Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [456,2,Mod(49,456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("456.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 456 = 2^{3} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 456.q (of order \(3\), degree \(2\), 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: | \(3.64117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.3 | ||
Root | \(0.939693 + 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 456.121 |
Dual form | 456.2.q.f.49.3 |
$q$-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 \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.87939 | + | 3.25519i | 0.840487 | + | 1.45577i | 0.889484 | + | 0.456967i | \(0.151064\pi\) |
−0.0489972 | + | 0.998799i | \(0.515603\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.75877 | 1.79865 | 0.899323 | − | 0.437285i | \(-0.144060\pi\) | ||||
0.899323 | + | 0.437285i | \(0.144060\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.36959 | −1.31748 | −0.658740 | − | 0.752371i | \(-0.728910\pi\) | ||||
−0.658740 | + | 0.752371i | \(0.728910\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | −0.926995 | − | 0.375073i | \(-0.877618\pi\) |
0.788320 | + | 0.615265i | \(0.210951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.87939 | + | 3.25519i | −0.485255 | + | 0.840487i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.06418 | − | 5.30731i | −0.743172 | − | 1.28721i | −0.951044 | − | 0.309056i | \(-0.899987\pi\) |
0.207872 | − | 0.978156i | \(-0.433346\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.694593 | − | 4.30320i | 0.159350 | − | 0.987222i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.37939 | + | 4.12122i | 0.519224 | + | 0.899323i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.87939 | − | 3.25519i | 0.391879 | − | 0.678754i | −0.600818 | − | 0.799385i | \(-0.705159\pi\) |
0.992697 | + | 0.120631i | \(0.0384919\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.56418 | + | 7.90539i | −0.912836 | + | 1.58108i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.69459 | + | 4.66717i | −0.500373 | + | 0.866672i | 0.499627 | + | 0.866241i | \(0.333471\pi\) |
−1.00000 | 0.000431109i | \(0.999863\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.36959 | 1.32362 | 0.661808 | − | 0.749673i | \(-0.269789\pi\) | ||||
0.661808 | + | 0.749673i | \(0.269789\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.18479 | − | 3.78417i | −0.380324 | − | 0.658740i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.94356 | + | 15.4907i | 1.51174 | + | 2.61841i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.12836 | −1.17189 | −0.585947 | − | 0.810349i | \(-0.699277\pi\) | ||||
−0.585947 | + | 0.810349i | \(0.699277\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.75877 | + | 3.04628i | 0.274674 | + | 0.475749i | 0.970053 | − | 0.242894i | \(-0.0780968\pi\) |
−0.695379 | + | 0.718643i | \(0.744763\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.379385 | + | 0.657115i | 0.0578557 | + | 0.100209i | 0.893503 | − | 0.449058i | \(-0.148240\pi\) |
−0.835647 | + | 0.549267i | \(0.814907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.75877 | −0.560324 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.6459 | 2.23513 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.06418 | − | 5.30731i | 0.429071 | − | 0.743172i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.57398 | + | 4.45826i | −0.353563 | + | 0.612389i | −0.986871 | − | 0.161511i | \(-0.948363\pi\) |
0.633308 | + | 0.773900i | \(0.281697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.21213 | − | 14.2238i | −1.10732 | − | 1.91794i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.07398 | − | 1.55007i | 0.539612 | − | 0.205311i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.63816 | − | 8.03352i | −0.603836 | − | 1.04588i | −0.992234 | − | 0.124384i | \(-0.960305\pi\) |
0.388398 | − | 0.921492i | \(-0.373029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.25877 | − | 7.37641i | 0.545280 | − | 0.944452i | −0.453310 | − | 0.891353i | \(-0.649757\pi\) |
0.998589 | − | 0.0530990i | \(-0.0169099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.37939 | + | 4.12122i | −0.299774 | + | 0.519224i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.75877 | −0.466218 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.684793 | + | 1.18610i | −0.0836607 | + | 0.144905i | −0.904820 | − | 0.425795i | \(-0.859995\pi\) |
0.821159 | + | 0.570699i | \(0.193328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.75877 | 0.452503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.82295 | + | 10.0856i | 0.691057 | + | 1.19695i | 0.971492 | + | 0.237073i | \(0.0761879\pi\) |
−0.280435 | + | 0.959873i | \(0.590479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.25877 | − | 3.91231i | −0.264369 | − | 0.457901i | 0.703029 | − | 0.711161i | \(-0.251830\pi\) |
−0.967398 | + | 0.253260i | \(0.918497\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.12836 | −1.05405 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −20.7939 | −2.36968 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.07398 | − | 12.2525i | −0.795885 | − | 1.37851i | −0.922276 | − | 0.386532i | \(-0.873673\pi\) |
0.126391 | − | 0.991980i | \(-0.459661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.90673 | 0.538583 | 0.269292 | − | 0.963059i | \(-0.413210\pi\) | ||||
0.269292 | + | 0.963059i | \(0.413210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5175 | − | 19.9490i | 1.24925 | − | 2.16377i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.38919 | −0.577781 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.18479 | + | 7.24827i | −0.443587 | + | 0.768315i | −0.997953 | − | 0.0639579i | \(-0.979628\pi\) |
0.554365 | + | 0.832273i | \(0.312961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.37939 | + | 4.12122i | −0.249427 | + | 0.432021i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.68479 | + | 6.38225i | 0.382095 | + | 0.661808i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.3131 | − | 5.82634i | 1.57110 | − | 0.597770i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.82295 | + | 10.0856i | 0.591231 | + | 1.02404i | 0.994067 | + | 0.108770i | \(0.0346911\pi\) |
−0.402836 | + | 0.915272i | \(0.631976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.18479 | − | 3.78417i | 0.219580 | − | 0.380324i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.06418 | − | 3.57526i | 0.205393 | − | 0.355752i | −0.744865 | − | 0.667216i | \(-0.767486\pi\) |
0.950258 | + | 0.311464i | \(0.100819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.75877 | −0.665961 | −0.332981 | − | 0.942934i | \(-0.608054\pi\) | ||||
−0.332981 | + | 0.942934i | \(0.608054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.94356 | + | 15.4907i | −0.872802 | + | 1.51174i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.12836 | −0.399103 | −0.199552 | − | 0.979887i | \(-0.563949\pi\) | ||||
−0.199552 | + | 0.979887i | \(0.563949\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0641778 | + | 0.111159i | 0.00614712 | + | 0.0106471i | 0.869083 | − | 0.494667i | \(-0.164710\pi\) |
−0.862935 | + | 0.505314i | \(0.831377\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.56418 | − | 6.17334i | −0.338297 | − | 0.585947i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.40879 | −0.226600 | −0.113300 | − | 0.993561i | \(-0.536142\pi\) | ||||
−0.113300 | + | 0.993561i | \(0.536142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1284 | 1.31748 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.5817 | − | 25.2563i | −1.33670 | − | 2.31524i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.09327 | 0.735752 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.75877 | + | 3.04628i | −0.158583 | + | 0.274674i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.5175 | −1.38793 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.241230 | + | 0.417822i | −0.0214057 | + | 0.0370757i | −0.876530 | − | 0.481348i | \(-0.840147\pi\) |
0.855124 | + | 0.518423i | \(0.173481\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.379385 | + | 0.657115i | −0.0334030 | + | 0.0578557i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.69459 | + | 2.93512i | 0.148057 | + | 0.256443i | 0.930509 | − | 0.366268i | \(-0.119365\pi\) |
−0.782452 | + | 0.622711i | \(0.786031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.30541 | − | 20.4779i | 0.286615 | − | 1.77566i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.87939 | − | 3.25519i | −0.161752 | − | 0.280162i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.21213 | − | 15.9559i | 0.787046 | − | 1.36320i | −0.140724 | − | 0.990049i | \(-0.544943\pi\) |
0.927769 | − | 0.373154i | \(-0.121724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.00980018 | + | 0.0169744i | −0.000831240 | + | 0.00143975i | −0.866441 | − | 0.499280i | \(-0.833598\pi\) |
0.865609 | + | 0.500720i | \(0.166931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.18479 | − | 3.78417i | 0.182702 | − | 0.316448i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.2567 | −1.68223 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.82295 | + | 13.5497i | 0.645226 | + | 1.11756i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.12061 | − | 5.40506i | −0.255651 | − | 0.442800i | 0.709421 | − | 0.704785i | \(-0.248956\pi\) |
−0.965072 | + | 0.261985i | \(0.915623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.739170 | 0.0601528 | 0.0300764 | − | 0.999548i | \(-0.490425\pi\) | ||||
0.0300764 | + | 0.999548i | \(0.490425\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.12836 | 0.495448 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8503 | + | 23.9894i | 1.11248 | + | 1.92688i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.32295 | + | 5.75552i | 0.265200 | + | 0.459340i | 0.967616 | − | 0.252427i | \(-0.0812286\pi\) |
−0.702416 | + | 0.711767i | \(0.747895\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.14796 | −0.408259 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.94356 | − | 15.4907i | 0.704852 | − | 1.22084i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3696 | −0.890535 | −0.445267 | − | 0.895398i | \(-0.646891\pi\) | ||||
−0.445267 | + | 0.895398i | \(0.646891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.21213 | − | 14.2238i | 0.639314 | − | 1.10732i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.49020 | + | 2.58110i | −0.115315 | + | 0.199732i | −0.917906 | − | 0.396799i | \(-0.870121\pi\) |
0.802591 | + | 0.596530i | \(0.203454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.37939 | + | 2.75314i | 0.258428 | + | 0.210538i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.69459 | + | 4.66717i | 0.204866 | + | 0.354838i | 0.950090 | − | 0.311976i | \(-0.100991\pi\) |
−0.745224 | + | 0.666814i | \(0.767657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.7199 | + | 37.6199i | −1.64187 | + | 2.84380i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.63816 | − | 8.03352i | 0.348625 | − | 0.603836i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.24123 | 0.317004 | 0.158502 | − | 0.987359i | \(-0.449334\pi\) | ||||
0.158502 | + | 0.987359i | \(0.449334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.30541 | + | 10.9213i | −0.468677 | + | 0.811773i | −0.999359 | − | 0.0357984i | \(-0.988603\pi\) |
0.530682 | + | 0.847571i | \(0.321936\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.51754 | 0.629635 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.3969 | − | 23.2042i | −0.984962 | − | 1.70600i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.3892 | + | 23.1907i | 0.979114 | + | 1.69588i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.75877 | −0.346150 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.6263 | −1.63718 | −0.818591 | − | 0.574377i | \(-0.805244\pi\) | ||||
−0.818591 | + | 0.574377i | \(0.805244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3229 | − | 21.3440i | −0.887025 | − | 1.53637i | −0.843375 | − | 0.537326i | \(-0.819435\pi\) |
−0.0436505 | − | 0.999047i | \(-0.513899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.87939 | − | 3.25519i | −0.134586 | − | 0.233109i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.6655 | 1.61485 | 0.807425 | − | 0.589970i | \(-0.200861\pi\) | ||||
0.807425 | + | 0.589970i | \(0.200861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.96110 | + | 12.0570i | −0.493460 | + | 0.854697i | −0.999972 | − | 0.00753584i | \(-0.997601\pi\) |
0.506512 | + | 0.862233i | \(0.330935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.36959 | −0.0966031 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.8229 | + | 22.2100i | −0.899995 | + | 1.55884i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.61081 | + | 11.4503i | −0.461719 | + | 0.799721i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.87939 | + | 3.25519i | 0.130626 | + | 0.226251i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.03508 | + | 18.8032i | −0.209941 | + | 1.30064i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00980 | + | 1.74903i | 0.0695175 | + | 0.120408i | 0.898689 | − | 0.438586i | \(-0.144521\pi\) |
−0.829172 | + | 0.558994i | \(0.811187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.82295 | + | 10.0856i | −0.398982 | + | 0.691057i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.42602 | + | 2.46994i | −0.0972539 | + | 0.168449i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.0702 | 2.38072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.25877 | − | 3.91231i | 0.152634 | − | 0.264369i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.12836 | 0.412238 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1827 | − | 24.5652i | −0.949746 | − | 1.64501i | −0.745958 | − | 0.665993i | \(-0.768008\pi\) |
−0.203789 | − | 0.979015i | \(-0.565325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.56418 | − | 7.90539i | −0.304279 | − | 0.527026i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.1830 | 1.33960 | 0.669798 | − | 0.742544i | \(-0.266381\pi\) | ||||
0.669798 | + | 0.742544i | \(0.266381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.7784 | 0.778337 | 0.389168 | − | 0.921167i | \(-0.372762\pi\) | ||||
0.389168 | + | 0.921167i | \(0.372762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3969 | − | 18.0080i | −0.684068 | − | 1.18484i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.0641778 | + | 0.111159i | 0.00420443 | + | 0.00728228i | 0.868120 | − | 0.496354i | \(-0.165328\pi\) |
−0.863916 | + | 0.503637i | \(0.831995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.5526 | 1.47117 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.07398 | − | 12.2525i | 0.459504 | − | 0.795885i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.10876 | 0.201089 | 0.100544 | − | 0.994933i | \(-0.467942\pi\) | ||||
0.100544 | + | 0.994933i | \(0.467942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.64796 | + | 9.78255i | −0.363817 | + | 0.630149i | −0.988586 | − | 0.150661i | \(-0.951860\pi\) |
0.624769 | + | 0.780810i | \(0.285193\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29.4047 | + | 50.9304i | 1.87860 | + | 3.25382i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.37939 | + | 2.75314i | 0.215025 | + | 0.175178i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.45336 | + | 4.24935i | 0.155476 | + | 0.269292i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.758770 | − | 1.31423i | 0.0478932 | − | 0.0829534i | −0.841085 | − | 0.540903i | \(-0.818083\pi\) |
0.888978 | + | 0.457950i | \(0.151416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.21213 | + | 14.2238i | −0.516292 | + | 0.894245i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.0351 | 1.44251 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.09152 | − | 10.5508i | 0.379979 | − | 0.658142i | −0.611080 | − | 0.791569i | \(-0.709265\pi\) |
0.991059 | + | 0.133427i | \(0.0425980\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −33.9222 | −2.10782 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.69459 | − | 4.66717i | −0.166791 | − | 0.288891i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.69459 | + | 16.7915i | 0.597794 | + | 1.03541i | 0.993146 | + | 0.116880i | \(0.0372893\pi\) |
−0.395352 | + | 0.918530i | \(0.629377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.3500 | −1.18866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.36959 | −0.512210 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.7023 | − | 20.2690i | −0.713504 | − | 1.23582i | −0.963534 | − | 0.267587i | \(-0.913774\pi\) |
0.250030 | − | 0.968238i | \(-0.419560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.482459 | − | 0.835644i | −0.0293073 | − | 0.0507617i | 0.851000 | − | 0.525166i | \(-0.175997\pi\) |
−0.880307 | + | 0.474404i | \(0.842663\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.75877 | −0.288014 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.9436 | − | 34.5433i | 1.20264 | − | 2.08304i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3892 | 0.924647 | 0.462323 | − | 0.886711i | \(-0.347016\pi\) | ||||
0.462323 | + | 0.886711i | \(0.347016\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.68479 | + | 6.38225i | −0.220603 | + | 0.382095i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.24897 | + | 7.35943i | −0.253472 | + | 0.439027i | −0.964479 | − | 0.264158i | \(-0.914906\pi\) |
0.711007 | + | 0.703185i | \(0.248239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.51754 | + | 9.55666i | 0.327984 | + | 0.568085i | 0.982112 | − | 0.188299i | \(-0.0602975\pi\) |
−0.654128 | + | 0.756384i | \(0.726964\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.7023 | + | 10.3484i | 0.752421 | + | 0.612987i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.36959 | + | 14.4965i | 0.494041 | + | 0.855704i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2784 | + | 17.8027i | −0.604610 | + | 1.04722i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.82295 | + | 10.0856i | −0.341347 | + | 0.591231i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.03508 | −0.0604701 | −0.0302351 | − | 0.999543i | \(-0.509626\pi\) | ||||
−0.0302351 | + | 0.999543i | \(0.509626\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4338 | − | 30.1962i | 1.01503 | − | 1.75809i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.36959 | 0.253549 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.87939 | + | 3.25519i | 0.108688 | + | 0.188253i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.80541 | + | 3.12706i | 0.104062 | + | 0.180241i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.12836 | 0.237168 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.0155 | 1.83320 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.43376 | − | 12.8757i | −0.424267 | − | 0.734852i | 0.572084 | − | 0.820195i | \(-0.306135\pi\) |
−0.996352 | + | 0.0853423i | \(0.972802\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.37939 | − | 5.85327i | −0.192247 | − | 0.332981i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0547 | −0.910378 | −0.455189 | − | 0.890395i | \(-0.650428\pi\) | ||||
−0.455189 | + | 0.890395i | \(0.650428\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5817 | + | 30.4524i | −0.993777 | + | 1.72127i | −0.400428 | + | 0.916328i | \(0.631138\pi\) |
−0.593350 | + | 0.804945i | \(0.702195\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.8871 | −1.00783 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.26857 | + | 16.0536i | −0.520575 | + | 0.901662i | 0.479139 | + | 0.877739i | \(0.340949\pi\) |
−0.999714 | + | 0.0239230i | \(0.992384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7743 | − | 20.3936i | 0.659232 | − | 1.14182i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.06418 | − | 3.57526i | −0.115211 | − | 0.199552i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.9668 | + | 9.49935i | −1.38919 | + | 0.528558i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.56418 | − | 7.90539i | −0.253175 | − | 0.438512i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.0641778 | + | 0.111159i | −0.00354904 | + | 0.00614712i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.2763 | − | 24.7273i | 0.787079 | − | 1.36326i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.75877 | −0.481426 | −0.240713 | − | 0.970596i | \(-0.577381\pi\) | ||||
−0.240713 | + | 0.970596i | \(0.577381\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.56418 | − | 6.17334i | 0.195316 | − | 0.338297i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.14796 | −0.281263 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6925 | + | 18.5200i | 0.582459 | + | 1.00885i | 0.995187 | + | 0.0979947i | \(0.0312428\pi\) |
−0.412728 | + | 0.910855i | \(0.635424\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.20439 | − | 2.08607i | −0.0654136 | − | 0.113300i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.2020 | −1.74384 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 41.1438 | 2.22156 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.06418 | + | 12.2355i | 0.380323 | + | 0.658738i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.9632 | − | 20.7208i | −0.642216 | − | 1.11235i | −0.984937 | − | 0.172914i | \(-0.944682\pi\) |
0.342721 | − | 0.939437i | \(-0.388652\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.0702 | −1.23492 | −0.617459 | − | 0.786603i | \(-0.711838\pi\) | ||||
−0.617459 | + | 0.786603i | \(0.711838\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.500000 | − | 0.866025i | 0.0266880 | − | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.4979 | −1.51679 | −0.758396 | − | 0.651794i | \(-0.774017\pi\) | ||||
−0.758396 | + | 0.651794i | \(0.774017\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.8871 | + | 37.9096i | −1.16165 | + | 2.01203i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.5817 | − | 25.2563i | 0.771746 | − | 1.33670i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.48246 | − | 4.29975i | −0.131019 | − | 0.226932i | 0.793051 | − | 0.609156i | \(-0.208492\pi\) |
−0.924070 | + | 0.382224i | \(0.875158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0351 | − | 5.97794i | −0.949215 | − | 0.314629i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.04664 | + | 7.00898i | 0.212393 | + | 0.367876i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.49020 | − | 14.7055i | 0.444397 | − | 0.769719i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.42396 | + | 16.3228i | −0.491927 | + | 0.852042i | −0.999957 | − | 0.00929712i | \(-0.997041\pi\) |
0.508030 | + | 0.861339i | \(0.330374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.51754 | −0.183116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.2490 | + | 21.2158i | −0.635935 | + | 1.10147i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.9026 | 1.85897 | 0.929483 | − | 0.368864i | \(-0.120253\pi\) | ||||
0.929483 | + | 0.368864i | \(0.120253\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.75877 | − | 13.4386i | −0.400661 | − | 0.693966i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.69459 | − | 4.66717i | −0.138779 | − | 0.240372i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.2763 | −0.630592 | −0.315296 | − | 0.948993i | \(-0.602104\pi\) | ||||
−0.315296 | + | 0.948993i | \(0.602104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.482459 | −0.0247171 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.20439 | − | 12.4784i | −0.368127 | − | 0.637615i | 0.621145 | − | 0.783695i | \(-0.286668\pi\) |
−0.989273 | + | 0.146080i | \(0.953334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −39.0797 | − | 67.6880i | −1.99168 | − | 3.44970i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.758770 | −0.0385705 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.18479 | + | 5.51622i | −0.161475 | + | 0.279684i | −0.935398 | − | 0.353597i | \(-0.884959\pi\) |
0.773923 | + | 0.633280i | \(0.218292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.0351 | −1.16493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.69459 | + | 2.93512i | −0.0854809 | + | 0.148057i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.5895 | − | 46.0543i | 1.33786 | − | 2.31724i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.27837 | + | 9.14241i | 0.264914 | + | 0.458844i | 0.967541 | − | 0.252714i | \(-0.0813231\pi\) |
−0.702627 | + | 0.711558i | \(0.747990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.3871 | − | 7.37641i | 0.970570 | − | 0.369282i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.7219 | − | 18.5709i | −0.535428 | − | 0.927388i | −0.999143 | − | 0.0414036i | \(-0.986817\pi\) |
0.463715 | − | 0.885985i | \(-0.346516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.68479 | + | 6.38225i | −0.183553 | + | 0.317922i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.87939 | − | 3.25519i | 0.0933874 | − | 0.161752i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.1480 | 1.54395 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.32501 | + | 5.75908i | −0.164411 | + | 0.284768i | −0.936446 | − | 0.350812i | \(-0.885906\pi\) |
0.772035 | + | 0.635580i | \(0.219239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.4243 | 0.908802 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.0719 | − | 38.2297i | −1.08609 | − | 1.88116i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.22163 | + | 15.9723i | 0.452672 | + | 0.784051i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0196004 | −0.000959834 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.84793 | 0.285690 | 0.142845 | − | 0.989745i | \(-0.454375\pi\) | ||||
0.142845 | + | 0.989745i | \(0.454375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.714193 | − | 1.23702i | −0.0348076 | − | 0.0602886i | 0.848097 | − | 0.529841i | \(-0.177749\pi\) |
−0.882904 | + | 0.469553i | \(0.844415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | + | 5.19615i | 0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 55.9418 | 2.71358 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.2665 | − | 35.1026i | 0.980765 | − | 1.69874i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.36959 | 0.210966 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.389185 | + | 0.674089i | −0.0187464 | + | 0.0324697i | −0.875246 | − | 0.483677i | \(-0.839301\pi\) |
0.856500 | + | 0.516147i | \(0.172634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.3425 | + | 23.1100i | −0.641202 | + | 1.11059i | 0.343963 | + | 0.938983i | \(0.388231\pi\) |
−0.985165 | + | 0.171611i | \(0.945103\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.1284 | − | 17.5428i | −0.485617 | − | 0.841114i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.7023 | − | 10.3484i | −0.607635 | − | 0.495031i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2665 | + | 24.7103i | 0.680903 | + | 1.17936i | 0.974706 | + | 0.223493i | \(0.0717460\pi\) |
−0.293802 | + | 0.955866i | \(0.594921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.82295 | + | 13.5497i | −0.372521 | + | 0.645226i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.82295 | − | 15.2818i | 0.419191 | − | 0.726060i | −0.576667 | − | 0.816979i | \(-0.695647\pi\) |
0.995858 | + | 0.0909191i | \(0.0289805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.4593 | −1.49132 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.12061 | − | 5.40506i | 0.147600 | − | 0.255651i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.38919 | −0.0655597 | −0.0327799 | − | 0.999463i | \(-0.510436\pi\) | ||||
−0.0327799 | + | 0.999463i | \(0.510436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.68510 | − | 13.3110i | −0.361877 | − | 0.626790i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.369585 | + | 0.640140i | 0.0173646 | + | 0.0300764i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.8871 | −0.838561 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6851 | 1.15472 | 0.577360 | − | 0.816490i | \(-0.304083\pi\) | ||||
0.577360 | + | 0.816490i | \(0.304083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.06418 | + | 5.30731i | 0.143024 | + | 0.247724i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.795607 | − | 1.37803i | −0.0370551 | − | 0.0641813i | 0.846903 | − | 0.531747i | \(-0.178464\pi\) |
−0.883958 | + | 0.467566i | \(0.845131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.7547 | −1.01102 | −0.505512 | − | 0.862819i | \(-0.668696\pi\) | ||||
−0.505512 | + | 0.862819i | \(0.668696\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.8503 | + | 23.9894i | −0.642292 | + | 1.11248i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.5175 | 0.718066 | 0.359033 | − | 0.933325i | \(-0.383107\pi\) | ||||
0.359033 | + | 0.933325i | \(0.383107\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.25877 | + | 5.64436i | −0.150476 | + | 0.260632i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.32295 | + | 5.75552i | −0.153113 | + | 0.265200i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.65776 | − | 2.87132i | −0.0762237 | − | 0.132023i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.8482 | + | 25.1316i | 1.41541 | + | 1.15312i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.57398 | − | 4.45826i | −0.117854 | − | 0.204130i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.82295 | − | 10.0856i | 0.266057 | − | 0.460825i | −0.701783 | − | 0.712391i | \(-0.747612\pi\) |
0.967840 | + | 0.251566i | \(0.0809456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.56418 | − | 6.17334i | 0.162513 | − | 0.281480i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.8871 | 0.813892 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.8871 | + | 37.9096i | −0.993843 | + | 1.72139i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.5526 | 1.74699 | 0.873493 | − | 0.486837i | \(-0.161849\pi\) | ||||
0.873493 | + | 0.486837i | \(0.161849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.68479 | − | 9.84635i | −0.257075 | − | 0.445267i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.82295 | − | 6.62154i | −0.172527 | − | 0.298826i | 0.766776 | − | 0.641915i | \(-0.221860\pi\) |
−0.939303 | + | 0.343089i | \(0.888527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.0268 | 1.48745 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.4243 | 0.738216 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.7101 | + | 47.9953i | 1.24297 | + | 2.15288i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3152 | − | 26.5267i | −0.685603 | − | 1.18750i | −0.973247 | − | 0.229762i | \(-0.926205\pi\) |
0.287644 | − | 0.957737i | \(-0.407128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.98040 | −0.133154 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.69459 | − | 4.66717i | 0.120146 | − | 0.208099i | −0.799679 | − | 0.600428i | \(-0.794997\pi\) |
0.919825 | + | 0.392329i | \(0.128330\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5175 | 0.690522 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.12836 | − | 1.95437i | 0.0500135 | − | 0.0866259i | −0.839935 | − | 0.542687i | \(-0.817407\pi\) |
0.889948 | + | 0.456061i | \(0.150740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.7490 | − | 18.6178i | −0.475506 | − | 0.823601i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.694593 | + | 4.30320i | −0.0306670 | + | 0.189991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.7023 | − | 22.0011i | −0.559732 | − | 0.969484i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1088 | + | 22.7050i | −0.576522 | + | 0.998566i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.69459 | + | 4.66717i | −0.118279 | + | 0.204866i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.2763 | 1.63310 | 0.816552 | − | 0.577271i | \(-0.195882\pi\) | ||||
0.816552 | + | 0.577271i | \(0.195882\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.186852 | − | 0.323637i | 0.00817046 | − | 0.0141517i | −0.861911 | − | 0.507059i | \(-0.830733\pi\) |
0.870082 | + | 0.492907i | \(0.164066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −43.4397 | −1.89587 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.5817 | − | 39.1127i | −0.983675 | − | 1.70378i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.43582 | + | 7.68307i | 0.192862 | + | 0.334046i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.27631 | 0.402558 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.51754 | −0.152362 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.75877 | − | 13.4386i | −0.335441 | − | 0.581001i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.12061 | + | 3.67301i | 0.0915113 | + | 0.158502i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −68.3661 | −2.94474 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.54458 | − | 16.5317i | 0.410353 | − | 0.710753i | −0.584575 | − | 0.811340i | \(-0.698739\pi\) |
0.994928 | + | 0.100587i | \(0.0320720\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.6108 | −0.541182 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.241230 | + | 0.417822i | −0.0103331 | + | 0.0178975i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.8773 | + | 37.8926i | −0.935407 | + | 1.62017i | −0.161500 | + | 0.986873i | \(0.551633\pi\) |
−0.773907 | + | 0.633300i | \(0.781700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.25877 | + | 7.37641i | 0.181760 | + | 0.314817i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.2121 | + | 14.8372i | 0.775863 | + | 0.632084i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.6634 | − | 58.3068i | −1.43151 | − | 2.47946i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.3969 | − | 23.2042i | 0.568668 | − | 0.984962i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9513 | + | 27.6285i | −0.675878 | + | 1.17066i | 0.300333 | + | 0.953834i | \(0.402902\pi\) |
−0.976211 | + | 0.216821i | \(0.930431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.758770 | −0.0320926 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.3892 | + | 23.1907i | −0.565292 | + | 0.979114i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.87164 | −0.163170 | −0.0815852 | − | 0.996666i | \(-0.525998\pi\) | ||||
−0.0815852 | + | 0.996666i | \(0.525998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.52704 | − | 7.84106i | −0.190454 | − | 0.329876i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.37939 | − | 4.12122i | −0.0999248 | − | 0.173075i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.9959 | −1.38326 | −0.691630 | − | 0.722252i | \(-0.743107\pi\) | ||||
−0.691630 | + | 0.722252i | \(0.743107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.1789 | −1.01186 | −0.505928 | − | 0.862576i | \(-0.668850\pi\) | ||||
−0.505928 | + | 0.862576i | \(0.668850\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.3131 | − | 19.5949i | −0.472614 | − | 0.818591i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.1557 | + | 29.7145i | 0.715442 | + | 1.23918i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.16344 | −0.131696 | −0.0658478 | − | 0.997830i | \(-0.520975\pi\) | ||||
−0.0658478 | + | 0.997830i | \(0.520975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.3229 | − | 21.3440i | 0.512124 | − | 0.887025i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.3500 | 0.968721 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.2472 | − | 19.4807i | 0.465812 | − | 0.806810i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.87939 | − | 3.25519i | 0.0777030 | − | 0.134586i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.00774 | + | 5.20956i | 0.124143 | + | 0.215022i | 0.921398 | − | 0.388621i | \(-0.127049\pi\) |
−0.797255 | + | 0.603643i | \(0.793715\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.11886 | − | 31.7128i | 0.210919 | − | 1.30670i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.3327 | + | 19.6289i | 0.466167 | + | 0.807425i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4611 | + | 19.8512i | −0.470651 | + | 0.815192i | −0.999437 | − | 0.0335639i | \(-0.989314\pi\) |
0.528785 | + | 0.848756i | \(0.322648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 54.8093 | − | 94.9326i | 2.24696 | − | 3.89186i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.9222 | −0.569798 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.2199 | + | 29.8257i | −0.703585 | + | 1.21864i | 0.263615 | + | 0.964628i | \(0.415085\pi\) |
−0.967200 | + | 0.254017i | \(0.918248\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.1634 | 0.985647 | 0.492824 | − | 0.870129i | \(-0.335965\pi\) | ||||
0.492824 | + | 0.870129i | \(0.335965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.684793 | − | 1.18610i | −0.0278869 | − | 0.0483015i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.2104 | + | 26.3451i | 0.618390 | + | 1.07108i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.84793 | −0.277949 | −0.138974 | − | 0.990296i | \(-0.544381\pi\) | ||||
−0.138974 | + | 0.990296i | \(0.544381\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.6459 | −1.03922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | + | 5.19615i | 0.121367 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.47296 | − | 14.6756i | −0.342220 | − | 0.592742i | 0.642625 | − | 0.766181i | \(-0.277845\pi\) |
−0.984845 | + | 0.173439i | \(0.944512\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.2216 | −0.533148 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.1361 | + | 36.6088i | −0.850907 | + | 1.47381i | 0.0294834 | + | 0.999565i | \(0.490614\pi\) |
−0.880391 | + | 0.474249i | \(0.842720\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.59121 | 0.184536 | 0.0922682 | − | 0.995734i | \(-0.470588\pi\) | ||||
0.0922682 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.87939 | + | 3.25519i | −0.0754171 | + | 0.130626i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.9145 | + | 34.4929i | −0.797856 | + | 1.38193i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.34255 | − | 10.9856i | −0.253702 | − | 0.439425i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.8016 | + | 6.77314i | −0.710927 | + | 0.270493i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.8425 | + | 37.8324i | 0.870919 | + | 1.50848i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.7841 | − | 32.5349i | 0.747781 | − | 1.29520i | −0.201103 | − | 0.979570i | \(-0.564452\pi\) |
0.948884 | − | 0.315625i | \(-0.102214\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.00980 | + | 1.74903i | −0.0401360 | + | 0.0695175i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.81345 | −0.0719647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.82295 | + | 13.5497i | −0.309956 | + | 0.536860i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.6459 | −0.460705 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.75877 | + | 4.77833i | 0.108965 | + | 0.188733i | 0.915351 | − | 0.402656i | \(-0.131913\pi\) |
−0.806386 | + | 0.591389i | \(0.798580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.5915 | + | 30.4694i | 0.693742 | + | 1.20160i | 0.970603 | + | 0.240686i | \(0.0773724\pi\) |
−0.276861 | + | 0.960910i | \(0.589294\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.85204 | −0.112299 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.57573 | −0.140577 | −0.0702883 | − | 0.997527i | \(-0.522392\pi\) | ||||
−0.0702883 | + | 0.997527i | \(0.522392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.2668 | + | 35.1032i | 0.795542 | + | 1.37792i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.5351 | + | 30.3717i | 0.687254 | + | 1.19036i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.6418 | 1.27737 | 0.638686 | − | 0.769468i | \(-0.279478\pi\) | ||||
0.638686 | + | 0.769468i | \(0.279478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.36959 | + | 11.0324i | −0.248880 | + | 0.431073i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.51754 | 0.176246 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.4807 | + | 42.4018i | −0.953633 | + | 1.65174i | −0.216167 | + | 0.976356i | \(0.569355\pi\) |
−0.737466 | + | 0.675384i | \(0.763978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7392 | + | 30.7251i | −0.689974 | + | 1.19507i | 0.281872 | + | 0.959452i | \(0.409045\pi\) |
−0.971846 | + | 0.235618i | \(0.924289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.06418 | + | 5.30731i | 0.119003 | + | 0.206119i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 72.8718 | − | 27.7262i | 2.82585 | − | 1.07518i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.1284 | + | 17.5428i | 0.392171 | + | 0.679261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.1827 | − | 24.5652i | 0.548336 | − | 0.949746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.6091 | + | 32.2318i | −0.718395 | + | 1.24430i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.68510 | 0.103503 | 0.0517514 | − | 0.998660i | \(-0.483520\pi\) | ||||
0.0517514 | + | 0.998660i | \(0.483520\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.56418 | − | 7.90539i | 0.175675 | − | 0.304279i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.3351 | 0.704676 | 0.352338 | − | 0.935873i | \(-0.385387\pi\) | ||||
0.352338 | + | 0.935873i | \(0.385387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7101 | + | 47.9953i | 1.06342 | + | 1.84189i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0915 | + | 17.4790i | 0.386708 | + | 0.669798i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.07367 | 0.155875 | 0.0779374 | − | 0.996958i | \(-0.475167\pi\) | ||||
0.0779374 | + | 0.996958i | \(0.475167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 69.2526 | 2.64601 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.88919 | + | 10.2004i | 0.224686 | + | 0.389168i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.57398 | − | 4.45826i | −0.0980608 | − | 0.169846i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.5485 | 1.65666 | 0.828332 | − | 0.560238i | \(-0.189290\pi\) | ||||
0.828332 | + | 0.560238i | \(0.189290\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.3969 | − | 18.0080i | 0.394947 | − | 0.684068i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0736733 | −0.00279459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.7784 | − | 18.6687i | 0.408260 | − | 0.707127i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0641778 | + | 0.111159i | −0.00242743 | + | 0.00420443i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.6536 | − | 27.1129i | −0.591230 | − | 1.02404i | −0.994067 | − | 0.108768i | \(-0.965309\pi\) |
0.402837 | − | 0.915272i | \(-0.368024\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.95130 | + | 30.6747i | −0.186742 | + | 1.15692i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.2763 | + | 19.5311i | 0.424690 | + | 0.735585i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.82295 | − | 17.0138i | 0.369430 | − | 0.639872i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.9047 | + | 20.6195i | −0.447089 | + | 0.774381i | −0.998195 | − | 0.0600541i | \(-0.980873\pi\) |
0.551106 | + | 0.834435i | \(0.314206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.1480 | 0.530590 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8503 | − | 23.9894i | 0.518697 | − | 0.898410i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.4243 | 0.614233 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.55438 | + | 2.69226i | 0.0580493 | + | 0.100544i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.8949 | − | 27.5307i | −0.592779 | − | 1.02672i | −0.993856 | − | 0.110678i | \(-0.964698\pi\) |
0.401078 | − | 0.916044i | \(-0.368636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.1634 | −1.19783 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.2959 | −0.420099 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.5972 | − | 42.6036i | −0.913517 | − | 1.58226i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.22193 | + | 5.58055i | 0.119495 | + | 0.206971i | 0.919568 | − | 0.392932i | \(-0.128539\pi\) |
−0.800073 | + | 0.599903i | \(0.795206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.32501 | − | 4.02703i | 0.0859935 | − | 0.148945i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.9728 | −1.25481 | −0.627406 | − | 0.778692i | \(-0.715884\pi\) | ||||
−0.627406 | + | 0.778692i | \(0.715884\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −29.4047 | + | 50.9304i | −1.08461 | + | 1.87860i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.99226 | − | 5.18274i | 0.110221 | − | 0.190909i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.4632 | − | 19.8548i | −0.421679 | − | 0.730370i | 0.574425 | − | 0.818557i | \(-0.305226\pi\) |
−0.996104 | + | 0.0881876i | \(0.971893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.694593 | + | 4.30320i | −0.0255165 | + | 0.158082i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.98276 | + | 6.89835i | 0.146113 | + | 0.253076i | 0.929788 | − | 0.368096i | \(-0.119990\pi\) |
−0.783674 | + | 0.621172i | \(0.786657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7297 | − | 20.3164i | 0.429742 | − | 0.744335i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.45336 | + | 4.24935i | −0.0897639 | + | 0.155476i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.6459 | −0.717845 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.3794 | − | 19.7097i | 0.415240 | − | 0.719216i | −0.580214 | − | 0.814464i | \(-0.697031\pi\) |
0.995454 | + | 0.0952479i | \(0.0303644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.51754 | 0.0553023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.38919 | + | 2.40614i | 0.0505576 | + | 0.0875684i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.38713 | − | 4.13462i | −0.0867616 | − | 0.150275i | 0.819379 | − | 0.573252i | \(-0.194318\pi\) |
−0.906140 | + | 0.422977i | \(0.860985\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.4243 | −0.596163 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.2222 | 1.02306 | 0.511528 | − | 0.859267i | \(-0.329080\pi\) | ||||
0.511528 | + | 0.859267i | \(0.329080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.305407 | + | 0.528981i | 0.0110565 | + | 0.0191504i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.5175 | + | 19.9490i | 0.416418 | + | 0.721256i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.27631 | 0.334948 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.1108 | + | 20.9765i | −0.436727 | + | 0.756434i | −0.997435 | − | 0.0715802i | \(-0.977196\pi\) |
0.560708 | + | 0.828014i | \(0.310529\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.1830 | 0.438761 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.9804 | + | 20.7507i | −0.430905 | + | 0.746349i | −0.996951 | − | 0.0780239i | \(-0.975139\pi\) |
0.566046 | + | 0.824373i | \(0.308472\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.6361 | + | 58.2594i | −1.20824 | + | 2.09274i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.9611 | − | 29.3775i | −0.608476 | − | 1.05391i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.3304 | − | 5.45242i | 0.513439 | − | 0.195353i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.4439 | − | 44.0701i | −0.910453 | − | 1.57695i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.69459 | − | 4.66717i | 0.0962969 | − | 0.166791i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.4902 | + | 21.6337i | −0.445794 | + | 0.772138i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.8871 | −1.02971 | −0.514857 | − | 0.857276i | \(-0.672155\pi\) | ||||
−0.514857 | + | 0.857276i | \(0.672155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.69459 | + | 16.7915i | −0.345137 | + | 0.597794i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.4629 | −0.407572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.25877 | + | 7.37641i | 0.151233 | + | 0.261944i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.67499 | − | 16.7576i | −0.343137 | − | 0.594330i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.61493 | −0.269735 | −0.134867 | − | 0.990864i | \(-0.543061\pi\) | ||||
−0.134867 | + | 0.990864i | \(0.543061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.7701 | −1.30083 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.18479 | − | 7.24827i | −0.147862 | − | 0.256105i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.86989 | + | 17.0952i | 0.348301 | + | 0.603275i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 67.2336 | 2.36967 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.7023 | − | 20.2690i | 0.411942 | − | 0.713504i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.5681 | 0.793452 | 0.396726 | − | 0.917937i | \(-0.370146\pi\) | ||||
0.396726 | + | 0.917937i | \(0.370146\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.3696 | − | 21.4247i | 0.434355 | − | 0.752325i | −0.562888 | − | 0.826533i | \(-0.690310\pi\) |
0.997243 | + | 0.0742086i | \(0.0236431\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.482459 | − | 0.835644i | 0.0169206 | − | 0.0293073i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.3678 | − | 37.0102i | −0.748482 | − | 1.29641i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.09121 | − | 1.17614i | 0.108148 | − | 0.0411481i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.37939 | − | 4.12122i | −0.0831424 | − | 0.144007i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.30541 | − | 16.1174i | 0.324761 | − | 0.562502i | −0.656703 | − | 0.754149i | \(-0.728049\pi\) |
0.981464 | + | 0.191647i | \(0.0613828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.9804 | − | 19.0186i | 0.382753 | − | 0.662947i | −0.608702 | − | 0.793399i | \(-0.708309\pi\) |
0.991455 | + | 0.130452i | \(0.0416428\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 39.8871 | 1.38869 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9513 | − | 22.4323i | 0.450361 | − | 0.780048i | −0.548047 | − | 0.836447i | \(-0.684629\pi\) |
0.998408 | + | 0.0563993i | \(0.0179620\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.0310 | −1.49453 | −0.747264 | − | 0.664528i | \(-0.768633\pi\) | ||||
−0.747264 | + | 0.664528i | \(0.768633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.69459 | + | 13.3274i | 0.266922 | + | 0.462323i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −47.9418 | − | 83.0376i | −1.66109 | − | 2.87708i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.2026 | −0.387683 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.36959 | −0.254730 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.16519 | − | 7.21432i | −0.143798 | − | 0.249066i | 0.785126 | − | 0.619337i | \(-0.212598\pi\) |
−0.928924 | + | 0.370270i | \(0.879265\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.0216598 | − | 0.0375158i | −0.000746888 | − | 0.00129365i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.49794 | −0.292685 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.5526 | + | 39.0623i | −0.775834 | + | 1.34378i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.5140 | 1.32336 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.51754 | + | 9.55666i | −0.189362 | + | 0.327984i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.3969 | + | 23.2042i | −0.459241 | + | 0.795428i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6925 | + | 37.5726i | 0.742738 | + | 1.28646i | 0.951244 | + | 0.308439i | \(0.0998066\pi\) |
−0.208506 | + | 0.978021i | \(0.566860\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.61081 | + | 16.1747i | −0.0892880 | + | 0.553165i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.2567 | − | 29.8895i | −0.589478 | − | 1.02101i | −0.994301 | − | 0.106611i | \(-0.966000\pi\) |
0.404823 | − | 0.914395i | \(-0.367333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.08946 | − | 15.7434i | 0.310128 | − | 0.537158i | −0.668262 | − | 0.743926i | \(-0.732961\pi\) |
0.978390 | + | 0.206768i | \(0.0662946\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.36959 | + | 14.4965i | −0.285235 | + | 0.494041i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.3269 | 1.50890 | 0.754452 | − | 0.656355i | \(-0.227903\pi\) | ||||
0.754452 | + | 0.656355i | \(0.227903\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.1284 | + | 17.5428i | −0.344374 | + | 0.596474i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.5567 | −0.698144 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.9103 | + | 53.5383i | 1.04856 | + | 1.81616i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.684793 | − | 1.18610i | −0.0232033 | − | 0.0401893i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.6459 | −0.394154 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −73.8444 | −2.49640 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.95336 | − | 10.3115i | −0.201031 | − | 0.348196i | 0.747830 | − | 0.663890i | \(-0.231096\pi\) |
−0.948861 | + | 0.315695i | \(0.897762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.517541 | − | 0.896407i | −0.0174562 | − | 0.0302351i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.9804 | 0.976374 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.23143 | + | 3.86495i | −0.0750936 | + | 0.130066i | −0.901127 | − | 0.433555i | \(-0.857259\pi\) |
0.826033 | + | 0.563621i | \(0.190592\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34.8675 | 1.17206 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.1557 | − | 24.5184i | 0.475302 | − | 0.823247i | −0.524298 | − | 0.851535i | \(-0.675672\pi\) |
0.999600 | + | 0.0282880i | \(0.00900555\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.14796 | + | 1.98832i | −0.0385012 | + | 0.0666860i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.18479 | + | 3.78417i | 0.0731933 | + | 0.126775i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.2763 | − | 16.5188i | −0.678521 | − | 0.552781i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.97090 | + | 13.8060i | 0.266438 | + | 0.461484i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.87939 | + | 3.25519i | −0.0627508 | + | 0.108688i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.8580 | + | 34.3951i | −0.662302 | + | 1.14714i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.5485 | 1.05103 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.80541 | + | 3.12706i | −0.0600802 | + | 0.104062i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47.4012 | −1.57567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2567 | − | 17.7651i | −0.340569 | − | 0.589882i | 0.643970 | − | 0.765051i | \(-0.277286\pi\) |
−0.984538 | + | 0.175169i | \(0.943953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.06418 | + | 3.57526i | 0.0684645 | + | 0.118584i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.9608 | 0.727594 | 0.363797 | − | 0.931478i | \(-0.381480\pi\) | ||||
0.363797 | + | 0.931478i | \(0.381480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.4404 | −0.709572 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.0077 | + | 27.7262i | 0.529200 | + | 0.916601i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.06418 | + | 13.9676i | 0.266303 | + | 0.461250i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0898 | −0.728674 | −0.364337 | − | 0.931267i | \(-0.618704\pi\) | ||||
−0.364337 | + | 0.931267i | \(0.618704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.43376 | − | 12.8757i | 0.244951 | − | 0.424267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.6459 | −0.383329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.5351 | − | 56.3524i | 1.06975 | − | 1.85286i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.37939 | − | 5.85327i | 0.110994 | − | 0.192247i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.2645 | − | 45.4914i | −0.861709 | − | 1.49252i | −0.870278 | − | 0.492560i | \(-0.836061\pi\) |
0.00856978 | − | 0.999963i | \(-0.497272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.8675 | − | 67.3274i | 0.356169 | − | 2.20657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.02734 | − | 13.9038i | −0.262803 | − | 0.455189i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −50.3269 | + | 87.1687i | −1.64586 | + | 2.85072i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.9688 | − | 22.4627i | 0.423674 | − | 0.733824i | −0.572622 | − | 0.819820i | \(-0.694074\pi\) |
0.996296 | + | 0.0859953i | \(0.0274070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.1634 | −1.14752 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.90673 | + | 15.4269i | −0.290351 | + | 0.502903i | −0.973893 | − | 0.227009i | \(-0.927105\pi\) |
0.683542 | + | 0.729911i | \(0.260439\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.2216 | 0.430555 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.94356 | − | 15.4907i | −0.290934 | − | 0.503913i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0446 | + | 29.5221i | 0.553874 | + | 0.959339i | 0.997990 | + | 0.0633691i | \(0.0201845\pi\) |
−0.444116 | + | 0.895969i | \(0.646482\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.51754 | 0.146646 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.5371 | −0.601108 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.34224 | + | 10.9851i | 0.205445 | + | 0.355842i | 0.950275 | − | 0.311413i | \(-0.100802\pi\) |
−0.744829 | + | 0.667255i | \(0.767469\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.5235 | − | 73.6529i | −1.37603 | − | 2.38335i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.5485 | 0.761215 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.8384 | − | 75.9304i | 1.41562 | − | 2.45192i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3108 | 0.751961 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.06418 | − | 3.57526i | 0.0665172 | − | 0.115211i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.3191 | − | 80.2271i | 1.49107 | − | 2.58260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.6266 | + | 40.9225i | 0.759780 | + | 1.31598i | 0.942962 | + | 0.332899i | \(0.108027\pi\) |
−0.183182 | + | 0.983079i | \(0.558640\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.7101 | − | 16.8722i | −0.665303 | − | 0.542013i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.6810 | + | 30.6244i | 0.567410 | + | 0.982782i | 0.996821 | + | 0.0796733i | \(0.0253877\pi\) |
−0.429411 | + | 0.903109i | \(0.641279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0466368 | + | 0.0807773i | −0.00149511 | + | 0.00258960i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.56418 | − | 7.90539i | 0.146171 | − | 0.253175i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.0660 | 1.44179 | 0.720895 | − | 0.693044i | \(-0.243731\pi\) | ||||
0.720895 | + | 0.693044i | \(0.243731\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.2858 | − | 31.6719i | 0.584417 | − | 1.01224i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.128356 | −0.00409808 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.0915 | + | 22.6752i | 0.417555 | + | 0.723226i | 0.995693 | − | 0.0927130i | \(-0.0295539\pi\) |
−0.578138 | + | 0.815939i | \(0.696221\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.5972 | + | 73.7805i | 1.35726 | + | 2.35084i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.5526 | 0.908840 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.85204 | 0.0906897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.6070 | + | 18.3719i | 0.336942 | + | 0.583601i | 0.983856 | − | 0.178962i | \(-0.0572739\pi\) |
−0.646914 | + | 0.762563i | \(0.723941\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.37939 | − | 7.58532i | −0.138976 | − | 0.240713i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52.3304 | −1.65898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.1364 | − | 47.0016i | 0.859418 | − | 1.48856i | −0.0130661 | − | 0.999915i | \(-0.504159\pi\) |
0.872485 | − | 0.488642i | \(-0.162507\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.12836 | 0.225531 |
(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 | 456.2.q.f.121.3 | yes | 6 | |
3.2 | odd | 2 | 1368.2.s.j.577.1 | 6 | |||
4.3 | odd | 2 | 912.2.q.k.577.3 | 6 | |||
12.11 | even | 2 | 2736.2.s.x.577.1 | 6 | |||
19.7 | even | 3 | 8664.2.a.x.1.1 | 3 | |||
19.11 | even | 3 | inner | 456.2.q.f.49.3 | ✓ | 6 | |
19.12 | odd | 6 | 8664.2.a.z.1.1 | 3 | |||
57.11 | odd | 6 | 1368.2.s.j.505.1 | 6 | |||
76.11 | odd | 6 | 912.2.q.k.49.3 | 6 | |||
228.11 | even | 6 | 2736.2.s.x.1873.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.q.f.49.3 | ✓ | 6 | 19.11 | even | 3 | inner | |
456.2.q.f.121.3 | yes | 6 | 1.1 | even | 1 | trivial | |
912.2.q.k.49.3 | 6 | 76.11 | odd | 6 | |||
912.2.q.k.577.3 | 6 | 4.3 | odd | 2 | |||
1368.2.s.j.505.1 | 6 | 57.11 | odd | 6 | |||
1368.2.s.j.577.1 | 6 | 3.2 | odd | 2 | |||
2736.2.s.x.577.1 | 6 | 12.11 | even | 2 | |||
2736.2.s.x.1873.1 | 6 | 228.11 | even | 6 | |||
8664.2.a.x.1.1 | 3 | 19.7 | even | 3 | |||
8664.2.a.z.1.1 | 3 | 19.12 | odd | 6 |