Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(1,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, 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("429.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.17009 | 1.53448 | 0.767241 | − | 0.641358i | \(-0.221629\pi\) | ||||
0.767241 | + | 0.641358i | \(0.221629\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.70928 | 1.35464 | ||||||||
\(5\) | −0.539189 | −0.241133 | −0.120566 | − | 0.992705i | \(-0.538471\pi\) | ||||
−0.120566 | + | 0.992705i | \(0.538471\pi\) | |||||||
\(6\) | 2.17009 | 0.885934 | ||||||||
\(7\) | 0.630898 | 0.238457 | 0.119228 | − | 0.992867i | \(-0.461958\pi\) | ||||
0.119228 | + | 0.992867i | \(0.461958\pi\) | |||||||
\(8\) | 1.53919 | 0.544185 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.17009 | −0.370014 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.70928 | 0.782100 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.36910 | 0.365908 | ||||||||
\(15\) | −0.539189 | −0.139218 | ||||||||
\(16\) | −2.07838 | −0.519594 | ||||||||
\(17\) | 1.90829 | 0.462829 | 0.231414 | − | 0.972855i | \(-0.425665\pi\) | ||||
0.231414 | + | 0.972855i | \(0.425665\pi\) | |||||||
\(18\) | 2.17009 | 0.511494 | ||||||||
\(19\) | −4.04945 | −0.929007 | −0.464504 | − | 0.885571i | \(-0.653767\pi\) | ||||
−0.464504 | + | 0.885571i | \(0.653767\pi\) | |||||||
\(20\) | −1.46081 | −0.326647 | ||||||||
\(21\) | 0.630898 | 0.137673 | ||||||||
\(22\) | 2.17009 | 0.462664 | ||||||||
\(23\) | 1.36910 | 0.285478 | 0.142739 | − | 0.989760i | \(-0.454409\pi\) | ||||
0.142739 | + | 0.989760i | \(0.454409\pi\) | |||||||
\(24\) | 1.53919 | 0.314186 | ||||||||
\(25\) | −4.70928 | −0.941855 | ||||||||
\(26\) | 2.17009 | 0.425589 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.70928 | 0.323023 | ||||||||
\(29\) | −2.24846 | −0.417529 | −0.208765 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208765 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(30\) | −1.17009 | −0.213628 | ||||||||
\(31\) | −1.46081 | −0.262369 | −0.131185 | − | 0.991358i | \(-0.541878\pi\) | ||||
−0.131185 | + | 0.991358i | \(0.541878\pi\) | |||||||
\(32\) | −7.58864 | −1.34149 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 4.14116 | 0.710203 | ||||||||
\(35\) | −0.340173 | −0.0574997 | ||||||||
\(36\) | 2.70928 | 0.451546 | ||||||||
\(37\) | −5.07838 | −0.834880 | −0.417440 | − | 0.908704i | \(-0.637073\pi\) | ||||
−0.417440 | + | 0.908704i | \(0.637073\pi\) | |||||||
\(38\) | −8.78765 | −1.42555 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −0.829914 | −0.131221 | ||||||||
\(41\) | −2.04945 | −0.320070 | −0.160035 | − | 0.987111i | \(-0.551161\pi\) | ||||
−0.160035 | + | 0.987111i | \(0.551161\pi\) | |||||||
\(42\) | 1.36910 | 0.211257 | ||||||||
\(43\) | 0.986669 | 0.150466 | 0.0752328 | − | 0.997166i | \(-0.476030\pi\) | ||||
0.0752328 | + | 0.997166i | \(0.476030\pi\) | |||||||
\(44\) | 2.70928 | 0.408439 | ||||||||
\(45\) | −0.539189 | −0.0803775 | ||||||||
\(46\) | 2.97107 | 0.438060 | ||||||||
\(47\) | 3.26180 | 0.475782 | 0.237891 | − | 0.971292i | \(-0.423544\pi\) | ||||
0.237891 | + | 0.971292i | \(0.423544\pi\) | |||||||
\(48\) | −2.07838 | −0.299988 | ||||||||
\(49\) | −6.60197 | −0.943138 | ||||||||
\(50\) | −10.2195 | −1.44526 | ||||||||
\(51\) | 1.90829 | 0.267214 | ||||||||
\(52\) | 2.70928 | 0.375709 | ||||||||
\(53\) | 9.91548 | 1.36200 | 0.680998 | − | 0.732285i | \(-0.261546\pi\) | ||||
0.680998 | + | 0.732285i | \(0.261546\pi\) | |||||||
\(54\) | 2.17009 | 0.295311 | ||||||||
\(55\) | −0.539189 | −0.0727042 | ||||||||
\(56\) | 0.971071 | 0.129765 | ||||||||
\(57\) | −4.04945 | −0.536363 | ||||||||
\(58\) | −4.87936 | −0.640692 | ||||||||
\(59\) | −3.60197 | −0.468936 | −0.234468 | − | 0.972124i | \(-0.575335\pi\) | ||||
−0.234468 | + | 0.972124i | \(0.575335\pi\) | |||||||
\(60\) | −1.46081 | −0.188590 | ||||||||
\(61\) | 3.41855 | 0.437701 | 0.218850 | − | 0.975758i | \(-0.429769\pi\) | ||||
0.218850 | + | 0.975758i | \(0.429769\pi\) | |||||||
\(62\) | −3.17009 | −0.402601 | ||||||||
\(63\) | 0.630898 | 0.0794856 | ||||||||
\(64\) | −12.3112 | −1.53891 | ||||||||
\(65\) | −0.539189 | −0.0668781 | ||||||||
\(66\) | 2.17009 | 0.267119 | ||||||||
\(67\) | 5.95774 | 0.727854 | 0.363927 | − | 0.931428i | \(-0.381436\pi\) | ||||
0.363927 | + | 0.931428i | \(0.381436\pi\) | |||||||
\(68\) | 5.17009 | 0.626965 | ||||||||
\(69\) | 1.36910 | 0.164821 | ||||||||
\(70\) | −0.738205 | −0.0882323 | ||||||||
\(71\) | −7.75872 | −0.920791 | −0.460396 | − | 0.887714i | \(-0.652292\pi\) | ||||
−0.460396 | + | 0.887714i | \(0.652292\pi\) | |||||||
\(72\) | 1.53919 | 0.181395 | ||||||||
\(73\) | 9.46800 | 1.10815 | 0.554073 | − | 0.832468i | \(-0.313073\pi\) | ||||
0.554073 | + | 0.832468i | \(0.313073\pi\) | |||||||
\(74\) | −11.0205 | −1.28111 | ||||||||
\(75\) | −4.70928 | −0.543780 | ||||||||
\(76\) | −10.9711 | −1.25847 | ||||||||
\(77\) | 0.630898 | 0.0718975 | ||||||||
\(78\) | 2.17009 | 0.245714 | ||||||||
\(79\) | 3.90829 | 0.439717 | 0.219859 | − | 0.975532i | \(-0.429440\pi\) | ||||
0.219859 | + | 0.975532i | \(0.429440\pi\) | |||||||
\(80\) | 1.12064 | 0.125291 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.44748 | −0.491142 | ||||||||
\(83\) | 2.34017 | 0.256867 | 0.128434 | − | 0.991718i | \(-0.459005\pi\) | ||||
0.128434 | + | 0.991718i | \(0.459005\pi\) | |||||||
\(84\) | 1.70928 | 0.186497 | ||||||||
\(85\) | −1.02893 | −0.111603 | ||||||||
\(86\) | 2.14116 | 0.230887 | ||||||||
\(87\) | −2.24846 | −0.241061 | ||||||||
\(88\) | 1.53919 | 0.164078 | ||||||||
\(89\) | 12.9783 | 1.37569 | 0.687846 | − | 0.725856i | \(-0.258556\pi\) | ||||
0.687846 | + | 0.725856i | \(0.258556\pi\) | |||||||
\(90\) | −1.17009 | −0.123338 | ||||||||
\(91\) | 0.630898 | 0.0661360 | ||||||||
\(92\) | 3.70928 | 0.386719 | ||||||||
\(93\) | −1.46081 | −0.151479 | ||||||||
\(94\) | 7.07838 | 0.730079 | ||||||||
\(95\) | 2.18342 | 0.224014 | ||||||||
\(96\) | −7.58864 | −0.774512 | ||||||||
\(97\) | −5.07838 | −0.515631 | −0.257816 | − | 0.966194i | \(-0.583003\pi\) | ||||
−0.257816 | + | 0.966194i | \(0.583003\pi\) | |||||||
\(98\) | −14.3268 | −1.44723 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −12.7587 | −1.27587 | ||||||||
\(101\) | 9.51026 | 0.946306 | 0.473153 | − | 0.880980i | \(-0.343116\pi\) | ||||
0.473153 | + | 0.880980i | \(0.343116\pi\) | |||||||
\(102\) | 4.14116 | 0.410036 | ||||||||
\(103\) | −4.58145 | −0.451424 | −0.225712 | − | 0.974194i | \(-0.572471\pi\) | ||||
−0.225712 | + | 0.974194i | \(0.572471\pi\) | |||||||
\(104\) | 1.53919 | 0.150930 | ||||||||
\(105\) | −0.340173 | −0.0331975 | ||||||||
\(106\) | 21.5174 | 2.08996 | ||||||||
\(107\) | 11.6020 | 1.12160 | 0.560802 | − | 0.827950i | \(-0.310493\pi\) | ||||
0.560802 | + | 0.827950i | \(0.310493\pi\) | |||||||
\(108\) | 2.70928 | 0.260700 | ||||||||
\(109\) | −13.1545 | −1.25997 | −0.629986 | − | 0.776607i | \(-0.716939\pi\) | ||||
−0.629986 | + | 0.776607i | \(0.716939\pi\) | |||||||
\(110\) | −1.17009 | −0.111563 | ||||||||
\(111\) | −5.07838 | −0.482018 | ||||||||
\(112\) | −1.31124 | −0.123901 | ||||||||
\(113\) | 6.18342 | 0.581687 | 0.290843 | − | 0.956771i | \(-0.406064\pi\) | ||||
0.290843 | + | 0.956771i | \(0.406064\pi\) | |||||||
\(114\) | −8.78765 | −0.823039 | ||||||||
\(115\) | −0.738205 | −0.0688379 | ||||||||
\(116\) | −6.09171 | −0.565601 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −7.81658 | −0.719575 | ||||||||
\(119\) | 1.20394 | 0.110365 | ||||||||
\(120\) | −0.829914 | −0.0757604 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.41855 | 0.671644 | ||||||||
\(123\) | −2.04945 | −0.184793 | ||||||||
\(124\) | −3.95774 | −0.355416 | ||||||||
\(125\) | 5.23513 | 0.468245 | ||||||||
\(126\) | 1.36910 | 0.121969 | ||||||||
\(127\) | −20.4463 | −1.81431 | −0.907156 | − | 0.420795i | \(-0.861751\pi\) | ||||
−0.907156 | + | 0.420795i | \(0.861751\pi\) | |||||||
\(128\) | −11.5392 | −1.01993 | ||||||||
\(129\) | 0.986669 | 0.0868714 | ||||||||
\(130\) | −1.17009 | −0.102623 | ||||||||
\(131\) | 13.9421 | 1.21813 | 0.609065 | − | 0.793120i | \(-0.291545\pi\) | ||||
0.609065 | + | 0.793120i | \(0.291545\pi\) | |||||||
\(132\) | 2.70928 | 0.235812 | ||||||||
\(133\) | −2.55479 | −0.221528 | ||||||||
\(134\) | 12.9288 | 1.11688 | ||||||||
\(135\) | −0.539189 | −0.0464060 | ||||||||
\(136\) | 2.93722 | 0.251865 | ||||||||
\(137\) | −2.90602 | −0.248278 | −0.124139 | − | 0.992265i | \(-0.539617\pi\) | ||||
−0.124139 | + | 0.992265i | \(0.539617\pi\) | |||||||
\(138\) | 2.97107 | 0.252914 | ||||||||
\(139\) | 18.6875 | 1.58506 | 0.792528 | − | 0.609836i | \(-0.208765\pi\) | ||||
0.792528 | + | 0.609836i | \(0.208765\pi\) | |||||||
\(140\) | −0.921622 | −0.0778913 | ||||||||
\(141\) | 3.26180 | 0.274693 | ||||||||
\(142\) | −16.8371 | −1.41294 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | −2.07838 | −0.173198 | ||||||||
\(145\) | 1.21235 | 0.100680 | ||||||||
\(146\) | 20.5464 | 1.70043 | ||||||||
\(147\) | −6.60197 | −0.544521 | ||||||||
\(148\) | −13.7587 | −1.13096 | ||||||||
\(149\) | −15.9916 | −1.31008 | −0.655041 | − | 0.755593i | \(-0.727349\pi\) | ||||
−0.655041 | + | 0.755593i | \(0.727349\pi\) | |||||||
\(150\) | −10.2195 | −0.834422 | ||||||||
\(151\) | 10.7877 | 0.877887 | 0.438943 | − | 0.898515i | \(-0.355353\pi\) | ||||
0.438943 | + | 0.898515i | \(0.355353\pi\) | |||||||
\(152\) | −6.23287 | −0.505552 | ||||||||
\(153\) | 1.90829 | 0.154276 | ||||||||
\(154\) | 1.36910 | 0.110325 | ||||||||
\(155\) | 0.787653 | 0.0632658 | ||||||||
\(156\) | 2.70928 | 0.216916 | ||||||||
\(157\) | −9.12783 | −0.728480 | −0.364240 | − | 0.931305i | \(-0.618671\pi\) | ||||
−0.364240 | + | 0.931305i | \(0.618671\pi\) | |||||||
\(158\) | 8.48133 | 0.674738 | ||||||||
\(159\) | 9.91548 | 0.786349 | ||||||||
\(160\) | 4.09171 | 0.323478 | ||||||||
\(161\) | 0.863763 | 0.0680741 | ||||||||
\(162\) | 2.17009 | 0.170498 | ||||||||
\(163\) | −7.27739 | −0.570009 | −0.285005 | − | 0.958526i | \(-0.591995\pi\) | ||||
−0.285005 | + | 0.958526i | \(0.591995\pi\) | |||||||
\(164\) | −5.55252 | −0.433579 | ||||||||
\(165\) | −0.539189 | −0.0419758 | ||||||||
\(166\) | 5.07838 | 0.394159 | ||||||||
\(167\) | 16.0989 | 1.24577 | 0.622885 | − | 0.782313i | \(-0.285960\pi\) | ||||
0.622885 | + | 0.782313i | \(0.285960\pi\) | |||||||
\(168\) | 0.971071 | 0.0749197 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.23287 | −0.171253 | ||||||||
\(171\) | −4.04945 | −0.309669 | ||||||||
\(172\) | 2.67316 | 0.203826 | ||||||||
\(173\) | 16.2485 | 1.23535 | 0.617674 | − | 0.786434i | \(-0.288075\pi\) | ||||
0.617674 | + | 0.786434i | \(0.288075\pi\) | |||||||
\(174\) | −4.87936 | −0.369903 | ||||||||
\(175\) | −2.97107 | −0.224592 | ||||||||
\(176\) | −2.07838 | −0.156664 | ||||||||
\(177\) | −3.60197 | −0.270741 | ||||||||
\(178\) | 28.1639 | 2.11098 | ||||||||
\(179\) | 18.5464 | 1.38622 | 0.693111 | − | 0.720831i | \(-0.256240\pi\) | ||||
0.693111 | + | 0.720831i | \(0.256240\pi\) | |||||||
\(180\) | −1.46081 | −0.108882 | ||||||||
\(181\) | −10.8722 | −0.808122 | −0.404061 | − | 0.914732i | \(-0.632402\pi\) | ||||
−0.404061 | + | 0.914732i | \(0.632402\pi\) | |||||||
\(182\) | 1.36910 | 0.101485 | ||||||||
\(183\) | 3.41855 | 0.252707 | ||||||||
\(184\) | 2.10731 | 0.155353 | ||||||||
\(185\) | 2.73820 | 0.201317 | ||||||||
\(186\) | −3.17009 | −0.232442 | ||||||||
\(187\) | 1.90829 | 0.139548 | ||||||||
\(188\) | 8.83710 | 0.644512 | ||||||||
\(189\) | 0.630898 | 0.0458910 | ||||||||
\(190\) | 4.73820 | 0.343746 | ||||||||
\(191\) | −9.17727 | −0.664044 | −0.332022 | − | 0.943272i | \(-0.607731\pi\) | ||||
−0.332022 | + | 0.943272i | \(0.607731\pi\) | |||||||
\(192\) | −12.3112 | −0.888487 | ||||||||
\(193\) | −17.1012 | −1.23097 | −0.615484 | − | 0.788149i | \(-0.711040\pi\) | ||||
−0.615484 | + | 0.788149i | \(0.711040\pi\) | |||||||
\(194\) | −11.0205 | −0.791227 | ||||||||
\(195\) | −0.539189 | −0.0386121 | ||||||||
\(196\) | −17.8865 | −1.27761 | ||||||||
\(197\) | −3.34244 | −0.238139 | −0.119070 | − | 0.992886i | \(-0.537991\pi\) | ||||
−0.119070 | + | 0.992886i | \(0.537991\pi\) | |||||||
\(198\) | 2.17009 | 0.154221 | ||||||||
\(199\) | −14.2557 | −1.01056 | −0.505278 | − | 0.862957i | \(-0.668610\pi\) | ||||
−0.505278 | + | 0.862957i | \(0.668610\pi\) | |||||||
\(200\) | −7.24846 | −0.512544 | ||||||||
\(201\) | 5.95774 | 0.420227 | ||||||||
\(202\) | 20.6381 | 1.45209 | ||||||||
\(203\) | −1.41855 | −0.0995627 | ||||||||
\(204\) | 5.17009 | 0.361978 | ||||||||
\(205\) | 1.10504 | 0.0771793 | ||||||||
\(206\) | −9.94214 | −0.692702 | ||||||||
\(207\) | 1.36910 | 0.0951592 | ||||||||
\(208\) | −2.07838 | −0.144110 | ||||||||
\(209\) | −4.04945 | −0.280106 | ||||||||
\(210\) | −0.738205 | −0.0509410 | ||||||||
\(211\) | 15.0133 | 1.03356 | 0.516780 | − | 0.856118i | \(-0.327130\pi\) | ||||
0.516780 | + | 0.856118i | \(0.327130\pi\) | |||||||
\(212\) | 26.8638 | 1.84501 | ||||||||
\(213\) | −7.75872 | −0.531619 | ||||||||
\(214\) | 25.1773 | 1.72108 | ||||||||
\(215\) | −0.532001 | −0.0362822 | ||||||||
\(216\) | 1.53919 | 0.104729 | ||||||||
\(217\) | −0.921622 | −0.0625638 | ||||||||
\(218\) | −28.5464 | −1.93340 | ||||||||
\(219\) | 9.46800 | 0.639788 | ||||||||
\(220\) | −1.46081 | −0.0984879 | ||||||||
\(221\) | 1.90829 | 0.128366 | ||||||||
\(222\) | −11.0205 | −0.739649 | ||||||||
\(223\) | 9.77432 | 0.654537 | 0.327269 | − | 0.944931i | \(-0.393872\pi\) | ||||
0.327269 | + | 0.944931i | \(0.393872\pi\) | |||||||
\(224\) | −4.78765 | −0.319889 | ||||||||
\(225\) | −4.70928 | −0.313952 | ||||||||
\(226\) | 13.4186 | 0.892589 | ||||||||
\(227\) | −11.0700 | −0.734740 | −0.367370 | − | 0.930075i | \(-0.619742\pi\) | ||||
−0.367370 | + | 0.930075i | \(0.619742\pi\) | |||||||
\(228\) | −10.9711 | −0.726577 | ||||||||
\(229\) | −17.0928 | −1.12952 | −0.564760 | − | 0.825255i | \(-0.691031\pi\) | ||||
−0.564760 | + | 0.825255i | \(0.691031\pi\) | |||||||
\(230\) | −1.60197 | −0.105631 | ||||||||
\(231\) | 0.630898 | 0.0415100 | ||||||||
\(232\) | −3.46081 | −0.227213 | ||||||||
\(233\) | −8.00719 | −0.524568 | −0.262284 | − | 0.964991i | \(-0.584476\pi\) | ||||
−0.262284 | + | 0.964991i | \(0.584476\pi\) | |||||||
\(234\) | 2.17009 | 0.141863 | ||||||||
\(235\) | −1.75872 | −0.114726 | ||||||||
\(236\) | −9.75872 | −0.635239 | ||||||||
\(237\) | 3.90829 | 0.253871 | ||||||||
\(238\) | 2.61265 | 0.169353 | ||||||||
\(239\) | −3.28458 | −0.212462 | −0.106231 | − | 0.994341i | \(-0.533878\pi\) | ||||
−0.106231 | + | 0.994341i | \(0.533878\pi\) | |||||||
\(240\) | 1.12064 | 0.0723369 | ||||||||
\(241\) | 13.5486 | 0.872745 | 0.436372 | − | 0.899766i | \(-0.356263\pi\) | ||||
0.436372 | + | 0.899766i | \(0.356263\pi\) | |||||||
\(242\) | 2.17009 | 0.139498 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.26180 | 0.592926 | ||||||||
\(245\) | 3.55971 | 0.227421 | ||||||||
\(246\) | −4.44748 | −0.283561 | ||||||||
\(247\) | −4.04945 | −0.257660 | ||||||||
\(248\) | −2.24846 | −0.142778 | ||||||||
\(249\) | 2.34017 | 0.148302 | ||||||||
\(250\) | 11.3607 | 0.718513 | ||||||||
\(251\) | 4.18342 | 0.264055 | 0.132027 | − | 0.991246i | \(-0.457851\pi\) | ||||
0.132027 | + | 0.991246i | \(0.457851\pi\) | |||||||
\(252\) | 1.70928 | 0.107674 | ||||||||
\(253\) | 1.36910 | 0.0860747 | ||||||||
\(254\) | −44.3701 | −2.78403 | ||||||||
\(255\) | −1.02893 | −0.0644341 | ||||||||
\(256\) | −0.418551 | −0.0261594 | ||||||||
\(257\) | 8.52359 | 0.531687 | 0.265843 | − | 0.964016i | \(-0.414350\pi\) | ||||
0.265843 | + | 0.964016i | \(0.414350\pi\) | |||||||
\(258\) | 2.14116 | 0.133303 | ||||||||
\(259\) | −3.20394 | −0.199083 | ||||||||
\(260\) | −1.46081 | −0.0905957 | ||||||||
\(261\) | −2.24846 | −0.139176 | ||||||||
\(262\) | 30.2557 | 1.86920 | ||||||||
\(263\) | 22.7526 | 1.40298 | 0.701492 | − | 0.712677i | \(-0.252518\pi\) | ||||
0.701492 | + | 0.712677i | \(0.252518\pi\) | |||||||
\(264\) | 1.53919 | 0.0947305 | ||||||||
\(265\) | −5.34632 | −0.328422 | ||||||||
\(266\) | −5.54411 | −0.339931 | ||||||||
\(267\) | 12.9783 | 0.794257 | ||||||||
\(268\) | 16.1412 | 0.985978 | ||||||||
\(269\) | −8.34017 | −0.508509 | −0.254255 | − | 0.967137i | \(-0.581830\pi\) | ||||
−0.254255 | + | 0.967137i | \(0.581830\pi\) | |||||||
\(270\) | −1.17009 | −0.0712092 | ||||||||
\(271\) | 26.7031 | 1.62210 | 0.811050 | − | 0.584977i | \(-0.198896\pi\) | ||||
0.811050 | + | 0.584977i | \(0.198896\pi\) | |||||||
\(272\) | −3.96615 | −0.240483 | ||||||||
\(273\) | 0.630898 | 0.0381837 | ||||||||
\(274\) | −6.30632 | −0.380979 | ||||||||
\(275\) | −4.70928 | −0.283980 | ||||||||
\(276\) | 3.70928 | 0.223272 | ||||||||
\(277\) | 7.62863 | 0.458360 | 0.229180 | − | 0.973384i | \(-0.426396\pi\) | ||||
0.229180 | + | 0.973384i | \(0.426396\pi\) | |||||||
\(278\) | 40.5536 | 2.43224 | ||||||||
\(279\) | −1.46081 | −0.0874565 | ||||||||
\(280\) | −0.523590 | −0.0312905 | ||||||||
\(281\) | −16.0228 | −0.955839 | −0.477920 | − | 0.878404i | \(-0.658609\pi\) | ||||
−0.477920 | + | 0.878404i | \(0.658609\pi\) | |||||||
\(282\) | 7.07838 | 0.421511 | ||||||||
\(283\) | 16.2485 | 0.965871 | 0.482935 | − | 0.875656i | \(-0.339571\pi\) | ||||
0.482935 | + | 0.875656i | \(0.339571\pi\) | |||||||
\(284\) | −21.0205 | −1.24734 | ||||||||
\(285\) | 2.18342 | 0.129334 | ||||||||
\(286\) | 2.17009 | 0.128320 | ||||||||
\(287\) | −1.29299 | −0.0763229 | ||||||||
\(288\) | −7.58864 | −0.447165 | ||||||||
\(289\) | −13.3584 | −0.785790 | ||||||||
\(290\) | 2.63090 | 0.154492 | ||||||||
\(291\) | −5.07838 | −0.297700 | ||||||||
\(292\) | 25.6514 | 1.50114 | ||||||||
\(293\) | −22.2329 | −1.29886 | −0.649429 | − | 0.760422i | \(-0.724992\pi\) | ||||
−0.649429 | + | 0.760422i | \(0.724992\pi\) | |||||||
\(294\) | −14.3268 | −0.835558 | ||||||||
\(295\) | 1.94214 | 0.113076 | ||||||||
\(296\) | −7.81658 | −0.454330 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −34.7031 | −2.01030 | ||||||||
\(299\) | 1.36910 | 0.0791772 | ||||||||
\(300\) | −12.7587 | −0.736625 | ||||||||
\(301\) | 0.622487 | 0.0358796 | ||||||||
\(302\) | 23.4101 | 1.34710 | ||||||||
\(303\) | 9.51026 | 0.546350 | ||||||||
\(304\) | 8.41628 | 0.482707 | ||||||||
\(305\) | −1.84324 | −0.105544 | ||||||||
\(306\) | 4.14116 | 0.236734 | ||||||||
\(307\) | −7.46800 | −0.426221 | −0.213111 | − | 0.977028i | \(-0.568359\pi\) | ||||
−0.213111 | + | 0.977028i | \(0.568359\pi\) | |||||||
\(308\) | 1.70928 | 0.0973950 | ||||||||
\(309\) | −4.58145 | −0.260630 | ||||||||
\(310\) | 1.70928 | 0.0970803 | ||||||||
\(311\) | 1.27021 | 0.0720268 | 0.0360134 | − | 0.999351i | \(-0.488534\pi\) | ||||
0.0360134 | + | 0.999351i | \(0.488534\pi\) | |||||||
\(312\) | 1.53919 | 0.0871394 | ||||||||
\(313\) | 12.8287 | 0.725120 | 0.362560 | − | 0.931960i | \(-0.381903\pi\) | ||||
0.362560 | + | 0.931960i | \(0.381903\pi\) | |||||||
\(314\) | −19.8082 | −1.11784 | ||||||||
\(315\) | −0.340173 | −0.0191666 | ||||||||
\(316\) | 10.5886 | 0.595657 | ||||||||
\(317\) | 13.2918 | 0.746540 | 0.373270 | − | 0.927723i | \(-0.378236\pi\) | ||||
0.373270 | + | 0.927723i | \(0.378236\pi\) | |||||||
\(318\) | 21.5174 | 1.20664 | ||||||||
\(319\) | −2.24846 | −0.125890 | ||||||||
\(320\) | 6.63809 | 0.371080 | ||||||||
\(321\) | 11.6020 | 0.647559 | ||||||||
\(322\) | 1.87444 | 0.104459 | ||||||||
\(323\) | −7.72753 | −0.429971 | ||||||||
\(324\) | 2.70928 | 0.150515 | ||||||||
\(325\) | −4.70928 | −0.261224 | ||||||||
\(326\) | −15.7926 | −0.874670 | ||||||||
\(327\) | −13.1545 | −0.727445 | ||||||||
\(328\) | −3.15449 | −0.174177 | ||||||||
\(329\) | 2.05786 | 0.113453 | ||||||||
\(330\) | −1.17009 | −0.0644111 | ||||||||
\(331\) | 31.6586 | 1.74011 | 0.870057 | − | 0.492951i | \(-0.164082\pi\) | ||||
0.870057 | + | 0.492951i | \(0.164082\pi\) | |||||||
\(332\) | 6.34017 | 0.347962 | ||||||||
\(333\) | −5.07838 | −0.278293 | ||||||||
\(334\) | 34.9360 | 1.91161 | ||||||||
\(335\) | −3.21235 | −0.175509 | ||||||||
\(336\) | −1.31124 | −0.0715342 | ||||||||
\(337\) | −1.71769 | −0.0935683 | −0.0467842 | − | 0.998905i | \(-0.514897\pi\) | ||||
−0.0467842 | + | 0.998905i | \(0.514897\pi\) | |||||||
\(338\) | 2.17009 | 0.118037 | ||||||||
\(339\) | 6.18342 | 0.335837 | ||||||||
\(340\) | −2.78765 | −0.151182 | ||||||||
\(341\) | −1.46081 | −0.0791074 | ||||||||
\(342\) | −8.78765 | −0.475182 | ||||||||
\(343\) | −8.58145 | −0.463355 | ||||||||
\(344\) | 1.51867 | 0.0818812 | ||||||||
\(345\) | −0.738205 | −0.0397436 | ||||||||
\(346\) | 35.2606 | 1.89562 | ||||||||
\(347\) | 1.60197 | 0.0859982 | 0.0429991 | − | 0.999075i | \(-0.486309\pi\) | ||||
0.0429991 | + | 0.999075i | \(0.486309\pi\) | |||||||
\(348\) | −6.09171 | −0.326550 | ||||||||
\(349\) | 16.4391 | 0.879963 | 0.439982 | − | 0.898007i | \(-0.354985\pi\) | ||||
0.439982 | + | 0.898007i | \(0.354985\pi\) | |||||||
\(350\) | −6.44748 | −0.344632 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −7.58864 | −0.404476 | ||||||||
\(353\) | −0.990545 | −0.0527214 | −0.0263607 | − | 0.999652i | \(-0.508392\pi\) | ||||
−0.0263607 | + | 0.999652i | \(0.508392\pi\) | |||||||
\(354\) | −7.81658 | −0.415447 | ||||||||
\(355\) | 4.18342 | 0.222033 | ||||||||
\(356\) | 35.1617 | 1.86357 | ||||||||
\(357\) | 1.20394 | 0.0637191 | ||||||||
\(358\) | 40.2472 | 2.12713 | ||||||||
\(359\) | −28.5464 | −1.50662 | −0.753310 | − | 0.657666i | \(-0.771544\pi\) | ||||
−0.753310 | + | 0.657666i | \(0.771544\pi\) | |||||||
\(360\) | −0.829914 | −0.0437403 | ||||||||
\(361\) | −2.60197 | −0.136946 | ||||||||
\(362\) | −23.5936 | −1.24005 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 1.70928 | 0.0895904 | ||||||||
\(365\) | −5.10504 | −0.267210 | ||||||||
\(366\) | 7.41855 | 0.387774 | ||||||||
\(367\) | −11.2351 | −0.586469 | −0.293235 | − | 0.956041i | \(-0.594732\pi\) | ||||
−0.293235 | + | 0.956041i | \(0.594732\pi\) | |||||||
\(368\) | −2.84551 | −0.148333 | ||||||||
\(369\) | −2.04945 | −0.106690 | ||||||||
\(370\) | 5.94214 | 0.308917 | ||||||||
\(371\) | 6.25565 | 0.324777 | ||||||||
\(372\) | −3.95774 | −0.205199 | ||||||||
\(373\) | −19.0784 | −0.987841 | −0.493920 | − | 0.869507i | \(-0.664437\pi\) | ||||
−0.493920 | + | 0.869507i | \(0.664437\pi\) | |||||||
\(374\) | 4.14116 | 0.214134 | ||||||||
\(375\) | 5.23513 | 0.270341 | ||||||||
\(376\) | 5.02052 | 0.258913 | ||||||||
\(377\) | −2.24846 | −0.115802 | ||||||||
\(378\) | 1.36910 | 0.0704190 | ||||||||
\(379\) | 1.80098 | 0.0925103 | 0.0462552 | − | 0.998930i | \(-0.485271\pi\) | ||||
0.0462552 | + | 0.998930i | \(0.485271\pi\) | |||||||
\(380\) | 5.91548 | 0.303458 | ||||||||
\(381\) | −20.4463 | −1.04749 | ||||||||
\(382\) | −19.9155 | −1.01896 | ||||||||
\(383\) | −0.979481 | −0.0500491 | −0.0250246 | − | 0.999687i | \(-0.507966\pi\) | ||||
−0.0250246 | + | 0.999687i | \(0.507966\pi\) | |||||||
\(384\) | −11.5392 | −0.588857 | ||||||||
\(385\) | −0.340173 | −0.0173368 | ||||||||
\(386\) | −37.1110 | −1.88890 | ||||||||
\(387\) | 0.986669 | 0.0501552 | ||||||||
\(388\) | −13.7587 | −0.698493 | ||||||||
\(389\) | −30.2823 | −1.53537 | −0.767687 | − | 0.640825i | \(-0.778592\pi\) | ||||
−0.767687 | + | 0.640825i | \(0.778592\pi\) | |||||||
\(390\) | −1.17009 | −0.0592496 | ||||||||
\(391\) | 2.61265 | 0.132127 | ||||||||
\(392\) | −10.1617 | −0.513242 | ||||||||
\(393\) | 13.9421 | 0.703288 | ||||||||
\(394\) | −7.25338 | −0.365420 | ||||||||
\(395\) | −2.10731 | −0.106030 | ||||||||
\(396\) | 2.70928 | 0.136146 | ||||||||
\(397\) | −31.7998 | −1.59598 | −0.797992 | − | 0.602668i | \(-0.794104\pi\) | ||||
−0.797992 | + | 0.602668i | \(0.794104\pi\) | |||||||
\(398\) | −30.9360 | −1.55068 | ||||||||
\(399\) | −2.55479 | −0.127899 | ||||||||
\(400\) | 9.78765 | 0.489383 | ||||||||
\(401\) | −1.34963 | −0.0673972 | −0.0336986 | − | 0.999432i | \(-0.510729\pi\) | ||||
−0.0336986 | + | 0.999432i | \(0.510729\pi\) | |||||||
\(402\) | 12.9288 | 0.644830 | ||||||||
\(403\) | −1.46081 | −0.0727682 | ||||||||
\(404\) | 25.7659 | 1.28190 | ||||||||
\(405\) | −0.539189 | −0.0267925 | ||||||||
\(406\) | −3.07838 | −0.152777 | ||||||||
\(407\) | −5.07838 | −0.251726 | ||||||||
\(408\) | 2.93722 | 0.145414 | ||||||||
\(409\) | 4.16063 | 0.205730 | 0.102865 | − | 0.994695i | \(-0.467199\pi\) | ||||
0.102865 | + | 0.994695i | \(0.467199\pi\) | |||||||
\(410\) | 2.39803 | 0.118430 | ||||||||
\(411\) | −2.90602 | −0.143344 | ||||||||
\(412\) | −12.4124 | −0.611515 | ||||||||
\(413\) | −2.27247 | −0.111821 | ||||||||
\(414\) | 2.97107 | 0.146020 | ||||||||
\(415\) | −1.26180 | −0.0619391 | ||||||||
\(416\) | −7.58864 | −0.372064 | ||||||||
\(417\) | 18.6875 | 0.915132 | ||||||||
\(418\) | −8.78765 | −0.429818 | ||||||||
\(419\) | −33.8492 | −1.65364 | −0.826821 | − | 0.562465i | \(-0.809853\pi\) | ||||
−0.826821 | + | 0.562465i | \(0.809853\pi\) | |||||||
\(420\) | −0.921622 | −0.0449706 | ||||||||
\(421\) | −23.2618 | −1.13371 | −0.566855 | − | 0.823817i | \(-0.691840\pi\) | ||||
−0.566855 | + | 0.823817i | \(0.691840\pi\) | |||||||
\(422\) | 32.5802 | 1.58598 | ||||||||
\(423\) | 3.26180 | 0.158594 | ||||||||
\(424\) | 15.2618 | 0.741178 | ||||||||
\(425\) | −8.98667 | −0.435917 | ||||||||
\(426\) | −16.8371 | −0.815760 | ||||||||
\(427\) | 2.15676 | 0.104373 | ||||||||
\(428\) | 31.4329 | 1.51937 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | −1.15449 | −0.0556744 | ||||||||
\(431\) | −14.3090 | −0.689239 | −0.344620 | − | 0.938742i | \(-0.611992\pi\) | ||||
−0.344620 | + | 0.938742i | \(0.611992\pi\) | |||||||
\(432\) | −2.07838 | −0.0999960 | ||||||||
\(433\) | −16.5236 | −0.794073 | −0.397037 | − | 0.917803i | \(-0.629961\pi\) | ||||
−0.397037 | + | 0.917803i | \(0.629961\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 1.21235 | 0.0581276 | ||||||||
\(436\) | −35.6391 | −1.70680 | ||||||||
\(437\) | −5.54411 | −0.265211 | ||||||||
\(438\) | 20.5464 | 0.981744 | ||||||||
\(439\) | −13.7971 | −0.658500 | −0.329250 | − | 0.944243i | \(-0.606796\pi\) | ||||
−0.329250 | + | 0.944243i | \(0.606796\pi\) | |||||||
\(440\) | −0.829914 | −0.0395646 | ||||||||
\(441\) | −6.60197 | −0.314379 | ||||||||
\(442\) | 4.14116 | 0.196975 | ||||||||
\(443\) | −24.5113 | −1.16457 | −0.582284 | − | 0.812986i | \(-0.697841\pi\) | ||||
−0.582284 | + | 0.812986i | \(0.697841\pi\) | |||||||
\(444\) | −13.7587 | −0.652960 | ||||||||
\(445\) | −6.99773 | −0.331724 | ||||||||
\(446\) | 21.2111 | 1.00438 | ||||||||
\(447\) | −15.9916 | −0.756376 | ||||||||
\(448\) | −7.76713 | −0.366963 | ||||||||
\(449\) | −35.1617 | −1.65938 | −0.829691 | − | 0.558223i | \(-0.811483\pi\) | ||||
−0.829691 | + | 0.558223i | \(0.811483\pi\) | |||||||
\(450\) | −10.2195 | −0.481753 | ||||||||
\(451\) | −2.04945 | −0.0965048 | ||||||||
\(452\) | 16.7526 | 0.787975 | ||||||||
\(453\) | 10.7877 | 0.506848 | ||||||||
\(454\) | −24.0228 | −1.12745 | ||||||||
\(455\) | −0.340173 | −0.0159476 | ||||||||
\(456\) | −6.23287 | −0.291881 | ||||||||
\(457\) | −36.2557 | −1.69597 | −0.847984 | − | 0.530022i | \(-0.822184\pi\) | ||||
−0.847984 | + | 0.530022i | \(0.822184\pi\) | |||||||
\(458\) | −37.0928 | −1.73323 | ||||||||
\(459\) | 1.90829 | 0.0890714 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | 23.6248 | 1.10031 | 0.550157 | − | 0.835061i | \(-0.314568\pi\) | ||||
0.550157 | + | 0.835061i | \(0.314568\pi\) | |||||||
\(462\) | 1.36910 | 0.0636964 | ||||||||
\(463\) | −4.85270 | −0.225524 | −0.112762 | − | 0.993622i | \(-0.535970\pi\) | ||||
−0.112762 | + | 0.993622i | \(0.535970\pi\) | |||||||
\(464\) | 4.67316 | 0.216946 | ||||||||
\(465\) | 0.787653 | 0.0365265 | ||||||||
\(466\) | −17.3763 | −0.804941 | ||||||||
\(467\) | 15.8927 | 0.735426 | 0.367713 | − | 0.929939i | \(-0.380141\pi\) | ||||
0.367713 | + | 0.929939i | \(0.380141\pi\) | |||||||
\(468\) | 2.70928 | 0.125236 | ||||||||
\(469\) | 3.75872 | 0.173562 | ||||||||
\(470\) | −3.81658 | −0.176046 | ||||||||
\(471\) | −9.12783 | −0.420588 | ||||||||
\(472\) | −5.54411 | −0.255188 | ||||||||
\(473\) | 0.986669 | 0.0453671 | ||||||||
\(474\) | 8.48133 | 0.389560 | ||||||||
\(475\) | 19.0700 | 0.874990 | ||||||||
\(476\) | 3.26180 | 0.149504 | ||||||||
\(477\) | 9.91548 | 0.453999 | ||||||||
\(478\) | −7.12783 | −0.326019 | ||||||||
\(479\) | −5.70928 | −0.260863 | −0.130432 | − | 0.991457i | \(-0.541636\pi\) | ||||
−0.130432 | + | 0.991457i | \(0.541636\pi\) | |||||||
\(480\) | 4.09171 | 0.186760 | ||||||||
\(481\) | −5.07838 | −0.231554 | ||||||||
\(482\) | 29.4017 | 1.33921 | ||||||||
\(483\) | 0.863763 | 0.0393026 | ||||||||
\(484\) | 2.70928 | 0.123149 | ||||||||
\(485\) | 2.73820 | 0.124335 | ||||||||
\(486\) | 2.17009 | 0.0984371 | ||||||||
\(487\) | −27.9265 | −1.26547 | −0.632736 | − | 0.774367i | \(-0.718068\pi\) | ||||
−0.632736 | + | 0.774367i | \(0.718068\pi\) | |||||||
\(488\) | 5.26180 | 0.238190 | ||||||||
\(489\) | −7.27739 | −0.329095 | ||||||||
\(490\) | 7.72487 | 0.348974 | ||||||||
\(491\) | 32.1711 | 1.45186 | 0.725931 | − | 0.687767i | \(-0.241409\pi\) | ||||
0.725931 | + | 0.687767i | \(0.241409\pi\) | |||||||
\(492\) | −5.55252 | −0.250327 | ||||||||
\(493\) | −4.29072 | −0.193245 | ||||||||
\(494\) | −8.78765 | −0.395375 | ||||||||
\(495\) | −0.539189 | −0.0242347 | ||||||||
\(496\) | 3.03612 | 0.136326 | ||||||||
\(497\) | −4.89496 | −0.219569 | ||||||||
\(498\) | 5.07838 | 0.227568 | ||||||||
\(499\) | −16.2979 | −0.729595 | −0.364797 | − | 0.931087i | \(-0.618862\pi\) | ||||
−0.364797 | + | 0.931087i | \(0.618862\pi\) | |||||||
\(500\) | 14.1834 | 0.634302 | ||||||||
\(501\) | 16.0989 | 0.719246 | ||||||||
\(502\) | 9.07838 | 0.405188 | ||||||||
\(503\) | −19.1194 | −0.852493 | −0.426246 | − | 0.904607i | \(-0.640164\pi\) | ||||
−0.426246 | + | 0.904607i | \(0.640164\pi\) | |||||||
\(504\) | 0.971071 | 0.0432549 | ||||||||
\(505\) | −5.12783 | −0.228185 | ||||||||
\(506\) | 2.97107 | 0.132080 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −55.3945 | −2.45774 | ||||||||
\(509\) | −23.5018 | −1.04170 | −0.520851 | − | 0.853648i | \(-0.674385\pi\) | ||||
−0.520851 | + | 0.853648i | \(0.674385\pi\) | |||||||
\(510\) | −2.23287 | −0.0988730 | ||||||||
\(511\) | 5.97334 | 0.264245 | ||||||||
\(512\) | 22.1701 | 0.979789 | ||||||||
\(513\) | −4.04945 | −0.178788 | ||||||||
\(514\) | 18.4969 | 0.815865 | ||||||||
\(515\) | 2.47027 | 0.108853 | ||||||||
\(516\) | 2.67316 | 0.117679 | ||||||||
\(517\) | 3.26180 | 0.143454 | ||||||||
\(518\) | −6.95282 | −0.305489 | ||||||||
\(519\) | 16.2485 | 0.713228 | ||||||||
\(520\) | −0.829914 | −0.0363941 | ||||||||
\(521\) | −6.99386 | −0.306406 | −0.153203 | − | 0.988195i | \(-0.548959\pi\) | ||||
−0.153203 | + | 0.988195i | \(0.548959\pi\) | |||||||
\(522\) | −4.87936 | −0.213564 | ||||||||
\(523\) | 32.2050 | 1.40823 | 0.704113 | − | 0.710088i | \(-0.251345\pi\) | ||||
0.704113 | + | 0.710088i | \(0.251345\pi\) | |||||||
\(524\) | 37.7731 | 1.65013 | ||||||||
\(525\) | −2.97107 | −0.129668 | ||||||||
\(526\) | 49.3751 | 2.15286 | ||||||||
\(527\) | −2.78765 | −0.121432 | ||||||||
\(528\) | −2.07838 | −0.0904498 | ||||||||
\(529\) | −21.1256 | −0.918503 | ||||||||
\(530\) | −11.6020 | −0.503957 | ||||||||
\(531\) | −3.60197 | −0.156312 | ||||||||
\(532\) | −6.92162 | −0.300090 | ||||||||
\(533\) | −2.04945 | −0.0887715 | ||||||||
\(534\) | 28.1639 | 1.21877 | ||||||||
\(535\) | −6.25565 | −0.270455 | ||||||||
\(536\) | 9.17009 | 0.396087 | ||||||||
\(537\) | 18.5464 | 0.800335 | ||||||||
\(538\) | −18.0989 | −0.780299 | ||||||||
\(539\) | −6.60197 | −0.284367 | ||||||||
\(540\) | −1.46081 | −0.0628633 | ||||||||
\(541\) | 9.94668 | 0.427641 | 0.213821 | − | 0.976873i | \(-0.431409\pi\) | ||||
0.213821 | + | 0.976873i | \(0.431409\pi\) | |||||||
\(542\) | 57.9481 | 2.48908 | ||||||||
\(543\) | −10.8722 | −0.466570 | ||||||||
\(544\) | −14.4813 | −0.620882 | ||||||||
\(545\) | 7.09275 | 0.303820 | ||||||||
\(546\) | 1.36910 | 0.0585922 | ||||||||
\(547\) | 37.3412 | 1.59660 | 0.798298 | − | 0.602263i | \(-0.205734\pi\) | ||||
0.798298 | + | 0.602263i | \(0.205734\pi\) | |||||||
\(548\) | −7.87322 | −0.336327 | ||||||||
\(549\) | 3.41855 | 0.145900 | ||||||||
\(550\) | −10.2195 | −0.435762 | ||||||||
\(551\) | 9.10504 | 0.387888 | ||||||||
\(552\) | 2.10731 | 0.0896929 | ||||||||
\(553\) | 2.46573 | 0.104854 | ||||||||
\(554\) | 16.5548 | 0.703346 | ||||||||
\(555\) | 2.73820 | 0.116230 | ||||||||
\(556\) | 50.6297 | 2.14718 | ||||||||
\(557\) | −2.31739 | −0.0981908 | −0.0490954 | − | 0.998794i | \(-0.515634\pi\) | ||||
−0.0490954 | + | 0.998794i | \(0.515634\pi\) | |||||||
\(558\) | −3.17009 | −0.134200 | ||||||||
\(559\) | 0.986669 | 0.0417317 | ||||||||
\(560\) | 0.707008 | 0.0298765 | ||||||||
\(561\) | 1.90829 | 0.0805681 | ||||||||
\(562\) | −34.7708 | −1.46672 | ||||||||
\(563\) | 33.8888 | 1.42824 | 0.714122 | − | 0.700022i | \(-0.246826\pi\) | ||||
0.714122 | + | 0.700022i | \(0.246826\pi\) | |||||||
\(564\) | 8.83710 | 0.372109 | ||||||||
\(565\) | −3.33403 | −0.140264 | ||||||||
\(566\) | 35.2606 | 1.48211 | ||||||||
\(567\) | 0.630898 | 0.0264952 | ||||||||
\(568\) | −11.9421 | −0.501081 | ||||||||
\(569\) | 27.1389 | 1.13772 | 0.568861 | − | 0.822434i | \(-0.307384\pi\) | ||||
0.568861 | + | 0.822434i | \(0.307384\pi\) | |||||||
\(570\) | 4.73820 | 0.198462 | ||||||||
\(571\) | 4.64196 | 0.194260 | 0.0971300 | − | 0.995272i | \(-0.469034\pi\) | ||||
0.0971300 | + | 0.995272i | \(0.469034\pi\) | |||||||
\(572\) | 2.70928 | 0.113280 | ||||||||
\(573\) | −9.17727 | −0.383386 | ||||||||
\(574\) | −2.80590 | −0.117116 | ||||||||
\(575\) | −6.44748 | −0.268879 | ||||||||
\(576\) | −12.3112 | −0.512968 | ||||||||
\(577\) | −33.4186 | −1.39123 | −0.695616 | − | 0.718414i | \(-0.744869\pi\) | ||||
−0.695616 | + | 0.718414i | \(0.744869\pi\) | |||||||
\(578\) | −28.9889 | −1.20578 | ||||||||
\(579\) | −17.1012 | −0.710700 | ||||||||
\(580\) | 3.28458 | 0.136385 | ||||||||
\(581\) | 1.47641 | 0.0612518 | ||||||||
\(582\) | −11.0205 | −0.456815 | ||||||||
\(583\) | 9.91548 | 0.410657 | ||||||||
\(584\) | 14.5730 | 0.603037 | ||||||||
\(585\) | −0.539189 | −0.0222927 | ||||||||
\(586\) | −48.2472 | −1.99308 | ||||||||
\(587\) | 0.595825 | 0.0245923 | 0.0122962 | − | 0.999924i | \(-0.496086\pi\) | ||||
0.0122962 | + | 0.999924i | \(0.496086\pi\) | |||||||
\(588\) | −17.8865 | −0.737629 | ||||||||
\(589\) | 5.91548 | 0.243743 | ||||||||
\(590\) | 4.21461 | 0.173513 | ||||||||
\(591\) | −3.34244 | −0.137490 | ||||||||
\(592\) | 10.5548 | 0.433799 | ||||||||
\(593\) | 28.8554 | 1.18495 | 0.592474 | − | 0.805590i | \(-0.298151\pi\) | ||||
0.592474 | + | 0.805590i | \(0.298151\pi\) | |||||||
\(594\) | 2.17009 | 0.0890397 | ||||||||
\(595\) | −0.649149 | −0.0266125 | ||||||||
\(596\) | −43.3256 | −1.77469 | ||||||||
\(597\) | −14.2557 | −0.583445 | ||||||||
\(598\) | 2.97107 | 0.121496 | ||||||||
\(599\) | 45.0616 | 1.84117 | 0.920583 | − | 0.390548i | \(-0.127714\pi\) | ||||
0.920583 | + | 0.390548i | \(0.127714\pi\) | |||||||
\(600\) | −7.24846 | −0.295917 | ||||||||
\(601\) | −13.1506 | −0.536425 | −0.268212 | − | 0.963360i | \(-0.586433\pi\) | ||||
−0.268212 | + | 0.963360i | \(0.586433\pi\) | |||||||
\(602\) | 1.35085 | 0.0550566 | ||||||||
\(603\) | 5.95774 | 0.242618 | ||||||||
\(604\) | 29.2267 | 1.18922 | ||||||||
\(605\) | −0.539189 | −0.0219211 | ||||||||
\(606\) | 20.6381 | 0.838365 | ||||||||
\(607\) | 22.4729 | 0.912148 | 0.456074 | − | 0.889942i | \(-0.349255\pi\) | ||||
0.456074 | + | 0.889942i | \(0.349255\pi\) | |||||||
\(608\) | 30.7298 | 1.24626 | ||||||||
\(609\) | −1.41855 | −0.0574826 | ||||||||
\(610\) | −4.00000 | −0.161955 | ||||||||
\(611\) | 3.26180 | 0.131958 | ||||||||
\(612\) | 5.17009 | 0.208988 | ||||||||
\(613\) | −37.5136 | −1.51516 | −0.757579 | − | 0.652743i | \(-0.773618\pi\) | ||||
−0.757579 | + | 0.652743i | \(0.773618\pi\) | |||||||
\(614\) | −16.2062 | −0.654029 | ||||||||
\(615\) | 1.10504 | 0.0445595 | ||||||||
\(616\) | 0.971071 | 0.0391255 | ||||||||
\(617\) | 7.72875 | 0.311148 | 0.155574 | − | 0.987824i | \(-0.450277\pi\) | ||||
0.155574 | + | 0.987824i | \(0.450277\pi\) | |||||||
\(618\) | −9.94214 | −0.399932 | ||||||||
\(619\) | −15.2918 | −0.614628 | −0.307314 | − | 0.951608i | \(-0.599430\pi\) | ||||
−0.307314 | + | 0.951608i | \(0.599430\pi\) | |||||||
\(620\) | 2.13397 | 0.0857023 | ||||||||
\(621\) | 1.36910 | 0.0549402 | ||||||||
\(622\) | 2.75646 | 0.110524 | ||||||||
\(623\) | 8.18795 | 0.328043 | ||||||||
\(624\) | −2.07838 | −0.0832017 | ||||||||
\(625\) | 20.7237 | 0.828946 | ||||||||
\(626\) | 27.8394 | 1.11268 | ||||||||
\(627\) | −4.04945 | −0.161719 | ||||||||
\(628\) | −24.7298 | −0.986826 | ||||||||
\(629\) | −9.69102 | −0.386406 | ||||||||
\(630\) | −0.738205 | −0.0294108 | ||||||||
\(631\) | 5.98440 | 0.238235 | 0.119118 | − | 0.992880i | \(-0.461993\pi\) | ||||
0.119118 | + | 0.992880i | \(0.461993\pi\) | |||||||
\(632\) | 6.01560 | 0.239288 | ||||||||
\(633\) | 15.0133 | 0.596726 | ||||||||
\(634\) | 28.8443 | 1.14555 | ||||||||
\(635\) | 11.0244 | 0.437490 | ||||||||
\(636\) | 26.8638 | 1.06522 | ||||||||
\(637\) | −6.60197 | −0.261580 | ||||||||
\(638\) | −4.87936 | −0.193176 | ||||||||
\(639\) | −7.75872 | −0.306930 | ||||||||
\(640\) | 6.22180 | 0.245938 | ||||||||
\(641\) | −20.2023 | −0.797944 | −0.398972 | − | 0.916963i | \(-0.630633\pi\) | ||||
−0.398972 | + | 0.916963i | \(0.630633\pi\) | |||||||
\(642\) | 25.1773 | 0.993668 | ||||||||
\(643\) | 16.5659 | 0.653293 | 0.326647 | − | 0.945147i | \(-0.394081\pi\) | ||||
0.326647 | + | 0.945147i | \(0.394081\pi\) | |||||||
\(644\) | 2.34017 | 0.0922157 | ||||||||
\(645\) | −0.532001 | −0.0209475 | ||||||||
\(646\) | −16.7694 | −0.659783 | ||||||||
\(647\) | 0.183417 | 0.00721089 | 0.00360544 | − | 0.999994i | \(-0.498852\pi\) | ||||
0.00360544 | + | 0.999994i | \(0.498852\pi\) | |||||||
\(648\) | 1.53919 | 0.0604650 | ||||||||
\(649\) | −3.60197 | −0.141390 | ||||||||
\(650\) | −10.2195 | −0.400843 | ||||||||
\(651\) | −0.921622 | −0.0361212 | ||||||||
\(652\) | −19.7165 | −0.772156 | ||||||||
\(653\) | −43.5052 | −1.70249 | −0.851244 | − | 0.524770i | \(-0.824151\pi\) | ||||
−0.851244 | + | 0.524770i | \(0.824151\pi\) | |||||||
\(654\) | −28.5464 | −1.11625 | ||||||||
\(655\) | −7.51745 | −0.293731 | ||||||||
\(656\) | 4.25953 | 0.166307 | ||||||||
\(657\) | 9.46800 | 0.369382 | ||||||||
\(658\) | 4.46573 | 0.174092 | ||||||||
\(659\) | 7.57531 | 0.295092 | 0.147546 | − | 0.989055i | \(-0.452863\pi\) | ||||
0.147546 | + | 0.989055i | \(0.452863\pi\) | |||||||
\(660\) | −1.46081 | −0.0568620 | ||||||||
\(661\) | 47.0616 | 1.83048 | 0.915241 | − | 0.402906i | \(-0.132000\pi\) | ||||
0.915241 | + | 0.402906i | \(0.132000\pi\) | |||||||
\(662\) | 68.7019 | 2.67018 | ||||||||
\(663\) | 1.90829 | 0.0741119 | ||||||||
\(664\) | 3.60197 | 0.139783 | ||||||||
\(665\) | 1.37751 | 0.0534177 | ||||||||
\(666\) | −11.0205 | −0.427036 | ||||||||
\(667\) | −3.07838 | −0.119195 | ||||||||
\(668\) | 43.6163 | 1.68757 | ||||||||
\(669\) | 9.77432 | 0.377897 | ||||||||
\(670\) | −6.97107 | −0.269316 | ||||||||
\(671\) | 3.41855 | 0.131972 | ||||||||
\(672\) | −4.78765 | −0.184688 | ||||||||
\(673\) | 37.1605 | 1.43243 | 0.716215 | − | 0.697880i | \(-0.245873\pi\) | ||||
0.716215 | + | 0.697880i | \(0.245873\pi\) | |||||||
\(674\) | −3.72753 | −0.143579 | ||||||||
\(675\) | −4.70928 | −0.181260 | ||||||||
\(676\) | 2.70928 | 0.104203 | ||||||||
\(677\) | 32.6030 | 1.25304 | 0.626518 | − | 0.779407i | \(-0.284480\pi\) | ||||
0.626518 | + | 0.779407i | \(0.284480\pi\) | |||||||
\(678\) | 13.4186 | 0.515336 | ||||||||
\(679\) | −3.20394 | −0.122956 | ||||||||
\(680\) | −1.58372 | −0.0607328 | ||||||||
\(681\) | −11.0700 | −0.424202 | ||||||||
\(682\) | −3.17009 | −0.121389 | ||||||||
\(683\) | −50.9914 | −1.95113 | −0.975566 | − | 0.219706i | \(-0.929490\pi\) | ||||
−0.975566 | + | 0.219706i | \(0.929490\pi\) | |||||||
\(684\) | −10.9711 | −0.419489 | ||||||||
\(685\) | 1.56690 | 0.0598680 | ||||||||
\(686\) | −18.6225 | −0.711010 | ||||||||
\(687\) | −17.0928 | −0.652129 | ||||||||
\(688\) | −2.05067 | −0.0781811 | ||||||||
\(689\) | 9.91548 | 0.377750 | ||||||||
\(690\) | −1.60197 | −0.0609859 | ||||||||
\(691\) | 15.9434 | 0.606514 | 0.303257 | − | 0.952909i | \(-0.401926\pi\) | ||||
0.303257 | + | 0.952909i | \(0.401926\pi\) | |||||||
\(692\) | 44.0216 | 1.67345 | ||||||||
\(693\) | 0.630898 | 0.0239658 | ||||||||
\(694\) | 3.47641 | 0.131963 | ||||||||
\(695\) | −10.0761 | −0.382209 | ||||||||
\(696\) | −3.46081 | −0.131182 | ||||||||
\(697\) | −3.91094 | −0.148138 | ||||||||
\(698\) | 35.6742 | 1.35029 | ||||||||
\(699\) | −8.00719 | −0.302860 | ||||||||
\(700\) | −8.04945 | −0.304241 | ||||||||
\(701\) | 4.88324 | 0.184437 | 0.0922187 | − | 0.995739i | \(-0.470604\pi\) | ||||
0.0922187 | + | 0.995739i | \(0.470604\pi\) | |||||||
\(702\) | 2.17009 | 0.0819046 | ||||||||
\(703\) | 20.5646 | 0.775610 | ||||||||
\(704\) | −12.3112 | −0.463997 | ||||||||
\(705\) | −1.75872 | −0.0662374 | ||||||||
\(706\) | −2.14957 | −0.0809000 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | −9.75872 | −0.366755 | ||||||||
\(709\) | −7.20394 | −0.270550 | −0.135275 | − | 0.990808i | \(-0.543192\pi\) | ||||
−0.135275 | + | 0.990808i | \(0.543192\pi\) | |||||||
\(710\) | 9.07838 | 0.340705 | ||||||||
\(711\) | 3.90829 | 0.146572 | ||||||||
\(712\) | 19.9760 | 0.748632 | ||||||||
\(713\) | −2.00000 | −0.0749006 | ||||||||
\(714\) | 2.61265 | 0.0977758 | ||||||||
\(715\) | −0.539189 | −0.0201645 | ||||||||
\(716\) | 50.2472 | 1.87783 | ||||||||
\(717\) | −3.28458 | −0.122665 | ||||||||
\(718\) | −61.9481 | −2.31188 | ||||||||
\(719\) | −4.84939 | −0.180852 | −0.0904258 | − | 0.995903i | \(-0.528823\pi\) | ||||
−0.0904258 | + | 0.995903i | \(0.528823\pi\) | |||||||
\(720\) | 1.12064 | 0.0417637 | ||||||||
\(721\) | −2.89043 | −0.107645 | ||||||||
\(722\) | −5.64650 | −0.210141 | ||||||||
\(723\) | 13.5486 | 0.503880 | ||||||||
\(724\) | −29.4557 | −1.09471 | ||||||||
\(725\) | 10.5886 | 0.393252 | ||||||||
\(726\) | 2.17009 | 0.0805395 | ||||||||
\(727\) | 34.8515 | 1.29257 | 0.646285 | − | 0.763096i | \(-0.276322\pi\) | ||||
0.646285 | + | 0.763096i | \(0.276322\pi\) | |||||||
\(728\) | 0.971071 | 0.0359903 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.0784 | −0.410029 | ||||||||
\(731\) | 1.88285 | 0.0696398 | ||||||||
\(732\) | 9.26180 | 0.342326 | ||||||||
\(733\) | 11.2579 | 0.415821 | 0.207910 | − | 0.978148i | \(-0.433334\pi\) | ||||
0.207910 | + | 0.978148i | \(0.433334\pi\) | |||||||
\(734\) | −24.3812 | −0.899927 | ||||||||
\(735\) | 3.55971 | 0.131302 | ||||||||
\(736\) | −10.3896 | −0.382967 | ||||||||
\(737\) | 5.95774 | 0.219456 | ||||||||
\(738\) | −4.44748 | −0.163714 | ||||||||
\(739\) | 16.1028 | 0.592350 | 0.296175 | − | 0.955134i | \(-0.404289\pi\) | ||||
0.296175 | + | 0.955134i | \(0.404289\pi\) | |||||||
\(740\) | 7.41855 | 0.272711 | ||||||||
\(741\) | −4.04945 | −0.148760 | ||||||||
\(742\) | 13.5753 | 0.498365 | ||||||||
\(743\) | −21.1317 | −0.775247 | −0.387623 | − | 0.921818i | \(-0.626704\pi\) | ||||
−0.387623 | + | 0.921818i | \(0.626704\pi\) | |||||||
\(744\) | −2.24846 | −0.0824327 | ||||||||
\(745\) | 8.62249 | 0.315903 | ||||||||
\(746\) | −41.4017 | −1.51583 | ||||||||
\(747\) | 2.34017 | 0.0856225 | ||||||||
\(748\) | 5.17009 | 0.189037 | ||||||||
\(749\) | 7.31965 | 0.267454 | ||||||||
\(750\) | 11.3607 | 0.414834 | ||||||||
\(751\) | 51.3172 | 1.87259 | 0.936296 | − | 0.351213i | \(-0.114231\pi\) | ||||
0.936296 | + | 0.351213i | \(0.114231\pi\) | |||||||
\(752\) | −6.77924 | −0.247214 | ||||||||
\(753\) | 4.18342 | 0.152452 | ||||||||
\(754\) | −4.87936 | −0.177696 | ||||||||
\(755\) | −5.81658 | −0.211687 | ||||||||
\(756\) | 1.70928 | 0.0621657 | ||||||||
\(757\) | 48.3773 | 1.75830 | 0.879152 | − | 0.476541i | \(-0.158110\pi\) | ||||
0.879152 | + | 0.476541i | \(0.158110\pi\) | |||||||
\(758\) | 3.90829 | 0.141956 | ||||||||
\(759\) | 1.36910 | 0.0496953 | ||||||||
\(760\) | 3.36069 | 0.121905 | ||||||||
\(761\) | 34.4307 | 1.24811 | 0.624055 | − | 0.781380i | \(-0.285484\pi\) | ||||
0.624055 | + | 0.781380i | \(0.285484\pi\) | |||||||
\(762\) | −44.3701 | −1.60736 | ||||||||
\(763\) | −8.29914 | −0.300449 | ||||||||
\(764\) | −24.8638 | −0.899539 | ||||||||
\(765\) | −1.02893 | −0.0372010 | ||||||||
\(766\) | −2.12556 | −0.0767996 | ||||||||
\(767\) | −3.60197 | −0.130060 | ||||||||
\(768\) | −0.418551 | −0.0151031 | ||||||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | −0.738205 | −0.0266031 | ||||||||
\(771\) | 8.52359 | 0.306970 | ||||||||
\(772\) | −46.3318 | −1.66752 | ||||||||
\(773\) | −38.7370 | −1.39327 | −0.696636 | − | 0.717425i | \(-0.745321\pi\) | ||||
−0.696636 | + | 0.717425i | \(0.745321\pi\) | |||||||
\(774\) | 2.14116 | 0.0769623 | ||||||||
\(775\) | 6.87936 | 0.247114 | ||||||||
\(776\) | −7.81658 | −0.280599 | ||||||||
\(777\) | −3.20394 | −0.114941 | ||||||||
\(778\) | −65.7152 | −2.35601 | ||||||||
\(779\) | 8.29914 | 0.297347 | ||||||||
\(780\) | −1.46081 | −0.0523054 | ||||||||
\(781\) | −7.75872 | −0.277629 | ||||||||
\(782\) | 5.66967 | 0.202747 | ||||||||
\(783\) | −2.24846 | −0.0803536 | ||||||||
\(784\) | 13.7214 | 0.490049 | ||||||||
\(785\) | 4.92162 | 0.175660 | ||||||||
\(786\) | 30.2557 | 1.07918 | ||||||||
\(787\) | 25.8927 | 0.922975 | 0.461487 | − | 0.887147i | \(-0.347316\pi\) | ||||
0.461487 | + | 0.887147i | \(0.347316\pi\) | |||||||
\(788\) | −9.05559 | −0.322592 | ||||||||
\(789\) | 22.7526 | 0.810013 | ||||||||
\(790\) | −4.57304 | −0.162701 | ||||||||
\(791\) | 3.90110 | 0.138707 | ||||||||
\(792\) | 1.53919 | 0.0546927 | ||||||||
\(793\) | 3.41855 | 0.121396 | ||||||||
\(794\) | −69.0082 | −2.44901 | ||||||||
\(795\) | −5.34632 | −0.189614 | ||||||||
\(796\) | −38.6225 | −1.36894 | ||||||||
\(797\) | 22.2967 | 0.789789 | 0.394895 | − | 0.918726i | \(-0.370781\pi\) | ||||
0.394895 | + | 0.918726i | \(0.370781\pi\) | |||||||
\(798\) | −5.54411 | −0.196259 | ||||||||
\(799\) | 6.22446 | 0.220205 | ||||||||
\(800\) | 35.7370 | 1.26349 | ||||||||
\(801\) | 12.9783 | 0.458564 | ||||||||
\(802\) | −2.92881 | −0.103420 | ||||||||
\(803\) | 9.46800 | 0.334118 | ||||||||
\(804\) | 16.1412 | 0.569255 | ||||||||
\(805\) | −0.465732 | −0.0164149 | ||||||||
\(806\) | −3.17009 | −0.111662 | ||||||||
\(807\) | −8.34017 | −0.293588 | ||||||||
\(808\) | 14.6381 | 0.514966 | ||||||||
\(809\) | 0.195140 | 0.00686077 | 0.00343038 | − | 0.999994i | \(-0.498908\pi\) | ||||
0.00343038 | + | 0.999994i | \(0.498908\pi\) | |||||||
\(810\) | −1.17009 | −0.0411126 | ||||||||
\(811\) | −45.3400 | −1.59210 | −0.796051 | − | 0.605229i | \(-0.793081\pi\) | ||||
−0.796051 | + | 0.605229i | \(0.793081\pi\) | |||||||
\(812\) | −3.84324 | −0.134871 | ||||||||
\(813\) | 26.7031 | 0.936520 | ||||||||
\(814\) | −11.0205 | −0.386269 | ||||||||
\(815\) | 3.92389 | 0.137448 | ||||||||
\(816\) | −3.96615 | −0.138843 | ||||||||
\(817\) | −3.99547 | −0.139784 | ||||||||
\(818\) | 9.02893 | 0.315689 | ||||||||
\(819\) | 0.630898 | 0.0220453 | ||||||||
\(820\) | 2.99386 | 0.104550 | ||||||||
\(821\) | 54.3605 | 1.89720 | 0.948598 | − | 0.316485i | \(-0.102503\pi\) | ||||
0.948598 | + | 0.316485i | \(0.102503\pi\) | |||||||
\(822\) | −6.30632 | −0.219958 | ||||||||
\(823\) | −31.0205 | −1.08131 | −0.540654 | − | 0.841245i | \(-0.681823\pi\) | ||||
−0.540654 | + | 0.841245i | \(0.681823\pi\) | |||||||
\(824\) | −7.05172 | −0.245658 | ||||||||
\(825\) | −4.70928 | −0.163956 | ||||||||
\(826\) | −4.93146 | −0.171588 | ||||||||
\(827\) | −50.0228 | −1.73946 | −0.869731 | − | 0.493525i | \(-0.835708\pi\) | ||||
−0.869731 | + | 0.493525i | \(0.835708\pi\) | |||||||
\(828\) | 3.70928 | 0.128906 | ||||||||
\(829\) | 38.9939 | 1.35431 | 0.677156 | − | 0.735839i | \(-0.263212\pi\) | ||||
0.677156 | + | 0.735839i | \(0.263212\pi\) | |||||||
\(830\) | −2.73820 | −0.0950445 | ||||||||
\(831\) | 7.62863 | 0.264634 | ||||||||
\(832\) | −12.3112 | −0.426816 | ||||||||
\(833\) | −12.5985 | −0.436511 | ||||||||
\(834\) | 40.5536 | 1.40426 | ||||||||
\(835\) | −8.68035 | −0.300396 | ||||||||
\(836\) | −10.9711 | −0.379442 | ||||||||
\(837\) | −1.46081 | −0.0504930 | ||||||||
\(838\) | −73.4557 | −2.53749 | ||||||||
\(839\) | −34.2557 | −1.18264 | −0.591318 | − | 0.806438i | \(-0.701392\pi\) | ||||
−0.591318 | + | 0.806438i | \(0.701392\pi\) | |||||||
\(840\) | −0.523590 | −0.0180656 | ||||||||
\(841\) | −23.9444 | −0.825669 | ||||||||
\(842\) | −50.4801 | −1.73966 | ||||||||
\(843\) | −16.0228 | −0.551854 | ||||||||
\(844\) | 40.6752 | 1.40010 | ||||||||
\(845\) | −0.539189 | −0.0185487 | ||||||||
\(846\) | 7.07838 | 0.243360 | ||||||||
\(847\) | 0.630898 | 0.0216779 | ||||||||
\(848\) | −20.6081 | −0.707685 | ||||||||
\(849\) | 16.2485 | 0.557646 | ||||||||
\(850\) | −19.5018 | −0.668908 | ||||||||
\(851\) | −6.95282 | −0.238340 | ||||||||
\(852\) | −21.0205 | −0.720151 | ||||||||
\(853\) | −34.6635 | −1.18686 | −0.593428 | − | 0.804887i | \(-0.702226\pi\) | ||||
−0.593428 | + | 0.804887i | \(0.702226\pi\) | |||||||
\(854\) | 4.68035 | 0.160158 | ||||||||
\(855\) | 2.18342 | 0.0746713 | ||||||||
\(856\) | 17.8576 | 0.610361 | ||||||||
\(857\) | 2.91443 | 0.0995552 | 0.0497776 | − | 0.998760i | \(-0.484149\pi\) | ||||
0.0497776 | + | 0.998760i | \(0.484149\pi\) | |||||||
\(858\) | 2.17009 | 0.0740855 | ||||||||
\(859\) | 49.9109 | 1.70294 | 0.851470 | − | 0.524404i | \(-0.175712\pi\) | ||||
0.851470 | + | 0.524404i | \(0.175712\pi\) | |||||||
\(860\) | −1.44134 | −0.0491492 | ||||||||
\(861\) | −1.29299 | −0.0440651 | ||||||||
\(862\) | −31.0517 | −1.05763 | ||||||||
\(863\) | 19.0205 | 0.647466 | 0.323733 | − | 0.946148i | \(-0.395062\pi\) | ||||
0.323733 | + | 0.946148i | \(0.395062\pi\) | |||||||
\(864\) | −7.58864 | −0.258171 | ||||||||
\(865\) | −8.76099 | −0.297883 | ||||||||
\(866\) | −35.8576 | −1.21849 | ||||||||
\(867\) | −13.3584 | −0.453676 | ||||||||
\(868\) | −2.49693 | −0.0847513 | ||||||||
\(869\) | 3.90829 | 0.132580 | ||||||||
\(870\) | 2.63090 | 0.0891958 | ||||||||
\(871\) | 5.95774 | 0.201870 | ||||||||
\(872\) | −20.2472 | −0.685658 | ||||||||
\(873\) | −5.07838 | −0.171877 | ||||||||
\(874\) | −12.0312 | −0.406961 | ||||||||
\(875\) | 3.30283 | 0.111656 | ||||||||
\(876\) | 25.6514 | 0.866681 | ||||||||
\(877\) | 7.75872 | 0.261993 | 0.130997 | − | 0.991383i | \(-0.458182\pi\) | ||||
0.130997 | + | 0.991383i | \(0.458182\pi\) | |||||||
\(878\) | −29.9409 | −1.01046 | ||||||||
\(879\) | −22.2329 | −0.749896 | ||||||||
\(880\) | 1.12064 | 0.0377767 | ||||||||
\(881\) | 8.63931 | 0.291066 | 0.145533 | − | 0.989353i | \(-0.453510\pi\) | ||||
0.145533 | + | 0.989353i | \(0.453510\pi\) | |||||||
\(882\) | −14.3268 | −0.482410 | ||||||||
\(883\) | 25.4596 | 0.856783 | 0.428392 | − | 0.903593i | \(-0.359080\pi\) | ||||
0.428392 | + | 0.903593i | \(0.359080\pi\) | |||||||
\(884\) | 5.17009 | 0.173889 | ||||||||
\(885\) | 1.94214 | 0.0652844 | ||||||||
\(886\) | −53.1917 | −1.78701 | ||||||||
\(887\) | −43.7198 | −1.46797 | −0.733983 | − | 0.679168i | \(-0.762341\pi\) | ||||
−0.733983 | + | 0.679168i | \(0.762341\pi\) | |||||||
\(888\) | −7.81658 | −0.262307 | ||||||||
\(889\) | −12.8995 | −0.432635 | ||||||||
\(890\) | −15.1857 | −0.509025 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 26.4813 | 0.886661 | ||||||||
\(893\) | −13.2085 | −0.442005 | ||||||||
\(894\) | −34.7031 | −1.16065 | ||||||||
\(895\) | −10.0000 | −0.334263 | ||||||||
\(896\) | −7.28005 | −0.243209 | ||||||||
\(897\) | 1.36910 | 0.0457130 | ||||||||
\(898\) | −76.3039 | −2.54629 | ||||||||
\(899\) | 3.28458 | 0.109547 | ||||||||
\(900\) | −12.7587 | −0.425291 | ||||||||
\(901\) | 18.9216 | 0.630371 | ||||||||
\(902\) | −4.44748 | −0.148085 | ||||||||
\(903\) | 0.622487 | 0.0207151 | ||||||||
\(904\) | 9.51745 | 0.316546 | ||||||||
\(905\) | 5.86216 | 0.194865 | ||||||||
\(906\) | 23.4101 | 0.777750 | ||||||||
\(907\) | −49.7875 | −1.65317 | −0.826583 | − | 0.562815i | \(-0.809718\pi\) | ||||
−0.826583 | + | 0.562815i | \(0.809718\pi\) | |||||||
\(908\) | −29.9916 | −0.995306 | ||||||||
\(909\) | 9.51026 | 0.315435 | ||||||||
\(910\) | −0.738205 | −0.0244712 | ||||||||
\(911\) | −11.4497 | −0.379347 | −0.189674 | − | 0.981847i | \(-0.560743\pi\) | ||||
−0.189674 | + | 0.981847i | \(0.560743\pi\) | |||||||
\(912\) | 8.41628 | 0.278691 | ||||||||
\(913\) | 2.34017 | 0.0774484 | ||||||||
\(914\) | −78.6779 | −2.60243 | ||||||||
\(915\) | −1.84324 | −0.0609358 | ||||||||
\(916\) | −46.3090 | −1.53009 | ||||||||
\(917\) | 8.79606 | 0.290472 | ||||||||
\(918\) | 4.14116 | 0.136679 | ||||||||
\(919\) | −9.41136 | −0.310452 | −0.155226 | − | 0.987879i | \(-0.549611\pi\) | ||||
−0.155226 | + | 0.987879i | \(0.549611\pi\) | |||||||
\(920\) | −1.13624 | −0.0374606 | ||||||||
\(921\) | −7.46800 | −0.246079 | ||||||||
\(922\) | 51.2678 | 1.68841 | ||||||||
\(923\) | −7.75872 | −0.255382 | ||||||||
\(924\) | 1.70928 | 0.0562310 | ||||||||
\(925\) | 23.9155 | 0.786336 | ||||||||
\(926\) | −10.5308 | −0.346063 | ||||||||
\(927\) | −4.58145 | −0.150475 | ||||||||
\(928\) | 17.0628 | 0.560113 | ||||||||
\(929\) | 30.5536 | 1.00243 | 0.501215 | − | 0.865323i | \(-0.332887\pi\) | ||||
0.501215 | + | 0.865323i | \(0.332887\pi\) | |||||||
\(930\) | 1.70928 | 0.0560493 | ||||||||
\(931\) | 26.7343 | 0.876182 | ||||||||
\(932\) | −21.6937 | −0.710600 | ||||||||
\(933\) | 1.27021 | 0.0415847 | ||||||||
\(934\) | 34.4885 | 1.12850 | ||||||||
\(935\) | −1.02893 | −0.0336496 | ||||||||
\(936\) | 1.53919 | 0.0503100 | ||||||||
\(937\) | −44.7480 | −1.46185 | −0.730927 | − | 0.682455i | \(-0.760912\pi\) | ||||
−0.730927 | + | 0.682455i | \(0.760912\pi\) | |||||||
\(938\) | 8.15676 | 0.266328 | ||||||||
\(939\) | 12.8287 | 0.418649 | ||||||||
\(940\) | −4.76487 | −0.155413 | ||||||||
\(941\) | −52.9153 | −1.72499 | −0.862495 | − | 0.506066i | \(-0.831099\pi\) | ||||
−0.862495 | + | 0.506066i | \(0.831099\pi\) | |||||||
\(942\) | −19.8082 | −0.645385 | ||||||||
\(943\) | −2.80590 | −0.0913728 | ||||||||
\(944\) | 7.48625 | 0.243657 | ||||||||
\(945\) | −0.340173 | −0.0110658 | ||||||||
\(946\) | 2.14116 | 0.0696150 | ||||||||
\(947\) | 52.6681 | 1.71148 | 0.855741 | − | 0.517404i | \(-0.173102\pi\) | ||||
0.855741 | + | 0.517404i | \(0.173102\pi\) | |||||||
\(948\) | 10.5886 | 0.343903 | ||||||||
\(949\) | 9.46800 | 0.307344 | ||||||||
\(950\) | 41.3835 | 1.34266 | ||||||||
\(951\) | 13.2918 | 0.431015 | ||||||||
\(952\) | 1.85309 | 0.0600588 | ||||||||
\(953\) | −14.0338 | −0.454601 | −0.227300 | − | 0.973825i | \(-0.572990\pi\) | ||||
−0.227300 | + | 0.973825i | \(0.572990\pi\) | |||||||
\(954\) | 21.5174 | 0.696653 | ||||||||
\(955\) | 4.94828 | 0.160123 | ||||||||
\(956\) | −8.89884 | −0.287809 | ||||||||
\(957\) | −2.24846 | −0.0726825 | ||||||||
\(958\) | −12.3896 | −0.400290 | ||||||||
\(959\) | −1.83340 | −0.0592037 | ||||||||
\(960\) | 6.63809 | 0.214243 | ||||||||
\(961\) | −28.8660 | −0.931162 | ||||||||
\(962\) | −11.0205 | −0.355316 | ||||||||
\(963\) | 11.6020 | 0.373868 | ||||||||
\(964\) | 36.7070 | 1.18225 | ||||||||
\(965\) | 9.22076 | 0.296827 | ||||||||
\(966\) | 1.87444 | 0.0603092 | ||||||||
\(967\) | −18.3440 | −0.589905 | −0.294952 | − | 0.955512i | \(-0.595304\pi\) | ||||
−0.294952 | + | 0.955512i | \(0.595304\pi\) | |||||||
\(968\) | 1.53919 | 0.0494714 | ||||||||
\(969\) | −7.72753 | −0.248244 | ||||||||
\(970\) | 5.94214 | 0.190791 | ||||||||
\(971\) | 45.4968 | 1.46006 | 0.730030 | − | 0.683415i | \(-0.239506\pi\) | ||||
0.730030 | + | 0.683415i | \(0.239506\pi\) | |||||||
\(972\) | 2.70928 | 0.0869000 | ||||||||
\(973\) | 11.7899 | 0.377967 | ||||||||
\(974\) | −60.6030 | −1.94185 | ||||||||
\(975\) | −4.70928 | −0.150818 | ||||||||
\(976\) | −7.10504 | −0.227427 | ||||||||
\(977\) | 24.5802 | 0.786391 | 0.393196 | − | 0.919455i | \(-0.371370\pi\) | ||||
0.393196 | + | 0.919455i | \(0.371370\pi\) | |||||||
\(978\) | −15.7926 | −0.504991 | ||||||||
\(979\) | 12.9783 | 0.414787 | ||||||||
\(980\) | 9.64423 | 0.308074 | ||||||||
\(981\) | −13.1545 | −0.419990 | ||||||||
\(982\) | 69.8141 | 2.22786 | ||||||||
\(983\) | −57.7198 | −1.84097 | −0.920487 | − | 0.390772i | \(-0.872208\pi\) | ||||
−0.920487 | + | 0.390772i | \(0.872208\pi\) | |||||||
\(984\) | −3.15449 | −0.100561 | ||||||||
\(985\) | 1.80221 | 0.0574231 | ||||||||
\(986\) | −9.31124 | −0.296530 | ||||||||
\(987\) | 2.05786 | 0.0655024 | ||||||||
\(988\) | −10.9711 | −0.349036 | ||||||||
\(989\) | 1.35085 | 0.0429546 | ||||||||
\(990\) | −1.17009 | −0.0371878 | ||||||||
\(991\) | 12.0221 | 0.381895 | 0.190948 | − | 0.981600i | \(-0.438844\pi\) | ||||
0.190948 | + | 0.981600i | \(0.438844\pi\) | |||||||
\(992\) | 11.0856 | 0.351967 | ||||||||
\(993\) | 31.6586 | 1.00466 | ||||||||
\(994\) | −10.6225 | −0.336925 | ||||||||
\(995\) | 7.68649 | 0.243678 | ||||||||
\(996\) | 6.34017 | 0.200896 | ||||||||
\(997\) | −34.5958 | −1.09566 | −0.547830 | − | 0.836589i | \(-0.684546\pi\) | ||||
−0.547830 | + | 0.836589i | \(0.684546\pi\) | |||||||
\(998\) | −35.3679 | −1.11955 | ||||||||
\(999\) | −5.07838 | −0.160673 |
(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 | 429.2.a.f.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 1287.2.a.i.1.1 | 3 | |||
4.3 | odd | 2 | 6864.2.a.bp.1.2 | 3 | |||
11.10 | odd | 2 | 4719.2.a.t.1.1 | 3 | |||
13.12 | even | 2 | 5577.2.a.k.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.a.f.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1287.2.a.i.1.1 | 3 | 3.2 | odd | 2 | |||
4719.2.a.t.1.1 | 3 | 11.10 | odd | 2 | |||
5577.2.a.k.1.1 | 3 | 13.12 | even | 2 | |||
6864.2.a.bp.1.2 | 3 | 4.3 | odd | 2 |