ||||
\(208\) | − | 1.15208i | − | 0.0798827i | ||||||
\(209\) | −0.0776864 | − | 8.71745i | −0.00537368 | − | 0.602999i | ||||
\(210\) | −1.04801 | − | 4.15133i | −0.0723195 | − | 0.286469i | ||||
\(211\) | 25.9010i | 1.78310i | 0.452926 | + | 0.891548i | \(0.350380\pi\) | ||||
−0.452926 | + | 0.891548i | \(0.649620\pi\) | |||||||
\(212\) | 2.33710 | 0.160513 | ||||||||
\(213\) | −12.1722 | + | 3.07289i | −0.834025 | + | 0.210551i | ||||
\(214\) | −4.03294 | −0.275686 | ||||||||
\(215\) | 0.978379i | 0.0667249i | ||||||||
\(216\) | −3.83069 | + | 3.51081i | −0.260646 | + | 0.238880i | ||||
\(217\) | − | 11.8879i | − | 0.807001i | ||||||
\(218\) | − | 7.65699i | − | 0.518597i | ||||||
\(219\) | 11.7167 | − | 2.95790i | 0.791741 | − | 0.199876i | ||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | −7.69432 | −0.517576 | ||||||||
\(222\) | 4.94393 | + | 19.5837i | 0.331815 | + | 1.31437i | ||||
\(223\) | 8.18680i | 0.548229i | 0.961697 | + | 0.274114i | \(0.0883847\pi\) | ||||
−0.961697 | + | 0.274114i | \(0.911615\pi\) | |||||||
\(224\) | −2.47197 | −0.165165 | ||||||||
\(225\) | −2.64052 | + | 1.42396i | −0.176035 | + | 0.0949305i | ||||
\(226\) | 7.08749 | 0.471453 | ||||||||
\(227\) | 11.6943 | 0.776179 | 0.388090 | − | 0.921622i | \(-0.373135\pi\) | ||||
0.388090 | + | 0.921622i | \(0.373135\pi\) | |||||||
\(228\) | −7.30341 | + | 1.91315i | −0.483680 | + | 0.126701i | ||||
\(229\) | 12.5621 | 0.830126 | 0.415063 | − | 0.909793i | \(-0.363760\pi\) | ||||
0.415063 | + | 0.909793i | \(0.363760\pi\) | |||||||
\(230\) | −5.79185 | −0.381903 | ||||||||
\(231\) | −2.09602 | − | 8.30266i | −0.137908 | − | 0.546275i | ||||
\(232\) | −3.35873 | −0.220511 | ||||||||
\(233\) | 13.0077i | 0.852162i | 0.904685 | + | 0.426081i | \(0.140106\pi\) | ||||
−0.904685 | + | 0.426081i | \(0.859894\pi\) | |||||||
\(234\) | −1.64052 | − | 3.04210i | −0.107244 | − | 0.198868i | ||||
\(235\) | 3.02162 | 0.197109 | ||||||||
\(236\) | −12.8076 | −0.833701 | ||||||||
\(237\) | 2.43903 | + | 9.66139i | 0.158432 | + | 0.627574i | ||||
\(238\) | 16.5093i | 1.07014i | ||||||||
\(239\) | − | 27.0780i | − | 1.75153i | −0.482740 | − | 0.875764i | \(-0.660358\pi\) | ||
0.482740 | − | 0.875764i | \(-0.339642\pi\) | |||||||
\(240\) | 0.423958 | + | 1.67936i | 0.0273664 | + | 0.108402i | ||||
\(241\) | − | 16.2697i | − | 1.04803i | −0.851711 | − | 0.524013i | \(-0.824434\pi\) | ||
0.851711 | − | 0.524013i | \(-0.175566\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | −5.11578 | + | 14.7251i | −0.328177 | + | 0.944616i | ||||
\(244\) | 11.9656 | 0.766016 | ||||||||
\(245\) | 0.889378i | 0.0568203i | ||||||||
\(246\) | −13.1506 | + | 3.31988i | −0.838450 | + | 0.211668i | ||||
\(247\) | −0.0447507 | − | 5.02162i | −0.00284742 | − | 0.319518i | ||||
\(248\) | 4.80907i | 0.305376i | ||||||||
\(249\) | −4.72988 | − | 18.7358i | −0.299744 | − | 1.18733i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | 18.0088i | 1.13671i | 0.822785 | + | 0.568353i | \(0.192419\pi\) | ||||
−0.822785 | + | 0.568353i | \(0.807581\pi\) | |||||||
\(252\) | −6.52728 | + | 3.51998i | −0.411180 | + | 0.221738i | ||||
\(253\) | −11.5837 | −0.728261 | ||||||||
\(254\) | − | 8.71745i | − | 0.546982i | ||||||
\(255\) | 11.2158 | − | 2.83145i | 0.702361 | − | 0.177312i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.639765 | 0.0399075 | 0.0199537 | − | 0.999801i | \(-0.493648\pi\) | ||||
0.0199537 | + | 0.999801i | \(0.493648\pi\) | |||||||
\(258\) | 1.64305 | − | 0.414791i | 0.102292 | − | 0.0258238i | ||||
\(259\) | 28.8266i | 1.79120i | ||||||||
\(260\) | −1.15208 | −0.0714493 | ||||||||
\(261\) | −8.86878 | + | 4.78268i | −0.548964 | + | 0.296041i | ||||
\(262\) | − | 0.795138i | − | 0.0491238i | ||||||
\(263\) | 0.186800i | 0.0115186i | 0.999983 | + | 0.00575928i | \(0.00183325\pi\) | ||||
−0.999983 | + | 0.00575928i | \(0.998167\pi\) | |||||||
\(264\) | 0.847915 | + | 3.35873i | 0.0521856 | + | 0.206715i | ||||
\(265\) | − | 2.33710i | − | 0.143567i | ||||||
\(266\) | −10.7746 | + | 0.0960191i | −0.660635 | + | 0.00588731i | ||||
\(267\) | 18.2828 | − | 4.61553i | 1.11889 | − | 0.282466i | ||||
\(268\) | 10.0183i | 0.611967i | ||||||||
\(269\) | −2.87282 | −0.175159 | −0.0875796 | − | 0.996158i | \(-0.527913\pi\) | ||||
−0.0875796 | + | 0.996158i | \(0.527913\pi\) | |||||||
\(270\) | 3.51081 | + | 3.83069i | 0.213661 | + | 0.233129i | ||||
\(271\) | −15.3557 | −0.932793 | −0.466396 | − | 0.884576i | \(-0.654448\pi\) | ||||
−0.466396 | + | 0.884576i | \(0.654448\pi\) | |||||||
\(272\) | − | 6.67861i | − | 0.404950i | ||||||
\(273\) | −1.20740 | − | 4.78268i | −0.0730749 | − | 0.289461i | ||||
\(274\) | 14.1480i | 0.854709i | ||||||||
\(275\) | 2.00000i | 0.120605i | ||||||||
\(276\) | 2.45550 | + | 9.72662i | 0.147804 | + | 0.585474i | ||||
\(277\) | 4.65370 | 0.279614 | 0.139807 | − | 0.990179i | \(-0.455352\pi\) | ||||
0.139807 | + | 0.990179i | \(0.455352\pi\) | |||||||
\(278\) | −5.39166 | −0.323370 | ||||||||
\(279\) | 6.84792 | + | 12.6985i | 0.409974 | + | 0.760236i | ||||
\(280\) | 2.47197i | 0.147728i | ||||||||
\(281\) | 15.6753 | 0.935111 | 0.467556 | − | 0.883964i | \(-0.345135\pi\) | ||||
0.467556 | + | 0.883964i | \(0.345135\pi\) | |||||||
\(282\) | −1.28104 | − | 5.07440i | −0.0762848 | − | 0.302176i | ||||
\(283\) | 12.4447 | 0.739761 | 0.369881 | − | 0.929079i | \(-0.379399\pi\) | ||||
0.369881 | + | 0.929079i | \(0.379399\pi\) | |||||||
\(284\) | 7.24810 | 0.430096 | ||||||||
\(285\) | 1.91315 | + | 7.30341i | 0.113325 | + | 0.432617i | ||||
\(286\) | −2.30417 | −0.136248 | ||||||||
\(287\) | −19.3572 | −1.14262 | ||||||||
\(288\) | 2.64052 | − | 1.42396i | 0.155594 | − | 0.0839075i | ||||
\(289\) | −27.6038 | −1.62375 | ||||||||
\(290\) | 3.35873i | 0.197231i | ||||||||
\(291\) | −2.94393 | − | 11.6614i | −0.172576 | − | 0.683603i | ||||
\(292\) | −6.97687 | −0.408290 | ||||||||
\(293\) | −3.84312 | −0.224517 | −0.112259 | − | 0.993679i | \(-0.535809\pi\) | ||||
−0.112259 | + | 0.993679i | \(0.535809\pi\) | |||||||
\(294\) | 1.49359 | − | 0.377059i | 0.0871078 | − | 0.0219905i | ||||
\(295\) | 12.8076i | 0.745685i | ||||||||
\(296\) | − | 11.6614i | − | 0.677804i | ||||||
\(297\) | 7.02162 | + | 7.66139i | 0.407436 | + | 0.444559i | ||||
\(298\) | 11.0530i | 0.640286i | ||||||||
\(299\) | −6.67270 | −0.385892 | ||||||||
\(300\) | 1.67936 | − | 0.423958i | 0.0969581 | − | 0.0244772i | ||||
\(301\) | 2.41852 | 0.139401 | ||||||||
\(302\) | − | 20.8837i | − | 1.20172i | ||||||
\(303\) | −6.92560 | − | 27.4334i | −0.397865 | − | 1.57601i | ||||
\(304\) | 4.35873 | − | 0.0388432i | 0.249990 | − | 0.00222781i | ||||
\(305\) | − | 11.9656i | − | 0.685146i | ||||||
\(306\) | −9.51006 | − | 17.6350i | −0.543654 | − | 1.00813i | ||||
\(307\) | 4.19204i | 0.239252i | 0.992819 | + | 0.119626i | \(0.0381696\pi\) | ||||
−0.992819 | + | 0.119626i | \(0.961830\pi\) | |||||||
\(308\) | 4.94393i | 0.281707i | ||||||||
\(309\) | −1.71416 | − | 6.79007i | −0.0975154 | − | 0.386274i | ||||
\(310\) | 4.80907 | 0.273137 | ||||||||
\(311\) | − | 14.8912i | − | 0.844400i | −0.906503 | − | 0.422200i | \(-0.861258\pi\) | ||
0.906503 | − | 0.422200i | \(-0.138742\pi\) | |||||||
\(312\) | 0.488435 | + | 1.93477i | 0.0276522 | + | 0.109535i | ||||
\(313\) | 6.42003 | 0.362882 | 0.181441 | − | 0.983402i | \(-0.441924\pi\) | ||||
0.181441 | + | 0.983402i | \(0.441924\pi\) | |||||||
\(314\) | −1.90838 | −0.107696 | ||||||||
\(315\) | 3.51998 | + | 6.52728i | 0.198328 | + | 0.367770i | ||||
\(316\) | − | 5.75301i | − | 0.323632i | ||||||
\(317\) | −18.0417 | −1.01332 | −0.506662 | − | 0.862145i | \(-0.669121\pi\) | ||||
−0.506662 | + | 0.862145i | \(0.669121\pi\) | |||||||
\(318\) | −3.92485 | + | 0.990834i | −0.220095 | + | 0.0555632i | ||||
\(319\) | 6.71745i | 0.376105i | ||||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 6.77276 | − | 1.70979i | 0.378019 | − | 0.0954314i | ||||
\(322\) | 14.3173i | 0.797870i | ||||||||
\(323\) | −0.259419 | − | 29.1102i | −0.0144344 | − | 1.61974i | ||||
\(324\) | 4.94469 | − | 7.51998i | 0.274705 | − | 0.417776i | ||||
\(325\) | 1.15208i | 0.0639062i | ||||||||
\(326\) | 14.0747 | 0.779524 | ||||||||
\(327\) | 3.24624 | + | 12.8589i | 0.179517 | + | 0.711097i | ||||
\(328\) | 7.83069 | 0.432378 | ||||||||
\(329\) | − | 7.46935i | − | 0.411798i | ||||||
\(330\) | 3.35873 | − | 0.847915i | 0.184892 | − | 0.0466762i | ||||
\(331\) | 23.1176i | 1.27066i | 0.772241 | + | 0.635330i | \(0.219136\pi\) | ||||
−0.772241 | + | 0.635330i | \(0.780864\pi\) | |||||||
\(332\) | 11.1565i | 0.612292i | ||||||||
\(333\) | −16.6053 | − | 30.7921i | −0.909966 | − | 1.68740i | ||||
\(334\) | −1.92231 | −0.105184 | ||||||||
\(335\) | 10.0183 | 0.547360 | ||||||||
\(336\) | 4.15133 | − | 1.04801i | 0.226474 | − | 0.0571736i | ||||
\(337\) | 19.6584i | 1.07086i | 0.844580 | + | 0.535430i | \(0.179850\pi\) | ||||
−0.844580 | + | 0.535430i | \(0.820150\pi\) | |||||||
\(338\) | 11.6727 | 0.634911 | ||||||||
\(339\) | −11.9025 | + | 3.00480i | −0.646454 | + | 0.163198i | ||||
\(340\) | −6.67861 | −0.362198 | ||||||||
\(341\) | 9.61814 | 0.520852 | ||||||||
\(342\) | 11.4540 | − | 6.30921i | 0.619361 | − | 0.341163i | ||||
\(343\) | 19.5023 | 1.05302 | ||||||||
\(344\) | −0.978379 | −0.0527507 | ||||||||
\(345\) | 9.72662 | − | 2.45550i | 0.523664 | − | 0.132200i | ||||
\(346\) | 18.2235 | 0.979700 | ||||||||
\(347\) | 6.62583i | 0.355693i | 0.984058 | + | 0.177847i | \(0.0569131\pi\) | ||||
−0.984058 | + | 0.177847i | \(0.943087\pi\) | |||||||
\(348\) | 5.64052 | − | 1.42396i | 0.302364 | − | 0.0763321i | ||||
\(349\) | −7.09931 | −0.380017 | −0.190009 | − | 0.981782i | \(-0.560852\pi\) | ||||
−0.190009 | + | 0.981782i | \(0.560852\pi\) | |||||||
\(350\) | 2.47197 | 0.132132 | ||||||||
\(351\) | 4.04475 | + | 4.41328i | 0.215893 | + | 0.235564i | ||||
\(352\) | − | 2.00000i | − | 0.106600i | ||||||
\(353\) | − | 8.98278i | − | 0.478105i | −0.971007 | − | 0.239053i | \(-0.923163\pi\) | ||
0.971007 | − | 0.239053i | \(-0.0768368\pi\) | |||||||
\(354\) | 21.5085 | − | 5.42987i | 1.14317 | − | 0.288594i | ||||
\(355\) | − | 7.24810i | − | 0.384689i | ||||||
\(356\) | −10.8868 | −0.576997 | ||||||||
\(357\) | −6.99925 | − | 27.7251i | −0.370439 | − | 1.46737i | ||||
\(358\) | 4.42722 | 0.233986 | ||||||||
\(359\) | 3.28907i | 0.173590i | 0.996226 | + | 0.0867951i | \(0.0276626\pi\) | ||||
−0.996226 | + | 0.0867951i | \(0.972337\pi\) | |||||||
\(360\) | −1.42396 | − | 2.64052i | −0.0750492 | − | 0.139168i | ||||
\(361\) | 18.9970 | − | 0.338614i | 0.999841 | − | 0.0178218i | ||||
\(362\) | − | 7.68190i | − | 0.403752i | ||||||
\(363\) | −11.7555 | + | 2.96770i | −0.617006 | + | 0.155764i | ||||
\(364\) | 2.84792i | 0.149271i | ||||||||
\(365\) | 6.97687i | 0.365186i | ||||||||
\(366\) | −20.0945 | + | 5.07289i | −1.05036 | + | 0.265164i | ||||
\(367\) | 24.1977 | 1.26311 | 0.631555 | − | 0.775331i | \(-0.282417\pi\) | ||||
0.631555 | + | 0.775331i | \(0.282417\pi\) | |||||||
\(368\) | − | 5.79185i | − | 0.301921i | ||||||
\(369\) | 20.6771 | − | 11.1506i | 1.07641 | − | 0.580476i | ||||
\(370\) | −11.6614 | −0.606247 | ||||||||
\(371\) | −5.77725 | −0.299940 | ||||||||
\(372\) | −2.03884 | − | 8.07618i | −0.105709 | − | 0.418730i | ||||
\(373\) | 9.22977i | 0.477899i | 0.971032 | + | 0.238950i | \(0.0768031\pi\) | ||||
−0.971032 | + | 0.238950i | \(0.923197\pi\) | |||||||
\(374\) | −13.3572 | −0.690685 | ||||||||
\(375\) | −0.423958 | − | 1.67936i | −0.0218931 | − | 0.0867219i | ||||
\(376\) | 3.02162i | 0.155828i | ||||||||
\(377\) | 3.86954i | 0.199291i | ||||||||
\(378\) | 9.46935 | − | 8.67861i | 0.487051 | − | 0.446379i | ||||
\(379\) | − | 14.8567i | − | 0.763138i | −0.924340 | − | 0.381569i | \(-0.875384\pi\) | ||
0.924340 | − | 0.381569i | \(-0.124616\pi\) | |||||||
\(380\) | −0.0388432 | − | 4.35873i | −0.00199261 | − | 0.223598i | ||||
\(381\) | 3.69583 | + | 14.6398i | 0.189343 | + | 0.750018i | ||||
\(382\) | − | 24.0153i | − | 1.22873i | ||||||
\(383\) | −36.7079 | −1.87568 | −0.937842 | − | 0.347063i | \(-0.887179\pi\) | ||||
−0.937842 | + | 0.347063i | \(0.887179\pi\) | |||||||
\(384\) | −1.67936 | + | 0.423958i | −0.0856996 | + | 0.0216350i | ||||
\(385\) | 4.94393 | 0.251966 | ||||||||
\(386\) | − | 21.2018i | − | 1.07915i | ||||||
\(387\) | −2.58343 | + | 1.39317i | −0.131323 | + | 0.0708188i | ||||
\(388\) | 6.94393i | 0.352525i | ||||||||
\(389\) | 35.0500i | 1.77711i | 0.458773 | + | 0.888554i | \(0.348289\pi\) | ||||
−0.458773 | + | 0.888554i | \(0.651711\pi\) | |||||||
\(390\) | 1.93477 | − | 0.488435i | 0.0979708 | − | 0.0247329i | ||||
\(391\) | −38.6815 | −1.95621 | ||||||||
\(392\) | −0.889378 | −0.0449204 | ||||||||
\(393\) | 0.337105 | + | 1.33533i | 0.0170047 | + | 0.0673583i | ||||
\(394\) | − | 6.53065i | − | 0.329009i | ||||||
\(395\) | −5.75301 | −0.289465 | ||||||||
\(396\) | −2.84792 | − | 5.28104i | −0.143113 | − | 0.265382i | ||||
\(397\) | −38.0197 | −1.90815 | −0.954077 | − | 0.299560i | \(-0.903160\pi\) | ||||
−0.954077 | + | 0.299560i | \(0.903160\pi\) | |||||||
\(398\) | 13.4020 | 0.671780 | ||||||||
\(399\) | 18.0538 | − | 4.72924i | 0.903821 | − | 0.236758i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 38.5451 | 1.92485 | 0.962426 | − | 0.271544i | \(-0.0875344\pi\) | ||||
0.962426 | + | 0.271544i | \(0.0875344\pi\) | |||||||
\(402\) | −4.24735 | − | 16.8244i | −0.211839 | − | 0.839126i | ||||
\(403\) | 5.54046 | 0.275990 | ||||||||
\(404\) | 16.3356i | 0.812726i | ||||||||
\(405\) | −7.51998 | − | 4.94469i | −0.373671 | − | 0.245704i | ||||
\(406\) | 8.30266 | 0.412054 | ||||||||
\(407\) | −23.3228 | −1.15607 | ||||||||
\(408\) | 2.83145 | + | 11.2158i | 0.140178 | + | 0.555265i | ||||
\(409\) | − | 7.99698i | − | 0.395425i | −0.980260 | − | 0.197713i | \(-0.936649\pi\) | ||
0.980260 | − | 0.197713i | \(-0.0633513\pi\) | |||||||
\(410\) | − | 7.83069i | − | 0.386730i | ||||||
\(411\) | −5.99814 | − | 23.7596i | −0.295866 | − | 1.17197i | ||||
\(412\) | 4.04324i | 0.199196i | ||||||||
\(413\) | 31.6599 | 1.55788 | ||||||||
\(414\) | −8.24735 | − | 15.2935i | −0.405335 | − | 0.751634i | ||||
\(415\) | 11.1565 | 0.547650 | ||||||||
\(416\) | − | 1.15208i | − | 0.0564856i | ||||||
\(417\) | 9.05456 | − | 2.28584i | 0.443404 | − | 0.111938i | ||||
\(418\) | −0.0776864 | − | 8.71745i | −0.00379977 | − | 0.426385i | ||||
\(419\) | − | 24.7144i | − | 1.20738i | −0.797219 | − | 0.603690i | \(-0.793697\pi\) | ||
0.797219 | − | 0.603690i | \(-0.206303\pi\) | |||||||
\(420\) | −1.04801 | − | 4.15133i | −0.0511376 | − | 0.202564i | ||||
\(421\) | 24.1449i | 1.17675i | 0.808587 | + | 0.588376i | \(0.200233\pi\) | ||||
−0.808587 | + | 0.588376i | \(0.799767\pi\) | |||||||
\(422\) | 25.9010i | 1.26084i | ||||||||
\(423\) | 4.30266 | + | 7.97865i | 0.209203 | + | 0.387935i | ||||
\(424\) | 2.33710 | 0.113500 | ||||||||
\(425\) | 6.67861i | 0.323960i | ||||||||
\(426\) | −12.1722 | + | 3.07289i | −0.589745 | + | 0.148882i | ||||
\(427\) | −29.5785 | −1.43140 | ||||||||
\(428\) | −4.03294 | −0.194939 | ||||||||
\(429\) | 3.86954 | − | 0.976870i | 0.186823 | − | 0.0471637i | ||||
\(430\) | 0.978379i | 0.0471816i | ||||||||
\(431\) | 34.6748 | 1.67022 | 0.835112 | − | 0.550080i | \(-0.185403\pi\) | ||||
0.835112 | + | 0.550080i | \(0.185403\pi\) | |||||||
\(432\) | −3.83069 | + | 3.51081i | −0.184304 | + | 0.168914i | ||||
\(433\) | 1.77653i | 0.0853748i | 0.999088 | + | 0.0426874i | \(0.0135920\pi\) | ||||
−0.999088 | + | 0.0426874i | \(0.986408\pi\) | |||||||
\(434\) | − | 11.8879i | − | 0.570636i | ||||||
\(435\) | −1.42396 | − | 5.64052i | −0.0682735 | − | 0.270442i | ||||
\(436\) | − | 7.65699i | − | 0.366703i | ||||||
\(437\) | −0.224974 | − | 25.2451i | −0.0107620 | − | 1.20764i | ||||
\(438\) | 11.7167 | − | 2.95790i | 0.559845 | − | 0.141334i | ||||
\(439\) | 11.1997i | 0.534534i | 0.963623 | + | 0.267267i | \(0.0861205\pi\) | ||||
−0.963623 | + | 0.267267i | \(0.913879\pi\) | |||||||
\(440\) | −2.00000 | −0.0953463 | ||||||||
\(441\) | −2.34842 | + | 1.26644i | −0.111830 | + | 0.0603065i | ||||
\(442\) | −7.69432 | −0.365982 | ||||||||
\(443\) | 0.969683i | 0.0460711i | 0.999735 | + | 0.0230355i | \(0.00733308\pi\) | ||||
−0.999735 | + | 0.0230355i | \(0.992667\pi\) | |||||||
\(444\) | 4.94393 | + | 19.5837i | 0.234629 | + | 0.929401i | ||||
\(445\) | 10.8868i | 0.516082i | ||||||||
\(446\) | 8.18680i | 0.387656i | ||||||||
\(447\) | −4.68602 | − | 18.5621i | −0.221641 | − | 0.877956i | ||||
\(448\) | −2.47197 | −0.116789 | ||||||||
\(449\) | −19.1168 | −0.902178 | −0.451089 | − | 0.892479i | \(-0.648964\pi\) | ||||
−0.451089 | + | 0.892479i | \(0.648964\pi\) | |||||||
\(450\) | −2.64052 | + | 1.42396i | −0.124475 | + | 0.0671260i | ||||
\(451\) | − | 15.6614i | − | 0.737466i | ||||||
\(452\) | 7.08749 | 0.333368 | ||||||||
\(453\) | 8.85382 | + | 35.0714i | 0.415989 | + | 1.64780i | ||||
\(454\) | 11.6943 | 0.548842 | ||||||||
\(455\) | 2.84792 | 0.133512 | ||||||||
\(456\) | −7.30341 | + | 1.91315i | −0.342014 | + | 0.0895913i | ||||
\(457\) | 11.1292 | 0.520603 | 0.260302 | − | 0.965527i | \(-0.416178\pi\) | ||||
0.260302 | + | 0.965527i | \(0.416178\pi\) | |||||||
\(458\) | 12.5621 | 0.586987 | ||||||||
\(459\) | 23.4473 | + | 25.5837i | 1.09443 | + | 1.19414i | ||||
\(460\) | −5.79185 | −0.270046 | ||||||||
\(461\) | 21.2861i | 0.991393i | 0.868496 | + | 0.495696i | \(0.165087\pi\) | ||||
−0.868496 | + | 0.495696i | \(0.834913\pi\) | |||||||
\(462\) | −2.09602 | − | 8.30266i | −0.0975156 | − | 0.386275i | ||||
\(463\) | 14.2060 | 0.660208 | 0.330104 | − | 0.943945i | \(-0.392916\pi\) | ||||
0.330104 | + | 0.943945i | \(0.392916\pi\) | |||||||
\(464\) | −3.35873 | −0.155925 | ||||||||
\(465\) | −8.07618 | + | 2.03884i | −0.374524 | + | 0.0945491i | ||||
\(466\) | 13.0077i | 0.602569i | ||||||||
\(467\) | − | 9.15124i | − | 0.423469i | −0.977327 | − | 0.211735i | \(-0.932089\pi\) | ||
0.977327 | − | 0.211735i | \(-0.0679112\pi\) | |||||||
\(468\) | −1.64052 | − | 3.04210i | −0.0758331 | − | 0.140621i | ||||
\(469\) | − | 24.7650i | − | 1.14354i | ||||||
\(470\) | 3.02162 | 0.139377 | ||||||||
\(471\) | 3.20486 | − | 0.809072i | 0.147672 | − | 0.0372801i | ||||
\(472\) | −12.8076 | −0.589516 | ||||||||
\(473\) | 1.95676i | 0.0899718i | ||||||||
\(474\) | 2.43903 | + | 9.66139i | 0.112028 | + | 0.443762i | ||||
\(475\) | −4.35873 | + | 0.0388432i | −0.199992 | + | 0.00178225i | ||||
\(476\) | 16.5093i | 0.756703i | ||||||||
\(477\) | 6.17117 | − | 3.32794i | 0.282559 | − | 0.152376i | ||||
\(478\) | − | 27.0780i | − | 1.23852i | ||||||
\(479\) | 1.58672i | 0.0724990i | 0.999343 | + | 0.0362495i | \(0.0115411\pi\) | ||||
−0.999343 | + | 0.0362495i | \(0.988459\pi\) | |||||||
\(480\) | 0.423958 | + | 1.67936i | 0.0193509 | + | 0.0766521i | ||||
\(481\) | −13.4349 | −0.612579 | ||||||||
\(482\) | − | 16.2697i | − | 0.741066i | ||||||
\(483\) | −6.06991 | − | 24.0439i | −0.276191 | − | 1.09403i | ||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 6.94393 | 0.315308 | ||||||||
\(486\) | −5.11578 | + | 14.7251i | −0.232056 | + | 0.667945i | ||||
\(487\) | − | 16.6398i | − | 0.754020i | −0.926209 | − | 0.377010i | \(-0.876952\pi\) | ||
0.926209 | − | 0.377010i | \(-0.123048\pi\) | |||||||
\(488\) | 11.9656 | 0.541655 | ||||||||
\(489\) | −23.6365 | + | 5.96706i | −1.06888 | + | 0.269840i | ||||
\(490\) | 0.889378i | 0.0401780i | ||||||||
\(491\) | − | 7.42611i | − | 0.335135i | −0.985861 | − | 0.167568i | \(-0.946409\pi\) | ||
0.985861 | − | 0.167568i | \(-0.0535913\pi\) | |||||||
\(492\) | −13.1506 | + | 3.31988i | −0.592874 | + | 0.149672i | ||||
\(493\) | 22.4316i | 1.01027i | ||||||||
\(494\) | −0.0447507 | − | 5.02162i | −0.00201343 | − | 0.225933i | ||||
\(495\) | −5.28104 | + | 2.84792i | −0.237365 | + | 0.128004i | ||||
\(496\) | 4.80907i | 0.215934i | ||||||||
\(497\) | −17.9171 | −0.803691 | ||||||||
\(498\) | −4.72988 | − | 18.7358i | −0.211951 | − | 0.839571i | ||||
\(499\) | 13.5178 | 0.605141 | 0.302571 | − | 0.953127i | \(-0.402155\pi\) | ||||
0.302571 | + | 0.953127i | \(0.402155\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 3.22826 | − | 0.814980i | 0.144228 | − | 0.0364106i | ||||
\(502\) | 18.0088i | 0.803772i | ||||||||
\(503\) | 24.4696i | 1.09105i | 0.838096 | + | 0.545523i | \(0.183669\pi\) | ||||
−0.838096 | + | 0.545523i | \(0.816331\pi\) | |||||||
\(504\) | −6.52728 | + | 3.51998i | −0.290748 | + | 0.156792i | ||||
\(505\) | 16.3356 | 0.726924 | ||||||||
\(506\) | −11.5837 | −0.514958 | ||||||||
\(507\) | −19.6027 | + | 4.94873i | −0.870587 | + | 0.219781i | ||||
\(508\) | − | 8.71745i | − | 0.386774i | ||||||
\(509\) | −24.0249 | −1.06488 | −0.532441 | − | 0.846467i | \(-0.678725\pi\) | ||||
−0.532441 | + | 0.846467i | \(0.678725\pi\) | |||||||
\(510\) | 11.2158 | − | 2.83145i | 0.496644 | − | 0.125379i | ||||
\(511\) | 17.2466 | 0.762944 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −16.5606 | + | 15.4515i | −0.731167 | + | 0.682198i | ||||
\(514\) | 0.639765 | 0.0282188 | ||||||||
\(515\) | 4.04324 | 0.178167 | ||||||||
\(516\) | 1.64305 | − | 0.414791i | 0.0723314 | − | 0.0182602i | ||||
\(517\) | 6.04324 | 0.265781 | ||||||||
\(518\) | 28.8266i | 1.26657i | ||||||||
\(519\) | −30.6038 | + | 7.72598i | −1.34336 | + | 0.339133i | ||||
\(520\) | −1.15208 | −0.0505223 | ||||||||
\(521\) | 26.4016 | 1.15667 | 0.578337 | − | 0.815798i | \(-0.303702\pi\) | ||||
0.578337 | + | 0.815798i | \(0.303702\pi\) | |||||||
\(522\) | −8.86878 | + | 4.78268i | −0.388176 | + | 0.209332i | ||||
\(523\) | − | 3.26120i | − | 0.142602i | −0.997455 | − | 0.0713011i | \(-0.977285\pi\) | ||
0.997455 | − | 0.0713011i | \(-0.0227151\pi\) | |||||||
\(524\) | − | 0.795138i | − | 0.0347358i | ||||||
\(525\) | −4.15133 | + | 1.04801i | −0.181179 | + | 0.0457389i | ||||
\(526\) | 0.186800i | 0.00814486i | ||||||||
\(527\) | 32.1179 | 1.39908 | ||||||||
\(528\) | 0.847915 | + | 3.35873i | 0.0369008 | + | 0.146170i | ||||
\(529\) | −10.5455 | −0.458501 | ||||||||
\(530\) | − | 2.33710i | − | 0.101517i | ||||||
\(531\) | −33.8186 | + | 18.2374i | −1.46760 | + | 0.791437i | ||||
\(532\) | −10.7746 | + | 0.0960191i | −0.467139 | + | 0.00416296i | ||||
\(533\) | − | 9.02162i | − | 0.390770i | ||||||
\(534\) | 18.2828 | − | 4.61553i | 0.791175 | − | 0.199733i | ||||
\(535\) | 4.03294i | 0.174359i | ||||||||
\(536\) | 10.0183i | 0.432726i | ||||||||
\(537\) | −7.43490 | + | 1.87695i | −0.320840 | + | 0.0809965i | ||||
\(538\) | −2.87282 | −0.123856 | ||||||||
\(539\) | 1.77876i | 0.0766164i | ||||||||
\(540\) | 3.51081 | + | 3.83069i | 0.151081 | + | 0.164847i | ||||
\(541\) | −39.2677 | −1.68825 | −0.844125 | − | 0.536146i | \(-0.819880\pi\) | ||||
−0.844125 | + | 0.536146i | \(0.819880\pi\) | |||||||
\(542\) | −15.3557 | −0.659584 | ||||||||
\(543\) | 3.25680 | + | 12.9007i | 0.139763 | + | 0.553622i | ||||
\(544\) | − | 6.67861i | − | 0.286343i | ||||||
\(545\) | −7.65699 | −0.327989 | ||||||||
\(546\) | −1.20740 | − | 4.78268i | −0.0516718 | − | 0.204680i | ||||
\(547\) | 40.5656i | 1.73446i | 0.497907 | + | 0.867231i | \(0.334102\pi\) | ||||
−0.497907 | + | 0.867231i | \(0.665898\pi\) | |||||||
\(548\) | 14.1480i | 0.604371i | ||||||||
\(549\) | 31.5953 | − | 17.0384i | 1.34845 | − | 0.727183i | ||||
\(550\) | 2.00000i | 0.0852803i | ||||||||
\(551\) | −14.6398 | + | 0.130464i | −0.623675 | + | 0.00555794i | ||||
\(552\) | 2.45550 | + | 9.72662i | 0.104513 | + | 0.413992i | ||||
\(553\) | 14.2212i | 0.604749i | ||||||||
\(554\) | 4.65370 | 0.197717 | ||||||||
\(555\) | 19.5837 | − | 4.94393i | 0.831282 | − | 0.209858i | ||||
\(556\) | −5.39166 | −0.228657 | ||||||||
\(557\) | 28.4844i | 1.20692i | 0.797392 | + | 0.603461i | \(0.206212\pi\) | ||||
−0.797392 | + | 0.603461i | \(0.793788\pi\) | |||||||
\(558\) | 6.84792 | + | 12.6985i | 0.289895 | + | 0.537568i | ||||
\(559\) | 1.12718i | 0.0476744i | ||||||||
\(560\) | 2.47197i | 0.104460i | ||||||||
\(561\) | 22.4316 | − | 5.66290i | 0.947064 | − | 0.239088i | ||||
\(562\) | 15.6753 | 0.661223 | ||||||||
\(563\) | 13.8600 | 0.584129 | 0.292065 | − | 0.956399i | \(-0.405658\pi\) | ||||
0.292065 | + | 0.956399i | \(0.405658\pi\) | |||||||
\(564\) | −1.28104 | − | 5.07440i | −0.0539415 | − | 0.213671i | ||||
\(565\) | − | 7.08749i | − | 0.298173i | ||||||
\(566\) | 12.4447 | 0.523090 | ||||||||
\(567\) | −12.2231 | + | 18.5891i | −0.513322 | + | 0.780670i | ||||
\(568\) | 7.24810 | 0.304124 | ||||||||
\(569\) | −33.5750 | −1.40754 | −0.703769 | − | 0.710429i | \(-0.748501\pi\) | ||||
−0.703769 | + | 0.710429i | \(0.748501\pi\) | |||||||
\(570\) | 1.91315 | + | 7.30341i | 0.0801329 | + | 0.305906i | ||||
\(571\) | −36.9527 | −1.54642 | −0.773212 | − | 0.634148i | \(-0.781351\pi\) | ||||
−0.773212 | + | 0.634148i | \(0.781351\pi\) | |||||||
\(572\) | −2.30417 | −0.0963422 | ||||||||
\(573\) | 10.1815 | + | 40.3304i | 0.425337 | + | 1.68483i | ||||
\(574\) | −19.3572 | −0.807955 | ||||||||
\(575\) | 5.79185i | 0.241537i | ||||||||
\(576\) | 2.64052 | − | 1.42396i | 0.110022 | − | 0.0593316i | ||||
\(577\) | 44.3839 | 1.84773 | 0.923863 | − | 0.382723i | \(-0.125014\pi\) | ||||
0.923863 | + | 0.382723i | \(0.125014\pi\) | |||||||
\(578\) | −27.6038 | −1.14817 | ||||||||
\(579\) | 8.98869 | + | 35.6056i | 0.373557 | + | 1.47972i | ||||
\(580\) | 3.35873i | 0.139464i | ||||||||
\(581\) | − | 27.5785i | − | 1.14415i | ||||||
\(582\) | −2.94393 | − | 11.6614i | −0.122030 | − | 0.483380i | ||||
\(583\) | − | 4.67421i | − | 0.193586i | ||||||
\(584\) | −6.97687 | −0.288705 | ||||||||
\(585\) | −3.04210 | + | 1.64052i | −0.125775 | + | 0.0678271i | ||||
\(586\) | −3.84312 | −0.158758 | ||||||||
\(587\) | 17.5003i | 0.722316i | 0.932505 | + | 0.361158i | \(0.117619\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882381\pi\) | |||||||
\(588\) | 1.49359 | − | 0.377059i | 0.0615945 | − | 0.0155496i | ||||
\(589\) | 0.186800 | + | 20.9614i | 0.00769695 | + | 0.863701i | ||||
\(590\) | 12.8076i | 0.527279i | ||||||||
\(591\) | 2.76872 | + | 10.9673i | 0.113890 | + | 0.451136i | ||||
\(592\) | − | 11.6614i | − | 0.479280i | ||||||
\(593\) | 16.9212i | 0.694871i | 0.937704 | + | 0.347435i | \(0.112947\pi\) | ||||
−0.937704 | + | 0.347435i | \(0.887053\pi\) | |||||||
\(594\) | 7.02162 | + | 7.66139i | 0.288101 | + | 0.314350i | ||||
\(595\) | 16.5093 | 0.676815 | ||||||||
\(596\) | 11.0530i | 0.452750i | ||||||||
\(597\) | −22.5068 | + | 5.68187i | −0.921141 | + | 0.232543i | ||||
\(598\) | −6.67270 | −0.272867 | ||||||||
\(599\) | 29.6928 | 1.21322 | 0.606608 | − | 0.795001i | \(-0.292530\pi\) | ||||
0.606608 | + | 0.795001i | \(0.292530\pi\) | |||||||
\(600\) | 1.67936 | − | 0.423958i | 0.0685597 | − | 0.0173080i | ||||
\(601\) | 33.0304i | 1.34734i | 0.739033 | + | 0.673669i | \(0.235283\pi\) | ||||
−0.739033 | + | 0.673669i | \(0.764717\pi\) | |||||||
\(602\) | 2.41852 | 0.0985716 | ||||||||
\(603\) | 14.2657 | + | 26.4536i | 0.580943 | + | 1.07727i | ||||
\(604\) | − | 20.8837i | − | 0.849747i | ||||||
\(605\) | − | 7.00000i | − | 0.284590i | ||||||
\(606\) | −6.92560 | − | 27.4334i | −0.281333 | − | 1.11441i | ||||
\(607\) | − | 4.60310i | − | 0.186834i | −0.995627 | − | 0.0934170i | \(-0.970221\pi\) | ||
0.995627 | − | 0.0934170i | \(-0.0297790\pi\) | |||||||
\(608\) | 4.35873 | − | 0.0388432i | 0.176770 | − | 0.00157530i | ||||
\(609\) | −13.9432 | + | 3.51998i | −0.565006 | + | 0.142637i | ||||
\(610\) | − | 11.9656i | − | 0.484471i | ||||||
\(611\) | 3.48116 | 0.140833 | ||||||||
\(612\) | −9.51006 | − | 17.6350i | −0.384421 | − | 0.712853i | ||||
\(613\) | 20.0293 | 0.808976 | 0.404488 | − | 0.914543i | \(-0.367450\pi\) | ||||
0.404488 | + | 0.914543i | \(0.367450\pi\) | |||||||
\(614\) | 4.19204i | 0.169177i | ||||||||
\(615\) | 3.31988 | + | 13.1506i | 0.133871 | + | 0.530282i | ||||
\(616\) | 4.94393i | 0.199197i | ||||||||
\(617\) | 25.3918i | 1.02223i | 0.859511 | + | 0.511117i | \(0.170768\pi\) | ||||
−0.859511 | + | 0.511117i | \(0.829232\pi\) | |||||||
\(618\) | −1.71416 | − | 6.79007i | −0.0689538 | − | 0.273137i | ||||
\(619\) | −12.8662 | −0.517138 | −0.258569 | − | 0.965993i | \(-0.583251\pi\) | ||||
−0.258569 | + | 0.965993i | \(0.583251\pi\) | |||||||
\(620\) | 4.80907 | 0.193137 | ||||||||
\(621\) | 20.3341 | + | 22.1868i | 0.815979 | + | 0.890326i | ||||
\(622\) | − | 14.8912i | − | 0.597081i | ||||||
\(623\) | 26.9117 | 1.07819 | ||||||||
\(624\) | 0.488435 | + | 1.93477i | 0.0195531 | + | 0.0774527i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.42003 | 0.256596 | ||||||||
\(627\) | 3.82629 | + | 14.6068i | 0.152807 | + | 0.583341i | ||||
\(628\) | −1.90838 | −0.0761526 | ||||||||
\(629\) | −77.8818 | −3.10535 | ||||||||
\(630\) | 3.51998 | + | 6.52728i | 0.140239 | + | 0.260053i | ||||
\(631\) | −18.8977 | −0.752305 | −0.376152 | − | 0.926558i | \(-0.622753\pi\) | ||||
−0.376152 | + | 0.926558i | \(0.622753\pi\) | |||||||
\(632\) | − | 5.75301i | − | 0.228842i | ||||||
\(633\) | −10.9809 | − | 43.4971i | −0.436452 | − | 1.72886i | ||||
\(634\) | −18.0417 | −0.716529 | ||||||||
\(635\) | −8.71745 | −0.345942 | ||||||||
\(636\) | −3.92485 | + | 0.990834i | −0.155630 | + | 0.0392891i | ||||
\(637\) | 1.02464i | 0.0405977i | ||||||||
\(638\) | 6.71745i | 0.265946i | ||||||||
\(639\) | 19.1388 | − | 10.3210i | 0.757118 | − | 0.408292i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | −27.2430 | −1.07603 | −0.538016 | − | 0.842934i | \(-0.680826\pi\) | ||||
−0.538016 | + | 0.842934i | \(0.680826\pi\) | |||||||
\(642\) | 6.77276 | − | 1.70979i | 0.267300 | − | 0.0674802i | ||||
\(643\) | 16.5342 | 0.652046 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(644\) | 14.3173i | 0.564179i | ||||||||
\(645\) | −0.414791 | − | 1.64305i | −0.0163324 | − | 0.0646952i | ||||
\(646\) | −0.259419 | − | 29.1102i | −0.0102067 | − | 1.14533i | ||||
\(647\) | − | 47.6797i | − | 1.87448i | −0.348681 | − | 0.937242i | \(-0.613370\pi\) | ||
0.348681 | − | 0.937242i | \(-0.386630\pi\) | |||||||
\(648\) | 4.94469 | − | 7.51998i | 0.194246 | − | 0.295413i | ||||
\(649\) | 25.6151i | 1.00548i | ||||||||
\(650\) | 1.15208i | 0.0451885i | ||||||||
\(651\) | 5.03995 | + | 19.9640i | 0.197531 | + | 0.782453i | ||||
\(652\) | 14.0747 | 0.551207 | ||||||||
\(653\) | − | 19.5374i | − | 0.764559i | −0.924047 | − | 0.382280i | \(-0.875139\pi\) | ||
0.924047 | − | 0.382280i | \(-0.124861\pi\) | |||||||
\(654\) | 3.24624 | + | 12.8589i | 0.126938 | + | 0.502821i | ||||
\(655\) | −0.795138 | −0.0310686 | ||||||||
\(656\) | 7.83069 | 0.305737 | ||||||||
\(657\) | −18.4226 | + | 9.93477i | −0.718733 | + | 0.387592i | ||||
\(658\) | − | 7.46935i | − | 0.291186i | ||||||
\(659\) | −25.0743 | −0.976755 | −0.488377 | − | 0.872632i | \(-0.662411\pi\) | ||||
−0.488377 | + | 0.872632i | \(0.662411\pi\) | |||||||
\(660\) | 3.35873 | − | 0.847915i | 0.130738 | − | 0.0330051i | ||||
\(661\) | 23.2407i | 0.903958i | 0.892029 | + | 0.451979i | \(0.149282\pi\) | ||||
−0.892029 | + | 0.451979i | \(0.850718\pi\) | |||||||
\(662\) | 23.1176i | 0.898493i | ||||||||
\(663\) | 12.9216 | − | 3.26207i | 0.501832 | − | 0.126688i | ||||
\(664\) | 11.1565i | 0.432956i | ||||||||
\(665\) | 0.0960191 | + | 10.7746i | 0.00372346 | + | 0.417822i | ||||
\(666\) | −16.6053 | − | 30.7921i | −0.643443 | − | 1.19317i | ||||
\(667\) | 19.4532i | 0.753232i | ||||||||
\(668\) | −1.92231 | −0.0743765 | ||||||||
\(669\) | −3.47086 | − | 13.7486i | −0.134191 | − | 0.531552i | ||||
\(670\) | 10.0183 | 0.387042 | ||||||||
\(671\) | − | 23.9311i | − | 0.923850i | ||||||
\(672\) | 4.15133 | − | 1.04801i | 0.160141 | − | 0.0404278i | ||||
\(673\) | 14.2491i | 0.549263i | 0.961550 | + | 0.274631i | \(0.0885558\pi\) | ||||
−0.961550 | + | 0.274631i | \(0.911444\pi\) | |||||||
\(674\) | 19.6584i | 0.757212i | ||||||||
\(675\) | 3.83069 | − | 3.51081i | 0.147443 | − | 0.135131i | ||||
\(676\) | 11.6727 | 0.448950 | ||||||||
\(677\) | 14.9372 | 0.574083 | 0.287041 | − | 0.957918i | \(-0.407328\pi\) | ||||
0.287041 | + | 0.957918i | \(0.407328\pi\) | |||||||
\(678\) | −11.9025 | + | 3.00480i | −0.457112 | + | 0.115399i | ||||
\(679\) | − | 17.1652i | − | 0.658739i | ||||||
\(680\) | −6.67861 | −0.256113 | ||||||||
\(681\) | −19.6390 | + | 4.95790i | −0.752569 | + | 0.189987i | ||||
\(682\) | 9.61814 | 0.368298 | ||||||||
\(683\) | −31.9940 | −1.22422 | −0.612108 | − | 0.790775i | \(-0.709678\pi\) | ||||
−0.612108 | + | 0.790775i | \(0.709678\pi\) | |||||||
\(684\) | 11.4540 | − | 6.30921i | 0.437954 | − | 0.241239i | ||||
\(685\) | 14.1480 | 0.540566 | ||||||||
\(686\) | 19.5023 | 0.744601 | ||||||||
\(687\) | −21.0963 | + | 5.32579i | −0.804874 | + | 0.203192i | ||||
\(688\) | −0.978379 | −0.0373004 | ||||||||
\(689\) | − | 2.69254i | − | 0.102578i | ||||||
\(690\) | 9.72662 | − | 2.45550i | 0.370286 | − | 0.0934793i | ||||
\(691\) | −25.8879 | −0.984821 | −0.492410 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492410 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(692\) | 18.2235 | 0.692752 | ||||||||
\(693\) | 7.03995 | + | 13.0546i | 0.267426 | + | 0.495902i | ||||
\(694\) | 6.62583i | 0.251513i | ||||||||
\(695\) | 5.39166i | 0.204517i | ||||||||
\(696\) | 5.64052 | − | 1.42396i | 0.213803 | − | 0.0539750i | ||||
\(697\) | − | 52.2981i | − | 1.98093i | ||||||
\(698\) | −7.09931 | −0.268713 | ||||||||
\(699\) | −5.51471 | − | 21.8446i | −0.208585 | − | 0.826240i | ||||
\(700\) | 2.47197 | 0.0934316 | ||||||||
\(701\) | − | 35.2765i | − | 1.33238i | −0.745784 | − | 0.666188i | \(-0.767925\pi\) | ||
0.745784 | − | 0.666188i | \(-0.232075\pi\) | |||||||
\(702\) | 4.04475 | + | 4.41328i | 0.152659 | + | 0.166569i | ||||
\(703\) | −0.452966 | − | 50.8288i | −0.0170839 | − | 1.91704i | ||||
\(704\) | − | 2.00000i | − | 0.0753778i | ||||||
\(705\) | −5.07440 | + | 1.28104i | −0.191113 | + | 0.0482467i | ||||
\(706\) | − | 8.98278i | − | 0.338071i | ||||||
\(707\) | − | 40.3811i | − | 1.51869i | ||||||
\(708\) | 21.5085 | − | 5.42987i | 0.808341 | − | 0.204067i | ||||
\(709\) | −25.1425 | −0.944248 | −0.472124 | − | 0.881532i | \(-0.656513\pi\) | ||||
−0.472124 | + | 0.881532i | \(0.656513\pi\) | |||||||
\(710\) | − | 7.24810i | − | 0.272016i | ||||||
\(711\) | −8.19204 | − | 15.1909i | −0.307225 | − | 0.569704i | ||||
\(712\) | −10.8868 | −0.407999 | ||||||||
\(713\) | 27.8534 | 1.04312 | ||||||||
\(714\) | −6.99925 | − | 27.7251i | −0.261940 | − | 1.03759i | ||||
\(715\) | 2.30417i | 0.0861710i | ||||||||
\(716\) | 4.42722 | 0.165453 | ||||||||
\(717\) | 11.4799 | + | 45.4737i | 0.428725 | + | 1.69825i | ||||
\(718\) | 3.28907i | 0.122747i | ||||||||
\(719\) | − | 2.66769i | − | 0.0994881i | −0.998762 | − | 0.0497441i | \(-0.984159\pi\) | ||
0.998762 | − | 0.0497441i | \(-0.0158406\pi\) | |||||||
\(720\) | −1.42396 | − | 2.64052i | −0.0530678 | − | 0.0984064i | ||||
\(721\) | − | 9.99476i | − | 0.372224i | ||||||
\(722\) | 18.9970 | − | 0.338614i | 0.706994 | − | 0.0126019i | ||||
\(723\) | 6.89768 | + | 27.3228i | 0.256527 | + | 1.01614i | ||||
\(724\) | − | 7.68190i | − | 0.285495i | ||||||
\(725\) | 3.35873 | 0.124740 | ||||||||
\(726\) | −11.7555 | + | 2.96770i | −0.436289 | + | 0.110142i | ||||
\(727\) | −27.8554 | −1.03310 | −0.516549 | − | 0.856257i | \(-0.672784\pi\) | ||||
−0.516549 | + | 0.856257i | \(0.672784\pi\) | |||||||
\(728\) | 2.84792i | 0.105551i | ||||||||
\(729\) | 2.34842 | − | 26.8977i | 0.0869785 | − | 0.996210i | ||||
\(730\) | 6.97687i | 0.258226i | ||||||||
\(731\) | 6.53421i | 0.241677i | ||||||||
\(732\) | −20.0945 | + | 5.07289i | −0.742714 | + | 0.187499i | ||||
\(733\) | 51.5235 | 1.90306 | 0.951532 | − | 0.307550i | \(-0.0995090\pi\) | ||||
0.951532 | + | 0.307550i | \(0.0995090\pi\) | |||||||
\(734\) | 24.1977 | 0.893154 | ||||||||
\(735\) | −0.377059 | − | 1.49359i | −0.0139080 | − | 0.0550918i | ||||
\(736\) | − | 5.79185i | − | 0.213490i | ||||||
\(737\) | 20.0367 | 0.738060 | ||||||||
\(738\) | 20.6771 | − | 11.1506i | 0.761135 | − | 0.410458i | ||||
\(739\) | 10.0036 | 0.367987 | 0.183993 | − | 0.982927i | \(-0.441097\pi\) | ||||
0.183993 | + | 0.982927i | \(0.441097\pi\) | |||||||
\(740\) | −11.6614 | −0.428681 | ||||||||
\(741\) | 2.20411 | + | 8.41415i | 0.0809699 | + | 0.309102i | ||||
\(742\) | −5.77725 | −0.212089 | ||||||||
\(743\) | 9.92533 | 0.364125 | 0.182063 | − | 0.983287i | \(-0.441723\pi\) | ||||
0.182063 | + | 0.983287i | \(0.441723\pi\) | |||||||
\(744\) | −2.03884 | − | 8.07618i | −0.0747476 | − | 0.296087i | ||||
\(745\) | 11.0530 | 0.404952 | ||||||||
\(746\) | 9.22977i | 0.337926i | ||||||||
\(747\) | 15.8864 | + | 29.4589i | 0.581252 | + | 1.07785i | ||||
\(748\) | −13.3572 | −0.488388 | ||||||||
\(749\) | 9.96929 | 0.364270 | ||||||||
\(750\) | −0.423958 | − | 1.67936i | −0.0154807 | − | 0.0613217i | ||||
\(751\) | − | 52.5936i | − | 1.91917i | −0.281422 | − | 0.959584i | \(-0.590806\pi\) | ||
0.281422 | − | 0.959584i | \(-0.409194\pi\) | |||||||
\(752\) | 3.02162i | 0.110187i | ||||||||
\(753\) | −7.63497 | − | 30.2433i | −0.278234 | − | 1.10213i | ||||
\(754\) | 3.86954i | 0.140920i | ||||||||
\(755\) | −20.8837 | −0.760037 | ||||||||
\(756\) | 9.46935 | − | 8.67861i | 0.344397 | − | 0.315638i | ||||
\(757\) | −7.97949 | −0.290019 | −0.145010 | − | 0.989430i | \(-0.546321\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546321\pi\) | |||||||
\(758\) | − | 14.8567i | − | 0.539620i | ||||||
\(759\) | 19.4532 | − | 4.91100i | 0.706108 | − | 0.178258i | ||||
\(760\) | −0.0388432 | − | 4.35873i | −0.00140899 | − | 0.158108i | ||||
\(761\) | 18.8069i | 0.681749i | 0.940109 | + | 0.340875i | \(0.110723\pi\) | ||||
−0.940109 | + | 0.340875i | \(0.889277\pi\) | |||||||
\(762\) | 3.69583 | + | 14.6398i | 0.133886 | + | 0.530343i | ||||
\(763\) | 18.9278i | 0.685233i | ||||||||
\(764\) | − | 24.0153i | − | 0.868844i | ||||||
\(765\) | −17.6350 | + | 9.51006i | −0.637595 | + | 0.343837i | ||||
\(766\) | −36.7079 | −1.32631 | ||||||||
\(767\) | 14.7554i | 0.532786i | ||||||||
\(768\) | −1.67936 | + | 0.423958i | −0.0605988 | + | 0.0152983i | ||||
\(769\) | −1.17193 | −0.0422607 | −0.0211304 | − | 0.999777i | \(-0.506727\pi\) | ||||
−0.0211304 | + | 0.999777i | \(0.506727\pi\) | |||||||
\(770\) | 4.94393 | 0.178167 | ||||||||
\(771\) | −1.07440 | + | 0.271233i | −0.0386935 | + | 0.00976823i | ||||
\(772\) | − | 21.2018i | − | 0.763071i | ||||||
\(773\) | 47.4582 | 1.70695 | 0.853477 | − | 0.521130i | \(-0.174489\pi\) | ||||
0.853477 | + | 0.521130i | \(0.174489\pi\) | |||||||
\(774\) | −2.58343 | + | 1.39317i | −0.0928594 | + | 0.0500765i | ||||
\(775\) | − | 4.80907i | − | 0.172747i | ||||||
\(776\) | 6.94393i | 0.249273i | ||||||||
\(777\) | −12.2212 | − | 48.4103i | −0.438435 | − | 1.73671i | ||||
\(778\) | 35.0500i | 1.25660i | ||||||||
\(779\) | 34.1318 | − | 0.304169i | 1.22290 | − | 0.0108980i | ||||
\(780\) | 1.93477 | − | 0.488435i | 0.0692758 | − | 0.0174888i | ||||
\(781\) | − | 14.4962i | − | 0.518715i | ||||||
\(782\) | −38.6815 | −1.38325 | ||||||||
\(783\) | 12.8662 | − | 11.7918i | 0.459802 | − | 0.421406i | ||||
\(784\) | −0.889378 | −0.0317635 | ||||||||
\(785\) | 1.90838i | 0.0681130i | ||||||||
\(786\) | 0.337105 | + | 1.33533i | 0.0120241 | + | 0.0476295i | ||||
\(787\) | − | 18.3693i | − | 0.654795i | −0.944887 | − | 0.327397i | \(-0.893828\pi\) | ||
0.944887 | − | 0.327397i | \(-0.106172\pi\) | |||||||
\(788\) | − | 6.53065i | − | 0.232645i | ||||||
\(789\) | −0.0791952 | − | 0.313705i | −0.00281942 | − | 0.0111682i | ||||
\(790\) | −5.75301 | −0.204683 | ||||||||
\(791\) | −17.5200 | −0.622941 | ||||||||
\(792\) | −2.84792 | − | 5.28104i | −0.101196 | − | 0.187654i | ||||
\(793\) | − | 13.7853i | − | 0.489531i | ||||||
\(794\) | −38.0197 | −1.34927 | ||||||||
\(795\) | 0.990834 | + | 3.92485i | 0.0351412 | + | 0.139200i | ||||
\(796\) | 13.4020 | 0.475020 | ||||||||
\(797\) | 34.1941 | 1.21122 | 0.605608 | − | 0.795763i | \(-0.292930\pi\) | ||||
0.605608 | + | 0.795763i | \(0.292930\pi\) | |||||||
\(798\) | 18.0538 | − | 4.72924i | 0.639098 | − | 0.167413i | ||||
\(799\) | 20.1802 | 0.713925 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −28.7467 | + | 15.5023i | −1.01571 | + | 0.547746i | ||||
\(802\) | 38.5451 | 1.36108 | ||||||||
\(803\) | 13.9537i | 0.492417i | ||||||||
\(804\) | −4.24735 | − | 16.8244i | −0.149792 | − | 0.593351i | ||||
\(805\) | 14.3173 | 0.504617 | ||||||||
\(806\) | 5.54046 | 0.195154 | ||||||||
\(807\) | 4.82452 | − | 1.21796i | 0.169831 | − | 0.0428741i | ||||
\(808\) | 16.3356i | 0.574684i | ||||||||
\(809\) | − | 17.3353i | − | 0.609478i | −0.952436 | − | 0.304739i | \(-0.901431\pi\) | ||
0.952436 | − | 0.304739i | \(-0.0985692\pi\) | |||||||
\(810\) | −7.51998 | − | 4.94469i | −0.264225 | − | 0.173739i | ||||
\(811\) | − | 7.08097i | − | 0.248647i | −0.992242 | − | 0.124323i | \(-0.960324\pi\) | ||
0.992242 | − | 0.124323i | \(-0.0396760\pi\) | |||||||
\(812\) | 8.30266 | 0.291366 | ||||||||
\(813\) | 25.7878 | − | 6.51017i | 0.904418 | − | 0.228322i | ||||
\(814\) | −23.3228 | −0.817463 | ||||||||
\(815\) | − | 14.0747i | − | 0.493014i | ||||||
\(816\) | 2.83145 | + | 11.2158i | 0.0991205 | + | 0.392632i | ||||
\(817\) | −4.26449 | + | 0.0380034i | −0.149195 | + | 0.00132957i | ||||
\(818\) | − | 7.99698i | − | 0.279608i | ||||||
\(819\) | 4.05531 | + | 7.51998i | 0.141704 | + | 0.262769i | ||||
\(820\) | − | 7.83069i | − | 0.273460i | ||||||
\(821\) | − | 15.2451i | − | 0.532057i | −0.963965 | − | 0.266029i | \(-0.914288\pi\) | ||
0.963965 | − | 0.266029i | \(-0.0857116\pi\) | |||||||
\(822\) | −5.99814 | − | 23.7596i | −0.209209 | − | 0.828710i | ||||
\(823\) | −13.6394 | −0.475438 | −0.237719 | − | 0.971334i | \(-0.576400\pi\) | ||||
−0.237719 | + | 0.971334i | \(0.576400\pi\) | |||||||
\(824\) | 4.04324i | 0.140853i | ||||||||
\(825\) | −0.847915 | − | 3.35873i | −0.0295206 | − | 0.116936i | ||||
\(826\) | 31.6599 | 1.10159 | ||||||||
\(827\) | −6.79887 | −0.236420 | −0.118210 | − | 0.992989i | \(-0.537716\pi\) | ||||
−0.118210 | + | 0.992989i | \(0.537716\pi\) | |||||||
\(828\) | −8.24735 | − | 15.2935i | −0.286615 | − | 0.531486i | ||||
\(829\) | − | 31.9355i | − | 1.10917i | −0.832128 | − | 0.554583i | \(-0.812878\pi\) | ||
0.832128 | − | 0.554583i | \(-0.187122\pi\) | |||||||
\(830\) | 11.1565 | 0.387247 | ||||||||
\(831\) | −7.81525 | + | 1.97297i | −0.271108 | + | 0.0684416i | ||||
\(832\) | − | 1.15208i | − | 0.0399413i | ||||||
\(833\) | 5.93981i | 0.205802i | ||||||||
\(834\) | 9.05456 | − | 2.28584i | 0.313534 | − | 0.0791520i | ||||
\(835\) | 1.92231i | 0.0665244i | ||||||||
\(836\) | −0.0776864 | − | 8.71745i | −0.00268684 | − | 0.301499i | ||||
\(837\) | −16.8837 | − | 18.4221i | −0.583587 | − | 0.636760i | ||||
\(838\) | − | 24.7144i | − | 0.853746i | ||||||
\(839\) | 31.6862 | 1.09393 | 0.546965 | − | 0.837155i | \(-0.315783\pi\) | ||||
0.546965 | + | 0.837155i | \(0.315783\pi\) | |||||||
\(840\) | −1.04801 | − | 4.15133i | −0.0361598 | − | 0.143234i | ||||
\(841\) | −17.7190 | −0.610999 | ||||||||
\(842\) | 24.1449i | 0.832090i | ||||||||
\(843\) | −26.3246 | + | 6.64567i | −0.906666 | + | 0.228889i | ||||
\(844\) | 25.9010i | 0.891548i | ||||||||
\(845\) | − | 11.6727i | − | 0.401553i | ||||||
\(846\) | 4.30266 | + | 7.97865i | 0.147929 | + | 0.274312i | ||||
\(847\) | −17.3038 | −0.594565 | ||||||||
\(848\) | 2.33710 | 0.0802565 | ||||||||
\(849\) | −20.8992 | + | 5.27603i | −0.717258 | + | 0.181073i | ||||
\(850\) | 6.67861i | 0.229074i | ||||||||
\(851\) | −67.5410 | −2.31528 | ||||||||
\(852\) | −12.1722 | + | 3.07289i | −0.417013 | + | 0.105275i | ||||
\(853\) | 16.4705 | 0.563938 | 0.281969 | − | 0.959424i | \(-0.409013\pi\) | ||||
0.281969 | + | 0.959424i | \(0.409013\pi\) | |||||||
\(854\) | −29.5785 | −1.01215 | ||||||||
\(855\) | −6.30921 | − | 11.4540i | −0.215770 | − | 0.391718i | ||||
\(856\) | −4.03294 | −0.137843 | ||||||||
\(857\) | −6.64634 | −0.227035 | −0.113517 | − | 0.993536i | \(-0.536212\pi\) | ||||
−0.113517 | + | 0.993536i | \(0.536212\pi\) | |||||||
\(858\) | 3.86954 | − | 0.976870i | 0.132104 | − | 0.0333498i | ||||
\(859\) | 1.47760 | 0.0504152 | 0.0252076 | − | 0.999682i | \(-0.491975\pi\) | ||||
0.0252076 | + | 0.999682i | \(0.491975\pi\) | |||||||
\(860\) | 0.978379i | 0.0333624i | ||||||||
\(861\) | 32.5078 | − | 8.20664i | 1.10786 | − | 0.279682i | ||||
\(862\) | 34.6748 | 1.18103 | ||||||||
\(863\) | 3.50735 | 0.119392 | 0.0596958 | − | 0.998217i | \(-0.480987\pi\) | ||||
0.0596958 | + | 0.998217i | \(0.480987\pi\) | |||||||
\(864\) | −3.83069 | + | 3.51081i | −0.130323 | + | 0.119440i | ||||
\(865\) | − | 18.2235i | − | 0.619616i | ||||||
\(866\) | 1.77653i | 0.0603691i | ||||||||
\(867\) | 46.3568 | − | 11.7028i | 1.57436 | − | 0.397450i | ||||
\(868\) | − | 11.8879i | − | 0.403501i | ||||||
\(869\) | −11.5060 | −0.390315 | ||||||||
\(870\) | −1.42396 | − | 5.64052i | −0.0482767 | − | 0.191232i | ||||
\(871\) | 11.5420 | 0.391085 | ||||||||
\(872\) | − | 7.65699i | − | 0.259298i | ||||||
\(873\) | 9.88787 | + | 18.3356i | 0.334654 | + | 0.620566i | ||||
\(874\) | −0.224974 | − | 25.2451i | −0.00760986 | − | 0.853928i | ||||
\(875\) | − | 2.47197i | − | 0.0835677i | ||||||
\(876\) | 11.7167 | − | 2.95790i | 0.395871 | − | 0.0999381i | ||||
\(877\) | 28.0219i | 0.946232i | 0.881000 | + | 0.473116i | \(0.156871\pi\) | ||||
−0.881000 | + | 0.473116i | \(0.843129\pi\) | |||||||
\(878\) | 11.1997i | 0.377972i | ||||||||
\(879\) | 6.45399 | − | 1.62932i | 0.217688 | − | 0.0549556i | ||||
\(880\) | −2.00000 | −0.0674200 | ||||||||
\(881\) | 9.03344i | 0.304344i | 0.988354 | + | 0.152172i | \(0.0486268\pi\) | ||||
−0.988354 | + | 0.152172i | \(0.951373\pi\) | |||||||
\(882\) | −2.34842 | + | 1.26644i | −0.0790754 | + | 0.0426431i | ||||
\(883\) | 39.7705 | 1.33838 | 0.669192 | − | 0.743090i | \(-0.266640\pi\) | ||||
0.669192 | + | 0.743090i | \(0.266640\pi\) | |||||||
\(884\) | −7.69432 | −0.258788 | ||||||||
\(885\) | −5.42987 | − | 21.5085i | −0.182523 | − | 0.723002i | ||||
\(886\) | 0.969683i | 0.0325772i | ||||||||
\(887\) | −13.8534 | −0.465152 | −0.232576 | − | 0.972578i | \(-0.574716\pi\) | ||||
−0.232576 | + | 0.972578i | \(0.574716\pi\) | |||||||
\(888\) | 4.94393 | + | 19.5837i | 0.165908 | + | 0.657186i | ||||
\(889\) | 21.5493i | 0.722739i | ||||||||
\(890\) | 10.8868i | 0.364925i | ||||||||
\(891\) | −15.0400 | − | 9.88938i | −0.503857 | − | 0.331307i | ||||
\(892\) | 8.18680i | 0.274114i | ||||||||
\(893\) | 0.117369 | + | 13.1704i | 0.00392762 | + | 0.440731i | ||||
\(894\) | −4.68602 | − | 18.5621i | −0.156724 | − | 0.620809i | ||||
\(895\) | − | 4.42722i | − | 0.147986i | ||||||
\(896\) | −2.47197 | −0.0825826 | ||||||||
\(897\) | 11.2059 | − | 2.82894i | 0.374154 | − | 0.0944557i | ||||
\(898\) | −19.1168 | −0.637936 | ||||||||
\(899\) | − | 16.1524i | − | 0.538711i | ||||||
\(900\) | −2.64052 | + | 1.42396i | −0.0880173 | + | 0.0474653i | ||||
\(901\) | − | 15.6086i | − | 0.519998i | ||||||
\(902\) | − | 15.6614i | − | 0.521467i | ||||||
\(903\) | −4.06157 | + | 1.02535i | −0.135161 | + | 0.0341215i | ||||
\(904\) | 7.08749 | 0.235726 | ||||||||
\(905\) | −7.68190 | −0.255355 | ||||||||
\(906\) | 8.85382 | + | 35.0714i | 0.294149 | + | 1.16517i | ||||
\(907\) | − | 48.9711i | − | 1.62606i | −0.582224 | − | 0.813029i | \(-0.697817\pi\) | ||
0.582224 | − | 0.813029i | \(-0.302183\pi\) | |||||||
\(908\) | 11.6943 | 0.388090 | ||||||||
\(909\) | 23.2612 | + | 43.1345i | 0.771525 | + | 1.43068i | ||||
\(910\) | 2.84792 | 0.0944075 | ||||||||
\(911\) | 15.6234 | 0.517626 | 0.258813 | − | 0.965927i | \(-0.416669\pi\) | ||||
0.258813 | + | 0.965927i | \(0.416669\pi\) | |||||||
\(912\) | −7.30341 | + | 1.91315i | −0.241840 | + | 0.0633506i | ||||
\(913\) | 22.3130 | 0.738451 | ||||||||
\(914\) | 11.1292 | 0.368122 | ||||||||
\(915\) | 5.07289 | + | 20.0945i | 0.167705 | + | 0.664304i | ||||
\(916\) | 12.5621 | 0.415063 | ||||||||
\(917\) | 1.96556i | 0.0649084i | ||||||||
\(918\) | 23.4473 | + | 25.5837i | 0.773877 | + | 0.844388i | ||||
\(919\) | −50.8997 | −1.67903 | −0.839514 | − | 0.543339i | \(-0.817160\pi\) | ||||
−0.839514 | + | 0.543339i | \(0.817160\pi\) | |||||||
\(920\) | −5.79185 | −0.190952 | ||||||||
\(921\) | −1.77725 | − | 7.03995i | −0.0585623 | − | 0.231974i | ||||
\(922\) | 21.2861i | 0.701021i | ||||||||
\(923\) | − | 8.35043i | − | 0.274858i | ||||||
\(924\) | −2.09602 | − | 8.30266i | −0.0689540 | − | 0.273137i | ||||
\(925\) | 11.6614i | 0.383424i | ||||||||
\(926\) | 14.2060 | 0.466837 | ||||||||
\(927\) | 5.75741 | + | 10.6763i | 0.189098 | + | 0.350654i | ||||
\(928\) | −3.35873 | −0.110256 | ||||||||
\(929\) | 9.10059i | 0.298581i | 0.988793 | + | 0.149290i | \(0.0476989\pi\) | ||||
−0.988793 | + | 0.149290i | \(0.952301\pi\) | |||||||
\(930\) | −8.07618 | + | 2.03884i | −0.264828 | + | 0.0668563i | ||||
\(931\) | −3.87655 | + | 0.0345463i | −0.127049 | + | 0.00113221i | ||||
\(932\) | 13.0077i | 0.426081i | ||||||||
\(933\) | 6.31322 | + | 25.0077i | 0.206686 | + | 0.818714i | ||||
\(934\) | − | 9.15124i | − | 0.299438i | ||||||
\(935\) | 13.3572i | 0.436828i | ||||||||
\(936\) | −1.64052 | − | 3.04210i | −0.0536221 | − | 0.0994342i | ||||
\(937\) | 39.0355 | 1.27523 | 0.637617 | − | 0.770354i | \(-0.279920\pi\) | ||||
0.637617 | + | 0.770354i | \(0.279920\pi\) | |||||||
\(938\) | − | 24.7650i | − | 0.808606i | ||||||
\(939\) | −10.7816 | + | 2.72182i | −0.351843 | + | 0.0888233i | ||||
\(940\) | 3.02162 | 0.0985544 | ||||||||
\(941\) | −36.8421 | −1.20102 | −0.600509 | − | 0.799618i | \(-0.705035\pi\) | ||||
−0.600509 | + | 0.799618i | \(0.705035\pi\) | |||||||
\(942\) | 3.20486 | − | 0.809072i | 0.104420 | − | 0.0263610i | ||||
\(943\) | − | 45.3542i | − | 1.47694i | ||||||
\(944\) | −12.8076 | −0.416851 | ||||||||
\(945\) | −8.67861 | − | 9.46935i | −0.282315 | − | 0.308038i | ||||
\(946\) | 1.95676i | 0.0636197i | ||||||||
\(947\) | 7.98305i | 0.259414i | 0.991552 | + | 0.129707i | \(0.0414037\pi\) | ||||
−0.991552 | + | 0.129707i | \(0.958596\pi\) | |||||||
\(948\) | 2.43903 | + | 9.66139i | 0.0792161 | + | 0.313787i | ||||
\(949\) | 8.03794i | 0.260923i | ||||||||
\(950\) | −4.35873 | + | 0.0388432i | −0.141416 | + | 0.00126024i | ||||
\(951\) | 30.2986 | − | 7.64893i | 0.982500 | − | 0.248034i | ||||
\(952\) | 16.5093i | 0.535070i | ||||||||
\(953\) | −33.1556 | −1.07401 | −0.537007 | − | 0.843578i | \(-0.680445\pi\) | ||||
−0.537007 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(954\) | 6.17117 | − | 3.32794i | 0.199799 | − | 0.107746i | ||||
\(955\) | −24.0153 | −0.777117 | ||||||||
\(956\) | − | 27.0780i | − | 0.875764i | ||||||
\(957\) | −2.84792 | − | 11.2810i | −0.0920600 | − | 0.364664i | ||||
\(958\) | 1.58672i | 0.0512645i | ||||||||
\(959\) | − | 34.9733i | − | 1.12935i | ||||||
\(960\) | 0.423958 | + | 1.67936i | 0.0136832 | + | 0.0542012i | ||||
\(961\) | 7.87282 | 0.253962 | ||||||||
\(962\) | −13.4349 | −0.433159 | ||||||||
\(963\) | −10.6490 | + | 5.74273i | −0.343161 | + | 0.185057i | ||||
\(964\) | − | 16.2697i | − | 0.524013i | ||||||
\(965\) | −21.2018 | −0.682512 | ||||||||
\(966\) | −6.06991 | − | 24.0439i | −0.195296 | − | 0.773599i | ||||
\(967\) | −35.1600 | −1.13067 | −0.565335 | − | 0.824861i | \(-0.691253\pi\) | ||||
−0.565335 | + | 0.824861i | \(0.691253\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 12.7772 | + | 48.7766i | 0.410462 | + | 1.56693i | ||||
\(970\) | 6.94393 | 0.222956 | ||||||||
\(971\) | 23.8425 | 0.765142 | 0.382571 | − | 0.923926i | \(-0.375039\pi\) | ||||
0.382571 | + | 0.923926i | \(0.375039\pi\) | |||||||
\(972\) | −5.11578 | + | 14.7251i | −0.164089 | + | 0.472308i | ||||
\(973\) | 13.3280 | 0.427276 | ||||||||
\(974\) | − | 16.6398i | − | 0.533172i | ||||||
\(975\) | −0.488435 | − | 1.93477i | −0.0156424 | − | 0.0619622i | ||||
\(976\) | 11.9656 | 0.383008 | ||||||||
\(977\) | 44.6398 | 1.42815 | 0.714076 | − | 0.700068i | \(-0.246847\pi\) | ||||
0.714076 | + | 0.700068i | \(0.246847\pi\) | |||||||
\(978\) | −23.6365 | + | 5.96706i | −0.755811 | + | 0.190806i | ||||
\(979\) | 21.7735i | 0.695885i | ||||||||
\(980\) | 0.889378i | 0.0284101i | ||||||||
\(981\) | −10.9032 | − | 20.2184i | −0.348113 | − | 0.645525i | ||||
\(982\) | − | 7.42611i | − | 0.236977i | ||||||
\(983\) | −20.1606 | −0.643024 | −0.321512 | − | 0.946906i | \(-0.604191\pi\) | ||||
−0.321512 | + | 0.946906i | \(0.604191\pi\) | |||||||
\(984\) | −13.1506 | + | 3.31988i | −0.419225 | + | 0.105834i | ||||
\(985\) | −6.53065 | −0.208084 | ||||||||
\(986\) | 22.4316i | 0.714368i | ||||||||
\(987\) | 3.16669 | + | 12.5437i | 0.100797 | + | 0.399272i | ||||
\(988\) | −0.0447507 | − | 5.02162i | −0.00142371 | − | 0.159759i | ||||
\(989\) | 5.66662i | 0.180188i | ||||||||
\(990\) | −5.28104 | + | 2.84792i | −0.167842 | + | 0.0905127i | ||||
\(991\) | − | 19.6849i | − | 0.625312i | −0.949866 | − | 0.312656i | \(-0.898781\pi\) | ||
0.949866 | − | 0.312656i | \(-0.101219\pi\) | |||||||
\(992\) | 4.80907i | 0.152688i | ||||||||
\(993\) | −9.80090 | − | 38.8229i | −0.311022 | − | 1.23201i | ||||
\(994\) | −17.9171 | −0.568295 | ||||||||
\(995\) | − | 13.4020i | − | 0.424871i | ||||||
\(996\) | −4.72988 | − | 18.7358i | −0.149872 | − | 0.593666i | ||||
\(997\) | −51.2596 | −1.62341 | −0.811703 | − | 0.584070i | \(-0.801459\pi\) | ||||
−0.811703 | + | 0.584070i | \(0.801459\pi\) | |||||||
\(998\) | 13.5178 | 0.427899 | ||||||||
\(999\) | 40.9409 | + | 44.6712i | 1.29531 | + | 1.41333i |
(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 | 570.2.f.d.341.2 | yes | 8 | |
3.2 | odd | 2 | 570.2.f.c.341.8 | yes | 8 | ||
19.18 | odd | 2 | 570.2.f.c.341.7 | ✓ | 8 | ||
57.56 | even | 2 | inner | 570.2.f.d.341.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.f.c.341.7 | ✓ | 8 | 19.18 | odd | 2 | ||
570.2.f.c.341.8 | yes | 8 | 3.2 | odd | 2 | ||
570.2.f.d.341.1 | yes | 8 | 57.56 | even | 2 | inner | |
570.2.f.d.341.2 | yes | 8 | 1.1 | even | 1 | trivial |