Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | 0.626459 | 0.361687 | 0.180843 | − | 0.983512i | \(-0.442117\pi\) | ||||
0.180843 | + | 0.983512i | \(0.442117\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.16763 | −1.86382 | −0.931910 | − | 0.362690i | \(-0.881858\pi\) | ||||
−0.931910 | + | 0.362690i | \(0.881858\pi\) | |||||||
\(6\) | −0.626459 | −0.255751 | ||||||||
\(7\) | 4.47360 | 1.69086 | 0.845430 | − | 0.534086i | \(-0.179344\pi\) | ||||
0.845430 | + | 0.534086i | \(0.179344\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.60755 | −0.869183 | ||||||||
\(10\) | 4.16763 | 1.31792 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.626459 | 0.180843 | ||||||||
\(13\) | −4.07211 | −1.12940 | −0.564700 | − | 0.825296i | \(-0.691008\pi\) | ||||
−0.564700 | + | 0.825296i | \(0.691008\pi\) | |||||||
\(14\) | −4.47360 | −1.19562 | ||||||||
\(15\) | −2.61085 | −0.674118 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.444921 | 0.107909 | 0.0539546 | − | 0.998543i | \(-0.482817\pi\) | ||||
0.0539546 | + | 0.998543i | \(0.482817\pi\) | |||||||
\(18\) | 2.60755 | 0.614605 | ||||||||
\(19\) | −4.25443 | −0.976034 | −0.488017 | − | 0.872834i | \(-0.662280\pi\) | ||||
−0.488017 | + | 0.872834i | \(0.662280\pi\) | |||||||
\(20\) | −4.16763 | −0.931910 | ||||||||
\(21\) | 2.80253 | 0.611561 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −7.47445 | −1.55853 | −0.779266 | − | 0.626694i | \(-0.784408\pi\) | ||||
−0.779266 | + | 0.626694i | \(0.784408\pi\) | |||||||
\(24\) | −0.626459 | −0.127875 | ||||||||
\(25\) | 12.3691 | 2.47382 | ||||||||
\(26\) | 4.07211 | 0.798606 | ||||||||
\(27\) | −3.51290 | −0.676058 | ||||||||
\(28\) | 4.47360 | 0.845430 | ||||||||
\(29\) | 4.69923 | 0.872625 | 0.436313 | − | 0.899795i | \(-0.356284\pi\) | ||||
0.436313 | + | 0.899795i | \(0.356284\pi\) | |||||||
\(30\) | 2.61085 | 0.476674 | ||||||||
\(31\) | 4.49682 | 0.807653 | 0.403826 | − | 0.914836i | \(-0.367680\pi\) | ||||
0.403826 | + | 0.914836i | \(0.367680\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.626459 | −0.109053 | ||||||||
\(34\) | −0.444921 | −0.0763033 | ||||||||
\(35\) | −18.6443 | −3.15146 | ||||||||
\(36\) | −2.60755 | −0.434591 | ||||||||
\(37\) | −2.54821 | −0.418923 | −0.209461 | − | 0.977817i | \(-0.567171\pi\) | ||||
−0.209461 | + | 0.977817i | \(0.567171\pi\) | |||||||
\(38\) | 4.25443 | 0.690160 | ||||||||
\(39\) | −2.55101 | −0.408489 | ||||||||
\(40\) | 4.16763 | 0.658960 | ||||||||
\(41\) | 4.86454 | 0.759714 | 0.379857 | − | 0.925045i | \(-0.375973\pi\) | ||||
0.379857 | + | 0.925045i | \(0.375973\pi\) | |||||||
\(42\) | −2.80253 | −0.432439 | ||||||||
\(43\) | −3.43878 | −0.524409 | −0.262204 | − | 0.965012i | \(-0.584449\pi\) | ||||
−0.262204 | + | 0.965012i | \(0.584449\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 10.8673 | 1.62000 | ||||||||
\(46\) | 7.47445 | 1.10205 | ||||||||
\(47\) | −10.9174 | −1.59247 | −0.796234 | − | 0.604989i | \(-0.793177\pi\) | ||||
−0.796234 | + | 0.604989i | \(0.793177\pi\) | |||||||
\(48\) | 0.626459 | 0.0904216 | ||||||||
\(49\) | 13.0131 | 1.85901 | ||||||||
\(50\) | −12.3691 | −1.74926 | ||||||||
\(51\) | 0.278725 | 0.0390293 | ||||||||
\(52\) | −4.07211 | −0.564700 | ||||||||
\(53\) | −9.00211 | −1.23653 | −0.618267 | − | 0.785968i | \(-0.712165\pi\) | ||||
−0.618267 | + | 0.785968i | \(0.712165\pi\) | |||||||
\(54\) | 3.51290 | 0.478045 | ||||||||
\(55\) | 4.16763 | 0.561963 | ||||||||
\(56\) | −4.47360 | −0.597809 | ||||||||
\(57\) | −2.66523 | −0.353018 | ||||||||
\(58\) | −4.69923 | −0.617039 | ||||||||
\(59\) | 5.40428 | 0.703577 | 0.351789 | − | 0.936079i | \(-0.385574\pi\) | ||||
0.351789 | + | 0.936079i | \(0.385574\pi\) | |||||||
\(60\) | −2.61085 | −0.337059 | ||||||||
\(61\) | 10.0903 | 1.29193 | 0.645965 | − | 0.763367i | \(-0.276455\pi\) | ||||
0.645965 | + | 0.763367i | \(0.276455\pi\) | |||||||
\(62\) | −4.49682 | −0.571097 | ||||||||
\(63\) | −11.6651 | −1.46967 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.9710 | 2.10500 | ||||||||
\(66\) | 0.626459 | 0.0771118 | ||||||||
\(67\) | 11.9951 | 1.46543 | 0.732717 | − | 0.680533i | \(-0.238252\pi\) | ||||
0.732717 | + | 0.680533i | \(0.238252\pi\) | |||||||
\(68\) | 0.444921 | 0.0539546 | ||||||||
\(69\) | −4.68244 | −0.563700 | ||||||||
\(70\) | 18.6443 | 2.22842 | ||||||||
\(71\) | 6.77175 | 0.803659 | 0.401829 | − | 0.915715i | \(-0.368374\pi\) | ||||
0.401829 | + | 0.915715i | \(0.368374\pi\) | |||||||
\(72\) | 2.60755 | 0.307303 | ||||||||
\(73\) | −7.28899 | −0.853112 | −0.426556 | − | 0.904461i | \(-0.640273\pi\) | ||||
−0.426556 | + | 0.904461i | \(0.640273\pi\) | |||||||
\(74\) | 2.54821 | 0.296223 | ||||||||
\(75\) | 7.74875 | 0.894749 | ||||||||
\(76\) | −4.25443 | −0.488017 | ||||||||
\(77\) | −4.47360 | −0.509813 | ||||||||
\(78\) | 2.55101 | 0.288845 | ||||||||
\(79\) | 6.11012 | 0.687443 | 0.343721 | − | 0.939072i | \(-0.388312\pi\) | ||||
0.343721 | + | 0.939072i | \(0.388312\pi\) | |||||||
\(80\) | −4.16763 | −0.465955 | ||||||||
\(81\) | 5.62196 | 0.624662 | ||||||||
\(82\) | −4.86454 | −0.537199 | ||||||||
\(83\) | −2.21493 | −0.243120 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(84\) | 2.80253 | 0.305781 | ||||||||
\(85\) | −1.85426 | −0.201123 | ||||||||
\(86\) | 3.43878 | 0.370813 | ||||||||
\(87\) | 2.94388 | 0.315617 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −5.18723 | −0.549845 | −0.274923 | − | 0.961466i | \(-0.588652\pi\) | ||||
−0.274923 | + | 0.961466i | \(0.588652\pi\) | |||||||
\(90\) | −10.8673 | −1.14551 | ||||||||
\(91\) | −18.2170 | −1.90966 | ||||||||
\(92\) | −7.47445 | −0.779266 | ||||||||
\(93\) | 2.81708 | 0.292117 | ||||||||
\(94\) | 10.9174 | 1.12604 | ||||||||
\(95\) | 17.7309 | 1.81915 | ||||||||
\(96\) | −0.626459 | −0.0639377 | ||||||||
\(97\) | 7.86006 | 0.798068 | 0.399034 | − | 0.916936i | \(-0.369346\pi\) | ||||
0.399034 | + | 0.916936i | \(0.369346\pi\) | |||||||
\(98\) | −13.0131 | −1.31452 | ||||||||
\(99\) | 2.60755 | 0.262068 | ||||||||
\(100\) | 12.3691 | 1.23691 | ||||||||
\(101\) | −3.88590 | −0.386661 | −0.193331 | − | 0.981134i | \(-0.561929\pi\) | ||||
−0.193331 | + | 0.981134i | \(0.561929\pi\) | |||||||
\(102\) | −0.278725 | −0.0275979 | ||||||||
\(103\) | 5.67975 | 0.559642 | 0.279821 | − | 0.960052i | \(-0.409725\pi\) | ||||
0.279821 | + | 0.960052i | \(0.409725\pi\) | |||||||
\(104\) | 4.07211 | 0.399303 | ||||||||
\(105\) | −11.6799 | −1.13984 | ||||||||
\(106\) | 9.00211 | 0.874362 | ||||||||
\(107\) | −11.7007 | −1.13115 | −0.565574 | − | 0.824697i | \(-0.691345\pi\) | ||||
−0.565574 | + | 0.824697i | \(0.691345\pi\) | |||||||
\(108\) | −3.51290 | −0.338029 | ||||||||
\(109\) | −1.34647 | −0.128969 | −0.0644844 | − | 0.997919i | \(-0.520540\pi\) | ||||
−0.0644844 | + | 0.997919i | \(0.520540\pi\) | |||||||
\(110\) | −4.16763 | −0.397368 | ||||||||
\(111\) | −1.59635 | −0.151519 | ||||||||
\(112\) | 4.47360 | 0.422715 | ||||||||
\(113\) | 17.7627 | 1.67098 | 0.835489 | − | 0.549507i | \(-0.185185\pi\) | ||||
0.835489 | + | 0.549507i | \(0.185185\pi\) | |||||||
\(114\) | 2.66523 | 0.249622 | ||||||||
\(115\) | 31.1507 | 2.90482 | ||||||||
\(116\) | 4.69923 | 0.436313 | ||||||||
\(117\) | 10.6182 | 0.981655 | ||||||||
\(118\) | −5.40428 | −0.497504 | ||||||||
\(119\) | 1.99040 | 0.182459 | ||||||||
\(120\) | 2.61085 | 0.238337 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −10.0903 | −0.913532 | ||||||||
\(123\) | 3.04744 | 0.274778 | ||||||||
\(124\) | 4.49682 | 0.403826 | ||||||||
\(125\) | −30.7117 | −2.74694 | ||||||||
\(126\) | 11.6651 | 1.03921 | ||||||||
\(127\) | −8.80634 | −0.781437 | −0.390718 | − | 0.920510i | \(-0.627773\pi\) | ||||
−0.390718 | + | 0.920510i | \(0.627773\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.15426 | −0.189672 | ||||||||
\(130\) | −16.9710 | −1.48846 | ||||||||
\(131\) | 12.2052 | 1.06637 | 0.533186 | − | 0.845998i | \(-0.320995\pi\) | ||||
0.533186 | + | 0.845998i | \(0.320995\pi\) | |||||||
\(132\) | −0.626459 | −0.0545263 | ||||||||
\(133\) | −19.0326 | −1.65034 | ||||||||
\(134\) | −11.9951 | −1.03622 | ||||||||
\(135\) | 14.6405 | 1.26005 | ||||||||
\(136\) | −0.444921 | −0.0381516 | ||||||||
\(137\) | 8.96291 | 0.765753 | 0.382877 | − | 0.923799i | \(-0.374933\pi\) | ||||
0.382877 | + | 0.923799i | \(0.374933\pi\) | |||||||
\(138\) | 4.68244 | 0.398596 | ||||||||
\(139\) | −8.13266 | −0.689803 | −0.344902 | − | 0.938639i | \(-0.612088\pi\) | ||||
−0.344902 | + | 0.938639i | \(0.612088\pi\) | |||||||
\(140\) | −18.6443 | −1.57573 | ||||||||
\(141\) | −6.83931 | −0.575974 | ||||||||
\(142\) | −6.77175 | −0.568273 | ||||||||
\(143\) | 4.07211 | 0.340527 | ||||||||
\(144\) | −2.60755 | −0.217296 | ||||||||
\(145\) | −19.5846 | −1.62642 | ||||||||
\(146\) | 7.28899 | 0.603241 | ||||||||
\(147\) | 8.15215 | 0.672378 | ||||||||
\(148\) | −2.54821 | −0.209461 | ||||||||
\(149\) | −8.96440 | −0.734393 | −0.367196 | − | 0.930143i | \(-0.619682\pi\) | ||||
−0.367196 | + | 0.930143i | \(0.619682\pi\) | |||||||
\(150\) | −7.74875 | −0.632683 | ||||||||
\(151\) | 1.89519 | 0.154228 | 0.0771140 | − | 0.997022i | \(-0.475429\pi\) | ||||
0.0771140 | + | 0.997022i | \(0.475429\pi\) | |||||||
\(152\) | 4.25443 | 0.345080 | ||||||||
\(153\) | −1.16015 | −0.0937928 | ||||||||
\(154\) | 4.47360 | 0.360493 | ||||||||
\(155\) | −18.7411 | −1.50532 | ||||||||
\(156\) | −2.55101 | −0.204244 | ||||||||
\(157\) | −2.60712 | −0.208070 | −0.104035 | − | 0.994574i | \(-0.533175\pi\) | ||||
−0.104035 | + | 0.994574i | \(0.533175\pi\) | |||||||
\(158\) | −6.11012 | −0.486095 | ||||||||
\(159\) | −5.63945 | −0.447238 | ||||||||
\(160\) | 4.16763 | 0.329480 | ||||||||
\(161\) | −33.4377 | −2.63526 | ||||||||
\(162\) | −5.62196 | −0.441703 | ||||||||
\(163\) | 1.01058 | 0.0791544 | 0.0395772 | − | 0.999217i | \(-0.487399\pi\) | ||||
0.0395772 | + | 0.999217i | \(0.487399\pi\) | |||||||
\(164\) | 4.86454 | 0.379857 | ||||||||
\(165\) | 2.61085 | 0.203254 | ||||||||
\(166\) | 2.21493 | 0.171912 | ||||||||
\(167\) | 8.19178 | 0.633899 | 0.316950 | − | 0.948442i | \(-0.397341\pi\) | ||||
0.316950 | + | 0.948442i | \(0.397341\pi\) | |||||||
\(168\) | −2.80253 | −0.216220 | ||||||||
\(169\) | 3.58208 | 0.275545 | ||||||||
\(170\) | 1.85426 | 0.142216 | ||||||||
\(171\) | 11.0936 | 0.848352 | ||||||||
\(172\) | −3.43878 | −0.262204 | ||||||||
\(173\) | 4.55859 | 0.346584 | 0.173292 | − | 0.984871i | \(-0.444560\pi\) | ||||
0.173292 | + | 0.984871i | \(0.444560\pi\) | |||||||
\(174\) | −2.94388 | −0.223175 | ||||||||
\(175\) | 55.3344 | 4.18289 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 3.38556 | 0.254474 | ||||||||
\(178\) | 5.18723 | 0.388799 | ||||||||
\(179\) | 1.88182 | 0.140654 | 0.0703270 | − | 0.997524i | \(-0.477596\pi\) | ||||
0.0703270 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(180\) | 10.8673 | 0.810000 | ||||||||
\(181\) | 16.3687 | 1.21668 | 0.608339 | − | 0.793677i | \(-0.291836\pi\) | ||||
0.608339 | + | 0.793677i | \(0.291836\pi\) | |||||||
\(182\) | 18.2170 | 1.35033 | ||||||||
\(183\) | 6.32116 | 0.467274 | ||||||||
\(184\) | 7.47445 | 0.551024 | ||||||||
\(185\) | 10.6200 | 0.780797 | ||||||||
\(186\) | −2.81708 | −0.206558 | ||||||||
\(187\) | −0.444921 | −0.0325358 | ||||||||
\(188\) | −10.9174 | −0.796234 | ||||||||
\(189\) | −15.7153 | −1.14312 | ||||||||
\(190\) | −17.7309 | −1.28633 | ||||||||
\(191\) | 23.1874 | 1.67778 | 0.838889 | − | 0.544302i | \(-0.183206\pi\) | ||||
0.838889 | + | 0.544302i | \(0.183206\pi\) | |||||||
\(192\) | 0.626459 | 0.0452108 | ||||||||
\(193\) | −14.0347 | −1.01024 | −0.505119 | − | 0.863050i | \(-0.668551\pi\) | ||||
−0.505119 | + | 0.863050i | \(0.668551\pi\) | |||||||
\(194\) | −7.86006 | −0.564319 | ||||||||
\(195\) | 10.6317 | 0.761349 | ||||||||
\(196\) | 13.0131 | 0.929504 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | −2.60755 | −0.185310 | ||||||||
\(199\) | −10.8008 | −0.765649 | −0.382825 | − | 0.923821i | \(-0.625049\pi\) | ||||
−0.382825 | + | 0.923821i | \(0.625049\pi\) | |||||||
\(200\) | −12.3691 | −0.874629 | ||||||||
\(201\) | 7.51444 | 0.530028 | ||||||||
\(202\) | 3.88590 | 0.273411 | ||||||||
\(203\) | 21.0225 | 1.47549 | ||||||||
\(204\) | 0.278725 | 0.0195146 | ||||||||
\(205\) | −20.2736 | −1.41597 | ||||||||
\(206\) | −5.67975 | −0.395727 | ||||||||
\(207\) | 19.4900 | 1.35465 | ||||||||
\(208\) | −4.07211 | −0.282350 | ||||||||
\(209\) | 4.25443 | 0.294285 | ||||||||
\(210\) | 11.6799 | 0.805989 | ||||||||
\(211\) | −22.0923 | −1.52090 | −0.760450 | − | 0.649397i | \(-0.775021\pi\) | ||||
−0.760450 | + | 0.649397i | \(0.775021\pi\) | |||||||
\(212\) | −9.00211 | −0.618267 | ||||||||
\(213\) | 4.24223 | 0.290673 | ||||||||
\(214\) | 11.7007 | 0.799843 | ||||||||
\(215\) | 14.3316 | 0.977404 | ||||||||
\(216\) | 3.51290 | 0.239023 | ||||||||
\(217\) | 20.1170 | 1.36563 | ||||||||
\(218\) | 1.34647 | 0.0911947 | ||||||||
\(219\) | −4.56626 | −0.308559 | ||||||||
\(220\) | 4.16763 | 0.280981 | ||||||||
\(221\) | −1.81177 | −0.121873 | ||||||||
\(222\) | 1.59635 | 0.107140 | ||||||||
\(223\) | −18.1199 | −1.21340 | −0.606701 | − | 0.794930i | \(-0.707507\pi\) | ||||
−0.606701 | + | 0.794930i | \(0.707507\pi\) | |||||||
\(224\) | −4.47360 | −0.298905 | ||||||||
\(225\) | −32.2531 | −2.15021 | ||||||||
\(226\) | −17.7627 | −1.18156 | ||||||||
\(227\) | 24.5850 | 1.63176 | 0.815882 | − | 0.578219i | \(-0.196252\pi\) | ||||
0.815882 | + | 0.578219i | \(0.196252\pi\) | |||||||
\(228\) | −2.66523 | −0.176509 | ||||||||
\(229\) | 27.5729 | 1.82207 | 0.911035 | − | 0.412330i | \(-0.135285\pi\) | ||||
0.911035 | + | 0.412330i | \(0.135285\pi\) | |||||||
\(230\) | −31.1507 | −2.05402 | ||||||||
\(231\) | −2.80253 | −0.184393 | ||||||||
\(232\) | −4.69923 | −0.308520 | ||||||||
\(233\) | −14.7600 | −0.966962 | −0.483481 | − | 0.875355i | \(-0.660628\pi\) | ||||
−0.483481 | + | 0.875355i | \(0.660628\pi\) | |||||||
\(234\) | −10.6182 | −0.694135 | ||||||||
\(235\) | 45.4997 | 2.96807 | ||||||||
\(236\) | 5.40428 | 0.351789 | ||||||||
\(237\) | 3.82774 | 0.248639 | ||||||||
\(238\) | −1.99040 | −0.129018 | ||||||||
\(239\) | −1.55374 | −0.100503 | −0.0502514 | − | 0.998737i | \(-0.516002\pi\) | ||||
−0.0502514 | + | 0.998737i | \(0.516002\pi\) | |||||||
\(240\) | −2.61085 | −0.168530 | ||||||||
\(241\) | 27.7317 | 1.78635 | 0.893177 | − | 0.449706i | \(-0.148471\pi\) | ||||
0.893177 | + | 0.449706i | \(0.148471\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 14.0606 | 0.901990 | ||||||||
\(244\) | 10.0903 | 0.645965 | ||||||||
\(245\) | −54.2336 | −3.46485 | ||||||||
\(246\) | −3.04744 | −0.194298 | ||||||||
\(247\) | 17.3245 | 1.10233 | ||||||||
\(248\) | −4.49682 | −0.285548 | ||||||||
\(249\) | −1.38756 | −0.0879333 | ||||||||
\(250\) | 30.7117 | 1.94238 | ||||||||
\(251\) | 30.1022 | 1.90003 | 0.950017 | − | 0.312198i | \(-0.101065\pi\) | ||||
0.950017 | + | 0.312198i | \(0.101065\pi\) | |||||||
\(252\) | −11.6651 | −0.734833 | ||||||||
\(253\) | 7.47445 | 0.469915 | ||||||||
\(254\) | 8.80634 | 0.552559 | ||||||||
\(255\) | −1.16162 | −0.0727436 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.71774 | 0.169528 | 0.0847641 | − | 0.996401i | \(-0.472986\pi\) | ||||
0.0847641 | + | 0.996401i | \(0.472986\pi\) | |||||||
\(258\) | 2.15426 | 0.134118 | ||||||||
\(259\) | −11.3997 | −0.708340 | ||||||||
\(260\) | 16.9710 | 1.05250 | ||||||||
\(261\) | −12.2535 | −0.758471 | ||||||||
\(262\) | −12.2052 | −0.754038 | ||||||||
\(263\) | 22.7444 | 1.40248 | 0.701239 | − | 0.712926i | \(-0.252630\pi\) | ||||
0.701239 | + | 0.712926i | \(0.252630\pi\) | |||||||
\(264\) | 0.626459 | 0.0385559 | ||||||||
\(265\) | 37.5174 | 2.30468 | ||||||||
\(266\) | 19.0326 | 1.16696 | ||||||||
\(267\) | −3.24959 | −0.198872 | ||||||||
\(268\) | 11.9951 | 0.732717 | ||||||||
\(269\) | 1.22328 | 0.0745847 | 0.0372923 | − | 0.999304i | \(-0.488127\pi\) | ||||
0.0372923 | + | 0.999304i | \(0.488127\pi\) | |||||||
\(270\) | −14.6405 | −0.890990 | ||||||||
\(271\) | 7.27048 | 0.441650 | 0.220825 | − | 0.975313i | \(-0.429125\pi\) | ||||
0.220825 | + | 0.975313i | \(0.429125\pi\) | |||||||
\(272\) | 0.444921 | 0.0269773 | ||||||||
\(273\) | −11.4122 | −0.690697 | ||||||||
\(274\) | −8.96291 | −0.541469 | ||||||||
\(275\) | −12.3691 | −0.745886 | ||||||||
\(276\) | −4.68244 | −0.281850 | ||||||||
\(277\) | 14.9228 | 0.896625 | 0.448312 | − | 0.893877i | \(-0.352025\pi\) | ||||
0.448312 | + | 0.893877i | \(0.352025\pi\) | |||||||
\(278\) | 8.13266 | 0.487764 | ||||||||
\(279\) | −11.7257 | −0.701998 | ||||||||
\(280\) | 18.6443 | 1.11421 | ||||||||
\(281\) | 12.5957 | 0.751397 | 0.375699 | − | 0.926742i | \(-0.377403\pi\) | ||||
0.375699 | + | 0.926742i | \(0.377403\pi\) | |||||||
\(282\) | 6.83931 | 0.407275 | ||||||||
\(283\) | −17.7153 | −1.05307 | −0.526533 | − | 0.850154i | \(-0.676508\pi\) | ||||
−0.526533 | + | 0.850154i | \(0.676508\pi\) | |||||||
\(284\) | 6.77175 | 0.401829 | ||||||||
\(285\) | 11.1077 | 0.657962 | ||||||||
\(286\) | −4.07211 | −0.240789 | ||||||||
\(287\) | 21.7620 | 1.28457 | ||||||||
\(288\) | 2.60755 | 0.153651 | ||||||||
\(289\) | −16.8020 | −0.988356 | ||||||||
\(290\) | 19.5846 | 1.15005 | ||||||||
\(291\) | 4.92401 | 0.288650 | ||||||||
\(292\) | −7.28899 | −0.426556 | ||||||||
\(293\) | 6.37338 | 0.372337 | 0.186168 | − | 0.982518i | \(-0.440393\pi\) | ||||
0.186168 | + | 0.982518i | \(0.440393\pi\) | |||||||
\(294\) | −8.15215 | −0.475443 | ||||||||
\(295\) | −22.5230 | −1.31134 | ||||||||
\(296\) | 2.54821 | 0.148112 | ||||||||
\(297\) | 3.51290 | 0.203839 | ||||||||
\(298\) | 8.96440 | 0.519294 | ||||||||
\(299\) | 30.4368 | 1.76021 | ||||||||
\(300\) | 7.74875 | 0.447374 | ||||||||
\(301\) | −15.3837 | −0.886702 | ||||||||
\(302\) | −1.89519 | −0.109056 | ||||||||
\(303\) | −2.43436 | −0.139850 | ||||||||
\(304\) | −4.25443 | −0.244008 | ||||||||
\(305\) | −42.0526 | −2.40792 | ||||||||
\(306\) | 1.16015 | 0.0663215 | ||||||||
\(307\) | 19.2388 | 1.09802 | 0.549008 | − | 0.835817i | \(-0.315006\pi\) | ||||
0.549008 | + | 0.835817i | \(0.315006\pi\) | |||||||
\(308\) | −4.47360 | −0.254907 | ||||||||
\(309\) | 3.55813 | 0.202415 | ||||||||
\(310\) | 18.7411 | 1.06442 | ||||||||
\(311\) | 16.1876 | 0.917915 | 0.458958 | − | 0.888458i | \(-0.348223\pi\) | ||||
0.458958 | + | 0.888458i | \(0.348223\pi\) | |||||||
\(312\) | 2.55101 | 0.144423 | ||||||||
\(313\) | 18.1215 | 1.02429 | 0.512143 | − | 0.858900i | \(-0.328852\pi\) | ||||
0.512143 | + | 0.858900i | \(0.328852\pi\) | |||||||
\(314\) | 2.60712 | 0.147128 | ||||||||
\(315\) | 48.6159 | 2.73919 | ||||||||
\(316\) | 6.11012 | 0.343721 | ||||||||
\(317\) | −14.8092 | −0.831769 | −0.415884 | − | 0.909418i | \(-0.636528\pi\) | ||||
−0.415884 | + | 0.909418i | \(0.636528\pi\) | |||||||
\(318\) | 5.63945 | 0.316245 | ||||||||
\(319\) | −4.69923 | −0.263106 | ||||||||
\(320\) | −4.16763 | −0.232977 | ||||||||
\(321\) | −7.33001 | −0.409121 | ||||||||
\(322\) | 33.4377 | 1.86341 | ||||||||
\(323\) | −1.89289 | −0.105323 | ||||||||
\(324\) | 5.62196 | 0.312331 | ||||||||
\(325\) | −50.3684 | −2.79394 | ||||||||
\(326\) | −1.01058 | −0.0559706 | ||||||||
\(327\) | −0.843511 | −0.0466463 | ||||||||
\(328\) | −4.86454 | −0.268599 | ||||||||
\(329\) | −48.8400 | −2.69264 | ||||||||
\(330\) | −2.61085 | −0.143723 | ||||||||
\(331\) | 18.7996 | 1.03332 | 0.516658 | − | 0.856192i | \(-0.327176\pi\) | ||||
0.516658 | + | 0.856192i | \(0.327176\pi\) | |||||||
\(332\) | −2.21493 | −0.121560 | ||||||||
\(333\) | 6.64458 | 0.364121 | ||||||||
\(334\) | −8.19178 | −0.448234 | ||||||||
\(335\) | −49.9911 | −2.73131 | ||||||||
\(336\) | 2.80253 | 0.152890 | ||||||||
\(337\) | 21.2196 | 1.15590 | 0.577951 | − | 0.816071i | \(-0.303852\pi\) | ||||
0.577951 | + | 0.816071i | \(0.303852\pi\) | |||||||
\(338\) | −3.58208 | −0.194839 | ||||||||
\(339\) | 11.1276 | 0.604370 | ||||||||
\(340\) | −1.85426 | −0.100562 | ||||||||
\(341\) | −4.49682 | −0.243517 | ||||||||
\(342\) | −11.0936 | −0.599875 | ||||||||
\(343\) | 26.9000 | 1.45246 | ||||||||
\(344\) | 3.43878 | 0.185407 | ||||||||
\(345\) | 19.5147 | 1.05063 | ||||||||
\(346\) | −4.55859 | −0.245072 | ||||||||
\(347\) | −13.5398 | −0.726856 | −0.363428 | − | 0.931622i | \(-0.618394\pi\) | ||||
−0.363428 | + | 0.931622i | \(0.618394\pi\) | |||||||
\(348\) | 2.94388 | 0.157808 | ||||||||
\(349\) | −22.8194 | −1.22149 | −0.610746 | − | 0.791827i | \(-0.709130\pi\) | ||||
−0.610746 | + | 0.791827i | \(0.709130\pi\) | |||||||
\(350\) | −55.3344 | −2.95775 | ||||||||
\(351\) | 14.3049 | 0.763540 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 21.6564 | 1.15265 | 0.576326 | − | 0.817220i | \(-0.304486\pi\) | ||||
0.576326 | + | 0.817220i | \(0.304486\pi\) | |||||||
\(354\) | −3.38556 | −0.179941 | ||||||||
\(355\) | −28.2221 | −1.49788 | ||||||||
\(356\) | −5.18723 | −0.274923 | ||||||||
\(357\) | 1.24690 | 0.0659931 | ||||||||
\(358\) | −1.88182 | −0.0994574 | ||||||||
\(359\) | 28.1899 | 1.48781 | 0.743904 | − | 0.668286i | \(-0.232972\pi\) | ||||
0.743904 | + | 0.668286i | \(0.232972\pi\) | |||||||
\(360\) | −10.8673 | −0.572757 | ||||||||
\(361\) | −0.899802 | −0.0473580 | ||||||||
\(362\) | −16.3687 | −0.860322 | ||||||||
\(363\) | 0.626459 | 0.0328806 | ||||||||
\(364\) | −18.2170 | −0.954829 | ||||||||
\(365\) | 30.3778 | 1.59005 | ||||||||
\(366\) | −6.32116 | −0.330412 | ||||||||
\(367\) | 19.0747 | 0.995692 | 0.497846 | − | 0.867265i | \(-0.334124\pi\) | ||||
0.497846 | + | 0.867265i | \(0.334124\pi\) | |||||||
\(368\) | −7.47445 | −0.389633 | ||||||||
\(369\) | −12.6845 | −0.660330 | ||||||||
\(370\) | −10.6200 | −0.552107 | ||||||||
\(371\) | −40.2718 | −2.09081 | ||||||||
\(372\) | 2.81708 | 0.146059 | ||||||||
\(373\) | −5.12196 | −0.265205 | −0.132603 | − | 0.991169i | \(-0.542333\pi\) | ||||
−0.132603 | + | 0.991169i | \(0.542333\pi\) | |||||||
\(374\) | 0.444921 | 0.0230063 | ||||||||
\(375\) | −19.2397 | −0.993532 | ||||||||
\(376\) | 10.9174 | 0.563022 | ||||||||
\(377\) | −19.1358 | −0.985543 | ||||||||
\(378\) | 15.7153 | 0.808308 | ||||||||
\(379\) | −18.5956 | −0.955191 | −0.477595 | − | 0.878580i | \(-0.658491\pi\) | ||||
−0.477595 | + | 0.878580i | \(0.658491\pi\) | |||||||
\(380\) | 17.7309 | 0.909576 | ||||||||
\(381\) | −5.51682 | −0.282635 | ||||||||
\(382\) | −23.1874 | −1.18637 | ||||||||
\(383\) | −24.9294 | −1.27383 | −0.636917 | − | 0.770932i | \(-0.719791\pi\) | ||||
−0.636917 | + | 0.770932i | \(0.719791\pi\) | |||||||
\(384\) | −0.626459 | −0.0319689 | ||||||||
\(385\) | 18.6443 | 0.950200 | ||||||||
\(386\) | 14.0347 | 0.714345 | ||||||||
\(387\) | 8.96678 | 0.455807 | ||||||||
\(388\) | 7.86006 | 0.399034 | ||||||||
\(389\) | −32.5822 | −1.65198 | −0.825991 | − | 0.563684i | \(-0.809384\pi\) | ||||
−0.825991 | + | 0.563684i | \(0.809384\pi\) | |||||||
\(390\) | −10.6317 | −0.538355 | ||||||||
\(391\) | −3.32554 | −0.168180 | ||||||||
\(392\) | −13.0131 | −0.657258 | ||||||||
\(393\) | 7.64605 | 0.385692 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | −25.4647 | −1.28127 | ||||||||
\(396\) | 2.60755 | 0.131034 | ||||||||
\(397\) | 18.4904 | 0.928007 | 0.464003 | − | 0.885833i | \(-0.346413\pi\) | ||||
0.464003 | + | 0.885833i | \(0.346413\pi\) | |||||||
\(398\) | 10.8008 | 0.541396 | ||||||||
\(399\) | −11.9232 | −0.596904 | ||||||||
\(400\) | 12.3691 | 0.618456 | ||||||||
\(401\) | 9.77410 | 0.488095 | 0.244048 | − | 0.969763i | \(-0.421525\pi\) | ||||
0.244048 | + | 0.969763i | \(0.421525\pi\) | |||||||
\(402\) | −7.51444 | −0.374786 | ||||||||
\(403\) | −18.3116 | −0.912163 | ||||||||
\(404\) | −3.88590 | −0.193331 | ||||||||
\(405\) | −23.4302 | −1.16426 | ||||||||
\(406\) | −21.0225 | −1.04333 | ||||||||
\(407\) | 2.54821 | 0.126310 | ||||||||
\(408\) | −0.278725 | −0.0137989 | ||||||||
\(409\) | 0.0983273 | 0.00486197 | 0.00243099 | − | 0.999997i | \(-0.499226\pi\) | ||||
0.00243099 | + | 0.999997i | \(0.499226\pi\) | |||||||
\(410\) | 20.2736 | 1.00124 | ||||||||
\(411\) | 5.61490 | 0.276963 | ||||||||
\(412\) | 5.67975 | 0.279821 | ||||||||
\(413\) | 24.1766 | 1.18965 | ||||||||
\(414\) | −19.4900 | −0.957881 | ||||||||
\(415\) | 9.23100 | 0.453132 | ||||||||
\(416\) | 4.07211 | 0.199652 | ||||||||
\(417\) | −5.09478 | −0.249492 | ||||||||
\(418\) | −4.25443 | −0.208091 | ||||||||
\(419\) | −39.0863 | −1.90949 | −0.954746 | − | 0.297424i | \(-0.903873\pi\) | ||||
−0.954746 | + | 0.297424i | \(0.903873\pi\) | |||||||
\(420\) | −11.6799 | −0.569920 | ||||||||
\(421\) | −6.01618 | −0.293211 | −0.146605 | − | 0.989195i | \(-0.546835\pi\) | ||||
−0.146605 | + | 0.989195i | \(0.546835\pi\) | |||||||
\(422\) | 22.0923 | 1.07544 | ||||||||
\(423\) | 28.4677 | 1.38415 | ||||||||
\(424\) | 9.00211 | 0.437181 | ||||||||
\(425\) | 5.50328 | 0.266948 | ||||||||
\(426\) | −4.24223 | −0.205537 | ||||||||
\(427\) | 45.1399 | 2.18447 | ||||||||
\(428\) | −11.7007 | −0.565574 | ||||||||
\(429\) | 2.55101 | 0.123164 | ||||||||
\(430\) | −14.3316 | −0.691129 | ||||||||
\(431\) | 8.12680 | 0.391454 | 0.195727 | − | 0.980658i | \(-0.437293\pi\) | ||||
0.195727 | + | 0.980658i | \(0.437293\pi\) | |||||||
\(432\) | −3.51290 | −0.169015 | ||||||||
\(433\) | 5.74742 | 0.276203 | 0.138102 | − | 0.990418i | \(-0.455900\pi\) | ||||
0.138102 | + | 0.990418i | \(0.455900\pi\) | |||||||
\(434\) | −20.1170 | −0.965645 | ||||||||
\(435\) | −12.2690 | −0.588253 | ||||||||
\(436\) | −1.34647 | −0.0644844 | ||||||||
\(437\) | 31.7996 | 1.52118 | ||||||||
\(438\) | 4.56626 | 0.218184 | ||||||||
\(439\) | 26.9288 | 1.28524 | 0.642621 | − | 0.766185i | \(-0.277847\pi\) | ||||
0.642621 | + | 0.766185i | \(0.277847\pi\) | |||||||
\(440\) | −4.16763 | −0.198684 | ||||||||
\(441\) | −33.9322 | −1.61582 | ||||||||
\(442\) | 1.81177 | 0.0861769 | ||||||||
\(443\) | −37.2622 | −1.77038 | −0.885191 | − | 0.465229i | \(-0.845972\pi\) | ||||
−0.885191 | + | 0.465229i | \(0.845972\pi\) | |||||||
\(444\) | −1.59635 | −0.0757594 | ||||||||
\(445\) | 21.6184 | 1.02481 | ||||||||
\(446\) | 18.1199 | 0.858004 | ||||||||
\(447\) | −5.61583 | −0.265620 | ||||||||
\(448\) | 4.47360 | 0.211357 | ||||||||
\(449\) | 4.55500 | 0.214964 | 0.107482 | − | 0.994207i | \(-0.465721\pi\) | ||||
0.107482 | + | 0.994207i | \(0.465721\pi\) | |||||||
\(450\) | 32.2531 | 1.52042 | ||||||||
\(451\) | −4.86454 | −0.229062 | ||||||||
\(452\) | 17.7627 | 0.835489 | ||||||||
\(453\) | 1.18726 | 0.0557822 | ||||||||
\(454\) | −24.5850 | −1.15383 | ||||||||
\(455\) | 75.9215 | 3.55926 | ||||||||
\(456\) | 2.66523 | 0.124811 | ||||||||
\(457\) | 7.01789 | 0.328283 | 0.164142 | − | 0.986437i | \(-0.447515\pi\) | ||||
0.164142 | + | 0.986437i | \(0.447515\pi\) | |||||||
\(458\) | −27.5729 | −1.28840 | ||||||||
\(459\) | −1.56296 | −0.0729529 | ||||||||
\(460\) | 31.1507 | 1.45241 | ||||||||
\(461\) | −18.7876 | −0.875027 | −0.437513 | − | 0.899212i | \(-0.644141\pi\) | ||||
−0.437513 | + | 0.899212i | \(0.644141\pi\) | |||||||
\(462\) | 2.80253 | 0.130385 | ||||||||
\(463\) | 7.49611 | 0.348374 | 0.174187 | − | 0.984713i | \(-0.444270\pi\) | ||||
0.174187 | + | 0.984713i | \(0.444270\pi\) | |||||||
\(464\) | 4.69923 | 0.218156 | ||||||||
\(465\) | −11.7405 | −0.544454 | ||||||||
\(466\) | 14.7600 | 0.683745 | ||||||||
\(467\) | 26.8727 | 1.24352 | 0.621760 | − | 0.783208i | \(-0.286418\pi\) | ||||
0.621760 | + | 0.783208i | \(0.286418\pi\) | |||||||
\(468\) | 10.6182 | 0.490828 | ||||||||
\(469\) | 53.6612 | 2.47784 | ||||||||
\(470\) | −45.4997 | −2.09874 | ||||||||
\(471\) | −1.63325 | −0.0752563 | ||||||||
\(472\) | −5.40428 | −0.248752 | ||||||||
\(473\) | 3.43878 | 0.158115 | ||||||||
\(474\) | −3.82774 | −0.175814 | ||||||||
\(475\) | −52.6236 | −2.41454 | ||||||||
\(476\) | 1.99040 | 0.0912296 | ||||||||
\(477\) | 23.4734 | 1.07477 | ||||||||
\(478\) | 1.55374 | 0.0710662 | ||||||||
\(479\) | −0.205380 | −0.00938406 | −0.00469203 | − | 0.999989i | \(-0.501494\pi\) | ||||
−0.00469203 | + | 0.999989i | \(0.501494\pi\) | |||||||
\(480\) | 2.61085 | 0.119168 | ||||||||
\(481\) | 10.3766 | 0.473132 | ||||||||
\(482\) | −27.7317 | −1.26314 | ||||||||
\(483\) | −20.9474 | −0.953138 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −32.7578 | −1.48745 | ||||||||
\(486\) | −14.0606 | −0.637803 | ||||||||
\(487\) | 22.5602 | 1.02230 | 0.511150 | − | 0.859491i | \(-0.329219\pi\) | ||||
0.511150 | + | 0.859491i | \(0.329219\pi\) | |||||||
\(488\) | −10.0903 | −0.456766 | ||||||||
\(489\) | 0.633085 | 0.0286291 | ||||||||
\(490\) | 54.2336 | 2.45002 | ||||||||
\(491\) | 5.88987 | 0.265806 | 0.132903 | − | 0.991129i | \(-0.457570\pi\) | ||||
0.132903 | + | 0.991129i | \(0.457570\pi\) | |||||||
\(492\) | 3.04744 | 0.137389 | ||||||||
\(493\) | 2.09079 | 0.0941642 | ||||||||
\(494\) | −17.3245 | −0.779467 | ||||||||
\(495\) | −10.8673 | −0.488448 | ||||||||
\(496\) | 4.49682 | 0.201913 | ||||||||
\(497\) | 30.2941 | 1.35887 | ||||||||
\(498\) | 1.38756 | 0.0621782 | ||||||||
\(499\) | 4.04749 | 0.181190 | 0.0905952 | − | 0.995888i | \(-0.471123\pi\) | ||||
0.0905952 | + | 0.995888i | \(0.471123\pi\) | |||||||
\(500\) | −30.7117 | −1.37347 | ||||||||
\(501\) | 5.13182 | 0.229273 | ||||||||
\(502\) | −30.1022 | −1.34353 | ||||||||
\(503\) | 6.35173 | 0.283209 | 0.141605 | − | 0.989923i | \(-0.454774\pi\) | ||||
0.141605 | + | 0.989923i | \(0.454774\pi\) | |||||||
\(504\) | 11.6651 | 0.519606 | ||||||||
\(505\) | 16.1950 | 0.720667 | ||||||||
\(506\) | −7.47445 | −0.332280 | ||||||||
\(507\) | 2.24403 | 0.0996607 | ||||||||
\(508\) | −8.80634 | −0.390718 | ||||||||
\(509\) | 21.3356 | 0.945684 | 0.472842 | − | 0.881147i | \(-0.343228\pi\) | ||||
0.472842 | + | 0.881147i | \(0.343228\pi\) | |||||||
\(510\) | 1.16162 | 0.0514375 | ||||||||
\(511\) | −32.6080 | −1.44249 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.9454 | 0.659856 | ||||||||
\(514\) | −2.71774 | −0.119874 | ||||||||
\(515\) | −23.6711 | −1.04307 | ||||||||
\(516\) | −2.15426 | −0.0948358 | ||||||||
\(517\) | 10.9174 | 0.480147 | ||||||||
\(518\) | 11.3997 | 0.500872 | ||||||||
\(519\) | 2.85577 | 0.125355 | ||||||||
\(520\) | −16.9710 | −0.744229 | ||||||||
\(521\) | −14.7531 | −0.646347 | −0.323173 | − | 0.946340i | \(-0.604750\pi\) | ||||
−0.323173 | + | 0.946340i | \(0.604750\pi\) | |||||||
\(522\) | 12.2535 | 0.536320 | ||||||||
\(523\) | −30.1474 | −1.31826 | −0.659128 | − | 0.752031i | \(-0.729074\pi\) | ||||
−0.659128 | + | 0.752031i | \(0.729074\pi\) | |||||||
\(524\) | 12.2052 | 0.533186 | ||||||||
\(525\) | 34.6648 | 1.51289 | ||||||||
\(526\) | −22.7444 | −0.991702 | ||||||||
\(527\) | 2.00073 | 0.0871531 | ||||||||
\(528\) | −0.626459 | −0.0272631 | ||||||||
\(529\) | 32.8675 | 1.42902 | ||||||||
\(530\) | −37.5174 | −1.62965 | ||||||||
\(531\) | −14.0919 | −0.611537 | ||||||||
\(532\) | −19.0326 | −0.825168 | ||||||||
\(533\) | −19.8090 | −0.858021 | ||||||||
\(534\) | 3.24959 | 0.140623 | ||||||||
\(535\) | 48.7641 | 2.10826 | ||||||||
\(536\) | −11.9951 | −0.518109 | ||||||||
\(537\) | 1.17889 | 0.0508727 | ||||||||
\(538\) | −1.22328 | −0.0527393 | ||||||||
\(539\) | −13.0131 | −0.560512 | ||||||||
\(540\) | 14.6405 | 0.630025 | ||||||||
\(541\) | 44.2864 | 1.90402 | 0.952010 | − | 0.306066i | \(-0.0990128\pi\) | ||||
0.952010 | + | 0.306066i | \(0.0990128\pi\) | |||||||
\(542\) | −7.27048 | −0.312294 | ||||||||
\(543\) | 10.2544 | 0.440056 | ||||||||
\(544\) | −0.444921 | −0.0190758 | ||||||||
\(545\) | 5.61160 | 0.240375 | ||||||||
\(546\) | 11.4122 | 0.488397 | ||||||||
\(547\) | 12.2836 | 0.525211 | 0.262605 | − | 0.964903i | \(-0.415418\pi\) | ||||
0.262605 | + | 0.964903i | \(0.415418\pi\) | |||||||
\(548\) | 8.96291 | 0.382877 | ||||||||
\(549\) | −26.3109 | −1.12292 | ||||||||
\(550\) | 12.3691 | 0.527421 | ||||||||
\(551\) | −19.9926 | −0.851712 | ||||||||
\(552\) | 4.68244 | 0.199298 | ||||||||
\(553\) | 27.3342 | 1.16237 | ||||||||
\(554\) | −14.9228 | −0.634010 | ||||||||
\(555\) | 6.65299 | 0.282404 | ||||||||
\(556\) | −8.13266 | −0.344902 | ||||||||
\(557\) | −22.2440 | −0.942507 | −0.471253 | − | 0.881998i | \(-0.656198\pi\) | ||||
−0.471253 | + | 0.881998i | \(0.656198\pi\) | |||||||
\(558\) | 11.7257 | 0.496388 | ||||||||
\(559\) | 14.0031 | 0.592267 | ||||||||
\(560\) | −18.6443 | −0.787865 | ||||||||
\(561\) | −0.278725 | −0.0117678 | ||||||||
\(562\) | −12.5957 | −0.531318 | ||||||||
\(563\) | 36.1852 | 1.52503 | 0.762513 | − | 0.646973i | \(-0.223965\pi\) | ||||
0.762513 | + | 0.646973i | \(0.223965\pi\) | |||||||
\(564\) | −6.83931 | −0.287987 | ||||||||
\(565\) | −74.0285 | −3.11440 | ||||||||
\(566\) | 17.7153 | 0.744631 | ||||||||
\(567\) | 25.1504 | 1.05622 | ||||||||
\(568\) | −6.77175 | −0.284136 | ||||||||
\(569\) | 9.53062 | 0.399544 | 0.199772 | − | 0.979842i | \(-0.435980\pi\) | ||||
0.199772 | + | 0.979842i | \(0.435980\pi\) | |||||||
\(570\) | −11.1077 | −0.465250 | ||||||||
\(571\) | 33.5689 | 1.40481 | 0.702407 | − | 0.711775i | \(-0.252109\pi\) | ||||
0.702407 | + | 0.711775i | \(0.252109\pi\) | |||||||
\(572\) | 4.07211 | 0.170263 | ||||||||
\(573\) | 14.5259 | 0.606830 | ||||||||
\(574\) | −21.7620 | −0.908328 | ||||||||
\(575\) | −92.4524 | −3.85553 | ||||||||
\(576\) | −2.60755 | −0.108648 | ||||||||
\(577\) | −14.5063 | −0.603907 | −0.301953 | − | 0.953323i | \(-0.597639\pi\) | ||||
−0.301953 | + | 0.953323i | \(0.597639\pi\) | |||||||
\(578\) | 16.8020 | 0.698873 | ||||||||
\(579\) | −8.79215 | −0.365389 | ||||||||
\(580\) | −19.5846 | −0.813208 | ||||||||
\(581\) | −9.90870 | −0.411082 | ||||||||
\(582\) | −4.92401 | −0.204107 | ||||||||
\(583\) | 9.00211 | 0.372829 | ||||||||
\(584\) | 7.28899 | 0.301621 | ||||||||
\(585\) | −44.2528 | −1.82963 | ||||||||
\(586\) | −6.37338 | −0.263282 | ||||||||
\(587\) | −48.2441 | −1.99125 | −0.995624 | − | 0.0934507i | \(-0.970210\pi\) | ||||
−0.995624 | + | 0.0934507i | \(0.970210\pi\) | |||||||
\(588\) | 8.15215 | 0.336189 | ||||||||
\(589\) | −19.1314 | −0.788297 | ||||||||
\(590\) | 22.5230 | 0.927258 | ||||||||
\(591\) | 0.626459 | 0.0257691 | ||||||||
\(592\) | −2.54821 | −0.104731 | ||||||||
\(593\) | −4.42315 | −0.181637 | −0.0908184 | − | 0.995867i | \(-0.528948\pi\) | ||||
−0.0908184 | + | 0.995867i | \(0.528948\pi\) | |||||||
\(594\) | −3.51290 | −0.144136 | ||||||||
\(595\) | −8.29523 | −0.340071 | ||||||||
\(596\) | −8.96440 | −0.367196 | ||||||||
\(597\) | −6.76627 | −0.276925 | ||||||||
\(598\) | −30.4368 | −1.24465 | ||||||||
\(599\) | −38.2203 | −1.56164 | −0.780820 | − | 0.624756i | \(-0.785198\pi\) | ||||
−0.780820 | + | 0.624756i | \(0.785198\pi\) | |||||||
\(600\) | −7.74875 | −0.316341 | ||||||||
\(601\) | −18.5598 | −0.757071 | −0.378535 | − | 0.925587i | \(-0.623572\pi\) | ||||
−0.378535 | + | 0.925587i | \(0.623572\pi\) | |||||||
\(602\) | 15.3837 | 0.626993 | ||||||||
\(603\) | −31.2778 | −1.27373 | ||||||||
\(604\) | 1.89519 | 0.0771140 | ||||||||
\(605\) | −4.16763 | −0.169438 | ||||||||
\(606\) | 2.43436 | 0.0988890 | ||||||||
\(607\) | −4.02069 | −0.163195 | −0.0815974 | − | 0.996665i | \(-0.526002\pi\) | ||||
−0.0815974 | + | 0.996665i | \(0.526002\pi\) | |||||||
\(608\) | 4.25443 | 0.172540 | ||||||||
\(609\) | 13.1697 | 0.533664 | ||||||||
\(610\) | 42.0526 | 1.70266 | ||||||||
\(611\) | 44.4569 | 1.79853 | ||||||||
\(612\) | −1.16015 | −0.0468964 | ||||||||
\(613\) | −3.69453 | −0.149221 | −0.0746103 | − | 0.997213i | \(-0.523771\pi\) | ||||
−0.0746103 | + | 0.997213i | \(0.523771\pi\) | |||||||
\(614\) | −19.2388 | −0.776415 | ||||||||
\(615\) | −12.7006 | −0.512137 | ||||||||
\(616\) | 4.47360 | 0.180246 | ||||||||
\(617\) | −25.0018 | −1.00653 | −0.503267 | − | 0.864131i | \(-0.667869\pi\) | ||||
−0.503267 | + | 0.864131i | \(0.667869\pi\) | |||||||
\(618\) | −3.55813 | −0.143129 | ||||||||
\(619\) | −15.5984 | −0.626952 | −0.313476 | − | 0.949596i | \(-0.601494\pi\) | ||||
−0.313476 | + | 0.949596i | \(0.601494\pi\) | |||||||
\(620\) | −18.7411 | −0.752660 | ||||||||
\(621\) | 26.2570 | 1.05366 | ||||||||
\(622\) | −16.1876 | −0.649064 | ||||||||
\(623\) | −23.2056 | −0.929711 | ||||||||
\(624\) | −2.55101 | −0.102122 | ||||||||
\(625\) | 66.1495 | 2.64598 | ||||||||
\(626\) | −18.1215 | −0.724280 | ||||||||
\(627\) | 2.66523 | 0.106439 | ||||||||
\(628\) | −2.60712 | −0.104035 | ||||||||
\(629\) | −1.13375 | −0.0452056 | ||||||||
\(630\) | −48.6159 | −1.93690 | ||||||||
\(631\) | −13.7411 | −0.547025 | −0.273512 | − | 0.961868i | \(-0.588185\pi\) | ||||
−0.273512 | + | 0.961868i | \(0.588185\pi\) | |||||||
\(632\) | −6.11012 | −0.243048 | ||||||||
\(633\) | −13.8400 | −0.550089 | ||||||||
\(634\) | 14.8092 | 0.588149 | ||||||||
\(635\) | 36.7016 | 1.45646 | ||||||||
\(636\) | −5.63945 | −0.223619 | ||||||||
\(637\) | −52.9906 | −2.09956 | ||||||||
\(638\) | 4.69923 | 0.186044 | ||||||||
\(639\) | −17.6577 | −0.698527 | ||||||||
\(640\) | 4.16763 | 0.164740 | ||||||||
\(641\) | 36.2459 | 1.43163 | 0.715813 | − | 0.698292i | \(-0.246056\pi\) | ||||
0.715813 | + | 0.698292i | \(0.246056\pi\) | |||||||
\(642\) | 7.33001 | 0.289292 | ||||||||
\(643\) | 40.5624 | 1.59962 | 0.799812 | − | 0.600250i | \(-0.204932\pi\) | ||||
0.799812 | + | 0.600250i | \(0.204932\pi\) | |||||||
\(644\) | −33.4377 | −1.31763 | ||||||||
\(645\) | 8.97814 | 0.353514 | ||||||||
\(646\) | 1.89289 | 0.0744746 | ||||||||
\(647\) | −10.7150 | −0.421249 | −0.210624 | − | 0.977567i | \(-0.567550\pi\) | ||||
−0.210624 | + | 0.977567i | \(0.567550\pi\) | |||||||
\(648\) | −5.62196 | −0.220851 | ||||||||
\(649\) | −5.40428 | −0.212137 | ||||||||
\(650\) | 50.3684 | 1.97561 | ||||||||
\(651\) | 12.6025 | 0.493929 | ||||||||
\(652\) | 1.01058 | 0.0395772 | ||||||||
\(653\) | 34.9546 | 1.36788 | 0.683939 | − | 0.729539i | \(-0.260265\pi\) | ||||
0.683939 | + | 0.729539i | \(0.260265\pi\) | |||||||
\(654\) | 0.843511 | 0.0329839 | ||||||||
\(655\) | −50.8666 | −1.98752 | ||||||||
\(656\) | 4.86454 | 0.189929 | ||||||||
\(657\) | 19.0064 | 0.741510 | ||||||||
\(658\) | 48.8400 | 1.90398 | ||||||||
\(659\) | 27.0845 | 1.05506 | 0.527532 | − | 0.849535i | \(-0.323118\pi\) | ||||
0.527532 | + | 0.849535i | \(0.323118\pi\) | |||||||
\(660\) | 2.61085 | 0.101627 | ||||||||
\(661\) | 42.9914 | 1.67217 | 0.836086 | − | 0.548598i | \(-0.184838\pi\) | ||||
0.836086 | + | 0.548598i | \(0.184838\pi\) | |||||||
\(662\) | −18.7996 | −0.730665 | ||||||||
\(663\) | −1.13500 | −0.0440797 | ||||||||
\(664\) | 2.21493 | 0.0859560 | ||||||||
\(665\) | 79.3208 | 3.07593 | ||||||||
\(666\) | −6.64458 | −0.257472 | ||||||||
\(667\) | −35.1242 | −1.36001 | ||||||||
\(668\) | 8.19178 | 0.316950 | ||||||||
\(669\) | −11.3514 | −0.438871 | ||||||||
\(670\) | 49.9911 | 1.93132 | ||||||||
\(671\) | −10.0903 | −0.389531 | ||||||||
\(672\) | −2.80253 | −0.108110 | ||||||||
\(673\) | −7.33126 | −0.282599 | −0.141300 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141300 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(674\) | −21.2196 | −0.817347 | ||||||||
\(675\) | −43.4515 | −1.67245 | ||||||||
\(676\) | 3.58208 | 0.137772 | ||||||||
\(677\) | 45.1797 | 1.73640 | 0.868198 | − | 0.496218i | \(-0.165278\pi\) | ||||
0.868198 | + | 0.496218i | \(0.165278\pi\) | |||||||
\(678\) | −11.1276 | −0.427354 | ||||||||
\(679\) | 35.1627 | 1.34942 | ||||||||
\(680\) | 1.85426 | 0.0711078 | ||||||||
\(681\) | 15.4015 | 0.590187 | ||||||||
\(682\) | 4.49682 | 0.172192 | ||||||||
\(683\) | 29.6601 | 1.13491 | 0.567456 | − | 0.823404i | \(-0.307928\pi\) | ||||
0.567456 | + | 0.823404i | \(0.307928\pi\) | |||||||
\(684\) | 11.0936 | 0.424176 | ||||||||
\(685\) | −37.3541 | −1.42723 | ||||||||
\(686\) | −26.9000 | −1.02705 | ||||||||
\(687\) | 17.2733 | 0.659018 | ||||||||
\(688\) | −3.43878 | −0.131102 | ||||||||
\(689\) | 36.6576 | 1.39654 | ||||||||
\(690\) | −19.5147 | −0.742911 | ||||||||
\(691\) | 8.83205 | 0.335987 | 0.167993 | − | 0.985788i | \(-0.446271\pi\) | ||||
0.167993 | + | 0.985788i | \(0.446271\pi\) | |||||||
\(692\) | 4.55859 | 0.173292 | ||||||||
\(693\) | 11.6651 | 0.443121 | ||||||||
\(694\) | 13.5398 | 0.513965 | ||||||||
\(695\) | 33.8939 | 1.28567 | ||||||||
\(696\) | −2.94388 | −0.111587 | ||||||||
\(697\) | 2.16434 | 0.0819801 | ||||||||
\(698\) | 22.8194 | 0.863725 | ||||||||
\(699\) | −9.24656 | −0.349737 | ||||||||
\(700\) | 55.3344 | 2.09144 | ||||||||
\(701\) | −45.5992 | −1.72226 | −0.861128 | − | 0.508388i | \(-0.830242\pi\) | ||||
−0.861128 | + | 0.508388i | \(0.830242\pi\) | |||||||
\(702\) | −14.3049 | −0.539904 | ||||||||
\(703\) | 10.8412 | 0.408883 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 28.5037 | 1.07351 | ||||||||
\(706\) | −21.6564 | −0.815048 | ||||||||
\(707\) | −17.3839 | −0.653790 | ||||||||
\(708\) | 3.38556 | 0.127237 | ||||||||
\(709\) | −45.1937 | −1.69729 | −0.848643 | − | 0.528966i | \(-0.822580\pi\) | ||||
−0.848643 | + | 0.528966i | \(0.822580\pi\) | |||||||
\(710\) | 28.2221 | 1.05916 | ||||||||
\(711\) | −15.9324 | −0.597513 | ||||||||
\(712\) | 5.18723 | 0.194400 | ||||||||
\(713\) | −33.6113 | −1.25875 | ||||||||
\(714\) | −1.24690 | −0.0466641 | ||||||||
\(715\) | −16.9710 | −0.634681 | ||||||||
\(716\) | 1.88182 | 0.0703270 | ||||||||
\(717\) | −0.973353 | −0.0363505 | ||||||||
\(718\) | −28.1899 | −1.05204 | ||||||||
\(719\) | −15.6177 | −0.582441 | −0.291220 | − | 0.956656i | \(-0.594061\pi\) | ||||
−0.291220 | + | 0.956656i | \(0.594061\pi\) | |||||||
\(720\) | 10.8673 | 0.405000 | ||||||||
\(721\) | 25.4089 | 0.946277 | ||||||||
\(722\) | 0.899802 | 0.0334872 | ||||||||
\(723\) | 17.3728 | 0.646100 | ||||||||
\(724\) | 16.3687 | 0.608339 | ||||||||
\(725\) | 58.1253 | 2.15872 | ||||||||
\(726\) | −0.626459 | −0.0232501 | ||||||||
\(727\) | −17.1544 | −0.636220 | −0.318110 | − | 0.948054i | \(-0.603048\pi\) | ||||
−0.318110 | + | 0.948054i | \(0.603048\pi\) | |||||||
\(728\) | 18.2170 | 0.675166 | ||||||||
\(729\) | −8.05745 | −0.298424 | ||||||||
\(730\) | −30.3778 | −1.12433 | ||||||||
\(731\) | −1.52998 | −0.0565885 | ||||||||
\(732\) | 6.32116 | 0.233637 | ||||||||
\(733\) | 7.68895 | 0.283998 | 0.141999 | − | 0.989867i | \(-0.454647\pi\) | ||||
0.141999 | + | 0.989867i | \(0.454647\pi\) | |||||||
\(734\) | −19.0747 | −0.704061 | ||||||||
\(735\) | −33.9751 | −1.25319 | ||||||||
\(736\) | 7.47445 | 0.275512 | ||||||||
\(737\) | −11.9951 | −0.441845 | ||||||||
\(738\) | 12.6845 | 0.466924 | ||||||||
\(739\) | 22.5548 | 0.829694 | 0.414847 | − | 0.909891i | \(-0.363835\pi\) | ||||
0.414847 | + | 0.909891i | \(0.363835\pi\) | |||||||
\(740\) | 10.6200 | 0.390398 | ||||||||
\(741\) | 10.8531 | 0.398699 | ||||||||
\(742\) | 40.2718 | 1.47842 | ||||||||
\(743\) | −7.22267 | −0.264974 | −0.132487 | − | 0.991185i | \(-0.542296\pi\) | ||||
−0.132487 | + | 0.991185i | \(0.542296\pi\) | |||||||
\(744\) | −2.81708 | −0.103279 | ||||||||
\(745\) | 37.3603 | 1.36878 | ||||||||
\(746\) | 5.12196 | 0.187528 | ||||||||
\(747\) | 5.77554 | 0.211316 | ||||||||
\(748\) | −0.444921 | −0.0162679 | ||||||||
\(749\) | −52.3441 | −1.91261 | ||||||||
\(750\) | 19.2397 | 0.702533 | ||||||||
\(751\) | −22.0384 | −0.804194 | −0.402097 | − | 0.915597i | \(-0.631719\pi\) | ||||
−0.402097 | + | 0.915597i | \(0.631719\pi\) | |||||||
\(752\) | −10.9174 | −0.398117 | ||||||||
\(753\) | 18.8578 | 0.687217 | ||||||||
\(754\) | 19.1358 | 0.696884 | ||||||||
\(755\) | −7.89843 | −0.287453 | ||||||||
\(756\) | −15.7153 | −0.571560 | ||||||||
\(757\) | −22.0851 | −0.802697 | −0.401349 | − | 0.915925i | \(-0.631458\pi\) | ||||
−0.401349 | + | 0.915925i | \(0.631458\pi\) | |||||||
\(758\) | 18.5956 | 0.675422 | ||||||||
\(759\) | 4.68244 | 0.169962 | ||||||||
\(760\) | −17.7309 | −0.643167 | ||||||||
\(761\) | 4.63588 | 0.168051 | 0.0840253 | − | 0.996464i | \(-0.473222\pi\) | ||||
0.0840253 | + | 0.996464i | \(0.473222\pi\) | |||||||
\(762\) | 5.51682 | 0.199853 | ||||||||
\(763\) | −6.02358 | −0.218068 | ||||||||
\(764\) | 23.1874 | 0.838889 | ||||||||
\(765\) | 4.83508 | 0.174813 | ||||||||
\(766\) | 24.9294 | 0.900736 | ||||||||
\(767\) | −22.0068 | −0.794620 | ||||||||
\(768\) | 0.626459 | 0.0226054 | ||||||||
\(769\) | −44.9088 | −1.61945 | −0.809727 | − | 0.586807i | \(-0.800385\pi\) | ||||
−0.809727 | + | 0.586807i | \(0.800385\pi\) | |||||||
\(770\) | −18.6443 | −0.671893 | ||||||||
\(771\) | 1.70256 | 0.0613160 | ||||||||
\(772\) | −14.0347 | −0.505119 | ||||||||
\(773\) | −9.84211 | −0.353996 | −0.176998 | − | 0.984211i | \(-0.556639\pi\) | ||||
−0.176998 | + | 0.984211i | \(0.556639\pi\) | |||||||
\(774\) | −8.96678 | −0.322304 | ||||||||
\(775\) | 55.6217 | 1.99799 | ||||||||
\(776\) | −7.86006 | −0.282160 | ||||||||
\(777\) | −7.14142 | −0.256197 | ||||||||
\(778\) | 32.5822 | 1.16813 | ||||||||
\(779\) | −20.6959 | −0.741507 | ||||||||
\(780\) | 10.6317 | 0.380675 | ||||||||
\(781\) | −6.77175 | −0.242312 | ||||||||
\(782\) | 3.32554 | 0.118921 | ||||||||
\(783\) | −16.5079 | −0.589945 | ||||||||
\(784\) | 13.0131 | 0.464752 | ||||||||
\(785\) | 10.8655 | 0.387806 | ||||||||
\(786\) | −7.64605 | −0.272725 | ||||||||
\(787\) | −34.1292 | −1.21658 | −0.608288 | − | 0.793716i | \(-0.708143\pi\) | ||||
−0.608288 | + | 0.793716i | \(0.708143\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 14.2484 | 0.507258 | ||||||||
\(790\) | 25.4647 | 0.905994 | ||||||||
\(791\) | 79.4633 | 2.82539 | ||||||||
\(792\) | −2.60755 | −0.0926552 | ||||||||
\(793\) | −41.0888 | −1.45911 | ||||||||
\(794\) | −18.4904 | −0.656200 | ||||||||
\(795\) | 23.5031 | 0.833571 | ||||||||
\(796\) | −10.8008 | −0.382825 | ||||||||
\(797\) | −13.3246 | −0.471980 | −0.235990 | − | 0.971755i | \(-0.575833\pi\) | ||||
−0.235990 | + | 0.971755i | \(0.575833\pi\) | |||||||
\(798\) | 11.9232 | 0.422075 | ||||||||
\(799\) | −4.85738 | −0.171842 | ||||||||
\(800\) | −12.3691 | −0.437314 | ||||||||
\(801\) | 13.5260 | 0.477916 | ||||||||
\(802\) | −9.77410 | −0.345135 | ||||||||
\(803\) | 7.28899 | 0.257223 | ||||||||
\(804\) | 7.51444 | 0.265014 | ||||||||
\(805\) | 139.356 | 4.91165 | ||||||||
\(806\) | 18.3116 | 0.644997 | ||||||||
\(807\) | 0.766335 | 0.0269763 | ||||||||
\(808\) | 3.88590 | 0.136705 | ||||||||
\(809\) | 37.0355 | 1.30210 | 0.651050 | − | 0.759035i | \(-0.274329\pi\) | ||||
0.651050 | + | 0.759035i | \(0.274329\pi\) | |||||||
\(810\) | 23.4302 | 0.823254 | ||||||||
\(811\) | 33.3196 | 1.17001 | 0.585005 | − | 0.811030i | \(-0.301093\pi\) | ||||
0.585005 | + | 0.811030i | \(0.301093\pi\) | |||||||
\(812\) | 21.0225 | 0.737743 | ||||||||
\(813\) | 4.55466 | 0.159739 | ||||||||
\(814\) | −2.54821 | −0.0893147 | ||||||||
\(815\) | −4.21170 | −0.147530 | ||||||||
\(816\) | 0.278725 | 0.00975732 | ||||||||
\(817\) | 14.6301 | 0.511841 | ||||||||
\(818\) | −0.0983273 | −0.00343793 | ||||||||
\(819\) | 47.5016 | 1.65984 | ||||||||
\(820\) | −20.2736 | −0.707985 | ||||||||
\(821\) | −11.4714 | −0.400356 | −0.200178 | − | 0.979760i | \(-0.564152\pi\) | ||||
−0.200178 | + | 0.979760i | \(0.564152\pi\) | |||||||
\(822\) | −5.61490 | −0.195842 | ||||||||
\(823\) | −36.2024 | −1.26193 | −0.630967 | − | 0.775809i | \(-0.717342\pi\) | ||||
−0.630967 | + | 0.775809i | \(0.717342\pi\) | |||||||
\(824\) | −5.67975 | −0.197863 | ||||||||
\(825\) | −7.74875 | −0.269777 | ||||||||
\(826\) | −24.1766 | −0.841210 | ||||||||
\(827\) | −3.80820 | −0.132424 | −0.0662120 | − | 0.997806i | \(-0.521091\pi\) | ||||
−0.0662120 | + | 0.997806i | \(0.521091\pi\) | |||||||
\(828\) | 19.4900 | 0.677324 | ||||||||
\(829\) | −32.3942 | −1.12510 | −0.562549 | − | 0.826764i | \(-0.690179\pi\) | ||||
−0.562549 | + | 0.826764i | \(0.690179\pi\) | |||||||
\(830\) | −9.23100 | −0.320413 | ||||||||
\(831\) | 9.34854 | 0.324297 | ||||||||
\(832\) | −4.07211 | −0.141175 | ||||||||
\(833\) | 5.78978 | 0.200604 | ||||||||
\(834\) | 5.09478 | 0.176418 | ||||||||
\(835\) | −34.1403 | −1.18147 | ||||||||
\(836\) | 4.25443 | 0.147143 | ||||||||
\(837\) | −15.7969 | −0.546020 | ||||||||
\(838\) | 39.0863 | 1.35021 | ||||||||
\(839\) | 43.9926 | 1.51879 | 0.759396 | − | 0.650629i | \(-0.225495\pi\) | ||||
0.759396 | + | 0.650629i | \(0.225495\pi\) | |||||||
\(840\) | 11.6799 | 0.402994 | ||||||||
\(841\) | −6.91724 | −0.238526 | ||||||||
\(842\) | 6.01618 | 0.207331 | ||||||||
\(843\) | 7.89070 | 0.271770 | ||||||||
\(844\) | −22.0923 | −0.760450 | ||||||||
\(845\) | −14.9288 | −0.513565 | ||||||||
\(846\) | −28.4677 | −0.978738 | ||||||||
\(847\) | 4.47360 | 0.153715 | ||||||||
\(848\) | −9.00211 | −0.309134 | ||||||||
\(849\) | −11.0979 | −0.380880 | ||||||||
\(850\) | −5.50328 | −0.188761 | ||||||||
\(851\) | 19.0465 | 0.652905 | ||||||||
\(852\) | 4.24223 | 0.145336 | ||||||||
\(853\) | −19.5873 | −0.670656 | −0.335328 | − | 0.942102i | \(-0.608847\pi\) | ||||
−0.335328 | + | 0.942102i | \(0.608847\pi\) | |||||||
\(854\) | −45.1399 | −1.54466 | ||||||||
\(855\) | −46.2342 | −1.58117 | ||||||||
\(856\) | 11.7007 | 0.399921 | ||||||||
\(857\) | 9.81358 | 0.335226 | 0.167613 | − | 0.985853i | \(-0.446394\pi\) | ||||
0.167613 | + | 0.985853i | \(0.446394\pi\) | |||||||
\(858\) | −2.55101 | −0.0870901 | ||||||||
\(859\) | 20.3992 | 0.696013 | 0.348006 | − | 0.937492i | \(-0.386859\pi\) | ||||
0.348006 | + | 0.937492i | \(0.386859\pi\) | |||||||
\(860\) | 14.3316 | 0.488702 | ||||||||
\(861\) | 13.6330 | 0.464612 | ||||||||
\(862\) | −8.12680 | −0.276800 | ||||||||
\(863\) | −32.9560 | −1.12184 | −0.560918 | − | 0.827871i | \(-0.689552\pi\) | ||||
−0.560918 | + | 0.827871i | \(0.689552\pi\) | |||||||
\(864\) | 3.51290 | 0.119511 | ||||||||
\(865\) | −18.9985 | −0.645969 | ||||||||
\(866\) | −5.74742 | −0.195305 | ||||||||
\(867\) | −10.5258 | −0.357475 | ||||||||
\(868\) | 20.1170 | 0.682814 | ||||||||
\(869\) | −6.11012 | −0.207272 | ||||||||
\(870\) | 12.2690 | 0.415957 | ||||||||
\(871\) | −48.8454 | −1.65506 | ||||||||
\(872\) | 1.34647 | 0.0455974 | ||||||||
\(873\) | −20.4955 | −0.693667 | ||||||||
\(874\) | −31.7996 | −1.07564 | ||||||||
\(875\) | −137.392 | −4.64469 | ||||||||
\(876\) | −4.56626 | −0.154280 | ||||||||
\(877\) | 6.04920 | 0.204267 | 0.102134 | − | 0.994771i | \(-0.467433\pi\) | ||||
0.102134 | + | 0.994771i | \(0.467433\pi\) | |||||||
\(878\) | −26.9288 | −0.908803 | ||||||||
\(879\) | 3.99266 | 0.134669 | ||||||||
\(880\) | 4.16763 | 0.140491 | ||||||||
\(881\) | 6.53949 | 0.220321 | 0.110161 | − | 0.993914i | \(-0.464863\pi\) | ||||
0.110161 | + | 0.993914i | \(0.464863\pi\) | |||||||
\(882\) | 33.9322 | 1.14256 | ||||||||
\(883\) | 9.44762 | 0.317938 | 0.158969 | − | 0.987284i | \(-0.449183\pi\) | ||||
0.158969 | + | 0.987284i | \(0.449183\pi\) | |||||||
\(884\) | −1.81177 | −0.0609363 | ||||||||
\(885\) | −14.1098 | −0.474294 | ||||||||
\(886\) | 37.2622 | 1.25185 | ||||||||
\(887\) | −12.4433 | −0.417805 | −0.208903 | − | 0.977936i | \(-0.566989\pi\) | ||||
−0.208903 | + | 0.977936i | \(0.566989\pi\) | |||||||
\(888\) | 1.59635 | 0.0535700 | ||||||||
\(889\) | −39.3960 | −1.32130 | ||||||||
\(890\) | −21.6184 | −0.724652 | ||||||||
\(891\) | −5.62196 | −0.188343 | ||||||||
\(892\) | −18.1199 | −0.606701 | ||||||||
\(893\) | 46.4474 | 1.55430 | ||||||||
\(894\) | 5.61583 | 0.187822 | ||||||||
\(895\) | −7.84274 | −0.262154 | ||||||||
\(896\) | −4.47360 | −0.149452 | ||||||||
\(897\) | 19.0674 | 0.636643 | ||||||||
\(898\) | −4.55500 | −0.152002 | ||||||||
\(899\) | 21.1316 | 0.704778 | ||||||||
\(900\) | −32.2531 | −1.07510 | ||||||||
\(901\) | −4.00522 | −0.133433 | ||||||||
\(902\) | 4.86454 | 0.161972 | ||||||||
\(903\) | −9.63727 | −0.320708 | ||||||||
\(904\) | −17.7627 | −0.590780 | ||||||||
\(905\) | −68.2188 | −2.26767 | ||||||||
\(906\) | −1.18726 | −0.0394440 | ||||||||
\(907\) | 38.1348 | 1.26624 | 0.633122 | − | 0.774052i | \(-0.281773\pi\) | ||||
0.633122 | + | 0.774052i | \(0.281773\pi\) | |||||||
\(908\) | 24.5850 | 0.815882 | ||||||||
\(909\) | 10.1327 | 0.336079 | ||||||||
\(910\) | −75.9215 | −2.51677 | ||||||||
\(911\) | 2.52811 | 0.0837601 | 0.0418801 | − | 0.999123i | \(-0.486665\pi\) | ||||
0.0418801 | + | 0.999123i | \(0.486665\pi\) | |||||||
\(912\) | −2.66523 | −0.0882546 | ||||||||
\(913\) | 2.21493 | 0.0733035 | ||||||||
\(914\) | −7.01789 | −0.232131 | ||||||||
\(915\) | −26.3442 | −0.870914 | ||||||||
\(916\) | 27.5729 | 0.911035 | ||||||||
\(917\) | 54.6010 | 1.80308 | ||||||||
\(918\) | 1.56296 | 0.0515855 | ||||||||
\(919\) | −41.9851 | −1.38496 | −0.692481 | − | 0.721436i | \(-0.743482\pi\) | ||||
−0.692481 | + | 0.721436i | \(0.743482\pi\) | |||||||
\(920\) | −31.1507 | −1.02701 | ||||||||
\(921\) | 12.0523 | 0.397138 | ||||||||
\(922\) | 18.7876 | 0.618737 | ||||||||
\(923\) | −27.5753 | −0.907652 | ||||||||
\(924\) | −2.80253 | −0.0921963 | ||||||||
\(925\) | −31.5191 | −1.03634 | ||||||||
\(926\) | −7.49611 | −0.246337 | ||||||||
\(927\) | −14.8102 | −0.486431 | ||||||||
\(928\) | −4.69923 | −0.154260 | ||||||||
\(929\) | 58.8996 | 1.93243 | 0.966217 | − | 0.257731i | \(-0.0829747\pi\) | ||||
0.966217 | + | 0.257731i | \(0.0829747\pi\) | |||||||
\(930\) | 11.7405 | 0.384987 | ||||||||
\(931\) | −55.3632 | −1.81445 | ||||||||
\(932\) | −14.7600 | −0.483481 | ||||||||
\(933\) | 10.1409 | 0.331998 | ||||||||
\(934\) | −26.8727 | −0.879301 | ||||||||
\(935\) | 1.85426 | 0.0606409 | ||||||||
\(936\) | −10.6182 | −0.347068 | ||||||||
\(937\) | 41.8501 | 1.36718 | 0.683591 | − | 0.729865i | \(-0.260417\pi\) | ||||
0.683591 | + | 0.729865i | \(0.260417\pi\) | |||||||
\(938\) | −53.6612 | −1.75210 | ||||||||
\(939\) | 11.3524 | 0.370471 | ||||||||
\(940\) | 45.4997 | 1.48404 | ||||||||
\(941\) | −23.9002 | −0.779126 | −0.389563 | − | 0.921000i | \(-0.627374\pi\) | ||||
−0.389563 | + | 0.921000i | \(0.627374\pi\) | |||||||
\(942\) | 1.63325 | 0.0532142 | ||||||||
\(943\) | −36.3598 | −1.18404 | ||||||||
\(944\) | 5.40428 | 0.175894 | ||||||||
\(945\) | 65.4955 | 2.13057 | ||||||||
\(946\) | −3.43878 | −0.111804 | ||||||||
\(947\) | −59.0902 | −1.92017 | −0.960086 | − | 0.279704i | \(-0.909764\pi\) | ||||
−0.960086 | + | 0.279704i | \(0.909764\pi\) | |||||||
\(948\) | 3.82774 | 0.124319 | ||||||||
\(949\) | 29.6816 | 0.963504 | ||||||||
\(950\) | 52.6236 | 1.70733 | ||||||||
\(951\) | −9.27737 | −0.300839 | ||||||||
\(952\) | −1.99040 | −0.0645091 | ||||||||
\(953\) | 14.5996 | 0.472928 | 0.236464 | − | 0.971640i | \(-0.424011\pi\) | ||||
0.236464 | + | 0.971640i | \(0.424011\pi\) | |||||||
\(954\) | −23.4734 | −0.759980 | ||||||||
\(955\) | −96.6363 | −3.12708 | ||||||||
\(956\) | −1.55374 | −0.0502514 | ||||||||
\(957\) | −2.94388 | −0.0951620 | ||||||||
\(958\) | 0.205380 | 0.00663553 | ||||||||
\(959\) | 40.0964 | 1.29478 | ||||||||
\(960\) | −2.61085 | −0.0842648 | ||||||||
\(961\) | −10.7786 | −0.347697 | ||||||||
\(962\) | −10.3766 | −0.334555 | ||||||||
\(963\) | 30.5101 | 0.983175 | ||||||||
\(964\) | 27.7317 | 0.893177 | ||||||||
\(965\) | 58.4912 | 1.88290 | ||||||||
\(966\) | 20.9474 | 0.673970 | ||||||||
\(967\) | −60.7609 | −1.95394 | −0.976970 | − | 0.213377i | \(-0.931554\pi\) | ||||
−0.976970 | + | 0.213377i | \(0.931554\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −1.18582 | −0.0380939 | ||||||||
\(970\) | 32.7578 | 1.05179 | ||||||||
\(971\) | −31.1634 | −1.00008 | −0.500040 | − | 0.866002i | \(-0.666681\pi\) | ||||
−0.500040 | + | 0.866002i | \(0.666681\pi\) | |||||||
\(972\) | 14.0606 | 0.450995 | ||||||||
\(973\) | −36.3822 | −1.16636 | ||||||||
\(974\) | −22.5602 | −0.722876 | ||||||||
\(975\) | −31.5538 | −1.01053 | ||||||||
\(976\) | 10.0903 | 0.322982 | ||||||||
\(977\) | −34.2463 | −1.09564 | −0.547819 | − | 0.836597i | \(-0.684542\pi\) | ||||
−0.547819 | + | 0.836597i | \(0.684542\pi\) | |||||||
\(978\) | −0.633085 | −0.0202438 | ||||||||
\(979\) | 5.18723 | 0.165785 | ||||||||
\(980\) | −54.2336 | −1.73243 | ||||||||
\(981\) | 3.51100 | 0.112097 | ||||||||
\(982\) | −5.88987 | −0.187953 | ||||||||
\(983\) | −16.7546 | −0.534389 | −0.267194 | − | 0.963643i | \(-0.586097\pi\) | ||||
−0.267194 | + | 0.963643i | \(0.586097\pi\) | |||||||
\(984\) | −3.04744 | −0.0971488 | ||||||||
\(985\) | −4.16763 | −0.132792 | ||||||||
\(986\) | −2.09079 | −0.0665842 | ||||||||
\(987\) | −30.5963 | −0.973891 | ||||||||
\(988\) | 17.3245 | 0.551166 | ||||||||
\(989\) | 25.7030 | 0.817308 | ||||||||
\(990\) | 10.8673 | 0.345385 | ||||||||
\(991\) | 14.4907 | 0.460312 | 0.230156 | − | 0.973154i | \(-0.426076\pi\) | ||||
0.230156 | + | 0.973154i | \(0.426076\pi\) | |||||||
\(992\) | −4.49682 | −0.142774 | ||||||||
\(993\) | 11.7772 | 0.373737 | ||||||||
\(994\) | −30.2941 | −0.960870 | ||||||||
\(995\) | 45.0138 | 1.42703 | ||||||||
\(996\) | −1.38756 | −0.0439666 | ||||||||
\(997\) | −45.3743 | −1.43702 | −0.718510 | − | 0.695517i | \(-0.755175\pi\) | ||||
−0.718510 | + | 0.695517i | \(0.755175\pi\) | |||||||
\(998\) | −4.04749 | −0.128121 | ||||||||
\(999\) | 8.95161 | 0.283216 |
(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 | 4334.2.a.e.1.15 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.e.1.15 | ✓ | 24 | 1.1 | even | 1 | trivial |