Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4030.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 46x^{6} + 80x^{5} - 212x^{4} - 133x^{3} + 294x^{2} + 52x - 112 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.25457\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4030.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.25457 | −1.87903 | −0.939513 | − | 0.342514i | \(-0.888721\pi\) | ||||
−0.939513 | + | 0.342514i | \(0.888721\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.25457 | 1.32867 | ||||||||
\(7\) | −1.51784 | −0.573689 | −0.286845 | − | 0.957977i | \(-0.592606\pi\) | ||||
−0.286845 | + | 0.957977i | \(0.592606\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.59221 | 2.53074 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.88520 | −0.869921 | −0.434961 | − | 0.900449i | \(-0.643238\pi\) | ||||
−0.434961 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(12\) | −3.25457 | −0.939513 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.51784 | 0.405660 | ||||||||
\(15\) | 3.25457 | 0.840326 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.75666 | −0.426053 | −0.213026 | − | 0.977046i | \(-0.568332\pi\) | ||||
−0.213026 | + | 0.977046i | \(0.568332\pi\) | |||||||
\(18\) | −7.59221 | −1.78950 | ||||||||
\(19\) | −4.82261 | −1.10638 | −0.553191 | − | 0.833054i | \(-0.686590\pi\) | ||||
−0.553191 | + | 0.833054i | \(0.686590\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 4.93991 | 1.07798 | ||||||||
\(22\) | 2.88520 | 0.615127 | ||||||||
\(23\) | −1.81249 | −0.377931 | −0.188966 | − | 0.981984i | \(-0.560513\pi\) | ||||
−0.188966 | + | 0.981984i | \(0.560513\pi\) | |||||||
\(24\) | 3.25457 | 0.664336 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −14.9456 | −2.87629 | ||||||||
\(28\) | −1.51784 | −0.286845 | ||||||||
\(29\) | −1.34372 | −0.249522 | −0.124761 | − | 0.992187i | \(-0.539816\pi\) | ||||
−0.124761 | + | 0.992187i | \(0.539816\pi\) | |||||||
\(30\) | −3.25457 | −0.594200 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 9.39008 | 1.63460 | ||||||||
\(34\) | 1.75666 | 0.301265 | ||||||||
\(35\) | 1.51784 | 0.256562 | ||||||||
\(36\) | 7.59221 | 1.26537 | ||||||||
\(37\) | 6.10218 | 1.00319 | 0.501596 | − | 0.865102i | \(-0.332746\pi\) | ||||
0.501596 | + | 0.865102i | \(0.332746\pi\) | |||||||
\(38\) | 4.82261 | 0.782331 | ||||||||
\(39\) | 3.25457 | 0.521148 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 8.61726 | 1.34579 | 0.672895 | − | 0.739738i | \(-0.265051\pi\) | ||||
0.672895 | + | 0.739738i | \(0.265051\pi\) | |||||||
\(42\) | −4.93991 | −0.762245 | ||||||||
\(43\) | −8.63631 | −1.31703 | −0.658513 | − | 0.752570i | \(-0.728814\pi\) | ||||
−0.658513 | + | 0.752570i | \(0.728814\pi\) | |||||||
\(44\) | −2.88520 | −0.434961 | ||||||||
\(45\) | −7.59221 | −1.13178 | ||||||||
\(46\) | 1.81249 | 0.267238 | ||||||||
\(47\) | −8.82339 | −1.28702 | −0.643512 | − | 0.765436i | \(-0.722523\pi\) | ||||
−0.643512 | + | 0.765436i | \(0.722523\pi\) | |||||||
\(48\) | −3.25457 | −0.469756 | ||||||||
\(49\) | −4.69616 | −0.670880 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 5.71717 | 0.800564 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 5.04595 | 0.693114 | 0.346557 | − | 0.938029i | \(-0.387351\pi\) | ||||
0.346557 | + | 0.938029i | \(0.387351\pi\) | |||||||
\(54\) | 14.9456 | 2.03384 | ||||||||
\(55\) | 2.88520 | 0.389041 | ||||||||
\(56\) | 1.51784 | 0.202830 | ||||||||
\(57\) | 15.6955 | 2.07892 | ||||||||
\(58\) | 1.34372 | 0.176439 | ||||||||
\(59\) | 0.167892 | 0.0218577 | 0.0109288 | − | 0.999940i | \(-0.496521\pi\) | ||||
0.0109288 | + | 0.999940i | \(0.496521\pi\) | |||||||
\(60\) | 3.25457 | 0.420163 | ||||||||
\(61\) | −12.5603 | −1.60818 | −0.804091 | − | 0.594506i | \(-0.797348\pi\) | ||||
−0.804091 | + | 0.594506i | \(0.797348\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | −11.5238 | −1.45186 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | −9.39008 | −1.15584 | ||||||||
\(67\) | −9.70815 | −1.18604 | −0.593020 | − | 0.805188i | \(-0.702064\pi\) | ||||
−0.593020 | + | 0.805188i | \(0.702064\pi\) | |||||||
\(68\) | −1.75666 | −0.213026 | ||||||||
\(69\) | 5.89888 | 0.710142 | ||||||||
\(70\) | −1.51784 | −0.181417 | ||||||||
\(71\) | −3.09566 | −0.367387 | −0.183694 | − | 0.982984i | \(-0.558805\pi\) | ||||
−0.183694 | + | 0.982984i | \(0.558805\pi\) | |||||||
\(72\) | −7.59221 | −0.894750 | ||||||||
\(73\) | −14.9215 | −1.74643 | −0.873217 | − | 0.487332i | \(-0.837970\pi\) | ||||
−0.873217 | + | 0.487332i | \(0.837970\pi\) | |||||||
\(74\) | −6.10218 | −0.709364 | ||||||||
\(75\) | −3.25457 | −0.375805 | ||||||||
\(76\) | −4.82261 | −0.553191 | ||||||||
\(77\) | 4.37927 | 0.499065 | ||||||||
\(78\) | −3.25457 | −0.368507 | ||||||||
\(79\) | 7.76579 | 0.873720 | 0.436860 | − | 0.899530i | \(-0.356091\pi\) | ||||
0.436860 | + | 0.899530i | \(0.356091\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 25.8650 | 2.87389 | ||||||||
\(82\) | −8.61726 | −0.951617 | ||||||||
\(83\) | −9.01972 | −0.990043 | −0.495021 | − | 0.868881i | \(-0.664840\pi\) | ||||
−0.495021 | + | 0.868881i | \(0.664840\pi\) | |||||||
\(84\) | 4.93991 | 0.538988 | ||||||||
\(85\) | 1.75666 | 0.190537 | ||||||||
\(86\) | 8.63631 | 0.931278 | ||||||||
\(87\) | 4.37321 | 0.468858 | ||||||||
\(88\) | 2.88520 | 0.307564 | ||||||||
\(89\) | 10.3332 | 1.09532 | 0.547661 | − | 0.836701i | \(-0.315518\pi\) | ||||
0.547661 | + | 0.836701i | \(0.315518\pi\) | |||||||
\(90\) | 7.59221 | 0.800289 | ||||||||
\(91\) | 1.51784 | 0.159113 | ||||||||
\(92\) | −1.81249 | −0.188966 | ||||||||
\(93\) | −3.25457 | −0.337483 | ||||||||
\(94\) | 8.82339 | 0.910063 | ||||||||
\(95\) | 4.82261 | 0.494789 | ||||||||
\(96\) | 3.25457 | 0.332168 | ||||||||
\(97\) | −18.0929 | −1.83706 | −0.918529 | − | 0.395354i | \(-0.870622\pi\) | ||||
−0.918529 | + | 0.395354i | \(0.870622\pi\) | |||||||
\(98\) | 4.69616 | 0.474384 | ||||||||
\(99\) | −21.9051 | −2.20154 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −19.0906 | −1.89959 | −0.949794 | − | 0.312877i | \(-0.898707\pi\) | ||||
−0.949794 | + | 0.312877i | \(0.898707\pi\) | |||||||
\(102\) | −5.71717 | −0.566084 | ||||||||
\(103\) | −10.2723 | −1.01216 | −0.506080 | − | 0.862486i | \(-0.668906\pi\) | ||||
−0.506080 | + | 0.862486i | \(0.668906\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −4.93991 | −0.482086 | ||||||||
\(106\) | −5.04595 | −0.490106 | ||||||||
\(107\) | 0.752780 | 0.0727740 | 0.0363870 | − | 0.999338i | \(-0.488415\pi\) | ||||
0.0363870 | + | 0.999338i | \(0.488415\pi\) | |||||||
\(108\) | −14.9456 | −1.43815 | ||||||||
\(109\) | −0.215107 | −0.0206036 | −0.0103018 | − | 0.999947i | \(-0.503279\pi\) | ||||
−0.0103018 | + | 0.999947i | \(0.503279\pi\) | |||||||
\(110\) | −2.88520 | −0.275093 | ||||||||
\(111\) | −19.8599 | −1.88502 | ||||||||
\(112\) | −1.51784 | −0.143422 | ||||||||
\(113\) | −11.0171 | −1.03640 | −0.518201 | − | 0.855259i | \(-0.673398\pi\) | ||||
−0.518201 | + | 0.855259i | \(0.673398\pi\) | |||||||
\(114\) | −15.6955 | −1.47002 | ||||||||
\(115\) | 1.81249 | 0.169016 | ||||||||
\(116\) | −1.34372 | −0.124761 | ||||||||
\(117\) | −7.59221 | −0.701900 | ||||||||
\(118\) | −0.167892 | −0.0154557 | ||||||||
\(119\) | 2.66633 | 0.244422 | ||||||||
\(120\) | −3.25457 | −0.297100 | ||||||||
\(121\) | −2.67561 | −0.243237 | ||||||||
\(122\) | 12.5603 | 1.13716 | ||||||||
\(123\) | −28.0455 | −2.52877 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 11.5238 | 1.02662 | ||||||||
\(127\) | −1.84777 | −0.163963 | −0.0819814 | − | 0.996634i | \(-0.526125\pi\) | ||||
−0.0819814 | + | 0.996634i | \(0.526125\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 28.1075 | 2.47472 | ||||||||
\(130\) | −1.00000 | −0.0877058 | ||||||||
\(131\) | 7.86380 | 0.687063 | 0.343532 | − | 0.939141i | \(-0.388377\pi\) | ||||
0.343532 | + | 0.939141i | \(0.388377\pi\) | |||||||
\(132\) | 9.39008 | 0.817302 | ||||||||
\(133\) | 7.31995 | 0.634720 | ||||||||
\(134\) | 9.70815 | 0.838656 | ||||||||
\(135\) | 14.9456 | 1.28632 | ||||||||
\(136\) | 1.75666 | 0.150632 | ||||||||
\(137\) | 13.3808 | 1.14320 | 0.571600 | − | 0.820533i | \(-0.306323\pi\) | ||||
0.571600 | + | 0.820533i | \(0.306323\pi\) | |||||||
\(138\) | −5.89888 | −0.502146 | ||||||||
\(139\) | 4.40179 | 0.373355 | 0.186678 | − | 0.982421i | \(-0.440228\pi\) | ||||
0.186678 | + | 0.982421i | \(0.440228\pi\) | |||||||
\(140\) | 1.51784 | 0.128281 | ||||||||
\(141\) | 28.7163 | 2.41835 | ||||||||
\(142\) | 3.09566 | 0.259782 | ||||||||
\(143\) | 2.88520 | 0.241273 | ||||||||
\(144\) | 7.59221 | 0.632684 | ||||||||
\(145\) | 1.34372 | 0.111590 | ||||||||
\(146\) | 14.9215 | 1.23491 | ||||||||
\(147\) | 15.2840 | 1.26060 | ||||||||
\(148\) | 6.10218 | 0.501596 | ||||||||
\(149\) | 0.984443 | 0.0806487 | 0.0403244 | − | 0.999187i | \(-0.487161\pi\) | ||||
0.0403244 | + | 0.999187i | \(0.487161\pi\) | |||||||
\(150\) | 3.25457 | 0.265734 | ||||||||
\(151\) | 3.33309 | 0.271243 | 0.135621 | − | 0.990761i | \(-0.456697\pi\) | ||||
0.135621 | + | 0.990761i | \(0.456697\pi\) | |||||||
\(152\) | 4.82261 | 0.391165 | ||||||||
\(153\) | −13.3369 | −1.07823 | ||||||||
\(154\) | −4.37927 | −0.352892 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 3.25457 | 0.260574 | ||||||||
\(157\) | −14.2429 | −1.13671 | −0.568355 | − | 0.822783i | \(-0.692420\pi\) | ||||
−0.568355 | + | 0.822783i | \(0.692420\pi\) | |||||||
\(158\) | −7.76579 | −0.617813 | ||||||||
\(159\) | −16.4224 | −1.30238 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.75108 | 0.216815 | ||||||||
\(162\) | −25.8650 | −2.03215 | ||||||||
\(163\) | 4.45499 | 0.348941 | 0.174471 | − | 0.984662i | \(-0.444179\pi\) | ||||
0.174471 | + | 0.984662i | \(0.444179\pi\) | |||||||
\(164\) | 8.61726 | 0.672895 | ||||||||
\(165\) | −9.39008 | −0.731017 | ||||||||
\(166\) | 9.01972 | 0.700066 | ||||||||
\(167\) | 23.1918 | 1.79464 | 0.897318 | − | 0.441384i | \(-0.145512\pi\) | ||||
0.897318 | + | 0.441384i | \(0.145512\pi\) | |||||||
\(168\) | −4.93991 | −0.381122 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.75666 | −0.134730 | ||||||||
\(171\) | −36.6143 | −2.79996 | ||||||||
\(172\) | −8.63631 | −0.658513 | ||||||||
\(173\) | −19.9078 | −1.51356 | −0.756780 | − | 0.653670i | \(-0.773229\pi\) | ||||
−0.756780 | + | 0.653670i | \(0.773229\pi\) | |||||||
\(174\) | −4.37321 | −0.331532 | ||||||||
\(175\) | −1.51784 | −0.114738 | ||||||||
\(176\) | −2.88520 | −0.217480 | ||||||||
\(177\) | −0.546416 | −0.0410712 | ||||||||
\(178\) | −10.3332 | −0.774509 | ||||||||
\(179\) | −1.80189 | −0.134680 | −0.0673399 | − | 0.997730i | \(-0.521451\pi\) | ||||
−0.0673399 | + | 0.997730i | \(0.521451\pi\) | |||||||
\(180\) | −7.59221 | −0.565890 | ||||||||
\(181\) | 15.5429 | 1.15529 | 0.577647 | − | 0.816287i | \(-0.303971\pi\) | ||||
0.577647 | + | 0.816287i | \(0.303971\pi\) | |||||||
\(182\) | −1.51784 | −0.112510 | ||||||||
\(183\) | 40.8784 | 3.02182 | ||||||||
\(184\) | 1.81249 | 0.133619 | ||||||||
\(185\) | −6.10218 | −0.448641 | ||||||||
\(186\) | 3.25457 | 0.238636 | ||||||||
\(187\) | 5.06832 | 0.370632 | ||||||||
\(188\) | −8.82339 | −0.643512 | ||||||||
\(189\) | 22.6851 | 1.65010 | ||||||||
\(190\) | −4.82261 | −0.349869 | ||||||||
\(191\) | −16.3449 | −1.18268 | −0.591338 | − | 0.806424i | \(-0.701400\pi\) | ||||
−0.591338 | + | 0.806424i | \(0.701400\pi\) | |||||||
\(192\) | −3.25457 | −0.234878 | ||||||||
\(193\) | −8.01480 | −0.576918 | −0.288459 | − | 0.957492i | \(-0.593143\pi\) | ||||
−0.288459 | + | 0.957492i | \(0.593143\pi\) | |||||||
\(194\) | 18.0929 | 1.29900 | ||||||||
\(195\) | −3.25457 | −0.233064 | ||||||||
\(196\) | −4.69616 | −0.335440 | ||||||||
\(197\) | −2.33801 | −0.166576 | −0.0832881 | − | 0.996526i | \(-0.526542\pi\) | ||||
−0.0832881 | + | 0.996526i | \(0.526542\pi\) | |||||||
\(198\) | 21.9051 | 1.55672 | ||||||||
\(199\) | −20.5746 | −1.45849 | −0.729246 | − | 0.684252i | \(-0.760129\pi\) | ||||
−0.729246 | + | 0.684252i | \(0.760129\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 31.5958 | 2.22860 | ||||||||
\(202\) | 19.0906 | 1.34321 | ||||||||
\(203\) | 2.03955 | 0.143148 | ||||||||
\(204\) | 5.71717 | 0.400282 | ||||||||
\(205\) | −8.61726 | −0.601856 | ||||||||
\(206\) | 10.2723 | 0.715706 | ||||||||
\(207\) | −13.7608 | −0.956444 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 13.9142 | 0.962466 | ||||||||
\(210\) | 4.93991 | 0.340886 | ||||||||
\(211\) | −20.5706 | −1.41614 | −0.708068 | − | 0.706144i | \(-0.750433\pi\) | ||||
−0.708068 | + | 0.706144i | \(0.750433\pi\) | |||||||
\(212\) | 5.04595 | 0.346557 | ||||||||
\(213\) | 10.0750 | 0.690330 | ||||||||
\(214\) | −0.752780 | −0.0514590 | ||||||||
\(215\) | 8.63631 | 0.588992 | ||||||||
\(216\) | 14.9456 | 1.01692 | ||||||||
\(217\) | −1.51784 | −0.103038 | ||||||||
\(218\) | 0.215107 | 0.0145689 | ||||||||
\(219\) | 48.5631 | 3.28159 | ||||||||
\(220\) | 2.88520 | 0.194520 | ||||||||
\(221\) | 1.75666 | 0.118166 | ||||||||
\(222\) | 19.8599 | 1.33291 | ||||||||
\(223\) | 23.6432 | 1.58326 | 0.791632 | − | 0.610998i | \(-0.209232\pi\) | ||||
0.791632 | + | 0.610998i | \(0.209232\pi\) | |||||||
\(224\) | 1.51784 | 0.101415 | ||||||||
\(225\) | 7.59221 | 0.506147 | ||||||||
\(226\) | 11.0171 | 0.732847 | ||||||||
\(227\) | 2.65873 | 0.176466 | 0.0882331 | − | 0.996100i | \(-0.471878\pi\) | ||||
0.0882331 | + | 0.996100i | \(0.471878\pi\) | |||||||
\(228\) | 15.6955 | 1.03946 | ||||||||
\(229\) | 15.0027 | 0.991407 | 0.495704 | − | 0.868492i | \(-0.334910\pi\) | ||||
0.495704 | + | 0.868492i | \(0.334910\pi\) | |||||||
\(230\) | −1.81249 | −0.119512 | ||||||||
\(231\) | −14.2526 | −0.937755 | ||||||||
\(232\) | 1.34372 | 0.0882193 | ||||||||
\(233\) | 19.9130 | 1.30454 | 0.652271 | − | 0.757986i | \(-0.273816\pi\) | ||||
0.652271 | + | 0.757986i | \(0.273816\pi\) | |||||||
\(234\) | 7.59221 | 0.496318 | ||||||||
\(235\) | 8.82339 | 0.575575 | ||||||||
\(236\) | 0.167892 | 0.0109288 | ||||||||
\(237\) | −25.2743 | −1.64174 | ||||||||
\(238\) | −2.66633 | −0.172832 | ||||||||
\(239\) | 15.5385 | 1.00510 | 0.502551 | − | 0.864547i | \(-0.332395\pi\) | ||||
0.502551 | + | 0.864547i | \(0.332395\pi\) | |||||||
\(240\) | 3.25457 | 0.210081 | ||||||||
\(241\) | 0.0119521 | 0.000769900 0 | 0.000384950 | − | 1.00000i | \(-0.499877\pi\) | ||||
0.000384950 | 1.00000i | \(0.499877\pi\) | ||||||||
\(242\) | 2.67561 | 0.171995 | ||||||||
\(243\) | −39.3424 | −2.52382 | ||||||||
\(244\) | −12.5603 | −0.804091 | ||||||||
\(245\) | 4.69616 | 0.300027 | ||||||||
\(246\) | 28.0455 | 1.78811 | ||||||||
\(247\) | 4.82261 | 0.306855 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 29.3553 | 1.86032 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −25.9516 | −1.63805 | −0.819027 | − | 0.573755i | \(-0.805486\pi\) | ||||
−0.819027 | + | 0.573755i | \(0.805486\pi\) | |||||||
\(252\) | −11.5238 | −0.725928 | ||||||||
\(253\) | 5.22941 | 0.328770 | ||||||||
\(254\) | 1.84777 | 0.115939 | ||||||||
\(255\) | −5.71717 | −0.358023 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.6042 | 1.34763 | 0.673817 | − | 0.738898i | \(-0.264653\pi\) | ||||
0.673817 | + | 0.738898i | \(0.264653\pi\) | |||||||
\(258\) | −28.1075 | −1.74989 | ||||||||
\(259\) | −9.26212 | −0.575520 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | −10.2018 | −0.631474 | ||||||||
\(262\) | −7.86380 | −0.485827 | ||||||||
\(263\) | 11.1658 | 0.688512 | 0.344256 | − | 0.938876i | \(-0.388131\pi\) | ||||
0.344256 | + | 0.938876i | \(0.388131\pi\) | |||||||
\(264\) | −9.39008 | −0.577920 | ||||||||
\(265\) | −5.04595 | −0.309970 | ||||||||
\(266\) | −7.31995 | −0.448815 | ||||||||
\(267\) | −33.6302 | −2.05814 | ||||||||
\(268\) | −9.70815 | −0.593020 | ||||||||
\(269\) | −22.6580 | −1.38148 | −0.690740 | − | 0.723103i | \(-0.742715\pi\) | ||||
−0.690740 | + | 0.723103i | \(0.742715\pi\) | |||||||
\(270\) | −14.9456 | −0.909563 | ||||||||
\(271\) | 12.6515 | 0.768524 | 0.384262 | − | 0.923224i | \(-0.374456\pi\) | ||||
0.384262 | + | 0.923224i | \(0.374456\pi\) | |||||||
\(272\) | −1.75666 | −0.106513 | ||||||||
\(273\) | −4.93991 | −0.298977 | ||||||||
\(274\) | −13.3808 | −0.808364 | ||||||||
\(275\) | −2.88520 | −0.173984 | ||||||||
\(276\) | 5.89888 | 0.355071 | ||||||||
\(277\) | 25.7039 | 1.54440 | 0.772199 | − | 0.635381i | \(-0.219157\pi\) | ||||
0.772199 | + | 0.635381i | \(0.219157\pi\) | |||||||
\(278\) | −4.40179 | −0.264002 | ||||||||
\(279\) | 7.59221 | 0.454534 | ||||||||
\(280\) | −1.51784 | −0.0907083 | ||||||||
\(281\) | −1.64618 | −0.0982031 | −0.0491016 | − | 0.998794i | \(-0.515636\pi\) | ||||
−0.0491016 | + | 0.998794i | \(0.515636\pi\) | |||||||
\(282\) | −28.7163 | −1.71003 | ||||||||
\(283\) | 16.3504 | 0.971933 | 0.485967 | − | 0.873977i | \(-0.338468\pi\) | ||||
0.485967 | + | 0.873977i | \(0.338468\pi\) | |||||||
\(284\) | −3.09566 | −0.183694 | ||||||||
\(285\) | −15.6955 | −0.929722 | ||||||||
\(286\) | −2.88520 | −0.170606 | ||||||||
\(287\) | −13.0796 | −0.772065 | ||||||||
\(288\) | −7.59221 | −0.447375 | ||||||||
\(289\) | −13.9141 | −0.818479 | ||||||||
\(290\) | −1.34372 | −0.0789057 | ||||||||
\(291\) | 58.8846 | 3.45188 | ||||||||
\(292\) | −14.9215 | −0.873217 | ||||||||
\(293\) | 13.1221 | 0.766602 | 0.383301 | − | 0.923624i | \(-0.374787\pi\) | ||||
0.383301 | + | 0.923624i | \(0.374787\pi\) | |||||||
\(294\) | −15.2840 | −0.891380 | ||||||||
\(295\) | −0.167892 | −0.00977506 | ||||||||
\(296\) | −6.10218 | −0.354682 | ||||||||
\(297\) | 43.1212 | 2.50215 | ||||||||
\(298\) | −0.984443 | −0.0570273 | ||||||||
\(299\) | 1.81249 | 0.104819 | ||||||||
\(300\) | −3.25457 | −0.187903 | ||||||||
\(301\) | 13.1085 | 0.755564 | ||||||||
\(302\) | −3.33309 | −0.191798 | ||||||||
\(303\) | 62.1317 | 3.56937 | ||||||||
\(304\) | −4.82261 | −0.276596 | ||||||||
\(305\) | 12.5603 | 0.719201 | ||||||||
\(306\) | 13.3369 | 0.762422 | ||||||||
\(307\) | 9.05852 | 0.516997 | 0.258498 | − | 0.966012i | \(-0.416772\pi\) | ||||
0.258498 | + | 0.966012i | \(0.416772\pi\) | |||||||
\(308\) | 4.37927 | 0.249532 | ||||||||
\(309\) | 33.4319 | 1.90188 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | 5.03422 | 0.285464 | 0.142732 | − | 0.989761i | \(-0.454411\pi\) | ||||
0.142732 | + | 0.989761i | \(0.454411\pi\) | |||||||
\(312\) | −3.25457 | −0.184254 | ||||||||
\(313\) | 6.84388 | 0.386839 | 0.193419 | − | 0.981116i | \(-0.438042\pi\) | ||||
0.193419 | + | 0.981116i | \(0.438042\pi\) | |||||||
\(314\) | 14.2429 | 0.803775 | ||||||||
\(315\) | 11.5238 | 0.649290 | ||||||||
\(316\) | 7.76579 | 0.436860 | ||||||||
\(317\) | −20.3489 | −1.14291 | −0.571455 | − | 0.820634i | \(-0.693621\pi\) | ||||
−0.571455 | + | 0.820634i | \(0.693621\pi\) | |||||||
\(318\) | 16.4224 | 0.920921 | ||||||||
\(319\) | 3.87689 | 0.217064 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −2.44997 | −0.136744 | ||||||||
\(322\) | −2.75108 | −0.153311 | ||||||||
\(323\) | 8.47169 | 0.471377 | ||||||||
\(324\) | 25.8650 | 1.43694 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −4.45499 | −0.246739 | ||||||||
\(327\) | 0.700081 | 0.0387146 | ||||||||
\(328\) | −8.61726 | −0.475809 | ||||||||
\(329\) | 13.3925 | 0.738352 | ||||||||
\(330\) | 9.39008 | 0.516907 | ||||||||
\(331\) | −11.7549 | −0.646108 | −0.323054 | − | 0.946381i | \(-0.604710\pi\) | ||||
−0.323054 | + | 0.946381i | \(0.604710\pi\) | |||||||
\(332\) | −9.01972 | −0.495021 | ||||||||
\(333\) | 46.3290 | 2.53881 | ||||||||
\(334\) | −23.1918 | −1.26900 | ||||||||
\(335\) | 9.70815 | 0.530413 | ||||||||
\(336\) | 4.93991 | 0.269494 | ||||||||
\(337\) | −21.0243 | −1.14527 | −0.572634 | − | 0.819811i | \(-0.694078\pi\) | ||||
−0.572634 | + | 0.819811i | \(0.694078\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 35.8559 | 1.94742 | ||||||||
\(340\) | 1.75666 | 0.0952683 | ||||||||
\(341\) | −2.88520 | −0.156242 | ||||||||
\(342\) | 36.6143 | 1.97987 | ||||||||
\(343\) | 17.7529 | 0.958566 | ||||||||
\(344\) | 8.63631 | 0.465639 | ||||||||
\(345\) | −5.89888 | −0.317585 | ||||||||
\(346\) | 19.9078 | 1.07025 | ||||||||
\(347\) | −13.6654 | −0.733599 | −0.366800 | − | 0.930300i | \(-0.619547\pi\) | ||||
−0.366800 | + | 0.930300i | \(0.619547\pi\) | |||||||
\(348\) | 4.37321 | 0.234429 | ||||||||
\(349\) | −28.5515 | −1.52833 | −0.764163 | − | 0.645023i | \(-0.776848\pi\) | ||||
−0.764163 | + | 0.645023i | \(0.776848\pi\) | |||||||
\(350\) | 1.51784 | 0.0811319 | ||||||||
\(351\) | 14.9456 | 0.797740 | ||||||||
\(352\) | 2.88520 | 0.153782 | ||||||||
\(353\) | 5.00976 | 0.266643 | 0.133321 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133321 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(354\) | 0.546416 | 0.0290417 | ||||||||
\(355\) | 3.09566 | 0.164300 | ||||||||
\(356\) | 10.3332 | 0.547661 | ||||||||
\(357\) | −8.67775 | −0.459275 | ||||||||
\(358\) | 1.80189 | 0.0952330 | ||||||||
\(359\) | 27.6641 | 1.46006 | 0.730029 | − | 0.683417i | \(-0.239507\pi\) | ||||
0.730029 | + | 0.683417i | \(0.239507\pi\) | |||||||
\(360\) | 7.59221 | 0.400144 | ||||||||
\(361\) | 4.25757 | 0.224082 | ||||||||
\(362\) | −15.5429 | −0.816916 | ||||||||
\(363\) | 8.70795 | 0.457049 | ||||||||
\(364\) | 1.51784 | 0.0795564 | ||||||||
\(365\) | 14.9215 | 0.781029 | ||||||||
\(366\) | −40.8784 | −2.13675 | ||||||||
\(367\) | −9.00019 | −0.469806 | −0.234903 | − | 0.972019i | \(-0.575477\pi\) | ||||
−0.234903 | + | 0.972019i | \(0.575477\pi\) | |||||||
\(368\) | −1.81249 | −0.0944828 | ||||||||
\(369\) | 65.4240 | 3.40584 | ||||||||
\(370\) | 6.10218 | 0.317237 | ||||||||
\(371\) | −7.65894 | −0.397632 | ||||||||
\(372\) | −3.25457 | −0.168741 | ||||||||
\(373\) | 35.3130 | 1.82844 | 0.914218 | − | 0.405222i | \(-0.132806\pi\) | ||||
0.914218 | + | 0.405222i | \(0.132806\pi\) | |||||||
\(374\) | −5.06832 | −0.262077 | ||||||||
\(375\) | 3.25457 | 0.168065 | ||||||||
\(376\) | 8.82339 | 0.455032 | ||||||||
\(377\) | 1.34372 | 0.0692049 | ||||||||
\(378\) | −22.6851 | −1.16680 | ||||||||
\(379\) | −15.8928 | −0.816357 | −0.408179 | − | 0.912902i | \(-0.633836\pi\) | ||||
−0.408179 | + | 0.912902i | \(0.633836\pi\) | |||||||
\(380\) | 4.82261 | 0.247395 | ||||||||
\(381\) | 6.01368 | 0.308090 | ||||||||
\(382\) | 16.3449 | 0.836278 | ||||||||
\(383\) | −8.98324 | −0.459022 | −0.229511 | − | 0.973306i | \(-0.573713\pi\) | ||||
−0.229511 | + | 0.973306i | \(0.573713\pi\) | |||||||
\(384\) | 3.25457 | 0.166084 | ||||||||
\(385\) | −4.37927 | −0.223188 | ||||||||
\(386\) | 8.01480 | 0.407942 | ||||||||
\(387\) | −65.5687 | −3.33304 | ||||||||
\(388\) | −18.0929 | −0.918529 | ||||||||
\(389\) | 34.7293 | 1.76085 | 0.880423 | − | 0.474188i | \(-0.157258\pi\) | ||||
0.880423 | + | 0.474188i | \(0.157258\pi\) | |||||||
\(390\) | 3.25457 | 0.164801 | ||||||||
\(391\) | 3.18394 | 0.161019 | ||||||||
\(392\) | 4.69616 | 0.237192 | ||||||||
\(393\) | −25.5933 | −1.29101 | ||||||||
\(394\) | 2.33801 | 0.117787 | ||||||||
\(395\) | −7.76579 | −0.390739 | ||||||||
\(396\) | −21.9051 | −1.10077 | ||||||||
\(397\) | 2.31500 | 0.116187 | 0.0580933 | − | 0.998311i | \(-0.481498\pi\) | ||||
0.0580933 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(398\) | 20.5746 | 1.03131 | ||||||||
\(399\) | −23.8233 | −1.19265 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 29.9444 | 1.49535 | 0.747677 | − | 0.664063i | \(-0.231169\pi\) | ||||
0.747677 | + | 0.664063i | \(0.231169\pi\) | |||||||
\(402\) | −31.5958 | −1.57586 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | −19.0906 | −0.949794 | ||||||||
\(405\) | −25.8650 | −1.28524 | ||||||||
\(406\) | −2.03955 | −0.101221 | ||||||||
\(407\) | −17.6060 | −0.872698 | ||||||||
\(408\) | −5.71717 | −0.283042 | ||||||||
\(409\) | 24.5992 | 1.21635 | 0.608176 | − | 0.793802i | \(-0.291902\pi\) | ||||
0.608176 | + | 0.793802i | \(0.291902\pi\) | |||||||
\(410\) | 8.61726 | 0.425576 | ||||||||
\(411\) | −43.5487 | −2.14810 | ||||||||
\(412\) | −10.2723 | −0.506080 | ||||||||
\(413\) | −0.254833 | −0.0125395 | ||||||||
\(414\) | 13.7608 | 0.676308 | ||||||||
\(415\) | 9.01972 | 0.442761 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −14.3259 | −0.701544 | ||||||||
\(418\) | −13.9142 | −0.680566 | ||||||||
\(419\) | −14.7647 | −0.721304 | −0.360652 | − | 0.932701i | \(-0.617446\pi\) | ||||
−0.360652 | + | 0.932701i | \(0.617446\pi\) | |||||||
\(420\) | −4.93991 | −0.241043 | ||||||||
\(421\) | 13.1348 | 0.640152 | 0.320076 | − | 0.947392i | \(-0.396292\pi\) | ||||
0.320076 | + | 0.947392i | \(0.396292\pi\) | |||||||
\(422\) | 20.5706 | 1.00136 | ||||||||
\(423\) | −66.9890 | −3.25712 | ||||||||
\(424\) | −5.04595 | −0.245053 | ||||||||
\(425\) | −1.75666 | −0.0852106 | ||||||||
\(426\) | −10.0750 | −0.488137 | ||||||||
\(427\) | 19.0645 | 0.922597 | ||||||||
\(428\) | 0.752780 | 0.0363870 | ||||||||
\(429\) | −9.39008 | −0.453358 | ||||||||
\(430\) | −8.63631 | −0.416480 | ||||||||
\(431\) | 10.4912 | 0.505345 | 0.252672 | − | 0.967552i | \(-0.418691\pi\) | ||||
0.252672 | + | 0.967552i | \(0.418691\pi\) | |||||||
\(432\) | −14.9456 | −0.719073 | ||||||||
\(433\) | 28.8205 | 1.38503 | 0.692514 | − | 0.721405i | \(-0.256503\pi\) | ||||
0.692514 | + | 0.721405i | \(0.256503\pi\) | |||||||
\(434\) | 1.51784 | 0.0728586 | ||||||||
\(435\) | −4.37321 | −0.209680 | ||||||||
\(436\) | −0.215107 | −0.0103018 | ||||||||
\(437\) | 8.74095 | 0.418136 | ||||||||
\(438\) | −48.5631 | −2.32044 | ||||||||
\(439\) | −14.3101 | −0.682982 | −0.341491 | − | 0.939885i | \(-0.610932\pi\) | ||||
−0.341491 | + | 0.939885i | \(0.610932\pi\) | |||||||
\(440\) | −2.88520 | −0.137547 | ||||||||
\(441\) | −35.6542 | −1.69782 | ||||||||
\(442\) | −1.75666 | −0.0835558 | ||||||||
\(443\) | 32.7324 | 1.55516 | 0.777581 | − | 0.628782i | \(-0.216446\pi\) | ||||
0.777581 | + | 0.628782i | \(0.216446\pi\) | |||||||
\(444\) | −19.8599 | −0.942511 | ||||||||
\(445\) | −10.3332 | −0.489843 | ||||||||
\(446\) | −23.6432 | −1.11954 | ||||||||
\(447\) | −3.20394 | −0.151541 | ||||||||
\(448\) | −1.51784 | −0.0717112 | ||||||||
\(449\) | −4.57873 | −0.216084 | −0.108042 | − | 0.994146i | \(-0.534458\pi\) | ||||
−0.108042 | + | 0.994146i | \(0.534458\pi\) | |||||||
\(450\) | −7.59221 | −0.357900 | ||||||||
\(451\) | −24.8625 | −1.17073 | ||||||||
\(452\) | −11.0171 | −0.518201 | ||||||||
\(453\) | −10.8478 | −0.509672 | ||||||||
\(454\) | −2.65873 | −0.124780 | ||||||||
\(455\) | −1.51784 | −0.0711574 | ||||||||
\(456\) | −15.6955 | −0.735009 | ||||||||
\(457\) | −29.7216 | −1.39032 | −0.695158 | − | 0.718857i | \(-0.744666\pi\) | ||||
−0.695158 | + | 0.718857i | \(0.744666\pi\) | |||||||
\(458\) | −15.0027 | −0.701031 | ||||||||
\(459\) | 26.2544 | 1.22545 | ||||||||
\(460\) | 1.81249 | 0.0845080 | ||||||||
\(461\) | −15.4727 | −0.720634 | −0.360317 | − | 0.932830i | \(-0.617332\pi\) | ||||
−0.360317 | + | 0.932830i | \(0.617332\pi\) | |||||||
\(462\) | 14.2526 | 0.663093 | ||||||||
\(463\) | −11.8854 | −0.552360 | −0.276180 | − | 0.961106i | \(-0.589069\pi\) | ||||
−0.276180 | + | 0.961106i | \(0.589069\pi\) | |||||||
\(464\) | −1.34372 | −0.0623804 | ||||||||
\(465\) | 3.25457 | 0.150927 | ||||||||
\(466\) | −19.9130 | −0.922450 | ||||||||
\(467\) | 13.1182 | 0.607036 | 0.303518 | − | 0.952826i | \(-0.401839\pi\) | ||||
0.303518 | + | 0.952826i | \(0.401839\pi\) | |||||||
\(468\) | −7.59221 | −0.350950 | ||||||||
\(469\) | 14.7354 | 0.680418 | ||||||||
\(470\) | −8.82339 | −0.406993 | ||||||||
\(471\) | 46.3546 | 2.13591 | ||||||||
\(472\) | −0.167892 | −0.00772786 | ||||||||
\(473\) | 24.9175 | 1.14571 | ||||||||
\(474\) | 25.2743 | 1.16089 | ||||||||
\(475\) | −4.82261 | −0.221277 | ||||||||
\(476\) | 2.66633 | 0.122211 | ||||||||
\(477\) | 38.3099 | 1.75409 | ||||||||
\(478\) | −15.5385 | −0.710715 | ||||||||
\(479\) | −10.9823 | −0.501792 | −0.250896 | − | 0.968014i | \(-0.580725\pi\) | ||||
−0.250896 | + | 0.968014i | \(0.580725\pi\) | |||||||
\(480\) | −3.25457 | −0.148550 | ||||||||
\(481\) | −6.10218 | −0.278235 | ||||||||
\(482\) | −0.0119521 | −0.000544402 0 | ||||||||
\(483\) | −8.95356 | −0.407401 | ||||||||
\(484\) | −2.67561 | −0.121619 | ||||||||
\(485\) | 18.0929 | 0.821557 | ||||||||
\(486\) | 39.3424 | 1.78461 | ||||||||
\(487\) | 13.1634 | 0.596490 | 0.298245 | − | 0.954489i | \(-0.403599\pi\) | ||||
0.298245 | + | 0.954489i | \(0.403599\pi\) | |||||||
\(488\) | 12.5603 | 0.568578 | ||||||||
\(489\) | −14.4991 | −0.655670 | ||||||||
\(490\) | −4.69616 | −0.212151 | ||||||||
\(491\) | −13.7510 | −0.620576 | −0.310288 | − | 0.950643i | \(-0.600425\pi\) | ||||
−0.310288 | + | 0.950643i | \(0.600425\pi\) | |||||||
\(492\) | −28.0455 | −1.26439 | ||||||||
\(493\) | 2.36045 | 0.106309 | ||||||||
\(494\) | −4.82261 | −0.216979 | ||||||||
\(495\) | 21.9051 | 0.984559 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 4.69871 | 0.210766 | ||||||||
\(498\) | −29.3553 | −1.31544 | ||||||||
\(499\) | 5.02756 | 0.225064 | 0.112532 | − | 0.993648i | \(-0.464104\pi\) | ||||
0.112532 | + | 0.993648i | \(0.464104\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −75.4793 | −3.37217 | ||||||||
\(502\) | 25.9516 | 1.15828 | ||||||||
\(503\) | 30.3408 | 1.35283 | 0.676415 | − | 0.736521i | \(-0.263533\pi\) | ||||
0.676415 | + | 0.736521i | \(0.263533\pi\) | |||||||
\(504\) | 11.5238 | 0.513309 | ||||||||
\(505\) | 19.0906 | 0.849521 | ||||||||
\(506\) | −5.22941 | −0.232476 | ||||||||
\(507\) | −3.25457 | −0.144540 | ||||||||
\(508\) | −1.84777 | −0.0819814 | ||||||||
\(509\) | 22.0452 | 0.977136 | 0.488568 | − | 0.872526i | \(-0.337520\pi\) | ||||
0.488568 | + | 0.872526i | \(0.337520\pi\) | |||||||
\(510\) | 5.71717 | 0.253161 | ||||||||
\(511\) | 22.6485 | 1.00191 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 72.0770 | 3.18228 | ||||||||
\(514\) | −21.6042 | −0.952922 | ||||||||
\(515\) | 10.2723 | 0.452652 | ||||||||
\(516\) | 28.1075 | 1.23736 | ||||||||
\(517\) | 25.4573 | 1.11961 | ||||||||
\(518\) | 9.26212 | 0.406954 | ||||||||
\(519\) | 64.7912 | 2.84402 | ||||||||
\(520\) | −1.00000 | −0.0438529 | ||||||||
\(521\) | −14.1827 | −0.621354 | −0.310677 | − | 0.950516i | \(-0.600556\pi\) | ||||
−0.310677 | + | 0.950516i | \(0.600556\pi\) | |||||||
\(522\) | 10.2018 | 0.446519 | ||||||||
\(523\) | 11.9919 | 0.524371 | 0.262186 | − | 0.965017i | \(-0.415557\pi\) | ||||
0.262186 | + | 0.965017i | \(0.415557\pi\) | |||||||
\(524\) | 7.86380 | 0.343532 | ||||||||
\(525\) | 4.93991 | 0.215595 | ||||||||
\(526\) | −11.1658 | −0.486852 | ||||||||
\(527\) | −1.75666 | −0.0765213 | ||||||||
\(528\) | 9.39008 | 0.408651 | ||||||||
\(529\) | −19.7149 | −0.857168 | ||||||||
\(530\) | 5.04595 | 0.219182 | ||||||||
\(531\) | 1.27467 | 0.0553161 | ||||||||
\(532\) | 7.31995 | 0.317360 | ||||||||
\(533\) | −8.61726 | −0.373255 | ||||||||
\(534\) | 33.6302 | 1.45532 | ||||||||
\(535\) | −0.752780 | −0.0325455 | ||||||||
\(536\) | 9.70815 | 0.419328 | ||||||||
\(537\) | 5.86438 | 0.253067 | ||||||||
\(538\) | 22.6580 | 0.976854 | ||||||||
\(539\) | 13.5494 | 0.583613 | ||||||||
\(540\) | 14.9456 | 0.643158 | ||||||||
\(541\) | −17.1915 | −0.739122 | −0.369561 | − | 0.929207i | \(-0.620492\pi\) | ||||
−0.369561 | + | 0.929207i | \(0.620492\pi\) | |||||||
\(542\) | −12.6515 | −0.543429 | ||||||||
\(543\) | −50.5854 | −2.17083 | ||||||||
\(544\) | 1.75666 | 0.0753162 | ||||||||
\(545\) | 0.215107 | 0.00921419 | ||||||||
\(546\) | 4.93991 | 0.211409 | ||||||||
\(547\) | −32.8323 | −1.40381 | −0.701905 | − | 0.712271i | \(-0.747667\pi\) | ||||
−0.701905 | + | 0.712271i | \(0.747667\pi\) | |||||||
\(548\) | 13.3808 | 0.571600 | ||||||||
\(549\) | −95.3605 | −4.06988 | ||||||||
\(550\) | 2.88520 | 0.123025 | ||||||||
\(551\) | 6.48022 | 0.276067 | ||||||||
\(552\) | −5.89888 | −0.251073 | ||||||||
\(553\) | −11.7872 | −0.501244 | ||||||||
\(554\) | −25.7039 | −1.09205 | ||||||||
\(555\) | 19.8599 | 0.843008 | ||||||||
\(556\) | 4.40179 | 0.186678 | ||||||||
\(557\) | 38.9688 | 1.65116 | 0.825580 | − | 0.564285i | \(-0.190848\pi\) | ||||
0.825580 | + | 0.564285i | \(0.190848\pi\) | |||||||
\(558\) | −7.59221 | −0.321404 | ||||||||
\(559\) | 8.63631 | 0.365277 | ||||||||
\(560\) | 1.51784 | 0.0641404 | ||||||||
\(561\) | −16.4952 | −0.696428 | ||||||||
\(562\) | 1.64618 | 0.0694401 | ||||||||
\(563\) | −26.7868 | −1.12893 | −0.564464 | − | 0.825458i | \(-0.690917\pi\) | ||||
−0.564464 | + | 0.825458i | \(0.690917\pi\) | |||||||
\(564\) | 28.7163 | 1.20918 | ||||||||
\(565\) | 11.0171 | 0.463493 | ||||||||
\(566\) | −16.3504 | −0.687261 | ||||||||
\(567\) | −39.2589 | −1.64872 | ||||||||
\(568\) | 3.09566 | 0.129891 | ||||||||
\(569\) | 25.0563 | 1.05041 | 0.525207 | − | 0.850974i | \(-0.323988\pi\) | ||||
0.525207 | + | 0.850974i | \(0.323988\pi\) | |||||||
\(570\) | 15.6955 | 0.657412 | ||||||||
\(571\) | −42.3338 | −1.77161 | −0.885807 | − | 0.464053i | \(-0.846395\pi\) | ||||
−0.885807 | + | 0.464053i | \(0.846395\pi\) | |||||||
\(572\) | 2.88520 | 0.120636 | ||||||||
\(573\) | 53.1956 | 2.22228 | ||||||||
\(574\) | 13.0796 | 0.545933 | ||||||||
\(575\) | −1.81249 | −0.0755862 | ||||||||
\(576\) | 7.59221 | 0.316342 | ||||||||
\(577\) | 27.1552 | 1.13048 | 0.565242 | − | 0.824925i | \(-0.308783\pi\) | ||||
0.565242 | + | 0.824925i | \(0.308783\pi\) | |||||||
\(578\) | 13.9141 | 0.578752 | ||||||||
\(579\) | 26.0847 | 1.08404 | ||||||||
\(580\) | 1.34372 | 0.0557948 | ||||||||
\(581\) | 13.6905 | 0.567977 | ||||||||
\(582\) | −58.8846 | −2.44085 | ||||||||
\(583\) | −14.5586 | −0.602955 | ||||||||
\(584\) | 14.9215 | 0.617457 | ||||||||
\(585\) | 7.59221 | 0.313899 | ||||||||
\(586\) | −13.1221 | −0.542069 | ||||||||
\(587\) | 14.9418 | 0.616714 | 0.308357 | − | 0.951271i | \(-0.400221\pi\) | ||||
0.308357 | + | 0.951271i | \(0.400221\pi\) | |||||||
\(588\) | 15.2840 | 0.630301 | ||||||||
\(589\) | −4.82261 | −0.198712 | ||||||||
\(590\) | 0.167892 | 0.00691201 | ||||||||
\(591\) | 7.60921 | 0.313001 | ||||||||
\(592\) | 6.10218 | 0.250798 | ||||||||
\(593\) | 24.7525 | 1.01646 | 0.508232 | − | 0.861220i | \(-0.330299\pi\) | ||||
0.508232 | + | 0.861220i | \(0.330299\pi\) | |||||||
\(594\) | −43.1212 | −1.76928 | ||||||||
\(595\) | −2.66633 | −0.109309 | ||||||||
\(596\) | 0.984443 | 0.0403244 | ||||||||
\(597\) | 66.9613 | 2.74054 | ||||||||
\(598\) | −1.81249 | −0.0741184 | ||||||||
\(599\) | −11.0424 | −0.451181 | −0.225591 | − | 0.974222i | \(-0.572431\pi\) | ||||
−0.225591 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(600\) | 3.25457 | 0.132867 | ||||||||
\(601\) | 1.46009 | 0.0595581 | 0.0297791 | − | 0.999557i | \(-0.490520\pi\) | ||||
0.0297791 | + | 0.999557i | \(0.490520\pi\) | |||||||
\(602\) | −13.1085 | −0.534264 | ||||||||
\(603\) | −73.7063 | −3.00155 | ||||||||
\(604\) | 3.33309 | 0.135621 | ||||||||
\(605\) | 2.67561 | 0.108779 | ||||||||
\(606\) | −62.1317 | −2.52393 | ||||||||
\(607\) | 9.83217 | 0.399075 | 0.199538 | − | 0.979890i | \(-0.436056\pi\) | ||||
0.199538 | + | 0.979890i | \(0.436056\pi\) | |||||||
\(608\) | 4.82261 | 0.195583 | ||||||||
\(609\) | −6.63784 | −0.268979 | ||||||||
\(610\) | −12.5603 | −0.508552 | ||||||||
\(611\) | 8.82339 | 0.356956 | ||||||||
\(612\) | −13.3369 | −0.539114 | ||||||||
\(613\) | −12.0717 | −0.487570 | −0.243785 | − | 0.969829i | \(-0.578389\pi\) | ||||
−0.243785 | + | 0.969829i | \(0.578389\pi\) | |||||||
\(614\) | −9.05852 | −0.365572 | ||||||||
\(615\) | 28.0455 | 1.13090 | ||||||||
\(616\) | −4.37927 | −0.176446 | ||||||||
\(617\) | −35.5836 | −1.43254 | −0.716271 | − | 0.697822i | \(-0.754152\pi\) | ||||
−0.716271 | + | 0.697822i | \(0.754152\pi\) | |||||||
\(618\) | −33.4319 | −1.34483 | ||||||||
\(619\) | −16.7610 | −0.673683 | −0.336842 | − | 0.941561i | \(-0.609359\pi\) | ||||
−0.336842 | + | 0.941561i | \(0.609359\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | 27.0889 | 1.08704 | ||||||||
\(622\) | −5.03422 | −0.201854 | ||||||||
\(623\) | −15.6842 | −0.628374 | ||||||||
\(624\) | 3.25457 | 0.130287 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −6.84388 | −0.273536 | ||||||||
\(627\) | −45.2847 | −1.80850 | ||||||||
\(628\) | −14.2429 | −0.568355 | ||||||||
\(629\) | −10.7195 | −0.427413 | ||||||||
\(630\) | −11.5238 | −0.459117 | ||||||||
\(631\) | −39.0561 | −1.55480 | −0.777400 | − | 0.629006i | \(-0.783462\pi\) | ||||
−0.777400 | + | 0.629006i | \(0.783462\pi\) | |||||||
\(632\) | −7.76579 | −0.308907 | ||||||||
\(633\) | 66.9483 | 2.66096 | ||||||||
\(634\) | 20.3489 | 0.808159 | ||||||||
\(635\) | 1.84777 | 0.0733264 | ||||||||
\(636\) | −16.4224 | −0.651189 | ||||||||
\(637\) | 4.69616 | 0.186069 | ||||||||
\(638\) | −3.87689 | −0.153488 | ||||||||
\(639\) | −23.5029 | −0.929760 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 1.93474 | 0.0764176 | 0.0382088 | − | 0.999270i | \(-0.487835\pi\) | ||||
0.0382088 | + | 0.999270i | \(0.487835\pi\) | |||||||
\(642\) | 2.44997 | 0.0966928 | ||||||||
\(643\) | −13.9835 | −0.551457 | −0.275728 | − | 0.961236i | \(-0.588919\pi\) | ||||
−0.275728 | + | 0.961236i | \(0.588919\pi\) | |||||||
\(644\) | 2.75108 | 0.108408 | ||||||||
\(645\) | −28.1075 | −1.10673 | ||||||||
\(646\) | −8.47169 | −0.333314 | ||||||||
\(647\) | −7.20166 | −0.283126 | −0.141563 | − | 0.989929i | \(-0.545213\pi\) | ||||
−0.141563 | + | 0.989929i | \(0.545213\pi\) | |||||||
\(648\) | −25.8650 | −1.01607 | ||||||||
\(649\) | −0.484403 | −0.0190145 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | 4.93991 | 0.193610 | ||||||||
\(652\) | 4.45499 | 0.174471 | ||||||||
\(653\) | 17.4178 | 0.681612 | 0.340806 | − | 0.940134i | \(-0.389300\pi\) | ||||
0.340806 | + | 0.940134i | \(0.389300\pi\) | |||||||
\(654\) | −0.700081 | −0.0273754 | ||||||||
\(655\) | −7.86380 | −0.307264 | ||||||||
\(656\) | 8.61726 | 0.336447 | ||||||||
\(657\) | −113.287 | −4.41976 | ||||||||
\(658\) | −13.3925 | −0.522094 | ||||||||
\(659\) | 33.3649 | 1.29971 | 0.649857 | − | 0.760057i | \(-0.274829\pi\) | ||||
0.649857 | + | 0.760057i | \(0.274829\pi\) | |||||||
\(660\) | −9.39008 | −0.365509 | ||||||||
\(661\) | 1.59456 | 0.0620212 | 0.0310106 | − | 0.999519i | \(-0.490127\pi\) | ||||
0.0310106 | + | 0.999519i | \(0.490127\pi\) | |||||||
\(662\) | 11.7549 | 0.456867 | ||||||||
\(663\) | −5.71717 | −0.222037 | ||||||||
\(664\) | 9.01972 | 0.350033 | ||||||||
\(665\) | −7.31995 | −0.283855 | ||||||||
\(666\) | −46.3290 | −1.79521 | ||||||||
\(667\) | 2.43548 | 0.0943020 | ||||||||
\(668\) | 23.1918 | 0.897318 | ||||||||
\(669\) | −76.9483 | −2.97499 | ||||||||
\(670\) | −9.70815 | −0.375059 | ||||||||
\(671\) | 36.2390 | 1.39899 | ||||||||
\(672\) | −4.93991 | −0.190561 | ||||||||
\(673\) | 11.9636 | 0.461164 | 0.230582 | − | 0.973053i | \(-0.425937\pi\) | ||||
0.230582 | + | 0.973053i | \(0.425937\pi\) | |||||||
\(674\) | 21.0243 | 0.809826 | ||||||||
\(675\) | −14.9456 | −0.575258 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −43.8752 | −1.68626 | −0.843131 | − | 0.537708i | \(-0.819290\pi\) | ||||
−0.843131 | + | 0.537708i | \(0.819290\pi\) | |||||||
\(678\) | −35.8559 | −1.37704 | ||||||||
\(679\) | 27.4621 | 1.05390 | ||||||||
\(680\) | −1.75666 | −0.0673649 | ||||||||
\(681\) | −8.65302 | −0.331584 | ||||||||
\(682\) | 2.88520 | 0.110480 | ||||||||
\(683\) | 32.5152 | 1.24416 | 0.622079 | − | 0.782954i | \(-0.286288\pi\) | ||||
0.622079 | + | 0.782954i | \(0.286288\pi\) | |||||||
\(684\) | −36.6143 | −1.39998 | ||||||||
\(685\) | −13.3808 | −0.511254 | ||||||||
\(686\) | −17.7529 | −0.677809 | ||||||||
\(687\) | −48.8273 | −1.86288 | ||||||||
\(688\) | −8.63631 | −0.329256 | ||||||||
\(689\) | −5.04595 | −0.192235 | ||||||||
\(690\) | 5.89888 | 0.224567 | ||||||||
\(691\) | −12.2965 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(692\) | −19.9078 | −0.756780 | ||||||||
\(693\) | 33.2484 | 1.26300 | ||||||||
\(694\) | 13.6654 | 0.518733 | ||||||||
\(695\) | −4.40179 | −0.166970 | ||||||||
\(696\) | −4.37321 | −0.165766 | ||||||||
\(697\) | −15.1376 | −0.573378 | ||||||||
\(698\) | 28.5515 | 1.08069 | ||||||||
\(699\) | −64.8081 | −2.45127 | ||||||||
\(700\) | −1.51784 | −0.0573689 | ||||||||
\(701\) | 5.93240 | 0.224064 | 0.112032 | − | 0.993705i | \(-0.464264\pi\) | ||||
0.112032 | + | 0.993705i | \(0.464264\pi\) | |||||||
\(702\) | −14.9456 | −0.564087 | ||||||||
\(703\) | −29.4284 | −1.10991 | ||||||||
\(704\) | −2.88520 | −0.108740 | ||||||||
\(705\) | −28.7163 | −1.08152 | ||||||||
\(706\) | −5.00976 | −0.188545 | ||||||||
\(707\) | 28.9765 | 1.08977 | ||||||||
\(708\) | −0.546416 | −0.0205356 | ||||||||
\(709\) | 43.2227 | 1.62326 | 0.811632 | − | 0.584169i | \(-0.198580\pi\) | ||||
0.811632 | + | 0.584169i | \(0.198580\pi\) | |||||||
\(710\) | −3.09566 | −0.116178 | ||||||||
\(711\) | 58.9595 | 2.21115 | ||||||||
\(712\) | −10.3332 | −0.387255 | ||||||||
\(713\) | −1.81249 | −0.0678784 | ||||||||
\(714\) | 8.67775 | 0.324757 | ||||||||
\(715\) | −2.88520 | −0.107900 | ||||||||
\(716\) | −1.80189 | −0.0673399 | ||||||||
\(717\) | −50.5711 | −1.88861 | ||||||||
\(718\) | −27.6641 | −1.03242 | ||||||||
\(719\) | 8.93000 | 0.333033 | 0.166516 | − | 0.986039i | \(-0.446748\pi\) | ||||
0.166516 | + | 0.986039i | \(0.446748\pi\) | |||||||
\(720\) | −7.59221 | −0.282945 | ||||||||
\(721\) | 15.5917 | 0.580666 | ||||||||
\(722\) | −4.25757 | −0.158450 | ||||||||
\(723\) | −0.0388988 | −0.00144666 | ||||||||
\(724\) | 15.5429 | 0.577647 | ||||||||
\(725\) | −1.34372 | −0.0499044 | ||||||||
\(726\) | −8.70795 | −0.323182 | ||||||||
\(727\) | 2.37993 | 0.0882668 | 0.0441334 | − | 0.999026i | \(-0.485947\pi\) | ||||
0.0441334 | + | 0.999026i | \(0.485947\pi\) | |||||||
\(728\) | −1.51784 | −0.0562549 | ||||||||
\(729\) | 50.4475 | 1.86843 | ||||||||
\(730\) | −14.9215 | −0.552271 | ||||||||
\(731\) | 15.1711 | 0.561122 | ||||||||
\(732\) | 40.8784 | 1.51091 | ||||||||
\(733\) | 30.2668 | 1.11793 | 0.558964 | − | 0.829192i | \(-0.311199\pi\) | ||||
0.558964 | + | 0.829192i | \(0.311199\pi\) | |||||||
\(734\) | 9.00019 | 0.332203 | ||||||||
\(735\) | −15.2840 | −0.563758 | ||||||||
\(736\) | 1.81249 | 0.0668094 | ||||||||
\(737\) | 28.0100 | 1.03176 | ||||||||
\(738\) | −65.4240 | −2.40829 | ||||||||
\(739\) | 26.4573 | 0.973249 | 0.486624 | − | 0.873611i | \(-0.338228\pi\) | ||||
0.486624 | + | 0.873611i | \(0.338228\pi\) | |||||||
\(740\) | −6.10218 | −0.224320 | ||||||||
\(741\) | −15.6955 | −0.576589 | ||||||||
\(742\) | 7.65894 | 0.281168 | ||||||||
\(743\) | −25.1284 | −0.921873 | −0.460936 | − | 0.887433i | \(-0.652486\pi\) | ||||
−0.460936 | + | 0.887433i | \(0.652486\pi\) | |||||||
\(744\) | 3.25457 | 0.119318 | ||||||||
\(745\) | −0.984443 | −0.0360672 | ||||||||
\(746\) | −35.3130 | −1.29290 | ||||||||
\(747\) | −68.4796 | −2.50554 | ||||||||
\(748\) | 5.06832 | 0.185316 | ||||||||
\(749\) | −1.14260 | −0.0417497 | ||||||||
\(750\) | −3.25457 | −0.118840 | ||||||||
\(751\) | −16.2502 | −0.592977 | −0.296489 | − | 0.955036i | \(-0.595816\pi\) | ||||
−0.296489 | + | 0.955036i | \(0.595816\pi\) | |||||||
\(752\) | −8.82339 | −0.321756 | ||||||||
\(753\) | 84.4614 | 3.07794 | ||||||||
\(754\) | −1.34372 | −0.0489352 | ||||||||
\(755\) | −3.33309 | −0.121303 | ||||||||
\(756\) | 22.6851 | 0.825049 | ||||||||
\(757\) | −7.05496 | −0.256417 | −0.128209 | − | 0.991747i | \(-0.540923\pi\) | ||||
−0.128209 | + | 0.991747i | \(0.540923\pi\) | |||||||
\(758\) | 15.8928 | 0.577252 | ||||||||
\(759\) | −17.0195 | −0.617768 | ||||||||
\(760\) | −4.82261 | −0.174934 | ||||||||
\(761\) | −19.2886 | −0.699210 | −0.349605 | − | 0.936897i | \(-0.613684\pi\) | ||||
−0.349605 | + | 0.936897i | \(0.613684\pi\) | |||||||
\(762\) | −6.01368 | −0.217853 | ||||||||
\(763\) | 0.326499 | 0.0118200 | ||||||||
\(764\) | −16.3449 | −0.591338 | ||||||||
\(765\) | 13.3369 | 0.482198 | ||||||||
\(766\) | 8.98324 | 0.324578 | ||||||||
\(767\) | −0.167892 | −0.00606223 | ||||||||
\(768\) | −3.25457 | −0.117439 | ||||||||
\(769\) | −8.35377 | −0.301245 | −0.150622 | − | 0.988591i | \(-0.548128\pi\) | ||||
−0.150622 | + | 0.988591i | \(0.548128\pi\) | |||||||
\(770\) | 4.37927 | 0.157818 | ||||||||
\(771\) | −70.3124 | −2.53224 | ||||||||
\(772\) | −8.01480 | −0.288459 | ||||||||
\(773\) | −26.6413 | −0.958221 | −0.479111 | − | 0.877755i | \(-0.659041\pi\) | ||||
−0.479111 | + | 0.877755i | \(0.659041\pi\) | |||||||
\(774\) | 65.5687 | 2.35682 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 18.0929 | 0.649498 | ||||||||
\(777\) | 30.1442 | 1.08142 | ||||||||
\(778\) | −34.7293 | −1.24511 | ||||||||
\(779\) | −41.5577 | −1.48896 | ||||||||
\(780\) | −3.25457 | −0.116532 | ||||||||
\(781\) | 8.93160 | 0.319598 | ||||||||
\(782\) | −3.18394 | −0.113857 | ||||||||
\(783\) | 20.0827 | 0.717697 | ||||||||
\(784\) | −4.69616 | −0.167720 | ||||||||
\(785\) | 14.2429 | 0.508352 | ||||||||
\(786\) | 25.5933 | 0.912881 | ||||||||
\(787\) | 10.3053 | 0.367346 | 0.183673 | − | 0.982987i | \(-0.441201\pi\) | ||||
0.183673 | + | 0.982987i | \(0.441201\pi\) | |||||||
\(788\) | −2.33801 | −0.0832881 | ||||||||
\(789\) | −36.3398 | −1.29373 | ||||||||
\(790\) | 7.76579 | 0.276294 | ||||||||
\(791\) | 16.7222 | 0.594573 | ||||||||
\(792\) | 21.9051 | 0.778362 | ||||||||
\(793\) | 12.5603 | 0.446030 | ||||||||
\(794\) | −2.31500 | −0.0821563 | ||||||||
\(795\) | 16.4224 | 0.582442 | ||||||||
\(796\) | −20.5746 | −0.729246 | ||||||||
\(797\) | −24.5349 | −0.869072 | −0.434536 | − | 0.900655i | \(-0.643088\pi\) | ||||
−0.434536 | + | 0.900655i | \(0.643088\pi\) | |||||||
\(798\) | 23.8233 | 0.843334 | ||||||||
\(799\) | 15.4997 | 0.548340 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 78.4521 | 2.77197 | ||||||||
\(802\) | −29.9444 | −1.05737 | ||||||||
\(803\) | 43.0516 | 1.51926 | ||||||||
\(804\) | 31.5958 | 1.11430 | ||||||||
\(805\) | −2.75108 | −0.0969627 | ||||||||
\(806\) | 1.00000 | 0.0352235 | ||||||||
\(807\) | 73.7419 | 2.59584 | ||||||||
\(808\) | 19.0906 | 0.671606 | ||||||||
\(809\) | 25.6199 | 0.900748 | 0.450374 | − | 0.892840i | \(-0.351291\pi\) | ||||
0.450374 | + | 0.892840i | \(0.351291\pi\) | |||||||
\(810\) | 25.8650 | 0.908803 | ||||||||
\(811\) | 48.0866 | 1.68855 | 0.844274 | − | 0.535912i | \(-0.180032\pi\) | ||||
0.844274 | + | 0.535912i | \(0.180032\pi\) | |||||||
\(812\) | 2.03955 | 0.0715740 | ||||||||
\(813\) | −41.1752 | −1.44408 | ||||||||
\(814\) | 17.6060 | 0.617090 | ||||||||
\(815\) | −4.45499 | −0.156051 | ||||||||
\(816\) | 5.71717 | 0.200141 | ||||||||
\(817\) | 41.6496 | 1.45713 | ||||||||
\(818\) | −24.5992 | −0.860090 | ||||||||
\(819\) | 11.5238 | 0.402673 | ||||||||
\(820\) | −8.61726 | −0.300928 | ||||||||
\(821\) | −19.2169 | −0.670674 | −0.335337 | − | 0.942098i | \(-0.608850\pi\) | ||||
−0.335337 | + | 0.942098i | \(0.608850\pi\) | |||||||
\(822\) | 43.5487 | 1.51894 | ||||||||
\(823\) | −24.4122 | −0.850957 | −0.425478 | − | 0.904969i | \(-0.639894\pi\) | ||||
−0.425478 | + | 0.904969i | \(0.639894\pi\) | |||||||
\(824\) | 10.2723 | 0.357853 | ||||||||
\(825\) | 9.39008 | 0.326921 | ||||||||
\(826\) | 0.254833 | 0.00886679 | ||||||||
\(827\) | 14.6459 | 0.509286 | 0.254643 | − | 0.967035i | \(-0.418042\pi\) | ||||
0.254643 | + | 0.967035i | \(0.418042\pi\) | |||||||
\(828\) | −13.7608 | −0.478222 | ||||||||
\(829\) | −22.5559 | −0.783400 | −0.391700 | − | 0.920093i | \(-0.628113\pi\) | ||||
−0.391700 | + | 0.920093i | \(0.628113\pi\) | |||||||
\(830\) | −9.01972 | −0.313079 | ||||||||
\(831\) | −83.6551 | −2.90196 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 8.24957 | 0.285831 | ||||||||
\(834\) | 14.3259 | 0.496066 | ||||||||
\(835\) | −23.1918 | −0.802586 | ||||||||
\(836\) | 13.9142 | 0.481233 | ||||||||
\(837\) | −14.9456 | −0.516597 | ||||||||
\(838\) | 14.7647 | 0.510039 | ||||||||
\(839\) | −25.8859 | −0.893679 | −0.446839 | − | 0.894614i | \(-0.647450\pi\) | ||||
−0.446839 | + | 0.894614i | \(0.647450\pi\) | |||||||
\(840\) | 4.93991 | 0.170443 | ||||||||
\(841\) | −27.1944 | −0.937739 | ||||||||
\(842\) | −13.1348 | −0.452656 | ||||||||
\(843\) | 5.35762 | 0.184526 | ||||||||
\(844\) | −20.5706 | −0.708068 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 66.9890 | 2.30313 | ||||||||
\(847\) | 4.06115 | 0.139543 | ||||||||
\(848\) | 5.04595 | 0.173279 | ||||||||
\(849\) | −53.2136 | −1.82629 | ||||||||
\(850\) | 1.75666 | 0.0602530 | ||||||||
\(851\) | −11.0602 | −0.379137 | ||||||||
\(852\) | 10.0750 | 0.345165 | ||||||||
\(853\) | −31.2726 | −1.07075 | −0.535376 | − | 0.844614i | \(-0.679830\pi\) | ||||
−0.535376 | + | 0.844614i | \(0.679830\pi\) | |||||||
\(854\) | −19.0645 | −0.652375 | ||||||||
\(855\) | 36.6143 | 1.25218 | ||||||||
\(856\) | −0.752780 | −0.0257295 | ||||||||
\(857\) | −48.4815 | −1.65610 | −0.828048 | − | 0.560657i | \(-0.810549\pi\) | ||||
−0.828048 | + | 0.560657i | \(0.810549\pi\) | |||||||
\(858\) | 9.39008 | 0.320572 | ||||||||
\(859\) | −51.7545 | −1.76584 | −0.882920 | − | 0.469523i | \(-0.844426\pi\) | ||||
−0.882920 | + | 0.469523i | \(0.844426\pi\) | |||||||
\(860\) | 8.63631 | 0.294496 | ||||||||
\(861\) | 42.5685 | 1.45073 | ||||||||
\(862\) | −10.4912 | −0.357333 | ||||||||
\(863\) | 10.5718 | 0.359868 | 0.179934 | − | 0.983679i | \(-0.442412\pi\) | ||||
0.179934 | + | 0.983679i | \(0.442412\pi\) | |||||||
\(864\) | 14.9456 | 0.508461 | ||||||||
\(865\) | 19.9078 | 0.676885 | ||||||||
\(866\) | −28.8205 | −0.979362 | ||||||||
\(867\) | 45.2845 | 1.53794 | ||||||||
\(868\) | −1.51784 | −0.0515188 | ||||||||
\(869\) | −22.4059 | −0.760067 | ||||||||
\(870\) | 4.37321 | 0.148266 | ||||||||
\(871\) | 9.70815 | 0.328948 | ||||||||
\(872\) | 0.215107 | 0.00728446 | ||||||||
\(873\) | −137.365 | −4.64911 | ||||||||
\(874\) | −8.74095 | −0.295667 | ||||||||
\(875\) | 1.51784 | 0.0513123 | ||||||||
\(876\) | 48.5631 | 1.64080 | ||||||||
\(877\) | −18.4891 | −0.624332 | −0.312166 | − | 0.950028i | \(-0.601055\pi\) | ||||
−0.312166 | + | 0.950028i | \(0.601055\pi\) | |||||||
\(878\) | 14.3101 | 0.482942 | ||||||||
\(879\) | −42.7068 | −1.44046 | ||||||||
\(880\) | 2.88520 | 0.0972601 | ||||||||
\(881\) | 17.8443 | 0.601190 | 0.300595 | − | 0.953752i | \(-0.402815\pi\) | ||||
0.300595 | + | 0.953752i | \(0.402815\pi\) | |||||||
\(882\) | 35.6542 | 1.20054 | ||||||||
\(883\) | 6.91818 | 0.232815 | 0.116408 | − | 0.993202i | \(-0.462862\pi\) | ||||
0.116408 | + | 0.993202i | \(0.462862\pi\) | |||||||
\(884\) | 1.75666 | 0.0590829 | ||||||||
\(885\) | 0.546416 | 0.0183676 | ||||||||
\(886\) | −32.7324 | −1.09967 | ||||||||
\(887\) | 38.3628 | 1.28810 | 0.644048 | − | 0.764985i | \(-0.277254\pi\) | ||||
0.644048 | + | 0.764985i | \(0.277254\pi\) | |||||||
\(888\) | 19.8599 | 0.666456 | ||||||||
\(889\) | 2.80461 | 0.0940638 | ||||||||
\(890\) | 10.3332 | 0.346371 | ||||||||
\(891\) | −74.6257 | −2.50006 | ||||||||
\(892\) | 23.6432 | 0.791632 | ||||||||
\(893\) | 42.5518 | 1.42394 | ||||||||
\(894\) | 3.20394 | 0.107156 | ||||||||
\(895\) | 1.80189 | 0.0602306 | ||||||||
\(896\) | 1.51784 | 0.0507075 | ||||||||
\(897\) | −5.89888 | −0.196958 | ||||||||
\(898\) | 4.57873 | 0.152794 | ||||||||
\(899\) | −1.34372 | −0.0448154 | ||||||||
\(900\) | 7.59221 | 0.253074 | ||||||||
\(901\) | −8.86402 | −0.295303 | ||||||||
\(902\) | 24.8625 | 0.827832 | ||||||||
\(903\) | −42.6626 | −1.41972 | ||||||||
\(904\) | 11.0171 | 0.366423 | ||||||||
\(905\) | −15.5429 | −0.516663 | ||||||||
\(906\) | 10.8478 | 0.360392 | ||||||||
\(907\) | −29.8056 | −0.989679 | −0.494839 | − | 0.868984i | \(-0.664773\pi\) | ||||
−0.494839 | + | 0.868984i | \(0.664773\pi\) | |||||||
\(908\) | 2.65873 | 0.0882331 | ||||||||
\(909\) | −144.940 | −4.80735 | ||||||||
\(910\) | 1.51784 | 0.0503159 | ||||||||
\(911\) | −16.4615 | −0.545395 | −0.272697 | − | 0.962100i | \(-0.587916\pi\) | ||||
−0.272697 | + | 0.962100i | \(0.587916\pi\) | |||||||
\(912\) | 15.6955 | 0.519730 | ||||||||
\(913\) | 26.0237 | 0.861259 | ||||||||
\(914\) | 29.7216 | 0.983102 | ||||||||
\(915\) | −40.8784 | −1.35140 | ||||||||
\(916\) | 15.0027 | 0.495704 | ||||||||
\(917\) | −11.9360 | −0.394161 | ||||||||
\(918\) | −26.2544 | −0.866525 | ||||||||
\(919\) | −13.1870 | −0.435001 | −0.217500 | − | 0.976060i | \(-0.569790\pi\) | ||||
−0.217500 | + | 0.976060i | \(0.569790\pi\) | |||||||
\(920\) | −1.81249 | −0.0597562 | ||||||||
\(921\) | −29.4816 | −0.971450 | ||||||||
\(922\) | 15.4727 | 0.509566 | ||||||||
\(923\) | 3.09566 | 0.101895 | ||||||||
\(924\) | −14.2526 | −0.468877 | ||||||||
\(925\) | 6.10218 | 0.200638 | ||||||||
\(926\) | 11.8854 | 0.390577 | ||||||||
\(927\) | −77.9895 | −2.56151 | ||||||||
\(928\) | 1.34372 | 0.0441096 | ||||||||
\(929\) | −14.6966 | −0.482181 | −0.241090 | − | 0.970503i | \(-0.577505\pi\) | ||||
−0.241090 | + | 0.970503i | \(0.577505\pi\) | |||||||
\(930\) | −3.25457 | −0.106721 | ||||||||
\(931\) | 22.6478 | 0.742250 | ||||||||
\(932\) | 19.9130 | 0.652271 | ||||||||
\(933\) | −16.3842 | −0.536394 | ||||||||
\(934\) | −13.1182 | −0.429240 | ||||||||
\(935\) | −5.06832 | −0.165752 | ||||||||
\(936\) | 7.59221 | 0.248159 | ||||||||
\(937\) | 41.0941 | 1.34249 | 0.671243 | − | 0.741237i | \(-0.265761\pi\) | ||||
0.671243 | + | 0.741237i | \(0.265761\pi\) | |||||||
\(938\) | −14.7354 | −0.481128 | ||||||||
\(939\) | −22.2739 | −0.726880 | ||||||||
\(940\) | 8.82339 | 0.287787 | ||||||||
\(941\) | −8.51154 | −0.277468 | −0.138734 | − | 0.990330i | \(-0.544303\pi\) | ||||
−0.138734 | + | 0.990330i | \(0.544303\pi\) | |||||||
\(942\) | −46.3546 | −1.51031 | ||||||||
\(943\) | −15.6187 | −0.508616 | ||||||||
\(944\) | 0.167892 | 0.00546442 | ||||||||
\(945\) | −22.6851 | −0.737946 | ||||||||
\(946\) | −24.9175 | −0.810138 | ||||||||
\(947\) | 32.9643 | 1.07120 | 0.535598 | − | 0.844473i | \(-0.320086\pi\) | ||||
0.535598 | + | 0.844473i | \(0.320086\pi\) | |||||||
\(948\) | −25.2743 | −0.820871 | ||||||||
\(949\) | 14.9215 | 0.484373 | ||||||||
\(950\) | 4.82261 | 0.156466 | ||||||||
\(951\) | 66.2270 | 2.14756 | ||||||||
\(952\) | −2.66633 | −0.0864162 | ||||||||
\(953\) | −16.8597 | −0.546138 | −0.273069 | − | 0.961994i | \(-0.588039\pi\) | ||||
−0.273069 | + | 0.961994i | \(0.588039\pi\) | |||||||
\(954\) | −38.3099 | −1.24033 | ||||||||
\(955\) | 16.3449 | 0.528909 | ||||||||
\(956\) | 15.5385 | 0.502551 | ||||||||
\(957\) | −12.6176 | −0.407869 | ||||||||
\(958\) | 10.9823 | 0.354821 | ||||||||
\(959\) | −20.3099 | −0.655841 | ||||||||
\(960\) | 3.25457 | 0.105041 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 6.10218 | 0.196742 | ||||||||
\(963\) | 5.71526 | 0.184172 | ||||||||
\(964\) | 0.0119521 | 0.000384950 0 | ||||||||
\(965\) | 8.01480 | 0.258005 | ||||||||
\(966\) | 8.95356 | 0.288076 | ||||||||
\(967\) | 4.85450 | 0.156110 | 0.0780551 | − | 0.996949i | \(-0.475129\pi\) | ||||
0.0780551 | + | 0.996949i | \(0.475129\pi\) | |||||||
\(968\) | 2.67561 | 0.0859973 | ||||||||
\(969\) | −27.5717 | −0.885730 | ||||||||
\(970\) | −18.0929 | −0.580929 | ||||||||
\(971\) | 17.6846 | 0.567525 | 0.283762 | − | 0.958895i | \(-0.408417\pi\) | ||||
0.283762 | + | 0.958895i | \(0.408417\pi\) | |||||||
\(972\) | −39.3424 | −1.26191 | ||||||||
\(973\) | −6.68122 | −0.214190 | ||||||||
\(974\) | −13.1634 | −0.421782 | ||||||||
\(975\) | 3.25457 | 0.104230 | ||||||||
\(976\) | −12.5603 | −0.402046 | ||||||||
\(977\) | 3.05627 | 0.0977787 | 0.0488893 | − | 0.998804i | \(-0.484432\pi\) | ||||
0.0488893 | + | 0.998804i | \(0.484432\pi\) | |||||||
\(978\) | 14.4991 | 0.463629 | ||||||||
\(979\) | −29.8135 | −0.952843 | ||||||||
\(980\) | 4.69616 | 0.150013 | ||||||||
\(981\) | −1.63314 | −0.0521421 | ||||||||
\(982\) | 13.7510 | 0.438813 | ||||||||
\(983\) | 48.6466 | 1.55159 | 0.775793 | − | 0.630987i | \(-0.217350\pi\) | ||||
0.775793 | + | 0.630987i | \(0.217350\pi\) | |||||||
\(984\) | 28.0455 | 0.894056 | ||||||||
\(985\) | 2.33801 | 0.0744952 | ||||||||
\(986\) | −2.36045 | −0.0751721 | ||||||||
\(987\) | −43.5868 | −1.38738 | ||||||||
\(988\) | 4.82261 | 0.153428 | ||||||||
\(989\) | 15.6533 | 0.497745 | ||||||||
\(990\) | −21.9051 | −0.696188 | ||||||||
\(991\) | −23.7061 | −0.753049 | −0.376524 | − | 0.926407i | \(-0.622881\pi\) | ||||
−0.376524 | + | 0.926407i | \(0.622881\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 38.2571 | 1.21405 | ||||||||
\(994\) | −4.69871 | −0.149034 | ||||||||
\(995\) | 20.5746 | 0.652257 | ||||||||
\(996\) | 29.3553 | 0.930158 | ||||||||
\(997\) | 21.3632 | 0.676578 | 0.338289 | − | 0.941042i | \(-0.390152\pi\) | ||||
0.338289 | + | 0.941042i | \(0.390152\pi\) | |||||||
\(998\) | −5.02756 | −0.159144 | ||||||||
\(999\) | −91.2010 | −2.88547 |
(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 | 4030.2.a.p.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4030.2.a.p.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |