Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,3,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (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: | \(14.4687020375\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.12 | ||
Root | \(1.08628i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.3.c.c.235.9 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.08628i | 0.543139i | 0.962419 | + | 0.271570i | \(0.0875427\pi\) | ||||
−0.962419 | + | 0.271570i | \(0.912457\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.82000 | 0.705000 | ||||||||
\(5\) | −3.33671 | −0.667343 | −0.333671 | − | 0.942689i | \(-0.608288\pi\) | ||||
−0.333671 | + | 0.942689i | \(0.608288\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.22637 | −0.175196 | −0.0875981 | − | 0.996156i | \(-0.527919\pi\) | ||||
−0.0875981 | + | 0.996156i | \(0.527919\pi\) | |||||||
\(8\) | 7.40842i | 0.926052i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 3.62460i | − | 0.362460i | ||||||
\(11\) | − | 1.21764i | − | 0.110695i | −0.998467 | − | 0.0553473i | \(-0.982373\pi\) | ||
0.998467 | − | 0.0553473i | \(-0.0176266\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.6555i | 0.973497i | 0.873542 | + | 0.486749i | \(0.161817\pi\) | ||||
−0.873542 | + | 0.486749i | \(0.838183\pi\) | |||||||
\(14\) | − | 1.33218i | − | 0.0951559i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.23240 | 0.202025 | ||||||||
\(17\) | 0.815320 | 0.0479600 | 0.0239800 | − | 0.999712i | \(-0.492366\pi\) | ||||
0.0239800 | + | 0.999712i | \(0.492366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.74812 | −0.407796 | −0.203898 | − | 0.978992i | \(-0.565361\pi\) | ||||
−0.203898 | + | 0.978992i | \(0.565361\pi\) | |||||||
\(20\) | −9.40954 | −0.470477 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.32270 | 0.0601226 | ||||||||
\(23\) | 33.8014i | 1.46963i | 0.678270 | + | 0.734813i | \(0.262730\pi\) | ||||
−0.678270 | + | 0.734813i | \(0.737270\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.8663 | −0.554653 | ||||||||
\(26\) | −13.7474 | −0.528744 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.45837 | −0.123513 | ||||||||
\(29\) | −7.53415 | −0.259798 | −0.129899 | − | 0.991527i | \(-0.541465\pi\) | ||||
−0.129899 | + | 0.991527i | \(0.541465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.71953i | 0.249017i | 0.992219 | + | 0.124509i | \(0.0397354\pi\) | ||||
−0.992219 | + | 0.124509i | \(0.960265\pi\) | |||||||
\(32\) | 33.1450i | 1.03578i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.885664i | 0.0260489i | ||||||||
\(35\) | 4.09206 | 0.116916 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.7957i | 0.453937i | 0.973902 | + | 0.226969i | \(0.0728815\pi\) | ||||
−0.973902 | + | 0.226969i | \(0.927119\pi\) | |||||||
\(38\) | − | 8.41661i | − | 0.221490i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 24.7198i | − | 0.617994i | ||||||
\(41\) | 19.0497 | 0.464627 | 0.232314 | − | 0.972641i | \(-0.425370\pi\) | ||||
0.232314 | + | 0.972641i | \(0.425370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.9576i | 1.13855i | 0.822148 | + | 0.569274i | \(0.192776\pi\) | ||||
−0.822148 | + | 0.569274i | \(0.807224\pi\) | |||||||
\(44\) | − | 3.43375i | − | 0.0780397i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −36.7177 | −0.798211 | ||||||||
\(47\) | 4.79310i | 0.101981i | 0.998699 | + | 0.0509904i | \(0.0162378\pi\) | ||||
−0.998699 | + | 0.0509904i | \(0.983762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −47.4960 | −0.969306 | ||||||||
\(50\) | − | 15.0627i | − | 0.301254i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 35.6884i | 0.686316i | ||||||||
\(53\) | 48.7328 | 0.919488 | 0.459744 | − | 0.888052i | \(-0.347941\pi\) | ||||
0.459744 | + | 0.888052i | \(0.347941\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.06292i | 0.0738713i | ||||||||
\(56\) | − | 9.08548i | − | 0.162241i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 8.18418i | − | 0.141107i | ||||||
\(59\) | −43.5656 | − | 39.7874i | −0.738400 | − | 0.674363i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 87.6284i | 1.43653i | 0.695769 | + | 0.718265i | \(0.255064\pi\) | ||||
−0.695769 | + | 0.718265i | \(0.744936\pi\) | |||||||
\(62\) | −8.38556 | −0.135251 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −23.0750 | −0.360547 | ||||||||
\(65\) | − | 42.2277i | − | 0.649657i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 42.6674i | − | 0.636826i | −0.947952 | − | 0.318413i | \(-0.896850\pi\) | ||
0.947952 | − | 0.318413i | \(-0.103150\pi\) | |||||||
\(68\) | 2.29920 | 0.0338118 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.44511i | 0.0635016i | ||||||||
\(71\) | 20.2245 | 0.284852 | 0.142426 | − | 0.989805i | \(-0.454510\pi\) | ||||
0.142426 | + | 0.989805i | \(0.454510\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 45.6107i | 0.624804i | 0.949950 | + | 0.312402i | \(0.101134\pi\) | ||||
−0.949950 | + | 0.312402i | \(0.898866\pi\) | |||||||
\(74\) | −18.2448 | −0.246551 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.8497 | −0.287496 | ||||||||
\(77\) | 1.49328i | 0.0193933i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −62.5528 | −0.791808 | −0.395904 | − | 0.918292i | \(-0.629569\pi\) | ||||
−0.395904 | + | 0.918292i | \(0.629569\pi\) | |||||||
\(80\) | −10.7856 | −0.134820 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 20.6933i | 0.252357i | ||||||||
\(83\) | − | 22.8390i | − | 0.275169i | −0.990490 | − | 0.137584i | \(-0.956066\pi\) | ||
0.990490 | − | 0.137584i | \(-0.0439338\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.72049 | −0.0320058 | ||||||||
\(86\) | −53.1815 | −0.618390 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.02079 | 0.102509 | ||||||||
\(89\) | − | 55.8982i | − | 0.628070i | −0.949411 | − | 0.314035i | \(-0.898319\pi\) | ||
0.949411 | − | 0.314035i | \(-0.101681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15.5203i | − | 0.170553i | ||||||
\(92\) | 95.3199i | 1.03609i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.20664 | −0.0553897 | ||||||||
\(95\) | 25.8533 | 0.272140 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 123.320i | − | 1.27134i | −0.771962 | − | 0.635669i | \(-0.780724\pi\) | ||
0.771962 | − | 0.635669i | \(-0.219276\pi\) | |||||||
\(98\) | − | 51.5939i | − | 0.526468i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −39.1031 | −0.391031 | ||||||||
\(101\) | 39.0946i | 0.387075i | 0.981093 | + | 0.193538i | \(0.0619962\pi\) | ||||
−0.981093 | + | 0.193538i | \(0.938004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 56.8713i | − | 0.552149i | −0.961136 | − | 0.276074i | \(-0.910966\pi\) | ||
0.961136 | − | 0.276074i | \(-0.0890336\pi\) | |||||||
\(104\) | −93.7570 | −0.901509 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 52.9374i | 0.499410i | ||||||||
\(107\) | −34.8029 | −0.325261 | −0.162630 | − | 0.986687i | \(-0.551998\pi\) | ||||
−0.162630 | + | 0.986687i | \(0.551998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.83542i | 0.0902332i | 0.998982 | + | 0.0451166i | \(0.0143659\pi\) | ||||
−0.998982 | + | 0.0451166i | \(0.985634\pi\) | |||||||
\(110\) | −4.41346 | −0.0401224 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.96413 | −0.0353940 | ||||||||
\(113\) | 145.812i | 1.29037i | 0.764025 | + | 0.645186i | \(0.223220\pi\) | ||||
−0.764025 | + | 0.645186i | \(0.776780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 112.786i | − | 0.980744i | ||||||
\(116\) | −21.2463 | −0.183158 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 43.2202 | − | 47.3244i | 0.366273 | − | 0.401054i | ||||
\(119\) | −0.999886 | −0.00840241 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119.517 | 0.987747 | ||||||||
\(122\) | −95.1888 | −0.780236 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 21.7691i | 0.175557i | ||||||||
\(125\) | 129.686 | 1.03749 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 145.827 | 1.14825 | 0.574123 | − | 0.818769i | \(-0.305343\pi\) | ||||
0.574123 | + | 0.818769i | \(0.305343\pi\) | |||||||
\(128\) | 107.514i | 0.839952i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 45.8710 | 0.352854 | ||||||||
\(131\) | 30.5967i | 0.233562i | 0.993158 | + | 0.116781i | \(0.0372576\pi\) | ||||
−0.993158 | + | 0.116781i | \(0.962742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.50208 | 0.0714442 | ||||||||
\(134\) | 46.3486 | 0.345885 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.04023i | 0.0444134i | ||||||||
\(137\) | 39.4511 | 0.287964 | 0.143982 | − | 0.989580i | \(-0.454009\pi\) | ||||
0.143982 | + | 0.989580i | \(0.454009\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 93.5556 | 0.673062 | 0.336531 | − | 0.941672i | \(-0.390746\pi\) | ||||
0.336531 | + | 0.941672i | \(0.390746\pi\) | |||||||
\(140\) | 11.5396 | 0.0824257 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.9694i | 0.154714i | ||||||||
\(143\) | 15.4098 | 0.107761 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.1393 | 0.173375 | ||||||||
\(146\) | −49.5459 | −0.339356 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 47.3638i | 0.320026i | ||||||||
\(149\) | − | 133.435i | − | 0.895536i | −0.894150 | − | 0.447768i | \(-0.852219\pi\) | ||
0.894150 | − | 0.447768i | \(-0.147781\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 95.5402i | − | 0.632717i | −0.948640 | − | 0.316358i | \(-0.897540\pi\) | ||
0.948640 | − | 0.316358i | \(-0.102460\pi\) | |||||||
\(152\) | − | 57.4013i | − | 0.377640i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.62212 | −0.0105332 | ||||||||
\(155\) | − | 25.7579i | − | 0.166180i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 245.077i | − | 1.56100i | −0.625157 | − | 0.780499i | \(-0.714965\pi\) | ||
0.625157 | − | 0.780499i | \(-0.285035\pi\) | |||||||
\(158\) | − | 67.9498i | − | 0.430062i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 110.595i | − | 0.691220i | ||||||
\(161\) | − | 41.4531i | − | 0.257473i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 204.601 | 1.25522 | 0.627611 | − | 0.778527i | \(-0.284033\pi\) | ||||
0.627611 | + | 0.778527i | \(0.284033\pi\) | |||||||
\(164\) | 53.7202 | 0.327562 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.8095 | 0.149455 | ||||||||
\(167\) | 100.875 | 0.604043 | 0.302022 | − | 0.953301i | \(-0.402339\pi\) | ||||
0.302022 | + | 0.953301i | \(0.402339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.83915 | 0.0523027 | ||||||||
\(170\) | − | 2.95521i | − | 0.0173836i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 138.060i | 0.802677i | ||||||||
\(173\) | − | 192.449i | − | 1.11242i | −0.831041 | − | 0.556212i | \(-0.812254\pi\) | ||
0.831041 | − | 0.556212i | \(-0.187746\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.0053 | 0.0971732 | ||||||||
\(176\) | − | 3.93590i | − | 0.0223631i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 60.7210 | 0.341129 | ||||||||
\(179\) | − | 66.4049i | − | 0.370977i | −0.982646 | − | 0.185488i | \(-0.940613\pi\) | ||
0.982646 | − | 0.185488i | \(-0.0593867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 100.811 | 0.556968 | 0.278484 | − | 0.960441i | \(-0.410168\pi\) | ||||
0.278484 | + | 0.960441i | \(0.410168\pi\) | |||||||
\(182\) | 16.8594 | 0.0926340 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −250.415 | −1.36095 | ||||||||
\(185\) | − | 56.0424i | − | 0.302932i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.992766i | − | 0.00530891i | ||||||
\(188\) | 13.5165i | 0.0718965i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 28.0838i | 0.147810i | ||||||||
\(191\) | 285.899i | 1.49686i | 0.663216 | + | 0.748428i | \(0.269191\pi\) | ||||
−0.663216 | + | 0.748428i | \(0.730809\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7169 | 0.0607093 | 0.0303546 | − | 0.999539i | \(-0.490336\pi\) | ||||
0.0303546 | + | 0.999539i | \(0.490336\pi\) | |||||||
\(194\) | 133.960 | 0.690513 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −133.939 | −0.683361 | ||||||||
\(197\) | 269.535 | 1.36820 | 0.684099 | − | 0.729389i | \(-0.260195\pi\) | ||||
0.684099 | + | 0.729389i | \(0.260195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 164.357 | 0.825912 | 0.412956 | − | 0.910751i | \(-0.364496\pi\) | ||||
0.412956 | + | 0.910751i | \(0.364496\pi\) | |||||||
\(200\) | − | 102.728i | − | 0.513638i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −42.4676 | −0.210236 | ||||||||
\(203\) | 9.23968 | 0.0455157 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −63.5635 | −0.310066 | ||||||||
\(206\) | 61.7781 | 0.299894 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 40.9075i | 0.196671i | ||||||||
\(209\) | 9.43442i | 0.0451408i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 155.167i | − | 0.735391i | −0.929946 | − | 0.367695i | \(-0.880147\pi\) | ||
0.929946 | − | 0.367695i | \(-0.119853\pi\) | |||||||
\(212\) | 137.427 | 0.648239 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 37.8056i | − | 0.176662i | ||||||
\(215\) | − | 163.357i | − | 0.759802i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.46703i | − | 0.0436269i | ||||||
\(218\) | −10.6840 | −0.0490092 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.4574i | 0.0520792i | ||||||||
\(221\) | 10.3183i | 0.0466889i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 212.798 | 0.954251 | 0.477126 | − | 0.878835i | \(-0.341679\pi\) | ||||
0.477126 | + | 0.878835i | \(0.341679\pi\) | |||||||
\(224\) | − | 40.6481i | − | 0.181465i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −158.392 | −0.700852 | ||||||||
\(227\) | 272.876i | 1.20210i | 0.799213 | + | 0.601048i | \(0.205250\pi\) | ||||
−0.799213 | + | 0.601048i | \(0.794750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 350.552i | 1.53080i | 0.643557 | + | 0.765398i | \(0.277458\pi\) | ||||
−0.643557 | + | 0.765398i | \(0.722542\pi\) | |||||||
\(230\) | 122.517 | 0.532681 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 55.8161i | − | 0.240587i | ||||||
\(233\) | 1.64412i | 0.00705630i | 0.999994 | + | 0.00352815i | \(0.00112305\pi\) | ||||
−0.999994 | + | 0.00352815i | \(0.998877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 15.9932i | − | 0.0680562i | ||||||
\(236\) | −122.855 | − | 112.200i | −0.520572 | − | 0.475426i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 1.08615i | − | 0.00456368i | ||||||
\(239\) | 74.5410 | 0.311887 | 0.155943 | − | 0.987766i | \(-0.450158\pi\) | ||||
0.155943 | + | 0.987766i | \(0.450158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −56.4597 | −0.234272 | −0.117136 | − | 0.993116i | \(-0.537371\pi\) | ||||
−0.117136 | + | 0.993116i | \(0.537371\pi\) | |||||||
\(242\) | 129.829i | 0.536484i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 247.112i | 1.01275i | ||||||||
\(245\) | 158.481 | 0.646860 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 98.0560i | − | 0.396988i | ||||||
\(248\) | −57.1895 | −0.230603 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 140.875i | 0.563500i | ||||||||
\(251\) | 21.6224 | 0.0861451 | 0.0430726 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430726 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.1580 | 0.162680 | ||||||||
\(254\) | 158.409i | 0.623657i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −209.090 | −0.816758 | ||||||||
\(257\) | −70.0007 | −0.272376 | −0.136188 | − | 0.990683i | \(-0.543485\pi\) | ||||
−0.136188 | + | 0.990683i | \(0.543485\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 20.5978i | − | 0.0795281i | ||||||
\(260\) | − | 119.082i | − | 0.458008i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −33.2365 | −0.126857 | ||||||||
\(263\) | −450.103 | −1.71142 | −0.855709 | − | 0.517457i | \(-0.826879\pi\) | ||||
−0.855709 | + | 0.517457i | \(0.826879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −162.608 | −0.613614 | ||||||||
\(266\) | 10.3219i | 0.0388042i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 120.322i | − | 0.448963i | ||||||
\(269\) | − | 167.392i | − | 0.622275i | −0.950365 | − | 0.311137i | \(-0.899290\pi\) | ||
0.950365 | − | 0.311137i | \(-0.100710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 136.135 | 0.502342 | 0.251171 | − | 0.967943i | \(-0.419184\pi\) | ||||
0.251171 | + | 0.967943i | \(0.419184\pi\) | |||||||
\(272\) | 2.63544 | 0.00968912 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 42.8549i | 0.156405i | ||||||||
\(275\) | 16.8842i | 0.0613971i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −195.176 | −0.704606 | −0.352303 | − | 0.935886i | \(-0.614601\pi\) | ||||
−0.352303 | + | 0.935886i | \(0.614601\pi\) | |||||||
\(278\) | 101.627i | 0.365566i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 30.3157i | 0.108270i | ||||||||
\(281\) | −475.581 | −1.69246 | −0.846229 | − | 0.532820i | \(-0.821132\pi\) | ||||
−0.846229 | + | 0.532820i | \(0.821132\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 444.223i | − | 1.56969i | −0.619691 | − | 0.784846i | \(-0.712742\pi\) | ||
0.619691 | − | 0.784846i | \(-0.287258\pi\) | |||||||
\(284\) | 57.0330 | 0.200821 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.7393i | 0.0585292i | ||||||||
\(287\) | −23.3621 | −0.0814009 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.335 | −0.997700 | ||||||||
\(290\) | 27.3083i | 0.0941665i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 128.622i | 0.440487i | ||||||||
\(293\) | 56.4950 | 0.192816 | 0.0964079 | − | 0.995342i | \(-0.469265\pi\) | ||||
0.0964079 | + | 0.995342i | \(0.469265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 145.366 | + | 132.759i | 0.492766 | + | 0.450031i | ||||
\(296\) | −124.429 | −0.420369 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 144.947 | 0.486401 | ||||||||
\(299\) | −427.772 | −1.43068 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 60.0403i | − | 0.199469i | ||||||
\(302\) | 103.783 | 0.343653 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −25.0450 | −0.0823849 | ||||||||
\(305\) | − | 292.391i | − | 0.958659i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 279.533 | 0.910530 | 0.455265 | − | 0.890356i | \(-0.349545\pi\) | ||||
0.455265 | + | 0.890356i | \(0.349545\pi\) | |||||||
\(308\) | 4.21106i | 0.0136723i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 27.9802 | 0.0902588 | ||||||||
\(311\) | −210.784 | −0.677762 | −0.338881 | − | 0.940829i | \(-0.610048\pi\) | ||||
−0.338881 | + | 0.940829i | \(0.610048\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 372.662i | − | 1.19061i | −0.803499 | − | 0.595306i | \(-0.797031\pi\) | ||
0.803499 | − | 0.595306i | \(-0.202969\pi\) | |||||||
\(314\) | 266.221 | 0.847839 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −176.399 | −0.558225 | ||||||||
\(317\) | −299.104 | −0.943544 | −0.471772 | − | 0.881720i | \(-0.656386\pi\) | ||||
−0.471772 | + | 0.881720i | \(0.656386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.17389i | 0.0287583i | ||||||||
\(320\) | 76.9948 | 0.240609 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 45.0296 | 0.139844 | ||||||||
\(323\) | −6.31719 | −0.0195579 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 175.485i | − | 0.539954i | ||||||
\(326\) | 222.254i | 0.681760i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 141.128i | 0.430269i | ||||||||
\(329\) | − | 5.87813i | − | 0.0178666i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 268.182 | 0.810217 | 0.405109 | − | 0.914269i | \(-0.367234\pi\) | ||||
0.405109 | + | 0.914269i | \(0.367234\pi\) | |||||||
\(332\) | − | 64.4060i | − | 0.193994i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 109.579i | 0.328079i | ||||||||
\(335\) | 142.369i | 0.424982i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 372.241i | 1.10457i | 0.833655 | + | 0.552286i | \(0.186244\pi\) | ||||
−0.833655 | + | 0.552286i | \(0.813756\pi\) | |||||||
\(338\) | 9.60178i | 0.0284076i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.67178 | −0.0225641 | ||||||||
\(341\) | 9.39962 | 0.0275649 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 118.340 | 0.345015 | ||||||||
\(344\) | −362.698 | −1.05436 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 209.053 | 0.604201 | ||||||||
\(347\) | 162.680i | 0.468820i | 0.972138 | + | 0.234410i | \(0.0753158\pi\) | ||||
−0.972138 | + | 0.234410i | \(0.924684\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 474.478i | 1.35954i | 0.733427 | + | 0.679768i | \(0.237920\pi\) | ||||
−0.733427 | + | 0.679768i | \(0.762080\pi\) | |||||||
\(350\) | 18.4725i | 0.0527785i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.3586 | 0.114655 | ||||||||
\(353\) | 553.231i | 1.56723i | 0.621248 | + | 0.783614i | \(0.286626\pi\) | ||||
−0.621248 | + | 0.783614i | \(0.713374\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −67.4833 | −0.190094 | ||||||||
\(356\) | − | 157.633i | − | 0.442790i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 72.1342 | 0.201492 | ||||||||
\(359\) | 347.072 | 0.966775 | 0.483387 | − | 0.875407i | \(-0.339406\pi\) | ||||
0.483387 | + | 0.875407i | \(0.339406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −300.967 | −0.833703 | ||||||||
\(362\) | 109.509i | 0.302511i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 43.7673i | − | 0.120240i | ||||||
\(365\) | − | 152.190i | − | 0.416959i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 617.839i | − | 1.68349i | −0.539879 | − | 0.841743i | \(-0.681530\pi\) | ||
0.539879 | − | 0.841743i | \(-0.318470\pi\) | |||||||
\(368\) | 109.260i | 0.296901i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 60.8776 | 0.164534 | ||||||||
\(371\) | −59.7647 | −0.161091 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −427.265 | −1.14548 | −0.572741 | − | 0.819736i | \(-0.694120\pi\) | ||||
−0.572741 | + | 0.819736i | \(0.694120\pi\) | |||||||
\(374\) | 1.07842 | 0.00288348 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −35.5093 | −0.0944395 | ||||||||
\(377\) | − | 95.3482i | − | 0.252913i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −400.731 | −1.05734 | −0.528668 | − | 0.848828i | \(-0.677308\pi\) | ||||
−0.528668 | + | 0.848828i | \(0.677308\pi\) | |||||||
\(380\) | 72.9062 | 0.191858 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −310.566 | −0.813001 | ||||||||
\(383\) | 18.1585 | 0.0474111 | 0.0237056 | − | 0.999719i | \(-0.492454\pi\) | ||||
0.0237056 | + | 0.999719i | \(0.492454\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 4.98266i | − | 0.0129420i | ||||||
\(386\) | 12.7278i | 0.0329736i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 347.762i | − | 0.896293i | ||||||
\(389\) | 308.582 | 0.793269 | 0.396635 | − | 0.917977i | \(-0.370178\pi\) | ||||
0.396635 | + | 0.917977i | \(0.370178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.5589i | 0.0704832i | ||||||||
\(392\) | − | 351.870i | − | 0.897628i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 292.790i | 0.743122i | ||||||||
\(395\) | 208.721 | 0.528407 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 193.629i | 0.487730i | 0.969809 | + | 0.243865i | \(0.0784154\pi\) | ||||
−0.969809 | + | 0.243865i | \(0.921585\pi\) | |||||||
\(398\) | 178.537i | 0.448585i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −44.8216 | −0.112054 | ||||||||
\(401\) | 148.241i | 0.369678i | 0.982769 | + | 0.184839i | \(0.0591763\pi\) | ||||
−0.982769 | + | 0.184839i | \(0.940824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −97.6943 | −0.242418 | ||||||||
\(404\) | 110.247i | 0.272888i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.0369i | 0.0247213i | ||||||||
\(407\) | 20.4511 | 0.0502484 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 486.132i | 1.18859i | 0.804249 | + | 0.594293i | \(0.202568\pi\) | ||||
−0.804249 | + | 0.594293i | \(0.797432\pi\) | |||||||
\(410\) | − | 69.0476i | − | 0.168409i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 160.377i | − | 0.389265i | ||||||
\(413\) | 53.4277 | + | 48.7942i | 0.129365 | + | 0.118146i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 76.2073i | 0.183632i | ||||||||
\(416\) | −419.465 | −1.00833 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.2484 | −0.0245177 | ||||||||
\(419\) | − | 393.978i | − | 0.940281i | −0.882592 | − | 0.470140i | \(-0.844203\pi\) | ||
0.882592 | − | 0.470140i | \(-0.155797\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 545.228i | 1.29508i | 0.762032 | + | 0.647539i | \(0.224202\pi\) | ||||
−0.762032 | + | 0.647539i | \(0.775798\pi\) | |||||||
\(422\) | 168.555 | 0.399420 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 361.033i | 0.851493i | ||||||||
\(425\) | −11.3055 | −0.0266012 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 107.465i | − | 0.251675i | ||||||
\(428\) | −98.1441 | −0.229309 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 177.452 | 0.412678 | ||||||||
\(431\) | − | 645.842i | − | 1.49847i | −0.662302 | − | 0.749237i | \(-0.730420\pi\) | ||
0.662302 | − | 0.749237i | \(-0.269580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −440.441 | −1.01719 | −0.508593 | − | 0.861007i | \(-0.669834\pi\) | ||||
−0.508593 | + | 0.861007i | \(0.669834\pi\) | |||||||
\(434\) | 10.2838 | 0.0236954 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.7359i | 0.0636144i | ||||||||
\(437\) | − | 261.897i | − | 0.599307i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −817.423 | −1.86201 | −0.931006 | − | 0.365003i | \(-0.881068\pi\) | ||||
−0.931006 | + | 0.365003i | \(0.881068\pi\) | |||||||
\(440\) | −30.0998 | −0.0684086 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.2085 | −0.0253586 | ||||||||
\(443\) | 522.987i | 1.18056i | 0.807200 | + | 0.590278i | \(0.200982\pi\) | ||||
−0.807200 | + | 0.590278i | \(0.799018\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 186.517i | 0.419138i | ||||||||
\(446\) | 231.158i | 0.518291i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 28.2986 | 0.0631665 | ||||||||
\(449\) | 721.573 | 1.60707 | 0.803533 | − | 0.595260i | \(-0.202951\pi\) | ||||
0.803533 | + | 0.595260i | \(0.202951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 23.1957i | − | 0.0514317i | ||||||
\(452\) | 411.190i | 0.909713i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −296.419 | −0.652905 | ||||||||
\(455\) | 51.7869i | 0.113817i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 899.045i | 1.96728i | 0.180157 | + | 0.983638i | \(0.442340\pi\) | ||||
−0.180157 | + | 0.983638i | \(0.557660\pi\) | |||||||
\(458\) | −380.797 | −0.831435 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 318.055i | − | 0.691425i | ||||||
\(461\) | −126.539 | −0.274489 | −0.137245 | − | 0.990537i | \(-0.543825\pi\) | ||||
−0.137245 | + | 0.990537i | \(0.543825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 169.302i | 0.365663i | 0.983144 | + | 0.182831i | \(0.0585263\pi\) | ||||
−0.983144 | + | 0.182831i | \(0.941474\pi\) | |||||||
\(464\) | −24.3534 | −0.0524858 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.78597 | −0.00383255 | ||||||||
\(467\) | − | 98.8969i | − | 0.211771i | −0.994378 | − | 0.105885i | \(-0.966232\pi\) | ||
0.994378 | − | 0.105885i | \(-0.0337676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 52.3261i | 0.111570i | ||||||||
\(470\) | 17.3731 | 0.0369640 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 294.762 | − | 322.752i | 0.624495 | − | 0.683797i | ||||
\(473\) | 59.6127 | 0.126031 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 107.438 | 0.226185 | ||||||||
\(476\) | −2.81968 | −0.00592370 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 80.9722i | 0.169398i | ||||||||
\(479\) | 91.0329 | 0.190048 | 0.0950240 | − | 0.995475i | \(-0.469707\pi\) | ||||
0.0950240 | + | 0.995475i | \(0.469707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −212.557 | −0.441907 | ||||||||
\(482\) | − | 61.3309i | − | 0.127242i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 337.039 | 0.696361 | ||||||||
\(485\) | 411.483i | 0.848419i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −72.6279 | −0.149133 | −0.0745667 | − | 0.997216i | \(-0.523757\pi\) | ||||
−0.0745667 | + | 0.997216i | \(0.523757\pi\) | |||||||
\(488\) | −649.187 | −1.33030 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 172.154i | 0.351335i | ||||||||
\(491\) | 269.921 | 0.549736 | 0.274868 | − | 0.961482i | \(-0.411366\pi\) | ||||
0.274868 | + | 0.961482i | \(0.411366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.14274 | −0.0124599 | ||||||||
\(494\) | 106.516 | 0.215620 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.9526i | 0.0503077i | ||||||||
\(497\) | −24.8028 | −0.0499050 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 219.786 | 0.440452 | 0.220226 | − | 0.975449i | \(-0.429320\pi\) | ||||
0.220226 | + | 0.975449i | \(0.429320\pi\) | |||||||
\(500\) | 365.714 | 0.731428 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.4880i | 0.0467888i | ||||||||
\(503\) | − | 800.462i | − | 1.59138i | −0.605707 | − | 0.795688i | \(-0.707110\pi\) | ||
0.605707 | − | 0.795688i | \(-0.292890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 130.448i | − | 0.258312i | ||||||
\(506\) | 44.7090i | 0.0883577i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 411.233 | 0.809513 | ||||||||
\(509\) | − | 12.6193i | − | 0.0247924i | −0.999923 | − | 0.0123962i | \(-0.996054\pi\) | ||
0.999923 | − | 0.0123962i | \(-0.00394593\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 55.9358i | − | 0.109463i | ||||||
\(512\) | 202.926i | 0.396339i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 76.0403i | − | 0.147938i | ||||||
\(515\) | 189.763i | 0.368473i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.83627 | 0.0112887 | ||||||||
\(518\) | 22.3749 | 0.0431948 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 312.840 | 0.601616 | ||||||||
\(521\) | −629.736 | −1.20871 | −0.604353 | − | 0.796717i | \(-0.706568\pi\) | ||||
−0.604353 | + | 0.796717i | \(0.706568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 852.513 | 1.63004 | 0.815022 | − | 0.579430i | \(-0.196725\pi\) | ||||
0.815022 | + | 0.579430i | \(0.196725\pi\) | |||||||
\(524\) | 86.2826i | 0.164661i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 488.937i | − | 0.929538i | ||||||
\(527\) | 6.29389i | 0.0119429i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −613.534 | −1.15980 | ||||||||
\(530\) | − | 176.637i | − | 0.333277i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.7959 | 0.0503682 | ||||||||
\(533\) | 241.083i | 0.452313i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 116.127 | 0.217060 | ||||||||
\(536\) | 316.098 | 0.589734 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 181.834 | 0.337982 | ||||||||
\(539\) | 57.8331i | 0.107297i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 463.558i | − | 0.856855i | −0.903576 | − | 0.428427i | \(-0.859068\pi\) | ||
0.903576 | − | 0.428427i | \(-0.140932\pi\) | |||||||
\(542\) | 147.880i | 0.272842i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 27.0237i | 0.0496760i | ||||||||
\(545\) | − | 32.8180i | − | 0.0602165i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 306.278 | 0.559922 | 0.279961 | − | 0.960011i | \(-0.409678\pi\) | ||||
0.279961 | + | 0.960011i | \(0.409678\pi\) | |||||||
\(548\) | 111.252 | 0.203015 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.3409 | −0.0333472 | ||||||||
\(551\) | 58.3755 | 0.105945 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 76.7131 | 0.138722 | ||||||||
\(554\) | − | 212.015i | − | 0.382699i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 263.827 | 0.474508 | ||||||||
\(557\) | 994.672 | 1.78577 | 0.892883 | − | 0.450288i | \(-0.148679\pi\) | ||||
0.892883 | + | 0.450288i | \(0.148679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −619.581 | −1.10837 | ||||||||
\(560\) | 13.2272 | 0.0236199 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 516.613i | − | 0.919240i | ||||||
\(563\) | 206.256i | 0.366352i | 0.983080 | + | 0.183176i | \(0.0586378\pi\) | ||||
−0.983080 | + | 0.183176i | \(0.941362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 486.533i | − | 0.861121i | ||||||
\(566\) | 482.550 | 0.852561 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 149.831i | 0.263788i | ||||||||
\(569\) | 588.448i | 1.03418i | 0.855931 | + | 0.517089i | \(0.172985\pi\) | ||||
−0.855931 | + | 0.517089i | \(0.827015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 139.611i | − | 0.244503i | −0.992499 | − | 0.122251i | \(-0.960989\pi\) | ||
0.992499 | − | 0.122251i | \(-0.0390114\pi\) | |||||||
\(572\) | 43.4557 | 0.0759714 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 25.3777i | − | 0.0442120i | ||||||
\(575\) | − | 468.701i | − | 0.815133i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 947.400 | 1.64194 | 0.820971 | − | 0.570970i | \(-0.193433\pi\) | ||||
0.820971 | + | 0.570970i | \(0.193433\pi\) | |||||||
\(578\) | − | 313.212i | − | 0.541890i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 70.8929 | 0.122229 | ||||||||
\(581\) | 28.0092i | 0.0482085i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 59.3391i | − | 0.101782i | ||||||
\(584\) | −337.903 | −0.578601 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 61.3693i | 0.104726i | ||||||||
\(587\) | − | 672.802i | − | 1.14617i | −0.819496 | − | 0.573085i | \(-0.805746\pi\) | ||
0.819496 | − | 0.573085i | \(-0.194254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 59.8118i | − | 0.101548i | ||||||
\(590\) | −144.213 | + | 157.908i | −0.244429 | + | 0.267641i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 54.2903i | 0.0917067i | ||||||||
\(593\) | −235.268 | −0.396742 | −0.198371 | − | 0.980127i | \(-0.563565\pi\) | ||||
−0.198371 | + | 0.980127i | \(0.563565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.33634 | 0.00560729 | ||||||||
\(596\) | − | 376.287i | − | 0.631353i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 464.680i | − | 0.777056i | ||||||
\(599\) | 938.758 | 1.56721 | 0.783604 | − | 0.621260i | \(-0.213379\pi\) | ||||
0.783604 | + | 0.621260i | \(0.213379\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 396.943i | − | 0.660470i | −0.943899 | − | 0.330235i | \(-0.892872\pi\) | ||
0.943899 | − | 0.330235i | \(-0.107128\pi\) | |||||||
\(602\) | 65.2204 | 0.108340 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 269.423i | − | 0.446065i | ||||||
\(605\) | −398.795 | −0.659166 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 794.727 | 1.30927 | 0.654635 | − | 0.755945i | \(-0.272822\pi\) | ||||
0.654635 | + | 0.755945i | \(0.272822\pi\) | |||||||
\(608\) | − | 256.811i | − | 0.422386i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 317.618 | 0.520685 | ||||||||
\(611\) | −60.6589 | −0.0992780 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.2456i | 0.0232392i | 0.999932 | + | 0.0116196i | \(0.00369872\pi\) | ||||
−0.999932 | + | 0.0116196i | \(0.996301\pi\) | |||||||
\(614\) | 303.650i | 0.494544i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.0629 | −0.0179592 | ||||||||
\(617\) | −739.753 | −1.19895 | −0.599476 | − | 0.800393i | \(-0.704624\pi\) | ||||
−0.599476 | + | 0.800393i | \(0.704624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 202.230 | 0.326705 | 0.163352 | − | 0.986568i | \(-0.447769\pi\) | ||||
0.163352 | + | 0.986568i | \(0.447769\pi\) | |||||||
\(620\) | − | 72.6372i | − | 0.117157i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 228.970i | − | 0.368119i | ||||||
\(623\) | 68.5521i | 0.110036i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −86.0664 | −0.137706 | ||||||||
\(626\) | 404.814 | 0.646668 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 691.116i | − | 1.10050i | ||||||
\(629\) | 13.6938i | 0.0217708i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −504.848 | −0.800076 | −0.400038 | − | 0.916499i | \(-0.631003\pi\) | ||||
−0.400038 | + | 0.916499i | \(0.631003\pi\) | |||||||
\(632\) | − | 463.417i | − | 0.733255i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 324.910i | − | 0.512476i | ||||||
\(635\) | −486.584 | −0.766274 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 601.084i | − | 0.943617i | ||||||
\(638\) | −9.96539 | −0.0156197 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 358.743i | − | 0.560536i | ||||||
\(641\) | −757.354 | −1.18152 | −0.590760 | − | 0.806847i | \(-0.701172\pi\) | ||||
−0.590760 | + | 0.806847i | \(0.701172\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 390.062 | 0.606628 | 0.303314 | − | 0.952891i | \(-0.401907\pi\) | ||||
0.303314 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(644\) | − | 116.898i | − | 0.181518i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 6.86223i | − | 0.0106226i | ||||||
\(647\) | 992.824 | 1.53450 | 0.767252 | − | 0.641346i | \(-0.221624\pi\) | ||||
0.767252 | + | 0.641346i | \(0.221624\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.4467 | + | 53.0473i | −0.0746483 | + | 0.0817369i | ||||
\(650\) | 190.625 | 0.293270 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 576.976 | 0.884932 | ||||||||
\(653\) | −1166.56 | −1.78646 | −0.893228 | − | 0.449604i | \(-0.851565\pi\) | ||||
−0.893228 | + | 0.449604i | \(0.851565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 102.092i | − | 0.155866i | ||||||
\(656\) | 61.5763 | 0.0938663 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.38528 | 0.00970407 | ||||||||
\(659\) | 689.431i | 1.04618i | 0.852278 | + | 0.523089i | \(0.175220\pi\) | ||||
−0.852278 | + | 0.523089i | \(0.824780\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1035.80 | 1.56703 | 0.783513 | − | 0.621376i | \(-0.213426\pi\) | ||||
0.783513 | + | 0.621376i | \(0.213426\pi\) | |||||||
\(662\) | 291.320i | 0.440061i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 169.201 | 0.254821 | ||||||||
\(665\) | −31.7057 | −0.0476778 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 254.665i | − | 0.381806i | ||||||
\(668\) | 284.468 | 0.425851 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −154.652 | −0.230824 | ||||||||
\(671\) | 106.700 | 0.159016 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 504.708i | 0.749937i | 0.927037 | + | 0.374969i | \(0.122347\pi\) | ||||
−0.927037 | + | 0.374969i | \(0.877653\pi\) | |||||||
\(674\) | −404.357 | −0.599936 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.9264 | 0.0368734 | ||||||||
\(677\) | −184.647 | −0.272743 | −0.136372 | − | 0.990658i | \(-0.543544\pi\) | ||||
−0.136372 | + | 0.990658i | \(0.543544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 151.236i | 0.222734i | ||||||||
\(680\) | − | 20.1545i | − | 0.0296390i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.2106i | 0.0149715i | ||||||||
\(683\) | 150.545i | 0.220417i | 0.993908 | + | 0.110209i | \(0.0351519\pi\) | ||||
−0.993908 | + | 0.110209i | \(0.964848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −131.637 | −0.192171 | ||||||||
\(686\) | 128.550i | 0.187391i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 158.251i | 0.230015i | ||||||||
\(689\) | 616.737i | 0.895119i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.87982i | − | 0.0128507i | −0.999979 | − | 0.00642534i | \(-0.997955\pi\) | ||
0.999979 | − | 0.00642534i | \(-0.00204526\pi\) | |||||||
\(692\) | − | 542.707i | − | 0.784259i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −176.716 | −0.254634 | ||||||||
\(695\) | −312.168 | −0.449163 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5316 | 0.0222835 | ||||||||
\(698\) | −515.415 | −0.738417 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 47.9550 | 0.0685071 | ||||||||
\(701\) | − | 672.703i | − | 0.959633i | −0.877369 | − | 0.479817i | \(-0.840703\pi\) | ||
0.877369 | − | 0.479817i | \(-0.159297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 130.135i | − | 0.185114i | ||||||
\(704\) | 28.0971i | 0.0399106i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −600.963 | −0.851223 | ||||||||
\(707\) | − | 47.9446i | − | 0.0678141i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −885.467 | −1.24890 | −0.624448 | − | 0.781067i | \(-0.714676\pi\) | ||||
−0.624448 | + | 0.781067i | \(0.714676\pi\) | |||||||
\(710\) | − | 73.3057i | − | 0.103247i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 414.117 | 0.581626 | ||||||||
\(713\) | −260.931 | −0.365962 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −51.4181 | −0.0719135 | ||||||||
\(716\) | − | 187.262i | − | 0.261539i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 377.017i | 0.525093i | ||||||||
\(719\) | − | 900.012i | − | 1.25175i | −0.779922 | − | 0.625877i | \(-0.784741\pi\) | ||
0.779922 | − | 0.625877i | \(-0.215259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 69.7455i | 0.0967344i | ||||||||
\(722\) | − | 326.934i | − | 0.452816i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 284.288 | 0.392662 | ||||||||
\(725\) | 104.471 | 0.144098 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −702.800 | −0.966713 | −0.483357 | − | 0.875424i | \(-0.660583\pi\) | ||||
−0.483357 | + | 0.875424i | \(0.660583\pi\) | |||||||
\(728\) | 114.981 | 0.157941 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 165.321 | 0.226467 | ||||||||
\(731\) | 39.9161i | 0.0546048i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −389.940 | −0.531978 | −0.265989 | − | 0.963976i | \(-0.585698\pi\) | ||||
−0.265989 | + | 0.963976i | \(0.585698\pi\) | |||||||
\(734\) | 671.145 | 0.914366 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1120.35 | −1.52221 | ||||||||
\(737\) | −51.9535 | −0.0704933 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1203.79i | 1.62894i | 0.580206 | + | 0.814470i | \(0.302972\pi\) | ||||
−0.580206 | + | 0.814470i | \(0.697028\pi\) | |||||||
\(740\) | − | 158.039i | − | 0.213567i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 64.9210i | − | 0.0874947i | ||||||
\(743\) | 1379.37 | 1.85649 | 0.928247 | − | 0.371965i | \(-0.121316\pi\) | ||||
0.928247 | + | 0.371965i | \(0.121316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 445.234i | 0.597630i | ||||||||
\(746\) | − | 464.128i | − | 0.622156i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 2.79960i | − | 0.00374278i | ||||||
\(749\) | 42.6813 | 0.0569844 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 855.872i | 1.13964i | 0.821769 | + | 0.569821i | \(0.192988\pi\) | ||||
−0.821769 | + | 0.569821i | \(0.807012\pi\) | |||||||
\(752\) | 15.4932i | 0.0206027i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 103.575 | 0.137367 | ||||||||
\(755\) | 318.791i | 0.422239i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −126.963 | −0.167719 | −0.0838593 | − | 0.996478i | \(-0.526725\pi\) | ||||
−0.0838593 | + | 0.996478i | \(0.526725\pi\) | |||||||
\(758\) | − | 435.305i | − | 0.574281i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 191.532i | 0.252015i | ||||||||
\(761\) | −615.423 | −0.808703 | −0.404351 | − | 0.914604i | \(-0.632503\pi\) | ||||
−0.404351 | + | 0.914604i | \(0.632503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 12.0619i | − | 0.0158085i | ||||||
\(764\) | 806.236i | 1.05528i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.7251i | 0.0257508i | ||||||||
\(767\) | 503.528 | − | 551.343i | 0.656490 | − | 0.718831i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 986.655i | 1.28304i | 0.767108 | + | 0.641518i | \(0.221695\pi\) | ||||
−0.767108 | + | 0.641518i | \(0.778305\pi\) | |||||||
\(770\) | 5.41255 | 0.00702929 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 33.0416 | 0.0428000 | ||||||||
\(773\) | 6.18406i | 0.00800008i | 0.999992 | + | 0.00400004i | \(0.00127326\pi\) | ||||
−0.999992 | + | 0.00400004i | \(0.998727\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 107.042i | − | 0.138118i | ||||||
\(776\) | 913.604 | 1.17733 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 335.206i | 0.430856i | ||||||||
\(779\) | −147.599 | −0.189473 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 24.6262i | − | 0.0315316i | ||||||
\(782\) | −29.9367 | −0.0382822 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −153.526 | −0.195824 | ||||||||
\(785\) | 817.751i | 1.04172i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 545.010 | 0.692516 | 0.346258 | − | 0.938139i | \(-0.387452\pi\) | ||||
0.346258 | + | 0.938139i | \(0.387452\pi\) | |||||||
\(788\) | 760.089 | 0.964580 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 226.729i | 0.286999i | ||||||||
\(791\) | − | 178.820i | − | 0.226068i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1108.98 | −1.39846 | ||||||||
\(794\) | −210.335 | −0.264905 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 463.486 | 0.582268 | ||||||||
\(797\) | 722.233i | 0.906190i | 0.891462 | + | 0.453095i | \(0.149680\pi\) | ||||
−0.891462 | + | 0.453095i | \(0.850320\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.90791i | 0.00489100i | ||||||||
\(800\) | − | 459.599i | − | 0.574499i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −161.031 | −0.200786 | ||||||||
\(803\) | 55.5375 | 0.0691625 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 138.317i | 0.171823i | ||||||||
\(806\) | − | 106.123i | − | 0.131666i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −289.629 | −0.358452 | ||||||||
\(809\) | 1019.92i | 1.26071i | 0.776305 | + | 0.630357i | \(0.217092\pi\) | ||||
−0.776305 | + | 0.630357i | \(0.782908\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1310.48i | − | 1.61588i | −0.589267 | − | 0.807939i | \(-0.700583\pi\) | ||
0.589267 | − | 0.807939i | \(-0.299417\pi\) | |||||||
\(812\) | 26.0559 | 0.0320886 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.2156i | 0.0272919i | ||||||||
\(815\) | −682.696 | −0.837664 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 379.329i | − | 0.464295i | ||||||
\(818\) | −528.074 | −0.645567 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −179.249 | −0.218596 | ||||||||
\(821\) | − | 504.163i | − | 0.614084i | −0.951696 | − | 0.307042i | \(-0.900661\pi\) | ||
0.951696 | − | 0.307042i | \(-0.0993392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 307.365i | 0.373469i | 0.982410 | + | 0.186734i | \(0.0597904\pi\) | ||||
−0.982410 | + | 0.186734i | \(0.940210\pi\) | |||||||
\(824\) | 421.327 | 0.511319 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −53.0041 | + | 58.0374i | −0.0641696 | + | 0.0702631i | ||||
\(827\) | 940.910 | 1.13774 | 0.568869 | − | 0.822428i | \(-0.307381\pi\) | ||||
0.568869 | + | 0.822428i | \(0.307381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 398.747 | 0.480997 | 0.240499 | − | 0.970649i | \(-0.422689\pi\) | ||||
0.240499 | + | 0.970649i | \(0.422689\pi\) | |||||||
\(830\) | −82.7823 | −0.0997377 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 292.025i | − | 0.350992i | ||||||
\(833\) | −38.7244 | −0.0464879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −336.592 | −0.403104 | ||||||||
\(836\) | 26.6051i | 0.0318242i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 427.969 | 0.510703 | ||||||||
\(839\) | − | 1542.84i | − | 1.83890i | −0.393203 | − | 0.919452i | \(-0.628633\pi\) | ||
0.393203 | − | 0.919452i | \(-0.371367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −784.237 | −0.932505 | ||||||||
\(842\) | −592.269 | −0.703407 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 437.572i | − | 0.518451i | ||||||
\(845\) | −29.4937 | −0.0349038 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −146.573 | −0.173049 | ||||||||
\(848\) | 157.524 | 0.185760 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 12.2809i | − | 0.0144481i | ||||||
\(851\) | −567.717 | −0.667118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −362.614 | −0.425105 | −0.212552 | − | 0.977150i | \(-0.568178\pi\) | ||||
−0.212552 | + | 0.977150i | \(0.568178\pi\) | |||||||
\(854\) | 116.737 | 0.136694 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 257.834i | − | 0.301208i | ||||||
\(857\) | 1243.72i | 1.45124i | 0.688093 | + | 0.725622i | \(0.258448\pi\) | ||||
−0.688093 | + | 0.725622i | \(0.741552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1101.40i | − | 1.28218i | −0.767464 | − | 0.641092i | \(-0.778482\pi\) | ||
0.767464 | − | 0.641092i | \(-0.221518\pi\) | |||||||
\(860\) | − | 460.668i | − | 0.535661i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 701.564 | 0.813880 | ||||||||
\(863\) | 1561.83i | 1.80977i | 0.425654 | + | 0.904886i | \(0.360044\pi\) | ||||
−0.425654 | + | 0.904886i | \(0.639956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 642.148i | 0.742368i | ||||||||
\(866\) | − | 478.442i | − | 0.552473i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 26.6970i | − | 0.0307569i | ||||||
\(869\) | 76.1669i | 0.0876489i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 539.976 | 0.619949 | ||||||||
\(872\) | −72.8649 | −0.0835606 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 284.493 | 0.325507 | ||||||||
\(875\) | −159.043 | −0.181764 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1001.36 | 1.14181 | 0.570903 | − | 0.821017i | \(-0.306593\pi\) | ||||
0.570903 | + | 0.821017i | \(0.306593\pi\) | |||||||
\(878\) | − | 887.949i | − | 1.01133i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.1330i | 0.0149238i | ||||||||
\(881\) | − | 9.37327i | − | 0.0106394i | −0.999986 | − | 0.00531968i | \(-0.998307\pi\) | ||
0.999986 | − | 0.00531968i | \(-0.00169331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1323.52 | −1.49889 | −0.749445 | − | 0.662067i | \(-0.769679\pi\) | ||||
−0.749445 | + | 0.662067i | \(0.769679\pi\) | |||||||
\(884\) | 29.0975i | 0.0329157i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −568.109 | −0.641207 | ||||||||
\(887\) | 351.395i | 0.396161i | 0.980186 | + | 0.198081i | \(0.0634708\pi\) | ||||
−0.980186 | + | 0.198081i | \(0.936529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −178.839 | −0.201168 | ||||||||
\(890\) | −202.609 | −0.227650 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 600.090 | 0.672747 | ||||||||
\(893\) | − | 37.1375i | − | 0.0415873i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 221.574i | 0.247569i | ||||||||
\(896\) | − | 131.852i | − | 0.147156i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 783.829i | 0.872860i | ||||||||
\(899\) | − | 58.1601i | − | 0.0646942i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.7328 | 0.0440986 | ||||||||
\(902\) | 25.1970 | 0.0279346 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1080.24 | −1.19495 | ||||||||
\(905\) | −336.378 | −0.371689 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1042.34 | 1.14922 | 0.574610 | − | 0.818427i | \(-0.305154\pi\) | ||||
0.574610 | + | 0.818427i | \(0.305154\pi\) | |||||||
\(908\) | 769.510i | 0.847478i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −56.2550 | −0.0618187 | ||||||||
\(911\) | 1072.22 | 1.17697 | 0.588483 | − | 0.808510i | \(-0.299725\pi\) | ||||
0.588483 | + | 0.808510i | \(0.299725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.8097 | −0.0304597 | ||||||||
\(914\) | −976.613 | −1.06850 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 988.558i | 1.07921i | ||||||||
\(917\) | − | 37.5229i | − | 0.0409192i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 321.264i | 0.349580i | 0.984606 | + | 0.174790i | \(0.0559247\pi\) | ||||
−0.984606 | + | 0.174790i | \(0.944075\pi\) | |||||||
\(920\) | 835.563 | 0.908220 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 137.457i | − | 0.149086i | ||||||
\(923\) | 255.950i | 0.277303i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 232.894i | − | 0.251778i | ||||||
\(926\) | −183.909 | −0.198606 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 249.719i | − | 0.269094i | ||||||
\(929\) | 537.335i | 0.578402i | 0.957268 | + | 0.289201i | \(0.0933896\pi\) | ||||
−0.957268 | + | 0.289201i | \(0.906610\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 368.005 | 0.395279 | ||||||||
\(932\) | 4.63641i | 0.00497469i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 107.430 | 0.115021 | ||||||||
\(935\) | 3.31258i | 0.00354286i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 200.809i | − | 0.214311i | −0.994242 | − | 0.107155i | \(-0.965826\pi\) | ||
0.994242 | − | 0.107155i | \(-0.0341742\pi\) | |||||||
\(938\) | −56.8407 | −0.0605978 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 45.1008i | − | 0.0479796i | ||||||
\(941\) | 1718.91i | 1.82668i | 0.407197 | + | 0.913340i | \(0.366506\pi\) | ||||
−0.407197 | + | 0.913340i | \(0.633494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 643.907i | 0.682828i | ||||||||
\(944\) | −140.822 | − | 128.609i | −0.149175 | − | 0.136238i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64.7560i | 0.0684524i | ||||||||
\(947\) | −684.394 | −0.722696 | −0.361348 | − | 0.932431i | \(-0.617683\pi\) | ||||
−0.361348 | + | 0.932431i | \(0.617683\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −577.225 | −0.608245 | ||||||||
\(950\) | 116.708i | 0.122850i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 7.40758i | − | 0.00778107i | ||||||
\(953\) | 1256.84 | 1.31882 | 0.659412 | − | 0.751781i | \(-0.270805\pi\) | ||||
0.659412 | + | 0.751781i | \(0.270805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 953.965i | − | 0.998916i | ||||||
\(956\) | 210.206 | 0.219880 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 98.8871i | 0.103222i | ||||||||
\(959\) | −48.3818 | −0.0504503 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 901.409 | 0.937990 | ||||||||
\(962\) | − | 230.896i | − | 0.240017i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −159.216 | −0.165162 | ||||||||
\(965\) | −39.0959 | −0.0405139 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1449.89i | 1.49937i | 0.661797 | + | 0.749683i | \(0.269794\pi\) | ||||
−0.661797 | + | 0.749683i | \(0.730206\pi\) | |||||||
\(968\) | 885.434i | 0.914705i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −446.985 | −0.460809 | ||||||||
\(971\) | −947.360 | −0.975654 | −0.487827 | − | 0.872940i | \(-0.662210\pi\) | ||||
−0.487827 | + | 0.872940i | \(0.662210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −114.734 | −0.117918 | ||||||||
\(974\) | − | 78.8941i | − | 0.0810001i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 283.250i | 0.290215i | ||||||||
\(977\) | − | 914.983i | − | 0.936523i | −0.883590 | − | 0.468261i | \(-0.844881\pi\) | ||
0.883590 | − | 0.468261i | \(-0.155119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.0640 | −0.0695240 | ||||||||
\(980\) | 446.915 | 0.456036 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 293.209i | 0.298583i | ||||||||
\(983\) | 729.129i | 0.741738i | 0.928685 | + | 0.370869i | \(0.120940\pi\) | ||||
−0.928685 | + | 0.370869i | \(0.879060\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −899.362 | −0.913058 | ||||||||
\(986\) | − | 6.67273i | − | 0.00676747i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 276.518i | − | 0.279877i | ||||||
\(989\) | −1654.83 | −1.67324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1025.34i | 1.03465i | 0.855788 | + | 0.517327i | \(0.173073\pi\) | ||||
−0.855788 | + | 0.517327i | \(0.826927\pi\) | |||||||
\(992\) | −255.863 | −0.257927 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 26.9427i | − | 0.0271053i | ||||||
\(995\) | −548.411 | −0.551167 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 626.916 | 0.628802 | 0.314401 | − | 0.949290i | \(-0.398196\pi\) | ||||
0.314401 | + | 0.949290i | \(0.398196\pi\) | |||||||
\(998\) | 238.748i | 0.239227i | ||||||||
\(999\) | 0 | 0 |
(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 | 531.3.c.c.235.12 | 20 | ||
3.2 | odd | 2 | 177.3.c.a.58.9 | ✓ | 20 | ||
59.58 | odd | 2 | inner | 531.3.c.c.235.9 | 20 | ||
177.176 | even | 2 | 177.3.c.a.58.12 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.9 | ✓ | 20 | 3.2 | odd | 2 | ||
177.3.c.a.58.12 | yes | 20 | 177.176 | even | 2 | ||
531.3.c.c.235.9 | 20 | 59.58 | odd | 2 | inner | ||
531.3.c.c.235.12 | 20 | 1.1 | even | 1 | trivial |