Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} - 5557 x^{3} - 483 x^{2} + 1648 x + 392 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.38729\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | ||||||||
\(3\) | 2.38729 | 1.37830 | 0.689151 | − | 0.724618i | \(-0.257984\pi\) | ||||
0.689151 | + | 0.724618i | \(0.257984\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.38729 | 0.974607 | ||||||||
\(7\) | 3.92530 | 1.48363 | 0.741813 | − | 0.670607i | \(-0.233966\pi\) | ||||
0.741813 | + | 0.670607i | \(0.233966\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.69915 | 0.899717 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.38729 | 0.689151 | ||||||||
\(13\) | 0.812933 | 0.225467 | 0.112734 | − | 0.993625i | \(-0.464039\pi\) | ||||
0.112734 | + | 0.993625i | \(0.464039\pi\) | |||||||
\(14\) | 3.92530 | 1.04908 | ||||||||
\(15\) | 2.38729 | 0.616395 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.34911 | −1.29735 | −0.648675 | − | 0.761065i | \(-0.724677\pi\) | ||||
−0.648675 | + | 0.761065i | \(0.724677\pi\) | |||||||
\(18\) | 2.69915 | 0.636196 | ||||||||
\(19\) | −0.405790 | −0.0930946 | −0.0465473 | − | 0.998916i | \(-0.514822\pi\) | ||||
−0.0465473 | + | 0.998916i | \(0.514822\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 9.37084 | 2.04488 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.18707 | 0.247521 | 0.123760 | − | 0.992312i | \(-0.460505\pi\) | ||||
0.123760 | + | 0.992312i | \(0.460505\pi\) | |||||||
\(24\) | 2.38729 | 0.487303 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.812933 | 0.159429 | ||||||||
\(27\) | −0.718217 | −0.138221 | ||||||||
\(28\) | 3.92530 | 0.741813 | ||||||||
\(29\) | 1.86640 | 0.346582 | 0.173291 | − | 0.984871i | \(-0.444560\pi\) | ||||
0.173291 | + | 0.984871i | \(0.444560\pi\) | |||||||
\(30\) | 2.38729 | 0.435857 | ||||||||
\(31\) | −10.0613 | −1.80707 | −0.903535 | − | 0.428513i | \(-0.859037\pi\) | ||||
−0.903535 | + | 0.428513i | \(0.859037\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.38729 | −0.415574 | ||||||||
\(34\) | −5.34911 | −0.917365 | ||||||||
\(35\) | 3.92530 | 0.663497 | ||||||||
\(36\) | 2.69915 | 0.449858 | ||||||||
\(37\) | 6.13412 | 1.00844 | 0.504221 | − | 0.863575i | \(-0.331780\pi\) | ||||
0.504221 | + | 0.863575i | \(0.331780\pi\) | |||||||
\(38\) | −0.405790 | −0.0658279 | ||||||||
\(39\) | 1.94071 | 0.310762 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 11.7137 | 1.82938 | 0.914689 | − | 0.404159i | \(-0.132436\pi\) | ||||
0.914689 | + | 0.404159i | \(0.132436\pi\) | |||||||
\(42\) | 9.37084 | 1.44595 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.69915 | 0.402365 | ||||||||
\(46\) | 1.18707 | 0.175023 | ||||||||
\(47\) | 8.05997 | 1.17567 | 0.587834 | − | 0.808982i | \(-0.299981\pi\) | ||||
0.587834 | + | 0.808982i | \(0.299981\pi\) | |||||||
\(48\) | 2.38729 | 0.344576 | ||||||||
\(49\) | 8.40801 | 1.20114 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −12.7699 | −1.78814 | ||||||||
\(52\) | 0.812933 | 0.112734 | ||||||||
\(53\) | 9.24636 | 1.27009 | 0.635043 | − | 0.772477i | \(-0.280983\pi\) | ||||
0.635043 | + | 0.772477i | \(0.280983\pi\) | |||||||
\(54\) | −0.718217 | −0.0977369 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 3.92530 | 0.524541 | ||||||||
\(57\) | −0.968738 | −0.128313 | ||||||||
\(58\) | 1.86640 | 0.245071 | ||||||||
\(59\) | 7.78548 | 1.01358 | 0.506792 | − | 0.862068i | \(-0.330831\pi\) | ||||
0.506792 | + | 0.862068i | \(0.330831\pi\) | |||||||
\(60\) | 2.38729 | 0.308198 | ||||||||
\(61\) | 11.1613 | 1.42905 | 0.714526 | − | 0.699608i | \(-0.246642\pi\) | ||||
0.714526 | + | 0.699608i | \(0.246642\pi\) | |||||||
\(62\) | −10.0613 | −1.27779 | ||||||||
\(63\) | 10.5950 | 1.33484 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.812933 | 0.100832 | ||||||||
\(66\) | −2.38729 | −0.293855 | ||||||||
\(67\) | −1.05981 | −0.129476 | −0.0647380 | − | 0.997902i | \(-0.520621\pi\) | ||||
−0.0647380 | + | 0.997902i | \(0.520621\pi\) | |||||||
\(68\) | −5.34911 | −0.648675 | ||||||||
\(69\) | 2.83387 | 0.341158 | ||||||||
\(70\) | 3.92530 | 0.469164 | ||||||||
\(71\) | −11.7969 | −1.40004 | −0.700018 | − | 0.714126i | \(-0.746825\pi\) | ||||
−0.700018 | + | 0.714126i | \(0.746825\pi\) | |||||||
\(72\) | 2.69915 | 0.318098 | ||||||||
\(73\) | −2.94467 | −0.344647 | −0.172324 | − | 0.985040i | \(-0.555127\pi\) | ||||
−0.172324 | + | 0.985040i | \(0.555127\pi\) | |||||||
\(74\) | 6.13412 | 0.713076 | ||||||||
\(75\) | 2.38729 | 0.275660 | ||||||||
\(76\) | −0.405790 | −0.0465473 | ||||||||
\(77\) | −3.92530 | −0.447330 | ||||||||
\(78\) | 1.94071 | 0.219742 | ||||||||
\(79\) | −7.82323 | −0.880182 | −0.440091 | − | 0.897953i | \(-0.645054\pi\) | ||||
−0.440091 | + | 0.897953i | \(0.645054\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −9.81204 | −1.09023 | ||||||||
\(82\) | 11.7137 | 1.29357 | ||||||||
\(83\) | −14.2689 | −1.56622 | −0.783109 | − | 0.621884i | \(-0.786367\pi\) | ||||
−0.783109 | + | 0.621884i | \(0.786367\pi\) | |||||||
\(84\) | 9.37084 | 1.02244 | ||||||||
\(85\) | −5.34911 | −0.580193 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 4.45565 | 0.477695 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 0.276107 | 0.0292673 | 0.0146336 | − | 0.999893i | \(-0.495342\pi\) | ||||
0.0146336 | + | 0.999893i | \(0.495342\pi\) | |||||||
\(90\) | 2.69915 | 0.284515 | ||||||||
\(91\) | 3.19101 | 0.334509 | ||||||||
\(92\) | 1.18707 | 0.123760 | ||||||||
\(93\) | −24.0193 | −2.49069 | ||||||||
\(94\) | 8.05997 | 0.831322 | ||||||||
\(95\) | −0.405790 | −0.0416332 | ||||||||
\(96\) | 2.38729 | 0.243652 | ||||||||
\(97\) | 3.54637 | 0.360079 | 0.180040 | − | 0.983659i | \(-0.442377\pi\) | ||||
0.180040 | + | 0.983659i | \(0.442377\pi\) | |||||||
\(98\) | 8.40801 | 0.849338 | ||||||||
\(99\) | −2.69915 | −0.271275 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.9091 | −1.18500 | −0.592499 | − | 0.805571i | \(-0.701858\pi\) | ||||
−0.592499 | + | 0.805571i | \(0.701858\pi\) | |||||||
\(102\) | −12.7699 | −1.26441 | ||||||||
\(103\) | −16.4288 | −1.61878 | −0.809388 | − | 0.587274i | \(-0.800201\pi\) | ||||
−0.809388 | + | 0.587274i | \(0.800201\pi\) | |||||||
\(104\) | 0.812933 | 0.0797147 | ||||||||
\(105\) | 9.37084 | 0.914500 | ||||||||
\(106\) | 9.24636 | 0.898086 | ||||||||
\(107\) | 8.32995 | 0.805287 | 0.402644 | − | 0.915357i | \(-0.368091\pi\) | ||||
0.402644 | + | 0.915357i | \(0.368091\pi\) | |||||||
\(108\) | −0.718217 | −0.0691104 | ||||||||
\(109\) | −15.7533 | −1.50889 | −0.754447 | − | 0.656361i | \(-0.772095\pi\) | ||||
−0.754447 | + | 0.656361i | \(0.772095\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 14.6439 | 1.38994 | ||||||||
\(112\) | 3.92530 | 0.370906 | ||||||||
\(113\) | 4.83624 | 0.454955 | 0.227477 | − | 0.973783i | \(-0.426952\pi\) | ||||
0.227477 | + | 0.973783i | \(0.426952\pi\) | |||||||
\(114\) | −0.968738 | −0.0907307 | ||||||||
\(115\) | 1.18707 | 0.110695 | ||||||||
\(116\) | 1.86640 | 0.173291 | ||||||||
\(117\) | 2.19423 | 0.202856 | ||||||||
\(118\) | 7.78548 | 0.716712 | ||||||||
\(119\) | −20.9969 | −1.92478 | ||||||||
\(120\) | 2.38729 | 0.217929 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.1613 | 1.01049 | ||||||||
\(123\) | 27.9641 | 2.52143 | ||||||||
\(124\) | −10.0613 | −0.903535 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 10.5950 | 0.943876 | ||||||||
\(127\) | 10.1467 | 0.900371 | 0.450185 | − | 0.892935i | \(-0.351358\pi\) | ||||
0.450185 | + | 0.892935i | \(0.351358\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.38729 | 0.210189 | ||||||||
\(130\) | 0.812933 | 0.0712990 | ||||||||
\(131\) | 4.88758 | 0.427029 | 0.213515 | − | 0.976940i | \(-0.431509\pi\) | ||||
0.213515 | + | 0.976940i | \(0.431509\pi\) | |||||||
\(132\) | −2.38729 | −0.207787 | ||||||||
\(133\) | −1.59285 | −0.138118 | ||||||||
\(134\) | −1.05981 | −0.0915533 | ||||||||
\(135\) | −0.718217 | −0.0618143 | ||||||||
\(136\) | −5.34911 | −0.458683 | ||||||||
\(137\) | −15.7894 | −1.34898 | −0.674492 | − | 0.738283i | \(-0.735637\pi\) | ||||
−0.674492 | + | 0.738283i | \(0.735637\pi\) | |||||||
\(138\) | 2.83387 | 0.241235 | ||||||||
\(139\) | −14.0825 | −1.19446 | −0.597232 | − | 0.802068i | \(-0.703733\pi\) | ||||
−0.597232 | + | 0.802068i | \(0.703733\pi\) | |||||||
\(140\) | 3.92530 | 0.331749 | ||||||||
\(141\) | 19.2415 | 1.62042 | ||||||||
\(142\) | −11.7969 | −0.989975 | ||||||||
\(143\) | −0.812933 | −0.0679809 | ||||||||
\(144\) | 2.69915 | 0.224929 | ||||||||
\(145\) | 1.86640 | 0.154996 | ||||||||
\(146\) | −2.94467 | −0.243702 | ||||||||
\(147\) | 20.0724 | 1.65554 | ||||||||
\(148\) | 6.13412 | 0.504221 | ||||||||
\(149\) | 5.70949 | 0.467740 | 0.233870 | − | 0.972268i | \(-0.424861\pi\) | ||||
0.233870 | + | 0.972268i | \(0.424861\pi\) | |||||||
\(150\) | 2.38729 | 0.194921 | ||||||||
\(151\) | −6.67469 | −0.543178 | −0.271589 | − | 0.962413i | \(-0.587549\pi\) | ||||
−0.271589 | + | 0.962413i | \(0.587549\pi\) | |||||||
\(152\) | −0.405790 | −0.0329139 | ||||||||
\(153\) | −14.4381 | −1.16725 | ||||||||
\(154\) | −3.92530 | −0.316310 | ||||||||
\(155\) | −10.0613 | −0.808147 | ||||||||
\(156\) | 1.94071 | 0.155381 | ||||||||
\(157\) | −20.2095 | −1.61290 | −0.806448 | − | 0.591305i | \(-0.798613\pi\) | ||||
−0.806448 | + | 0.591305i | \(0.798613\pi\) | |||||||
\(158\) | −7.82323 | −0.622383 | ||||||||
\(159\) | 22.0737 | 1.75056 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 4.65960 | 0.367228 | ||||||||
\(162\) | −9.81204 | −0.770907 | ||||||||
\(163\) | 7.78522 | 0.609785 | 0.304893 | − | 0.952387i | \(-0.401379\pi\) | ||||
0.304893 | + | 0.952387i | \(0.401379\pi\) | |||||||
\(164\) | 11.7137 | 0.914689 | ||||||||
\(165\) | −2.38729 | −0.185850 | ||||||||
\(166\) | −14.2689 | −1.10748 | ||||||||
\(167\) | −23.0156 | −1.78100 | −0.890502 | − | 0.454979i | \(-0.849647\pi\) | ||||
−0.890502 | + | 0.454979i | \(0.849647\pi\) | |||||||
\(168\) | 9.37084 | 0.722976 | ||||||||
\(169\) | −12.3391 | −0.949165 | ||||||||
\(170\) | −5.34911 | −0.410258 | ||||||||
\(171\) | −1.09529 | −0.0837588 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 4.79082 | 0.364239 | 0.182119 | − | 0.983276i | \(-0.441704\pi\) | ||||
0.182119 | + | 0.983276i | \(0.441704\pi\) | |||||||
\(174\) | 4.45565 | 0.337782 | ||||||||
\(175\) | 3.92530 | 0.296725 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 18.5862 | 1.39702 | ||||||||
\(178\) | 0.276107 | 0.0206951 | ||||||||
\(179\) | 12.9298 | 0.966421 | 0.483211 | − | 0.875504i | \(-0.339470\pi\) | ||||
0.483211 | + | 0.875504i | \(0.339470\pi\) | |||||||
\(180\) | 2.69915 | 0.201183 | ||||||||
\(181\) | −0.164956 | −0.0122611 | −0.00613053 | − | 0.999981i | \(-0.501951\pi\) | ||||
−0.00613053 | + | 0.999981i | \(0.501951\pi\) | |||||||
\(182\) | 3.19101 | 0.236533 | ||||||||
\(183\) | 26.6452 | 1.96967 | ||||||||
\(184\) | 1.18707 | 0.0875117 | ||||||||
\(185\) | 6.13412 | 0.450989 | ||||||||
\(186\) | −24.0193 | −1.76118 | ||||||||
\(187\) | 5.34911 | 0.391166 | ||||||||
\(188\) | 8.05997 | 0.587834 | ||||||||
\(189\) | −2.81922 | −0.205068 | ||||||||
\(190\) | −0.405790 | −0.0294391 | ||||||||
\(191\) | −25.0988 | −1.81608 | −0.908042 | − | 0.418878i | \(-0.862423\pi\) | ||||
−0.908042 | + | 0.418878i | \(0.862423\pi\) | |||||||
\(192\) | 2.38729 | 0.172288 | ||||||||
\(193\) | 8.07002 | 0.580893 | 0.290446 | − | 0.956891i | \(-0.406196\pi\) | ||||
0.290446 | + | 0.956891i | \(0.406196\pi\) | |||||||
\(194\) | 3.54637 | 0.254614 | ||||||||
\(195\) | 1.94071 | 0.138977 | ||||||||
\(196\) | 8.40801 | 0.600572 | ||||||||
\(197\) | −18.0918 | −1.28899 | −0.644493 | − | 0.764610i | \(-0.722932\pi\) | ||||
−0.644493 | + | 0.764610i | \(0.722932\pi\) | |||||||
\(198\) | −2.69915 | −0.191820 | ||||||||
\(199\) | 9.19769 | 0.652007 | 0.326003 | − | 0.945369i | \(-0.394298\pi\) | ||||
0.326003 | + | 0.945369i | \(0.394298\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −2.53006 | −0.178457 | ||||||||
\(202\) | −11.9091 | −0.837920 | ||||||||
\(203\) | 7.32620 | 0.514199 | ||||||||
\(204\) | −12.7699 | −0.894070 | ||||||||
\(205\) | 11.7137 | 0.818122 | ||||||||
\(206\) | −16.4288 | −1.14465 | ||||||||
\(207\) | 3.20407 | 0.222698 | ||||||||
\(208\) | 0.812933 | 0.0563668 | ||||||||
\(209\) | 0.405790 | 0.0280691 | ||||||||
\(210\) | 9.37084 | 0.646649 | ||||||||
\(211\) | 2.78371 | 0.191638 | 0.0958191 | − | 0.995399i | \(-0.469453\pi\) | ||||
0.0958191 | + | 0.995399i | \(0.469453\pi\) | |||||||
\(212\) | 9.24636 | 0.635043 | ||||||||
\(213\) | −28.1626 | −1.92967 | ||||||||
\(214\) | 8.32995 | 0.569424 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | −0.718217 | −0.0488685 | ||||||||
\(217\) | −39.4938 | −2.68102 | ||||||||
\(218\) | −15.7533 | −1.06695 | ||||||||
\(219\) | −7.02977 | −0.475028 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −4.34847 | −0.292510 | ||||||||
\(222\) | 14.6439 | 0.982835 | ||||||||
\(223\) | 10.5184 | 0.704366 | 0.352183 | − | 0.935931i | \(-0.385440\pi\) | ||||
0.352183 | + | 0.935931i | \(0.385440\pi\) | |||||||
\(224\) | 3.92530 | 0.262270 | ||||||||
\(225\) | 2.69915 | 0.179943 | ||||||||
\(226\) | 4.83624 | 0.321702 | ||||||||
\(227\) | −17.8730 | −1.18627 | −0.593135 | − | 0.805103i | \(-0.702110\pi\) | ||||
−0.593135 | + | 0.805103i | \(0.702110\pi\) | |||||||
\(228\) | −0.968738 | −0.0641563 | ||||||||
\(229\) | 13.1275 | 0.867491 | 0.433746 | − | 0.901035i | \(-0.357192\pi\) | ||||
0.433746 | + | 0.901035i | \(0.357192\pi\) | |||||||
\(230\) | 1.18707 | 0.0782729 | ||||||||
\(231\) | −9.37084 | −0.616556 | ||||||||
\(232\) | 1.86640 | 0.122535 | ||||||||
\(233\) | −24.2231 | −1.58691 | −0.793453 | − | 0.608632i | \(-0.791719\pi\) | ||||
−0.793453 | + | 0.608632i | \(0.791719\pi\) | |||||||
\(234\) | 2.19423 | 0.143441 | ||||||||
\(235\) | 8.05997 | 0.525774 | ||||||||
\(236\) | 7.78548 | 0.506792 | ||||||||
\(237\) | −18.6763 | −1.21316 | ||||||||
\(238\) | −20.9969 | −1.36103 | ||||||||
\(239\) | 6.88492 | 0.445348 | 0.222674 | − | 0.974893i | \(-0.428521\pi\) | ||||
0.222674 | + | 0.974893i | \(0.428521\pi\) | |||||||
\(240\) | 2.38729 | 0.154099 | ||||||||
\(241\) | 28.1350 | 1.81234 | 0.906168 | − | 0.422919i | \(-0.138994\pi\) | ||||
0.906168 | + | 0.422919i | \(0.138994\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −21.2695 | −1.36444 | ||||||||
\(244\) | 11.1613 | 0.714526 | ||||||||
\(245\) | 8.40801 | 0.537168 | ||||||||
\(246\) | 27.9641 | 1.78292 | ||||||||
\(247\) | −0.329880 | −0.0209898 | ||||||||
\(248\) | −10.0613 | −0.638896 | ||||||||
\(249\) | −34.0641 | −2.15872 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 2.91600 | 0.184056 | 0.0920280 | − | 0.995756i | \(-0.470665\pi\) | ||||
0.0920280 | + | 0.995756i | \(0.470665\pi\) | |||||||
\(252\) | 10.5950 | 0.667421 | ||||||||
\(253\) | −1.18707 | −0.0746302 | ||||||||
\(254\) | 10.1467 | 0.636658 | ||||||||
\(255\) | −12.7699 | −0.799681 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.6806 | −1.41477 | −0.707387 | − | 0.706826i | \(-0.750126\pi\) | ||||
−0.707387 | + | 0.706826i | \(0.750126\pi\) | |||||||
\(258\) | 2.38729 | 0.148626 | ||||||||
\(259\) | 24.0783 | 1.49615 | ||||||||
\(260\) | 0.812933 | 0.0504160 | ||||||||
\(261\) | 5.03770 | 0.311826 | ||||||||
\(262\) | 4.88758 | 0.301955 | ||||||||
\(263\) | −31.0321 | −1.91352 | −0.956761 | − | 0.290875i | \(-0.906054\pi\) | ||||
−0.956761 | + | 0.290875i | \(0.906054\pi\) | |||||||
\(264\) | −2.38729 | −0.146927 | ||||||||
\(265\) | 9.24636 | 0.567999 | ||||||||
\(266\) | −1.59285 | −0.0976639 | ||||||||
\(267\) | 0.659147 | 0.0403391 | ||||||||
\(268\) | −1.05981 | −0.0647380 | ||||||||
\(269\) | −17.5504 | −1.07006 | −0.535032 | − | 0.844832i | \(-0.679700\pi\) | ||||
−0.535032 | + | 0.844832i | \(0.679700\pi\) | |||||||
\(270\) | −0.718217 | −0.0437093 | ||||||||
\(271\) | 21.3862 | 1.29912 | 0.649561 | − | 0.760310i | \(-0.274953\pi\) | ||||
0.649561 | + | 0.760310i | \(0.274953\pi\) | |||||||
\(272\) | −5.34911 | −0.324338 | ||||||||
\(273\) | 7.61786 | 0.461054 | ||||||||
\(274\) | −15.7894 | −0.953875 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 2.83387 | 0.170579 | ||||||||
\(277\) | 29.2162 | 1.75543 | 0.877715 | − | 0.479183i | \(-0.159067\pi\) | ||||
0.877715 | + | 0.479183i | \(0.159067\pi\) | |||||||
\(278\) | −14.0825 | −0.844614 | ||||||||
\(279\) | −27.1571 | −1.62585 | ||||||||
\(280\) | 3.92530 | 0.234582 | ||||||||
\(281\) | 20.3275 | 1.21264 | 0.606320 | − | 0.795221i | \(-0.292645\pi\) | ||||
0.606320 | + | 0.795221i | \(0.292645\pi\) | |||||||
\(282\) | 19.2415 | 1.14581 | ||||||||
\(283\) | 29.9954 | 1.78304 | 0.891520 | − | 0.452982i | \(-0.149640\pi\) | ||||
0.891520 | + | 0.452982i | \(0.149640\pi\) | |||||||
\(284\) | −11.7969 | −0.700018 | ||||||||
\(285\) | −0.968738 | −0.0573831 | ||||||||
\(286\) | −0.812933 | −0.0480698 | ||||||||
\(287\) | 45.9800 | 2.71411 | ||||||||
\(288\) | 2.69915 | 0.159049 | ||||||||
\(289\) | 11.6130 | 0.683119 | ||||||||
\(290\) | 1.86640 | 0.109599 | ||||||||
\(291\) | 8.46621 | 0.496298 | ||||||||
\(292\) | −2.94467 | −0.172324 | ||||||||
\(293\) | −19.8554 | −1.15997 | −0.579983 | − | 0.814628i | \(-0.696941\pi\) | ||||
−0.579983 | + | 0.814628i | \(0.696941\pi\) | |||||||
\(294\) | 20.0724 | 1.17064 | ||||||||
\(295\) | 7.78548 | 0.453288 | ||||||||
\(296\) | 6.13412 | 0.356538 | ||||||||
\(297\) | 0.718217 | 0.0416752 | ||||||||
\(298\) | 5.70949 | 0.330742 | ||||||||
\(299\) | 0.965006 | 0.0558077 | ||||||||
\(300\) | 2.38729 | 0.137830 | ||||||||
\(301\) | 3.92530 | 0.226251 | ||||||||
\(302\) | −6.67469 | −0.384085 | ||||||||
\(303\) | −28.4304 | −1.63328 | ||||||||
\(304\) | −0.405790 | −0.0232737 | ||||||||
\(305\) | 11.1613 | 0.639092 | ||||||||
\(306\) | −14.4381 | −0.825369 | ||||||||
\(307\) | 11.1521 | 0.636486 | 0.318243 | − | 0.948009i | \(-0.396907\pi\) | ||||
0.318243 | + | 0.948009i | \(0.396907\pi\) | |||||||
\(308\) | −3.92530 | −0.223665 | ||||||||
\(309\) | −39.2202 | −2.23116 | ||||||||
\(310\) | −10.0613 | −0.571446 | ||||||||
\(311\) | −5.42995 | −0.307904 | −0.153952 | − | 0.988078i | \(-0.549200\pi\) | ||||
−0.153952 | + | 0.988078i | \(0.549200\pi\) | |||||||
\(312\) | 1.94071 | 0.109871 | ||||||||
\(313\) | −5.87031 | −0.331809 | −0.165905 | − | 0.986142i | \(-0.553054\pi\) | ||||
−0.165905 | + | 0.986142i | \(0.553054\pi\) | |||||||
\(314\) | −20.2095 | −1.14049 | ||||||||
\(315\) | 10.5950 | 0.596960 | ||||||||
\(316\) | −7.82323 | −0.440091 | ||||||||
\(317\) | 17.0584 | 0.958095 | 0.479048 | − | 0.877789i | \(-0.340982\pi\) | ||||
0.479048 | + | 0.877789i | \(0.340982\pi\) | |||||||
\(318\) | 22.0737 | 1.23783 | ||||||||
\(319\) | −1.86640 | −0.104499 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 19.8860 | 1.10993 | ||||||||
\(322\) | 4.65960 | 0.259669 | ||||||||
\(323\) | 2.17062 | 0.120776 | ||||||||
\(324\) | −9.81204 | −0.545113 | ||||||||
\(325\) | 0.812933 | 0.0450934 | ||||||||
\(326\) | 7.78522 | 0.431183 | ||||||||
\(327\) | −37.6077 | −2.07971 | ||||||||
\(328\) | 11.7137 | 0.646783 | ||||||||
\(329\) | 31.6378 | 1.74425 | ||||||||
\(330\) | −2.38729 | −0.131416 | ||||||||
\(331\) | −9.13065 | −0.501866 | −0.250933 | − | 0.968004i | \(-0.580737\pi\) | ||||
−0.250933 | + | 0.968004i | \(0.580737\pi\) | |||||||
\(332\) | −14.2689 | −0.783109 | ||||||||
\(333\) | 16.5569 | 0.907312 | ||||||||
\(334\) | −23.0156 | −1.25936 | ||||||||
\(335\) | −1.05981 | −0.0579034 | ||||||||
\(336\) | 9.37084 | 0.511221 | ||||||||
\(337\) | 29.1566 | 1.58826 | 0.794129 | − | 0.607749i | \(-0.207927\pi\) | ||||
0.794129 | + | 0.607749i | \(0.207927\pi\) | |||||||
\(338\) | −12.3391 | −0.671161 | ||||||||
\(339\) | 11.5455 | 0.627065 | ||||||||
\(340\) | −5.34911 | −0.290096 | ||||||||
\(341\) | 10.0613 | 0.544852 | ||||||||
\(342\) | −1.09529 | −0.0592264 | ||||||||
\(343\) | 5.52688 | 0.298423 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 2.83387 | 0.152571 | ||||||||
\(346\) | 4.79082 | 0.257556 | ||||||||
\(347\) | 3.01791 | 0.162010 | 0.0810049 | − | 0.996714i | \(-0.474187\pi\) | ||||
0.0810049 | + | 0.996714i | \(0.474187\pi\) | |||||||
\(348\) | 4.45565 | 0.238848 | ||||||||
\(349\) | 5.69395 | 0.304790 | 0.152395 | − | 0.988320i | \(-0.451301\pi\) | ||||
0.152395 | + | 0.988320i | \(0.451301\pi\) | |||||||
\(350\) | 3.92530 | 0.209816 | ||||||||
\(351\) | −0.583862 | −0.0311643 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −22.5135 | −1.19827 | −0.599136 | − | 0.800648i | \(-0.704489\pi\) | ||||
−0.599136 | + | 0.800648i | \(0.704489\pi\) | |||||||
\(354\) | 18.5862 | 0.987846 | ||||||||
\(355\) | −11.7969 | −0.626115 | ||||||||
\(356\) | 0.276107 | 0.0146336 | ||||||||
\(357\) | −50.1257 | −2.65293 | ||||||||
\(358\) | 12.9298 | 0.683363 | ||||||||
\(359\) | 23.1603 | 1.22235 | 0.611176 | − | 0.791495i | \(-0.290697\pi\) | ||||
0.611176 | + | 0.791495i | \(0.290697\pi\) | |||||||
\(360\) | 2.69915 | 0.142258 | ||||||||
\(361\) | −18.8353 | −0.991333 | ||||||||
\(362\) | −0.164956 | −0.00866988 | ||||||||
\(363\) | 2.38729 | 0.125300 | ||||||||
\(364\) | 3.19101 | 0.167254 | ||||||||
\(365\) | −2.94467 | −0.154131 | ||||||||
\(366\) | 26.6452 | 1.39276 | ||||||||
\(367\) | 10.8593 | 0.566851 | 0.283425 | − | 0.958994i | \(-0.408529\pi\) | ||||
0.283425 | + | 0.958994i | \(0.408529\pi\) | |||||||
\(368\) | 1.18707 | 0.0618801 | ||||||||
\(369\) | 31.6171 | 1.64592 | ||||||||
\(370\) | 6.13412 | 0.318898 | ||||||||
\(371\) | 36.2948 | 1.88433 | ||||||||
\(372\) | −24.0193 | −1.24534 | ||||||||
\(373\) | −18.9180 | −0.979535 | −0.489768 | − | 0.871853i | \(-0.662918\pi\) | ||||
−0.489768 | + | 0.871853i | \(0.662918\pi\) | |||||||
\(374\) | 5.34911 | 0.276596 | ||||||||
\(375\) | 2.38729 | 0.123279 | ||||||||
\(376\) | 8.05997 | 0.415661 | ||||||||
\(377\) | 1.51726 | 0.0781429 | ||||||||
\(378\) | −2.81922 | −0.145005 | ||||||||
\(379\) | −5.27705 | −0.271064 | −0.135532 | − | 0.990773i | \(-0.543274\pi\) | ||||
−0.135532 | + | 0.990773i | \(0.543274\pi\) | |||||||
\(380\) | −0.405790 | −0.0208166 | ||||||||
\(381\) | 24.2230 | 1.24098 | ||||||||
\(382\) | −25.0988 | −1.28417 | ||||||||
\(383\) | −36.4918 | −1.86465 | −0.932323 | − | 0.361627i | \(-0.882221\pi\) | ||||
−0.932323 | + | 0.361627i | \(0.882221\pi\) | |||||||
\(384\) | 2.38729 | 0.121826 | ||||||||
\(385\) | −3.92530 | −0.200052 | ||||||||
\(386\) | 8.07002 | 0.410753 | ||||||||
\(387\) | 2.69915 | 0.137205 | ||||||||
\(388\) | 3.54637 | 0.180040 | ||||||||
\(389\) | 4.06976 | 0.206345 | 0.103172 | − | 0.994663i | \(-0.467101\pi\) | ||||
0.103172 | + | 0.994663i | \(0.467101\pi\) | |||||||
\(390\) | 1.94071 | 0.0982715 | ||||||||
\(391\) | −6.34975 | −0.321121 | ||||||||
\(392\) | 8.40801 | 0.424669 | ||||||||
\(393\) | 11.6681 | 0.588576 | ||||||||
\(394\) | −18.0918 | −0.911451 | ||||||||
\(395\) | −7.82323 | −0.393630 | ||||||||
\(396\) | −2.69915 | −0.135637 | ||||||||
\(397\) | 7.75558 | 0.389242 | 0.194621 | − | 0.980879i | \(-0.437652\pi\) | ||||
0.194621 | + | 0.980879i | \(0.437652\pi\) | |||||||
\(398\) | 9.19769 | 0.461038 | ||||||||
\(399\) | −3.80259 | −0.190368 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 12.4546 | 0.621953 | 0.310976 | − | 0.950418i | \(-0.399344\pi\) | ||||
0.310976 | + | 0.950418i | \(0.399344\pi\) | |||||||
\(402\) | −2.53006 | −0.126188 | ||||||||
\(403\) | −8.17920 | −0.407435 | ||||||||
\(404\) | −11.9091 | −0.592499 | ||||||||
\(405\) | −9.81204 | −0.487564 | ||||||||
\(406\) | 7.32620 | 0.363593 | ||||||||
\(407\) | −6.13412 | −0.304057 | ||||||||
\(408\) | −12.7699 | −0.632203 | ||||||||
\(409\) | −19.2547 | −0.952083 | −0.476042 | − | 0.879423i | \(-0.657929\pi\) | ||||
−0.476042 | + | 0.879423i | \(0.657929\pi\) | |||||||
\(410\) | 11.7137 | 0.578500 | ||||||||
\(411\) | −37.6940 | −1.85931 | ||||||||
\(412\) | −16.4288 | −0.809388 | ||||||||
\(413\) | 30.5604 | 1.50378 | ||||||||
\(414\) | 3.20407 | 0.157471 | ||||||||
\(415\) | −14.2689 | −0.700434 | ||||||||
\(416\) | 0.812933 | 0.0398573 | ||||||||
\(417\) | −33.6191 | −1.64633 | ||||||||
\(418\) | 0.405790 | 0.0198478 | ||||||||
\(419\) | −28.1001 | −1.37278 | −0.686390 | − | 0.727234i | \(-0.740806\pi\) | ||||
−0.686390 | + | 0.727234i | \(0.740806\pi\) | |||||||
\(420\) | 9.37084 | 0.457250 | ||||||||
\(421\) | 16.8136 | 0.819444 | 0.409722 | − | 0.912211i | \(-0.365626\pi\) | ||||
0.409722 | + | 0.912211i | \(0.365626\pi\) | |||||||
\(422\) | 2.78371 | 0.135509 | ||||||||
\(423\) | 21.7551 | 1.05777 | ||||||||
\(424\) | 9.24636 | 0.449043 | ||||||||
\(425\) | −5.34911 | −0.259470 | ||||||||
\(426\) | −28.1626 | −1.36448 | ||||||||
\(427\) | 43.8113 | 2.12018 | ||||||||
\(428\) | 8.32995 | 0.402644 | ||||||||
\(429\) | −1.94071 | −0.0936982 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | −16.5619 | −0.797760 | −0.398880 | − | 0.917003i | \(-0.630601\pi\) | ||||
−0.398880 | + | 0.917003i | \(0.630601\pi\) | |||||||
\(432\) | −0.718217 | −0.0345552 | ||||||||
\(433\) | −24.0005 | −1.15339 | −0.576696 | − | 0.816959i | \(-0.695658\pi\) | ||||
−0.576696 | + | 0.816959i | \(0.695658\pi\) | |||||||
\(434\) | −39.4938 | −1.89576 | ||||||||
\(435\) | 4.45565 | 0.213632 | ||||||||
\(436\) | −15.7533 | −0.754447 | ||||||||
\(437\) | −0.481700 | −0.0230428 | ||||||||
\(438\) | −7.02977 | −0.335895 | ||||||||
\(439\) | 16.7666 | 0.800228 | 0.400114 | − | 0.916465i | \(-0.368970\pi\) | ||||
0.400114 | + | 0.916465i | \(0.368970\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 22.6945 | 1.08069 | ||||||||
\(442\) | −4.34847 | −0.206836 | ||||||||
\(443\) | −7.53930 | −0.358203 | −0.179101 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179101 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(444\) | 14.6439 | 0.694969 | ||||||||
\(445\) | 0.276107 | 0.0130887 | ||||||||
\(446\) | 10.5184 | 0.498062 | ||||||||
\(447\) | 13.6302 | 0.644687 | ||||||||
\(448\) | 3.92530 | 0.185453 | ||||||||
\(449\) | −29.5577 | −1.39492 | −0.697458 | − | 0.716626i | \(-0.745686\pi\) | ||||
−0.697458 | + | 0.716626i | \(0.745686\pi\) | |||||||
\(450\) | 2.69915 | 0.127239 | ||||||||
\(451\) | −11.7137 | −0.551578 | ||||||||
\(452\) | 4.83624 | 0.227477 | ||||||||
\(453\) | −15.9344 | −0.748664 | ||||||||
\(454\) | −17.8730 | −0.838820 | ||||||||
\(455\) | 3.19101 | 0.149597 | ||||||||
\(456\) | −0.968738 | −0.0453653 | ||||||||
\(457\) | 33.4690 | 1.56561 | 0.782806 | − | 0.622266i | \(-0.213788\pi\) | ||||
0.782806 | + | 0.622266i | \(0.213788\pi\) | |||||||
\(458\) | 13.1275 | 0.613409 | ||||||||
\(459\) | 3.84182 | 0.179321 | ||||||||
\(460\) | 1.18707 | 0.0553473 | ||||||||
\(461\) | 1.75000 | 0.0815056 | 0.0407528 | − | 0.999169i | \(-0.487024\pi\) | ||||
0.0407528 | + | 0.999169i | \(0.487024\pi\) | |||||||
\(462\) | −9.37084 | −0.435971 | ||||||||
\(463\) | −5.58904 | −0.259745 | −0.129872 | − | 0.991531i | \(-0.541457\pi\) | ||||
−0.129872 | + | 0.991531i | \(0.541457\pi\) | |||||||
\(464\) | 1.86640 | 0.0866456 | ||||||||
\(465\) | −24.0193 | −1.11387 | ||||||||
\(466\) | −24.2231 | −1.12211 | ||||||||
\(467\) | −8.21645 | −0.380212 | −0.190106 | − | 0.981764i | \(-0.560883\pi\) | ||||
−0.190106 | + | 0.981764i | \(0.560883\pi\) | |||||||
\(468\) | 2.19423 | 0.101428 | ||||||||
\(469\) | −4.16006 | −0.192094 | ||||||||
\(470\) | 8.05997 | 0.371779 | ||||||||
\(471\) | −48.2460 | −2.22306 | ||||||||
\(472\) | 7.78548 | 0.358356 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −18.6763 | −0.857832 | ||||||||
\(475\) | −0.405790 | −0.0186189 | ||||||||
\(476\) | −20.9969 | −0.962391 | ||||||||
\(477\) | 24.9573 | 1.14272 | ||||||||
\(478\) | 6.88492 | 0.314909 | ||||||||
\(479\) | −20.6013 | −0.941297 | −0.470649 | − | 0.882321i | \(-0.655980\pi\) | ||||
−0.470649 | + | 0.882321i | \(0.655980\pi\) | |||||||
\(480\) | 2.38729 | 0.108964 | ||||||||
\(481\) | 4.98663 | 0.227371 | ||||||||
\(482\) | 28.1350 | 1.28151 | ||||||||
\(483\) | 11.1238 | 0.506151 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 3.54637 | 0.161032 | ||||||||
\(486\) | −21.2695 | −0.964805 | ||||||||
\(487\) | 12.5620 | 0.569239 | 0.284620 | − | 0.958640i | \(-0.408133\pi\) | ||||
0.284620 | + | 0.958640i | \(0.408133\pi\) | |||||||
\(488\) | 11.1613 | 0.505246 | ||||||||
\(489\) | 18.5856 | 0.840468 | ||||||||
\(490\) | 8.40801 | 0.379835 | ||||||||
\(491\) | −15.5086 | −0.699895 | −0.349948 | − | 0.936769i | \(-0.613801\pi\) | ||||
−0.349948 | + | 0.936769i | \(0.613801\pi\) | |||||||
\(492\) | 27.9641 | 1.26072 | ||||||||
\(493\) | −9.98360 | −0.449639 | ||||||||
\(494\) | −0.329880 | −0.0148420 | ||||||||
\(495\) | −2.69915 | −0.121318 | ||||||||
\(496\) | −10.0613 | −0.451768 | ||||||||
\(497\) | −46.3065 | −2.07713 | ||||||||
\(498\) | −34.0641 | −1.52645 | ||||||||
\(499\) | 18.3476 | 0.821350 | 0.410675 | − | 0.911782i | \(-0.365293\pi\) | ||||
0.410675 | + | 0.911782i | \(0.365293\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −54.9450 | −2.45476 | ||||||||
\(502\) | 2.91600 | 0.130147 | ||||||||
\(503\) | −11.9948 | −0.534820 | −0.267410 | − | 0.963583i | \(-0.586168\pi\) | ||||
−0.267410 | + | 0.963583i | \(0.586168\pi\) | |||||||
\(504\) | 10.5950 | 0.471938 | ||||||||
\(505\) | −11.9091 | −0.529947 | ||||||||
\(506\) | −1.18707 | −0.0527716 | ||||||||
\(507\) | −29.4571 | −1.30824 | ||||||||
\(508\) | 10.1467 | 0.450185 | ||||||||
\(509\) | 20.1205 | 0.891825 | 0.445912 | − | 0.895077i | \(-0.352879\pi\) | ||||
0.445912 | + | 0.895077i | \(0.352879\pi\) | |||||||
\(510\) | −12.7699 | −0.565460 | ||||||||
\(511\) | −11.5587 | −0.511327 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.291445 | 0.0128676 | ||||||||
\(514\) | −22.6806 | −1.00040 | ||||||||
\(515\) | −16.4288 | −0.723939 | ||||||||
\(516\) | 2.38729 | 0.105095 | ||||||||
\(517\) | −8.05997 | −0.354477 | ||||||||
\(518\) | 24.0783 | 1.05794 | ||||||||
\(519\) | 11.4371 | 0.502031 | ||||||||
\(520\) | 0.812933 | 0.0356495 | ||||||||
\(521\) | 24.7788 | 1.08558 | 0.542790 | − | 0.839868i | \(-0.317368\pi\) | ||||
0.542790 | + | 0.839868i | \(0.317368\pi\) | |||||||
\(522\) | 5.03770 | 0.220494 | ||||||||
\(523\) | 17.1383 | 0.749406 | 0.374703 | − | 0.927145i | \(-0.377745\pi\) | ||||
0.374703 | + | 0.927145i | \(0.377745\pi\) | |||||||
\(524\) | 4.88758 | 0.213515 | ||||||||
\(525\) | 9.37084 | 0.408977 | ||||||||
\(526\) | −31.0321 | −1.35306 | ||||||||
\(527\) | 53.8193 | 2.34440 | ||||||||
\(528\) | −2.38729 | −0.103893 | ||||||||
\(529\) | −21.5909 | −0.938734 | ||||||||
\(530\) | 9.24636 | 0.401636 | ||||||||
\(531\) | 21.0142 | 0.911938 | ||||||||
\(532\) | −1.59285 | −0.0690588 | ||||||||
\(533\) | 9.52248 | 0.412464 | ||||||||
\(534\) | 0.659147 | 0.0285241 | ||||||||
\(535\) | 8.32995 | 0.360135 | ||||||||
\(536\) | −1.05981 | −0.0457767 | ||||||||
\(537\) | 30.8673 | 1.33202 | ||||||||
\(538\) | −17.5504 | −0.756650 | ||||||||
\(539\) | −8.40801 | −0.362159 | ||||||||
\(540\) | −0.718217 | −0.0309071 | ||||||||
\(541\) | 29.4682 | 1.26694 | 0.633468 | − | 0.773769i | \(-0.281631\pi\) | ||||
0.633468 | + | 0.773769i | \(0.281631\pi\) | |||||||
\(542\) | 21.3862 | 0.918617 | ||||||||
\(543\) | −0.393797 | −0.0168994 | ||||||||
\(544\) | −5.34911 | −0.229341 | ||||||||
\(545\) | −15.7533 | −0.674798 | ||||||||
\(546\) | 7.61786 | 0.326014 | ||||||||
\(547\) | 38.7145 | 1.65531 | 0.827657 | − | 0.561235i | \(-0.189674\pi\) | ||||
0.827657 | + | 0.561235i | \(0.189674\pi\) | |||||||
\(548\) | −15.7894 | −0.674492 | ||||||||
\(549\) | 30.1259 | 1.28574 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −0.757368 | −0.0322650 | ||||||||
\(552\) | 2.83387 | 0.120618 | ||||||||
\(553\) | −30.7086 | −1.30586 | ||||||||
\(554\) | 29.2162 | 1.24128 | ||||||||
\(555\) | 14.6439 | 0.621599 | ||||||||
\(556\) | −14.0825 | −0.597232 | ||||||||
\(557\) | 16.3853 | 0.694267 | 0.347133 | − | 0.937816i | \(-0.387155\pi\) | ||||
0.347133 | + | 0.937816i | \(0.387155\pi\) | |||||||
\(558\) | −27.1571 | −1.14965 | ||||||||
\(559\) | 0.812933 | 0.0343834 | ||||||||
\(560\) | 3.92530 | 0.165874 | ||||||||
\(561\) | 12.7699 | 0.539145 | ||||||||
\(562\) | 20.3275 | 0.857465 | ||||||||
\(563\) | −23.1756 | −0.976735 | −0.488368 | − | 0.872638i | \(-0.662407\pi\) | ||||
−0.488368 | + | 0.872638i | \(0.662407\pi\) | |||||||
\(564\) | 19.2415 | 0.810212 | ||||||||
\(565\) | 4.83624 | 0.203462 | ||||||||
\(566\) | 29.9954 | 1.26080 | ||||||||
\(567\) | −38.5152 | −1.61749 | ||||||||
\(568\) | −11.7969 | −0.494987 | ||||||||
\(569\) | 45.3924 | 1.90295 | 0.951475 | − | 0.307727i | \(-0.0995682\pi\) | ||||
0.951475 | + | 0.307727i | \(0.0995682\pi\) | |||||||
\(570\) | −0.968738 | −0.0405760 | ||||||||
\(571\) | 46.1854 | 1.93280 | 0.966400 | − | 0.257044i | \(-0.0827484\pi\) | ||||
0.966400 | + | 0.257044i | \(0.0827484\pi\) | |||||||
\(572\) | −0.812933 | −0.0339904 | ||||||||
\(573\) | −59.9181 | −2.50311 | ||||||||
\(574\) | 45.9800 | 1.91917 | ||||||||
\(575\) | 1.18707 | 0.0495041 | ||||||||
\(576\) | 2.69915 | 0.112465 | ||||||||
\(577\) | −32.7305 | −1.36259 | −0.681295 | − | 0.732009i | \(-0.738583\pi\) | ||||
−0.681295 | + | 0.732009i | \(0.738583\pi\) | |||||||
\(578\) | 11.6130 | 0.483038 | ||||||||
\(579\) | 19.2655 | 0.800645 | ||||||||
\(580\) | 1.86640 | 0.0774982 | ||||||||
\(581\) | −56.0099 | −2.32368 | ||||||||
\(582\) | 8.46621 | 0.350935 | ||||||||
\(583\) | −9.24636 | −0.382945 | ||||||||
\(584\) | −2.94467 | −0.121851 | ||||||||
\(585\) | 2.19423 | 0.0907202 | ||||||||
\(586\) | −19.8554 | −0.820220 | ||||||||
\(587\) | 13.7346 | 0.566889 | 0.283444 | − | 0.958989i | \(-0.408523\pi\) | ||||
0.283444 | + | 0.958989i | \(0.408523\pi\) | |||||||
\(588\) | 20.0724 | 0.827770 | ||||||||
\(589\) | 4.08279 | 0.168229 | ||||||||
\(590\) | 7.78548 | 0.320523 | ||||||||
\(591\) | −43.1903 | −1.77661 | ||||||||
\(592\) | 6.13412 | 0.252111 | ||||||||
\(593\) | 10.0242 | 0.411646 | 0.205823 | − | 0.978589i | \(-0.434013\pi\) | ||||
0.205823 | + | 0.978589i | \(0.434013\pi\) | |||||||
\(594\) | 0.718217 | 0.0294688 | ||||||||
\(595\) | −20.9969 | −0.860789 | ||||||||
\(596\) | 5.70949 | 0.233870 | ||||||||
\(597\) | 21.9575 | 0.898662 | ||||||||
\(598\) | 0.965006 | 0.0394620 | ||||||||
\(599\) | 20.6244 | 0.842689 | 0.421344 | − | 0.906901i | \(-0.361558\pi\) | ||||
0.421344 | + | 0.906901i | \(0.361558\pi\) | |||||||
\(600\) | 2.38729 | 0.0974607 | ||||||||
\(601\) | 44.4507 | 1.81318 | 0.906590 | − | 0.422012i | \(-0.138676\pi\) | ||||
0.906590 | + | 0.422012i | \(0.138676\pi\) | |||||||
\(602\) | 3.92530 | 0.159983 | ||||||||
\(603\) | −2.86058 | −0.116492 | ||||||||
\(604\) | −6.67469 | −0.271589 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −28.4304 | −1.15491 | ||||||||
\(607\) | −18.3201 | −0.743591 | −0.371796 | − | 0.928315i | \(-0.621258\pi\) | ||||
−0.371796 | + | 0.928315i | \(0.621258\pi\) | |||||||
\(608\) | −0.405790 | −0.0164570 | ||||||||
\(609\) | 17.4898 | 0.708721 | ||||||||
\(610\) | 11.1613 | 0.451906 | ||||||||
\(611\) | 6.55222 | 0.265074 | ||||||||
\(612\) | −14.4381 | −0.583624 | ||||||||
\(613\) | −22.0525 | −0.890694 | −0.445347 | − | 0.895358i | \(-0.646920\pi\) | ||||
−0.445347 | + | 0.895358i | \(0.646920\pi\) | |||||||
\(614\) | 11.1521 | 0.450063 | ||||||||
\(615\) | 27.9641 | 1.12762 | ||||||||
\(616\) | −3.92530 | −0.158155 | ||||||||
\(617\) | 20.3489 | 0.819215 | 0.409607 | − | 0.912262i | \(-0.365666\pi\) | ||||
0.409607 | + | 0.912262i | \(0.365666\pi\) | |||||||
\(618\) | −39.2202 | −1.57767 | ||||||||
\(619\) | −43.6503 | −1.75446 | −0.877228 | − | 0.480075i | \(-0.840610\pi\) | ||||
−0.877228 | + | 0.480075i | \(0.840610\pi\) | |||||||
\(620\) | −10.0613 | −0.404073 | ||||||||
\(621\) | −0.852571 | −0.0342125 | ||||||||
\(622\) | −5.42995 | −0.217721 | ||||||||
\(623\) | 1.08380 | 0.0434217 | ||||||||
\(624\) | 1.94071 | 0.0776904 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.87031 | −0.234625 | ||||||||
\(627\) | 0.968738 | 0.0386877 | ||||||||
\(628\) | −20.2095 | −0.806448 | ||||||||
\(629\) | −32.8121 | −1.30830 | ||||||||
\(630\) | 10.5950 | 0.422114 | ||||||||
\(631\) | −0.442788 | −0.0176271 | −0.00881355 | − | 0.999961i | \(-0.502805\pi\) | ||||
−0.00881355 | + | 0.999961i | \(0.502805\pi\) | |||||||
\(632\) | −7.82323 | −0.311191 | ||||||||
\(633\) | 6.64551 | 0.264135 | ||||||||
\(634\) | 17.0584 | 0.677476 | ||||||||
\(635\) | 10.1467 | 0.402658 | ||||||||
\(636\) | 22.0737 | 0.875281 | ||||||||
\(637\) | 6.83515 | 0.270819 | ||||||||
\(638\) | −1.86640 | −0.0738916 | ||||||||
\(639\) | −31.8416 | −1.25964 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −15.0798 | −0.595616 | −0.297808 | − | 0.954626i | \(-0.596256\pi\) | ||||
−0.297808 | + | 0.954626i | \(0.596256\pi\) | |||||||
\(642\) | 19.8860 | 0.784838 | ||||||||
\(643\) | −10.5018 | −0.414151 | −0.207076 | − | 0.978325i | \(-0.566395\pi\) | ||||
−0.207076 | + | 0.978325i | \(0.566395\pi\) | |||||||
\(644\) | 4.65960 | 0.183614 | ||||||||
\(645\) | 2.38729 | 0.0939994 | ||||||||
\(646\) | 2.17062 | 0.0854018 | ||||||||
\(647\) | 49.9513 | 1.96379 | 0.981893 | − | 0.189435i | \(-0.0606656\pi\) | ||||
0.981893 | + | 0.189435i | \(0.0606656\pi\) | |||||||
\(648\) | −9.81204 | −0.385453 | ||||||||
\(649\) | −7.78548 | −0.305607 | ||||||||
\(650\) | 0.812933 | 0.0318859 | ||||||||
\(651\) | −94.2832 | −3.69525 | ||||||||
\(652\) | 7.78522 | 0.304893 | ||||||||
\(653\) | −0.741876 | −0.0290318 | −0.0145159 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145159 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(654\) | −37.6077 | −1.47058 | ||||||||
\(655\) | 4.88758 | 0.190973 | ||||||||
\(656\) | 11.7137 | 0.457344 | ||||||||
\(657\) | −7.94810 | −0.310085 | ||||||||
\(658\) | 31.6378 | 1.23337 | ||||||||
\(659\) | 1.03186 | 0.0401955 | 0.0200978 | − | 0.999798i | \(-0.493602\pi\) | ||||
0.0200978 | + | 0.999798i | \(0.493602\pi\) | |||||||
\(660\) | −2.38729 | −0.0929251 | ||||||||
\(661\) | 17.8340 | 0.693661 | 0.346831 | − | 0.937928i | \(-0.387258\pi\) | ||||
0.346831 | + | 0.937928i | \(0.387258\pi\) | |||||||
\(662\) | −9.13065 | −0.354873 | ||||||||
\(663\) | −10.3811 | −0.403167 | ||||||||
\(664\) | −14.2689 | −0.553742 | ||||||||
\(665\) | −1.59285 | −0.0617681 | ||||||||
\(666\) | 16.5569 | 0.641567 | ||||||||
\(667\) | 2.21555 | 0.0857863 | ||||||||
\(668\) | −23.0156 | −0.890502 | ||||||||
\(669\) | 25.1105 | 0.970829 | ||||||||
\(670\) | −1.05981 | −0.0409439 | ||||||||
\(671\) | −11.1613 | −0.430876 | ||||||||
\(672\) | 9.37084 | 0.361488 | ||||||||
\(673\) | −20.3742 | −0.785369 | −0.392684 | − | 0.919673i | \(-0.628453\pi\) | ||||
−0.392684 | + | 0.919673i | \(0.628453\pi\) | |||||||
\(674\) | 29.1566 | 1.12307 | ||||||||
\(675\) | −0.718217 | −0.0276442 | ||||||||
\(676\) | −12.3391 | −0.474582 | ||||||||
\(677\) | −10.7885 | −0.414638 | −0.207319 | − | 0.978273i | \(-0.566474\pi\) | ||||
−0.207319 | + | 0.978273i | \(0.566474\pi\) | |||||||
\(678\) | 11.5455 | 0.443402 | ||||||||
\(679\) | 13.9206 | 0.534223 | ||||||||
\(680\) | −5.34911 | −0.205129 | ||||||||
\(681\) | −42.6679 | −1.63504 | ||||||||
\(682\) | 10.0613 | 0.385269 | ||||||||
\(683\) | −33.0968 | −1.26641 | −0.633207 | − | 0.773982i | \(-0.718262\pi\) | ||||
−0.633207 | + | 0.773982i | \(0.718262\pi\) | |||||||
\(684\) | −1.09529 | −0.0418794 | ||||||||
\(685\) | −15.7894 | −0.603284 | ||||||||
\(686\) | 5.52688 | 0.211017 | ||||||||
\(687\) | 31.3392 | 1.19567 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 7.51667 | 0.286362 | ||||||||
\(690\) | 2.83387 | 0.107884 | ||||||||
\(691\) | 25.0195 | 0.951788 | 0.475894 | − | 0.879503i | \(-0.342125\pi\) | ||||
0.475894 | + | 0.879503i | \(0.342125\pi\) | |||||||
\(692\) | 4.79082 | 0.182119 | ||||||||
\(693\) | −10.5950 | −0.402470 | ||||||||
\(694\) | 3.01791 | 0.114558 | ||||||||
\(695\) | −14.0825 | −0.534181 | ||||||||
\(696\) | 4.45565 | 0.168891 | ||||||||
\(697\) | −62.6581 | −2.37334 | ||||||||
\(698\) | 5.69395 | 0.215519 | ||||||||
\(699\) | −57.8274 | −2.18723 | ||||||||
\(700\) | 3.92530 | 0.148363 | ||||||||
\(701\) | −12.9498 | −0.489109 | −0.244554 | − | 0.969636i | \(-0.578642\pi\) | ||||
−0.244554 | + | 0.969636i | \(0.578642\pi\) | |||||||
\(702\) | −0.583862 | −0.0220365 | ||||||||
\(703\) | −2.48916 | −0.0938806 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 19.2415 | 0.724676 | ||||||||
\(706\) | −22.5135 | −0.847306 | ||||||||
\(707\) | −46.7467 | −1.75809 | ||||||||
\(708\) | 18.5862 | 0.698512 | ||||||||
\(709\) | −1.17477 | −0.0441195 | −0.0220598 | − | 0.999757i | \(-0.507022\pi\) | ||||
−0.0220598 | + | 0.999757i | \(0.507022\pi\) | |||||||
\(710\) | −11.7969 | −0.442730 | ||||||||
\(711\) | −21.1161 | −0.791915 | ||||||||
\(712\) | 0.276107 | 0.0103475 | ||||||||
\(713\) | −11.9435 | −0.447287 | ||||||||
\(714\) | −50.1257 | −1.87591 | ||||||||
\(715\) | −0.812933 | −0.0304020 | ||||||||
\(716\) | 12.9298 | 0.483211 | ||||||||
\(717\) | 16.4363 | 0.613824 | ||||||||
\(718\) | 23.1603 | 0.864334 | ||||||||
\(719\) | −15.5216 | −0.578857 | −0.289428 | − | 0.957200i | \(-0.593465\pi\) | ||||
−0.289428 | + | 0.957200i | \(0.593465\pi\) | |||||||
\(720\) | 2.69915 | 0.100591 | ||||||||
\(721\) | −64.4880 | −2.40166 | ||||||||
\(722\) | −18.8353 | −0.700979 | ||||||||
\(723\) | 67.1664 | 2.49795 | ||||||||
\(724\) | −0.164956 | −0.00613053 | ||||||||
\(725\) | 1.86640 | 0.0693165 | ||||||||
\(726\) | 2.38729 | 0.0886006 | ||||||||
\(727\) | 26.1274 | 0.969011 | 0.484505 | − | 0.874788i | \(-0.339000\pi\) | ||||
0.484505 | + | 0.874788i | \(0.339000\pi\) | |||||||
\(728\) | 3.19101 | 0.118267 | ||||||||
\(729\) | −21.3404 | −0.790385 | ||||||||
\(730\) | −2.94467 | −0.108987 | ||||||||
\(731\) | −5.34911 | −0.197844 | ||||||||
\(732\) | 26.6452 | 0.984833 | ||||||||
\(733\) | 48.5419 | 1.79294 | 0.896468 | − | 0.443109i | \(-0.146124\pi\) | ||||
0.896468 | + | 0.443109i | \(0.146124\pi\) | |||||||
\(734\) | 10.8593 | 0.400824 | ||||||||
\(735\) | 20.0724 | 0.740380 | ||||||||
\(736\) | 1.18707 | 0.0437559 | ||||||||
\(737\) | 1.05981 | 0.0390385 | ||||||||
\(738\) | 31.6171 | 1.16384 | ||||||||
\(739\) | −7.99208 | −0.293994 | −0.146997 | − | 0.989137i | \(-0.546961\pi\) | ||||
−0.146997 | + | 0.989137i | \(0.546961\pi\) | |||||||
\(740\) | 6.13412 | 0.225495 | ||||||||
\(741\) | −0.787520 | −0.0289303 | ||||||||
\(742\) | 36.2948 | 1.33242 | ||||||||
\(743\) | 37.4068 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259295\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259295\pi\) | |||||||
\(744\) | −24.0193 | −0.880592 | ||||||||
\(745\) | 5.70949 | 0.209180 | ||||||||
\(746\) | −18.9180 | −0.692636 | ||||||||
\(747\) | −38.5140 | −1.40915 | ||||||||
\(748\) | 5.34911 | 0.195583 | ||||||||
\(749\) | 32.6976 | 1.19474 | ||||||||
\(750\) | 2.38729 | 0.0871715 | ||||||||
\(751\) | 42.9305 | 1.56656 | 0.783278 | − | 0.621672i | \(-0.213546\pi\) | ||||
0.783278 | + | 0.621672i | \(0.213546\pi\) | |||||||
\(752\) | 8.05997 | 0.293917 | ||||||||
\(753\) | 6.96133 | 0.253685 | ||||||||
\(754\) | 1.51726 | 0.0552554 | ||||||||
\(755\) | −6.67469 | −0.242917 | ||||||||
\(756\) | −2.81922 | −0.102534 | ||||||||
\(757\) | −12.6484 | −0.459714 | −0.229857 | − | 0.973224i | \(-0.573826\pi\) | ||||
−0.229857 | + | 0.973224i | \(0.573826\pi\) | |||||||
\(758\) | −5.27705 | −0.191671 | ||||||||
\(759\) | −2.83387 | −0.102863 | ||||||||
\(760\) | −0.405790 | −0.0147196 | ||||||||
\(761\) | 7.52832 | 0.272901 | 0.136451 | − | 0.990647i | \(-0.456430\pi\) | ||||
0.136451 | + | 0.990647i | \(0.456430\pi\) | |||||||
\(762\) | 24.2230 | 0.877507 | ||||||||
\(763\) | −61.8366 | −2.23863 | ||||||||
\(764\) | −25.0988 | −0.908042 | ||||||||
\(765\) | −14.4381 | −0.522009 | ||||||||
\(766\) | −36.4918 | −1.31850 | ||||||||
\(767\) | 6.32908 | 0.228530 | ||||||||
\(768\) | 2.38729 | 0.0861439 | ||||||||
\(769\) | −32.9311 | −1.18753 | −0.593763 | − | 0.804640i | \(-0.702358\pi\) | ||||
−0.593763 | + | 0.804640i | \(0.702358\pi\) | |||||||
\(770\) | −3.92530 | −0.141458 | ||||||||
\(771\) | −54.1450 | −1.94999 | ||||||||
\(772\) | 8.07002 | 0.290446 | ||||||||
\(773\) | −35.8391 | −1.28904 | −0.644521 | − | 0.764587i | \(-0.722943\pi\) | ||||
−0.644521 | + | 0.764587i | \(0.722943\pi\) | |||||||
\(774\) | 2.69915 | 0.0970189 | ||||||||
\(775\) | −10.0613 | −0.361414 | ||||||||
\(776\) | 3.54637 | 0.127307 | ||||||||
\(777\) | 57.4818 | 2.06215 | ||||||||
\(778\) | 4.06976 | 0.145908 | ||||||||
\(779\) | −4.75332 | −0.170305 | ||||||||
\(780\) | 1.94071 | 0.0694884 | ||||||||
\(781\) | 11.7969 | 0.422127 | ||||||||
\(782\) | −6.34975 | −0.227067 | ||||||||
\(783\) | −1.34048 | −0.0479049 | ||||||||
\(784\) | 8.40801 | 0.300286 | ||||||||
\(785\) | −20.2095 | −0.721309 | ||||||||
\(786\) | 11.6681 | 0.416186 | ||||||||
\(787\) | −40.5948 | −1.44705 | −0.723525 | − | 0.690299i | \(-0.757479\pi\) | ||||
−0.723525 | + | 0.690299i | \(0.757479\pi\) | |||||||
\(788\) | −18.0918 | −0.644493 | ||||||||
\(789\) | −74.0826 | −2.63741 | ||||||||
\(790\) | −7.82323 | −0.278338 | ||||||||
\(791\) | 18.9837 | 0.674982 | ||||||||
\(792\) | −2.69915 | −0.0959101 | ||||||||
\(793\) | 9.07336 | 0.322204 | ||||||||
\(794\) | 7.75558 | 0.275235 | ||||||||
\(795\) | 22.0737 | 0.782875 | ||||||||
\(796\) | 9.19769 | 0.326003 | ||||||||
\(797\) | 34.1345 | 1.20911 | 0.604554 | − | 0.796565i | \(-0.293352\pi\) | ||||
0.604554 | + | 0.796565i | \(0.293352\pi\) | |||||||
\(798\) | −3.80259 | −0.134610 | ||||||||
\(799\) | −43.1137 | −1.52525 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0.745254 | 0.0263322 | ||||||||
\(802\) | 12.4546 | 0.439787 | ||||||||
\(803\) | 2.94467 | 0.103915 | ||||||||
\(804\) | −2.53006 | −0.0892285 | ||||||||
\(805\) | 4.65960 | 0.164229 | ||||||||
\(806\) | −8.17920 | −0.288100 | ||||||||
\(807\) | −41.8978 | −1.47487 | ||||||||
\(808\) | −11.9091 | −0.418960 | ||||||||
\(809\) | −5.99334 | −0.210715 | −0.105357 | − | 0.994434i | \(-0.533599\pi\) | ||||
−0.105357 | + | 0.994434i | \(0.533599\pi\) | |||||||
\(810\) | −9.81204 | −0.344760 | ||||||||
\(811\) | 37.2917 | 1.30949 | 0.654744 | − | 0.755851i | \(-0.272776\pi\) | ||||
0.654744 | + | 0.755851i | \(0.272776\pi\) | |||||||
\(812\) | 7.32620 | 0.257099 | ||||||||
\(813\) | 51.0551 | 1.79058 | ||||||||
\(814\) | −6.13412 | −0.215001 | ||||||||
\(815\) | 7.78522 | 0.272704 | ||||||||
\(816\) | −12.7699 | −0.447035 | ||||||||
\(817\) | −0.405790 | −0.0141968 | ||||||||
\(818\) | −19.2547 | −0.673224 | ||||||||
\(819\) | 8.61301 | 0.300963 | ||||||||
\(820\) | 11.7137 | 0.409061 | ||||||||
\(821\) | 20.2387 | 0.706337 | 0.353169 | − | 0.935560i | \(-0.385104\pi\) | ||||
0.353169 | + | 0.935560i | \(0.385104\pi\) | |||||||
\(822\) | −37.6940 | −1.31473 | ||||||||
\(823\) | 35.4228 | 1.23476 | 0.617381 | − | 0.786664i | \(-0.288194\pi\) | ||||
0.617381 | + | 0.786664i | \(0.288194\pi\) | |||||||
\(824\) | −16.4288 | −0.572324 | ||||||||
\(825\) | −2.38729 | −0.0831147 | ||||||||
\(826\) | 30.5604 | 1.06333 | ||||||||
\(827\) | −36.7247 | −1.27704 | −0.638521 | − | 0.769605i | \(-0.720453\pi\) | ||||
−0.638521 | + | 0.769605i | \(0.720453\pi\) | |||||||
\(828\) | 3.20407 | 0.111349 | ||||||||
\(829\) | 1.07736 | 0.0374183 | 0.0187092 | − | 0.999825i | \(-0.494044\pi\) | ||||
0.0187092 | + | 0.999825i | \(0.494044\pi\) | |||||||
\(830\) | −14.2689 | −0.495282 | ||||||||
\(831\) | 69.7475 | 2.41951 | ||||||||
\(832\) | 0.812933 | 0.0281834 | ||||||||
\(833\) | −44.9754 | −1.55831 | ||||||||
\(834\) | −33.6191 | −1.16413 | ||||||||
\(835\) | −23.0156 | −0.796489 | ||||||||
\(836\) | 0.405790 | 0.0140345 | ||||||||
\(837\) | 7.22623 | 0.249775 | ||||||||
\(838\) | −28.1001 | −0.970702 | ||||||||
\(839\) | 14.4935 | 0.500371 | 0.250186 | − | 0.968198i | \(-0.419508\pi\) | ||||
0.250186 | + | 0.968198i | \(0.419508\pi\) | |||||||
\(840\) | 9.37084 | 0.323325 | ||||||||
\(841\) | −25.5165 | −0.879881 | ||||||||
\(842\) | 16.8136 | 0.579434 | ||||||||
\(843\) | 48.5277 | 1.67138 | ||||||||
\(844\) | 2.78371 | 0.0958191 | ||||||||
\(845\) | −12.3391 | −0.424479 | ||||||||
\(846\) | 21.7551 | 0.747954 | ||||||||
\(847\) | 3.92530 | 0.134875 | ||||||||
\(848\) | 9.24636 | 0.317521 | ||||||||
\(849\) | 71.6076 | 2.45757 | ||||||||
\(850\) | −5.34911 | −0.183473 | ||||||||
\(851\) | 7.28161 | 0.249610 | ||||||||
\(852\) | −28.1626 | −0.964836 | ||||||||
\(853\) | 10.4133 | 0.356545 | 0.178273 | − | 0.983981i | \(-0.442949\pi\) | ||||
0.178273 | + | 0.983981i | \(0.442949\pi\) | |||||||
\(854\) | 43.8113 | 1.49919 | ||||||||
\(855\) | −1.09529 | −0.0374581 | ||||||||
\(856\) | 8.32995 | 0.284712 | ||||||||
\(857\) | −17.7157 | −0.605158 | −0.302579 | − | 0.953124i | \(-0.597848\pi\) | ||||
−0.302579 | + | 0.953124i | \(0.597848\pi\) | |||||||
\(858\) | −1.94071 | −0.0662546 | ||||||||
\(859\) | 14.2764 | 0.487104 | 0.243552 | − | 0.969888i | \(-0.421687\pi\) | ||||
0.243552 | + | 0.969888i | \(0.421687\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | 109.767 | 3.74086 | ||||||||
\(862\) | −16.5619 | −0.564101 | ||||||||
\(863\) | 19.0979 | 0.650101 | 0.325051 | − | 0.945697i | \(-0.394619\pi\) | ||||
0.325051 | + | 0.945697i | \(0.394619\pi\) | |||||||
\(864\) | −0.718217 | −0.0244342 | ||||||||
\(865\) | 4.79082 | 0.162893 | ||||||||
\(866\) | −24.0005 | −0.815571 | ||||||||
\(867\) | 27.7236 | 0.941544 | ||||||||
\(868\) | −39.4938 | −1.34051 | ||||||||
\(869\) | 7.82323 | 0.265385 | ||||||||
\(870\) | 4.45565 | 0.151061 | ||||||||
\(871\) | −0.861552 | −0.0291926 | ||||||||
\(872\) | −15.7533 | −0.533475 | ||||||||
\(873\) | 9.57218 | 0.323969 | ||||||||
\(874\) | −0.481700 | −0.0162937 | ||||||||
\(875\) | 3.92530 | 0.132699 | ||||||||
\(876\) | −7.02977 | −0.237514 | ||||||||
\(877\) | 1.36115 | 0.0459627 | 0.0229813 | − | 0.999736i | \(-0.492684\pi\) | ||||
0.0229813 | + | 0.999736i | \(0.492684\pi\) | |||||||
\(878\) | 16.7666 | 0.565847 | ||||||||
\(879\) | −47.4006 | −1.59878 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −21.8139 | −0.734927 | −0.367464 | − | 0.930038i | \(-0.619774\pi\) | ||||
−0.367464 | + | 0.930038i | \(0.619774\pi\) | |||||||
\(882\) | 22.6945 | 0.764163 | ||||||||
\(883\) | 9.99369 | 0.336315 | 0.168157 | − | 0.985760i | \(-0.446218\pi\) | ||||
0.168157 | + | 0.985760i | \(0.446218\pi\) | |||||||
\(884\) | −4.34847 | −0.146255 | ||||||||
\(885\) | 18.5862 | 0.624768 | ||||||||
\(886\) | −7.53930 | −0.253288 | ||||||||
\(887\) | 4.23285 | 0.142125 | 0.0710626 | − | 0.997472i | \(-0.477361\pi\) | ||||
0.0710626 | + | 0.997472i | \(0.477361\pi\) | |||||||
\(888\) | 14.6439 | 0.491417 | ||||||||
\(889\) | 39.8287 | 1.33581 | ||||||||
\(890\) | 0.276107 | 0.00925512 | ||||||||
\(891\) | 9.81204 | 0.328716 | ||||||||
\(892\) | 10.5184 | 0.352183 | ||||||||
\(893\) | −3.27066 | −0.109448 | ||||||||
\(894\) | 13.6302 | 0.455862 | ||||||||
\(895\) | 12.9298 | 0.432197 | ||||||||
\(896\) | 3.92530 | 0.131135 | ||||||||
\(897\) | 2.30375 | 0.0769199 | ||||||||
\(898\) | −29.5577 | −0.986354 | ||||||||
\(899\) | −18.7785 | −0.626299 | ||||||||
\(900\) | 2.69915 | 0.0899717 | ||||||||
\(901\) | −49.4598 | −1.64775 | ||||||||
\(902\) | −11.7137 | −0.390025 | ||||||||
\(903\) | 9.37084 | 0.311842 | ||||||||
\(904\) | 4.83624 | 0.160851 | ||||||||
\(905\) | −0.164956 | −0.00548331 | ||||||||
\(906\) | −15.9344 | −0.529385 | ||||||||
\(907\) | −4.74007 | −0.157391 | −0.0786957 | − | 0.996899i | \(-0.525076\pi\) | ||||
−0.0786957 | + | 0.996899i | \(0.525076\pi\) | |||||||
\(908\) | −17.8730 | −0.593135 | ||||||||
\(909\) | −32.1444 | −1.06616 | ||||||||
\(910\) | 3.19101 | 0.105781 | ||||||||
\(911\) | 2.72992 | 0.0904464 | 0.0452232 | − | 0.998977i | \(-0.485600\pi\) | ||||
0.0452232 | + | 0.998977i | \(0.485600\pi\) | |||||||
\(912\) | −0.968738 | −0.0320781 | ||||||||
\(913\) | 14.2689 | 0.472233 | ||||||||
\(914\) | 33.4690 | 1.10705 | ||||||||
\(915\) | 26.6452 | 0.880862 | ||||||||
\(916\) | 13.1275 | 0.433746 | ||||||||
\(917\) | 19.1852 | 0.633552 | ||||||||
\(918\) | 3.84182 | 0.126799 | ||||||||
\(919\) | −14.3248 | −0.472531 | −0.236265 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236265 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(920\) | 1.18707 | 0.0391364 | ||||||||
\(921\) | 26.6234 | 0.877270 | ||||||||
\(922\) | 1.75000 | 0.0576331 | ||||||||
\(923\) | −9.59010 | −0.315662 | ||||||||
\(924\) | −9.37084 | −0.308278 | ||||||||
\(925\) | 6.13412 | 0.201688 | ||||||||
\(926\) | −5.58904 | −0.183667 | ||||||||
\(927\) | −44.3437 | −1.45644 | ||||||||
\(928\) | 1.86640 | 0.0612677 | ||||||||
\(929\) | −3.43268 | −0.112623 | −0.0563113 | − | 0.998413i | \(-0.517934\pi\) | ||||
−0.0563113 | + | 0.998413i | \(0.517934\pi\) | |||||||
\(930\) | −24.0193 | −0.787625 | ||||||||
\(931\) | −3.41189 | −0.111820 | ||||||||
\(932\) | −24.2231 | −0.793453 | ||||||||
\(933\) | −12.9629 | −0.424385 | ||||||||
\(934\) | −8.21645 | −0.268850 | ||||||||
\(935\) | 5.34911 | 0.174935 | ||||||||
\(936\) | 2.19423 | 0.0717206 | ||||||||
\(937\) | 44.7878 | 1.46315 | 0.731576 | − | 0.681760i | \(-0.238785\pi\) | ||||
0.731576 | + | 0.681760i | \(0.238785\pi\) | |||||||
\(938\) | −4.16006 | −0.135831 | ||||||||
\(939\) | −14.0141 | −0.457333 | ||||||||
\(940\) | 8.05997 | 0.262887 | ||||||||
\(941\) | −10.2556 | −0.334322 | −0.167161 | − | 0.985930i | \(-0.553460\pi\) | ||||
−0.167161 | + | 0.985930i | \(0.553460\pi\) | |||||||
\(942\) | −48.2460 | −1.57194 | ||||||||
\(943\) | 13.9050 | 0.452808 | ||||||||
\(944\) | 7.78548 | 0.253396 | ||||||||
\(945\) | −2.81922 | −0.0917092 | ||||||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | −31.1886 | −1.01349 | −0.506747 | − | 0.862095i | \(-0.669152\pi\) | ||||
−0.506747 | + | 0.862095i | \(0.669152\pi\) | |||||||
\(948\) | −18.6763 | −0.606579 | ||||||||
\(949\) | −2.39382 | −0.0777066 | ||||||||
\(950\) | −0.405790 | −0.0131656 | ||||||||
\(951\) | 40.7233 | 1.32054 | ||||||||
\(952\) | −20.9969 | −0.680513 | ||||||||
\(953\) | −24.6453 | −0.798338 | −0.399169 | − | 0.916877i | \(-0.630701\pi\) | ||||
−0.399169 | + | 0.916877i | \(0.630701\pi\) | |||||||
\(954\) | 24.9573 | 0.808023 | ||||||||
\(955\) | −25.0988 | −0.812178 | ||||||||
\(956\) | 6.88492 | 0.222674 | ||||||||
\(957\) | −4.45565 | −0.144031 | ||||||||
\(958\) | −20.6013 | −0.665598 | ||||||||
\(959\) | −61.9784 | −2.00139 | ||||||||
\(960\) | 2.38729 | 0.0770494 | ||||||||
\(961\) | 70.2307 | 2.26550 | ||||||||
\(962\) | 4.98663 | 0.160775 | ||||||||
\(963\) | 22.4838 | 0.724530 | ||||||||
\(964\) | 28.1350 | 0.906168 | ||||||||
\(965\) | 8.07002 | 0.259783 | ||||||||
\(966\) | 11.1238 | 0.357903 | ||||||||
\(967\) | 28.7288 | 0.923855 | 0.461927 | − | 0.886918i | \(-0.347158\pi\) | ||||
0.461927 | + | 0.886918i | \(0.347158\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 5.18189 | 0.166466 | ||||||||
\(970\) | 3.54637 | 0.113867 | ||||||||
\(971\) | 43.6728 | 1.40153 | 0.700763 | − | 0.713394i | \(-0.252843\pi\) | ||||
0.700763 | + | 0.713394i | \(0.252843\pi\) | |||||||
\(972\) | −21.2695 | −0.682220 | ||||||||
\(973\) | −55.2782 | −1.77214 | ||||||||
\(974\) | 12.5620 | 0.402513 | ||||||||
\(975\) | 1.94071 | 0.0621524 | ||||||||
\(976\) | 11.1613 | 0.357263 | ||||||||
\(977\) | 56.1895 | 1.79766 | 0.898831 | − | 0.438296i | \(-0.144418\pi\) | ||||
0.898831 | + | 0.438296i | \(0.144418\pi\) | |||||||
\(978\) | 18.5856 | 0.594301 | ||||||||
\(979\) | −0.276107 | −0.00882441 | ||||||||
\(980\) | 8.40801 | 0.268584 | ||||||||
\(981\) | −42.5206 | −1.35758 | ||||||||
\(982\) | −15.5086 | −0.494901 | ||||||||
\(983\) | −18.5707 | −0.592313 | −0.296157 | − | 0.955139i | \(-0.595705\pi\) | ||||
−0.296157 | + | 0.955139i | \(0.595705\pi\) | |||||||
\(984\) | 27.9641 | 0.891462 | ||||||||
\(985\) | −18.0918 | −0.576452 | ||||||||
\(986\) | −9.98360 | −0.317943 | ||||||||
\(987\) | 75.5286 | 2.40410 | ||||||||
\(988\) | −0.329880 | −0.0104949 | ||||||||
\(989\) | 1.18707 | 0.0377465 | ||||||||
\(990\) | −2.69915 | −0.0857846 | ||||||||
\(991\) | −8.77508 | −0.278750 | −0.139375 | − | 0.990240i | \(-0.544509\pi\) | ||||
−0.139375 | + | 0.990240i | \(0.544509\pi\) | |||||||
\(992\) | −10.0613 | −0.319448 | ||||||||
\(993\) | −21.7975 | −0.691723 | ||||||||
\(994\) | −46.3065 | −1.46875 | ||||||||
\(995\) | 9.19769 | 0.291586 | ||||||||
\(996\) | −34.0641 | −1.07936 | ||||||||
\(997\) | 47.3802 | 1.50054 | 0.750272 | − | 0.661129i | \(-0.229922\pi\) | ||||
0.750272 | + | 0.661129i | \(0.229922\pi\) | |||||||
\(998\) | 18.3476 | 0.580782 | ||||||||
\(999\) | −4.40562 | −0.139388 |
(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 | 4730.2.a.be.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.be.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial |