Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(545,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.545");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.e (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 545.7 | ||
Root | \(1.26217 - 1.18614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.545 |
Dual form | 546.2.e.g.545.8 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.26217 | − | 1.18614i | 0.728714 | − | 0.684819i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.37228i | 1.50813i | 0.656800 | + | 0.754065i | \(0.271910\pi\) | ||||
−0.656800 | + | 0.754065i | \(0.728090\pi\) | |||||||
\(6\) | 1.26217 | − | 1.18614i | 0.515278 | − | 0.484240i | ||||
\(7\) | 2.52434 | + | 0.792287i | 0.954110 | + | 0.299456i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.186141 | − | 2.99422i | 0.0620469 | − | 0.998073i | ||||
\(10\) | 3.37228i | 1.06641i | ||||||||
\(11\) | −5.74456 | −1.73205 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 1.26217 | − | 1.18614i | 0.364357 | − | 0.342409i | ||||
\(13\) | 3.46410 | + | 1.00000i | 0.960769 | + | 0.277350i | ||||
\(14\) | 2.52434 | + | 0.792287i | 0.674658 | + | 0.211748i | ||||
\(15\) | 4.00000 | + | 4.25639i | 1.03280 | + | 1.09899i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.792287 | −0.192158 | −0.0960789 | − | 0.995374i | \(-0.530630\pi\) | ||||
−0.0960789 | + | 0.995374i | \(0.530630\pi\) | |||||||
\(18\) | 0.186141 | − | 2.99422i | 0.0438738 | − | 0.705744i | ||||
\(19\) | 2.37686 | 0.545289 | 0.272645 | − | 0.962115i | \(-0.412102\pi\) | ||||
0.272645 | + | 0.962115i | \(0.412102\pi\) | |||||||
\(20\) | 3.37228i | 0.754065i | ||||||||
\(21\) | 4.12590 | − | 1.99422i | 0.900346 | − | 0.435174i | ||||
\(22\) | −5.74456 | −1.22474 | ||||||||
\(23\) | − | 0.147477i | − | 0.0307510i | −0.999882 | − | 0.0153755i | \(-0.995106\pi\) | ||
0.999882 | − | 0.0153755i | \(-0.00489437\pi\) | |||||||
\(24\) | 1.26217 | − | 1.18614i | 0.257639 | − | 0.242120i | ||||
\(25\) | −6.37228 | −1.27446 | ||||||||
\(26\) | 3.46410 | + | 1.00000i | 0.679366 | + | 0.196116i | ||||
\(27\) | −3.31662 | − | 4.00000i | −0.638285 | − | 0.769800i | ||||
\(28\) | 2.52434 | + | 0.792287i | 0.477055 | + | 0.149728i | ||||
\(29\) | − | 2.37686i | − | 0.441372i | −0.975345 | − | 0.220686i | \(-0.929170\pi\) | ||
0.975345 | − | 0.220686i | \(-0.0708296\pi\) | |||||||
\(30\) | 4.00000 | + | 4.25639i | 0.730297 | + | 0.777107i | ||||
\(31\) | −4.10891 | −0.737982 | −0.368991 | − | 0.929433i | \(-0.620297\pi\) | ||||
−0.368991 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.25061 | + | 6.81386i | −1.26217 | + | 1.18614i | ||||
\(34\) | −0.792287 | −0.135876 | ||||||||
\(35\) | −2.67181 | + | 8.51278i | −0.451619 | + | 1.43892i | ||||
\(36\) | 0.186141 | − | 2.99422i | 0.0310234 | − | 0.499037i | ||||
\(37\) | − | 8.36530i | − | 1.37525i | −0.726067 | − | 0.687623i | \(-0.758654\pi\) | ||
0.726067 | − | 0.687623i | \(-0.241346\pi\) | |||||||
\(38\) | 2.37686 | 0.385578 | ||||||||
\(39\) | 5.55842 | − | 2.84674i | 0.890060 | − | 0.455844i | ||||
\(40\) | 3.37228i | 0.533204i | ||||||||
\(41\) | − | 8.37228i | − | 1.30753i | −0.756697 | − | 0.653765i | \(-0.773188\pi\) | ||
0.756697 | − | 0.653765i | \(-0.226812\pi\) | |||||||
\(42\) | 4.12590 | − | 1.99422i | 0.636641 | − | 0.307715i | ||||
\(43\) | −2.62772 | −0.400723 | −0.200362 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200362 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(44\) | −5.74456 | −0.866025 | ||||||||
\(45\) | 10.0974 | + | 0.627719i | 1.50522 | + | 0.0935748i | ||||
\(46\) | − | 0.147477i | − | 0.0217443i | ||||||
\(47\) | 10.3723i | 1.51295i | 0.654021 | + | 0.756476i | \(0.273081\pi\) | ||||
−0.654021 | + | 0.756476i | \(0.726919\pi\) | |||||||
\(48\) | 1.26217 | − | 1.18614i | 0.182178 | − | 0.171205i | ||||
\(49\) | 5.74456 | + | 4.00000i | 0.820652 | + | 0.571429i | ||||
\(50\) | −6.37228 | −0.901177 | ||||||||
\(51\) | −1.00000 | + | 0.939764i | −0.140028 | + | 0.131593i | ||||
\(52\) | 3.46410 | + | 1.00000i | 0.480384 | + | 0.138675i | ||||
\(53\) | − | 10.0974i | − | 1.38698i | −0.720467 | − | 0.693489i | \(-0.756073\pi\) | ||
0.720467 | − | 0.693489i | \(-0.243927\pi\) | |||||||
\(54\) | −3.31662 | − | 4.00000i | −0.451335 | − | 0.544331i | ||||
\(55\) | − | 19.3723i | − | 2.61216i | ||||||
\(56\) | 2.52434 | + | 0.792287i | 0.337329 | + | 0.105874i | ||||
\(57\) | 3.00000 | − | 2.81929i | 0.397360 | − | 0.373424i | ||||
\(58\) | − | 2.37686i | − | 0.312097i | ||||||
\(59\) | 2.74456i | 0.357312i | 0.983912 | + | 0.178656i | \(0.0571749\pi\) | ||||
−0.983912 | + | 0.178656i | \(0.942825\pi\) | |||||||
\(60\) | 4.00000 | + | 4.25639i | 0.516398 | + | 0.549497i | ||||
\(61\) | − | 7.74456i | − | 0.991590i | −0.868440 | − | 0.495795i | \(-0.834877\pi\) | ||
0.868440 | − | 0.495795i | \(-0.165123\pi\) | |||||||
\(62\) | −4.10891 | −0.521832 | ||||||||
\(63\) | 2.84216 | − | 7.41095i | 0.358079 | − | 0.933691i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.37228 | + | 11.6819i | −0.418280 | + | 1.44896i | ||||
\(66\) | −7.25061 | + | 6.81386i | −0.892488 | + | 0.838728i | ||||
\(67\) | 5.98844i | 0.731604i | 0.930693 | + | 0.365802i | \(0.119205\pi\) | ||||
−0.930693 | + | 0.365802i | \(0.880795\pi\) | |||||||
\(68\) | −0.792287 | −0.0960789 | ||||||||
\(69\) | −0.174928 | − | 0.186141i | −0.0210589 | − | 0.0224087i | ||||
\(70\) | −2.67181 | + | 8.51278i | −0.319343 | + | 1.01747i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0.186141 | − | 2.99422i | 0.0219369 | − | 0.352872i | ||||
\(73\) | −10.2448 | −1.19907 | −0.599533 | − | 0.800350i | \(-0.704647\pi\) | ||||
−0.599533 | + | 0.800350i | \(0.704647\pi\) | |||||||
\(74\) | − | 8.36530i | − | 0.972446i | ||||||
\(75\) | −8.04290 | + | 7.55842i | −0.928714 | + | 0.872771i | ||||
\(76\) | 2.37686 | 0.272645 | ||||||||
\(77\) | −14.5012 | − | 4.55134i | −1.65257 | − | 0.518674i | ||||
\(78\) | 5.55842 | − | 2.84674i | 0.629367 | − | 0.322330i | ||||
\(79\) | −3.62772 | −0.408150 | −0.204075 | − | 0.978955i | \(-0.565419\pi\) | ||||
−0.204075 | + | 0.978955i | \(0.565419\pi\) | |||||||
\(80\) | 3.37228i | 0.377033i | ||||||||
\(81\) | −8.93070 | − | 1.11469i | −0.992300 | − | 0.123855i | ||||
\(82\) | − | 8.37228i | − | 0.924564i | ||||||
\(83\) | 6.74456i | 0.740312i | 0.928970 | + | 0.370156i | \(0.120696\pi\) | ||||
−0.928970 | + | 0.370156i | \(0.879304\pi\) | |||||||
\(84\) | 4.12590 | − | 1.99422i | 0.450173 | − | 0.217587i | ||||
\(85\) | − | 2.67181i | − | 0.289799i | ||||||
\(86\) | −2.62772 | −0.283354 | ||||||||
\(87\) | −2.81929 | − | 3.00000i | −0.302260 | − | 0.321634i | ||||
\(88\) | −5.74456 | −0.612372 | ||||||||
\(89\) | − | 10.0000i | − | 1.06000i | −0.847998 | − | 0.529999i | \(-0.822192\pi\) | ||
0.847998 | − | 0.529999i | \(-0.177808\pi\) | |||||||
\(90\) | 10.0974 | + | 0.627719i | 1.06435 | + | 0.0661674i | ||||
\(91\) | 7.95228 | + | 5.26890i | 0.833625 | + | 0.552331i | ||||
\(92\) | − | 0.147477i | − | 0.0153755i | ||||||
\(93\) | −5.18614 | + | 4.87375i | −0.537778 | + | 0.505384i | ||||
\(94\) | 10.3723i | 1.06982i | ||||||||
\(95\) | 8.01544i | 0.822367i | ||||||||
\(96\) | 1.26217 | − | 1.18614i | 0.128820 | − | 0.121060i | ||||
\(97\) | −9.15759 | −0.929812 | −0.464906 | − | 0.885360i | \(-0.653912\pi\) | ||||
−0.464906 | + | 0.885360i | \(0.653912\pi\) | |||||||
\(98\) | 5.74456 | + | 4.00000i | 0.580288 | + | 0.404061i | ||||
\(99\) | −1.06930 | + | 17.2005i | −0.107468 | + | 1.72871i | ||||
\(100\) | −6.37228 | −0.637228 | ||||||||
\(101\) | 17.6704 | 1.75827 | 0.879133 | − | 0.476576i | \(-0.158122\pi\) | ||||
0.879133 | + | 0.476576i | \(0.158122\pi\) | |||||||
\(102\) | −1.00000 | + | 0.939764i | −0.0990148 | + | 0.0930505i | ||||
\(103\) | 7.37228i | 0.726412i | 0.931709 | + | 0.363206i | \(0.118318\pi\) | ||||
−0.931709 | + | 0.363206i | \(0.881682\pi\) | |||||||
\(104\) | 3.46410 | + | 1.00000i | 0.339683 | + | 0.0980581i | ||||
\(105\) | 6.72507 | + | 13.9137i | 0.656300 | + | 1.35784i | ||||
\(106\) | − | 10.0974i | − | 0.980741i | ||||||
\(107\) | 17.0256i | 1.64592i | 0.568098 | + | 0.822961i | \(0.307680\pi\) | ||||
−0.568098 | + | 0.822961i | \(0.692320\pi\) | |||||||
\(108\) | −3.31662 | − | 4.00000i | −0.319142 | − | 0.384900i | ||||
\(109\) | 19.6974i | 1.88667i | 0.331848 | + | 0.943333i | \(0.392328\pi\) | ||||
−0.331848 | + | 0.943333i | \(0.607672\pi\) | |||||||
\(110\) | − | 19.3723i | − | 1.84707i | ||||||
\(111\) | −9.92242 | − | 10.5584i | −0.941795 | − | 1.00216i | ||||
\(112\) | 2.52434 | + | 0.792287i | 0.238528 | + | 0.0748641i | ||||
\(113\) | − | 5.69349i | − | 0.535598i | −0.963475 | − | 0.267799i | \(-0.913704\pi\) | ||
0.963475 | − | 0.267799i | \(-0.0862963\pi\) | |||||||
\(114\) | 3.00000 | − | 2.81929i | 0.280976 | − | 0.264051i | ||||
\(115\) | 0.497333 | 0.0463766 | ||||||||
\(116\) | − | 2.37686i | − | 0.220686i | ||||||
\(117\) | 3.63903 | − | 10.1861i | 0.336428 | − | 0.941709i | ||||
\(118\) | 2.74456i | 0.252657i | ||||||||
\(119\) | −2.00000 | − | 0.627719i | −0.183340 | − | 0.0575429i | ||||
\(120\) | 4.00000 | + | 4.25639i | 0.365148 | + | 0.388553i | ||||
\(121\) | 22.0000 | 2.00000 | ||||||||
\(122\) | − | 7.74456i | − | 0.701160i | ||||||
\(123\) | −9.93070 | − | 10.5672i | −0.895421 | − | 0.952815i | ||||
\(124\) | −4.10891 | −0.368991 | ||||||||
\(125\) | − | 4.62772i | − | 0.413916i | ||||||
\(126\) | 2.84216 | − | 7.41095i | 0.253200 | − | 0.660219i | ||||
\(127\) | −10.3723 | −0.920391 | −0.460196 | − | 0.887818i | \(-0.652221\pi\) | ||||
−0.460196 | + | 0.887818i | \(0.652221\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.31662 | + | 3.11684i | −0.292013 | + | 0.274423i | ||||
\(130\) | −3.37228 | + | 11.6819i | −0.295769 | + | 1.02457i | ||||
\(131\) | 3.96143 | 0.346112 | 0.173056 | − | 0.984912i | \(-0.444636\pi\) | ||||
0.173056 | + | 0.984912i | \(0.444636\pi\) | |||||||
\(132\) | −7.25061 | + | 6.81386i | −0.631084 | + | 0.593070i | ||||
\(133\) | 6.00000 | + | 1.88316i | 0.520266 | + | 0.163290i | ||||
\(134\) | 5.98844i | 0.517322i | ||||||||
\(135\) | 13.4891 | − | 11.1846i | 1.16096 | − | 0.962616i | ||||
\(136\) | −0.792287 | −0.0679380 | ||||||||
\(137\) | −18.1168 | −1.54783 | −0.773913 | − | 0.633292i | \(-0.781703\pi\) | ||||
−0.773913 | + | 0.633292i | \(0.781703\pi\) | |||||||
\(138\) | −0.174928 | − | 0.186141i | −0.0148909 | − | 0.0158453i | ||||
\(139\) | 5.25544i | 0.445760i | 0.974846 | + | 0.222880i | \(0.0715459\pi\) | ||||
−0.974846 | + | 0.222880i | \(0.928454\pi\) | |||||||
\(140\) | −2.67181 | + | 8.51278i | −0.225810 | + | 0.719461i | ||||
\(141\) | 12.3030 | + | 13.0916i | 1.03610 | + | 1.10251i | ||||
\(142\) | −2.00000 | −0.167836 | ||||||||
\(143\) | −19.8997 | − | 5.74456i | −1.66410 | − | 0.480384i | ||||
\(144\) | 0.186141 | − | 2.99422i | 0.0155117 | − | 0.249518i | ||||
\(145\) | 8.01544 | 0.665646 | ||||||||
\(146\) | −10.2448 | −0.847868 | ||||||||
\(147\) | 11.9952 | − | 1.76518i | 0.989345 | − | 0.145590i | ||||
\(148\) | − | 8.36530i | − | 0.687623i | ||||||
\(149\) | −7.62772 | −0.624887 | −0.312444 | − | 0.949936i | \(-0.601148\pi\) | ||||
−0.312444 | + | 0.949936i | \(0.601148\pi\) | |||||||
\(150\) | −8.04290 | + | 7.55842i | −0.656700 | + | 0.617143i | ||||
\(151\) | − | 17.8178i | − | 1.45000i | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||
0.688751 | − | 0.724998i | \(-0.258159\pi\) | |||||||
\(152\) | 2.37686 | 0.192789 | ||||||||
\(153\) | −0.147477 | + | 2.37228i | −0.0119228 | + | 0.191788i | ||||
\(154\) | −14.5012 | − | 4.55134i | −1.16854 | − | 0.366758i | ||||
\(155\) | − | 13.8564i | − | 1.11297i | ||||||
\(156\) | 5.55842 | − | 2.84674i | 0.445030 | − | 0.227922i | ||||
\(157\) | 8.25544i | 0.658856i | 0.944181 | + | 0.329428i | \(0.106856\pi\) | ||||
−0.944181 | + | 0.329428i | \(0.893144\pi\) | |||||||
\(158\) | −3.62772 | −0.288606 | ||||||||
\(159\) | −11.9769 | − | 12.7446i | −0.949828 | − | 1.01071i | ||||
\(160\) | 3.37228i | 0.266602i | ||||||||
\(161\) | 0.116844 | − | 0.372281i | 0.00920859 | − | 0.0293399i | ||||
\(162\) | −8.93070 | − | 1.11469i | −0.701662 | − | 0.0875785i | ||||
\(163\) | − | 8.21782i | − | 0.643670i | −0.946796 | − | 0.321835i | \(-0.895700\pi\) | ||
0.946796 | − | 0.321835i | \(-0.104300\pi\) | |||||||
\(164\) | − | 8.37228i | − | 0.653765i | ||||||
\(165\) | −22.9783 | − | 24.4511i | −1.78885 | − | 1.90351i | ||||
\(166\) | 6.74456i | 0.523480i | ||||||||
\(167\) | 12.6277i | 0.977162i | 0.872518 | + | 0.488581i | \(0.162485\pi\) | ||||
−0.872518 | + | 0.488581i | \(0.837515\pi\) | |||||||
\(168\) | 4.12590 | − | 1.99422i | 0.318320 | − | 0.153857i | ||||
\(169\) | 11.0000 | + | 6.92820i | 0.846154 | + | 0.532939i | ||||
\(170\) | − | 2.67181i | − | 0.204919i | ||||||
\(171\) | 0.442430 | − | 7.11684i | 0.0338335 | − | 0.544239i | ||||
\(172\) | −2.62772 | −0.200362 | ||||||||
\(173\) | 10.6873 | 0.812537 | 0.406269 | − | 0.913754i | \(-0.366830\pi\) | ||||
0.406269 | + | 0.913754i | \(0.366830\pi\) | |||||||
\(174\) | −2.81929 | − | 3.00000i | −0.213730 | − | 0.227429i | ||||
\(175\) | −16.0858 | − | 5.04868i | −1.21597 | − | 0.381644i | ||||
\(176\) | −5.74456 | −0.433013 | ||||||||
\(177\) | 3.25544 | + | 3.46410i | 0.244694 | + | 0.260378i | ||||
\(178\) | − | 10.0000i | − | 0.749532i | ||||||
\(179\) | − | 20.1947i | − | 1.50942i | −0.656057 | − | 0.754711i | \(-0.727777\pi\) | ||
0.656057 | − | 0.754711i | \(-0.272223\pi\) | |||||||
\(180\) | 10.0974 | + | 0.627719i | 0.752612 | + | 0.0467874i | ||||
\(181\) | 20.3723i | 1.51426i | 0.653264 | + | 0.757130i | \(0.273399\pi\) | ||||
−0.653264 | + | 0.757130i | \(0.726601\pi\) | |||||||
\(182\) | 7.95228 | + | 5.26890i | 0.589462 | + | 0.390557i | ||||
\(183\) | −9.18614 | − | 9.77495i | −0.679059 | − | 0.722585i | ||||
\(184\) | − | 0.147477i | − | 0.0108721i | ||||||
\(185\) | 28.2101 | 2.07405 | ||||||||
\(186\) | −5.18614 | + | 4.87375i | −0.380266 | + | 0.357360i | ||||
\(187\) | 4.55134 | 0.332827 | ||||||||
\(188\) | 10.3723i | 0.756476i | ||||||||
\(189\) | −5.20313 | − | 12.7251i | −0.378472 | − | 0.925613i | ||||
\(190\) | 8.01544i | 0.581501i | ||||||||
\(191\) | − | 2.96677i | − | 0.214668i | −0.994223 | − | 0.107334i | \(-0.965769\pi\) | ||
0.994223 | − | 0.107334i | \(-0.0342314\pi\) | |||||||
\(192\) | 1.26217 | − | 1.18614i | 0.0910892 | − | 0.0856023i | ||||
\(193\) | − | 20.7846i | − | 1.49611i | −0.663637 | − | 0.748054i | \(-0.730988\pi\) | ||
0.663637 | − | 0.748054i | \(-0.269012\pi\) | |||||||
\(194\) | −9.15759 | −0.657476 | ||||||||
\(195\) | 9.60002 | + | 18.7446i | 0.687472 | + | 1.34233i | ||||
\(196\) | 5.74456 | + | 4.00000i | 0.410326 | + | 0.285714i | ||||
\(197\) | 21.1168 | 1.50451 | 0.752256 | − | 0.658870i | \(-0.228965\pi\) | ||||
0.752256 | + | 0.658870i | \(0.228965\pi\) | |||||||
\(198\) | −1.06930 | + | 17.2005i | −0.0759916 | + | 1.22239i | ||||
\(199\) | − | 12.1168i | − | 0.858940i | −0.903081 | − | 0.429470i | \(-0.858700\pi\) | ||
0.903081 | − | 0.429470i | \(-0.141300\pi\) | |||||||
\(200\) | −6.37228 | −0.450588 | ||||||||
\(201\) | 7.10313 | + | 7.55842i | 0.501016 | + | 0.533130i | ||||
\(202\) | 17.6704 | 1.24328 | ||||||||
\(203\) | 1.88316 | − | 6.00000i | 0.132172 | − | 0.421117i | ||||
\(204\) | −1.00000 | + | 0.939764i | −0.0700140 | + | 0.0657966i | ||||
\(205\) | 28.2337 | 1.97193 | ||||||||
\(206\) | 7.37228i | 0.513651i | ||||||||
\(207\) | −0.441578 | − | 0.0274514i | −0.0306918 | − | 0.00190801i | ||||
\(208\) | 3.46410 | + | 1.00000i | 0.240192 | + | 0.0693375i | ||||
\(209\) | −13.6540 | −0.944469 | ||||||||
\(210\) | 6.72507 | + | 13.9137i | 0.464074 | + | 0.960137i | ||||
\(211\) | 17.3723 | 1.19596 | 0.597979 | − | 0.801512i | \(-0.295971\pi\) | ||||
0.597979 | + | 0.801512i | \(0.295971\pi\) | |||||||
\(212\) | − | 10.0974i | − | 0.693489i | ||||||
\(213\) | −2.52434 | + | 2.37228i | −0.172965 | + | 0.162546i | ||||
\(214\) | 17.0256i | 1.16384i | ||||||||
\(215\) | − | 8.86141i | − | 0.604343i | ||||||
\(216\) | −3.31662 | − | 4.00000i | −0.225668 | − | 0.272166i | ||||
\(217\) | −10.3723 | − | 3.25544i | −0.704116 | − | 0.220993i | ||||
\(218\) | 19.6974i | 1.33407i | ||||||||
\(219\) | −12.9307 | + | 12.1518i | −0.873776 | + | 0.821143i | ||||
\(220\) | − | 19.3723i | − | 1.30608i | ||||||
\(221\) | −2.74456 | − | 0.792287i | −0.184619 | − | 0.0532950i | ||||
\(222\) | −9.92242 | − | 10.5584i | −0.665949 | − | 0.708635i | ||||
\(223\) | −0.644810 | −0.0431797 | −0.0215898 | − | 0.999767i | \(-0.506873\pi\) | ||||
−0.0215898 | + | 0.999767i | \(0.506873\pi\) | |||||||
\(224\) | 2.52434 | + | 0.792287i | 0.168664 | + | 0.0529369i | ||||
\(225\) | −1.18614 | + | 19.0800i | −0.0790760 | + | 1.27200i | ||||
\(226\) | − | 5.69349i | − | 0.378725i | ||||||
\(227\) | 11.4891i | 0.762560i | 0.924460 | + | 0.381280i | \(0.124517\pi\) | ||||
−0.924460 | + | 0.381280i | \(0.875483\pi\) | |||||||
\(228\) | 3.00000 | − | 2.81929i | 0.198680 | − | 0.186712i | ||||
\(229\) | 5.04868 | 0.333626 | 0.166813 | − | 0.985989i | \(-0.446652\pi\) | ||||
0.166813 | + | 0.985989i | \(0.446652\pi\) | |||||||
\(230\) | 0.497333 | 0.0327932 | ||||||||
\(231\) | −23.7015 | + | 11.4559i | −1.55945 | + | 0.753744i | ||||
\(232\) | − | 2.37686i | − | 0.156049i | ||||||
\(233\) | 10.7422i | 0.703742i | 0.936048 | + | 0.351871i | \(0.114454\pi\) | ||||
−0.936048 | + | 0.351871i | \(0.885546\pi\) | |||||||
\(234\) | 3.63903 | − | 10.1861i | 0.237891 | − | 0.665889i | ||||
\(235\) | −34.9783 | −2.28173 | ||||||||
\(236\) | 2.74456i | 0.178656i | ||||||||
\(237\) | −4.57879 | + | 4.30298i | −0.297425 | + | 0.279509i | ||||
\(238\) | −2.00000 | − | 0.627719i | −0.129641 | − | 0.0406890i | ||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 4.00000 | + | 4.25639i | 0.258199 | + | 0.274749i | ||||
\(241\) | 16.4356 | 1.05871 | 0.529357 | − | 0.848399i | \(-0.322433\pi\) | ||||
0.529357 | + | 0.848399i | \(0.322433\pi\) | |||||||
\(242\) | 22.0000 | 1.41421 | ||||||||
\(243\) | −12.5942 | + | 9.18614i | −0.807921 | + | 0.589291i | ||||
\(244\) | − | 7.74456i | − | 0.495795i | ||||||
\(245\) | −13.4891 | + | 19.3723i | −0.861789 | + | 1.23765i | ||||
\(246\) | −9.93070 | − | 10.5672i | −0.633159 | − | 0.673742i | ||||
\(247\) | 8.23369 | + | 2.37686i | 0.523897 | + | 0.151236i | ||||
\(248\) | −4.10891 | −0.260916 | ||||||||
\(249\) | 8.00000 | + | 8.51278i | 0.506979 | + | 0.539475i | ||||
\(250\) | − | 4.62772i | − | 0.292683i | ||||||
\(251\) | 6.78073 | 0.427996 | 0.213998 | − | 0.976834i | \(-0.431351\pi\) | ||||
0.213998 | + | 0.976834i | \(0.431351\pi\) | |||||||
\(252\) | 2.84216 | − | 7.41095i | 0.179039 | − | 0.466846i | ||||
\(253\) | 0.847190i | 0.0532624i | ||||||||
\(254\) | −10.3723 | −0.650815 | ||||||||
\(255\) | −3.16915 | − | 3.37228i | −0.198460 | − | 0.211180i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.9051 | 1.17927 | 0.589633 | − | 0.807671i | \(-0.299272\pi\) | ||||
0.589633 | + | 0.807671i | \(0.299272\pi\) | |||||||
\(258\) | −3.31662 | + | 3.11684i | −0.206484 | + | 0.194046i | ||||
\(259\) | 6.62772 | − | 21.1168i | 0.411826 | − | 1.31214i | ||||
\(260\) | −3.37228 | + | 11.6819i | −0.209140 | + | 0.724482i | ||||
\(261\) | −7.11684 | − | 0.442430i | −0.440522 | − | 0.0273858i | ||||
\(262\) | 3.96143 | 0.244738 | ||||||||
\(263\) | 7.22316i | 0.445399i | 0.974887 | + | 0.222699i | \(0.0714869\pi\) | ||||
−0.974887 | + | 0.222699i | \(0.928513\pi\) | |||||||
\(264\) | −7.25061 | + | 6.81386i | −0.446244 | + | 0.419364i | ||||
\(265\) | 34.0511 | 2.09174 | ||||||||
\(266\) | 6.00000 | + | 1.88316i | 0.367884 | + | 0.115464i | ||||
\(267\) | −11.8614 | − | 12.6217i | −0.725906 | − | 0.772435i | ||||
\(268\) | 5.98844i | 0.365802i | ||||||||
\(269\) | −14.5012 | −0.884155 | −0.442077 | − | 0.896977i | \(-0.645758\pi\) | ||||
−0.442077 | + | 0.896977i | \(0.645758\pi\) | |||||||
\(270\) | 13.4891 | − | 11.1846i | 0.820922 | − | 0.680673i | ||||
\(271\) | −11.3321 | −0.688374 | −0.344187 | − | 0.938901i | \(-0.611845\pi\) | ||||
−0.344187 | + | 0.938901i | \(0.611845\pi\) | |||||||
\(272\) | −0.792287 | −0.0480395 | ||||||||
\(273\) | 16.2868 | − | 2.78228i | 0.985720 | − | 0.168391i | ||||
\(274\) | −18.1168 | −1.09448 | ||||||||
\(275\) | 36.6060 | 2.20742 | ||||||||
\(276\) | −0.174928 | − | 0.186141i | −0.0105294 | − | 0.0112044i | ||||
\(277\) | 17.4891 | 1.05082 | 0.525410 | − | 0.850849i | \(-0.323912\pi\) | ||||
0.525410 | + | 0.850849i | \(0.323912\pi\) | |||||||
\(278\) | 5.25544i | 0.315200i | ||||||||
\(279\) | −0.764836 | + | 12.3030i | −0.0457895 | + | 0.736560i | ||||
\(280\) | −2.67181 | + | 8.51278i | −0.159671 | + | 0.508736i | ||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | 12.3030 | + | 13.0916i | 0.732632 | + | 0.779592i | ||||
\(283\) | 0.372281i | 0.0221298i | 0.999939 | + | 0.0110649i | \(0.00352214\pi\) | ||||
−0.999939 | + | 0.0110649i | \(0.996478\pi\) | |||||||
\(284\) | −2.00000 | −0.118678 | ||||||||
\(285\) | 9.50744 | + | 10.1168i | 0.563172 | + | 0.599270i | ||||
\(286\) | −19.8997 | − | 5.74456i | −1.17670 | − | 0.339683i | ||||
\(287\) | 6.63325 | − | 21.1345i | 0.391548 | − | 1.24753i | ||||
\(288\) | 0.186141 | − | 2.99422i | 0.0109684 | − | 0.176436i | ||||
\(289\) | −16.3723 | −0.963075 | ||||||||
\(290\) | 8.01544 | 0.470683 | ||||||||
\(291\) | −11.5584 | + | 10.8622i | −0.677567 | + | 0.636753i | ||||
\(292\) | −10.2448 | −0.599533 | ||||||||
\(293\) | − | 11.4891i | − | 0.671202i | −0.942004 | − | 0.335601i | \(-0.891061\pi\) | ||
0.942004 | − | 0.335601i | \(-0.108939\pi\) | |||||||
\(294\) | 11.9952 | − | 1.76518i | 0.699573 | − | 0.102948i | ||||
\(295\) | −9.25544 | −0.538872 | ||||||||
\(296\) | − | 8.36530i | − | 0.486223i | ||||||
\(297\) | 19.0526 | + | 22.9783i | 1.10554 | + | 1.33333i | ||||
\(298\) | −7.62772 | −0.441862 | ||||||||
\(299\) | 0.147477 | − | 0.510875i | 0.00852880 | − | 0.0295446i | ||||
\(300\) | −8.04290 | + | 7.55842i | −0.464357 | + | 0.436386i | ||||
\(301\) | −6.63325 | − | 2.08191i | −0.382334 | − | 0.119999i | ||||
\(302\) | − | 17.8178i | − | 1.02530i | ||||||
\(303\) | 22.3030 | − | 20.9595i | 1.28127 | − | 1.20409i | ||||
\(304\) | 2.37686 | 0.136322 | ||||||||
\(305\) | 26.1168 | 1.49545 | ||||||||
\(306\) | −0.147477 | + | 2.37228i | −0.00843069 | + | 0.135614i | ||||
\(307\) | 31.8766 | 1.81930 | 0.909648 | − | 0.415381i | \(-0.136352\pi\) | ||||
0.909648 | + | 0.415381i | \(0.136352\pi\) | |||||||
\(308\) | −14.5012 | − | 4.55134i | −0.826284 | − | 0.259337i | ||||
\(309\) | 8.74456 | + | 9.30506i | 0.497461 | + | 0.529347i | ||||
\(310\) | − | 13.8564i | − | 0.786991i | ||||||
\(311\) | −10.3923 | −0.589294 | −0.294647 | − | 0.955606i | \(-0.595202\pi\) | ||||
−0.294647 | + | 0.955606i | \(0.595202\pi\) | |||||||
\(312\) | 5.55842 | − | 2.84674i | 0.314684 | − | 0.161165i | ||||
\(313\) | − | 2.74456i | − | 0.155132i | −0.996987 | − | 0.0775659i | \(-0.975285\pi\) | ||
0.996987 | − | 0.0775659i | \(-0.0247148\pi\) | |||||||
\(314\) | 8.25544i | 0.465881i | ||||||||
\(315\) | 24.9918 | + | 9.58457i | 1.40813 | + | 0.540030i | ||||
\(316\) | −3.62772 | −0.204075 | ||||||||
\(317\) | −3.86141 | −0.216878 | −0.108439 | − | 0.994103i | \(-0.534585\pi\) | ||||
−0.108439 | + | 0.994103i | \(0.534585\pi\) | |||||||
\(318\) | −11.9769 | − | 12.7446i | −0.671630 | − | 0.714680i | ||||
\(319\) | 13.6540i | 0.764479i | ||||||||
\(320\) | 3.37228i | 0.188516i | ||||||||
\(321\) | 20.1947 | + | 21.4891i | 1.12716 | + | 1.19941i | ||||
\(322\) | 0.116844 | − | 0.372281i | 0.00651146 | − | 0.0207464i | ||||
\(323\) | −1.88316 | −0.104782 | ||||||||
\(324\) | −8.93070 | − | 1.11469i | −0.496150 | − | 0.0619273i | ||||
\(325\) | −22.0742 | − | 6.37228i | −1.22446 | − | 0.353471i | ||||
\(326\) | − | 8.21782i | − | 0.455143i | ||||||
\(327\) | 23.3639 | + | 24.8614i | 1.29202 | + | 1.37484i | ||||
\(328\) | − | 8.37228i | − | 0.462282i | ||||||
\(329\) | −8.21782 | + | 26.1831i | −0.453063 | + | 1.44352i | ||||
\(330\) | −22.9783 | − | 24.4511i | −1.26491 | − | 1.34599i | ||||
\(331\) | 17.0805i | 0.938827i | 0.882979 | + | 0.469413i | \(0.155535\pi\) | ||||
−0.882979 | + | 0.469413i | \(0.844465\pi\) | |||||||
\(332\) | 6.74456i | 0.370156i | ||||||||
\(333\) | −25.0475 | − | 1.55712i | −1.37260 | − | 0.0853298i | ||||
\(334\) | 12.6277i | 0.690958i | ||||||||
\(335\) | −20.1947 | −1.10335 | ||||||||
\(336\) | 4.12590 | − | 1.99422i | 0.225087 | − | 0.108794i | ||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 11.0000 | + | 6.92820i | 0.598321 | + | 0.376845i | ||||
\(339\) | −6.75327 | − | 7.18614i | −0.366788 | − | 0.390298i | ||||
\(340\) | − | 2.67181i | − | 0.144899i | ||||||
\(341\) | 23.6039 | 1.27822 | ||||||||
\(342\) | 0.442430 | − | 7.11684i | 0.0239239 | − | 0.384835i | ||||
\(343\) | 11.3321 | + | 14.6487i | 0.611874 | + | 0.790955i | ||||
\(344\) | −2.62772 | −0.141677 | ||||||||
\(345\) | 0.627719 | − | 0.589907i | 0.0337952 | − | 0.0317595i | ||||
\(346\) | 10.6873 | 0.574551 | ||||||||
\(347\) | − | 19.2000i | − | 1.03071i | −0.856976 | − | 0.515356i | \(-0.827660\pi\) | ||
0.856976 | − | 0.515356i | \(-0.172340\pi\) | |||||||
\(348\) | −2.81929 | − | 3.00000i | −0.151130 | − | 0.160817i | ||||
\(349\) | −16.4356 | −0.879780 | −0.439890 | − | 0.898052i | \(-0.644983\pi\) | ||||
−0.439890 | + | 0.898052i | \(0.644983\pi\) | |||||||
\(350\) | −16.0858 | − | 5.04868i | −0.859822 | − | 0.269863i | ||||
\(351\) | −7.48913 | − | 17.1730i | −0.399740 | − | 0.916629i | ||||
\(352\) | −5.74456 | −0.306186 | ||||||||
\(353\) | − | 11.1168i | − | 0.591690i | −0.955236 | − | 0.295845i | \(-0.904399\pi\) | ||
0.955236 | − | 0.295845i | \(-0.0956012\pi\) | |||||||
\(354\) | 3.25544 | + | 3.46410i | 0.173025 | + | 0.184115i | ||||
\(355\) | − | 6.74456i | − | 0.357964i | ||||||
\(356\) | − | 10.0000i | − | 0.529999i | ||||||
\(357\) | −3.26890 | + | 1.57999i | −0.173009 | + | 0.0836222i | ||||
\(358\) | − | 20.1947i | − | 1.06732i | ||||||
\(359\) | 6.23369 | 0.329001 | 0.164501 | − | 0.986377i | \(-0.447399\pi\) | ||||
0.164501 | + | 0.986377i | \(0.447399\pi\) | |||||||
\(360\) | 10.0974 | + | 0.627719i | 0.532177 | + | 0.0330837i | ||||
\(361\) | −13.3505 | −0.702660 | ||||||||
\(362\) | 20.3723i | 1.07074i | ||||||||
\(363\) | 27.7677 | − | 26.0951i | 1.45743 | − | 1.36964i | ||||
\(364\) | 7.95228 | + | 5.26890i | 0.416812 | + | 0.276165i | ||||
\(365\) | − | 34.5484i | − | 1.80835i | ||||||
\(366\) | −9.18614 | − | 9.77495i | −0.480167 | − | 0.510945i | ||||
\(367\) | 4.74456i | 0.247664i | 0.992303 | + | 0.123832i | \(0.0395184\pi\) | ||||
−0.992303 | + | 0.123832i | \(0.960482\pi\) | |||||||
\(368\) | − | 0.147477i | − | 0.00768776i | ||||||
\(369\) | −25.0684 | − | 1.55842i | −1.30501 | − | 0.0811282i | ||||
\(370\) | 28.2101 | 1.46658 | ||||||||
\(371\) | 8.00000 | − | 25.4891i | 0.415339 | − | 1.32333i | ||||
\(372\) | −5.18614 | + | 4.87375i | −0.268889 | + | 0.252692i | ||||
\(373\) | −12.2337 | −0.633436 | −0.316718 | − | 0.948520i | \(-0.602581\pi\) | ||||
−0.316718 | + | 0.948520i | \(0.602581\pi\) | |||||||
\(374\) | 4.55134 | 0.235344 | ||||||||
\(375\) | −5.48913 | − | 5.84096i | −0.283457 | − | 0.301626i | ||||
\(376\) | 10.3723i | 0.534910i | ||||||||
\(377\) | 2.37686 | − | 8.23369i | 0.122415 | − | 0.424057i | ||||
\(378\) | −5.20313 | − | 12.7251i | −0.267620 | − | 0.654507i | ||||
\(379\) | 18.3152i | 0.940787i | 0.882457 | + | 0.470394i | \(0.155888\pi\) | ||||
−0.882457 | + | 0.470394i | \(0.844112\pi\) | |||||||
\(380\) | 8.01544i | 0.411184i | ||||||||
\(381\) | −13.0916 | + | 12.3030i | −0.670701 | + | 0.630301i | ||||
\(382\) | − | 2.96677i | − | 0.151793i | ||||||
\(383\) | 3.51087i | 0.179397i | 0.995969 | + | 0.0896987i | \(0.0285904\pi\) | ||||
−0.995969 | + | 0.0896987i | \(0.971410\pi\) | |||||||
\(384\) | 1.26217 | − | 1.18614i | 0.0644098 | − | 0.0605300i | ||||
\(385\) | 15.3484 | − | 48.9022i | 0.782227 | − | 2.49229i | ||||
\(386\) | − | 20.7846i | − | 1.05791i | ||||||
\(387\) | −0.489125 | + | 7.86797i | −0.0248636 | + | 0.399951i | ||||
\(388\) | −9.15759 | −0.464906 | ||||||||
\(389\) | 25.2434i | 1.27989i | 0.768421 | + | 0.639945i | \(0.221043\pi\) | ||||
−0.768421 | + | 0.639945i | \(0.778957\pi\) | |||||||
\(390\) | 9.60002 | + | 18.7446i | 0.486116 | + | 0.949168i | ||||
\(391\) | 0.116844i | 0.00590905i | ||||||||
\(392\) | 5.74456 | + | 4.00000i | 0.290144 | + | 0.202031i | ||||
\(393\) | 5.00000 | − | 4.69882i | 0.252217 | − | 0.237024i | ||||
\(394\) | 21.1168 | 1.06385 | ||||||||
\(395\) | − | 12.2337i | − | 0.615544i | ||||||
\(396\) | −1.06930 | + | 17.2005i | −0.0537342 | + | 0.864357i | ||||
\(397\) | −6.63325 | −0.332913 | −0.166457 | − | 0.986049i | \(-0.553233\pi\) | ||||
−0.166457 | + | 0.986049i | \(0.553233\pi\) | |||||||
\(398\) | − | 12.1168i | − | 0.607363i | ||||||
\(399\) | 9.80670 | − | 4.73998i | 0.490949 | − | 0.237296i | ||||
\(400\) | −6.37228 | −0.318614 | ||||||||
\(401\) | 28.9783 | 1.44710 | 0.723552 | − | 0.690269i | \(-0.242508\pi\) | ||||
0.723552 | + | 0.690269i | \(0.242508\pi\) | |||||||
\(402\) | 7.10313 | + | 7.55842i | 0.354272 | + | 0.376980i | ||||
\(403\) | −14.2337 | − | 4.10891i | −0.709030 | − | 0.204679i | ||||
\(404\) | 17.6704 | 0.879133 | ||||||||
\(405\) | 3.75906 | − | 30.1168i | 0.186789 | − | 1.49652i | ||||
\(406\) | 1.88316 | − | 6.00000i | 0.0934595 | − | 0.297775i | ||||
\(407\) | 48.0550i | 2.38200i | ||||||||
\(408\) | −1.00000 | + | 0.939764i | −0.0495074 | + | 0.0465252i | ||||
\(409\) | −29.7947 | −1.47325 | −0.736627 | − | 0.676299i | \(-0.763583\pi\) | ||||
−0.736627 | + | 0.676299i | \(0.763583\pi\) | |||||||
\(410\) | 28.2337 | 1.39436 | ||||||||
\(411\) | −22.8665 | + | 21.4891i | −1.12792 | + | 1.05998i | ||||
\(412\) | 7.37228i | 0.363206i | ||||||||
\(413\) | −2.17448 | + | 6.92820i | −0.106999 | + | 0.340915i | ||||
\(414\) | −0.441578 | − | 0.0274514i | −0.0217024 | − | 0.00134916i | ||||
\(415\) | −22.7446 | −1.11649 | ||||||||
\(416\) | 3.46410 | + | 1.00000i | 0.169842 | + | 0.0490290i | ||||
\(417\) | 6.23369 | + | 6.63325i | 0.305265 | + | 0.324832i | ||||
\(418\) | −13.6540 | −0.667840 | ||||||||
\(419\) | −4.90120 | −0.239439 | −0.119720 | − | 0.992808i | \(-0.538200\pi\) | ||||
−0.119720 | + | 0.992808i | \(0.538200\pi\) | |||||||
\(420\) | 6.72507 | + | 13.9137i | 0.328150 | + | 0.678920i | ||||
\(421\) | − | 23.0140i | − | 1.12163i | −0.827940 | − | 0.560817i | \(-0.810487\pi\) | ||
0.827940 | − | 0.560817i | \(-0.189513\pi\) | |||||||
\(422\) | 17.3723 | 0.845669 | ||||||||
\(423\) | 31.0569 | + | 1.93070i | 1.51004 | + | 0.0938740i | ||||
\(424\) | − | 10.0974i | − | 0.490371i | ||||||
\(425\) | 5.04868 | 0.244897 | ||||||||
\(426\) | −2.52434 | + | 2.37228i | −0.122305 | + | 0.114937i | ||||
\(427\) | 6.13592 | − | 19.5499i | 0.296938 | − | 0.946086i | ||||
\(428\) | 17.0256i | 0.822961i | ||||||||
\(429\) | −31.9307 | + | 16.3533i | −1.54163 | + | 0.789544i | ||||
\(430\) | − | 8.86141i | − | 0.427335i | ||||||
\(431\) | −28.2337 | −1.35997 | −0.679984 | − | 0.733227i | \(-0.738013\pi\) | ||||
−0.679984 | + | 0.733227i | \(0.738013\pi\) | |||||||
\(432\) | −3.31662 | − | 4.00000i | −0.159571 | − | 0.192450i | ||||
\(433\) | 30.4674i | 1.46417i | 0.681214 | + | 0.732084i | \(0.261452\pi\) | ||||
−0.681214 | + | 0.732084i | \(0.738548\pi\) | |||||||
\(434\) | −10.3723 | − | 3.25544i | −0.497885 | − | 0.156266i | ||||
\(435\) | 10.1168 | − | 9.50744i | 0.485066 | − | 0.455847i | ||||
\(436\) | 19.6974i | 0.943333i | ||||||||
\(437\) | − | 0.350532i | − | 0.0167682i | ||||||
\(438\) | −12.9307 | + | 12.1518i | −0.617853 | + | 0.580636i | ||||
\(439\) | 5.60597i | 0.267558i | 0.991011 | + | 0.133779i | \(0.0427113\pi\) | ||||
−0.991011 | + | 0.133779i | \(0.957289\pi\) | |||||||
\(440\) | − | 19.3723i | − | 0.923537i | ||||||
\(441\) | 13.0462 | − | 16.4559i | 0.621246 | − | 0.783615i | ||||
\(442\) | −2.74456 | − | 0.792287i | −0.130546 | − | 0.0376852i | ||||
\(443\) | − | 16.7306i | − | 0.794895i | −0.917625 | − | 0.397447i | \(-0.869896\pi\) | ||
0.917625 | − | 0.397447i | \(-0.130104\pi\) | |||||||
\(444\) | −9.92242 | − | 10.5584i | −0.470897 | − | 0.501081i | ||||
\(445\) | 33.7228 | 1.59861 | ||||||||
\(446\) | −0.644810 | −0.0305326 | ||||||||
\(447\) | −9.62747 | + | 9.04755i | −0.455364 | + | 0.427934i | ||||
\(448\) | 2.52434 | + | 0.792287i | 0.119264 | + | 0.0374320i | ||||
\(449\) | 14.1168 | 0.666215 | 0.333108 | − | 0.942889i | \(-0.391903\pi\) | ||||
0.333108 | + | 0.942889i | \(0.391903\pi\) | |||||||
\(450\) | −1.18614 | + | 19.0800i | −0.0559152 | + | 0.899440i | ||||
\(451\) | 48.0951i | 2.26471i | ||||||||
\(452\) | − | 5.69349i | − | 0.267799i | ||||||
\(453\) | −21.1345 | − | 22.4891i | −0.992984 | − | 1.05663i | ||||
\(454\) | 11.4891i | 0.539211i | ||||||||
\(455\) | −17.7682 | + | 26.8173i | −0.832987 | + | 1.25721i | ||||
\(456\) | 3.00000 | − | 2.81929i | 0.140488 | − | 0.132025i | ||||
\(457\) | 23.6588i | 1.10671i | 0.832945 | + | 0.553356i | \(0.186653\pi\) | ||||
−0.832945 | + | 0.553356i | \(0.813347\pi\) | |||||||
\(458\) | 5.04868 | 0.235909 | ||||||||
\(459\) | 2.62772 | + | 3.16915i | 0.122651 | + | 0.147923i | ||||
\(460\) | 0.497333 | 0.0231883 | ||||||||
\(461\) | 21.6060i | 1.00629i | 0.864202 | + | 0.503145i | \(0.167824\pi\) | ||||
−0.864202 | + | 0.503145i | \(0.832176\pi\) | |||||||
\(462\) | −23.7015 | + | 11.4559i | −1.10269 | + | 0.532978i | ||||
\(463\) | 31.6742i | 1.47203i | 0.676967 | + | 0.736014i | \(0.263294\pi\) | ||||
−0.676967 | + | 0.736014i | \(0.736706\pi\) | |||||||
\(464\) | − | 2.37686i | − | 0.110343i | ||||||
\(465\) | −16.4356 | − | 17.4891i | −0.762185 | − | 0.811039i | ||||
\(466\) | 10.7422i | 0.497621i | ||||||||
\(467\) | 21.5769 | 0.998460 | 0.499230 | − | 0.866470i | \(-0.333616\pi\) | ||||
0.499230 | + | 0.866470i | \(0.333616\pi\) | |||||||
\(468\) | 3.63903 | − | 10.1861i | 0.168214 | − | 0.470855i | ||||
\(469\) | −4.74456 | + | 15.1168i | −0.219084 | + | 0.698031i | ||||
\(470\) | −34.9783 | −1.61343 | ||||||||
\(471\) | 9.79211 | + | 10.4198i | 0.451197 | + | 0.480117i | ||||
\(472\) | 2.74456i | 0.126329i | ||||||||
\(473\) | 15.0951 | 0.694073 | ||||||||
\(474\) | −4.57879 | + | 4.30298i | −0.210311 | + | 0.197643i | ||||
\(475\) | −15.1460 | −0.694947 | ||||||||
\(476\) | −2.00000 | − | 0.627719i | −0.0916698 | − | 0.0287714i | ||||
\(477\) | −30.2337 | − | 1.87953i | −1.38431 | − | 0.0860577i | ||||
\(478\) | 18.0000 | 0.823301 | ||||||||
\(479\) | − | 28.6277i | − | 1.30803i | −0.756480 | − | 0.654017i | \(-0.773082\pi\) | ||
0.756480 | − | 0.654017i | \(-0.226918\pi\) | |||||||
\(480\) | 4.00000 | + | 4.25639i | 0.182574 | + | 0.194277i | ||||
\(481\) | 8.36530 | − | 28.9783i | 0.381425 | − | 1.32129i | ||||
\(482\) | 16.4356 | 0.748623 | ||||||||
\(483\) | −0.294101 | − | 0.608475i | −0.0133821 | − | 0.0276866i | ||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | − | 30.8820i | − | 1.40228i | ||||||
\(486\) | −12.5942 | + | 9.18614i | −0.571286 | + | 0.416692i | ||||
\(487\) | − | 37.5152i | − | 1.69998i | −0.526802 | − | 0.849988i | \(-0.676609\pi\) | ||
0.526802 | − | 0.849988i | \(-0.323391\pi\) | |||||||
\(488\) | − | 7.74456i | − | 0.350580i | ||||||
\(489\) | −9.74749 | − | 10.3723i | −0.440797 | − | 0.469051i | ||||
\(490\) | −13.4891 | + | 19.3723i | −0.609377 | + | 0.875150i | ||||
\(491\) | − | 11.6819i | − | 0.527198i | −0.964632 | − | 0.263599i | \(-0.915090\pi\) | ||
0.964632 | − | 0.263599i | \(-0.0849095\pi\) | |||||||
\(492\) | −9.93070 | − | 10.5672i | −0.447711 | − | 0.476408i | ||||
\(493\) | 1.88316i | 0.0848131i | ||||||||
\(494\) | 8.23369 | + | 2.37686i | 0.370451 | + | 0.106940i | ||||
\(495\) | −58.0049 | − | 3.60597i | −2.60712 | − | 0.162076i | ||||
\(496\) | −4.10891 | −0.184496 | ||||||||
\(497\) | −5.04868 | − | 1.58457i | −0.226464 | − | 0.0710779i | ||||
\(498\) | 8.00000 | + | 8.51278i | 0.358489 | + | 0.381467i | ||||
\(499\) | 10.4472i | 0.467681i | 0.972275 | + | 0.233841i | \(0.0751294\pi\) | ||||
−0.972275 | + | 0.233841i | \(0.924871\pi\) | |||||||
\(500\) | − | 4.62772i | − | 0.206958i | ||||||
\(501\) | 14.9783 | + | 15.9383i | 0.669179 | + | 0.712071i | ||||
\(502\) | 6.78073 | 0.302639 | ||||||||
\(503\) | −27.4179 | −1.22250 | −0.611251 | − | 0.791437i | \(-0.709333\pi\) | ||||
−0.611251 | + | 0.791437i | \(0.709333\pi\) | |||||||
\(504\) | 2.84216 | − | 7.41095i | 0.126600 | − | 0.330110i | ||||
\(505\) | 59.5894i | 2.65170i | ||||||||
\(506\) | 0.847190i | 0.0376622i | ||||||||
\(507\) | 22.1017 | − | 4.30298i | 0.981570 | − | 0.191102i | ||||
\(508\) | −10.3723 | −0.460196 | ||||||||
\(509\) | − | 22.1168i | − | 0.980312i | −0.871635 | − | 0.490156i | \(-0.836940\pi\) | ||
0.871635 | − | 0.490156i | \(-0.163060\pi\) | |||||||
\(510\) | −3.16915 | − | 3.37228i | −0.140332 | − | 0.149327i | ||||
\(511\) | −25.8614 | − | 8.11684i | −1.14404 | − | 0.359068i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.88316 | − | 9.50744i | −0.348050 | − | 0.419764i | ||||
\(514\) | 18.9051 | 0.833867 | ||||||||
\(515\) | −24.8614 | −1.09552 | ||||||||
\(516\) | −3.31662 | + | 3.11684i | −0.146006 | + | 0.137211i | ||||
\(517\) | − | 59.5842i | − | 2.62051i | ||||||
\(518\) | 6.62772 | − | 21.1168i | 0.291205 | − | 0.927821i | ||||
\(519\) | 13.4891 | − | 12.6766i | 0.592107 | − | 0.556441i | ||||
\(520\) | −3.37228 | + | 11.6819i | −0.147884 | + | 0.512286i | ||||
\(521\) | 20.3971 | 0.893612 | 0.446806 | − | 0.894631i | \(-0.352561\pi\) | ||||
0.446806 | + | 0.894631i | \(0.352561\pi\) | |||||||
\(522\) | −7.11684 | − | 0.442430i | −0.311496 | − | 0.0193647i | ||||
\(523\) | 37.3505i | 1.63322i | 0.577186 | + | 0.816612i | \(0.304151\pi\) | ||||
−0.577186 | + | 0.816612i | \(0.695849\pi\) | |||||||
\(524\) | 3.96143 | 0.173056 | ||||||||
\(525\) | −26.2914 | + | 12.7077i | −1.14745 | + | 0.554611i | ||||
\(526\) | 7.22316i | 0.314945i | ||||||||
\(527\) | 3.25544 | 0.141809 | ||||||||
\(528\) | −7.25061 | + | 6.81386i | −0.315542 | + | 0.296535i | ||||
\(529\) | 22.9783 | 0.999054 | ||||||||
\(530\) | 34.0511 | 1.47909 | ||||||||
\(531\) | 8.21782 | + | 0.510875i | 0.356623 | + | 0.0221701i | ||||
\(532\) | 6.00000 | + | 1.88316i | 0.260133 | + | 0.0816452i | ||||
\(533\) | 8.37228 | − | 29.0024i | 0.362644 | − | 1.25623i | ||||
\(534\) | −11.8614 | − | 12.6217i | −0.513293 | − | 0.546194i | ||||
\(535\) | −57.4150 | −2.48227 | ||||||||
\(536\) | 5.98844i | 0.258661i | ||||||||
\(537\) | −23.9538 | − | 25.4891i | −1.03368 | − | 1.09994i | ||||
\(538\) | −14.5012 | −0.625192 | ||||||||
\(539\) | −33.0000 | − | 22.9783i | −1.42141 | − | 0.989743i | ||||
\(540\) | 13.4891 | − | 11.1846i | 0.580480 | − | 0.481308i | ||||
\(541\) | − | 24.4511i | − | 1.05123i | −0.850721 | − | 0.525617i | \(-0.823834\pi\) | ||
0.850721 | − | 0.525617i | \(-0.176166\pi\) | |||||||
\(542\) | −11.3321 | −0.486754 | ||||||||
\(543\) | 24.1644 | + | 25.7133i | 1.03699 | + | 1.10346i | ||||
\(544\) | −0.792287 | −0.0339690 | ||||||||
\(545\) | −66.4251 | −2.84534 | ||||||||
\(546\) | 16.2868 | − | 2.78228i | 0.697009 | − | 0.119070i | ||||
\(547\) | −5.48913 | −0.234698 | −0.117349 | − | 0.993091i | \(-0.537440\pi\) | ||||
−0.117349 | + | 0.993091i | \(0.537440\pi\) | |||||||
\(548\) | −18.1168 | −0.773913 | ||||||||
\(549\) | −23.1889 | − | 1.44158i | −0.989679 | − | 0.0615251i | ||||
\(550\) | 36.6060 | 1.56088 | ||||||||
\(551\) | − | 5.64947i | − | 0.240675i | ||||||
\(552\) | −0.174928 | − | 0.186141i | −0.00744544 | − | 0.00792267i | ||||
\(553\) | −9.15759 | − | 2.87419i | −0.389420 | − | 0.122223i | ||||
\(554\) | 17.4891 | 0.743042 | ||||||||
\(555\) | 35.6060 | − | 33.4612i | 1.51139 | − | 1.42035i | ||||
\(556\) | 5.25544i | 0.222880i | ||||||||
\(557\) | 30.3723 | 1.28691 | 0.643457 | − | 0.765482i | \(-0.277499\pi\) | ||||
0.643457 | + | 0.765482i | \(0.277499\pi\) | |||||||
\(558\) | −0.764836 | + | 12.3030i | −0.0323781 | + | 0.520827i | ||||
\(559\) | −9.10268 | − | 2.62772i | −0.385003 | − | 0.111141i | ||||
\(560\) | −2.67181 | + | 8.51278i | −0.112905 | + | 0.359730i | ||||
\(561\) | 5.74456 | − | 5.39853i | 0.242536 | − | 0.227926i | ||||
\(562\) | −14.0000 | −0.590554 | ||||||||
\(563\) | 9.25016 | 0.389848 | 0.194924 | − | 0.980818i | \(-0.437554\pi\) | ||||
0.194924 | + | 0.980818i | \(0.437554\pi\) | |||||||
\(564\) | 12.3030 | + | 13.0916i | 0.518049 | + | 0.551255i | ||||
\(565\) | 19.2000 | 0.807752 | ||||||||
\(566\) | 0.372281i | 0.0156482i | ||||||||
\(567\) | −21.6610 | − | 9.88954i | −0.909675 | − | 0.415322i | ||||
\(568\) | −2.00000 | −0.0839181 | ||||||||
\(569\) | − | 10.1523i | − | 0.425605i | −0.977095 | − | 0.212802i | \(-0.931741\pi\) | ||
0.977095 | − | 0.212802i | \(-0.0682590\pi\) | |||||||
\(570\) | 9.50744 | + | 10.1168i | 0.398223 | + | 0.423748i | ||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | −19.8997 | − | 5.74456i | −0.832050 | − | 0.240192i | ||||
\(573\) | −3.51900 | − | 3.74456i | −0.147009 | − | 0.156431i | ||||
\(574\) | 6.63325 | − | 21.1345i | 0.276866 | − | 0.882136i | ||||
\(575\) | 0.939764i | 0.0391909i | ||||||||
\(576\) | 0.186141 | − | 2.99422i | 0.00775586 | − | 0.124759i | ||||
\(577\) | −6.92820 | −0.288425 | −0.144212 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(578\) | −16.3723 | −0.680997 | ||||||||
\(579\) | −24.6535 | − | 26.2337i | −1.02456 | − | 1.09023i | ||||
\(580\) | 8.01544 | 0.332823 | ||||||||
\(581\) | −5.34363 | + | 17.0256i | −0.221691 | + | 0.706339i | ||||
\(582\) | −11.5584 | + | 10.8622i | −0.479112 | + | 0.450252i | ||||
\(583\) | 58.0049i | 2.40232i | ||||||||
\(584\) | −10.2448 | −0.423934 | ||||||||
\(585\) | 34.3505 | + | 12.2718i | 1.42022 | + | 0.507378i | ||||
\(586\) | − | 11.4891i | − | 0.474611i | ||||||
\(587\) | 16.7446i | 0.691122i | 0.938396 | + | 0.345561i | \(0.112311\pi\) | ||||
−0.938396 | + | 0.345561i | \(0.887689\pi\) | |||||||
\(588\) | 11.9952 | − | 1.76518i | 0.494673 | − | 0.0727950i | ||||
\(589\) | −9.76631 | −0.402414 | ||||||||
\(590\) | −9.25544 | −0.381040 | ||||||||
\(591\) | 26.6530 | − | 25.0475i | 1.09636 | − | 1.03032i | ||||
\(592\) | − | 8.36530i | − | 0.343812i | ||||||
\(593\) | − | 19.2554i | − | 0.790726i | −0.918525 | − | 0.395363i | \(-0.870619\pi\) | ||
0.918525 | − | 0.395363i | \(-0.129381\pi\) | |||||||
\(594\) | 19.0526 | + | 22.9783i | 0.781736 | + | 0.942809i | ||||
\(595\) | 2.11684 | − | 6.74456i | 0.0867821 | − | 0.276500i | ||||
\(596\) | −7.62772 | −0.312444 | ||||||||
\(597\) | −14.3723 | − | 15.2935i | −0.588218 | − | 0.625921i | ||||
\(598\) | 0.147477 | − | 0.510875i | 0.00603078 | − | 0.0208912i | ||||
\(599\) | 11.8294i | 0.483336i | 0.970359 | + | 0.241668i | \(0.0776945\pi\) | ||||
−0.970359 | + | 0.241668i | \(0.922305\pi\) | |||||||
\(600\) | −8.04290 | + | 7.55842i | −0.328350 | + | 0.308571i | ||||
\(601\) | 26.0000i | 1.06056i | 0.847822 | + | 0.530281i | \(0.177914\pi\) | ||||
−0.847822 | + | 0.530281i | \(0.822086\pi\) | |||||||
\(602\) | −6.63325 | − | 2.08191i | −0.270351 | − | 0.0848522i | ||||
\(603\) | 17.9307 | + | 1.11469i | 0.730195 | + | 0.0453938i | ||||
\(604\) | − | 17.8178i | − | 0.724998i | ||||||
\(605\) | 74.1902i | 3.01626i | ||||||||
\(606\) | 22.3030 | − | 20.9595i | 0.905997 | − | 0.851423i | ||||
\(607\) | − | 18.1168i | − | 0.735340i | −0.929956 | − | 0.367670i | \(-0.880156\pi\) | ||
0.929956 | − | 0.367670i | \(-0.119844\pi\) | |||||||
\(608\) | 2.37686 | 0.0963944 | ||||||||
\(609\) | −4.73998 | − | 9.80670i | −0.192074 | − | 0.397388i | ||||
\(610\) | 26.1168 | 1.05744 | ||||||||
\(611\) | −10.3723 | + | 35.9306i | −0.419618 | + | 1.45360i | ||||
\(612\) | −0.147477 | + | 2.37228i | −0.00596140 | + | 0.0958938i | ||||
\(613\) | − | 16.8781i | − | 0.681699i | −0.940118 | − | 0.340850i | \(-0.889285\pi\) | ||
0.940118 | − | 0.340850i | \(-0.110715\pi\) | |||||||
\(614\) | 31.8766 | 1.28644 | ||||||||
\(615\) | 35.6357 | − | 33.4891i | 1.43697 | − | 1.35041i | ||||
\(616\) | −14.5012 | − | 4.55134i | −0.584271 | − | 0.183379i | ||||
\(617\) | −17.6060 | −0.708790 | −0.354395 | − | 0.935096i | \(-0.615313\pi\) | ||||
−0.354395 | + | 0.935096i | \(0.615313\pi\) | |||||||
\(618\) | 8.74456 | + | 9.30506i | 0.351758 | + | 0.374305i | ||||
\(619\) | −13.0641 | −0.525091 | −0.262546 | − | 0.964920i | \(-0.584562\pi\) | ||||
−0.262546 | + | 0.964920i | \(0.584562\pi\) | |||||||
\(620\) | − | 13.8564i | − | 0.556487i | ||||||
\(621\) | −0.589907 | + | 0.489125i | −0.0236722 | + | 0.0196279i | ||||
\(622\) | −10.3923 | −0.416693 | ||||||||
\(623\) | 7.92287 | − | 25.2434i | 0.317423 | − | 1.01135i | ||||
\(624\) | 5.55842 | − | 2.84674i | 0.222515 | − | 0.113961i | ||||
\(625\) | −16.2554 | −0.650217 | ||||||||
\(626\) | − | 2.74456i | − | 0.109695i | ||||||
\(627\) | −17.2337 | + | 16.1956i | −0.688247 | + | 0.646790i | ||||
\(628\) | 8.25544i | 0.329428i | ||||||||
\(629\) | 6.62772i | 0.264264i | ||||||||
\(630\) | 24.9918 | + | 9.58457i | 0.995697 | + | 0.381859i | ||||
\(631\) | 12.1793i | 0.484849i | 0.970170 | + | 0.242424i | \(0.0779426\pi\) | ||||
−0.970170 | + | 0.242424i | \(0.922057\pi\) | |||||||
\(632\) | −3.62772 | −0.144303 | ||||||||
\(633\) | 21.9268 | − | 20.6060i | 0.871510 | − | 0.819014i | ||||
\(634\) | −3.86141 | −0.153356 | ||||||||
\(635\) | − | 34.9783i | − | 1.38807i | ||||||
\(636\) | −11.9769 | − | 12.7446i | −0.474914 | − | 0.505355i | ||||
\(637\) | 15.8997 | + | 19.6010i | 0.629971 | + | 0.776619i | ||||
\(638\) | 13.6540i | 0.540568i | ||||||||
\(639\) | −0.372281 | + | 5.98844i | −0.0147272 | + | 0.236899i | ||||
\(640\) | 3.37228i | 0.133301i | ||||||||
\(641\) | 8.86263i | 0.350053i | 0.984564 | + | 0.175026i | \(0.0560011\pi\) | ||||
−0.984564 | + | 0.175026i | \(0.943999\pi\) | |||||||
\(642\) | 20.1947 | + | 21.4891i | 0.797021 | + | 0.848108i | ||||
\(643\) | −18.4077 | −0.725931 | −0.362965 | − | 0.931803i | \(-0.618236\pi\) | ||||
−0.362965 | + | 0.931803i | \(0.618236\pi\) | |||||||
\(644\) | 0.116844 | − | 0.372281i | 0.00460430 | − | 0.0146699i | ||||
\(645\) | −10.5109 | − | 11.1846i | −0.413865 | − | 0.440393i | ||||
\(646\) | −1.88316 | −0.0740918 | ||||||||
\(647\) | −26.1282 | −1.02721 | −0.513604 | − | 0.858028i | \(-0.671690\pi\) | ||||
−0.513604 | + | 0.858028i | \(0.671690\pi\) | |||||||
\(648\) | −8.93070 | − | 1.11469i | −0.350831 | − | 0.0437892i | ||||
\(649\) | − | 15.7663i | − | 0.618882i | ||||||
\(650\) | −22.0742 | − | 6.37228i | −0.865823 | − | 0.249941i | ||||
\(651\) | −16.9530 | + | 8.19407i | −0.664440 | + | 0.321151i | ||||
\(652\) | − | 8.21782i | − | 0.321835i | ||||||
\(653\) | 14.6487i | 0.573248i | 0.958043 | + | 0.286624i | \(0.0925330\pi\) | ||||
−0.958043 | + | 0.286624i | \(0.907467\pi\) | |||||||
\(654\) | 23.3639 | + | 24.8614i | 0.913599 | + | 0.972158i | ||||
\(655\) | 13.3591i | 0.521982i | ||||||||
\(656\) | − | 8.37228i | − | 0.326883i | ||||||
\(657\) | −1.90698 | + | 30.6753i | −0.0743983 | + | 1.19676i | ||||
\(658\) | −8.21782 | + | 26.1831i | −0.320364 | + | 1.02073i | ||||
\(659\) | 37.9200i | 1.47715i | 0.674170 | + | 0.738576i | \(0.264501\pi\) | ||||
−0.674170 | + | 0.738576i | \(0.735499\pi\) | |||||||
\(660\) | −22.9783 | − | 24.4511i | −0.894427 | − | 0.951757i | ||||
\(661\) | 42.2689 | 1.64407 | 0.822035 | − | 0.569436i | \(-0.192838\pi\) | ||||
0.822035 | + | 0.569436i | \(0.192838\pi\) | |||||||
\(662\) | 17.0805i | 0.663851i | ||||||||
\(663\) | −4.40387 | + | 2.25544i | −0.171032 | + | 0.0875939i | ||||
\(664\) | 6.74456i | 0.261740i | ||||||||
\(665\) | −6.35053 | + | 20.2337i | −0.246263 | + | 0.784629i | ||||
\(666\) | −25.0475 | − | 1.55712i | −0.970573 | − | 0.0603373i | ||||
\(667\) | −0.350532 | −0.0135726 | ||||||||
\(668\) | 12.6277i | 0.488581i | ||||||||
\(669\) | −0.813859 | + | 0.764836i | −0.0314656 | + | 0.0295703i | ||||
\(670\) | −20.1947 | −0.780189 | ||||||||
\(671\) | 44.4891i | 1.71748i | ||||||||
\(672\) | 4.12590 | − | 1.99422i | 0.159160 | − | 0.0769287i | ||||
\(673\) | −45.2337 | −1.74363 | −0.871815 | − | 0.489835i | \(-0.837057\pi\) | ||||
−0.871815 | + | 0.489835i | \(0.837057\pi\) | |||||||
\(674\) | 5.00000 | 0.192593 | ||||||||
\(675\) | 21.1345 | + | 25.4891i | 0.813466 | + | 0.981077i | ||||
\(676\) | 11.0000 | + | 6.92820i | 0.423077 | + | 0.266469i | ||||
\(677\) | −20.5446 | −0.789592 | −0.394796 | − | 0.918769i | \(-0.629185\pi\) | ||||
−0.394796 | + | 0.918769i | \(0.629185\pi\) | |||||||
\(678\) | −6.75327 | − | 7.18614i | −0.259358 | − | 0.275982i | ||||
\(679\) | −23.1168 | − | 7.25544i | −0.887143 | − | 0.278438i | ||||
\(680\) | − | 2.67181i | − | 0.102459i | ||||||
\(681\) | 13.6277 | + | 14.5012i | 0.522215 | + | 0.555688i | ||||
\(682\) | 23.6039 | 0.903840 | ||||||||
\(683\) | −19.0000 | −0.727015 | −0.363507 | − | 0.931591i | \(-0.618421\pi\) | ||||
−0.363507 | + | 0.931591i | \(0.618421\pi\) | |||||||
\(684\) | 0.442430 | − | 7.11684i | 0.0169168 | − | 0.272119i | ||||
\(685\) | − | 61.0951i | − | 2.33432i | ||||||
\(686\) | 11.3321 | + | 14.6487i | 0.432660 | + | 0.559290i | ||||
\(687\) | 6.37228 | − | 5.98844i | 0.243118 | − | 0.228473i | ||||
\(688\) | −2.62772 | −0.100181 | ||||||||
\(689\) | 10.0974 | − | 34.9783i | 0.384678 | − | 1.33257i | ||||
\(690\) | 0.627719 | − | 0.589907i | 0.0238968 | − | 0.0224574i | ||||
\(691\) | 31.1769 | 1.18603 | 0.593013 | − | 0.805193i | \(-0.297938\pi\) | ||||
0.593013 | + | 0.805193i | \(0.297938\pi\) | |||||||
\(692\) | 10.6873 | 0.406269 | ||||||||
\(693\) | −16.3270 | + | 42.5726i | −0.620211 | + | 1.61720i | ||||
\(694\) | − | 19.2000i | − | 0.728823i | ||||||
\(695\) | −17.7228 | −0.672265 | ||||||||
\(696\) | −2.81929 | − | 3.00000i | −0.106865 | − | 0.113715i | ||||
\(697\) | 6.63325i | 0.251252i | ||||||||
\(698\) | −16.4356 | −0.622098 | ||||||||
\(699\) | 12.7417 | + | 13.5584i | 0.481936 | + | 0.512827i | ||||
\(700\) | −16.0858 | − | 5.04868i | −0.607986 | − | 0.190822i | ||||
\(701\) | 13.2665i | 0.501069i | 0.968108 | + | 0.250534i | \(0.0806063\pi\) | ||||
−0.968108 | + | 0.250534i | \(0.919394\pi\) | |||||||
\(702\) | −7.48913 | − | 17.1730i | −0.282659 | − | 0.648154i | ||||
\(703\) | − | 19.8832i | − | 0.749907i | ||||||
\(704\) | −5.74456 | −0.216506 | ||||||||
\(705\) | −44.1485 | + | 41.4891i | −1.66273 | + | 1.56257i | ||||
\(706\) | − | 11.1168i | − | 0.418388i | ||||||
\(707\) | 44.6060 | + | 14.0000i | 1.67758 | + | 0.526524i | ||||
\(708\) | 3.25544 | + | 3.46410i | 0.122347 | + | 0.130189i | ||||
\(709\) | − | 33.7013i | − | 1.26568i | −0.774284 | − | 0.632839i | \(-0.781890\pi\) | ||
0.774284 | − | 0.632839i | \(-0.218110\pi\) | |||||||
\(710\) | − | 6.74456i | − | 0.253119i | ||||||
\(711\) | −0.675266 | + | 10.8622i | −0.0253245 | + | 0.407364i | ||||
\(712\) | − | 10.0000i | − | 0.374766i | ||||||
\(713\) | 0.605969i | 0.0226937i | ||||||||
\(714\) | −3.26890 | + | 1.57999i | −0.122336 | + | 0.0591298i | ||||
\(715\) | 19.3723 | − | 67.1076i | 0.724482 | − | 2.50968i | ||||
\(716\) | − | 20.1947i | − | 0.754711i | ||||||
\(717\) | 22.7190 | − | 21.3505i | 0.848458 | − | 0.797350i | ||||
\(718\) | 6.23369 | 0.232639 | ||||||||
\(719\) | −16.4356 | −0.612946 | −0.306473 | − | 0.951879i | \(-0.599149\pi\) | ||||
−0.306473 | + | 0.951879i | \(0.599149\pi\) | |||||||
\(720\) | 10.0974 | + | 0.627719i | 0.376306 | + | 0.0233937i | ||||
\(721\) | −5.84096 | + | 18.6101i | −0.217529 | + | 0.693077i | ||||
\(722\) | −13.3505 | −0.496855 | ||||||||
\(723\) | 20.7446 | − | 19.4950i | 0.771499 | − | 0.725026i | ||||
\(724\) | 20.3723i | 0.757130i | ||||||||
\(725\) | 15.1460i | 0.562509i | ||||||||
\(726\) | 27.7677 | − | 26.0951i | 1.03056 | − | 0.968480i | ||||
\(727\) | − | 1.13859i | − | 0.0422281i | −0.999777 | − | 0.0211140i | \(-0.993279\pi\) | ||
0.999777 | − | 0.0211140i | \(-0.00672131\pi\) | |||||||
\(728\) | 7.95228 | + | 5.26890i | 0.294731 | + | 0.195278i | ||||
\(729\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(730\) | − | 34.5484i | − | 1.27870i | ||||||
\(731\) | 2.08191 | 0.0770021 | ||||||||
\(732\) | −9.18614 | − | 9.77495i | −0.339530 | − | 0.361292i | ||||
\(733\) | 18.6101 | 0.687381 | 0.343690 | − | 0.939083i | \(-0.388323\pi\) | ||||
0.343690 | + | 0.939083i | \(0.388323\pi\) | |||||||
\(734\) | 4.74456i | 0.175125i | ||||||||
\(735\) | 5.95270 | + | 40.4511i | 0.219569 | + | 1.49206i | ||||
\(736\) | − | 0.147477i | − | 0.00543607i | ||||||
\(737\) | − | 34.4010i | − | 1.26718i | ||||||
\(738\) | −25.0684 | − | 1.55842i | −0.922782 | − | 0.0573663i | ||||
\(739\) | − | 44.8482i | − | 1.64977i | −0.565303 | − | 0.824883i | \(-0.691241\pi\) | ||
0.565303 | − | 0.824883i | \(-0.308759\pi\) | |||||||
\(740\) | 28.2101 | 1.03703 | ||||||||
\(741\) | 13.2116 | − | 6.76631i | 0.485340 | − | 0.248567i | ||||
\(742\) | 8.00000 | − | 25.4891i | 0.293689 | − | 0.935735i | ||||
\(743\) | 0.978251 | 0.0358885 | 0.0179443 | − | 0.999839i | \(-0.494288\pi\) | ||||
0.0179443 | + | 0.999839i | \(0.494288\pi\) | |||||||
\(744\) | −5.18614 | + | 4.87375i | −0.190133 | + | 0.178680i | ||||
\(745\) | − | 25.7228i | − | 0.942411i | ||||||
\(746\) | −12.2337 | −0.447907 | ||||||||
\(747\) | 20.1947 | + | 1.25544i | 0.738886 | + | 0.0459341i | ||||
\(748\) | 4.55134 | 0.166414 | ||||||||
\(749\) | −13.4891 | + | 42.9783i | −0.492882 | + | 1.57039i | ||||
\(750\) | −5.48913 | − | 5.84096i | −0.200435 | − | 0.213282i | ||||
\(751\) | 18.6060 | 0.678941 | 0.339471 | − | 0.940617i | \(-0.389752\pi\) | ||||
0.339471 | + | 0.940617i | \(0.389752\pi\) | |||||||
\(752\) | 10.3723i | 0.378238i | ||||||||
\(753\) | 8.55842 | − | 8.04290i | 0.311886 | − | 0.293099i | ||||
\(754\) | 2.37686 | − | 8.23369i | 0.0865602 | − | 0.299853i | ||||
\(755\) | 60.0868 | 2.18678 | ||||||||
\(756\) | −5.20313 | − | 12.7251i | −0.189236 | − | 0.462806i | ||||
\(757\) | 50.4674 | 1.83427 | 0.917134 | − | 0.398579i | \(-0.130497\pi\) | ||||
0.917134 | + | 0.398579i | \(0.130497\pi\) | |||||||
\(758\) | 18.3152i | 0.665237i | ||||||||
\(759\) | 1.00489 | + | 1.06930i | 0.0364751 | + | 0.0388130i | ||||
\(760\) | 8.01544i | 0.290751i | ||||||||
\(761\) | 2.13859i | 0.0775239i | 0.999248 | + | 0.0387620i | \(0.0123414\pi\) | ||||
−0.999248 | + | 0.0387620i | \(0.987659\pi\) | |||||||
\(762\) | −13.0916 | + | 12.3030i | −0.474258 | + | 0.445690i | ||||
\(763\) | −15.6060 | + | 49.7228i | −0.564974 | + | 1.80009i | ||||
\(764\) | − | 2.96677i | − | 0.107334i | ||||||
\(765\) | −8.00000 | − | 0.497333i | −0.289241 | − | 0.0179811i | ||||
\(766\) | 3.51087i | 0.126853i | ||||||||
\(767\) | −2.74456 | + | 9.50744i | −0.0991004 | + | 0.343294i | ||||
\(768\) | 1.26217 | − | 1.18614i | 0.0455446 | − | 0.0428012i | ||||
\(769\) | −34.1986 | −1.23323 | −0.616616 | − | 0.787264i | \(-0.711497\pi\) | ||||
−0.616616 | + | 0.787264i | \(0.711497\pi\) | |||||||
\(770\) | 15.3484 | − | 48.9022i | 0.553118 | − | 1.76231i | ||||
\(771\) | 23.8614 | − | 22.4241i | 0.859348 | − | 0.807584i | ||||
\(772\) | − | 20.7846i | − | 0.748054i | ||||||
\(773\) | 18.8614i | 0.678398i | 0.940715 | + | 0.339199i | \(0.110156\pi\) | ||||
−0.940715 | + | 0.339199i | \(0.889844\pi\) | |||||||
\(774\) | −0.489125 | + | 7.86797i | −0.0175812 | + | 0.282808i | ||||
\(775\) | 26.1831 | 0.940526 | ||||||||
\(776\) | −9.15759 | −0.328738 | ||||||||
\(777\) | −16.6822 | − | 34.5144i | −0.598472 | − | 1.23820i | ||||
\(778\) | 25.2434i | 0.905019i | ||||||||
\(779\) | − | 19.8997i | − | 0.712982i | ||||||
\(780\) | 9.60002 | + | 18.7446i | 0.343736 | + | 0.671163i | ||||
\(781\) | 11.4891 | 0.411113 | ||||||||
\(782\) | 0.116844i | 0.00417833i | ||||||||
\(783\) | −9.50744 | + | 7.88316i | −0.339768 | + | 0.281721i | ||||
\(784\) | 5.74456 | + | 4.00000i | 0.205163 | + | 0.142857i | ||||
\(785\) | −27.8397 | −0.993640 | ||||||||
\(786\) | 5.00000 | − | 4.69882i | 0.178344 | − | 0.167601i | ||||
\(787\) | 36.7229 | 1.30903 | 0.654515 | − | 0.756049i | \(-0.272873\pi\) | ||||
0.654515 | + | 0.756049i | \(0.272873\pi\) | |||||||
\(788\) | 21.1168 | 0.752256 | ||||||||
\(789\) | 8.56768 | + | 9.11684i | 0.305017 | + | 0.324568i | ||||
\(790\) | − | 12.2337i | − | 0.435255i | ||||||
\(791\) | 4.51087 | − | 14.3723i | 0.160388 | − | 0.511019i | ||||
\(792\) | −1.06930 | + | 17.2005i | −0.0379958 | + | 0.611193i | ||||
\(793\) | 7.74456 | − | 26.8280i | 0.275017 | − | 0.952689i | ||||
\(794\) | −6.63325 | −0.235405 | ||||||||
\(795\) | 42.9783 | − | 40.3894i | 1.52428 | − | 1.43246i | ||||
\(796\) | − | 12.1168i | − | 0.429470i | ||||||
\(797\) | 14.2063 | 0.503212 | 0.251606 | − | 0.967830i | \(-0.419041\pi\) | ||||
0.251606 | + | 0.967830i | \(0.419041\pi\) | |||||||
\(798\) | 9.80670 | − | 4.73998i | 0.347153 | − | 0.167794i | ||||
\(799\) | − | 8.21782i | − | 0.290726i | ||||||
\(800\) | −6.37228 | −0.225294 | ||||||||
\(801\) | −29.9422 | − | 1.86141i | −1.05796 | − | 0.0657696i | ||||
\(802\) | 28.9783 | 1.02326 | ||||||||
\(803\) | 58.8521 | 2.07684 | ||||||||
\(804\) | 7.10313 | + | 7.55842i | 0.250508 | + | 0.266565i | ||||
\(805\) | 1.25544 | + | 0.394031i | 0.0442484 | + | 0.0138878i | ||||
\(806\) | −14.2337 | − | 4.10891i | −0.501360 | − | 0.144730i | ||||
\(807\) | −18.3030 | + | 17.2005i | −0.644296 | + | 0.605486i | ||||
\(808\) | 17.6704 | 0.621641 | ||||||||
\(809\) | − | 1.58457i | − | 0.0557107i | −0.999612 | − | 0.0278553i | \(-0.991132\pi\) | ||
0.999612 | − | 0.0278553i | \(-0.00886777\pi\) | |||||||
\(810\) | 3.75906 | − | 30.1168i | 0.132080 | − | 1.05820i | ||||
\(811\) | −9.60002 | −0.337102 | −0.168551 | − | 0.985693i | \(-0.553909\pi\) | ||||
−0.168551 | + | 0.985693i | \(0.553909\pi\) | |||||||
\(812\) | 1.88316 | − | 6.00000i | 0.0660858 | − | 0.210559i | ||||
\(813\) | −14.3030 | + | 13.4414i | −0.501628 | + | 0.471411i | ||||
\(814\) | 48.0550i | 1.68433i | ||||||||
\(815\) | 27.7128 | 0.970737 | ||||||||
\(816\) | −1.00000 | + | 0.939764i | −0.0350070 | + | 0.0328983i | ||||
\(817\) | −6.24572 | −0.218510 | ||||||||
\(818\) | −29.7947 | −1.04175 | ||||||||
\(819\) | 17.2565 | − | 22.8301i | 0.602990 | − | 0.797748i | ||||
\(820\) | 28.2337 | 0.985963 | ||||||||
\(821\) | −43.7228 | −1.52594 | −0.762968 | − | 0.646436i | \(-0.776259\pi\) | ||||
−0.762968 | + | 0.646436i | \(0.776259\pi\) | |||||||
\(822\) | −22.8665 | + | 21.4891i | −0.797561 | + | 0.749519i | ||||
\(823\) | 35.8614 | 1.25005 | 0.625025 | − | 0.780605i | \(-0.285089\pi\) | ||||
0.625025 | + | 0.780605i | \(0.285089\pi\) | |||||||
\(824\) | 7.37228i | 0.256826i | ||||||||
\(825\) | 46.2029 | − | 43.4198i | 1.60858 | − | 1.51168i | ||||
\(826\) | −2.17448 | + | 6.92820i | −0.0756599 | + | 0.241063i | ||||
\(827\) | 22.1168 | 0.769078 | 0.384539 | − | 0.923109i | \(-0.374360\pi\) | ||||
0.384539 | + | 0.923109i | \(0.374360\pi\) | |||||||
\(828\) | −0.441578 | − | 0.0274514i | −0.0153459 | − | 0.000954003i | ||||
\(829\) | 33.6060i | 1.16718i | 0.812047 | + | 0.583592i | \(0.198353\pi\) | ||||
−0.812047 | + | 0.583592i | \(0.801647\pi\) | |||||||
\(830\) | −22.7446 | −0.789475 | ||||||||
\(831\) | 22.0742 | − | 20.7446i | 0.765747 | − | 0.719621i | ||||
\(832\) | 3.46410 | + | 1.00000i | 0.120096 | + | 0.0346688i | ||||
\(833\) | −4.55134 | − | 3.16915i | −0.157695 | − | 0.109804i | ||||
\(834\) | 6.23369 | + | 6.63325i | 0.215855 | + | 0.229691i | ||||
\(835\) | −42.5842 | −1.47369 | ||||||||
\(836\) | −13.6540 | −0.472234 | ||||||||
\(837\) | 13.6277 | + | 16.4356i | 0.471043 | + | 0.568099i | ||||
\(838\) | −4.90120 | −0.169309 | ||||||||
\(839\) | − | 5.62772i | − | 0.194290i | −0.995270 | − | 0.0971452i | \(-0.969029\pi\) | ||
0.995270 | − | 0.0971452i | \(-0.0309711\pi\) | |||||||
\(840\) | 6.72507 | + | 13.9137i | 0.232037 | + | 0.480069i | ||||
\(841\) | 23.3505 | 0.805191 | ||||||||
\(842\) | − | 23.0140i | − | 0.793115i | ||||||
\(843\) | −17.6704 | + | 16.6060i | −0.608600 | + | 0.571940i | ||||
\(844\) | 17.3723 | 0.597979 | ||||||||
\(845\) | −23.3639 | + | 37.0951i | −0.803741 | + | 1.27611i | ||||
\(846\) | 31.0569 | + | 1.93070i | 1.06776 | + | 0.0663789i | ||||
\(847\) | 55.5354 | + | 17.4303i | 1.90822 | + | 0.598913i | ||||
\(848\) | − | 10.0974i | − | 0.346744i | ||||||
\(849\) | 0.441578 | + | 0.469882i | 0.0151549 | + | 0.0161263i | ||||
\(850\) | 5.04868 | 0.173168 | ||||||||
\(851\) | −1.23369 | −0.0422903 | ||||||||
\(852\) | −2.52434 | + | 2.37228i | −0.0864824 | + | 0.0812730i | ||||
\(853\) | −56.7152 | −1.94189 | −0.970947 | − | 0.239297i | \(-0.923083\pi\) | ||||
−0.970947 | + | 0.239297i | \(0.923083\pi\) | |||||||
\(854\) | 6.13592 | − | 19.5499i | 0.209967 | − | 0.668984i | ||||
\(855\) | 24.0000 | + | 1.49200i | 0.820783 | + | 0.0510253i | ||||
\(856\) | 17.0256i | 0.581921i | ||||||||
\(857\) | −24.6535 | −0.842147 | −0.421073 | − | 0.907027i | \(-0.638346\pi\) | ||||
−0.421073 | + | 0.907027i | \(0.638346\pi\) | |||||||
\(858\) | −31.9307 | + | 16.3533i | −1.09010 | + | 0.558292i | ||||
\(859\) | − | 10.0951i | − | 0.344440i | −0.985058 | − | 0.172220i | \(-0.944906\pi\) | ||
0.985058 | − | 0.172220i | \(-0.0550940\pi\) | |||||||
\(860\) | − | 8.86141i | − | 0.302171i | ||||||
\(861\) | −16.6962 | − | 34.5432i | −0.569004 | − | 1.17723i | ||||
\(862\) | −28.2337 | −0.961643 | ||||||||
\(863\) | 11.4891 | 0.391094 | 0.195547 | − | 0.980694i | \(-0.437352\pi\) | ||||
0.195547 | + | 0.980694i | \(0.437352\pi\) | |||||||
\(864\) | −3.31662 | − | 4.00000i | −0.112834 | − | 0.136083i | ||||
\(865\) | 36.0404i | 1.22541i | ||||||||
\(866\) | 30.4674i | 1.03532i | ||||||||
\(867\) | −20.6646 | + | 19.4198i | −0.701806 | + | 0.659532i | ||||
\(868\) | −10.3723 | − | 3.25544i | −0.352058 | − | 0.110497i | ||||
\(869\) | 20.8397 | 0.706937 | ||||||||
\(870\) | 10.1168 | − | 9.50744i | 0.342993 | − | 0.322333i | ||||
\(871\) | −5.98844 | + | 20.7446i | −0.202911 | + | 0.702903i | ||||
\(872\) | 19.6974i | 0.667037i | ||||||||
\(873\) | −1.70460 | + | 27.4198i | −0.0576919 | + | 0.928021i | ||||
\(874\) | − | 0.350532i | − | 0.0118569i | ||||||
\(875\) | 3.66648 | − | 11.6819i | 0.123950 | − | 0.394921i | ||||
\(876\) | −12.9307 | + | 12.1518i | −0.436888 | + | 0.410572i | ||||
\(877\) | 13.5065i | 0.456084i | 0.973651 | + | 0.228042i | \(0.0732323\pi\) | ||||
−0.973651 | + | 0.228042i | \(0.926768\pi\) | |||||||
\(878\) | 5.60597i | 0.189192i | ||||||||
\(879\) | −13.6277 | − | 14.5012i | −0.459652 | − | 0.489114i | ||||
\(880\) | − | 19.3723i | − | 0.653039i | ||||||
\(881\) | −15.9383 | −0.536975 | −0.268488 | − | 0.963283i | \(-0.586524\pi\) | ||||
−0.268488 | + | 0.963283i | \(0.586524\pi\) | |||||||
\(882\) | 13.0462 | − | 16.4559i | 0.439288 | − | 0.554100i | ||||
\(883\) | −9.09509 | −0.306074 | −0.153037 | − | 0.988220i | \(-0.548905\pi\) | ||||
−0.153037 | + | 0.988220i | \(0.548905\pi\) | |||||||
\(884\) | −2.74456 | − | 0.792287i | −0.0923096 | − | 0.0266475i | ||||
\(885\) | −11.6819 | + | 10.9783i | −0.392684 | + | 0.369030i | ||||
\(886\) | − | 16.7306i | − | 0.562076i | ||||||
\(887\) | 48.6072 | 1.63207 | 0.816035 | − | 0.578002i | \(-0.196167\pi\) | ||||
0.816035 | + | 0.578002i | \(0.196167\pi\) | |||||||
\(888\) | −9.92242 | − | 10.5584i | −0.332975 | − | 0.354317i | ||||
\(889\) | −26.1831 | − | 8.21782i | −0.878154 | − | 0.275617i | ||||
\(890\) | 33.7228 | 1.13039 | ||||||||
\(891\) | 51.3030 | + | 6.40342i | 1.71871 | + | 0.214523i | ||||
\(892\) | −0.644810 | −0.0215898 | ||||||||
\(893\) | 24.6535i | 0.824997i | ||||||||
\(894\) | −9.62747 | + | 9.04755i | −0.321991 | + | 0.302595i | ||||
\(895\) | 68.1022 | 2.27641 | ||||||||
\(896\) | 2.52434 | + | 0.792287i | 0.0843322 | + | 0.0264685i | ||||
\(897\) | −0.419829 | − | 0.819738i | −0.0140177 | − | 0.0273703i | ||||
\(898\) | 14.1168 | 0.471085 | ||||||||
\(899\) | 9.76631i | 0.325725i | ||||||||
\(900\) | −1.18614 | + | 19.0800i | −0.0395380 | + | 0.636000i | ||||
\(901\) | 8.00000i | 0.266519i | ||||||||
\(902\) | 48.0951i | 1.60139i | ||||||||
\(903\) | −10.8417 | + | 5.24025i | −0.360790 | + | 0.174385i | ||||
\(904\) | − | 5.69349i | − | 0.189363i | ||||||
\(905\) | −68.7011 | −2.28370 | ||||||||
\(906\) | −21.1345 | − | 22.4891i | −0.702146 | − | 0.747151i | ||||
\(907\) | 20.0000 | 0.664089 | 0.332045 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332045 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(908\) | 11.4891i | 0.381280i | ||||||||
\(909\) | 3.28917 | − | 52.9090i | 0.109095 | − | 1.75488i | ||||
\(910\) | −17.7682 | + | 26.8173i | −0.589011 | + | 0.888985i | ||||
\(911\) | 24.1561i | 0.800329i | 0.916443 | + | 0.400164i | \(0.131047\pi\) | ||||
−0.916443 | + | 0.400164i | \(0.868953\pi\) | |||||||
\(912\) | 3.00000 | − | 2.81929i | 0.0993399 | − | 0.0933561i | ||||
\(913\) | − | 38.7446i | − | 1.28226i | ||||||
\(914\) | 23.6588i | 0.782564i | ||||||||
\(915\) | 32.9639 | − | 30.9783i | 1.08975 | − | 1.02411i | ||||
\(916\) | 5.04868 | 0.166813 | ||||||||
\(917\) | 10.0000 | + | 3.13859i | 0.330229 | + | 0.103645i | ||||
\(918\) | 2.62772 | + | 3.16915i | 0.0867276 | + | 0.104597i | ||||
\(919\) | −45.5842 | −1.50368 | −0.751842 | − | 0.659343i | \(-0.770835\pi\) | ||||
−0.751842 | + | 0.659343i | \(0.770835\pi\) | |||||||
\(920\) | 0.497333 | 0.0163966 | ||||||||
\(921\) | 40.2337 | − | 37.8102i | 1.32575 | − | 1.24589i | ||||
\(922\) | 21.6060i | 0.711555i | ||||||||
\(923\) | −6.92820 | − | 2.00000i | −0.228045 | − | 0.0658308i | ||||
\(924\) | −23.7015 | + | 11.4559i | −0.779723 | + | 0.376872i | ||||
\(925\) | 53.3060i | 1.75269i | ||||||||
\(926\) | 31.6742i | 1.04088i | ||||||||
\(927\) | 22.0742 | + | 1.37228i | 0.725013 | + | 0.0450716i | ||||
\(928\) | − | 2.37686i | − | 0.0780243i | ||||||
\(929\) | − | 24.6060i | − | 0.807296i | −0.914914 | − | 0.403648i | \(-0.867742\pi\) | ||
0.914914 | − | 0.403648i | \(-0.132258\pi\) | |||||||
\(930\) | −16.4356 | − | 17.4891i | −0.538946 | − | 0.573491i | ||||
\(931\) | 13.6540 | + | 9.50744i | 0.447493 | + | 0.311594i | ||||
\(932\) | 10.7422i | 0.351871i | ||||||||
\(933\) | −13.1168 | + | 12.3267i | −0.429426 | + | 0.403559i | ||||
\(934\) | 21.5769 | 0.706018 | ||||||||
\(935\) | 15.3484i | 0.501947i | ||||||||
\(936\) | 3.63903 | − | 10.1861i | 0.118945 | − | 0.332944i | ||||
\(937\) | 43.4891i | 1.42073i | 0.703835 | + | 0.710364i | \(0.251470\pi\) | ||||
−0.703835 | + | 0.710364i | \(0.748530\pi\) | |||||||
\(938\) | −4.74456 | + | 15.1168i | −0.154915 | + | 0.493582i | ||||
\(939\) | −3.25544 | − | 3.46410i | −0.106237 | − | 0.113047i | ||||
\(940\) | −34.9783 | −1.14086 | ||||||||
\(941\) | − | 51.4891i | − | 1.67850i | −0.543748 | − | 0.839249i | \(-0.682995\pi\) | ||
0.543748 | − | 0.839249i | \(-0.317005\pi\) | |||||||
\(942\) | 9.79211 | + | 10.4198i | 0.319044 | + | 0.339494i | ||||
\(943\) | −1.23472 | −0.0402079 | ||||||||
\(944\) | 2.74456i | 0.0893279i | ||||||||
\(945\) | 42.9125 | − | 17.5464i | 1.39594 | − | 0.570785i | ||||
\(946\) | 15.0951 | 0.490784 | ||||||||
\(947\) | −22.1168 | −0.718701 | −0.359350 | − | 0.933203i | \(-0.617002\pi\) | ||||
−0.359350 | + | 0.933203i | \(0.617002\pi\) | |||||||
\(948\) | −4.57879 | + | 4.30298i | −0.148712 | + | 0.139754i | ||||
\(949\) | −35.4891 | − | 10.2448i | −1.15203 | − | 0.332561i | ||||
\(950\) | −15.1460 | −0.491402 | ||||||||
\(951\) | −4.87375 | + | 4.58017i | −0.158042 | + | 0.148522i | ||||
\(952\) | −2.00000 | − | 0.627719i | −0.0648204 | − | 0.0203445i | ||||
\(953\) | − | 19.7899i | − | 0.641059i | −0.947239 | − | 0.320530i | \(-0.896139\pi\) | ||
0.947239 | − | 0.320530i | \(-0.103861\pi\) | |||||||
\(954\) | −30.2337 | − | 1.87953i | −0.978852 | − | 0.0608520i | ||||
\(955\) | 10.0048 | 0.323747 | ||||||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | 16.1956 | + | 17.2337i | 0.523529 | + | 0.557086i | ||||
\(958\) | − | 28.6277i | − | 0.924920i | ||||||
\(959\) | −45.7330 | − | 14.3537i | −1.47680 | − | 0.463506i | ||||
\(960\) | 4.00000 | + | 4.25639i | 0.129099 | + | 0.137374i | ||||
\(961\) | −14.1168 | −0.455382 | ||||||||
\(962\) | 8.36530 | − | 28.9783i | 0.269708 | − | 0.934296i | ||||
\(963\) | 50.9783 | + | 3.16915i | 1.64275 | + | 0.102124i | ||||
\(964\) | 16.4356 | 0.529357 | ||||||||
\(965\) | 70.0916 | 2.25633 | ||||||||
\(966\) | −0.294101 | − | 0.608475i | −0.00946255 | − | 0.0195774i | ||||
\(967\) | − | 29.2048i | − | 0.939163i | −0.882889 | − | 0.469582i | \(-0.844405\pi\) | ||
0.882889 | − | 0.469582i | \(-0.155595\pi\) | |||||||
\(968\) | 22.0000 | 0.707107 | ||||||||
\(969\) | −2.37686 | + | 2.23369i | −0.0763558 | + | 0.0717564i | ||||
\(970\) | − | 30.8820i | − | 0.991560i | ||||||
\(971\) | −3.22405 | −0.103465 | −0.0517324 | − | 0.998661i | \(-0.516474\pi\) | ||||
−0.0517324 | + | 0.998661i | \(0.516474\pi\) | |||||||
\(972\) | −12.5942 | + | 9.18614i | −0.403960 | + | 0.294646i | ||||
\(973\) | −4.16381 | + | 13.2665i | −0.133486 | + | 0.425304i | ||||
\(974\) | − | 37.5152i | − | 1.20206i | ||||||
\(975\) | −35.4198 | + | 18.1402i | −1.13434 | + | 0.580953i | ||||
\(976\) | − | 7.74456i | − | 0.247897i | ||||||
\(977\) | 40.3505 | 1.29093 | 0.645464 | − | 0.763791i | \(-0.276664\pi\) | ||||
0.645464 | + | 0.763791i | \(0.276664\pi\) | |||||||
\(978\) | −9.74749 | − | 10.3723i | −0.311691 | − | 0.331669i | ||||
\(979\) | 57.4456i | 1.83597i | ||||||||
\(980\) | −13.4891 | + | 19.3723i | −0.430894 | + | 0.618825i | ||||
\(981\) | 58.9783 | + | 3.66648i | 1.88303 | + | 0.117062i | ||||
\(982\) | − | 11.6819i | − | 0.372785i | ||||||
\(983\) | − | 54.1168i | − | 1.72606i | −0.505153 | − | 0.863030i | \(-0.668564\pi\) | ||
0.505153 | − | 0.863030i | \(-0.331436\pi\) | |||||||
\(984\) | −9.93070 | − | 10.5672i | −0.316579 | − | 0.336871i | ||||
\(985\) | 71.2119i | 2.26900i | ||||||||
\(986\) | 1.88316i | 0.0599719i | ||||||||
\(987\) | 20.6846 | + | 42.7950i | 0.658398 | + | 1.36218i | ||||
\(988\) | 8.23369 | + | 2.37686i | 0.261949 | + | 0.0756180i | ||||
\(989\) | 0.387528i | 0.0123227i | ||||||||
\(990\) | −58.0049 | − | 3.60597i | −1.84352 | − | 0.114605i | ||||
\(991\) | −15.1168 | −0.480202 | −0.240101 | − | 0.970748i | \(-0.577181\pi\) | ||||
−0.240101 | + | 0.970748i | \(0.577181\pi\) | |||||||
\(992\) | −4.10891 | −0.130458 | ||||||||
\(993\) | 20.2598 | + | 21.5584i | 0.642926 | + | 0.684136i | ||||
\(994\) | −5.04868 | − | 1.58457i | −0.160134 | − | 0.0502596i | ||||
\(995\) | 40.8614 | 1.29539 | ||||||||
\(996\) | 8.00000 | + | 8.51278i | 0.253490 | + | 0.269738i | ||||
\(997\) | 8.37228i | 0.265153i | 0.991173 | + | 0.132576i | \(0.0423250\pi\) | ||||
−0.991173 | + | 0.132576i | \(0.957675\pi\) | |||||||
\(998\) | 10.4472i | 0.330701i | ||||||||
\(999\) | −33.4612 | + | 27.7446i | −1.05867 | + | 0.877799i |
(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 | 546.2.e.g.545.7 | yes | 8 | |
3.2 | odd | 2 | 546.2.e.e.545.1 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 546.2.e.g.545.2 | yes | 8 | |
13.12 | even | 2 | 546.2.e.e.545.7 | yes | 8 | ||
21.20 | even | 2 | 546.2.e.e.545.8 | yes | 8 | ||
39.38 | odd | 2 | inner | 546.2.e.g.545.1 | yes | 8 | |
91.90 | odd | 2 | 546.2.e.e.545.2 | yes | 8 | ||
273.272 | even | 2 | inner | 546.2.e.g.545.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.e.e.545.1 | ✓ | 8 | 3.2 | odd | 2 | ||
546.2.e.e.545.2 | yes | 8 | 91.90 | odd | 2 | ||
546.2.e.e.545.7 | yes | 8 | 13.12 | even | 2 | ||
546.2.e.e.545.8 | yes | 8 | 21.20 | even | 2 | ||
546.2.e.g.545.1 | yes | 8 | 39.38 | odd | 2 | inner | |
546.2.e.g.545.2 | yes | 8 | 7.6 | odd | 2 | inner | |
546.2.e.g.545.7 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.e.g.545.8 | yes | 8 | 273.272 | even | 2 | inner |