Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, 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("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.8 | ||
Root | \(0.312065 + 1.70371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.b.881.2 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.581597 | + | 1.63149i | −0.335785 | + | 0.941939i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.63149 | − | 0.581597i | −0.666051 | − | 0.237436i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.32349 | − | 1.89773i | −0.774497 | − | 0.632578i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | − | 0.963479i | − | 0.290500i | −0.989395 | − | 0.145250i | \(-0.953601\pi\) | ||
0.989395 | − | 0.145250i | \(-0.0463986\pi\) | |||||||
\(12\) | 0.581597 | − | 1.63149i | 0.167892 | − | 0.470969i | ||||
\(13\) | − | 1.98782i | − | 0.551321i | −0.961255 | − | 0.275660i | \(-0.911103\pi\) | ||
0.961255 | − | 0.275660i | \(-0.0888966\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.581597 | − | 1.63149i | 0.150168 | − | 0.421248i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.63227 | −0.638420 | −0.319210 | − | 0.947684i | \(-0.603418\pi\) | ||||
−0.319210 | + | 0.947684i | \(0.603418\pi\) | |||||||
\(18\) | 1.89773 | − | 2.32349i | 0.447300 | − | 0.547652i | ||||
\(19\) | 5.16784i | 1.18558i | 0.805355 | + | 0.592792i | \(0.201974\pi\) | ||||
−0.805355 | + | 0.592792i | \(0.798026\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.963479 | 0.205414 | ||||||||
\(23\) | − | 2.69411i | − | 0.561762i | −0.959743 | − | 0.280881i | \(-0.909373\pi\) | ||
0.959743 | − | 0.280881i | \(-0.0906265\pi\) | |||||||
\(24\) | 1.63149 | + | 0.581597i | 0.333026 | + | 0.118718i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.98782 | 0.389843 | ||||||||
\(27\) | 4.44746 | − | 2.68703i | 0.855914 | − | 0.517119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.90498i | − | 1.83931i | −0.392730 | − | 0.919654i | \(-0.628469\pi\) | ||
0.392730 | − | 0.919654i | \(-0.371531\pi\) | |||||||
\(30\) | 1.63149 | + | 0.581597i | 0.297867 | + | 0.106185i | ||||
\(31\) | − | 3.42151i | − | 0.614522i | −0.951625 | − | 0.307261i | \(-0.900588\pi\) | ||
0.951625 | − | 0.307261i | \(-0.0994125\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.57190 | + | 0.560356i | 0.273633 | + | 0.0975454i | ||||
\(34\) | − | 2.63227i | − | 0.451431i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.32349 | + | 1.89773i | 0.387248 | + | 0.316289i | ||||
\(37\) | 9.14603 | 1.50360 | 0.751799 | − | 0.659392i | \(-0.229186\pi\) | ||||
0.751799 | + | 0.659392i | \(0.229186\pi\) | |||||||
\(38\) | −5.16784 | −0.838335 | ||||||||
\(39\) | 3.24309 | + | 1.15611i | 0.519311 | + | 0.185125i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −1.12202 | −0.175230 | −0.0876152 | − | 0.996154i | \(-0.527925\pi\) | ||||
−0.0876152 | + | 0.996154i | \(0.527925\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.54917 | 0.236246 | 0.118123 | − | 0.992999i | \(-0.462312\pi\) | ||||
0.118123 | + | 0.992999i | \(0.462312\pi\) | |||||||
\(44\) | 0.963479i | 0.145250i | ||||||||
\(45\) | 2.32349 | + | 1.89773i | 0.346366 | + | 0.282897i | ||||
\(46\) | 2.69411 | 0.397225 | ||||||||
\(47\) | 10.3888 | 1.51536 | 0.757679 | − | 0.652628i | \(-0.226334\pi\) | ||||
0.757679 | + | 0.652628i | \(0.226334\pi\) | |||||||
\(48\) | −0.581597 | + | 1.63149i | −0.0839462 | + | 0.235485i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 1.53092 | − | 4.29451i | 0.214372 | − | 0.601352i | ||||
\(52\) | 1.98782i | 0.275660i | ||||||||
\(53\) | − | 13.1742i | − | 1.80961i | −0.425825 | − | 0.904806i | \(-0.640016\pi\) | ||
0.425825 | − | 0.904806i | \(-0.359984\pi\) | |||||||
\(54\) | 2.68703 | + | 4.44746i | 0.365658 | + | 0.605222i | ||||
\(55\) | 0.963479i | 0.129915i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.43126 | − | 3.00560i | −1.11675 | − | 0.398101i | ||||
\(58\) | 9.90498 | 1.30059 | ||||||||
\(59\) | 2.10246 | 0.273717 | 0.136859 | − | 0.990591i | \(-0.456299\pi\) | ||||
0.136859 | + | 0.990591i | \(0.456299\pi\) | |||||||
\(60\) | −0.581597 | + | 1.63149i | −0.0750838 | + | 0.210624i | ||||
\(61\) | 8.96260i | 1.14754i | 0.819015 | + | 0.573772i | \(0.194520\pi\) | ||||
−0.819015 | + | 0.573772i | \(0.805480\pi\) | |||||||
\(62\) | 3.42151 | 0.434533 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.98782i | 0.246558i | ||||||||
\(66\) | −0.560356 | + | 1.57190i | −0.0689750 | + | 0.193488i | ||||
\(67\) | −1.79547 | −0.219351 | −0.109676 | − | 0.993967i | \(-0.534981\pi\) | ||||
−0.109676 | + | 0.993967i | \(0.534981\pi\) | |||||||
\(68\) | 2.63227 | 0.319210 | ||||||||
\(69\) | 4.39541 | + | 1.56689i | 0.529145 | + | 0.188631i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1501i | 1.32328i | 0.749823 | + | 0.661639i | \(0.230139\pi\) | ||||
−0.749823 | + | 0.661639i | \(0.769861\pi\) | |||||||
\(72\) | −1.89773 | + | 2.32349i | −0.223650 | + | 0.273826i | ||||
\(73\) | 11.7735i | 1.37798i | 0.724770 | + | 0.688991i | \(0.241946\pi\) | ||||
−0.724770 | + | 0.688991i | \(0.758054\pi\) | |||||||
\(74\) | 9.14603i | 1.06320i | ||||||||
\(75\) | −0.581597 | + | 1.63149i | −0.0671570 | + | 0.188388i | ||||
\(76\) | − | 5.16784i | − | 0.592792i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.15611 | + | 3.24309i | −0.130903 | + | 0.367208i | ||||
\(79\) | −0.408348 | −0.0459428 | −0.0229714 | − | 0.999736i | \(-0.507313\pi\) | ||||
−0.0229714 | + | 0.999736i | \(0.507313\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.79722 | + | 8.81873i | 0.199691 | + | 0.979859i | ||||
\(82\) | − | 1.12202i | − | 0.123907i | ||||||
\(83\) | −4.53092 | −0.497333 | −0.248667 | − | 0.968589i | \(-0.579992\pi\) | ||||
−0.248667 | + | 0.968589i | \(0.579992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.63227 | 0.285510 | ||||||||
\(86\) | 1.54917i | 0.167051i | ||||||||
\(87\) | 16.1598 | + | 5.76070i | 1.73252 | + | 0.617612i | ||||
\(88\) | −0.963479 | −0.102707 | ||||||||
\(89\) | −11.5214 | −1.22127 | −0.610633 | − | 0.791914i | \(-0.709085\pi\) | ||||
−0.610633 | + | 0.791914i | \(0.709085\pi\) | |||||||
\(90\) | −1.89773 | + | 2.32349i | −0.200039 | + | 0.244917i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.69411i | 0.280881i | ||||||||
\(93\) | 5.58215 | + | 1.98994i | 0.578842 | + | 0.206347i | ||||
\(94\) | 10.3888i | 1.07152i | ||||||||
\(95\) | − | 5.16784i | − | 0.530210i | ||||||
\(96\) | −1.63149 | − | 0.581597i | −0.166513 | − | 0.0593589i | ||||
\(97\) | − | 14.6992i | − | 1.49248i | −0.665679 | − | 0.746239i | \(-0.731858\pi\) | ||
0.665679 | − | 0.746239i | \(-0.268142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.82842 | + | 2.23863i | −0.183764 | + | 0.224991i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 15.1630 | 1.50877 | 0.754386 | − | 0.656431i | \(-0.227935\pi\) | ||||
0.754386 | + | 0.656431i | \(0.227935\pi\) | |||||||
\(102\) | 4.29451 | + | 1.53092i | 0.425220 | + | 0.151584i | ||||
\(103\) | − | 9.07046i | − | 0.893739i | −0.894599 | − | 0.446870i | \(-0.852539\pi\) | ||
0.894599 | − | 0.446870i | \(-0.147461\pi\) | |||||||
\(104\) | −1.98782 | −0.194921 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.1742 | 1.27959 | ||||||||
\(107\) | − | 13.8590i | − | 1.33980i | −0.742452 | − | 0.669899i | \(-0.766337\pi\) | ||
0.742452 | − | 0.669899i | \(-0.233663\pi\) | |||||||
\(108\) | −4.44746 | + | 2.68703i | −0.427957 | + | 0.258559i | ||||
\(109\) | −16.7334 | −1.60277 | −0.801385 | − | 0.598150i | \(-0.795903\pi\) | ||||
−0.801385 | + | 0.598150i | \(0.795903\pi\) | |||||||
\(110\) | −0.963479 | −0.0918641 | ||||||||
\(111\) | −5.31930 | + | 14.9216i | −0.504886 | + | 1.41630i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.9355i | − | 1.31095i | −0.755219 | − | 0.655473i | \(-0.772470\pi\) | ||
0.755219 | − | 0.655473i | \(-0.227530\pi\) | |||||||
\(114\) | 3.00560 | − | 8.43126i | 0.281500 | − | 0.789660i | ||||
\(115\) | 2.69411i | 0.251227i | ||||||||
\(116\) | 9.90498i | 0.919654i | ||||||||
\(117\) | −3.77234 | + | 4.61867i | −0.348753 | + | 0.426996i | ||||
\(118\) | 2.10246i | 0.193547i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.63149 | − | 0.581597i | −0.148934 | − | 0.0530923i | ||||
\(121\) | 10.0717 | 0.915610 | ||||||||
\(122\) | −8.96260 | −0.811436 | ||||||||
\(123\) | 0.652564 | − | 1.83056i | 0.0588397 | − | 0.165056i | ||||
\(124\) | 3.42151i | 0.307261i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1937 | 1.43696 | 0.718479 | − | 0.695548i | \(-0.244839\pi\) | ||||
0.718479 | + | 0.695548i | \(0.244839\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −0.900992 | + | 2.52745i | −0.0793279 | + | 0.222530i | ||||
\(130\) | −1.98782 | −0.174343 | ||||||||
\(131\) | −5.92214 | −0.517420 | −0.258710 | − | 0.965955i | \(-0.583297\pi\) | ||||
−0.258710 | + | 0.965955i | \(0.583297\pi\) | |||||||
\(132\) | −1.57190 | − | 0.560356i | −0.136816 | − | 0.0487727i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.79547i | − | 0.155105i | ||||||
\(135\) | −4.44746 | + | 2.68703i | −0.382776 | + | 0.231263i | ||||
\(136\) | 2.63227i | 0.225716i | ||||||||
\(137\) | − | 7.62107i | − | 0.651112i | −0.945523 | − | 0.325556i | \(-0.894449\pi\) | ||
0.945523 | − | 0.325556i | \(-0.105551\pi\) | |||||||
\(138\) | −1.56689 | + | 4.39541i | −0.133382 | + | 0.374162i | ||||
\(139\) | − | 7.13772i | − | 0.605413i | −0.953084 | − | 0.302707i | \(-0.902110\pi\) | ||
0.953084 | − | 0.302707i | \(-0.0978902\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.04207 | + | 16.9491i | −0.508834 | + | 1.42737i | ||||
\(142\) | −11.1501 | −0.935698 | ||||||||
\(143\) | −1.91522 | −0.160159 | ||||||||
\(144\) | −2.32349 | − | 1.89773i | −0.193624 | − | 0.158144i | ||||
\(145\) | 9.90498i | 0.822563i | ||||||||
\(146\) | −11.7735 | −0.974380 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.14603 | −0.751799 | ||||||||
\(149\) | 11.9687i | 0.980516i | 0.871577 | + | 0.490258i | \(0.163097\pi\) | ||||
−0.871577 | + | 0.490258i | \(0.836903\pi\) | |||||||
\(150\) | −1.63149 | − | 0.581597i | −0.133210 | − | 0.0474872i | ||||
\(151\) | 8.99700 | 0.732165 | 0.366083 | − | 0.930582i | \(-0.380699\pi\) | ||||
0.366083 | + | 0.930582i | \(0.380699\pi\) | |||||||
\(152\) | 5.16784 | 0.419167 | ||||||||
\(153\) | 6.11606 | + | 4.99535i | 0.494454 | + | 0.403850i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.42151i | 0.274823i | ||||||||
\(156\) | −3.24309 | − | 1.15611i | −0.259655 | − | 0.0925626i | ||||
\(157\) | − | 6.58680i | − | 0.525684i | −0.964839 | − | 0.262842i | \(-0.915340\pi\) | ||
0.964839 | − | 0.262842i | \(-0.0846598\pi\) | |||||||
\(158\) | − | 0.408348i | − | 0.0324864i | ||||||
\(159\) | 21.4935 | + | 7.66205i | 1.70454 | + | 0.607640i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −8.81873 | + | 1.79722i | −0.692865 | + | 0.141203i | ||||
\(163\) | 2.65049 | 0.207603 | 0.103801 | − | 0.994598i | \(-0.466899\pi\) | ||||
0.103801 | + | 0.994598i | \(0.466899\pi\) | |||||||
\(164\) | 1.12202 | 0.0876152 | ||||||||
\(165\) | −1.57190 | − | 0.560356i | −0.122372 | − | 0.0436236i | ||||
\(166\) | − | 4.53092i | − | 0.351668i | ||||||
\(167\) | 7.68946 | 0.595029 | 0.297514 | − | 0.954717i | \(-0.403842\pi\) | ||||
0.297514 | + | 0.954717i | \(0.403842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.04859 | 0.696045 | ||||||||
\(170\) | 2.63227i | 0.201886i | ||||||||
\(171\) | 9.80719 | − | 12.0074i | 0.749974 | − | 0.918232i | ||||
\(172\) | −1.54917 | −0.118123 | ||||||||
\(173\) | −21.2908 | −1.61871 | −0.809355 | − | 0.587320i | \(-0.800183\pi\) | ||||
−0.809355 | + | 0.587320i | \(0.800183\pi\) | |||||||
\(174\) | −5.76070 | + | 16.1598i | −0.436717 | + | 1.22507i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.963479i | − | 0.0726249i | ||||||
\(177\) | −1.22278 | + | 3.43014i | −0.0919101 | + | 0.257825i | ||||
\(178\) | − | 11.5214i | − | 0.863565i | ||||||
\(179\) | − | 1.32636i | − | 0.0991371i | −0.998771 | − | 0.0495686i | \(-0.984215\pi\) | ||
0.998771 | − | 0.0495686i | \(-0.0157846\pi\) | |||||||
\(180\) | −2.32349 | − | 1.89773i | −0.173183 | − | 0.141449i | ||||
\(181\) | − | 2.17439i | − | 0.161621i | −0.996729 | − | 0.0808107i | \(-0.974249\pi\) | ||
0.996729 | − | 0.0808107i | \(-0.0257509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.6224 | − | 5.21262i | −1.08092 | − | 0.385328i | ||||
\(184\) | −2.69411 | −0.198613 | ||||||||
\(185\) | −9.14603 | −0.672430 | ||||||||
\(186\) | −1.98994 | + | 5.58215i | −0.145910 | + | 0.409303i | ||||
\(187\) | 2.53614i | 0.185461i | ||||||||
\(188\) | −10.3888 | −0.757679 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.16784 | 0.374915 | ||||||||
\(191\) | − | 17.0570i | − | 1.23420i | −0.786885 | − | 0.617099i | \(-0.788308\pi\) | ||
0.786885 | − | 0.617099i | \(-0.211692\pi\) | |||||||
\(192\) | 0.581597 | − | 1.63149i | 0.0419731 | − | 0.117742i | ||||
\(193\) | 2.05067 | 0.147611 | 0.0738053 | − | 0.997273i | \(-0.476486\pi\) | ||||
0.0738053 | + | 0.997273i | \(0.476486\pi\) | |||||||
\(194\) | 14.6992 | 1.05534 | ||||||||
\(195\) | −3.24309 | − | 1.15611i | −0.232243 | − | 0.0827905i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9420i | 0.922083i | 0.887379 | + | 0.461041i | \(0.152524\pi\) | ||||
−0.887379 | + | 0.461041i | \(0.847476\pi\) | |||||||
\(198\) | −2.23863 | − | 1.82842i | −0.159093 | − | 0.129941i | ||||
\(199\) | − | 17.1869i | − | 1.21835i | −0.793037 | − | 0.609174i | \(-0.791501\pi\) | ||
0.793037 | − | 0.609174i | \(-0.208499\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 1.04424 | − | 2.92928i | 0.0736548 | − | 0.206615i | ||||
\(202\) | 15.1630i | 1.06686i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.53092 | + | 4.29451i | −0.107186 | + | 0.300676i | ||||
\(205\) | 1.12202 | 0.0783654 | ||||||||
\(206\) | 9.07046 | 0.631969 | ||||||||
\(207\) | −5.11271 | + | 6.25975i | −0.355358 | + | 0.435083i | ||||
\(208\) | − | 1.98782i | − | 0.137830i | ||||||
\(209\) | 4.97911 | 0.344412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.19691 | 0.151242 | 0.0756208 | − | 0.997137i | \(-0.475906\pi\) | ||||
0.0756208 | + | 0.997137i | \(0.475906\pi\) | |||||||
\(212\) | 13.1742i | 0.904806i | ||||||||
\(213\) | −18.1913 | − | 6.48488i | −1.24645 | − | 0.444336i | ||||
\(214\) | 13.8590 | 0.947381 | ||||||||
\(215\) | −1.54917 | −0.105653 | ||||||||
\(216\) | −2.68703 | − | 4.44746i | −0.182829 | − | 0.302611i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 16.7334i | − | 1.13333i | ||||||
\(219\) | −19.2083 | − | 6.84742i | −1.29797 | − | 0.462706i | ||||
\(220\) | − | 0.963479i | − | 0.0649577i | ||||||
\(221\) | 5.23247i | 0.351974i | ||||||||
\(222\) | −14.9216 | − | 5.31930i | −1.00147 | − | 0.357008i | ||||
\(223\) | − | 23.8443i | − | 1.59673i | −0.602173 | − | 0.798365i | \(-0.705698\pi\) | ||
0.602173 | − | 0.798365i | \(-0.294302\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.32349 | − | 1.89773i | −0.154899 | − | 0.126516i | ||||
\(226\) | 13.9355 | 0.926978 | ||||||||
\(227\) | 4.67171 | 0.310072 | 0.155036 | − | 0.987909i | \(-0.450451\pi\) | ||||
0.155036 | + | 0.987909i | \(0.450451\pi\) | |||||||
\(228\) | 8.43126 | + | 3.00560i | 0.558374 | + | 0.199051i | ||||
\(229\) | − | 23.1514i | − | 1.52989i | −0.644097 | − | 0.764944i | \(-0.722767\pi\) | ||
0.644097 | − | 0.764944i | \(-0.277233\pi\) | |||||||
\(230\) | −2.69411 | −0.177645 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.90498 | −0.650293 | ||||||||
\(233\) | 13.2418i | 0.867499i | 0.901033 | + | 0.433750i | \(0.142810\pi\) | ||||
−0.901033 | + | 0.433750i | \(0.857190\pi\) | |||||||
\(234\) | −4.61867 | − | 3.77234i | −0.301932 | − | 0.246606i | ||||
\(235\) | −10.3888 | −0.677688 | ||||||||
\(236\) | −2.10246 | −0.136859 | ||||||||
\(237\) | 0.237494 | − | 0.666214i | 0.0154269 | − | 0.0432753i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.7280i | 0.952675i | 0.879263 | + | 0.476337i | \(0.158036\pi\) | ||||
−0.879263 | + | 0.476337i | \(0.841964\pi\) | |||||||
\(240\) | 0.581597 | − | 1.63149i | 0.0375419 | − | 0.105312i | ||||
\(241\) | − | 5.92695i | − | 0.381788i | −0.981611 | − | 0.190894i | \(-0.938861\pi\) | ||
0.981611 | − | 0.190894i | \(-0.0611387\pi\) | |||||||
\(242\) | 10.0717i | 0.647434i | ||||||||
\(243\) | −15.4329 | − | 2.19680i | −0.990020 | − | 0.140925i | ||||
\(244\) | − | 8.96260i | − | 0.573772i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.83056 | + | 0.652564i | 0.116712 | + | 0.0416059i | ||||
\(247\) | 10.2727 | 0.653638 | ||||||||
\(248\) | −3.42151 | −0.217266 | ||||||||
\(249\) | 2.63517 | − | 7.39213i | 0.166997 | − | 0.468457i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 19.4694 | 1.22890 | 0.614450 | − | 0.788956i | \(-0.289378\pi\) | ||||
0.614450 | + | 0.788956i | \(0.289378\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.59572 | −0.163192 | ||||||||
\(254\) | 16.1937i | 1.01608i | ||||||||
\(255\) | −1.53092 | + | 4.29451i | −0.0958700 | + | 0.268933i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.83792 | −0.177024 | −0.0885122 | − | 0.996075i | \(-0.528211\pi\) | ||||
−0.0885122 | + | 0.996075i | \(0.528211\pi\) | |||||||
\(258\) | −2.52745 | − | 0.900992i | −0.157352 | − | 0.0560933i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.98782i | − | 0.123279i | ||||||
\(261\) | −18.7970 | + | 23.0141i | −1.16350 | + | 1.42454i | ||||
\(262\) | − | 5.92214i | − | 0.365871i | ||||||
\(263\) | − | 18.0716i | − | 1.11435i | −0.830397 | − | 0.557173i | \(-0.811886\pi\) | ||
0.830397 | − | 0.557173i | \(-0.188114\pi\) | |||||||
\(264\) | 0.560356 | − | 1.57190i | 0.0344875 | − | 0.0967439i | ||||
\(265\) | 13.1742i | 0.809283i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.70081 | − | 18.7970i | 0.410083 | − | 1.15036i | ||||
\(268\) | 1.79547 | 0.109676 | ||||||||
\(269\) | −17.1417 | −1.04515 | −0.522575 | − | 0.852593i | \(-0.675029\pi\) | ||||
−0.522575 | + | 0.852593i | \(0.675029\pi\) | |||||||
\(270\) | −2.68703 | − | 4.44746i | −0.163527 | − | 0.270664i | ||||
\(271\) | − | 20.3877i | − | 1.23847i | −0.785207 | − | 0.619233i | \(-0.787444\pi\) | ||
0.785207 | − | 0.619233i | \(-0.212556\pi\) | |||||||
\(272\) | −2.63227 | −0.159605 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.62107 | 0.460406 | ||||||||
\(275\) | − | 0.963479i | − | 0.0580999i | ||||||
\(276\) | −4.39541 | − | 1.56689i | −0.264572 | − | 0.0943155i | ||||
\(277\) | 7.62035 | 0.457862 | 0.228931 | − | 0.973443i | \(-0.426477\pi\) | ||||
0.228931 | + | 0.973443i | \(0.426477\pi\) | |||||||
\(278\) | 7.13772 | 0.428092 | ||||||||
\(279\) | −6.49312 | + | 7.94986i | −0.388733 | + | 0.475946i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.58608i | 0.273583i | 0.990600 | + | 0.136791i | \(0.0436790\pi\) | ||||
−0.990600 | + | 0.136791i | \(0.956321\pi\) | |||||||
\(282\) | −16.9491 | − | 6.04207i | −1.00931 | − | 0.359800i | ||||
\(283\) | − | 15.9756i | − | 0.949653i | −0.880079 | − | 0.474826i | \(-0.842511\pi\) | ||
0.880079 | − | 0.474826i | \(-0.157489\pi\) | |||||||
\(284\) | − | 11.1501i | − | 0.661639i | ||||||
\(285\) | 8.43126 | + | 3.00560i | 0.499425 | + | 0.178036i | ||||
\(286\) | − | 1.91522i | − | 0.113249i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.89773 | − | 2.32349i | 0.111825 | − | 0.136913i | ||||
\(289\) | −10.0711 | −0.592420 | ||||||||
\(290\) | −9.90498 | −0.581640 | ||||||||
\(291\) | 23.9815 | + | 8.54900i | 1.40582 | + | 0.501151i | ||||
\(292\) | − | 11.7735i | − | 0.688991i | ||||||
\(293\) | 1.03780 | 0.0606290 | 0.0303145 | − | 0.999540i | \(-0.490349\pi\) | ||||
0.0303145 | + | 0.999540i | \(0.490349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.10246 | −0.122410 | ||||||||
\(296\) | − | 9.14603i | − | 0.531602i | ||||||
\(297\) | −2.58889 | − | 4.28503i | −0.150223 | − | 0.248643i | ||||
\(298\) | −11.9687 | −0.693329 | ||||||||
\(299\) | −5.35540 | −0.309711 | ||||||||
\(300\) | 0.581597 | − | 1.63149i | 0.0335785 | − | 0.0941939i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.99700i | 0.517719i | ||||||||
\(303\) | −8.81873 | + | 24.7382i | −0.506623 | + | 1.42117i | ||||
\(304\) | 5.16784i | 0.296396i | ||||||||
\(305\) | − | 8.96260i | − | 0.513197i | ||||||
\(306\) | −4.99535 | + | 6.11606i | −0.285565 | + | 0.349632i | ||||
\(307\) | 3.19308i | 0.182238i | 0.995840 | + | 0.0911192i | \(0.0290444\pi\) | ||||
−0.995840 | + | 0.0911192i | \(0.970956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7983 | + | 5.27535i | 0.841848 | + | 0.300104i | ||||
\(310\) | −3.42151 | −0.194329 | ||||||||
\(311\) | 30.9813 | 1.75679 | 0.878395 | − | 0.477935i | \(-0.158615\pi\) | ||||
0.878395 | + | 0.477935i | \(0.158615\pi\) | |||||||
\(312\) | 1.15611 | − | 3.24309i | 0.0654517 | − | 0.183604i | ||||
\(313\) | − | 9.85129i | − | 0.556828i | −0.960461 | − | 0.278414i | \(-0.910191\pi\) | ||
0.960461 | − | 0.278414i | \(-0.0898087\pi\) | |||||||
\(314\) | 6.58680 | 0.371715 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.408348 | 0.0229714 | ||||||||
\(317\) | − | 18.6337i | − | 1.04657i | −0.852156 | − | 0.523287i | \(-0.824705\pi\) | ||
0.852156 | − | 0.523287i | \(-0.175295\pi\) | |||||||
\(318\) | −7.66205 | + | 21.4935i | −0.429667 | + | 1.20529i | ||||
\(319\) | −9.54323 | −0.534318 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 22.6107 | + | 8.06034i | 1.26201 | + | 0.449884i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 13.6032i | − | 0.756901i | ||||||
\(324\) | −1.79722 | − | 8.81873i | −0.0998456 | − | 0.489929i | ||||
\(325\) | − | 1.98782i | − | 0.110264i | ||||||
\(326\) | 2.65049i | 0.146797i | ||||||||
\(327\) | 9.73209 | − | 27.3003i | 0.538186 | − | 1.50971i | ||||
\(328\) | 1.12202i | 0.0619533i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.560356 | − | 1.57190i | 0.0308466 | − | 0.0865303i | ||||
\(331\) | −34.6782 | −1.90609 | −0.953044 | − | 0.302832i | \(-0.902068\pi\) | ||||
−0.953044 | + | 0.302832i | \(0.902068\pi\) | |||||||
\(332\) | 4.53092 | 0.248667 | ||||||||
\(333\) | −21.2507 | − | 17.3567i | −1.16453 | − | 0.951143i | ||||
\(334\) | 7.68946i | 0.420749i | ||||||||
\(335\) | 1.79547 | 0.0980968 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.1938 | 0.827657 | 0.413828 | − | 0.910355i | \(-0.364191\pi\) | ||||
0.413828 | + | 0.910355i | \(0.364191\pi\) | |||||||
\(338\) | 9.04859i | 0.492178i | ||||||||
\(339\) | 22.7356 | + | 8.10486i | 1.23483 | + | 0.440196i | ||||
\(340\) | −2.63227 | −0.142755 | ||||||||
\(341\) | −3.29656 | −0.178519 | ||||||||
\(342\) | 12.0074 | + | 9.80719i | 0.649288 | + | 0.530312i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1.54917i | − | 0.0835257i | ||||||
\(345\) | −4.39541 | − | 1.56689i | −0.236641 | − | 0.0843584i | ||||
\(346\) | − | 21.2908i | − | 1.14460i | ||||||
\(347\) | 15.4938i | 0.831752i | 0.909421 | + | 0.415876i | \(0.136525\pi\) | ||||
−0.909421 | + | 0.415876i | \(0.863475\pi\) | |||||||
\(348\) | −16.1598 | − | 5.76070i | −0.866258 | − | 0.308806i | ||||
\(349\) | − | 1.85927i | − | 0.0995246i | −0.998761 | − | 0.0497623i | \(-0.984154\pi\) | ||
0.998761 | − | 0.0497623i | \(-0.0158464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.34132 | − | 8.84073i | −0.285098 | − | 0.471883i | ||||
\(352\) | 0.963479 | 0.0513536 | ||||||||
\(353\) | −34.9105 | −1.85810 | −0.929050 | − | 0.369955i | \(-0.879373\pi\) | ||||
−0.929050 | + | 0.369955i | \(0.879373\pi\) | |||||||
\(354\) | −3.43014 | − | 1.22278i | −0.182310 | − | 0.0649903i | ||||
\(355\) | − | 11.1501i | − | 0.591787i | ||||||
\(356\) | 11.5214 | 0.610633 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.32636 | 0.0701005 | ||||||||
\(359\) | 8.21688i | 0.433670i | 0.976208 | + | 0.216835i | \(0.0695734\pi\) | ||||
−0.976208 | + | 0.216835i | \(0.930427\pi\) | |||||||
\(360\) | 1.89773 | − | 2.32349i | 0.100019 | − | 0.122459i | ||||
\(361\) | −7.70660 | −0.405611 | ||||||||
\(362\) | 2.17439 | 0.114284 | ||||||||
\(363\) | −5.85767 | + | 16.4318i | −0.307448 | + | 0.862448i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 11.7735i | − | 0.616252i | ||||||
\(366\) | 5.21262 | − | 14.6224i | 0.272468 | − | 0.764323i | ||||
\(367\) | − | 13.3705i | − | 0.697934i | −0.937135 | − | 0.348967i | \(-0.886533\pi\) | ||
0.937135 | − | 0.348967i | \(-0.113467\pi\) | |||||||
\(368\) | − | 2.69411i | − | 0.140440i | ||||||
\(369\) | 2.60701 | + | 2.12930i | 0.135715 | + | 0.110847i | ||||
\(370\) | − | 9.14603i | − | 0.475480i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.58215 | − | 1.98994i | −0.289421 | − | 0.103174i | ||||
\(373\) | 10.0857 | 0.522218 | 0.261109 | − | 0.965309i | \(-0.415912\pi\) | ||||
0.261109 | + | 0.965309i | \(0.415912\pi\) | |||||||
\(374\) | −2.53614 | −0.131141 | ||||||||
\(375\) | 0.581597 | − | 1.63149i | 0.0300335 | − | 0.0842496i | ||||
\(376\) | − | 10.3888i | − | 0.535760i | ||||||
\(377\) | −19.6893 | −1.01405 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.9625 | −1.17951 | −0.589753 | − | 0.807583i | \(-0.700775\pi\) | ||||
−0.589753 | + | 0.807583i | \(0.700775\pi\) | |||||||
\(380\) | 5.16784i | 0.265105i | ||||||||
\(381\) | −9.41820 | + | 26.4198i | −0.482509 | + | 1.35353i | ||||
\(382\) | 17.0570 | 0.872710 | ||||||||
\(383\) | 16.8876 | 0.862918 | 0.431459 | − | 0.902132i | \(-0.357999\pi\) | ||||
0.431459 | + | 0.902132i | \(0.357999\pi\) | |||||||
\(384\) | 1.63149 | + | 0.581597i | 0.0832564 | + | 0.0296795i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.05067i | 0.104376i | ||||||||
\(387\) | −3.59948 | − | 2.93991i | −0.182972 | − | 0.149444i | ||||
\(388\) | 14.6992i | 0.746239i | ||||||||
\(389\) | 20.1754i | 1.02293i | 0.859303 | + | 0.511467i | \(0.170898\pi\) | ||||
−0.859303 | + | 0.511467i | \(0.829102\pi\) | |||||||
\(390\) | 1.15611 | − | 3.24309i | 0.0585417 | − | 0.164220i | ||||
\(391\) | 7.09164i | 0.358640i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.44429 | − | 9.66188i | 0.173742 | − | 0.487377i | ||||
\(394\) | −12.9420 | −0.652011 | ||||||||
\(395\) | 0.408348 | 0.0205462 | ||||||||
\(396\) | 1.82842 | − | 2.23863i | 0.0918818 | − | 0.112496i | ||||
\(397\) | 19.0214i | 0.954655i | 0.878725 | + | 0.477327i | \(0.158394\pi\) | ||||
−0.878725 | + | 0.477327i | \(0.841606\pi\) | |||||||
\(398\) | 17.1869 | 0.861502 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − | 4.78840i | − | 0.239121i | −0.992827 | − | 0.119561i | \(-0.961851\pi\) | ||
0.992827 | − | 0.119561i | \(-0.0381486\pi\) | |||||||
\(402\) | 2.92928 | + | 1.04424i | 0.146099 | + | 0.0520818i | ||||
\(403\) | −6.80134 | −0.338799 | ||||||||
\(404\) | −15.1630 | −0.754386 | ||||||||
\(405\) | −1.79722 | − | 8.81873i | −0.0893046 | − | 0.438206i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.81201i | − | 0.436795i | ||||||
\(408\) | −4.29451 | − | 1.53092i | −0.212610 | − | 0.0757919i | ||||
\(409\) | 0.339562i | 0.0167903i | 0.999965 | + | 0.00839514i | \(0.00267229\pi\) | ||||
−0.999965 | + | 0.00839514i | \(0.997328\pi\) | |||||||
\(410\) | 1.12202i | 0.0554127i | ||||||||
\(411\) | 12.4337 | + | 4.43239i | 0.613308 | + | 0.218634i | ||||
\(412\) | 9.07046i | 0.446870i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.25975 | − | 5.11271i | −0.307650 | − | 0.251276i | ||||
\(415\) | 4.53092 | 0.222414 | ||||||||
\(416\) | 1.98782 | 0.0974607 | ||||||||
\(417\) | 11.6451 | + | 4.15127i | 0.570262 | + | 0.203289i | ||||
\(418\) | 4.97911i | 0.243536i | ||||||||
\(419\) | 15.1963 | 0.742389 | 0.371194 | − | 0.928555i | \(-0.378948\pi\) | ||||
0.371194 | + | 0.928555i | \(0.378948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5755 | −0.954052 | −0.477026 | − | 0.878889i | \(-0.658285\pi\) | ||||
−0.477026 | + | 0.878889i | \(0.658285\pi\) | |||||||
\(422\) | 2.19691i | 0.106944i | ||||||||
\(423\) | −24.1382 | − | 19.7151i | −1.17364 | − | 0.958581i | ||||
\(424\) | −13.1742 | −0.639794 | ||||||||
\(425\) | −2.63227 | −0.127684 | ||||||||
\(426\) | 6.48488 | − | 18.1913i | 0.314193 | − | 0.881370i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.8590i | 0.669899i | ||||||||
\(429\) | 1.11388 | − | 3.12465i | 0.0537788 | − | 0.150860i | ||||
\(430\) | − | 1.54917i | − | 0.0747076i | ||||||
\(431\) | 1.19150i | 0.0573926i | 0.999588 | + | 0.0286963i | \(0.00913558\pi\) | ||||
−0.999588 | + | 0.0286963i | \(0.990864\pi\) | |||||||
\(432\) | 4.44746 | − | 2.68703i | 0.213978 | − | 0.129280i | ||||
\(433\) | 18.9398i | 0.910188i | 0.890443 | + | 0.455094i | \(0.150394\pi\) | ||||
−0.890443 | + | 0.455094i | \(0.849606\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.1598 | − | 5.76070i | −0.774804 | − | 0.276204i | ||||
\(436\) | 16.7334 | 0.801385 | ||||||||
\(437\) | 13.9228 | 0.666016 | ||||||||
\(438\) | 6.84742 | − | 19.2083i | 0.327182 | − | 0.917807i | ||||
\(439\) | 2.85620i | 0.136319i | 0.997674 | + | 0.0681594i | \(0.0217127\pi\) | ||||
−0.997674 | + | 0.0681594i | \(0.978287\pi\) | |||||||
\(440\) | 0.963479 | 0.0459320 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.23247 | −0.248883 | ||||||||
\(443\) | − | 34.9144i | − | 1.65883i | −0.558630 | − | 0.829417i | \(-0.688673\pi\) | ||
0.558630 | − | 0.829417i | \(-0.311327\pi\) | |||||||
\(444\) | 5.31930 | − | 14.9216i | 0.252443 | − | 0.708149i | ||||
\(445\) | 11.5214 | 0.546167 | ||||||||
\(446\) | 23.8443 | 1.12906 | ||||||||
\(447\) | −19.5268 | − | 6.96096i | −0.923586 | − | 0.329242i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.6789i | 0.975895i | 0.872873 | + | 0.487948i | \(0.162254\pi\) | ||||
−0.872873 | + | 0.487948i | \(0.837746\pi\) | |||||||
\(450\) | 1.89773 | − | 2.32349i | 0.0894600 | − | 0.109530i | ||||
\(451\) | 1.08104i | 0.0509044i | ||||||||
\(452\) | 13.9355i | 0.655473i | ||||||||
\(453\) | −5.23262 | + | 14.6785i | −0.245850 | + | 0.689655i | ||||
\(454\) | 4.67171i | 0.219254i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00560 | + | 8.43126i | −0.140750 | + | 0.394830i | ||||
\(457\) | 4.34281 | 0.203148 | 0.101574 | − | 0.994828i | \(-0.467612\pi\) | ||||
0.101574 | + | 0.994828i | \(0.467612\pi\) | |||||||
\(458\) | 23.1514 | 1.08179 | ||||||||
\(459\) | −11.7069 | + | 7.07299i | −0.546432 | + | 0.330139i | ||||
\(460\) | − | 2.69411i | − | 0.125614i | ||||||
\(461\) | −10.7827 | −0.502203 | −0.251101 | − | 0.967961i | \(-0.580793\pi\) | ||||
−0.251101 | + | 0.967961i | \(0.580793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.5503 | −0.862105 | −0.431053 | − | 0.902327i | \(-0.641858\pi\) | ||||
−0.431053 | + | 0.902327i | \(0.641858\pi\) | |||||||
\(464\) | − | 9.90498i | − | 0.459827i | ||||||
\(465\) | −5.58215 | − | 1.98994i | −0.258866 | − | 0.0922813i | ||||
\(466\) | −13.2418 | −0.613415 | ||||||||
\(467\) | −5.55332 | −0.256977 | −0.128489 | − | 0.991711i | \(-0.541013\pi\) | ||||
−0.128489 | + | 0.991711i | \(0.541013\pi\) | |||||||
\(468\) | 3.77234 | − | 4.61867i | 0.174377 | − | 0.213498i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 10.3888i | − | 0.479198i | ||||||
\(471\) | 10.7463 | + | 3.83086i | 0.495162 | + | 0.176517i | ||||
\(472\) | − | 2.10246i | − | 0.0967736i | ||||||
\(473\) | − | 1.49259i | − | 0.0686295i | ||||||
\(474\) | 0.666214 | + | 0.237494i | 0.0306002 | + | 0.0109085i | ||||
\(475\) | 5.16784i | 0.237117i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.0011 | + | 30.6101i | −1.14472 | + | 1.40154i | ||||
\(478\) | −14.7280 | −0.673643 | ||||||||
\(479\) | −1.51336 | −0.0691470 | −0.0345735 | − | 0.999402i | \(-0.511007\pi\) | ||||
−0.0345735 | + | 0.999402i | \(0.511007\pi\) | |||||||
\(480\) | 1.63149 | + | 0.581597i | 0.0744668 | + | 0.0265461i | ||||
\(481\) | − | 18.1806i | − | 0.828965i | ||||||
\(482\) | 5.92695 | 0.269965 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0717 | −0.457805 | ||||||||
\(485\) | 14.6992i | 0.667456i | ||||||||
\(486\) | 2.19680 | − | 15.4329i | 0.0996490 | − | 0.700050i | ||||
\(487\) | −10.6043 | −0.480527 | −0.240264 | − | 0.970708i | \(-0.577234\pi\) | ||||
−0.240264 | + | 0.970708i | \(0.577234\pi\) | |||||||
\(488\) | 8.96260 | 0.405718 | ||||||||
\(489\) | −1.54152 | + | 4.32424i | −0.0697098 | + | 0.195549i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2648i | 0.553504i | 0.960941 | + | 0.276752i | \(0.0892580\pi\) | ||||
−0.960941 | + | 0.276752i | \(0.910742\pi\) | |||||||
\(492\) | −0.652564 | + | 1.83056i | −0.0294198 | + | 0.0825281i | ||||
\(493\) | 26.0726i | 1.17425i | ||||||||
\(494\) | 10.2727i | 0.462192i | ||||||||
\(495\) | 1.82842 | − | 2.23863i | 0.0821816 | − | 0.100619i | ||||
\(496\) | − | 3.42151i | − | 0.153631i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.39213 | + | 2.63517i | 0.331249 | + | 0.118085i | ||||
\(499\) | 27.8286 | 1.24578 | 0.622889 | − | 0.782311i | \(-0.285959\pi\) | ||||
0.622889 | + | 0.782311i | \(0.285959\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −4.47217 | + | 12.5452i | −0.199802 | + | 0.560480i | ||||
\(502\) | 19.4694i | 0.868964i | ||||||||
\(503\) | −31.7645 | −1.41631 | −0.708154 | − | 0.706058i | \(-0.750472\pi\) | ||||
−0.708154 | + | 0.706058i | \(0.750472\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.1630 | −0.674743 | ||||||||
\(506\) | − | 2.59572i | − | 0.115394i | ||||||
\(507\) | −5.26263 | + | 14.7626i | −0.233721 | + | 0.655632i | ||||
\(508\) | −16.1937 | −0.718479 | ||||||||
\(509\) | −39.3135 | −1.74254 | −0.871270 | − | 0.490803i | \(-0.836703\pi\) | ||||
−0.871270 | + | 0.490803i | \(0.836703\pi\) | |||||||
\(510\) | −4.29451 | − | 1.53092i | −0.190164 | − | 0.0677903i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 13.8861 | + | 22.9838i | 0.613088 | + | 1.01476i | ||||
\(514\) | − | 2.83792i | − | 0.125175i | ||||||
\(515\) | 9.07046i | 0.399692i | ||||||||
\(516\) | 0.900992 | − | 2.52745i | 0.0396640 | − | 0.111265i | ||||
\(517\) | − | 10.0094i | − | 0.440211i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.3827 | − | 34.7356i | 0.543538 | − | 1.52473i | ||||
\(520\) | 1.98782 | 0.0871715 | ||||||||
\(521\) | −8.79770 | −0.385434 | −0.192717 | − | 0.981254i | \(-0.561730\pi\) | ||||
−0.192717 | + | 0.981254i | \(0.561730\pi\) | |||||||
\(522\) | −23.0141 | − | 18.7970i | −1.00730 | − | 0.822722i | ||||
\(523\) | 7.76366i | 0.339481i | 0.985489 | + | 0.169741i | \(0.0542930\pi\) | ||||
−0.985489 | + | 0.169741i | \(0.945707\pi\) | |||||||
\(524\) | 5.92214 | 0.258710 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0716 | 0.787961 | ||||||||
\(527\) | 9.00636i | 0.392323i | ||||||||
\(528\) | 1.57190 | + | 0.560356i | 0.0684082 | + | 0.0243864i | ||||
\(529\) | 15.7418 | 0.684424 | ||||||||
\(530\) | −13.1742 | −0.572249 | ||||||||
\(531\) | −4.88505 | − | 3.98991i | −0.211993 | − | 0.173147i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.23037i | 0.0966081i | ||||||||
\(534\) | 18.7970 | + | 6.70081i | 0.813426 | + | 0.289972i | ||||
\(535\) | 13.8590i | 0.599176i | ||||||||
\(536\) | 1.79547i | 0.0775523i | ||||||||
\(537\) | 2.16394 | + | 0.771409i | 0.0933811 | + | 0.0332888i | ||||
\(538\) | − | 17.1417i | − | 0.739033i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.44746 | − | 2.68703i | 0.191388 | − | 0.115631i | ||||
\(541\) | −37.1600 | −1.59763 | −0.798816 | − | 0.601576i | \(-0.794540\pi\) | ||||
−0.798816 | + | 0.601576i | \(0.794540\pi\) | |||||||
\(542\) | 20.3877 | 0.875727 | ||||||||
\(543\) | 3.54749 | + | 1.26462i | 0.152238 | + | 0.0542701i | ||||
\(544\) | − | 2.63227i | − | 0.112858i | ||||||
\(545\) | 16.7334 | 0.716780 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9929 | 1.53895 | 0.769473 | − | 0.638679i | \(-0.220519\pi\) | ||||
0.769473 | + | 0.638679i | \(0.220519\pi\) | |||||||
\(548\) | 7.62107i | 0.325556i | ||||||||
\(549\) | 17.0086 | − | 20.8245i | 0.725910 | − | 0.888769i | ||||
\(550\) | 0.963479 | 0.0410829 | ||||||||
\(551\) | 51.1874 | 2.18065 | ||||||||
\(552\) | 1.56689 | − | 4.39541i | 0.0666911 | − | 0.187081i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.62035i | 0.323758i | ||||||||
\(555\) | 5.31930 | − | 14.9216i | 0.225792 | − | 0.633387i | ||||
\(556\) | 7.13772i | 0.302707i | ||||||||
\(557\) | 32.2770i | 1.36762i | 0.729660 | + | 0.683810i | \(0.239678\pi\) | ||||
−0.729660 | + | 0.683810i | \(0.760322\pi\) | |||||||
\(558\) | −7.94986 | − | 6.49312i | −0.336544 | − | 0.274876i | ||||
\(559\) | − | 3.07947i | − | 0.130248i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.13767 | − | 1.47501i | −0.174693 | − | 0.0622749i | ||||
\(562\) | −4.58608 | −0.193452 | ||||||||
\(563\) | −0.464662 | −0.0195832 | −0.00979159 | − | 0.999952i | \(-0.503117\pi\) | ||||
−0.00979159 | + | 0.999952i | \(0.503117\pi\) | |||||||
\(564\) | 6.04207 | − | 16.9491i | 0.254417 | − | 0.713687i | ||||
\(565\) | 13.9355i | 0.586272i | ||||||||
\(566\) | 15.9756 | 0.671506 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1501 | 0.467849 | ||||||||
\(569\) | 11.0130i | 0.461690i | 0.972991 | + | 0.230845i | \(0.0741490\pi\) | ||||
−0.972991 | + | 0.230845i | \(0.925851\pi\) | |||||||
\(570\) | −3.00560 | + | 8.43126i | −0.125891 | + | 0.353147i | ||||
\(571\) | 11.0838 | 0.463842 | 0.231921 | − | 0.972735i | \(-0.425499\pi\) | ||||
0.231921 | + | 0.972735i | \(0.425499\pi\) | |||||||
\(572\) | 1.91522 | 0.0800793 | ||||||||
\(573\) | 27.8282 | + | 9.92027i | 1.16254 | + | 0.414425i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.69411i | − | 0.112352i | ||||||
\(576\) | 2.32349 | + | 1.89773i | 0.0968121 | + | 0.0790722i | ||||
\(577\) | 10.1245i | 0.421489i | 0.977541 | + | 0.210745i | \(0.0675888\pi\) | ||||
−0.977541 | + | 0.210745i | \(0.932411\pi\) | |||||||
\(578\) | − | 10.0711i | − | 0.418904i | ||||||
\(579\) | −1.19266 | + | 3.34564i | −0.0495654 | + | 0.139040i | ||||
\(580\) | − | 9.90498i | − | 0.411282i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.54900 | + | 23.9815i | −0.354367 | + | 0.994066i | ||||
\(583\) | −12.6930 | −0.525692 | ||||||||
\(584\) | 11.7735 | 0.487190 | ||||||||
\(585\) | 3.77234 | − | 4.61867i | 0.155967 | − | 0.190959i | ||||
\(586\) | 1.03780i | 0.0428712i | ||||||||
\(587\) | −36.0697 | −1.48876 | −0.744378 | − | 0.667759i | \(-0.767254\pi\) | ||||
−0.744378 | + | 0.667759i | \(0.767254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.6818 | 0.728568 | ||||||||
\(590\) | − | 2.10246i | − | 0.0865570i | ||||||
\(591\) | −21.1148 | − | 7.52705i | −0.868545 | − | 0.309621i | ||||
\(592\) | 9.14603 | 0.375900 | ||||||||
\(593\) | 31.8476 | 1.30783 | 0.653913 | − | 0.756570i | \(-0.273126\pi\) | ||||
0.653913 | + | 0.756570i | \(0.273126\pi\) | |||||||
\(594\) | 4.28503 | − | 2.58889i | 0.175817 | − | 0.106224i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 11.9687i | − | 0.490258i | ||||||
\(597\) | 28.0402 | + | 9.99585i | 1.14761 | + | 0.409103i | ||||
\(598\) | − | 5.35540i | − | 0.218999i | ||||||
\(599\) | 13.5175i | 0.552312i | 0.961113 | + | 0.276156i | \(0.0890607\pi\) | ||||
−0.961113 | + | 0.276156i | \(0.910939\pi\) | |||||||
\(600\) | 1.63149 | + | 0.581597i | 0.0666051 | + | 0.0237436i | ||||
\(601\) | − | 15.7057i | − | 0.640650i | −0.947308 | − | 0.320325i | \(-0.896208\pi\) | ||
0.947308 | − | 0.320325i | \(-0.103792\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.17175 | + | 3.40731i | 0.169887 | + | 0.138757i | ||||
\(604\) | −8.99700 | −0.366083 | ||||||||
\(605\) | −10.0717 | −0.409473 | ||||||||
\(606\) | −24.7382 | − | 8.81873i | −1.00492 | − | 0.358236i | ||||
\(607\) | 1.05341i | 0.0427565i | 0.999771 | + | 0.0213782i | \(0.00680542\pi\) | ||||
−0.999771 | + | 0.0213782i | \(0.993195\pi\) | |||||||
\(608\) | −5.16784 | −0.209584 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.96260 | 0.362885 | ||||||||
\(611\) | − | 20.6510i | − | 0.835448i | ||||||
\(612\) | −6.11606 | − | 4.99535i | −0.247227 | − | 0.201925i | ||||
\(613\) | −5.40639 | −0.218362 | −0.109181 | − | 0.994022i | \(-0.534823\pi\) | ||||
−0.109181 | + | 0.994022i | \(0.534823\pi\) | |||||||
\(614\) | −3.19308 | −0.128862 | ||||||||
\(615\) | −0.652564 | + | 1.83056i | −0.0263139 | + | 0.0738154i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.10356i | − | 0.124945i | −0.998047 | − | 0.0624723i | \(-0.980101\pi\) | ||
0.998047 | − | 0.0624723i | \(-0.0198985\pi\) | |||||||
\(618\) | −5.27535 | + | 14.7983i | −0.212206 | + | 0.595276i | ||||
\(619\) | 18.3738i | 0.738504i | 0.929329 | + | 0.369252i | \(0.120386\pi\) | ||||
−0.929329 | + | 0.369252i | \(0.879614\pi\) | |||||||
\(620\) | − | 3.42151i | − | 0.137411i | ||||||
\(621\) | −7.23916 | − | 11.9820i | −0.290497 | − | 0.480819i | ||||
\(622\) | 30.9813i | 1.24224i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.24309 | + | 1.15611i | 0.129828 | + | 0.0462813i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.85129 | 0.393737 | ||||||||
\(627\) | −2.89583 | + | 8.12334i | −0.115648 | + | 0.324415i | ||||
\(628\) | 6.58680i | 0.262842i | ||||||||
\(629\) | −24.0748 | −0.959927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.40873 | 0.135699 | 0.0678496 | − | 0.997696i | \(-0.478386\pi\) | ||||
0.0678496 | + | 0.997696i | \(0.478386\pi\) | |||||||
\(632\) | 0.408348i | 0.0162432i | ||||||||
\(633\) | −1.27772 | + | 3.58423i | −0.0507847 | + | 0.142460i | ||||
\(634\) | 18.6337 | 0.740040 | ||||||||
\(635\) | −16.1937 | −0.642627 | ||||||||
\(636\) | −21.4935 | − | 7.66205i | −0.852272 | − | 0.303820i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 9.54323i | − | 0.377820i | ||||||
\(639\) | 21.1600 | − | 25.9072i | 0.837075 | − | 1.02487i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 17.6475i | 0.697036i | 0.937302 | + | 0.348518i | \(0.113315\pi\) | ||||
−0.937302 | + | 0.348518i | \(0.886685\pi\) | |||||||
\(642\) | −8.06034 | + | 22.6107i | −0.318116 | + | 0.892374i | ||||
\(643\) | 7.27025i | 0.286711i | 0.989671 | + | 0.143355i | \(0.0457892\pi\) | ||||
−0.989671 | + | 0.143355i | \(0.954211\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.900992 | − | 2.52745i | 0.0354765 | − | 0.0995182i | ||||
\(646\) | 13.6032 | 0.535210 | ||||||||
\(647\) | 11.5139 | 0.452658 | 0.226329 | − | 0.974051i | \(-0.427328\pi\) | ||||
0.226329 | + | 0.974051i | \(0.427328\pi\) | |||||||
\(648\) | 8.81873 | − | 1.79722i | 0.346432 | − | 0.0706015i | ||||
\(649\) | − | 2.02568i | − | 0.0795148i | ||||||
\(650\) | 1.98782 | 0.0779686 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.65049 | −0.103801 | ||||||||
\(653\) | − | 19.0233i | − | 0.744441i | −0.928144 | − | 0.372221i | \(-0.878596\pi\) | ||
0.928144 | − | 0.372221i | \(-0.121404\pi\) | |||||||
\(654\) | 27.3003 | + | 9.73209i | 1.06753 | + | 0.380555i | ||||
\(655\) | 5.92214 | 0.231397 | ||||||||
\(656\) | −1.12202 | −0.0438076 | ||||||||
\(657\) | 22.3429 | − | 27.3556i | 0.871681 | − | 1.06724i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.0201i | 0.546146i | 0.961993 | + | 0.273073i | \(0.0880401\pi\) | ||||
−0.961993 | + | 0.273073i | \(0.911960\pi\) | |||||||
\(660\) | 1.57190 | + | 0.560356i | 0.0611862 | + | 0.0218118i | ||||
\(661\) | 10.9172i | 0.424632i | 0.977201 | + | 0.212316i | \(0.0681006\pi\) | ||||
−0.977201 | + | 0.212316i | \(0.931899\pi\) | |||||||
\(662\) | − | 34.6782i | − | 1.34781i | ||||||
\(663\) | −8.53671 | − | 3.04319i | −0.331538 | − | 0.118188i | ||||
\(664\) | 4.53092i | 0.175834i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.3567 | − | 21.2507i | 0.672559 | − | 0.823449i | ||||
\(667\) | −26.6851 | −1.03325 | ||||||||
\(668\) | −7.68946 | −0.297514 | ||||||||
\(669\) | 38.9016 | + | 13.8677i | 1.50402 | + | 0.536158i | ||||
\(670\) | 1.79547i | 0.0693649i | ||||||||
\(671\) | 8.63527 | 0.333361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.4579 | 0.518765 | 0.259382 | − | 0.965775i | \(-0.416481\pi\) | ||||
0.259382 | + | 0.965775i | \(0.416481\pi\) | |||||||
\(674\) | 15.1938i | 0.585242i | ||||||||
\(675\) | 4.44746 | − | 2.68703i | 0.171183 | − | 0.103424i | ||||
\(676\) | −9.04859 | −0.348023 | ||||||||
\(677\) | −32.2781 | −1.24055 | −0.620274 | − | 0.784385i | \(-0.712979\pi\) | ||||
−0.620274 | + | 0.784385i | \(0.712979\pi\) | |||||||
\(678\) | −8.10486 | + | 22.7356i | −0.311265 | + | 0.873157i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 2.63227i | − | 0.100943i | ||||||
\(681\) | −2.71705 | + | 7.62183i | −0.104118 | + | 0.292069i | ||||
\(682\) | − | 3.29656i | − | 0.126232i | ||||||
\(683\) | − | 46.4991i | − | 1.77924i | −0.456704 | − | 0.889619i | \(-0.650970\pi\) | ||
0.456704 | − | 0.889619i | \(-0.349030\pi\) | |||||||
\(684\) | −9.80719 | + | 12.0074i | −0.374987 | + | 0.459116i | ||||
\(685\) | 7.62107i | 0.291186i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.7712 | + | 13.4648i | 1.44106 | + | 0.513713i | ||||
\(688\) | 1.54917 | 0.0590616 | ||||||||
\(689\) | −26.1878 | −0.997677 | ||||||||
\(690\) | 1.56689 | − | 4.39541i | 0.0596504 | − | 0.167330i | ||||
\(691\) | 48.4752i | 1.84408i | 0.387092 | + | 0.922041i | \(0.373480\pi\) | ||||
−0.387092 | + | 0.922041i | \(0.626520\pi\) | |||||||
\(692\) | 21.2908 | 0.809355 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.4938 | −0.588137 | ||||||||
\(695\) | 7.13772i | 0.270749i | ||||||||
\(696\) | 5.76070 | − | 16.1598i | 0.218359 | − | 0.612537i | ||||
\(697\) | 2.95347 | 0.111871 | ||||||||
\(698\) | 1.85927 | 0.0703745 | ||||||||
\(699\) | −21.6038 | − | 7.70139i | −0.817131 | − | 0.291293i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.0722i | 0.758118i | 0.925372 | + | 0.379059i | \(0.123752\pi\) | ||||
−0.925372 | + | 0.379059i | \(0.876248\pi\) | |||||||
\(702\) | 8.84073 | − | 5.34132i | 0.333672 | − | 0.201595i | ||||
\(703\) | 47.2653i | 1.78264i | ||||||||
\(704\) | 0.963479i | 0.0363125i | ||||||||
\(705\) | 6.04207 | − | 16.9491i | 0.227557 | − | 0.638341i | ||||
\(706\) | − | 34.9105i | − | 1.31387i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.22278 | − | 3.43014i | 0.0459551 | − | 0.128912i | ||||
\(709\) | 22.6496 | 0.850623 | 0.425311 | − | 0.905047i | \(-0.360165\pi\) | ||||
0.425311 | + | 0.905047i | \(0.360165\pi\) | |||||||
\(710\) | 11.1501 | 0.418457 | ||||||||
\(711\) | 0.948793 | + | 0.774936i | 0.0355825 | + | 0.0290624i | ||||
\(712\) | 11.5214i | 0.431783i | ||||||||
\(713\) | −9.21795 | −0.345215 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.91522 | 0.0716251 | ||||||||
\(716\) | 1.32636i | 0.0495686i | ||||||||
\(717\) | −24.0285 | − | 8.56575i | −0.897361 | − | 0.319894i | ||||
\(718\) | −8.21688 | −0.306651 | ||||||||
\(719\) | 1.22573 | 0.0457121 | 0.0228561 | − | 0.999739i | \(-0.492724\pi\) | ||||
0.0228561 | + | 0.999739i | \(0.492724\pi\) | |||||||
\(720\) | 2.32349 | + | 1.89773i | 0.0865914 | + | 0.0707243i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 7.70660i | − | 0.286810i | ||||||
\(723\) | 9.66973 | + | 3.44709i | 0.359621 | + | 0.128199i | ||||
\(724\) | 2.17439i | 0.0808107i | ||||||||
\(725\) | − | 9.90498i | − | 0.367862i | ||||||
\(726\) | −16.4318 | − | 5.85767i | −0.609843 | − | 0.217399i | ||||
\(727\) | 33.9559i | 1.25936i | 0.776856 | + | 0.629678i | \(0.216813\pi\) | ||||
−0.776856 | + | 0.629678i | \(0.783187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.5598 | − | 23.9009i | 0.465177 | − | 0.885218i | ||||
\(730\) | 11.7735 | 0.435756 | ||||||||
\(731\) | −4.07784 | −0.150824 | ||||||||
\(732\) | 14.6224 | + | 5.21262i | 0.540458 | + | 0.192664i | ||||
\(733\) | 20.8063i | 0.768500i | 0.923229 | + | 0.384250i | \(0.125540\pi\) | ||||
−0.923229 | + | 0.384250i | \(0.874460\pi\) | |||||||
\(734\) | 13.3705 | 0.493514 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.69411 | 0.0993063 | ||||||||
\(737\) | 1.72989i | 0.0637214i | ||||||||
\(738\) | −2.12930 | + | 2.60701i | −0.0783805 | + | 0.0959652i | ||||
\(739\) | 9.86421 | 0.362861 | 0.181430 | − | 0.983404i | \(-0.441927\pi\) | ||||
0.181430 | + | 0.983404i | \(0.441927\pi\) | |||||||
\(740\) | 9.14603 | 0.336215 | ||||||||
\(741\) | −5.97458 | + | 16.7598i | −0.219482 | + | 0.615687i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.9248i | 0.694283i | 0.937813 | + | 0.347141i | \(0.112848\pi\) | ||||
−0.937813 | + | 0.347141i | \(0.887152\pi\) | |||||||
\(744\) | 1.98994 | − | 5.58215i | 0.0729548 | − | 0.204652i | ||||
\(745\) | − | 11.9687i | − | 0.438500i | ||||||
\(746\) | 10.0857i | 0.369264i | ||||||||
\(747\) | 10.5276 | + | 8.59848i | 0.385183 | + | 0.314602i | ||||
\(748\) | − | 2.53614i | − | 0.0927304i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.63149 | + | 0.581597i | 0.0595734 | + | 0.0212369i | ||||
\(751\) | 9.78087 | 0.356909 | 0.178455 | − | 0.983948i | \(-0.442890\pi\) | ||||
0.178455 | + | 0.983948i | \(0.442890\pi\) | |||||||
\(752\) | 10.3888 | 0.378839 | ||||||||
\(753\) | −11.3234 | + | 31.7641i | −0.412646 | + | 1.15755i | ||||
\(754\) | − | 19.6893i | − | 0.717041i | ||||||
\(755\) | −8.99700 | −0.327434 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5979 | 0.930373 | 0.465187 | − | 0.885213i | \(-0.345987\pi\) | ||||
0.465187 | + | 0.885213i | \(0.345987\pi\) | |||||||
\(758\) | − | 22.9625i | − | 0.834037i | ||||||
\(759\) | 1.50966 | − | 4.23488i | 0.0547973 | − | 0.153716i | ||||
\(760\) | −5.16784 | −0.187457 | ||||||||
\(761\) | 1.50256 | 0.0544677 | 0.0272338 | − | 0.999629i | \(-0.491330\pi\) | ||||
0.0272338 | + | 0.999629i | \(0.491330\pi\) | |||||||
\(762\) | −26.4198 | − | 9.41820i | −0.957088 | − | 0.341185i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.0570i | 0.617099i | ||||||||
\(765\) | −6.11606 | − | 4.99535i | −0.221127 | − | 0.180607i | ||||
\(766\) | 16.8876i | 0.610175i | ||||||||
\(767\) | − | 4.17931i | − | 0.150906i | ||||||
\(768\) | −0.581597 | + | 1.63149i | −0.0209866 | + | 0.0588712i | ||||
\(769\) | − | 34.5776i | − | 1.24690i | −0.781863 | − | 0.623451i | \(-0.785730\pi\) | ||
0.781863 | − | 0.623451i | \(-0.214270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.65052 | − | 4.63002i | 0.0594421 | − | 0.166746i | ||||
\(772\) | −2.05067 | −0.0738053 | ||||||||
\(773\) | 31.8854 | 1.14684 | 0.573418 | − | 0.819263i | \(-0.305617\pi\) | ||||
0.573418 | + | 0.819263i | \(0.305617\pi\) | |||||||
\(774\) | 2.93991 | − | 3.59948i | 0.105673 | − | 0.129381i | ||||
\(775\) | − | 3.42151i | − | 0.122904i | ||||||
\(776\) | −14.6992 | −0.527670 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.1754 | −0.723324 | ||||||||
\(779\) | − | 5.79843i | − | 0.207750i | ||||||
\(780\) | 3.24309 | + | 1.15611i | 0.116121 | + | 0.0413953i | ||||
\(781\) | 10.7429 | 0.384412 | ||||||||
\(782\) | −7.09164 | −0.253597 | ||||||||
\(783\) | −26.6149 | − | 44.0520i | −0.951140 | − | 1.57429i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.58680i | 0.235093i | ||||||||
\(786\) | 9.66188 | + | 3.44429i | 0.344628 | + | 0.122854i | ||||
\(787\) | − | 36.8450i | − | 1.31338i | −0.754159 | − | 0.656692i | \(-0.771955\pi\) | ||
0.754159 | − | 0.656692i | \(-0.228045\pi\) | |||||||
\(788\) | − | 12.9420i | − | 0.461041i | ||||||
\(789\) | 29.4836 | + | 10.5104i | 1.04965 | + | 0.374180i | ||||
\(790\) | 0.408348i | 0.0145284i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.23863 | + | 1.82842i | 0.0795464 | + | 0.0649703i | ||||
\(793\) | 17.8160 | 0.632665 | ||||||||
\(794\) | −19.0214 | −0.675043 | ||||||||
\(795\) | −21.4935 | − | 7.66205i | −0.762295 | − | 0.271745i | ||||
\(796\) | 17.1869i | 0.609174i | ||||||||
\(797\) | −23.2407 | −0.823228 | −0.411614 | − | 0.911358i | \(-0.635035\pi\) | ||||
−0.411614 | + | 0.911358i | \(0.635035\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.3461 | −0.967434 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 26.7699 | + | 21.8645i | 0.945867 | + | 0.772545i | ||||
\(802\) | 4.78840 | 0.169084 | ||||||||
\(803\) | 11.3435 | 0.400303 | ||||||||
\(804\) | −1.04424 | + | 2.92928i | −0.0368274 | + | 0.103308i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.80134i | − | 0.239567i | ||||||
\(807\) | 9.96958 | − | 27.9665i | 0.350946 | − | 0.984468i | ||||
\(808\) | − | 15.1630i | − | 0.533431i | ||||||
\(809\) | − | 29.5774i | − | 1.03989i | −0.854200 | − | 0.519944i | \(-0.825953\pi\) | ||
0.854200 | − | 0.519944i | \(-0.174047\pi\) | |||||||
\(810\) | 8.81873 | − | 1.79722i | 0.309859 | − | 0.0631479i | ||||
\(811\) | 23.3350i | 0.819404i | 0.912219 | + | 0.409702i | \(0.134367\pi\) | ||||
−0.912219 | + | 0.409702i | \(0.865633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.2623 | + | 11.8574i | 1.16656 | + | 0.415858i | ||||
\(814\) | 8.81201 | 0.308861 | ||||||||
\(815\) | −2.65049 | −0.0928427 | ||||||||
\(816\) | 1.53092 | − | 4.29451i | 0.0535929 | − | 0.150338i | ||||
\(817\) | 8.00587i | 0.280090i | ||||||||
\(818\) | −0.339562 | −0.0118725 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.12202 | −0.0391827 | ||||||||
\(821\) | 14.6669i | 0.511879i | 0.966693 | + | 0.255939i | \(0.0823847\pi\) | ||||
−0.966693 | + | 0.255939i | \(0.917615\pi\) | |||||||
\(822\) | −4.43239 | + | 12.4337i | −0.154597 | + | 0.433674i | ||||
\(823\) | 51.9093 | 1.80944 | 0.904722 | − | 0.426002i | \(-0.140078\pi\) | ||||
0.904722 | + | 0.426002i | \(0.140078\pi\) | |||||||
\(824\) | −9.07046 | −0.315985 | ||||||||
\(825\) | 1.57190 | + | 0.560356i | 0.0547266 | + | 0.0195091i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.36232i | 0.116919i | 0.998290 | + | 0.0584596i | \(0.0186189\pi\) | ||||
−0.998290 | + | 0.0584596i | \(0.981381\pi\) | |||||||
\(828\) | 5.11271 | − | 6.25975i | 0.177679 | − | 0.217541i | ||||
\(829\) | − | 6.86065i | − | 0.238280i | −0.992877 | − | 0.119140i | \(-0.961986\pi\) | ||
0.992877 | − | 0.119140i | \(-0.0380138\pi\) | |||||||
\(830\) | 4.53092i | 0.157271i | ||||||||
\(831\) | −4.43197 | + | 12.4325i | −0.153743 | + | 0.431278i | ||||
\(832\) | 1.98782i | 0.0689151i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.15127 | + | 11.6451i | −0.143747 | + | 0.403236i | ||||
\(835\) | −7.68946 | −0.266105 | ||||||||
\(836\) | −4.97911 | −0.172206 | ||||||||
\(837\) | −9.19370 | − | 15.2170i | −0.317781 | − | 0.525978i | ||||
\(838\) | 15.1963i | 0.524948i | ||||||||
\(839\) | −8.29693 | −0.286442 | −0.143221 | − | 0.989691i | \(-0.545746\pi\) | ||||
−0.143221 | + | 0.989691i | \(0.545746\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −69.1085 | −2.38305 | ||||||||
\(842\) | − | 19.5755i | − | 0.674616i | ||||||
\(843\) | −7.48213 | − | 2.66725i | −0.257698 | − | 0.0918649i | ||||
\(844\) | −2.19691 | −0.0756208 | ||||||||
\(845\) | −9.04859 | −0.311281 | ||||||||
\(846\) | 19.7151 | − | 24.1382i | 0.677819 | − | 0.829888i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 13.1742i | − | 0.452403i | ||||||
\(849\) | 26.0640 | + | 9.29137i | 0.894515 | + | 0.318879i | ||||
\(850\) | − | 2.63227i | − | 0.0902862i | ||||||
\(851\) | − | 24.6404i | − | 0.844664i | ||||||
\(852\) | 18.1913 | + | 6.48488i | 0.623223 | + | 0.222168i | ||||
\(853\) | 50.8963i | 1.74266i | 0.490700 | + | 0.871328i | \(0.336741\pi\) | ||||
−0.490700 | + | 0.871328i | \(0.663259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.80719 | + | 12.0074i | −0.335399 | + | 0.410646i | ||||
\(856\) | −13.8590 | −0.473690 | ||||||||
\(857\) | 2.07412 | 0.0708505 | 0.0354252 | − | 0.999372i | \(-0.488721\pi\) | ||||
0.0354252 | + | 0.999372i | \(0.488721\pi\) | |||||||
\(858\) | 3.12465 | + | 1.11388i | 0.106674 | + | 0.0380274i | ||||
\(859\) | − | 18.3210i | − | 0.625103i | −0.949901 | − | 0.312552i | \(-0.898816\pi\) | ||
0.949901 | − | 0.312552i | \(-0.101184\pi\) | |||||||
\(860\) | 1.54917 | 0.0528263 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.19150 | −0.0405827 | ||||||||
\(863\) | 24.4440i | 0.832084i | 0.909345 | + | 0.416042i | \(0.136583\pi\) | ||||
−0.909345 | + | 0.416042i | \(0.863417\pi\) | |||||||
\(864\) | 2.68703 | + | 4.44746i | 0.0914145 | + | 0.151306i | ||||
\(865\) | 21.2908 | 0.723909 | ||||||||
\(866\) | −18.9398 | −0.643600 | ||||||||
\(867\) | 5.85734 | − | 16.4309i | 0.198926 | − | 0.558023i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.393435i | 0.0133464i | ||||||||
\(870\) | 5.76070 | − | 16.1598i | 0.195306 | − | 0.547869i | ||||
\(871\) | 3.56906i | 0.120933i | ||||||||
\(872\) | 16.7334i | 0.566664i | ||||||||
\(873\) | −27.8951 | + | 34.1534i | −0.944108 | + | 1.15592i | ||||
\(874\) | 13.9228i | 0.470944i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.2083 | + | 6.84742i | 0.648987 | + | 0.231353i | ||||
\(877\) | 30.5364 | 1.03114 | 0.515571 | − | 0.856847i | \(-0.327580\pi\) | ||||
0.515571 | + | 0.856847i | \(0.327580\pi\) | |||||||
\(878\) | −2.85620 | −0.0963920 | ||||||||
\(879\) | −0.603581 | + | 1.69316i | −0.0203583 | + | 0.0571088i | ||||
\(880\) | 0.963479i | 0.0324789i | ||||||||
\(881\) | 12.8329 | 0.432352 | 0.216176 | − | 0.976354i | \(-0.430642\pi\) | ||||
0.216176 | + | 0.976354i | \(0.430642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8658 | 0.432970 | 0.216485 | − | 0.976286i | \(-0.430541\pi\) | ||||
0.216485 | + | 0.976286i | \(0.430541\pi\) | |||||||
\(884\) | − | 5.23247i | − | 0.175987i | ||||||
\(885\) | 1.22278 | − | 3.43014i | 0.0411034 | − | 0.115303i | ||||
\(886\) | 34.9144 | 1.17297 | ||||||||
\(887\) | 10.9822 | 0.368745 | 0.184373 | − | 0.982856i | \(-0.440975\pi\) | ||||
0.184373 | + | 0.982856i | \(0.440975\pi\) | |||||||
\(888\) | 14.9216 | + | 5.31930i | 0.500737 | + | 0.178504i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.5214i | 0.386198i | ||||||||
\(891\) | 8.49666 | − | 1.73158i | 0.284649 | − | 0.0580102i | ||||
\(892\) | 23.8443i | 0.798365i | ||||||||
\(893\) | 53.6875i | 1.79658i | ||||||||
\(894\) | 6.96096 | − | 19.5268i | 0.232809 | − | 0.653074i | ||||
\(895\) | 1.32636i | 0.0443355i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.11468 | − | 8.73726i | 0.103996 | − | 0.291729i | ||||
\(898\) | −20.6789 | −0.690062 | ||||||||
\(899\) | −33.8900 | −1.13030 | ||||||||
\(900\) | 2.32349 | + | 1.89773i | 0.0774497 | + | 0.0632578i | ||||
\(901\) | 34.6780i | 1.15529i | ||||||||
\(902\) | −1.08104 | −0.0359948 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.9355 | −0.463489 | ||||||||
\(905\) | 2.17439i | 0.0722793i | ||||||||
\(906\) | −14.6785 | − | 5.23262i | −0.487660 | − | 0.173842i | ||||
\(907\) | −28.7217 | −0.953688 | −0.476844 | − | 0.878988i | \(-0.658219\pi\) | ||||
−0.476844 | + | 0.878988i | \(0.658219\pi\) | |||||||
\(908\) | −4.67171 | −0.155036 | ||||||||
\(909\) | −35.2310 | − | 28.7753i | −1.16854 | − | 0.954415i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 41.5041i | − | 1.37509i | −0.726141 | − | 0.687546i | \(-0.758688\pi\) | ||
0.726141 | − | 0.687546i | \(-0.241312\pi\) | |||||||
\(912\) | −8.43126 | − | 3.00560i | −0.279187 | − | 0.0995253i | ||||
\(913\) | 4.36545i | 0.144475i | ||||||||
\(914\) | 4.34281i | 0.143647i | ||||||||
\(915\) | 14.6224 | + | 5.21262i | 0.483400 | + | 0.172324i | ||||
\(916\) | 23.1514i | 0.764944i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.07299 | − | 11.7069i | −0.233443 | − | 0.386386i | ||||
\(919\) | 21.8342 | 0.720244 | 0.360122 | − | 0.932905i | \(-0.382735\pi\) | ||||
0.360122 | + | 0.932905i | \(0.382735\pi\) | |||||||
\(920\) | 2.69411 | 0.0888223 | ||||||||
\(921\) | −5.20946 | − | 1.85708i | −0.171657 | − | 0.0611929i | ||||
\(922\) | − | 10.7827i | − | 0.355111i | ||||||
\(923\) | 22.1644 | 0.729550 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.14603 | 0.300720 | ||||||||
\(926\) | − | 18.5503i | − | 0.609600i | ||||||
\(927\) | −17.2133 | + | 21.0751i | −0.565359 | + | 0.692198i | ||||
\(928\) | 9.90498 | 0.325147 | ||||||||
\(929\) | 3.41675 | 0.112100 | 0.0560500 | − | 0.998428i | \(-0.482149\pi\) | ||||
0.0560500 | + | 0.998428i | \(0.482149\pi\) | |||||||
\(930\) | 1.98994 | − | 5.58215i | 0.0652527 | − | 0.183046i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 13.2418i | − | 0.433750i | ||||||
\(933\) | −18.0186 | + | 50.5456i | −0.589904 | + | 1.65479i | ||||
\(934\) | − | 5.55332i | − | 0.181710i | ||||||
\(935\) | − | 2.53614i | − | 0.0829406i | ||||||
\(936\) | 4.61867 | + | 3.77234i | 0.150966 | + | 0.123303i | ||||
\(937\) | − | 3.57133i | − | 0.116670i | −0.998297 | − | 0.0583351i | \(-0.981421\pi\) | ||
0.998297 | − | 0.0583351i | \(-0.0185792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0722 | + | 5.72948i | 0.524498 | + | 0.186974i | ||||
\(940\) | 10.3888 | 0.338844 | ||||||||
\(941\) | 18.4180 | 0.600411 | 0.300205 | − | 0.953875i | \(-0.402945\pi\) | ||||
0.300205 | + | 0.953875i | \(0.402945\pi\) | |||||||
\(942\) | −3.83086 | + | 10.7463i | −0.124816 | + | 0.350132i | ||||
\(943\) | 3.02285i | 0.0984376i | ||||||||
\(944\) | 2.10246 | 0.0684293 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.49259 | 0.0485284 | ||||||||
\(947\) | 20.8836i | 0.678625i | 0.940674 | + | 0.339312i | \(0.110194\pi\) | ||||
−0.940674 | + | 0.339312i | \(0.889806\pi\) | |||||||
\(948\) | −0.237494 | + | 0.666214i | −0.00771344 | + | 0.0216376i | ||||
\(949\) | 23.4035 | 0.759710 | ||||||||
\(950\) | −5.16784 | −0.167667 | ||||||||
\(951\) | 30.4007 | + | 10.8373i | 0.985809 | + | 0.351424i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 52.2153i | − | 1.69142i | −0.533644 | − | 0.845709i | \(-0.679178\pi\) | ||
0.533644 | − | 0.845709i | \(-0.320822\pi\) | |||||||
\(954\) | −30.6101 | − | 25.0011i | −0.991037 | − | 0.809439i | ||||
\(955\) | 17.0570i | 0.551951i | ||||||||
\(956\) | − | 14.7280i | − | 0.476337i | ||||||
\(957\) | 5.55031 | − | 15.5696i | 0.179416 | − | 0.503295i | ||||
\(958\) | − | 1.51336i | − | 0.0488943i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.581597 | + | 1.63149i | −0.0187709 | + | 0.0526560i | ||||
\(961\) | 19.2932 | 0.622363 | ||||||||
\(962\) | 18.1806 | 0.586167 | ||||||||
\(963\) | −26.3006 | + | 32.2012i | −0.847527 | + | 1.03767i | ||||
\(964\) | 5.92695i | 0.190894i | ||||||||
\(965\) | −2.05067 | −0.0660135 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.2991 | −1.48888 | −0.744440 | − | 0.667689i | \(-0.767283\pi\) | ||||
−0.744440 | + | 0.667689i | \(0.767283\pi\) | |||||||
\(968\) | − | 10.0717i | − | 0.323717i | ||||||
\(969\) | 22.1934 | + | 7.91156i | 0.712954 | + | 0.254156i | ||||
\(970\) | −14.6992 | −0.471963 | ||||||||
\(971\) | 9.45635 | 0.303469 | 0.151734 | − | 0.988421i | \(-0.451514\pi\) | ||||
0.151734 | + | 0.988421i | \(0.451514\pi\) | |||||||
\(972\) | 15.4329 | + | 2.19680i | 0.495010 | + | 0.0704625i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 10.6043i | − | 0.339784i | ||||||
\(975\) | 3.24309 | + | 1.15611i | 0.103862 | + | 0.0370251i | ||||
\(976\) | 8.96260i | 0.286886i | ||||||||
\(977\) | − | 4.82225i | − | 0.154278i | −0.997020 | − | 0.0771388i | \(-0.975422\pi\) | ||
0.997020 | − | 0.0771388i | \(-0.0245785\pi\) | |||||||
\(978\) | −4.32424 | − | 1.54152i | −0.138274 | − | 0.0492923i | ||||
\(979\) | 11.1006i | 0.354777i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.8799 | + | 31.7555i | 1.24134 | + | 1.01388i | ||||
\(982\) | −12.2648 | −0.391386 | ||||||||
\(983\) | 44.6626 | 1.42452 | 0.712258 | − | 0.701918i | \(-0.247673\pi\) | ||||
0.712258 | + | 0.701918i | \(0.247673\pi\) | |||||||
\(984\) | −1.83056 | − | 0.652564i | −0.0583562 | − | 0.0208030i | ||||
\(985\) | − | 12.9420i | − | 0.412368i | ||||||
\(986\) | −26.0726 | −0.830321 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.2727 | −0.326819 | ||||||||
\(989\) | − | 4.17364i | − | 0.132714i | ||||||
\(990\) | 2.23863 | + | 1.82842i | 0.0711485 | + | 0.0581112i | ||||
\(991\) | −33.3133 | −1.05823 | −0.529116 | − | 0.848550i | \(-0.677476\pi\) | ||||
−0.529116 | + | 0.848550i | \(0.677476\pi\) | |||||||
\(992\) | 3.42151 | 0.108633 | ||||||||
\(993\) | 20.1687 | − | 56.5770i | 0.640036 | − | 1.79542i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.1869i | 0.544862i | ||||||||
\(996\) | −2.63517 | + | 7.39213i | −0.0834985 | + | 0.234229i | ||||
\(997\) | 17.0203i | 0.539037i | 0.962995 | + | 0.269519i | \(0.0868646\pi\) | ||||
−0.962995 | + | 0.269519i | \(0.913135\pi\) | |||||||
\(998\) | 27.8286i | 0.880897i | ||||||||
\(999\) | 40.6766 | − | 24.5756i | 1.28695 | − | 0.777539i |
(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 | 1470.2.b.b.881.8 | 12 | ||
3.2 | odd | 2 | 1470.2.b.a.881.5 | 12 | |||
7.4 | even | 3 | 210.2.r.a.131.3 | yes | 12 | ||
7.5 | odd | 6 | 210.2.r.b.101.5 | yes | 12 | ||
7.6 | odd | 2 | 1470.2.b.a.881.11 | 12 | |||
21.5 | even | 6 | 210.2.r.a.101.3 | ✓ | 12 | ||
21.11 | odd | 6 | 210.2.r.b.131.5 | yes | 12 | ||
21.20 | even | 2 | inner | 1470.2.b.b.881.2 | 12 | ||
35.4 | even | 6 | 1050.2.s.g.551.4 | 12 | |||
35.12 | even | 12 | 1050.2.u.h.899.5 | 12 | |||
35.18 | odd | 12 | 1050.2.u.f.299.4 | 12 | |||
35.19 | odd | 6 | 1050.2.s.f.101.2 | 12 | |||
35.32 | odd | 12 | 1050.2.u.g.299.3 | 12 | |||
35.33 | even | 12 | 1050.2.u.e.899.2 | 12 | |||
105.32 | even | 12 | 1050.2.u.e.299.2 | 12 | |||
105.47 | odd | 12 | 1050.2.u.f.899.4 | 12 | |||
105.53 | even | 12 | 1050.2.u.h.299.5 | 12 | |||
105.68 | odd | 12 | 1050.2.u.g.899.3 | 12 | |||
105.74 | odd | 6 | 1050.2.s.f.551.2 | 12 | |||
105.89 | even | 6 | 1050.2.s.g.101.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.r.a.101.3 | ✓ | 12 | 21.5 | even | 6 | ||
210.2.r.a.131.3 | yes | 12 | 7.4 | even | 3 | ||
210.2.r.b.101.5 | yes | 12 | 7.5 | odd | 6 | ||
210.2.r.b.131.5 | yes | 12 | 21.11 | odd | 6 | ||
1050.2.s.f.101.2 | 12 | 35.19 | odd | 6 | |||
1050.2.s.f.551.2 | 12 | 105.74 | odd | 6 | |||
1050.2.s.g.101.4 | 12 | 105.89 | even | 6 | |||
1050.2.s.g.551.4 | 12 | 35.4 | even | 6 | |||
1050.2.u.e.299.2 | 12 | 105.32 | even | 12 | |||
1050.2.u.e.899.2 | 12 | 35.33 | even | 12 | |||
1050.2.u.f.299.4 | 12 | 35.18 | odd | 12 | |||
1050.2.u.f.899.4 | 12 | 105.47 | odd | 12 | |||
1050.2.u.g.299.3 | 12 | 35.32 | odd | 12 | |||
1050.2.u.g.899.3 | 12 | 105.68 | odd | 12 | |||
1050.2.u.h.299.5 | 12 | 105.53 | even | 12 | |||
1050.2.u.h.899.5 | 12 | 35.12 | even | 12 | |||
1470.2.b.a.881.5 | 12 | 3.2 | odd | 2 | |||
1470.2.b.a.881.11 | 12 | 7.6 | odd | 2 | |||
1470.2.b.b.881.2 | 12 | 21.20 | even | 2 | inner | ||
1470.2.b.b.881.8 | 12 | 1.1 | even | 1 | trivial |