Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 31x^{4} + 9x^{3} + 230x^{2} + 32x - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.98965\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.98965 | −1.76411 | −0.882054 | − | 0.471148i | \(-0.843840\pi\) | ||||
−0.882054 | + | 0.471148i | \(0.843840\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 16.8966 | 2.11208 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 14.9690 | 1.01851 | ||||||||
\(7\) | 22.5076 | 1.21530 | 0.607648 | − | 0.794207i | \(-0.292113\pi\) | ||||
0.607648 | + | 0.794207i | \(0.292113\pi\) | |||||||
\(8\) | −44.3911 | −1.96183 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −24.9483 | −0.788933 | ||||||||
\(11\) | −32.8384 | −0.900106 | −0.450053 | − | 0.893002i | \(-0.648595\pi\) | ||||
−0.450053 | + | 0.893002i | \(0.648595\pi\) | |||||||
\(12\) | −50.6899 | −1.21941 | ||||||||
\(13\) | 31.3437 | 0.668707 | 0.334353 | − | 0.942448i | \(-0.391482\pi\) | ||||
0.334353 | + | 0.942448i | \(0.391482\pi\) | |||||||
\(14\) | −112.305 | −2.14391 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 86.3230 | 1.34880 | ||||||||
\(17\) | −66.5556 | −0.949536 | −0.474768 | − | 0.880111i | \(-0.657468\pi\) | ||||
−0.474768 | + | 0.880111i | \(0.657468\pi\) | |||||||
\(18\) | −44.9069 | −0.588036 | ||||||||
\(19\) | −103.349 | −1.24789 | −0.623943 | − | 0.781470i | \(-0.714470\pi\) | ||||
−0.623943 | + | 0.781470i | \(0.714470\pi\) | |||||||
\(20\) | 84.4831 | 0.944550 | ||||||||
\(21\) | −67.5228 | −0.701651 | ||||||||
\(22\) | 163.852 | 1.58788 | ||||||||
\(23\) | 5.86439 | 0.0531657 | 0.0265828 | − | 0.999647i | \(-0.491537\pi\) | ||||
0.0265828 | + | 0.999647i | \(0.491537\pi\) | |||||||
\(24\) | 133.173 | 1.13266 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −156.394 | −1.17967 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 380.302 | 2.56680 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 74.8448 | 0.455491 | ||||||||
\(31\) | −26.9324 | −0.156039 | −0.0780195 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780195 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(32\) | −75.5933 | −0.417598 | ||||||||
\(33\) | 98.5153 | 0.519676 | ||||||||
\(34\) | 332.089 | 1.67508 | ||||||||
\(35\) | 112.538 | 0.543497 | ||||||||
\(36\) | 152.070 | 0.704026 | ||||||||
\(37\) | −18.2548 | −0.0811099 | −0.0405550 | − | 0.999177i | \(-0.512913\pi\) | ||||
−0.0405550 | + | 0.999177i | \(0.512913\pi\) | |||||||
\(38\) | 515.675 | 2.20141 | ||||||||
\(39\) | −94.0312 | −0.386078 | ||||||||
\(40\) | −221.955 | −0.877356 | ||||||||
\(41\) | −115.564 | −0.440196 | −0.220098 | − | 0.975478i | \(-0.570638\pi\) | ||||
−0.220098 | + | 0.975478i | \(0.570638\pi\) | |||||||
\(42\) | 336.915 | 1.23779 | ||||||||
\(43\) | 415.780 | 1.47455 | 0.737277 | − | 0.675591i | \(-0.236111\pi\) | ||||
0.737277 | + | 0.675591i | \(0.236111\pi\) | |||||||
\(44\) | −554.859 | −1.90109 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −29.2613 | −0.0937900 | ||||||||
\(47\) | 11.7223 | 0.0363804 | 0.0181902 | − | 0.999835i | \(-0.494210\pi\) | ||||
0.0181902 | + | 0.999835i | \(0.494210\pi\) | |||||||
\(48\) | −258.969 | −0.778729 | ||||||||
\(49\) | 163.592 | 0.476943 | ||||||||
\(50\) | −124.741 | −0.352822 | ||||||||
\(51\) | 199.667 | 0.548215 | ||||||||
\(52\) | 529.604 | 1.41236 | ||||||||
\(53\) | −275.059 | −0.712872 | −0.356436 | − | 0.934320i | \(-0.616008\pi\) | ||||
−0.356436 | + | 0.934320i | \(0.616008\pi\) | |||||||
\(54\) | 134.721 | 0.339503 | ||||||||
\(55\) | −164.192 | −0.402540 | ||||||||
\(56\) | −999.136 | −2.38420 | ||||||||
\(57\) | 310.046 | 0.720467 | ||||||||
\(58\) | 144.700 | 0.327587 | ||||||||
\(59\) | 212.467 | 0.468829 | 0.234414 | − | 0.972137i | \(-0.424683\pi\) | ||||
0.234414 | + | 0.972137i | \(0.424683\pi\) | |||||||
\(60\) | −253.449 | −0.545336 | ||||||||
\(61\) | −766.954 | −1.60981 | −0.804905 | − | 0.593403i | \(-0.797784\pi\) | ||||
−0.804905 | + | 0.593403i | \(0.797784\pi\) | |||||||
\(62\) | 134.383 | 0.275270 | ||||||||
\(63\) | 202.568 | 0.405099 | ||||||||
\(64\) | −313.400 | −0.612110 | ||||||||
\(65\) | 156.719 | 0.299055 | ||||||||
\(66\) | −491.557 | −0.916765 | ||||||||
\(67\) | 256.113 | 0.467003 | 0.233501 | − | 0.972356i | \(-0.424982\pi\) | ||||
0.233501 | + | 0.972356i | \(0.424982\pi\) | |||||||
\(68\) | −1124.57 | −2.00549 | ||||||||
\(69\) | −17.5932 | −0.0306952 | ||||||||
\(70\) | −561.525 | −0.958787 | ||||||||
\(71\) | −711.750 | −1.18971 | −0.594854 | − | 0.803834i | \(-0.702790\pi\) | ||||
−0.594854 | + | 0.803834i | \(0.702790\pi\) | |||||||
\(72\) | −399.520 | −0.653942 | ||||||||
\(73\) | 45.4465 | 0.0728646 | 0.0364323 | − | 0.999336i | \(-0.488401\pi\) | ||||
0.0364323 | + | 0.999336i | \(0.488401\pi\) | |||||||
\(74\) | 91.0850 | 0.143087 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −1746.25 | −2.63563 | ||||||||
\(77\) | −739.114 | −1.09389 | ||||||||
\(78\) | 469.183 | 0.681084 | ||||||||
\(79\) | 329.147 | 0.468759 | 0.234380 | − | 0.972145i | \(-0.424694\pi\) | ||||
0.234380 | + | 0.972145i | \(0.424694\pi\) | |||||||
\(80\) | 431.615 | 0.603201 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 576.623 | 0.776553 | ||||||||
\(83\) | −283.281 | −0.374628 | −0.187314 | − | 0.982300i | \(-0.559978\pi\) | ||||
−0.187314 | + | 0.982300i | \(0.559978\pi\) | |||||||
\(84\) | −1140.91 | −1.48194 | ||||||||
\(85\) | −332.778 | −0.424645 | ||||||||
\(86\) | −2074.60 | −2.60127 | ||||||||
\(87\) | 87.0000 | 0.107211 | ||||||||
\(88\) | 1457.73 | 1.76585 | ||||||||
\(89\) | −802.821 | −0.956167 | −0.478083 | − | 0.878314i | \(-0.658668\pi\) | ||||
−0.478083 | + | 0.878314i | \(0.658668\pi\) | |||||||
\(90\) | −224.534 | −0.262978 | ||||||||
\(91\) | 705.472 | 0.812677 | ||||||||
\(92\) | 99.0885 | 0.112290 | ||||||||
\(93\) | 80.7973 | 0.0900891 | ||||||||
\(94\) | −58.4903 | −0.0641789 | ||||||||
\(95\) | −516.744 | −0.558072 | ||||||||
\(96\) | 226.780 | 0.241100 | ||||||||
\(97\) | 389.532 | 0.407742 | 0.203871 | − | 0.978998i | \(-0.434648\pi\) | ||||
0.203871 | + | 0.978998i | \(0.434648\pi\) | |||||||
\(98\) | −816.265 | −0.841379 | ||||||||
\(99\) | −295.546 | −0.300035 | ||||||||
\(100\) | 422.416 | 0.422416 | ||||||||
\(101\) | 274.559 | 0.270492 | 0.135246 | − | 0.990812i | \(-0.456818\pi\) | ||||
0.135246 | + | 0.990812i | \(0.456818\pi\) | |||||||
\(102\) | −996.268 | −0.967110 | ||||||||
\(103\) | −841.113 | −0.804635 | −0.402317 | − | 0.915500i | \(-0.631795\pi\) | ||||
−0.402317 | + | 0.915500i | \(0.631795\pi\) | |||||||
\(104\) | −1391.38 | −1.31189 | ||||||||
\(105\) | −337.614 | −0.313788 | ||||||||
\(106\) | 1372.45 | 1.25758 | ||||||||
\(107\) | −1489.04 | −1.34534 | −0.672670 | − | 0.739943i | \(-0.734853\pi\) | ||||
−0.672670 | + | 0.739943i | \(0.734853\pi\) | |||||||
\(108\) | −456.209 | −0.406470 | ||||||||
\(109\) | −987.120 | −0.867422 | −0.433711 | − | 0.901052i | \(-0.642796\pi\) | ||||
−0.433711 | + | 0.901052i | \(0.642796\pi\) | |||||||
\(110\) | 819.262 | 0.710123 | ||||||||
\(111\) | 54.7643 | 0.0468288 | ||||||||
\(112\) | 1942.92 | 1.63919 | ||||||||
\(113\) | 135.446 | 0.112758 | 0.0563791 | − | 0.998409i | \(-0.482044\pi\) | ||||
0.0563791 | + | 0.998409i | \(0.482044\pi\) | |||||||
\(114\) | −1547.02 | −1.27098 | ||||||||
\(115\) | 29.3220 | 0.0237764 | ||||||||
\(116\) | −490.002 | −0.392203 | ||||||||
\(117\) | 282.094 | 0.222902 | ||||||||
\(118\) | −1060.14 | −0.827065 | ||||||||
\(119\) | −1498.01 | −1.15397 | ||||||||
\(120\) | 665.866 | 0.506542 | ||||||||
\(121\) | −252.636 | −0.189809 | ||||||||
\(122\) | 3826.84 | 2.83988 | ||||||||
\(123\) | 346.691 | 0.254147 | ||||||||
\(124\) | −455.067 | −0.329567 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −1010.75 | −0.714638 | ||||||||
\(127\) | 1539.42 | 1.07560 | 0.537802 | − | 0.843071i | \(-0.319255\pi\) | ||||
0.537802 | + | 0.843071i | \(0.319255\pi\) | |||||||
\(128\) | 2168.50 | 1.49743 | ||||||||
\(129\) | −1247.34 | −0.851334 | ||||||||
\(130\) | −781.972 | −0.527565 | ||||||||
\(131\) | 1625.05 | 1.08383 | 0.541914 | − | 0.840434i | \(-0.317700\pi\) | ||||
0.541914 | + | 0.840434i | \(0.317700\pi\) | |||||||
\(132\) | 1664.58 | 1.09760 | ||||||||
\(133\) | −2326.13 | −1.51655 | ||||||||
\(134\) | −1277.91 | −0.823843 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 2954.48 | 1.86282 | ||||||||
\(137\) | −925.116 | −0.576920 | −0.288460 | − | 0.957492i | \(-0.593143\pi\) | ||||
−0.288460 | + | 0.957492i | \(0.593143\pi\) | |||||||
\(138\) | 87.7839 | 0.0541497 | ||||||||
\(139\) | −3232.14 | −1.97228 | −0.986138 | − | 0.165928i | \(-0.946938\pi\) | ||||
−0.986138 | + | 0.165928i | \(0.946938\pi\) | |||||||
\(140\) | 1901.51 | 1.14791 | ||||||||
\(141\) | −35.1670 | −0.0210042 | ||||||||
\(142\) | 3551.39 | 2.09877 | ||||||||
\(143\) | −1029.28 | −0.601907 | ||||||||
\(144\) | 776.907 | 0.449599 | ||||||||
\(145\) | −145.000 | −0.0830455 | ||||||||
\(146\) | −226.762 | −0.128541 | ||||||||
\(147\) | −490.775 | −0.275363 | ||||||||
\(148\) | −308.444 | −0.171311 | ||||||||
\(149\) | 764.349 | 0.420255 | 0.210127 | − | 0.977674i | \(-0.432612\pi\) | ||||
0.210127 | + | 0.977674i | \(0.432612\pi\) | |||||||
\(150\) | 374.224 | 0.203702 | ||||||||
\(151\) | 2721.64 | 1.46678 | 0.733390 | − | 0.679808i | \(-0.237937\pi\) | ||||
0.733390 | + | 0.679808i | \(0.237937\pi\) | |||||||
\(152\) | 4587.76 | 2.44814 | ||||||||
\(153\) | −599.000 | −0.316512 | ||||||||
\(154\) | 3687.92 | 1.92975 | ||||||||
\(155\) | −134.662 | −0.0697827 | ||||||||
\(156\) | −1588.81 | −0.815427 | ||||||||
\(157\) | 1760.38 | 0.894862 | 0.447431 | − | 0.894319i | \(-0.352339\pi\) | ||||
0.447431 | + | 0.894319i | \(0.352339\pi\) | |||||||
\(158\) | −1642.33 | −0.826942 | ||||||||
\(159\) | 825.176 | 0.411577 | ||||||||
\(160\) | −377.966 | −0.186755 | ||||||||
\(161\) | 131.993 | 0.0646120 | ||||||||
\(162\) | −404.162 | −0.196012 | ||||||||
\(163\) | −3566.14 | −1.71363 | −0.856816 | − | 0.515622i | \(-0.827561\pi\) | ||||
−0.856816 | + | 0.515622i | \(0.827561\pi\) | |||||||
\(164\) | −1952.64 | −0.929728 | ||||||||
\(165\) | 492.577 | 0.232406 | ||||||||
\(166\) | 1413.47 | 0.660885 | ||||||||
\(167\) | −1976.07 | −0.915647 | −0.457824 | − | 0.889043i | \(-0.651371\pi\) | ||||
−0.457824 | + | 0.889043i | \(0.651371\pi\) | |||||||
\(168\) | 2997.41 | 1.37652 | ||||||||
\(169\) | −1214.57 | −0.552831 | ||||||||
\(170\) | 1660.45 | 0.749120 | ||||||||
\(171\) | −930.139 | −0.415962 | ||||||||
\(172\) | 7025.28 | 3.11437 | ||||||||
\(173\) | −1836.14 | −0.806934 | −0.403467 | − | 0.914994i | \(-0.632195\pi\) | ||||
−0.403467 | + | 0.914994i | \(0.632195\pi\) | |||||||
\(174\) | −434.100 | −0.189132 | ||||||||
\(175\) | 562.690 | 0.243059 | ||||||||
\(176\) | −2834.71 | −1.21406 | ||||||||
\(177\) | −637.402 | −0.270678 | ||||||||
\(178\) | 4005.80 | 1.68678 | ||||||||
\(179\) | 2241.87 | 0.936117 | 0.468058 | − | 0.883698i | \(-0.344954\pi\) | ||||
0.468058 | + | 0.883698i | \(0.344954\pi\) | |||||||
\(180\) | 760.348 | 0.314850 | ||||||||
\(181\) | 2084.75 | 0.856122 | 0.428061 | − | 0.903750i | \(-0.359197\pi\) | ||||
0.428061 | + | 0.903750i | \(0.359197\pi\) | |||||||
\(182\) | −3520.06 | −1.43365 | ||||||||
\(183\) | 2300.86 | 0.929425 | ||||||||
\(184\) | −260.327 | −0.104302 | ||||||||
\(185\) | −91.2739 | −0.0362735 | ||||||||
\(186\) | −403.150 | −0.158927 | ||||||||
\(187\) | 2185.58 | 0.854682 | ||||||||
\(188\) | 198.068 | 0.0768382 | ||||||||
\(189\) | −607.705 | −0.233884 | ||||||||
\(190\) | 2578.37 | 0.984499 | ||||||||
\(191\) | 4206.24 | 1.59347 | 0.796735 | − | 0.604328i | \(-0.206558\pi\) | ||||
0.796735 | + | 0.604328i | \(0.206558\pi\) | |||||||
\(192\) | 940.201 | 0.353402 | ||||||||
\(193\) | −2047.28 | −0.763558 | −0.381779 | − | 0.924254i | \(-0.624688\pi\) | ||||
−0.381779 | + | 0.924254i | \(0.624688\pi\) | |||||||
\(194\) | −1943.63 | −0.719301 | ||||||||
\(195\) | −470.156 | −0.172659 | ||||||||
\(196\) | 2764.15 | 1.00734 | ||||||||
\(197\) | 4461.88 | 1.61369 | 0.806843 | − | 0.590766i | \(-0.201174\pi\) | ||||
0.806843 | + | 0.590766i | \(0.201174\pi\) | |||||||
\(198\) | 1474.67 | 0.529295 | ||||||||
\(199\) | −1926.80 | −0.686367 | −0.343183 | − | 0.939268i | \(-0.611505\pi\) | ||||
−0.343183 | + | 0.939268i | \(0.611505\pi\) | |||||||
\(200\) | −1109.78 | −0.392365 | ||||||||
\(201\) | −768.339 | −0.269624 | ||||||||
\(202\) | −1369.95 | −0.477177 | ||||||||
\(203\) | −652.720 | −0.225675 | ||||||||
\(204\) | 3373.70 | 1.15787 | ||||||||
\(205\) | −577.819 | −0.196862 | ||||||||
\(206\) | 4196.86 | 1.41946 | ||||||||
\(207\) | 52.7796 | 0.0177219 | ||||||||
\(208\) | 2705.69 | 0.901950 | ||||||||
\(209\) | 3393.81 | 1.12323 | ||||||||
\(210\) | 1684.58 | 0.553556 | ||||||||
\(211\) | −4487.22 | −1.46404 | −0.732021 | − | 0.681282i | \(-0.761423\pi\) | ||||
−0.732021 | + | 0.681282i | \(0.761423\pi\) | |||||||
\(212\) | −4647.57 | −1.50564 | ||||||||
\(213\) | 2135.25 | 0.686878 | ||||||||
\(214\) | 7429.81 | 2.37332 | ||||||||
\(215\) | 2078.90 | 0.659441 | ||||||||
\(216\) | 1198.56 | 0.377554 | ||||||||
\(217\) | −606.184 | −0.189633 | ||||||||
\(218\) | 4925.39 | 1.53023 | ||||||||
\(219\) | −136.340 | −0.0420684 | ||||||||
\(220\) | −2774.30 | −0.850195 | ||||||||
\(221\) | −2086.10 | −0.634961 | ||||||||
\(222\) | −273.255 | −0.0826111 | ||||||||
\(223\) | −5113.28 | −1.53547 | −0.767737 | − | 0.640765i | \(-0.778617\pi\) | ||||
−0.767737 | + | 0.640765i | \(0.778617\pi\) | |||||||
\(224\) | −1701.42 | −0.507505 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −675.827 | −0.198918 | ||||||||
\(227\) | −5258.42 | −1.53751 | −0.768753 | − | 0.639546i | \(-0.779122\pi\) | ||||
−0.768753 | + | 0.639546i | \(0.779122\pi\) | |||||||
\(228\) | 5238.74 | 1.52168 | ||||||||
\(229\) | −5242.30 | −1.51276 | −0.756378 | − | 0.654135i | \(-0.773033\pi\) | ||||
−0.756378 | + | 0.654135i | \(0.773033\pi\) | |||||||
\(230\) | −146.306 | −0.0419442 | ||||||||
\(231\) | 2217.34 | 0.631560 | ||||||||
\(232\) | 1287.34 | 0.364302 | ||||||||
\(233\) | −6046.86 | −1.70018 | −0.850092 | − | 0.526635i | \(-0.823453\pi\) | ||||
−0.850092 | + | 0.526635i | \(0.823453\pi\) | |||||||
\(234\) | −1407.55 | −0.393224 | ||||||||
\(235\) | 58.6116 | 0.0162698 | ||||||||
\(236\) | 3589.98 | 0.990203 | ||||||||
\(237\) | −987.442 | −0.270638 | ||||||||
\(238\) | 7474.53 | 2.03572 | ||||||||
\(239\) | −212.645 | −0.0575518 | −0.0287759 | − | 0.999586i | \(-0.509161\pi\) | ||||
−0.0287759 | + | 0.999586i | \(0.509161\pi\) | |||||||
\(240\) | −1294.85 | −0.348258 | ||||||||
\(241\) | −5857.59 | −1.56565 | −0.782823 | − | 0.622245i | \(-0.786221\pi\) | ||||
−0.782823 | + | 0.622245i | \(0.786221\pi\) | |||||||
\(242\) | 1260.57 | 0.334844 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −12958.9 | −3.40005 | ||||||||
\(245\) | 817.958 | 0.213295 | ||||||||
\(246\) | −1729.87 | −0.448343 | ||||||||
\(247\) | −3239.34 | −0.834470 | ||||||||
\(248\) | 1195.56 | 0.306121 | ||||||||
\(249\) | 849.844 | 0.216292 | ||||||||
\(250\) | −623.707 | −0.157787 | ||||||||
\(251\) | −3510.70 | −0.882842 | −0.441421 | − | 0.897300i | \(-0.645525\pi\) | ||||
−0.441421 | + | 0.897300i | \(0.645525\pi\) | |||||||
\(252\) | 3422.72 | 0.855600 | ||||||||
\(253\) | −192.578 | −0.0478547 | ||||||||
\(254\) | −7681.18 | −1.89748 | ||||||||
\(255\) | 998.334 | 0.245169 | ||||||||
\(256\) | −8312.88 | −2.02951 | ||||||||
\(257\) | 2682.10 | 0.650990 | 0.325495 | − | 0.945544i | \(-0.394469\pi\) | ||||
0.325495 | + | 0.945544i | \(0.394469\pi\) | |||||||
\(258\) | 6223.79 | 1.50185 | ||||||||
\(259\) | −410.871 | −0.0985725 | ||||||||
\(260\) | 2648.02 | 0.631627 | ||||||||
\(261\) | −261.000 | −0.0618984 | ||||||||
\(262\) | −8108.45 | −1.91199 | ||||||||
\(263\) | 4147.94 | 0.972521 | 0.486261 | − | 0.873814i | \(-0.338361\pi\) | ||||
0.486261 | + | 0.873814i | \(0.338361\pi\) | |||||||
\(264\) | −4373.20 | −1.01952 | ||||||||
\(265\) | −1375.29 | −0.318806 | ||||||||
\(266\) | 11606.6 | 2.67536 | ||||||||
\(267\) | 2408.46 | 0.552043 | ||||||||
\(268\) | 4327.45 | 0.986346 | ||||||||
\(269\) | −7462.57 | −1.69145 | −0.845726 | − | 0.533617i | \(-0.820832\pi\) | ||||
−0.845726 | + | 0.533617i | \(0.820832\pi\) | |||||||
\(270\) | 673.603 | 0.151830 | ||||||||
\(271\) | 6848.81 | 1.53519 | 0.767594 | − | 0.640937i | \(-0.221454\pi\) | ||||
0.767594 | + | 0.640937i | \(0.221454\pi\) | |||||||
\(272\) | −5745.28 | −1.28073 | ||||||||
\(273\) | −2116.42 | −0.469199 | ||||||||
\(274\) | 4616.01 | 1.01775 | ||||||||
\(275\) | −820.961 | −0.180021 | ||||||||
\(276\) | −297.266 | −0.0648307 | ||||||||
\(277\) | −100.396 | −0.0217769 | −0.0108884 | − | 0.999941i | \(-0.503466\pi\) | ||||
−0.0108884 | + | 0.999941i | \(0.503466\pi\) | |||||||
\(278\) | 16127.2 | 3.47931 | ||||||||
\(279\) | −242.392 | −0.0520130 | ||||||||
\(280\) | −4995.68 | −1.06625 | ||||||||
\(281\) | 3619.61 | 0.768426 | 0.384213 | − | 0.923244i | \(-0.374473\pi\) | ||||
0.384213 | + | 0.923244i | \(0.374473\pi\) | |||||||
\(282\) | 175.471 | 0.0370537 | ||||||||
\(283\) | −3692.84 | −0.775677 | −0.387839 | − | 0.921727i | \(-0.626778\pi\) | ||||
−0.387839 | + | 0.921727i | \(0.626778\pi\) | |||||||
\(284\) | −12026.2 | −2.51276 | ||||||||
\(285\) | 1550.23 | 0.322203 | ||||||||
\(286\) | 5135.75 | 1.06183 | ||||||||
\(287\) | −2601.06 | −0.534968 | ||||||||
\(288\) | −680.339 | −0.139199 | ||||||||
\(289\) | −483.352 | −0.0983823 | ||||||||
\(290\) | 723.500 | 0.146501 | ||||||||
\(291\) | −1168.60 | −0.235410 | ||||||||
\(292\) | 767.893 | 0.153896 | ||||||||
\(293\) | −1172.85 | −0.233851 | −0.116926 | − | 0.993141i | \(-0.537304\pi\) | ||||
−0.116926 | + | 0.993141i | \(0.537304\pi\) | |||||||
\(294\) | 2448.79 | 0.485771 | ||||||||
\(295\) | 1062.34 | 0.209667 | ||||||||
\(296\) | 810.349 | 0.159124 | ||||||||
\(297\) | 886.638 | 0.173225 | ||||||||
\(298\) | −3813.84 | −0.741375 | ||||||||
\(299\) | 183.812 | 0.0355523 | ||||||||
\(300\) | −1267.25 | −0.243882 | ||||||||
\(301\) | 9358.20 | 1.79202 | ||||||||
\(302\) | −13580.0 | −2.58756 | ||||||||
\(303\) | −823.678 | −0.156168 | ||||||||
\(304\) | −8921.38 | −1.68315 | ||||||||
\(305\) | −3834.77 | −0.719929 | ||||||||
\(306\) | 2988.80 | 0.558361 | ||||||||
\(307\) | −4625.08 | −0.859829 | −0.429915 | − | 0.902870i | \(-0.641456\pi\) | ||||
−0.429915 | + | 0.902870i | \(0.641456\pi\) | |||||||
\(308\) | −12488.5 | −2.31039 | ||||||||
\(309\) | 2523.34 | 0.464556 | ||||||||
\(310\) | 671.917 | 0.123104 | ||||||||
\(311\) | 5757.91 | 1.04984 | 0.524921 | − | 0.851151i | \(-0.324095\pi\) | ||||
0.524921 | + | 0.851151i | \(0.324095\pi\) | |||||||
\(312\) | 4174.15 | 0.757419 | ||||||||
\(313\) | −7518.69 | −1.35777 | −0.678884 | − | 0.734246i | \(-0.737536\pi\) | ||||
−0.678884 | + | 0.734246i | \(0.737536\pi\) | |||||||
\(314\) | −8783.66 | −1.57863 | ||||||||
\(315\) | 1012.84 | 0.181166 | ||||||||
\(316\) | 5561.48 | 0.990056 | ||||||||
\(317\) | 695.769 | 0.123275 | 0.0616376 | − | 0.998099i | \(-0.480368\pi\) | ||||
0.0616376 | + | 0.998099i | \(0.480368\pi\) | |||||||
\(318\) | −4117.34 | −0.726066 | ||||||||
\(319\) | 952.315 | 0.167145 | ||||||||
\(320\) | −1567.00 | −0.273744 | ||||||||
\(321\) | 4467.13 | 0.776732 | ||||||||
\(322\) | −658.601 | −0.113983 | ||||||||
\(323\) | 6878.44 | 1.18491 | ||||||||
\(324\) | 1368.63 | 0.234675 | ||||||||
\(325\) | 783.594 | 0.133741 | ||||||||
\(326\) | 17793.8 | 3.02303 | ||||||||
\(327\) | 2961.36 | 0.500806 | ||||||||
\(328\) | 5130.00 | 0.863588 | ||||||||
\(329\) | 263.841 | 0.0442129 | ||||||||
\(330\) | −2457.79 | −0.409990 | ||||||||
\(331\) | −7536.11 | −1.25143 | −0.625713 | − | 0.780053i | \(-0.715192\pi\) | ||||
−0.625713 | + | 0.780053i | \(0.715192\pi\) | |||||||
\(332\) | −4786.50 | −0.791245 | ||||||||
\(333\) | −164.293 | −0.0270366 | ||||||||
\(334\) | 9859.92 | 1.61530 | ||||||||
\(335\) | 1280.56 | 0.208850 | ||||||||
\(336\) | −5828.77 | −0.946385 | ||||||||
\(337\) | 6481.09 | 1.04762 | 0.523809 | − | 0.851836i | \(-0.324511\pi\) | ||||
0.523809 | + | 0.851836i | \(0.324511\pi\) | |||||||
\(338\) | 6060.28 | 0.975254 | ||||||||
\(339\) | −406.337 | −0.0651009 | ||||||||
\(340\) | −5622.83 | −0.896884 | ||||||||
\(341\) | 884.419 | 0.140452 | ||||||||
\(342\) | 4641.07 | 0.733802 | ||||||||
\(343\) | −4038.05 | −0.635669 | ||||||||
\(344\) | −18456.9 | −2.89282 | ||||||||
\(345\) | −87.9659 | −0.0137273 | ||||||||
\(346\) | 9161.72 | 1.42352 | ||||||||
\(347\) | −1154.45 | −0.178600 | −0.0893000 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0893000 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(348\) | 1470.01 | 0.226439 | ||||||||
\(349\) | 7656.69 | 1.17436 | 0.587182 | − | 0.809455i | \(-0.300237\pi\) | ||||
0.587182 | + | 0.809455i | \(0.300237\pi\) | |||||||
\(350\) | −2807.63 | −0.428783 | ||||||||
\(351\) | −846.281 | −0.128693 | ||||||||
\(352\) | 2482.37 | 0.375882 | ||||||||
\(353\) | 1112.90 | 0.167801 | 0.0839003 | − | 0.996474i | \(-0.473262\pi\) | ||||
0.0839003 | + | 0.996474i | \(0.473262\pi\) | |||||||
\(354\) | 3180.41 | 0.477506 | ||||||||
\(355\) | −3558.75 | −0.532053 | ||||||||
\(356\) | −13565.0 | −2.01950 | ||||||||
\(357\) | 4494.02 | 0.666243 | ||||||||
\(358\) | −11186.1 | −1.65141 | ||||||||
\(359\) | 12401.6 | 1.82321 | 0.911604 | − | 0.411068i | \(-0.134844\pi\) | ||||
0.911604 | + | 0.411068i | \(0.134844\pi\) | |||||||
\(360\) | −1997.60 | −0.292452 | ||||||||
\(361\) | 3821.97 | 0.557220 | ||||||||
\(362\) | −10402.2 | −1.51029 | ||||||||
\(363\) | 757.909 | 0.109587 | ||||||||
\(364\) | 11920.1 | 1.71644 | ||||||||
\(365\) | 227.233 | 0.0325860 | ||||||||
\(366\) | −11480.5 | −1.63961 | ||||||||
\(367\) | 11259.8 | 1.60152 | 0.800759 | − | 0.598987i | \(-0.204430\pi\) | ||||
0.800759 | + | 0.598987i | \(0.204430\pi\) | |||||||
\(368\) | 506.232 | 0.0717097 | ||||||||
\(369\) | −1040.07 | −0.146732 | ||||||||
\(370\) | 455.425 | 0.0639903 | ||||||||
\(371\) | −6190.91 | −0.866350 | ||||||||
\(372\) | 1365.20 | 0.190275 | ||||||||
\(373\) | −8049.64 | −1.11741 | −0.558706 | − | 0.829366i | \(-0.688702\pi\) | ||||
−0.558706 | + | 0.829366i | \(0.688702\pi\) | |||||||
\(374\) | −10905.3 | −1.50775 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | −520.367 | −0.0713720 | ||||||||
\(377\) | −908.969 | −0.124176 | ||||||||
\(378\) | 3032.24 | 0.412596 | ||||||||
\(379\) | 9811.51 | 1.32977 | 0.664886 | − | 0.746945i | \(-0.268480\pi\) | ||||
0.664886 | + | 0.746945i | \(0.268480\pi\) | |||||||
\(380\) | −8731.23 | −1.17869 | ||||||||
\(381\) | −4618.27 | −0.621000 | ||||||||
\(382\) | −20987.7 | −2.81106 | ||||||||
\(383\) | 6660.10 | 0.888551 | 0.444276 | − | 0.895890i | \(-0.353461\pi\) | ||||
0.444276 | + | 0.895890i | \(0.353461\pi\) | |||||||
\(384\) | −6505.51 | −0.864539 | ||||||||
\(385\) | −3695.57 | −0.489205 | ||||||||
\(386\) | 10215.2 | 1.34700 | ||||||||
\(387\) | 3742.02 | 0.491518 | ||||||||
\(388\) | 6581.78 | 0.861183 | ||||||||
\(389\) | −15036.0 | −1.95979 | −0.979894 | − | 0.199521i | \(-0.936061\pi\) | ||||
−0.979894 | + | 0.199521i | \(0.936061\pi\) | |||||||
\(390\) | 2345.92 | 0.304590 | ||||||||
\(391\) | −390.308 | −0.0504827 | ||||||||
\(392\) | −7262.00 | −0.935680 | ||||||||
\(393\) | −4875.16 | −0.625749 | ||||||||
\(394\) | −22263.2 | −2.84672 | ||||||||
\(395\) | 1645.74 | 0.209636 | ||||||||
\(396\) | −4993.73 | −0.633698 | ||||||||
\(397\) | −2227.56 | −0.281607 | −0.140804 | − | 0.990038i | \(-0.544969\pi\) | ||||
−0.140804 | + | 0.990038i | \(0.544969\pi\) | |||||||
\(398\) | 9614.05 | 1.21083 | ||||||||
\(399\) | 6978.40 | 0.875581 | ||||||||
\(400\) | 2158.08 | 0.269759 | ||||||||
\(401\) | −7601.22 | −0.946600 | −0.473300 | − | 0.880901i | \(-0.656937\pi\) | ||||
−0.473300 | + | 0.880901i | \(0.656937\pi\) | |||||||
\(402\) | 3833.74 | 0.475646 | ||||||||
\(403\) | −844.163 | −0.104344 | ||||||||
\(404\) | 4639.13 | 0.571300 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 3256.85 | 0.398115 | ||||||||
\(407\) | 599.458 | 0.0730075 | ||||||||
\(408\) | −8863.43 | −1.07550 | ||||||||
\(409\) | −13097.7 | −1.58347 | −0.791733 | − | 0.610867i | \(-0.790821\pi\) | ||||
−0.791733 | + | 0.610867i | \(0.790821\pi\) | |||||||
\(410\) | 2883.12 | 0.347285 | ||||||||
\(411\) | 2775.35 | 0.333085 | ||||||||
\(412\) | −14212.0 | −1.69945 | ||||||||
\(413\) | 4782.13 | 0.569765 | ||||||||
\(414\) | −263.352 | −0.0312633 | ||||||||
\(415\) | −1416.41 | −0.167539 | ||||||||
\(416\) | −2369.38 | −0.279251 | ||||||||
\(417\) | 9696.41 | 1.13869 | ||||||||
\(418\) | −16934.0 | −1.98150 | ||||||||
\(419\) | 10997.7 | 1.28227 | 0.641135 | − | 0.767428i | \(-0.278464\pi\) | ||||
0.641135 | + | 0.767428i | \(0.278464\pi\) | |||||||
\(420\) | −5704.54 | −0.662745 | ||||||||
\(421\) | −13032.2 | −1.50867 | −0.754333 | − | 0.656492i | \(-0.772040\pi\) | ||||
−0.754333 | + | 0.656492i | \(0.772040\pi\) | |||||||
\(422\) | 22389.7 | 2.58273 | ||||||||
\(423\) | 105.501 | 0.0121268 | ||||||||
\(424\) | 12210.2 | 1.39853 | ||||||||
\(425\) | −1663.89 | −0.189907 | ||||||||
\(426\) | −10654.2 | −1.21173 | ||||||||
\(427\) | −17262.3 | −1.95640 | ||||||||
\(428\) | −25159.8 | −2.84146 | ||||||||
\(429\) | 3087.84 | 0.347511 | ||||||||
\(430\) | −10373.0 | −1.16332 | ||||||||
\(431\) | −781.858 | −0.0873800 | −0.0436900 | − | 0.999045i | \(-0.513911\pi\) | ||||
−0.0436900 | + | 0.999045i | \(0.513911\pi\) | |||||||
\(432\) | −2330.72 | −0.259576 | ||||||||
\(433\) | 9159.83 | 1.01661 | 0.508306 | − | 0.861176i | \(-0.330272\pi\) | ||||
0.508306 | + | 0.861176i | \(0.330272\pi\) | |||||||
\(434\) | 3024.65 | 0.334534 | ||||||||
\(435\) | 435.000 | 0.0479463 | ||||||||
\(436\) | −16679.0 | −1.83206 | ||||||||
\(437\) | −606.078 | −0.0663447 | ||||||||
\(438\) | 680.287 | 0.0742132 | ||||||||
\(439\) | −4048.62 | −0.440160 | −0.220080 | − | 0.975482i | \(-0.570632\pi\) | ||||
−0.220080 | + | 0.975482i | \(0.570632\pi\) | |||||||
\(440\) | 7288.67 | 0.789713 | ||||||||
\(441\) | 1472.32 | 0.158981 | ||||||||
\(442\) | 10408.9 | 1.12014 | ||||||||
\(443\) | −6522.28 | −0.699510 | −0.349755 | − | 0.936841i | \(-0.613735\pi\) | ||||
−0.349755 | + | 0.936841i | \(0.613735\pi\) | |||||||
\(444\) | 925.332 | 0.0989062 | ||||||||
\(445\) | −4014.10 | −0.427611 | ||||||||
\(446\) | 25513.5 | 2.70874 | ||||||||
\(447\) | −2293.05 | −0.242634 | ||||||||
\(448\) | −7053.88 | −0.743894 | ||||||||
\(449\) | −4946.78 | −0.519940 | −0.259970 | − | 0.965617i | \(-0.583713\pi\) | ||||
−0.259970 | + | 0.965617i | \(0.583713\pi\) | |||||||
\(450\) | −1122.67 | −0.117607 | ||||||||
\(451\) | 3794.94 | 0.396223 | ||||||||
\(452\) | 2288.58 | 0.238154 | ||||||||
\(453\) | −8164.91 | −0.846846 | ||||||||
\(454\) | 26237.7 | 2.71233 | ||||||||
\(455\) | 3527.36 | 0.363440 | ||||||||
\(456\) | −13763.3 | −1.41343 | ||||||||
\(457\) | 16111.7 | 1.64918 | 0.824590 | − | 0.565731i | \(-0.191406\pi\) | ||||
0.824590 | + | 0.565731i | \(0.191406\pi\) | |||||||
\(458\) | 26157.3 | 2.66866 | ||||||||
\(459\) | 1797.00 | 0.182738 | ||||||||
\(460\) | 495.443 | 0.0502177 | ||||||||
\(461\) | 3232.48 | 0.326576 | 0.163288 | − | 0.986578i | \(-0.447790\pi\) | ||||
0.163288 | + | 0.986578i | \(0.447790\pi\) | |||||||
\(462\) | −11063.8 | −1.11414 | ||||||||
\(463\) | 6763.53 | 0.678894 | 0.339447 | − | 0.940625i | \(-0.389760\pi\) | ||||
0.339447 | + | 0.940625i | \(0.389760\pi\) | |||||||
\(464\) | −2503.37 | −0.250465 | ||||||||
\(465\) | 403.986 | 0.0402891 | ||||||||
\(466\) | 30171.7 | 2.99931 | ||||||||
\(467\) | 2459.52 | 0.243711 | 0.121855 | − | 0.992548i | \(-0.461116\pi\) | ||||
0.121855 | + | 0.992548i | \(0.461116\pi\) | |||||||
\(468\) | 4766.43 | 0.470787 | ||||||||
\(469\) | 5764.48 | 0.567546 | ||||||||
\(470\) | −292.452 | −0.0287017 | ||||||||
\(471\) | −5281.13 | −0.516649 | ||||||||
\(472\) | −9431.66 | −0.919761 | ||||||||
\(473\) | −13653.6 | −1.32725 | ||||||||
\(474\) | 4926.99 | 0.477435 | ||||||||
\(475\) | −2583.72 | −0.249577 | ||||||||
\(476\) | −25311.3 | −2.43727 | ||||||||
\(477\) | −2475.53 | −0.237624 | ||||||||
\(478\) | 1061.03 | 0.101528 | ||||||||
\(479\) | 3207.84 | 0.305991 | 0.152996 | − | 0.988227i | \(-0.451108\pi\) | ||||
0.152996 | + | 0.988227i | \(0.451108\pi\) | |||||||
\(480\) | 1133.90 | 0.107823 | ||||||||
\(481\) | −572.173 | −0.0542388 | ||||||||
\(482\) | 29227.3 | 2.76197 | ||||||||
\(483\) | −395.980 | −0.0373038 | ||||||||
\(484\) | −4268.70 | −0.400892 | ||||||||
\(485\) | 1947.66 | 0.182348 | ||||||||
\(486\) | 1212.49 | 0.113168 | ||||||||
\(487\) | 12362.0 | 1.15026 | 0.575130 | − | 0.818062i | \(-0.304952\pi\) | ||||
0.575130 | + | 0.818062i | \(0.304952\pi\) | |||||||
\(488\) | 34045.9 | 3.15817 | ||||||||
\(489\) | 10698.4 | 0.989366 | ||||||||
\(490\) | −4081.32 | −0.376276 | ||||||||
\(491\) | 18430.3 | 1.69399 | 0.846993 | − | 0.531604i | \(-0.178410\pi\) | ||||
0.846993 | + | 0.531604i | \(0.178410\pi\) | |||||||
\(492\) | 5857.92 | 0.536779 | ||||||||
\(493\) | 1930.11 | 0.176324 | ||||||||
\(494\) | 16163.2 | 1.47210 | ||||||||
\(495\) | −1477.73 | −0.134180 | ||||||||
\(496\) | −2324.89 | −0.210465 | ||||||||
\(497\) | −16019.8 | −1.44585 | ||||||||
\(498\) | −4240.42 | −0.381562 | ||||||||
\(499\) | 9338.78 | 0.837798 | 0.418899 | − | 0.908033i | \(-0.362416\pi\) | ||||
0.418899 | + | 0.908033i | \(0.362416\pi\) | |||||||
\(500\) | 2112.08 | 0.188910 | ||||||||
\(501\) | 5928.22 | 0.528649 | ||||||||
\(502\) | 17517.2 | 1.55743 | ||||||||
\(503\) | 19444.6 | 1.72364 | 0.861819 | − | 0.507216i | \(-0.169326\pi\) | ||||
0.861819 | + | 0.507216i | \(0.169326\pi\) | |||||||
\(504\) | −8992.23 | −0.794733 | ||||||||
\(505\) | 1372.80 | 0.120968 | ||||||||
\(506\) | 960.895 | 0.0844210 | ||||||||
\(507\) | 3643.71 | 0.319177 | ||||||||
\(508\) | 26011.0 | 2.27176 | ||||||||
\(509\) | 11959.2 | 1.04142 | 0.520711 | − | 0.853733i | \(-0.325667\pi\) | ||||
0.520711 | + | 0.853733i | \(0.325667\pi\) | |||||||
\(510\) | −4981.34 | −0.432505 | ||||||||
\(511\) | 1022.89 | 0.0885520 | ||||||||
\(512\) | 24130.3 | 2.08285 | ||||||||
\(513\) | 2790.42 | 0.240156 | ||||||||
\(514\) | −13382.7 | −1.14842 | ||||||||
\(515\) | −4205.57 | −0.359844 | ||||||||
\(516\) | −21075.8 | −1.79808 | ||||||||
\(517\) | −384.943 | −0.0327462 | ||||||||
\(518\) | 2050.10 | 0.173893 | ||||||||
\(519\) | 5508.43 | 0.465883 | ||||||||
\(520\) | −6956.91 | −0.586694 | ||||||||
\(521\) | −2757.67 | −0.231892 | −0.115946 | − | 0.993256i | \(-0.536990\pi\) | ||||
−0.115946 | + | 0.993256i | \(0.536990\pi\) | |||||||
\(522\) | 1302.30 | 0.109196 | ||||||||
\(523\) | 3886.64 | 0.324954 | 0.162477 | − | 0.986712i | \(-0.448052\pi\) | ||||
0.162477 | + | 0.986712i | \(0.448052\pi\) | |||||||
\(524\) | 27457.9 | 2.28913 | ||||||||
\(525\) | −1688.07 | −0.140330 | ||||||||
\(526\) | −20696.8 | −1.71563 | ||||||||
\(527\) | 1792.50 | 0.148165 | ||||||||
\(528\) | 8504.14 | 0.700938 | ||||||||
\(529\) | −12132.6 | −0.997173 | ||||||||
\(530\) | 6862.24 | 0.562409 | ||||||||
\(531\) | 1912.21 | 0.156276 | ||||||||
\(532\) | −39303.8 | −3.20307 | ||||||||
\(533\) | −3622.20 | −0.294362 | ||||||||
\(534\) | −12017.4 | −0.973864 | ||||||||
\(535\) | −7445.22 | −0.601654 | ||||||||
\(536\) | −11369.1 | −0.916178 | ||||||||
\(537\) | −6725.60 | −0.540467 | ||||||||
\(538\) | 37235.6 | 2.98390 | ||||||||
\(539\) | −5372.09 | −0.429299 | ||||||||
\(540\) | −2281.04 | −0.181779 | ||||||||
\(541\) | −11307.5 | −0.898610 | −0.449305 | − | 0.893379i | \(-0.648328\pi\) | ||||
−0.449305 | + | 0.893379i | \(0.648328\pi\) | |||||||
\(542\) | −34173.2 | −2.70824 | ||||||||
\(543\) | −6254.24 | −0.494282 | ||||||||
\(544\) | 5031.15 | 0.396524 | ||||||||
\(545\) | −4935.60 | −0.387923 | ||||||||
\(546\) | 10560.2 | 0.827718 | ||||||||
\(547\) | 9195.12 | 0.718748 | 0.359374 | − | 0.933194i | \(-0.382990\pi\) | ||||
0.359374 | + | 0.933194i | \(0.382990\pi\) | |||||||
\(548\) | −15631.3 | −1.21850 | ||||||||
\(549\) | −6902.59 | −0.536604 | ||||||||
\(550\) | 4096.31 | 0.317577 | ||||||||
\(551\) | 2997.11 | 0.231727 | ||||||||
\(552\) | 780.981 | 0.0602187 | ||||||||
\(553\) | 7408.32 | 0.569681 | ||||||||
\(554\) | 500.940 | 0.0384168 | ||||||||
\(555\) | 273.822 | 0.0209425 | ||||||||
\(556\) | −54612.2 | −4.16560 | ||||||||
\(557\) | 12391.1 | 0.942596 | 0.471298 | − | 0.881974i | \(-0.343786\pi\) | ||||
0.471298 | + | 0.881974i | \(0.343786\pi\) | |||||||
\(558\) | 1209.45 | 0.0917565 | ||||||||
\(559\) | 13032.1 | 0.986045 | ||||||||
\(560\) | 9714.62 | 0.733067 | ||||||||
\(561\) | −6556.75 | −0.493451 | ||||||||
\(562\) | −18060.6 | −1.35559 | ||||||||
\(563\) | 9161.81 | 0.685834 | 0.342917 | − | 0.939366i | \(-0.388585\pi\) | ||||
0.342917 | + | 0.939366i | \(0.388585\pi\) | |||||||
\(564\) | −594.203 | −0.0443625 | ||||||||
\(565\) | 677.229 | 0.0504270 | ||||||||
\(566\) | 18426.0 | 1.36838 | ||||||||
\(567\) | 1823.11 | 0.135033 | ||||||||
\(568\) | 31595.4 | 2.33400 | ||||||||
\(569\) | −15614.8 | −1.15045 | −0.575226 | − | 0.817994i | \(-0.695086\pi\) | ||||
−0.575226 | + | 0.817994i | \(0.695086\pi\) | |||||||
\(570\) | −7735.12 | −0.568401 | ||||||||
\(571\) | 13526.3 | 0.991345 | 0.495673 | − | 0.868509i | \(-0.334922\pi\) | ||||
0.495673 | + | 0.868509i | \(0.334922\pi\) | |||||||
\(572\) | −17391.4 | −1.27128 | ||||||||
\(573\) | −12618.7 | −0.919991 | ||||||||
\(574\) | 12978.4 | 0.943742 | ||||||||
\(575\) | 146.610 | 0.0106331 | ||||||||
\(576\) | −2820.60 | −0.204037 | ||||||||
\(577\) | 21208.3 | 1.53018 | 0.765090 | − | 0.643923i | \(-0.222694\pi\) | ||||
0.765090 | + | 0.643923i | \(0.222694\pi\) | |||||||
\(578\) | 2411.76 | 0.173557 | ||||||||
\(579\) | 6141.85 | 0.440841 | ||||||||
\(580\) | −2450.01 | −0.175399 | ||||||||
\(581\) | −6375.98 | −0.455284 | ||||||||
\(582\) | 5830.89 | 0.415289 | ||||||||
\(583\) | 9032.50 | 0.641660 | ||||||||
\(584\) | −2017.42 | −0.142948 | ||||||||
\(585\) | 1410.47 | 0.0996850 | ||||||||
\(586\) | 5852.09 | 0.412539 | ||||||||
\(587\) | 7975.12 | 0.560764 | 0.280382 | − | 0.959888i | \(-0.409539\pi\) | ||||
0.280382 | + | 0.959888i | \(0.409539\pi\) | |||||||
\(588\) | −8292.44 | −0.581589 | ||||||||
\(589\) | 2783.43 | 0.194719 | ||||||||
\(590\) | −5300.69 | −0.369875 | ||||||||
\(591\) | −13385.7 | −0.931662 | ||||||||
\(592\) | −1575.81 | −0.109401 | ||||||||
\(593\) | −6169.18 | −0.427214 | −0.213607 | − | 0.976920i | \(-0.568521\pi\) | ||||
−0.213607 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(594\) | −4424.02 | −0.305588 | ||||||||
\(595\) | −7490.03 | −0.516069 | ||||||||
\(596\) | 12914.9 | 0.887611 | ||||||||
\(597\) | 5780.39 | 0.396274 | ||||||||
\(598\) | −917.158 | −0.0627181 | ||||||||
\(599\) | 10909.8 | 0.744180 | 0.372090 | − | 0.928197i | \(-0.378641\pi\) | ||||
0.372090 | + | 0.928197i | \(0.378641\pi\) | |||||||
\(600\) | 3329.33 | 0.226532 | ||||||||
\(601\) | −11926.7 | −0.809483 | −0.404741 | − | 0.914431i | \(-0.632638\pi\) | ||||
−0.404741 | + | 0.914431i | \(0.632638\pi\) | |||||||
\(602\) | −46694.2 | −3.16132 | ||||||||
\(603\) | 2305.02 | 0.155668 | ||||||||
\(604\) | 45986.5 | 3.09795 | ||||||||
\(605\) | −1263.18 | −0.0848853 | ||||||||
\(606\) | 4109.86 | 0.275498 | ||||||||
\(607\) | −12043.2 | −0.805301 | −0.402650 | − | 0.915354i | \(-0.631911\pi\) | ||||
−0.402650 | + | 0.915354i | \(0.631911\pi\) | |||||||
\(608\) | 7812.47 | 0.521114 | ||||||||
\(609\) | 1958.16 | 0.130293 | ||||||||
\(610\) | 19134.2 | 1.27003 | ||||||||
\(611\) | 367.422 | 0.0243278 | ||||||||
\(612\) | −10121.1 | −0.668498 | ||||||||
\(613\) | 11777.4 | 0.775992 | 0.387996 | − | 0.921661i | \(-0.373168\pi\) | ||||
0.387996 | + | 0.921661i | \(0.373168\pi\) | |||||||
\(614\) | 23077.6 | 1.51683 | ||||||||
\(615\) | 1733.46 | 0.113658 | ||||||||
\(616\) | 32810.1 | 2.14603 | ||||||||
\(617\) | −2907.19 | −0.189691 | −0.0948454 | − | 0.995492i | \(-0.530236\pi\) | ||||
−0.0948454 | + | 0.995492i | \(0.530236\pi\) | |||||||
\(618\) | −12590.6 | −0.819527 | ||||||||
\(619\) | −839.647 | −0.0545206 | −0.0272603 | − | 0.999628i | \(-0.508678\pi\) | ||||
−0.0272603 | + | 0.999628i | \(0.508678\pi\) | |||||||
\(620\) | −2275.34 | −0.147387 | ||||||||
\(621\) | −158.339 | −0.0102317 | ||||||||
\(622\) | −28730.0 | −1.85204 | ||||||||
\(623\) | −18069.6 | −1.16203 | ||||||||
\(624\) | −8117.06 | −0.520741 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 37515.6 | 2.39525 | ||||||||
\(627\) | −10181.4 | −0.648497 | ||||||||
\(628\) | 29744.4 | 1.89002 | ||||||||
\(629\) | 1214.96 | 0.0770167 | ||||||||
\(630\) | −5053.73 | −0.319596 | ||||||||
\(631\) | 9825.37 | 0.619876 | 0.309938 | − | 0.950757i | \(-0.399692\pi\) | ||||
0.309938 | + | 0.950757i | \(0.399692\pi\) | |||||||
\(632\) | −14611.2 | −0.919625 | ||||||||
\(633\) | 13461.7 | 0.845265 | ||||||||
\(634\) | −3471.64 | −0.217471 | ||||||||
\(635\) | 7697.11 | 0.481024 | ||||||||
\(636\) | 13942.7 | 0.869283 | ||||||||
\(637\) | 5127.57 | 0.318935 | ||||||||
\(638\) | −4751.72 | −0.294863 | ||||||||
\(639\) | −6405.75 | −0.396569 | ||||||||
\(640\) | 10842.5 | 0.669669 | ||||||||
\(641\) | −22040.3 | −1.35810 | −0.679049 | − | 0.734093i | \(-0.737608\pi\) | ||||
−0.679049 | + | 0.734093i | \(0.737608\pi\) | |||||||
\(642\) | −22289.4 | −1.37024 | ||||||||
\(643\) | −21366.9 | −1.31047 | −0.655233 | − | 0.755427i | \(-0.727429\pi\) | ||||
−0.655233 | + | 0.755427i | \(0.727429\pi\) | |||||||
\(644\) | 2230.24 | 0.136466 | ||||||||
\(645\) | −6236.70 | −0.380728 | ||||||||
\(646\) | −34321.0 | −2.09031 | ||||||||
\(647\) | −5826.03 | −0.354011 | −0.177005 | − | 0.984210i | \(-0.556641\pi\) | ||||
−0.177005 | + | 0.984210i | \(0.556641\pi\) | |||||||
\(648\) | −3595.68 | −0.217981 | ||||||||
\(649\) | −6977.10 | −0.421995 | ||||||||
\(650\) | −3909.86 | −0.235934 | ||||||||
\(651\) | 1818.55 | 0.109485 | ||||||||
\(652\) | −60255.8 | −3.61933 | ||||||||
\(653\) | −20058.4 | −1.20206 | −0.601030 | − | 0.799227i | \(-0.705243\pi\) | ||||
−0.601030 | + | 0.799227i | \(0.705243\pi\) | |||||||
\(654\) | −14776.2 | −0.883477 | ||||||||
\(655\) | 8125.26 | 0.484703 | ||||||||
\(656\) | −9975.82 | −0.593735 | ||||||||
\(657\) | 409.019 | 0.0242882 | ||||||||
\(658\) | −1316.48 | −0.0779963 | ||||||||
\(659\) | −28535.3 | −1.68676 | −0.843382 | − | 0.537315i | \(-0.819439\pi\) | ||||
−0.843382 | + | 0.537315i | \(0.819439\pi\) | |||||||
\(660\) | 8322.89 | 0.490860 | ||||||||
\(661\) | 15044.6 | 0.885274 | 0.442637 | − | 0.896701i | \(-0.354043\pi\) | ||||
0.442637 | + | 0.896701i | \(0.354043\pi\) | |||||||
\(662\) | 37602.6 | 2.20765 | ||||||||
\(663\) | 6258.31 | 0.366595 | ||||||||
\(664\) | 12575.2 | 0.734956 | ||||||||
\(665\) | −11630.7 | −0.678222 | ||||||||
\(666\) | 819.765 | 0.0476956 | ||||||||
\(667\) | −170.067 | −0.00987262 | ||||||||
\(668\) | −33389.0 | −1.93392 | ||||||||
\(669\) | 15339.8 | 0.886506 | ||||||||
\(670\) | −6389.57 | −0.368434 | ||||||||
\(671\) | 25185.6 | 1.44900 | ||||||||
\(672\) | 5104.27 | 0.293008 | ||||||||
\(673\) | 15511.3 | 0.888434 | 0.444217 | − | 0.895919i | \(-0.353482\pi\) | ||||
0.444217 | + | 0.895919i | \(0.353482\pi\) | |||||||
\(674\) | −32338.4 | −1.84811 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −20522.1 | −1.16762 | ||||||||
\(677\) | −10695.3 | −0.607170 | −0.303585 | − | 0.952804i | \(-0.598184\pi\) | ||||
−0.303585 | + | 0.952804i | \(0.598184\pi\) | |||||||
\(678\) | 2027.48 | 0.114845 | ||||||||
\(679\) | 8767.43 | 0.495527 | ||||||||
\(680\) | 14772.4 | 0.833081 | ||||||||
\(681\) | 15775.3 | 0.887679 | ||||||||
\(682\) | −4412.94 | −0.247772 | ||||||||
\(683\) | −11144.8 | −0.624367 | −0.312184 | − | 0.950022i | \(-0.601060\pi\) | ||||
−0.312184 | + | 0.950022i | \(0.601060\pi\) | |||||||
\(684\) | −15716.2 | −0.878545 | ||||||||
\(685\) | −4625.58 | −0.258006 | ||||||||
\(686\) | 20148.5 | 1.12139 | ||||||||
\(687\) | 15726.9 | 0.873390 | ||||||||
\(688\) | 35891.4 | 1.98887 | ||||||||
\(689\) | −8621.37 | −0.476703 | ||||||||
\(690\) | 438.919 | 0.0242165 | ||||||||
\(691\) | −5380.30 | −0.296203 | −0.148102 | − | 0.988972i | \(-0.547316\pi\) | ||||
−0.148102 | + | 0.988972i | \(0.547316\pi\) | |||||||
\(692\) | −31024.7 | −1.70431 | ||||||||
\(693\) | −6652.03 | −0.364632 | ||||||||
\(694\) | 5760.31 | 0.315070 | ||||||||
\(695\) | −16160.7 | −0.882029 | ||||||||
\(696\) | −3862.02 | −0.210330 | ||||||||
\(697\) | 7691.42 | 0.417982 | ||||||||
\(698\) | −38204.2 | −2.07171 | ||||||||
\(699\) | 18140.6 | 0.981601 | ||||||||
\(700\) | 9507.56 | 0.513360 | ||||||||
\(701\) | 21377.2 | 1.15179 | 0.575896 | − | 0.817523i | \(-0.304653\pi\) | ||||
0.575896 | + | 0.817523i | \(0.304653\pi\) | |||||||
\(702\) | 4222.65 | 0.227028 | ||||||||
\(703\) | 1886.61 | 0.101216 | ||||||||
\(704\) | 10291.6 | 0.550964 | ||||||||
\(705\) | −175.835 | −0.00939337 | ||||||||
\(706\) | −5552.97 | −0.296018 | ||||||||
\(707\) | 6179.67 | 0.328727 | ||||||||
\(708\) | −10769.9 | −0.571694 | ||||||||
\(709\) | −1384.02 | −0.0733116 | −0.0366558 | − | 0.999328i | \(-0.511671\pi\) | ||||
−0.0366558 | + | 0.999328i | \(0.511671\pi\) | |||||||
\(710\) | 17756.9 | 0.938600 | ||||||||
\(711\) | 2962.33 | 0.156253 | ||||||||
\(712\) | 35638.1 | 1.87583 | ||||||||
\(713\) | −157.942 | −0.00829592 | ||||||||
\(714\) | −22423.6 | −1.17532 | ||||||||
\(715\) | −5146.40 | −0.269181 | ||||||||
\(716\) | 37880.0 | 1.97715 | ||||||||
\(717\) | 637.936 | 0.0332275 | ||||||||
\(718\) | −61879.7 | −3.21634 | ||||||||
\(719\) | −10439.9 | −0.541504 | −0.270752 | − | 0.962649i | \(-0.587272\pi\) | ||||
−0.270752 | + | 0.962649i | \(0.587272\pi\) | |||||||
\(720\) | 3884.54 | 0.201067 | ||||||||
\(721\) | −18931.4 | −0.977869 | ||||||||
\(722\) | −19070.3 | −0.982996 | ||||||||
\(723\) | 17572.8 | 0.903926 | ||||||||
\(724\) | 35225.2 | 1.80820 | ||||||||
\(725\) | −725.000 | −0.0371391 | ||||||||
\(726\) | −3781.70 | −0.193322 | ||||||||
\(727\) | 24684.5 | 1.25928 | 0.629640 | − | 0.776887i | \(-0.283203\pi\) | ||||
0.629640 | + | 0.776887i | \(0.283203\pi\) | |||||||
\(728\) | −31316.7 | −1.59433 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −1133.81 | −0.0574853 | ||||||||
\(731\) | −27672.5 | −1.40014 | ||||||||
\(732\) | 38876.8 | 1.96302 | ||||||||
\(733\) | −858.035 | −0.0432363 | −0.0216182 | − | 0.999766i | \(-0.506882\pi\) | ||||
−0.0216182 | + | 0.999766i | \(0.506882\pi\) | |||||||
\(734\) | −56182.5 | −2.82525 | ||||||||
\(735\) | −2453.87 | −0.123146 | ||||||||
\(736\) | −443.309 | −0.0222019 | ||||||||
\(737\) | −8410.35 | −0.420352 | ||||||||
\(738\) | 5189.61 | 0.258851 | ||||||||
\(739\) | −10331.9 | −0.514299 | −0.257149 | − | 0.966372i | \(-0.582783\pi\) | ||||
−0.257149 | + | 0.966372i | \(0.582783\pi\) | |||||||
\(740\) | −1542.22 | −0.0766124 | ||||||||
\(741\) | 9718.01 | 0.481782 | ||||||||
\(742\) | 30890.5 | 1.52834 | ||||||||
\(743\) | −27385.1 | −1.35217 | −0.676084 | − | 0.736824i | \(-0.736324\pi\) | ||||
−0.676084 | + | 0.736824i | \(0.736324\pi\) | |||||||
\(744\) | −3586.68 | −0.176739 | ||||||||
\(745\) | 3821.75 | 0.187944 | ||||||||
\(746\) | 40164.9 | 1.97123 | ||||||||
\(747\) | −2549.53 | −0.124876 | ||||||||
\(748\) | 36929.0 | 1.80516 | ||||||||
\(749\) | −33514.8 | −1.63499 | ||||||||
\(750\) | 1871.12 | 0.0910982 | ||||||||
\(751\) | −40267.8 | −1.95658 | −0.978291 | − | 0.207234i | \(-0.933554\pi\) | ||||
−0.978291 | + | 0.207234i | \(0.933554\pi\) | |||||||
\(752\) | 1011.91 | 0.0490697 | ||||||||
\(753\) | 10532.1 | 0.509709 | ||||||||
\(754\) | 4535.44 | 0.219060 | ||||||||
\(755\) | 13608.2 | 0.655964 | ||||||||
\(756\) | −10268.2 | −0.493981 | ||||||||
\(757\) | −7047.02 | −0.338346 | −0.169173 | − | 0.985586i | \(-0.554110\pi\) | ||||
−0.169173 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(758\) | −48956.0 | −2.34586 | ||||||||
\(759\) | 577.733 | 0.0276290 | ||||||||
\(760\) | 22938.8 | 1.09484 | ||||||||
\(761\) | 38699.3 | 1.84343 | 0.921714 | − | 0.387871i | \(-0.126789\pi\) | ||||
0.921714 | + | 0.387871i | \(0.126789\pi\) | |||||||
\(762\) | 23043.5 | 1.09551 | ||||||||
\(763\) | −22217.7 | −1.05417 | ||||||||
\(764\) | 71071.3 | 3.36554 | ||||||||
\(765\) | −2995.00 | −0.141548 | ||||||||
\(766\) | −33231.6 | −1.56750 | ||||||||
\(767\) | 6659.52 | 0.313509 | ||||||||
\(768\) | 24938.6 | 1.17174 | ||||||||
\(769\) | −2374.27 | −0.111337 | −0.0556686 | − | 0.998449i | \(-0.517729\pi\) | ||||
−0.0556686 | + | 0.998449i | \(0.517729\pi\) | |||||||
\(770\) | 18439.6 | 0.863010 | ||||||||
\(771\) | −8046.29 | −0.375850 | ||||||||
\(772\) | −34592.2 | −1.61270 | ||||||||
\(773\) | −12947.9 | −0.602464 | −0.301232 | − | 0.953551i | \(-0.597398\pi\) | ||||
−0.301232 | + | 0.953551i | \(0.597398\pi\) | |||||||
\(774\) | −18671.4 | −0.867091 | ||||||||
\(775\) | −673.311 | −0.0312078 | ||||||||
\(776\) | −17291.7 | −0.799920 | ||||||||
\(777\) | 1232.61 | 0.0569109 | ||||||||
\(778\) | 75024.6 | 3.45728 | ||||||||
\(779\) | 11943.4 | 0.549314 | ||||||||
\(780\) | −7944.05 | −0.364670 | ||||||||
\(781\) | 23372.8 | 1.07086 | ||||||||
\(782\) | 1947.50 | 0.0890570 | ||||||||
\(783\) | 783.000 | 0.0357371 | ||||||||
\(784\) | 14121.7 | 0.643300 | ||||||||
\(785\) | 8801.88 | 0.400194 | ||||||||
\(786\) | 24325.3 | 1.10389 | ||||||||
\(787\) | −15659.1 | −0.709260 | −0.354630 | − | 0.935007i | \(-0.615393\pi\) | ||||
−0.354630 | + | 0.935007i | \(0.615393\pi\) | |||||||
\(788\) | 75390.8 | 3.40823 | ||||||||
\(789\) | −12443.8 | −0.561485 | ||||||||
\(790\) | −8211.66 | −0.369820 | ||||||||
\(791\) | 3048.56 | 0.137034 | ||||||||
\(792\) | 13119.6 | 0.588617 | ||||||||
\(793\) | −24039.2 | −1.07649 | ||||||||
\(794\) | 11114.7 | 0.496786 | ||||||||
\(795\) | 4125.88 | 0.184063 | ||||||||
\(796\) | −32556.4 | −1.44966 | ||||||||
\(797\) | 36033.7 | 1.60148 | 0.800739 | − | 0.599013i | \(-0.204440\pi\) | ||||
0.800739 | + | 0.599013i | \(0.204440\pi\) | |||||||
\(798\) | −34819.8 | −1.54462 | ||||||||
\(799\) | −780.186 | −0.0345444 | ||||||||
\(800\) | −1889.83 | −0.0835195 | ||||||||
\(801\) | −7225.39 | −0.318722 | ||||||||
\(802\) | 37927.4 | 1.66991 | ||||||||
\(803\) | −1492.39 | −0.0655858 | ||||||||
\(804\) | −12982.3 | −0.569467 | ||||||||
\(805\) | 659.967 | 0.0288954 | ||||||||
\(806\) | 4212.08 | 0.184075 | ||||||||
\(807\) | 22387.7 | 0.976560 | ||||||||
\(808\) | −12188.0 | −0.530658 | ||||||||
\(809\) | 8941.26 | 0.388576 | 0.194288 | − | 0.980945i | \(-0.437760\pi\) | ||||
0.194288 | + | 0.980945i | \(0.437760\pi\) | |||||||
\(810\) | −2020.81 | −0.0876593 | ||||||||
\(811\) | 31988.8 | 1.38506 | 0.692528 | − | 0.721391i | \(-0.256497\pi\) | ||||
0.692528 | + | 0.721391i | \(0.256497\pi\) | |||||||
\(812\) | −11028.8 | −0.476643 | ||||||||
\(813\) | −20546.4 | −0.886341 | ||||||||
\(814\) | −2991.09 | −0.128793 | ||||||||
\(815\) | −17830.7 | −0.766359 | ||||||||
\(816\) | 17235.8 | 0.739430 | ||||||||
\(817\) | −42970.3 | −1.84008 | ||||||||
\(818\) | 65352.8 | 2.79341 | ||||||||
\(819\) | 6349.25 | 0.270892 | ||||||||
\(820\) | −9763.19 | −0.415787 | ||||||||
\(821\) | −27919.3 | −1.18683 | −0.593417 | − | 0.804895i | \(-0.702222\pi\) | ||||
−0.593417 | + | 0.804895i | \(0.702222\pi\) | |||||||
\(822\) | −13848.0 | −0.587597 | ||||||||
\(823\) | 44835.5 | 1.89899 | 0.949494 | − | 0.313784i | \(-0.101597\pi\) | ||||
0.949494 | + | 0.313784i | \(0.101597\pi\) | |||||||
\(824\) | 37337.9 | 1.57855 | ||||||||
\(825\) | 2462.88 | 0.103935 | ||||||||
\(826\) | −23861.2 | −1.00513 | ||||||||
\(827\) | −26829.4 | −1.12811 | −0.564056 | − | 0.825737i | \(-0.690760\pi\) | ||||
−0.564056 | + | 0.825737i | \(0.690760\pi\) | |||||||
\(828\) | 891.797 | 0.0374300 | ||||||||
\(829\) | −34790.3 | −1.45756 | −0.728780 | − | 0.684748i | \(-0.759912\pi\) | ||||
−0.728780 | + | 0.684748i | \(0.759912\pi\) | |||||||
\(830\) | 7067.37 | 0.295557 | ||||||||
\(831\) | 301.187 | 0.0125729 | ||||||||
\(832\) | −9823.14 | −0.409322 | ||||||||
\(833\) | −10887.9 | −0.452874 | ||||||||
\(834\) | −48381.7 | −2.00878 | ||||||||
\(835\) | −9880.36 | −0.409490 | ||||||||
\(836\) | 57344.0 | 2.37235 | ||||||||
\(837\) | 727.176 | 0.0300297 | ||||||||
\(838\) | −54874.6 | −2.26206 | ||||||||
\(839\) | 23387.9 | 0.962383 | 0.481192 | − | 0.876615i | \(-0.340204\pi\) | ||||
0.481192 | + | 0.876615i | \(0.340204\pi\) | |||||||
\(840\) | 14987.0 | 0.615598 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 65025.9 | 2.66145 | ||||||||
\(843\) | −10858.8 | −0.443651 | ||||||||
\(844\) | −75818.9 | −3.09217 | ||||||||
\(845\) | −6072.85 | −0.247234 | ||||||||
\(846\) | −526.413 | −0.0213930 | ||||||||
\(847\) | −5686.23 | −0.230675 | ||||||||
\(848\) | −23743.9 | −0.961520 | ||||||||
\(849\) | 11078.5 | 0.447838 | ||||||||
\(850\) | 8302.23 | 0.335017 | ||||||||
\(851\) | −107.053 | −0.00431226 | ||||||||
\(852\) | 36078.5 | 1.45074 | ||||||||
\(853\) | 3915.34 | 0.157161 | 0.0785807 | − | 0.996908i | \(-0.474961\pi\) | ||||
0.0785807 | + | 0.996908i | \(0.474961\pi\) | |||||||
\(854\) | 86132.8 | 3.45129 | ||||||||
\(855\) | −4650.70 | −0.186024 | ||||||||
\(856\) | 66100.3 | 2.63932 | ||||||||
\(857\) | 31094.8 | 1.23942 | 0.619708 | − | 0.784833i | \(-0.287251\pi\) | ||||
0.619708 | + | 0.784833i | \(0.287251\pi\) | |||||||
\(858\) | −15407.2 | −0.613047 | ||||||||
\(859\) | 9069.15 | 0.360227 | 0.180114 | − | 0.983646i | \(-0.442353\pi\) | ||||
0.180114 | + | 0.983646i | \(0.442353\pi\) | |||||||
\(860\) | 35126.4 | 1.39279 | ||||||||
\(861\) | 7803.19 | 0.308864 | ||||||||
\(862\) | 3901.20 | 0.154148 | ||||||||
\(863\) | −18282.8 | −0.721151 | −0.360576 | − | 0.932730i | \(-0.617420\pi\) | ||||
−0.360576 | + | 0.932730i | \(0.617420\pi\) | |||||||
\(864\) | 2041.02 | 0.0803667 | ||||||||
\(865\) | −9180.72 | −0.360872 | ||||||||
\(866\) | −45704.3 | −1.79341 | ||||||||
\(867\) | 1450.06 | 0.0568011 | ||||||||
\(868\) | −10242.5 | −0.400521 | ||||||||
\(869\) | −10808.7 | −0.421933 | ||||||||
\(870\) | −2170.50 | −0.0845825 | ||||||||
\(871\) | 8027.54 | 0.312288 | ||||||||
\(872\) | 43819.3 | 1.70173 | ||||||||
\(873\) | 3505.79 | 0.135914 | ||||||||
\(874\) | 3024.12 | 0.117039 | ||||||||
\(875\) | 2813.45 | 0.108699 | ||||||||
\(876\) | −2303.68 | −0.0888517 | ||||||||
\(877\) | 4534.49 | 0.174594 | 0.0872970 | − | 0.996182i | \(-0.472177\pi\) | ||||
0.0872970 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(878\) | 20201.2 | 0.776490 | ||||||||
\(879\) | 3518.54 | 0.135014 | ||||||||
\(880\) | −14173.6 | −0.542944 | ||||||||
\(881\) | 27949.4 | 1.06883 | 0.534415 | − | 0.845223i | \(-0.320532\pi\) | ||||
0.534415 | + | 0.845223i | \(0.320532\pi\) | |||||||
\(882\) | −7346.38 | −0.280460 | ||||||||
\(883\) | 7755.96 | 0.295593 | 0.147797 | − | 0.989018i | \(-0.452782\pi\) | ||||
0.147797 | + | 0.989018i | \(0.452782\pi\) | |||||||
\(884\) | −35248.1 | −1.34109 | ||||||||
\(885\) | −3187.01 | −0.121051 | ||||||||
\(886\) | 32543.9 | 1.23401 | ||||||||
\(887\) | 28219.5 | 1.06823 | 0.534115 | − | 0.845412i | \(-0.320645\pi\) | ||||
0.534115 | + | 0.845412i | \(0.320645\pi\) | |||||||
\(888\) | −2431.05 | −0.0918701 | ||||||||
\(889\) | 34648.7 | 1.30718 | ||||||||
\(890\) | 20029.0 | 0.754352 | ||||||||
\(891\) | −2659.91 | −0.100012 | ||||||||
\(892\) | −86397.2 | −3.24304 | ||||||||
\(893\) | −1211.49 | −0.0453985 | ||||||||
\(894\) | 11441.5 | 0.428033 | ||||||||
\(895\) | 11209.3 | 0.418644 | ||||||||
\(896\) | 48807.8 | 1.81981 | ||||||||
\(897\) | −551.436 | −0.0205261 | ||||||||
\(898\) | 24682.7 | 0.917230 | ||||||||
\(899\) | 781.041 | 0.0289757 | ||||||||
\(900\) | 3801.74 | 0.140805 | ||||||||
\(901\) | 18306.7 | 0.676897 | ||||||||
\(902\) | −18935.4 | −0.698980 | ||||||||
\(903\) | −28074.6 | −1.03462 | ||||||||
\(904\) | −6012.58 | −0.221212 | ||||||||
\(905\) | 10423.7 | 0.382869 | ||||||||
\(906\) | 40740.1 | 1.49393 | ||||||||
\(907\) | 182.994 | 0.00669926 | 0.00334963 | − | 0.999994i | \(-0.498934\pi\) | ||||
0.00334963 | + | 0.999994i | \(0.498934\pi\) | |||||||
\(908\) | −88849.6 | −3.24733 | ||||||||
\(909\) | 2471.03 | 0.0901639 | ||||||||
\(910\) | −17600.3 | −0.641148 | ||||||||
\(911\) | −15870.4 | −0.577179 | −0.288590 | − | 0.957453i | \(-0.593186\pi\) | ||||
−0.288590 | + | 0.957453i | \(0.593186\pi\) | |||||||
\(912\) | 26764.1 | 0.971765 | ||||||||
\(913\) | 9302.52 | 0.337205 | ||||||||
\(914\) | −80391.9 | −2.90933 | ||||||||
\(915\) | 11504.3 | 0.415651 | ||||||||
\(916\) | −88577.2 | −3.19506 | ||||||||
\(917\) | 36576.0 | 1.31717 | ||||||||
\(918\) | −8966.41 | −0.322370 | ||||||||
\(919\) | −14707.3 | −0.527908 | −0.263954 | − | 0.964535i | \(-0.585027\pi\) | ||||
−0.263954 | + | 0.964535i | \(0.585027\pi\) | |||||||
\(920\) | −1301.63 | −0.0466452 | ||||||||
\(921\) | 13875.3 | 0.496423 | ||||||||
\(922\) | −16129.0 | −0.576116 | ||||||||
\(923\) | −22308.9 | −0.795566 | ||||||||
\(924\) | 37465.6 | 1.33391 | ||||||||
\(925\) | −456.369 | −0.0162220 | ||||||||
\(926\) | −33747.6 | −1.19764 | ||||||||
\(927\) | −7570.02 | −0.268212 | ||||||||
\(928\) | 2192.20 | 0.0775459 | ||||||||
\(929\) | 4008.12 | 0.141552 | 0.0707762 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707762 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(930\) | −2015.75 | −0.0710743 | ||||||||
\(931\) | −16907.0 | −0.595171 | ||||||||
\(932\) | −102171. | −3.59092 | ||||||||
\(933\) | −17273.7 | −0.606127 | ||||||||
\(934\) | −12272.1 | −0.429932 | ||||||||
\(935\) | 10927.9 | 0.382226 | ||||||||
\(936\) | −12522.4 | −0.437296 | ||||||||
\(937\) | 17088.4 | 0.595788 | 0.297894 | − | 0.954599i | \(-0.403716\pi\) | ||||
0.297894 | + | 0.954599i | \(0.403716\pi\) | |||||||
\(938\) | −28762.8 | −1.00121 | ||||||||
\(939\) | 22556.1 | 0.783908 | ||||||||
\(940\) | 990.339 | 0.0343631 | ||||||||
\(941\) | 1981.60 | 0.0686486 | 0.0343243 | − | 0.999411i | \(-0.489072\pi\) | ||||
0.0343243 | + | 0.999411i | \(0.489072\pi\) | |||||||
\(942\) | 26351.0 | 0.911424 | ||||||||
\(943\) | −677.712 | −0.0234033 | ||||||||
\(944\) | 18340.8 | 0.632355 | ||||||||
\(945\) | −3038.52 | −0.104596 | ||||||||
\(946\) | 68126.5 | 2.34142 | ||||||||
\(947\) | −19125.0 | −0.656260 | −0.328130 | − | 0.944633i | \(-0.606418\pi\) | ||||
−0.328130 | + | 0.944633i | \(0.606418\pi\) | |||||||
\(948\) | −16684.4 | −0.571609 | ||||||||
\(949\) | 1424.46 | 0.0487251 | ||||||||
\(950\) | 12891.9 | 0.440281 | ||||||||
\(951\) | −2087.31 | −0.0711730 | ||||||||
\(952\) | 66498.1 | 2.26388 | ||||||||
\(953\) | 10338.6 | 0.351416 | 0.175708 | − | 0.984442i | \(-0.443778\pi\) | ||||
0.175708 | + | 0.984442i | \(0.443778\pi\) | |||||||
\(954\) | 12352.0 | 0.419195 | ||||||||
\(955\) | 21031.2 | 0.712622 | ||||||||
\(956\) | −3592.99 | −0.121554 | ||||||||
\(957\) | −2856.95 | −0.0965015 | ||||||||
\(958\) | −16006.0 | −0.539802 | ||||||||
\(959\) | −20822.1 | −0.701128 | ||||||||
\(960\) | 4701.00 | 0.158046 | ||||||||
\(961\) | −29065.6 | −0.975652 | ||||||||
\(962\) | 2854.94 | 0.0956831 | ||||||||
\(963\) | −13401.4 | −0.448447 | ||||||||
\(964\) | −98973.5 | −3.30677 | ||||||||
\(965\) | −10236.4 | −0.341474 | ||||||||
\(966\) | 1975.80 | 0.0658079 | ||||||||
\(967\) | −18633.6 | −0.619664 | −0.309832 | − | 0.950791i | \(-0.600273\pi\) | ||||
−0.309832 | + | 0.950791i | \(0.600273\pi\) | |||||||
\(968\) | 11214.8 | 0.372373 | ||||||||
\(969\) | −20635.3 | −0.684109 | ||||||||
\(970\) | −9718.15 | −0.321681 | ||||||||
\(971\) | −39486.5 | −1.30503 | −0.652515 | − | 0.757776i | \(-0.726286\pi\) | ||||
−0.652515 | + | 0.757776i | \(0.726286\pi\) | |||||||
\(972\) | −4105.88 | −0.135490 | ||||||||
\(973\) | −72747.6 | −2.39690 | ||||||||
\(974\) | −61682.1 | −2.02918 | ||||||||
\(975\) | −2350.78 | −0.0772156 | ||||||||
\(976\) | −66205.8 | −2.17131 | ||||||||
\(977\) | 33392.3 | 1.09346 | 0.546731 | − | 0.837308i | \(-0.315872\pi\) | ||||
0.546731 | + | 0.837308i | \(0.315872\pi\) | |||||||
\(978\) | −53381.5 | −1.74535 | ||||||||
\(979\) | 26363.4 | 0.860651 | ||||||||
\(980\) | 13820.7 | 0.450497 | ||||||||
\(981\) | −8884.08 | −0.289141 | ||||||||
\(982\) | −91960.7 | −2.98838 | ||||||||
\(983\) | 20923.0 | 0.678880 | 0.339440 | − | 0.940628i | \(-0.389762\pi\) | ||||
0.339440 | + | 0.940628i | \(0.389762\pi\) | |||||||
\(984\) | −15390.0 | −0.498593 | ||||||||
\(985\) | 22309.4 | 0.721662 | ||||||||
\(986\) | −9630.59 | −0.311055 | ||||||||
\(987\) | −791.524 | −0.0255263 | ||||||||
\(988\) | −54733.9 | −1.76247 | ||||||||
\(989\) | 2438.30 | 0.0783957 | ||||||||
\(990\) | 7373.36 | 0.236708 | ||||||||
\(991\) | 44681.6 | 1.43225 | 0.716124 | − | 0.697973i | \(-0.245914\pi\) | ||||
0.716124 | + | 0.697973i | \(0.245914\pi\) | |||||||
\(992\) | 2035.91 | 0.0651615 | ||||||||
\(993\) | 22608.3 | 0.722512 | ||||||||
\(994\) | 79933.2 | 2.55063 | ||||||||
\(995\) | −9633.98 | −0.306953 | ||||||||
\(996\) | 14359.5 | 0.456825 | ||||||||
\(997\) | −49844.7 | −1.58335 | −0.791674 | − | 0.610944i | \(-0.790790\pi\) | ||||
−0.791674 | + | 0.610944i | \(0.790790\pi\) | |||||||
\(998\) | −46597.2 | −1.47797 | ||||||||
\(999\) | 492.879 | 0.0156096 |
(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 | 435.4.a.g.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 1305.4.a.i.1.6 | 6 | |||
5.4 | even | 2 | 2175.4.a.l.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.g.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1305.4.a.i.1.6 | 6 | 3.2 | odd | 2 | |||
2175.4.a.l.1.6 | 6 | 5.4 | even | 2 |