Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1445,2,Mod(1,1445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1445, 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("1445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1445 = 5 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1445.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: | \(11.5383830921\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 21 x^{8} - 232 x^{7} + 44 x^{6} + 424 x^{5} - 137 x^{4} + \cdots + 17 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 85) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80583\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80583 | −1.27691 | −0.638457 | − | 0.769657i | \(-0.720427\pi\) | ||||
−0.638457 | + | 0.769657i | \(0.720427\pi\) | |||||||
\(3\) | −0.687917 | −0.397169 | −0.198585 | − | 0.980084i | \(-0.563634\pi\) | ||||
−0.198585 | + | 0.980084i | \(0.563634\pi\) | |||||||
\(4\) | 1.26102 | 0.630511 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.24226 | 0.507151 | ||||||||
\(7\) | 4.34193 | 1.64109 | 0.820547 | − | 0.571579i | \(-0.193669\pi\) | ||||
0.820547 | + | 0.571579i | \(0.193669\pi\) | |||||||
\(8\) | 1.33447 | 0.471806 | ||||||||
\(9\) | −2.52677 | −0.842257 | ||||||||
\(10\) | 1.80583 | 0.571054 | ||||||||
\(11\) | 0.0525004 | 0.0158295 | 0.00791474 | − | 0.999969i | \(-0.497481\pi\) | ||||
0.00791474 | + | 0.999969i | \(0.497481\pi\) | |||||||
\(12\) | −0.867478 | −0.250419 | ||||||||
\(13\) | 3.02508 | 0.839006 | 0.419503 | − | 0.907754i | \(-0.362204\pi\) | ||||
0.419503 | + | 0.907754i | \(0.362204\pi\) | |||||||
\(14\) | −7.84078 | −2.09554 | ||||||||
\(15\) | 0.687917 | 0.177619 | ||||||||
\(16\) | −4.93187 | −1.23297 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 4.56292 | 1.07549 | ||||||||
\(19\) | 7.82043 | 1.79413 | 0.897065 | − | 0.441898i | \(-0.145695\pi\) | ||||
0.897065 | + | 0.441898i | \(0.145695\pi\) | |||||||
\(20\) | −1.26102 | −0.281973 | ||||||||
\(21\) | −2.98689 | −0.651792 | ||||||||
\(22\) | −0.0948069 | −0.0202129 | ||||||||
\(23\) | −1.04197 | −0.217266 | −0.108633 | − | 0.994082i | \(-0.534647\pi\) | ||||
−0.108633 | + | 0.994082i | \(0.534647\pi\) | |||||||
\(24\) | −0.918004 | −0.187387 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.46278 | −1.07134 | ||||||||
\(27\) | 3.80196 | 0.731687 | ||||||||
\(28\) | 5.47526 | 1.03473 | ||||||||
\(29\) | 0.420754 | 0.0781321 | 0.0390661 | − | 0.999237i | \(-0.487562\pi\) | ||||
0.0390661 | + | 0.999237i | \(0.487562\pi\) | |||||||
\(30\) | −1.24226 | −0.226805 | ||||||||
\(31\) | −1.38429 | −0.248626 | −0.124313 | − | 0.992243i | \(-0.539673\pi\) | ||||
−0.124313 | + | 0.992243i | \(0.539673\pi\) | |||||||
\(32\) | 6.23717 | 1.10259 | ||||||||
\(33\) | −0.0361159 | −0.00628698 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.34193 | −0.733920 | ||||||||
\(36\) | −3.18631 | −0.531052 | ||||||||
\(37\) | −0.336949 | −0.0553941 | −0.0276971 | − | 0.999616i | \(-0.508817\pi\) | ||||
−0.0276971 | + | 0.999616i | \(0.508817\pi\) | |||||||
\(38\) | −14.1224 | −2.29095 | ||||||||
\(39\) | −2.08100 | −0.333227 | ||||||||
\(40\) | −1.33447 | −0.210998 | ||||||||
\(41\) | 6.59268 | 1.02960 | 0.514802 | − | 0.857309i | \(-0.327865\pi\) | ||||
0.514802 | + | 0.857309i | \(0.327865\pi\) | |||||||
\(42\) | 5.39381 | 0.832283 | ||||||||
\(43\) | −9.99466 | −1.52417 | −0.762086 | − | 0.647476i | \(-0.775825\pi\) | ||||
−0.762086 | + | 0.647476i | \(0.775825\pi\) | |||||||
\(44\) | 0.0662042 | 0.00998065 | ||||||||
\(45\) | 2.52677 | 0.376669 | ||||||||
\(46\) | 1.88162 | 0.277430 | ||||||||
\(47\) | −6.13168 | −0.894398 | −0.447199 | − | 0.894435i | \(-0.647578\pi\) | ||||
−0.447199 | + | 0.894435i | \(0.647578\pi\) | |||||||
\(48\) | 3.39272 | 0.489696 | ||||||||
\(49\) | 11.8523 | 1.69319 | ||||||||
\(50\) | −1.80583 | −0.255383 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.81469 | 0.529002 | ||||||||
\(53\) | −12.0629 | −1.65696 | −0.828482 | − | 0.560016i | \(-0.810795\pi\) | ||||
−0.828482 | + | 0.560016i | \(0.810795\pi\) | |||||||
\(54\) | −6.86569 | −0.934302 | ||||||||
\(55\) | −0.0525004 | −0.00707916 | ||||||||
\(56\) | 5.79417 | 0.774279 | ||||||||
\(57\) | −5.37981 | −0.712573 | ||||||||
\(58\) | −0.759811 | −0.0997681 | ||||||||
\(59\) | −5.09779 | −0.663676 | −0.331838 | − | 0.943336i | \(-0.607669\pi\) | ||||
−0.331838 | + | 0.943336i | \(0.607669\pi\) | |||||||
\(60\) | 0.867478 | 0.111991 | ||||||||
\(61\) | 5.97063 | 0.764461 | 0.382230 | − | 0.924067i | \(-0.375156\pi\) | ||||
0.382230 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(62\) | 2.49979 | 0.317474 | ||||||||
\(63\) | −10.9711 | −1.38222 | ||||||||
\(64\) | −1.39954 | −0.174943 | ||||||||
\(65\) | −3.02508 | −0.375215 | ||||||||
\(66\) | 0.0652192 | 0.00802793 | ||||||||
\(67\) | −0.916040 | −0.111912 | −0.0559561 | − | 0.998433i | \(-0.517821\pi\) | ||||
−0.0559561 | + | 0.998433i | \(0.517821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.716788 | 0.0862912 | ||||||||
\(70\) | 7.84078 | 0.937153 | ||||||||
\(71\) | −4.17986 | −0.496058 | −0.248029 | − | 0.968753i | \(-0.579783\pi\) | ||||
−0.248029 | + | 0.968753i | \(0.579783\pi\) | |||||||
\(72\) | −3.37190 | −0.397382 | ||||||||
\(73\) | 5.39059 | 0.630920 | 0.315460 | − | 0.948939i | \(-0.397841\pi\) | ||||
0.315460 | + | 0.948939i | \(0.397841\pi\) | |||||||
\(74\) | 0.608473 | 0.0707336 | ||||||||
\(75\) | −0.687917 | −0.0794338 | ||||||||
\(76\) | 9.86173 | 1.13122 | ||||||||
\(77\) | 0.227953 | 0.0259777 | ||||||||
\(78\) | 3.75794 | 0.425503 | ||||||||
\(79\) | 9.98296 | 1.12317 | 0.561585 | − | 0.827419i | \(-0.310192\pi\) | ||||
0.561585 | + | 0.827419i | \(0.310192\pi\) | |||||||
\(80\) | 4.93187 | 0.551400 | ||||||||
\(81\) | 4.96488 | 0.551653 | ||||||||
\(82\) | −11.9053 | −1.31472 | ||||||||
\(83\) | 6.53008 | 0.716770 | 0.358385 | − | 0.933574i | \(-0.383328\pi\) | ||||
0.358385 | + | 0.933574i | \(0.383328\pi\) | |||||||
\(84\) | −3.76653 | −0.410962 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.0487 | 1.94624 | ||||||||
\(87\) | −0.289444 | −0.0310317 | ||||||||
\(88\) | 0.0700602 | 0.00746845 | ||||||||
\(89\) | 10.2159 | 1.08289 | 0.541443 | − | 0.840738i | \(-0.317878\pi\) | ||||
0.541443 | + | 0.840738i | \(0.317878\pi\) | |||||||
\(90\) | −4.56292 | −0.480974 | ||||||||
\(91\) | 13.1347 | 1.37689 | ||||||||
\(92\) | −1.31395 | −0.136988 | ||||||||
\(93\) | 0.952278 | 0.0987466 | ||||||||
\(94\) | 11.0728 | 1.14207 | ||||||||
\(95\) | −7.82043 | −0.802359 | ||||||||
\(96\) | −4.29066 | −0.437914 | ||||||||
\(97\) | 19.2238 | 1.95188 | 0.975940 | − | 0.218037i | \(-0.0699654\pi\) | ||||
0.975940 | + | 0.218037i | \(0.0699654\pi\) | |||||||
\(98\) | −21.4033 | −2.16206 | ||||||||
\(99\) | −0.132657 | −0.0133325 | ||||||||
\(100\) | 1.26102 | 0.126102 | ||||||||
\(101\) | 13.2926 | 1.32266 | 0.661331 | − | 0.750094i | \(-0.269992\pi\) | ||||
0.661331 | + | 0.750094i | \(0.269992\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.91299 | −0.681157 | −0.340579 | − | 0.940216i | \(-0.610623\pi\) | ||||
−0.340579 | + | 0.940216i | \(0.610623\pi\) | |||||||
\(104\) | 4.03687 | 0.395848 | ||||||||
\(105\) | 2.98689 | 0.291490 | ||||||||
\(106\) | 21.7835 | 2.11580 | ||||||||
\(107\) | 14.7407 | 1.42504 | 0.712520 | − | 0.701651i | \(-0.247554\pi\) | ||||
0.712520 | + | 0.701651i | \(0.247554\pi\) | |||||||
\(108\) | 4.79435 | 0.461337 | ||||||||
\(109\) | −4.74828 | −0.454803 | −0.227402 | − | 0.973801i | \(-0.573023\pi\) | ||||
−0.227402 | + | 0.973801i | \(0.573023\pi\) | |||||||
\(110\) | 0.0948069 | 0.00903948 | ||||||||
\(111\) | 0.231793 | 0.0220008 | ||||||||
\(112\) | −21.4138 | −2.02342 | ||||||||
\(113\) | 3.01331 | 0.283468 | 0.141734 | − | 0.989905i | \(-0.454732\pi\) | ||||
0.141734 | + | 0.989905i | \(0.454732\pi\) | |||||||
\(114\) | 9.71502 | 0.909895 | ||||||||
\(115\) | 1.04197 | 0.0971641 | ||||||||
\(116\) | 0.530580 | 0.0492631 | ||||||||
\(117\) | −7.64368 | −0.706658 | ||||||||
\(118\) | 9.20574 | 0.847457 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.918004 | 0.0838020 | ||||||||
\(121\) | −10.9972 | −0.999749 | ||||||||
\(122\) | −10.7819 | −0.976151 | ||||||||
\(123\) | −4.53522 | −0.408927 | ||||||||
\(124\) | −1.74562 | −0.156761 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 19.8119 | 1.76498 | ||||||||
\(127\) | −0.00828706 | −0.000735358 0 | −0.000367679 | − | 1.00000i | \(-0.500117\pi\) | ||||
−0.000367679 | 1.00000i | \(0.500117\pi\) | ||||||||
\(128\) | −9.94702 | −0.879200 | ||||||||
\(129\) | 6.87550 | 0.605354 | ||||||||
\(130\) | 5.46278 | 0.479117 | ||||||||
\(131\) | −8.18458 | −0.715090 | −0.357545 | − | 0.933896i | \(-0.616386\pi\) | ||||
−0.357545 | + | 0.933896i | \(0.616386\pi\) | |||||||
\(132\) | −0.0455430 | −0.00396401 | ||||||||
\(133\) | 33.9558 | 2.94434 | ||||||||
\(134\) | 1.65421 | 0.142902 | ||||||||
\(135\) | −3.80196 | −0.327221 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.23387 | −0.190852 | −0.0954260 | − | 0.995437i | \(-0.530421\pi\) | ||||
−0.0954260 | + | 0.995437i | \(0.530421\pi\) | |||||||
\(138\) | −1.29440 | −0.110186 | ||||||||
\(139\) | 19.7358 | 1.67397 | 0.836985 | − | 0.547225i | \(-0.184316\pi\) | ||||
0.836985 | + | 0.547225i | \(0.184316\pi\) | |||||||
\(140\) | −5.47526 | −0.462744 | ||||||||
\(141\) | 4.21809 | 0.355227 | ||||||||
\(142\) | 7.54812 | 0.633424 | ||||||||
\(143\) | 0.158818 | 0.0132810 | ||||||||
\(144\) | 12.4617 | 1.03847 | ||||||||
\(145\) | −0.420754 | −0.0349418 | ||||||||
\(146\) | −9.73448 | −0.805632 | ||||||||
\(147\) | −8.15343 | −0.672483 | ||||||||
\(148\) | −0.424900 | −0.0349266 | ||||||||
\(149\) | 10.1835 | 0.834263 | 0.417132 | − | 0.908846i | \(-0.363035\pi\) | ||||
0.417132 | + | 0.908846i | \(0.363035\pi\) | |||||||
\(150\) | 1.24226 | 0.101430 | ||||||||
\(151\) | −15.3484 | −1.24903 | −0.624516 | − | 0.781012i | \(-0.714704\pi\) | ||||
−0.624516 | + | 0.781012i | \(0.714704\pi\) | |||||||
\(152\) | 10.4361 | 0.846482 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.411645 | −0.0331713 | ||||||||
\(155\) | 1.38429 | 0.111189 | ||||||||
\(156\) | −2.62419 | −0.210103 | ||||||||
\(157\) | 9.41222 | 0.751177 | 0.375588 | − | 0.926787i | \(-0.377441\pi\) | ||||
0.375588 | + | 0.926787i | \(0.377441\pi\) | |||||||
\(158\) | −18.0275 | −1.43419 | ||||||||
\(159\) | 8.29826 | 0.658095 | ||||||||
\(160\) | −6.23717 | −0.493092 | ||||||||
\(161\) | −4.52415 | −0.356553 | ||||||||
\(162\) | −8.96572 | −0.704414 | ||||||||
\(163\) | 12.4453 | 0.974793 | 0.487397 | − | 0.873181i | \(-0.337947\pi\) | ||||
0.487397 | + | 0.873181i | \(0.337947\pi\) | |||||||
\(164\) | 8.31351 | 0.649176 | ||||||||
\(165\) | 0.0361159 | 0.00281162 | ||||||||
\(166\) | −11.7922 | −0.915253 | ||||||||
\(167\) | 12.6025 | 0.975211 | 0.487605 | − | 0.873064i | \(-0.337870\pi\) | ||||
0.487605 | + | 0.873064i | \(0.337870\pi\) | |||||||
\(168\) | −3.98591 | −0.307520 | ||||||||
\(169\) | −3.84890 | −0.296069 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.7604 | −1.51112 | ||||||||
\(172\) | −12.6035 | −0.961007 | ||||||||
\(173\) | −12.1965 | −0.927284 | −0.463642 | − | 0.886023i | \(-0.653458\pi\) | ||||
−0.463642 | + | 0.886023i | \(0.653458\pi\) | |||||||
\(174\) | 0.522687 | 0.0396248 | ||||||||
\(175\) | 4.34193 | 0.328219 | ||||||||
\(176\) | −0.258925 | −0.0195172 | ||||||||
\(177\) | 3.50686 | 0.263592 | ||||||||
\(178\) | −18.4482 | −1.38275 | ||||||||
\(179\) | 13.8608 | 1.03600 | 0.518002 | − | 0.855379i | \(-0.326676\pi\) | ||||
0.518002 | + | 0.855379i | \(0.326676\pi\) | |||||||
\(180\) | 3.18631 | 0.237494 | ||||||||
\(181\) | 2.04424 | 0.151947 | 0.0759736 | − | 0.997110i | \(-0.475794\pi\) | ||||
0.0759736 | + | 0.997110i | \(0.475794\pi\) | |||||||
\(182\) | −23.7190 | −1.75817 | ||||||||
\(183\) | −4.10730 | −0.303620 | ||||||||
\(184\) | −1.39048 | −0.102507 | ||||||||
\(185\) | 0.336949 | 0.0247730 | ||||||||
\(186\) | −1.71965 | −0.126091 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.73218 | −0.563927 | ||||||||
\(189\) | 16.5078 | 1.20077 | ||||||||
\(190\) | 14.1224 | 1.02454 | ||||||||
\(191\) | −3.08056 | −0.222902 | −0.111451 | − | 0.993770i | \(-0.535550\pi\) | ||||
−0.111451 | + | 0.993770i | \(0.535550\pi\) | |||||||
\(192\) | 0.962768 | 0.0694818 | ||||||||
\(193\) | −20.6419 | −1.48584 | −0.742918 | − | 0.669382i | \(-0.766559\pi\) | ||||
−0.742918 | + | 0.669382i | \(0.766559\pi\) | |||||||
\(194\) | −34.7149 | −2.49239 | ||||||||
\(195\) | 2.08100 | 0.149024 | ||||||||
\(196\) | 14.9461 | 1.06758 | ||||||||
\(197\) | 18.2365 | 1.29930 | 0.649649 | − | 0.760235i | \(-0.274916\pi\) | ||||
0.649649 | + | 0.760235i | \(0.274916\pi\) | |||||||
\(198\) | 0.239555 | 0.0170244 | ||||||||
\(199\) | 26.6677 | 1.89042 | 0.945210 | − | 0.326463i | \(-0.105857\pi\) | ||||
0.945210 | + | 0.326463i | \(0.105857\pi\) | |||||||
\(200\) | 1.33447 | 0.0943613 | ||||||||
\(201\) | 0.630160 | 0.0444480 | ||||||||
\(202\) | −24.0041 | −1.68893 | ||||||||
\(203\) | 1.82689 | 0.128222 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.59268 | −0.460453 | ||||||||
\(206\) | 12.4837 | 0.869779 | ||||||||
\(207\) | 2.63282 | 0.182993 | ||||||||
\(208\) | −14.9193 | −1.03447 | ||||||||
\(209\) | 0.410576 | 0.0284001 | ||||||||
\(210\) | −5.39381 | −0.372208 | ||||||||
\(211\) | 7.80566 | 0.537364 | 0.268682 | − | 0.963229i | \(-0.413412\pi\) | ||||
0.268682 | + | 0.963229i | \(0.413412\pi\) | |||||||
\(212\) | −15.2115 | −1.04473 | ||||||||
\(213\) | 2.87540 | 0.197019 | ||||||||
\(214\) | −26.6193 | −1.81966 | ||||||||
\(215\) | 9.99466 | 0.681630 | ||||||||
\(216\) | 5.07360 | 0.345215 | ||||||||
\(217\) | −6.01049 | −0.408019 | ||||||||
\(218\) | 8.57459 | 0.580745 | ||||||||
\(219\) | −3.70828 | −0.250582 | ||||||||
\(220\) | −0.0662042 | −0.00446348 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.418579 | −0.0280932 | ||||||||
\(223\) | 4.76891 | 0.319350 | 0.159675 | − | 0.987170i | \(-0.448955\pi\) | ||||
0.159675 | + | 0.987170i | \(0.448955\pi\) | |||||||
\(224\) | 27.0814 | 1.80945 | ||||||||
\(225\) | −2.52677 | −0.168451 | ||||||||
\(226\) | −5.44152 | −0.361964 | ||||||||
\(227\) | 11.2111 | 0.744105 | 0.372053 | − | 0.928212i | \(-0.378654\pi\) | ||||
0.372053 | + | 0.928212i | \(0.378654\pi\) | |||||||
\(228\) | −6.78405 | −0.449285 | ||||||||
\(229\) | 20.6484 | 1.36449 | 0.682244 | − | 0.731125i | \(-0.261004\pi\) | ||||
0.682244 | + | 0.731125i | \(0.261004\pi\) | |||||||
\(230\) | −1.88162 | −0.124070 | ||||||||
\(231\) | −0.156813 | −0.0103175 | ||||||||
\(232\) | 0.561484 | 0.0368632 | ||||||||
\(233\) | 3.05851 | 0.200370 | 0.100185 | − | 0.994969i | \(-0.468057\pi\) | ||||
0.100185 | + | 0.994969i | \(0.468057\pi\) | |||||||
\(234\) | 13.8032 | 0.902342 | ||||||||
\(235\) | 6.13168 | 0.399987 | ||||||||
\(236\) | −6.42842 | −0.418455 | ||||||||
\(237\) | −6.86745 | −0.446089 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.94072 | 0.319588 | 0.159794 | − | 0.987150i | \(-0.448917\pi\) | ||||
0.159794 | + | 0.987150i | \(0.448917\pi\) | |||||||
\(240\) | −3.39272 | −0.218999 | ||||||||
\(241\) | −1.66176 | −0.107043 | −0.0535217 | − | 0.998567i | \(-0.517045\pi\) | ||||
−0.0535217 | + | 0.998567i | \(0.517045\pi\) | |||||||
\(242\) | 19.8592 | 1.27659 | ||||||||
\(243\) | −14.8213 | −0.950787 | ||||||||
\(244\) | 7.52909 | 0.482001 | ||||||||
\(245\) | −11.8523 | −0.757218 | ||||||||
\(246\) | 8.18983 | 0.522165 | ||||||||
\(247\) | 23.6574 | 1.50529 | ||||||||
\(248\) | −1.84729 | −0.117303 | ||||||||
\(249\) | −4.49215 | −0.284679 | ||||||||
\(250\) | 1.80583 | 0.114211 | ||||||||
\(251\) | 9.14240 | 0.577063 | 0.288531 | − | 0.957470i | \(-0.406833\pi\) | ||||
0.288531 | + | 0.957470i | \(0.406833\pi\) | |||||||
\(252\) | −13.8347 | −0.871506 | ||||||||
\(253\) | −0.0547038 | −0.00343920 | ||||||||
\(254\) | 0.0149650 | 0.000938989 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.7617 | 1.29761 | ||||||||
\(257\) | −16.6522 | −1.03874 | −0.519369 | − | 0.854550i | \(-0.673833\pi\) | ||||
−0.519369 | + | 0.854550i | \(0.673833\pi\) | |||||||
\(258\) | −12.4160 | −0.772985 | ||||||||
\(259\) | −1.46301 | −0.0909070 | ||||||||
\(260\) | −3.81469 | −0.236577 | ||||||||
\(261\) | −1.06315 | −0.0658073 | ||||||||
\(262\) | 14.7800 | 0.913109 | ||||||||
\(263\) | −21.7280 | −1.33981 | −0.669903 | − | 0.742448i | \(-0.733665\pi\) | ||||
−0.669903 | + | 0.742448i | \(0.733665\pi\) | |||||||
\(264\) | −0.0481956 | −0.00296624 | ||||||||
\(265\) | 12.0629 | 0.741017 | ||||||||
\(266\) | −61.3183 | −3.75967 | ||||||||
\(267\) | −7.02771 | −0.430089 | ||||||||
\(268\) | −1.15515 | −0.0705618 | ||||||||
\(269\) | −23.1721 | −1.41283 | −0.706414 | − | 0.707799i | \(-0.749688\pi\) | ||||
−0.706414 | + | 0.707799i | \(0.749688\pi\) | |||||||
\(270\) | 6.86569 | 0.417833 | ||||||||
\(271\) | 3.95595 | 0.240307 | 0.120153 | − | 0.992755i | \(-0.461661\pi\) | ||||
0.120153 | + | 0.992755i | \(0.461661\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.03556 | −0.546857 | ||||||||
\(274\) | 4.03398 | 0.243702 | ||||||||
\(275\) | 0.0525004 | 0.00316590 | ||||||||
\(276\) | 0.903885 | 0.0544075 | ||||||||
\(277\) | −16.9099 | −1.01602 | −0.508009 | − | 0.861352i | \(-0.669618\pi\) | ||||
−0.508009 | + | 0.861352i | \(0.669618\pi\) | |||||||
\(278\) | −35.6395 | −2.13752 | ||||||||
\(279\) | 3.49779 | 0.209407 | ||||||||
\(280\) | −5.79417 | −0.346268 | ||||||||
\(281\) | 4.66987 | 0.278581 | 0.139291 | − | 0.990252i | \(-0.455518\pi\) | ||||
0.139291 | + | 0.990252i | \(0.455518\pi\) | |||||||
\(282\) | −7.61715 | −0.453595 | ||||||||
\(283\) | −8.70036 | −0.517183 | −0.258591 | − | 0.965987i | \(-0.583258\pi\) | ||||
−0.258591 | + | 0.965987i | \(0.583258\pi\) | |||||||
\(284\) | −5.27089 | −0.312770 | ||||||||
\(285\) | 5.37981 | 0.318672 | ||||||||
\(286\) | −0.286798 | −0.0169587 | ||||||||
\(287\) | 28.6250 | 1.68968 | ||||||||
\(288\) | −15.7599 | −0.928661 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0.759811 | 0.0446176 | ||||||||
\(291\) | −13.2244 | −0.775227 | ||||||||
\(292\) | 6.79765 | 0.397802 | ||||||||
\(293\) | 0.739100 | 0.0431787 | 0.0215893 | − | 0.999767i | \(-0.493127\pi\) | ||||
0.0215893 | + | 0.999767i | \(0.493127\pi\) | |||||||
\(294\) | 14.7237 | 0.858704 | ||||||||
\(295\) | 5.09779 | 0.296805 | ||||||||
\(296\) | −0.449649 | −0.0261353 | ||||||||
\(297\) | 0.199605 | 0.0115822 | ||||||||
\(298\) | −18.3896 | −1.06528 | ||||||||
\(299\) | −3.15204 | −0.182287 | ||||||||
\(300\) | −0.867478 | −0.0500839 | ||||||||
\(301\) | −43.3961 | −2.50131 | ||||||||
\(302\) | 27.7165 | 1.59491 | ||||||||
\(303\) | −9.14419 | −0.525320 | ||||||||
\(304\) | −38.5693 | −2.21210 | ||||||||
\(305\) | −5.97063 | −0.341877 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.86108 | −0.163290 | −0.0816451 | − | 0.996661i | \(-0.526017\pi\) | ||||
−0.0816451 | + | 0.996661i | \(0.526017\pi\) | |||||||
\(308\) | 0.287454 | 0.0163792 | ||||||||
\(309\) | 4.75556 | 0.270535 | ||||||||
\(310\) | −2.49979 | −0.141979 | ||||||||
\(311\) | 20.4980 | 1.16233 | 0.581167 | − | 0.813784i | \(-0.302596\pi\) | ||||
0.581167 | + | 0.813784i | \(0.302596\pi\) | |||||||
\(312\) | −2.77703 | −0.157219 | ||||||||
\(313\) | 8.46543 | 0.478494 | 0.239247 | − | 0.970959i | \(-0.423099\pi\) | ||||
0.239247 | + | 0.970959i | \(0.423099\pi\) | |||||||
\(314\) | −16.9969 | −0.959189 | ||||||||
\(315\) | 10.9711 | 0.618149 | ||||||||
\(316\) | 12.5887 | 0.708171 | ||||||||
\(317\) | −21.0918 | −1.18463 | −0.592317 | − | 0.805705i | \(-0.701787\pi\) | ||||
−0.592317 | + | 0.805705i | \(0.701787\pi\) | |||||||
\(318\) | −14.9852 | −0.840331 | ||||||||
\(319\) | 0.0220898 | 0.00123679 | ||||||||
\(320\) | 1.39954 | 0.0782367 | ||||||||
\(321\) | −10.1404 | −0.565982 | ||||||||
\(322\) | 8.16985 | 0.455288 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 6.26082 | 0.347823 | ||||||||
\(325\) | 3.02508 | 0.167801 | ||||||||
\(326\) | −22.4741 | −1.24473 | ||||||||
\(327\) | 3.26643 | 0.180634 | ||||||||
\(328\) | 8.79773 | 0.485774 | ||||||||
\(329\) | −26.6233 | −1.46779 | ||||||||
\(330\) | −0.0652192 | −0.00359020 | ||||||||
\(331\) | −15.2261 | −0.836903 | −0.418451 | − | 0.908239i | \(-0.637427\pi\) | ||||
−0.418451 | + | 0.908239i | \(0.637427\pi\) | |||||||
\(332\) | 8.23457 | 0.451931 | ||||||||
\(333\) | 0.851393 | 0.0466561 | ||||||||
\(334\) | −22.7580 | −1.24526 | ||||||||
\(335\) | 0.916040 | 0.0500486 | ||||||||
\(336\) | 14.7309 | 0.803638 | ||||||||
\(337\) | 11.4737 | 0.625011 | 0.312506 | − | 0.949916i | \(-0.398832\pi\) | ||||
0.312506 | + | 0.949916i | \(0.398832\pi\) | |||||||
\(338\) | 6.95046 | 0.378055 | ||||||||
\(339\) | −2.07290 | −0.112585 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0726759 | −0.00393562 | ||||||||
\(342\) | 35.6840 | 1.92957 | ||||||||
\(343\) | 21.0685 | 1.13759 | ||||||||
\(344\) | −13.3376 | −0.719114 | ||||||||
\(345\) | −0.716788 | −0.0385906 | ||||||||
\(346\) | 22.0248 | 1.18406 | ||||||||
\(347\) | −14.9843 | −0.804399 | −0.402199 | − | 0.915552i | \(-0.631754\pi\) | ||||
−0.402199 | + | 0.915552i | \(0.631754\pi\) | |||||||
\(348\) | −0.364995 | −0.0195658 | ||||||||
\(349\) | −4.53667 | −0.242842 | −0.121421 | − | 0.992601i | \(-0.538745\pi\) | ||||
−0.121421 | + | 0.992601i | \(0.538745\pi\) | |||||||
\(350\) | −7.84078 | −0.419108 | ||||||||
\(351\) | 11.5012 | 0.613890 | ||||||||
\(352\) | 0.327454 | 0.0174534 | ||||||||
\(353\) | −7.71469 | −0.410612 | −0.205306 | − | 0.978698i | \(-0.565819\pi\) | ||||
−0.205306 | + | 0.978698i | \(0.565819\pi\) | |||||||
\(354\) | −6.33279 | −0.336584 | ||||||||
\(355\) | 4.17986 | 0.221844 | ||||||||
\(356\) | 12.8825 | 0.682771 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.0302 | −1.32289 | ||||||||
\(359\) | −11.0284 | −0.582057 | −0.291029 | − | 0.956714i | \(-0.593997\pi\) | ||||
−0.291029 | + | 0.956714i | \(0.593997\pi\) | |||||||
\(360\) | 3.37190 | 0.177715 | ||||||||
\(361\) | 42.1592 | 2.21890 | ||||||||
\(362\) | −3.69155 | −0.194023 | ||||||||
\(363\) | 7.56519 | 0.397070 | ||||||||
\(364\) | 16.5631 | 0.868142 | ||||||||
\(365\) | −5.39059 | −0.282156 | ||||||||
\(366\) | 7.41708 | 0.387697 | ||||||||
\(367\) | 16.0285 | 0.836683 | 0.418342 | − | 0.908290i | \(-0.362611\pi\) | ||||
0.418342 | + | 0.908290i | \(0.362611\pi\) | |||||||
\(368\) | 5.13885 | 0.267881 | ||||||||
\(369\) | −16.6582 | −0.867191 | ||||||||
\(370\) | −0.608473 | −0.0316330 | ||||||||
\(371\) | −52.3761 | −2.71923 | ||||||||
\(372\) | 1.20084 | 0.0622608 | ||||||||
\(373\) | 10.2501 | 0.530732 | 0.265366 | − | 0.964148i | \(-0.414507\pi\) | ||||
0.265366 | + | 0.964148i | \(0.414507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.687917 | 0.0355239 | ||||||||
\(376\) | −8.18254 | −0.421982 | ||||||||
\(377\) | 1.27281 | 0.0655533 | ||||||||
\(378\) | −29.8103 | −1.53328 | ||||||||
\(379\) | −13.9520 | −0.716664 | −0.358332 | − | 0.933594i | \(-0.616654\pi\) | ||||
−0.358332 | + | 0.933594i | \(0.616654\pi\) | |||||||
\(380\) | −9.86173 | −0.505896 | ||||||||
\(381\) | 0.00570081 | 0.000292061 0 | ||||||||
\(382\) | 5.56297 | 0.284626 | ||||||||
\(383\) | −5.62186 | −0.287264 | −0.143632 | − | 0.989631i | \(-0.545878\pi\) | ||||
−0.143632 | + | 0.989631i | \(0.545878\pi\) | |||||||
\(384\) | 6.84272 | 0.349191 | ||||||||
\(385\) | −0.227953 | −0.0116176 | ||||||||
\(386\) | 37.2757 | 1.89729 | ||||||||
\(387\) | 25.2542 | 1.28374 | ||||||||
\(388\) | 24.2416 | 1.23068 | ||||||||
\(389\) | 35.8157 | 1.81593 | 0.907965 | − | 0.419047i | \(-0.137636\pi\) | ||||
0.907965 | + | 0.419047i | \(0.137636\pi\) | |||||||
\(390\) | −3.75794 | −0.190291 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15.8166 | 0.798858 | ||||||||
\(393\) | 5.63032 | 0.284012 | ||||||||
\(394\) | −32.9320 | −1.65909 | ||||||||
\(395\) | −9.98296 | −0.502297 | ||||||||
\(396\) | −0.167283 | −0.00840627 | ||||||||
\(397\) | −3.89017 | −0.195242 | −0.0976211 | − | 0.995224i | \(-0.531123\pi\) | ||||
−0.0976211 | + | 0.995224i | \(0.531123\pi\) | |||||||
\(398\) | −48.1573 | −2.41390 | ||||||||
\(399\) | −23.3587 | −1.16940 | ||||||||
\(400\) | −4.93187 | −0.246593 | ||||||||
\(401\) | −36.7386 | −1.83464 | −0.917318 | − | 0.398156i | \(-0.869650\pi\) | ||||
−0.917318 | + | 0.398156i | \(0.869650\pi\) | |||||||
\(402\) | −1.13796 | −0.0567564 | ||||||||
\(403\) | −4.18759 | −0.208599 | ||||||||
\(404\) | 16.7622 | 0.833952 | ||||||||
\(405\) | −4.96488 | −0.246707 | ||||||||
\(406\) | −3.29904 | −0.163729 | ||||||||
\(407\) | −0.0176900 | −0.000876860 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3529 | −1.10528 | −0.552641 | − | 0.833419i | \(-0.686380\pi\) | ||||
−0.552641 | + | 0.833419i | \(0.686380\pi\) | |||||||
\(410\) | 11.9053 | 0.587959 | ||||||||
\(411\) | 1.53671 | 0.0758005 | ||||||||
\(412\) | −8.71743 | −0.429477 | ||||||||
\(413\) | −22.1342 | −1.08915 | ||||||||
\(414\) | −4.75442 | −0.233667 | ||||||||
\(415\) | −6.53008 | −0.320549 | ||||||||
\(416\) | 18.8679 | 0.925077 | ||||||||
\(417\) | −13.5766 | −0.664849 | ||||||||
\(418\) | −0.741431 | −0.0362646 | ||||||||
\(419\) | 21.8658 | 1.06821 | 0.534107 | − | 0.845417i | \(-0.320648\pi\) | ||||
0.534107 | + | 0.845417i | \(0.320648\pi\) | |||||||
\(420\) | 3.76653 | 0.183788 | ||||||||
\(421\) | 20.6111 | 1.00453 | 0.502263 | − | 0.864715i | \(-0.332501\pi\) | ||||
0.502263 | + | 0.864715i | \(0.332501\pi\) | |||||||
\(422\) | −14.0957 | −0.686168 | ||||||||
\(423\) | 15.4934 | 0.753313 | ||||||||
\(424\) | −16.0975 | −0.781766 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.19248 | −0.251576 | ||||||||
\(427\) | 25.9241 | 1.25455 | ||||||||
\(428\) | 18.5884 | 0.898503 | ||||||||
\(429\) | −0.109254 | −0.00527481 | ||||||||
\(430\) | −18.0487 | −0.870384 | ||||||||
\(431\) | −22.3052 | −1.07441 | −0.537203 | − | 0.843453i | \(-0.680519\pi\) | ||||
−0.537203 | + | 0.843453i | \(0.680519\pi\) | |||||||
\(432\) | −18.7508 | −0.902146 | ||||||||
\(433\) | 8.93127 | 0.429210 | 0.214605 | − | 0.976701i | \(-0.431154\pi\) | ||||
0.214605 | + | 0.976701i | \(0.431154\pi\) | |||||||
\(434\) | 10.8539 | 0.521005 | ||||||||
\(435\) | 0.289444 | 0.0138778 | ||||||||
\(436\) | −5.98769 | −0.286758 | ||||||||
\(437\) | −8.14865 | −0.389803 | ||||||||
\(438\) | 6.69652 | 0.319972 | ||||||||
\(439\) | 22.2643 | 1.06262 | 0.531308 | − | 0.847179i | \(-0.321701\pi\) | ||||
0.531308 | + | 0.847179i | \(0.321701\pi\) | |||||||
\(440\) | −0.0700602 | −0.00333999 | ||||||||
\(441\) | −29.9481 | −1.42610 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.17421 | −0.293346 | −0.146673 | − | 0.989185i | \(-0.546856\pi\) | ||||
−0.146673 | + | 0.989185i | \(0.546856\pi\) | |||||||
\(444\) | 0.292296 | 0.0138718 | ||||||||
\(445\) | −10.2159 | −0.484281 | ||||||||
\(446\) | −8.61184 | −0.407783 | ||||||||
\(447\) | −7.00539 | −0.331344 | ||||||||
\(448\) | −6.07671 | −0.287097 | ||||||||
\(449\) | 30.2985 | 1.42988 | 0.714938 | − | 0.699188i | \(-0.246455\pi\) | ||||
0.714938 | + | 0.699188i | \(0.246455\pi\) | |||||||
\(450\) | 4.56292 | 0.215098 | ||||||||
\(451\) | 0.346119 | 0.0162981 | ||||||||
\(452\) | 3.79984 | 0.178730 | ||||||||
\(453\) | 10.5584 | 0.496077 | ||||||||
\(454\) | −20.2453 | −0.950159 | ||||||||
\(455\) | −13.1347 | −0.615763 | ||||||||
\(456\) | −7.17919 | −0.336196 | ||||||||
\(457\) | −25.5756 | −1.19638 | −0.598188 | − | 0.801356i | \(-0.704112\pi\) | ||||
−0.598188 | + | 0.801356i | \(0.704112\pi\) | |||||||
\(458\) | −37.2876 | −1.74233 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.31395 | 0.0612630 | ||||||||
\(461\) | −14.0565 | −0.654677 | −0.327338 | − | 0.944907i | \(-0.606152\pi\) | ||||
−0.327338 | + | 0.944907i | \(0.606152\pi\) | |||||||
\(462\) | 0.283177 | 0.0131746 | ||||||||
\(463\) | −25.1233 | −1.16758 | −0.583789 | − | 0.811905i | \(-0.698431\pi\) | ||||
−0.583789 | + | 0.811905i | \(0.698431\pi\) | |||||||
\(464\) | −2.07511 | −0.0963343 | ||||||||
\(465\) | −0.952278 | −0.0441608 | ||||||||
\(466\) | −5.52315 | −0.255855 | ||||||||
\(467\) | 22.2900 | 1.03146 | 0.515730 | − | 0.856751i | \(-0.327521\pi\) | ||||
0.515730 | + | 0.856751i | \(0.327521\pi\) | |||||||
\(468\) | −9.63884 | −0.445556 | ||||||||
\(469\) | −3.97738 | −0.183658 | ||||||||
\(470\) | −11.0728 | −0.510749 | ||||||||
\(471\) | −6.47483 | −0.298344 | ||||||||
\(472\) | −6.80285 | −0.313126 | ||||||||
\(473\) | −0.524724 | −0.0241268 | ||||||||
\(474\) | 12.4014 | 0.569617 | ||||||||
\(475\) | 7.82043 | 0.358826 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.4801 | 1.39559 | ||||||||
\(478\) | −8.92209 | −0.408087 | ||||||||
\(479\) | −26.7496 | −1.22222 | −0.611111 | − | 0.791545i | \(-0.709277\pi\) | ||||
−0.611111 | + | 0.791545i | \(0.709277\pi\) | |||||||
\(480\) | 4.29066 | 0.195841 | ||||||||
\(481\) | −1.01930 | −0.0464760 | ||||||||
\(482\) | 3.00086 | 0.136685 | ||||||||
\(483\) | 3.11224 | 0.141612 | ||||||||
\(484\) | −13.8678 | −0.630353 | ||||||||
\(485\) | −19.2238 | −0.872908 | ||||||||
\(486\) | 26.7647 | 1.21407 | ||||||||
\(487\) | −23.1460 | −1.04885 | −0.524423 | − | 0.851458i | \(-0.675719\pi\) | ||||
−0.524423 | + | 0.851458i | \(0.675719\pi\) | |||||||
\(488\) | 7.96763 | 0.360677 | ||||||||
\(489\) | −8.56135 | −0.387158 | ||||||||
\(490\) | 21.4033 | 0.966903 | ||||||||
\(491\) | 7.78981 | 0.351549 | 0.175775 | − | 0.984430i | \(-0.443757\pi\) | ||||
0.175775 | + | 0.984430i | \(0.443757\pi\) | |||||||
\(492\) | −5.71901 | −0.257833 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −42.7213 | −1.92212 | ||||||||
\(495\) | 0.132657 | 0.00596247 | ||||||||
\(496\) | 6.82714 | 0.306548 | ||||||||
\(497\) | −18.1487 | −0.814079 | ||||||||
\(498\) | 8.11207 | 0.363510 | ||||||||
\(499\) | 8.79764 | 0.393837 | 0.196918 | − | 0.980420i | \(-0.436907\pi\) | ||||
0.196918 | + | 0.980420i | \(0.436907\pi\) | |||||||
\(500\) | −1.26102 | −0.0563946 | ||||||||
\(501\) | −8.66948 | −0.387324 | ||||||||
\(502\) | −16.5096 | −0.736860 | ||||||||
\(503\) | 7.83946 | 0.349544 | 0.174772 | − | 0.984609i | \(-0.444081\pi\) | ||||
0.174772 | + | 0.984609i | \(0.444081\pi\) | |||||||
\(504\) | −14.6405 | −0.652141 | ||||||||
\(505\) | −13.2926 | −0.591512 | ||||||||
\(506\) | 0.0987858 | 0.00439156 | ||||||||
\(507\) | 2.64773 | 0.117590 | ||||||||
\(508\) | −0.0104502 | −0.000463651 0 | ||||||||
\(509\) | −2.52868 | −0.112082 | −0.0560409 | − | 0.998428i | \(-0.517848\pi\) | ||||
−0.0560409 | + | 0.998428i | \(0.517848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.4055 | 1.03540 | ||||||||
\(512\) | −17.5981 | −0.777732 | ||||||||
\(513\) | 29.7330 | 1.31274 | ||||||||
\(514\) | 30.0711 | 1.32638 | ||||||||
\(515\) | 6.91299 | 0.304623 | ||||||||
\(516\) | 8.67015 | 0.381682 | ||||||||
\(517\) | −0.321916 | −0.0141578 | ||||||||
\(518\) | 2.64195 | 0.116080 | ||||||||
\(519\) | 8.39019 | 0.368289 | ||||||||
\(520\) | −4.03687 | −0.177029 | ||||||||
\(521\) | 10.1083 | 0.442853 | 0.221426 | − | 0.975177i | \(-0.428929\pi\) | ||||
0.221426 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(522\) | 1.91987 | 0.0840303 | ||||||||
\(523\) | −5.80494 | −0.253833 | −0.126916 | − | 0.991913i | \(-0.540508\pi\) | ||||
−0.126916 | + | 0.991913i | \(0.540508\pi\) | |||||||
\(524\) | −10.3209 | −0.450872 | ||||||||
\(525\) | −2.98689 | −0.130358 | ||||||||
\(526\) | 39.2371 | 1.71082 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.178119 | 0.00775164 | ||||||||
\(529\) | −21.9143 | −0.952796 | ||||||||
\(530\) | −21.7835 | −0.946215 | ||||||||
\(531\) | 12.8809 | 0.558985 | ||||||||
\(532\) | 42.8189 | 1.85644 | ||||||||
\(533\) | 19.9434 | 0.863844 | ||||||||
\(534\) | 12.6908 | 0.549187 | ||||||||
\(535\) | −14.7407 | −0.637298 | ||||||||
\(536\) | −1.22243 | −0.0528009 | ||||||||
\(537\) | −9.53508 | −0.411469 | ||||||||
\(538\) | 41.8449 | 1.80406 | ||||||||
\(539\) | 0.622253 | 0.0268023 | ||||||||
\(540\) | −4.79435 | −0.206316 | ||||||||
\(541\) | 42.3404 | 1.82035 | 0.910177 | − | 0.414219i | \(-0.135945\pi\) | ||||
0.910177 | + | 0.414219i | \(0.135945\pi\) | |||||||
\(542\) | −7.14377 | −0.306851 | ||||||||
\(543\) | −1.40627 | −0.0603487 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.74828 | 0.203394 | ||||||||
\(546\) | 16.3167 | 0.698290 | ||||||||
\(547\) | −20.0061 | −0.855398 | −0.427699 | − | 0.903921i | \(-0.640676\pi\) | ||||
−0.427699 | + | 0.903921i | \(0.640676\pi\) | |||||||
\(548\) | −2.81695 | −0.120334 | ||||||||
\(549\) | −15.0864 | −0.643872 | ||||||||
\(550\) | −0.0948069 | −0.00404258 | ||||||||
\(551\) | 3.29048 | 0.140179 | ||||||||
\(552\) | 0.956532 | 0.0407127 | ||||||||
\(553\) | 43.3453 | 1.84323 | ||||||||
\(554\) | 30.5364 | 1.29737 | ||||||||
\(555\) | −0.231793 | −0.00983907 | ||||||||
\(556\) | 24.8873 | 1.05546 | ||||||||
\(557\) | −25.8965 | −1.09727 | −0.548636 | − | 0.836062i | \(-0.684853\pi\) | ||||
−0.548636 | + | 0.836062i | \(0.684853\pi\) | |||||||
\(558\) | −6.31641 | −0.267395 | ||||||||
\(559\) | −30.2346 | −1.27879 | ||||||||
\(560\) | 21.4138 | 0.904899 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.43299 | −0.355724 | ||||||||
\(563\) | 28.0309 | 1.18136 | 0.590681 | − | 0.806905i | \(-0.298859\pi\) | ||||
0.590681 | + | 0.806905i | \(0.298859\pi\) | |||||||
\(564\) | 5.31910 | 0.223975 | ||||||||
\(565\) | −3.01331 | −0.126771 | ||||||||
\(566\) | 15.7114 | 0.660398 | ||||||||
\(567\) | 21.5571 | 0.905315 | ||||||||
\(568\) | −5.57790 | −0.234043 | ||||||||
\(569\) | 39.1921 | 1.64302 | 0.821509 | − | 0.570195i | \(-0.193132\pi\) | ||||
0.821509 | + | 0.570195i | \(0.193132\pi\) | |||||||
\(570\) | −9.71502 | −0.406917 | ||||||||
\(571\) | −3.86762 | −0.161855 | −0.0809275 | − | 0.996720i | \(-0.525788\pi\) | ||||
−0.0809275 | + | 0.996720i | \(0.525788\pi\) | |||||||
\(572\) | 0.200273 | 0.00837383 | ||||||||
\(573\) | 2.11917 | 0.0885297 | ||||||||
\(574\) | −51.6918 | −2.15757 | ||||||||
\(575\) | −1.04197 | −0.0434531 | ||||||||
\(576\) | 3.53632 | 0.147347 | ||||||||
\(577\) | −14.4808 | −0.602845 | −0.301423 | − | 0.953491i | \(-0.597461\pi\) | ||||
−0.301423 | + | 0.953491i | \(0.597461\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1999 | 0.590128 | ||||||||
\(580\) | −0.530580 | −0.0220311 | ||||||||
\(581\) | 28.3531 | 1.17629 | ||||||||
\(582\) | 23.8810 | 0.989898 | ||||||||
\(583\) | −0.633306 | −0.0262289 | ||||||||
\(584\) | 7.19357 | 0.297672 | ||||||||
\(585\) | 7.64368 | 0.316027 | ||||||||
\(586\) | −1.33469 | −0.0551355 | ||||||||
\(587\) | 31.2452 | 1.28963 | 0.644814 | − | 0.764339i | \(-0.276935\pi\) | ||||
0.644814 | + | 0.764339i | \(0.276935\pi\) | |||||||
\(588\) | −10.2816 | −0.424008 | ||||||||
\(589\) | −10.8258 | −0.446068 | ||||||||
\(590\) | −9.20574 | −0.378994 | ||||||||
\(591\) | −12.5452 | −0.516041 | ||||||||
\(592\) | 1.66179 | 0.0682991 | ||||||||
\(593\) | −2.00543 | −0.0823530 | −0.0411765 | − | 0.999152i | \(-0.513111\pi\) | ||||
−0.0411765 | + | 0.999152i | \(0.513111\pi\) | |||||||
\(594\) | −0.360452 | −0.0147895 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.8416 | 0.526012 | ||||||||
\(597\) | −18.3451 | −0.750816 | ||||||||
\(598\) | 5.69204 | 0.232765 | ||||||||
\(599\) | 36.0451 | 1.47276 | 0.736381 | − | 0.676567i | \(-0.236533\pi\) | ||||
0.736381 | + | 0.676567i | \(0.236533\pi\) | |||||||
\(600\) | −0.918004 | −0.0374774 | ||||||||
\(601\) | 38.7948 | 1.58247 | 0.791237 | − | 0.611510i | \(-0.209438\pi\) | ||||
0.791237 | + | 0.611510i | \(0.209438\pi\) | |||||||
\(602\) | 78.3660 | 3.19396 | ||||||||
\(603\) | 2.31462 | 0.0942588 | ||||||||
\(604\) | −19.3546 | −0.787529 | ||||||||
\(605\) | 10.9972 | 0.447102 | ||||||||
\(606\) | 16.5129 | 0.670789 | ||||||||
\(607\) | 28.9535 | 1.17519 | 0.587594 | − | 0.809156i | \(-0.300075\pi\) | ||||
0.587594 | + | 0.809156i | \(0.300075\pi\) | |||||||
\(608\) | 48.7774 | 1.97818 | ||||||||
\(609\) | −1.25675 | −0.0509259 | ||||||||
\(610\) | 10.7819 | 0.436548 | ||||||||
\(611\) | −18.5488 | −0.750405 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.10707 | 0.367831 | 0.183915 | − | 0.982942i | \(-0.441123\pi\) | ||||
0.183915 | + | 0.982942i | \(0.441123\pi\) | |||||||
\(614\) | 5.16662 | 0.208508 | ||||||||
\(615\) | 4.53522 | 0.182878 | ||||||||
\(616\) | 0.304197 | 0.0122564 | ||||||||
\(617\) | −5.05551 | −0.203527 | −0.101764 | − | 0.994809i | \(-0.532449\pi\) | ||||
−0.101764 | + | 0.994809i | \(0.532449\pi\) | |||||||
\(618\) | −8.58774 | −0.345450 | ||||||||
\(619\) | 16.8593 | 0.677632 | 0.338816 | − | 0.940853i | \(-0.389974\pi\) | ||||
0.338816 | + | 0.940853i | \(0.389974\pi\) | |||||||
\(620\) | 1.74562 | 0.0701058 | ||||||||
\(621\) | −3.96152 | −0.158970 | ||||||||
\(622\) | −37.0159 | −1.48420 | ||||||||
\(623\) | 44.3568 | 1.77712 | ||||||||
\(624\) | 10.2632 | 0.410858 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.2871 | −0.610996 | ||||||||
\(627\) | −0.282442 | −0.0112797 | ||||||||
\(628\) | 11.8690 | 0.473625 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −19.8119 | −0.789323 | ||||||||
\(631\) | 2.71309 | 0.108007 | 0.0540033 | − | 0.998541i | \(-0.482802\pi\) | ||||
0.0540033 | + | 0.998541i | \(0.482802\pi\) | |||||||
\(632\) | 13.3220 | 0.529919 | ||||||||
\(633\) | −5.36965 | −0.213424 | ||||||||
\(634\) | 38.0882 | 1.51268 | ||||||||
\(635\) | 0.00828706 | 0.000328862 0 | ||||||||
\(636\) | 10.4643 | 0.414936 | ||||||||
\(637\) | 35.8543 | 1.42060 | ||||||||
\(638\) | −0.0398904 | −0.00157928 | ||||||||
\(639\) | 10.5615 | 0.417808 | ||||||||
\(640\) | 9.94702 | 0.393190 | ||||||||
\(641\) | 22.8123 | 0.901030 | 0.450515 | − | 0.892769i | \(-0.351240\pi\) | ||||
0.450515 | + | 0.892769i | \(0.351240\pi\) | |||||||
\(642\) | 18.3118 | 0.722711 | ||||||||
\(643\) | −19.2771 | −0.760214 | −0.380107 | − | 0.924942i | \(-0.624113\pi\) | ||||
−0.380107 | + | 0.924942i | \(0.624113\pi\) | |||||||
\(644\) | −5.70506 | −0.224811 | ||||||||
\(645\) | −6.87550 | −0.270722 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.8098 | 0.503606 | 0.251803 | − | 0.967778i | \(-0.418976\pi\) | ||||
0.251803 | + | 0.967778i | \(0.418976\pi\) | |||||||
\(648\) | 6.62548 | 0.260273 | ||||||||
\(649\) | −0.267636 | −0.0105056 | ||||||||
\(650\) | −5.46278 | −0.214268 | ||||||||
\(651\) | 4.13472 | 0.162052 | ||||||||
\(652\) | 15.6938 | 0.614618 | ||||||||
\(653\) | −41.7200 | −1.63263 | −0.816315 | − | 0.577607i | \(-0.803987\pi\) | ||||
−0.816315 | + | 0.577607i | \(0.803987\pi\) | |||||||
\(654\) | −5.89861 | −0.230654 | ||||||||
\(655\) | 8.18458 | 0.319798 | ||||||||
\(656\) | −32.5142 | −1.26947 | ||||||||
\(657\) | −13.6208 | −0.531397 | ||||||||
\(658\) | 48.0772 | 1.87424 | ||||||||
\(659\) | −34.3290 | −1.33727 | −0.668633 | − | 0.743592i | \(-0.733120\pi\) | ||||
−0.668633 | + | 0.743592i | \(0.733120\pi\) | |||||||
\(660\) | 0.0455430 | 0.00177276 | ||||||||
\(661\) | 27.7009 | 1.07744 | 0.538720 | − | 0.842485i | \(-0.318908\pi\) | ||||
0.538720 | + | 0.842485i | \(0.318908\pi\) | |||||||
\(662\) | 27.4958 | 1.06865 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.71419 | 0.338176 | ||||||||
\(665\) | −33.9558 | −1.31675 | ||||||||
\(666\) | −1.53747 | −0.0595758 | ||||||||
\(667\) | −0.438413 | −0.0169754 | ||||||||
\(668\) | 15.8920 | 0.614881 | ||||||||
\(669\) | −3.28062 | −0.126836 | ||||||||
\(670\) | −1.65421 | −0.0639078 | ||||||||
\(671\) | 0.313461 | 0.0121010 | ||||||||
\(672\) | −18.6297 | −0.718658 | ||||||||
\(673\) | −36.2078 | −1.39571 | −0.697854 | − | 0.716240i | \(-0.745862\pi\) | ||||
−0.697854 | + | 0.716240i | \(0.745862\pi\) | |||||||
\(674\) | −20.7195 | −0.798086 | ||||||||
\(675\) | 3.80196 | 0.146337 | ||||||||
\(676\) | −4.85355 | −0.186675 | ||||||||
\(677\) | 17.1158 | 0.657812 | 0.328906 | − | 0.944363i | \(-0.393320\pi\) | ||||
0.328906 | + | 0.944363i | \(0.393320\pi\) | |||||||
\(678\) | 3.74331 | 0.143761 | ||||||||
\(679\) | 83.4684 | 3.20322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.71229 | −0.295536 | ||||||||
\(682\) | 0.131240 | 0.00502545 | ||||||||
\(683\) | −8.85022 | −0.338644 | −0.169322 | − | 0.985561i | \(-0.554158\pi\) | ||||
−0.169322 | + | 0.985561i | \(0.554158\pi\) | |||||||
\(684\) | −24.9183 | −0.952776 | ||||||||
\(685\) | 2.23387 | 0.0853516 | ||||||||
\(686\) | −38.0462 | −1.45261 | ||||||||
\(687\) | −14.2044 | −0.541932 | ||||||||
\(688\) | 49.2924 | 1.87925 | ||||||||
\(689\) | −36.4911 | −1.39020 | ||||||||
\(690\) | 1.29440 | 0.0492769 | ||||||||
\(691\) | 1.39834 | 0.0531953 | 0.0265977 | − | 0.999646i | \(-0.491533\pi\) | ||||
0.0265977 | + | 0.999646i | \(0.491533\pi\) | |||||||
\(692\) | −15.3801 | −0.584663 | ||||||||
\(693\) | −0.575985 | −0.0218799 | ||||||||
\(694\) | 27.0591 | 1.02715 | ||||||||
\(695\) | −19.7358 | −0.748622 | ||||||||
\(696\) | −0.386254 | −0.0146409 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 8.19245 | 0.310089 | ||||||||
\(699\) | −2.10400 | −0.0795806 | ||||||||
\(700\) | 5.47526 | 0.206946 | ||||||||
\(701\) | 2.36331 | 0.0892608 | 0.0446304 | − | 0.999004i | \(-0.485789\pi\) | ||||
0.0446304 | + | 0.999004i | \(0.485789\pi\) | |||||||
\(702\) | −20.7693 | −0.783885 | ||||||||
\(703\) | −2.63509 | −0.0993843 | ||||||||
\(704\) | −0.0734765 | −0.00276925 | ||||||||
\(705\) | −4.21809 | −0.158862 | ||||||||
\(706\) | 13.9314 | 0.524316 | ||||||||
\(707\) | 57.7154 | 2.17061 | ||||||||
\(708\) | 4.42222 | 0.166197 | ||||||||
\(709\) | −32.5266 | −1.22156 | −0.610782 | − | 0.791799i | \(-0.709145\pi\) | ||||
−0.610782 | + | 0.791799i | \(0.709145\pi\) | |||||||
\(710\) | −7.54812 | −0.283276 | ||||||||
\(711\) | −25.2247 | −0.945998 | ||||||||
\(712\) | 13.6328 | 0.510912 | ||||||||
\(713\) | 1.44239 | 0.0540179 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.158818 | −0.00593945 | ||||||||
\(716\) | 17.4788 | 0.653212 | ||||||||
\(717\) | −3.39880 | −0.126931 | ||||||||
\(718\) | 19.9154 | 0.743237 | ||||||||
\(719\) | −16.4302 | −0.612744 | −0.306372 | − | 0.951912i | \(-0.599115\pi\) | ||||
−0.306372 | + | 0.951912i | \(0.599115\pi\) | |||||||
\(720\) | −12.4617 | −0.464420 | ||||||||
\(721\) | −30.0157 | −1.11784 | ||||||||
\(722\) | −76.1323 | −2.83335 | ||||||||
\(723\) | 1.14315 | 0.0425143 | ||||||||
\(724\) | 2.57783 | 0.0958043 | ||||||||
\(725\) | 0.420754 | 0.0156264 | ||||||||
\(726\) | −13.6614 | −0.507024 | ||||||||
\(727\) | −32.4709 | −1.20428 | −0.602139 | − | 0.798391i | \(-0.705685\pi\) | ||||
−0.602139 | + | 0.798391i | \(0.705685\pi\) | |||||||
\(728\) | 17.5278 | 0.649624 | ||||||||
\(729\) | −4.69881 | −0.174030 | ||||||||
\(730\) | 9.73448 | 0.360289 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5.17939 | −0.191436 | ||||||||
\(733\) | −8.63424 | −0.318913 | −0.159456 | − | 0.987205i | \(-0.550974\pi\) | ||||
−0.159456 | + | 0.987205i | \(0.550974\pi\) | |||||||
\(734\) | −28.9448 | −1.06837 | ||||||||
\(735\) | 8.15343 | 0.300744 | ||||||||
\(736\) | −6.49894 | −0.239554 | ||||||||
\(737\) | −0.0480925 | −0.00177151 | ||||||||
\(738\) | 30.0819 | 1.10733 | ||||||||
\(739\) | 10.6026 | 0.390022 | 0.195011 | − | 0.980801i | \(-0.437526\pi\) | ||||
0.195011 | + | 0.980801i | \(0.437526\pi\) | |||||||
\(740\) | 0.424900 | 0.0156196 | ||||||||
\(741\) | −16.2743 | −0.597853 | ||||||||
\(742\) | 94.5824 | 3.47223 | ||||||||
\(743\) | 22.3424 | 0.819665 | 0.409832 | − | 0.912161i | \(-0.365587\pi\) | ||||
0.409832 | + | 0.912161i | \(0.365587\pi\) | |||||||
\(744\) | 1.27079 | 0.0465893 | ||||||||
\(745\) | −10.1835 | −0.373094 | ||||||||
\(746\) | −18.5100 | −0.677700 | ||||||||
\(747\) | −16.5000 | −0.603704 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 64.0032 | 2.33863 | ||||||||
\(750\) | −1.24226 | −0.0453610 | ||||||||
\(751\) | −7.13989 | −0.260538 | −0.130269 | − | 0.991479i | \(-0.541584\pi\) | ||||
−0.130269 | + | 0.991479i | \(0.541584\pi\) | |||||||
\(752\) | 30.2406 | 1.10276 | ||||||||
\(753\) | −6.28921 | −0.229192 | ||||||||
\(754\) | −2.29849 | −0.0837060 | ||||||||
\(755\) | 15.3484 | 0.558584 | ||||||||
\(756\) | 20.8167 | 0.757097 | ||||||||
\(757\) | 18.0266 | 0.655186 | 0.327593 | − | 0.944819i | \(-0.393762\pi\) | ||||
0.327593 | + | 0.944819i | \(0.393762\pi\) | |||||||
\(758\) | 25.1949 | 0.915119 | ||||||||
\(759\) | 0.0376317 | 0.00136594 | ||||||||
\(760\) | −10.4361 | −0.378558 | ||||||||
\(761\) | −49.9437 | −1.81046 | −0.905230 | − | 0.424923i | \(-0.860301\pi\) | ||||
−0.905230 | + | 0.424923i | \(0.860301\pi\) | |||||||
\(762\) | −0.0102947 | −0.000372937 0 | ||||||||
\(763\) | −20.6167 | −0.746375 | ||||||||
\(764\) | −3.88466 | −0.140542 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.1521 | 0.366811 | ||||||||
\(767\) | −15.4212 | −0.556828 | ||||||||
\(768\) | −14.2823 | −0.515369 | ||||||||
\(769\) | −43.9115 | −1.58349 | −0.791745 | − | 0.610852i | \(-0.790827\pi\) | ||||
−0.791745 | + | 0.610852i | \(0.790827\pi\) | |||||||
\(770\) | 0.411645 | 0.0148346 | ||||||||
\(771\) | 11.4554 | 0.412554 | ||||||||
\(772\) | −26.0299 | −0.936836 | ||||||||
\(773\) | −9.67759 | −0.348079 | −0.174039 | − | 0.984739i | \(-0.555682\pi\) | ||||
−0.174039 | + | 0.984739i | \(0.555682\pi\) | |||||||
\(774\) | −45.6048 | −1.63923 | ||||||||
\(775\) | −1.38429 | −0.0497252 | ||||||||
\(776\) | 25.6536 | 0.920910 | ||||||||
\(777\) | 1.00643 | 0.0361055 | ||||||||
\(778\) | −64.6771 | −2.31879 | ||||||||
\(779\) | 51.5576 | 1.84724 | ||||||||
\(780\) | 2.62419 | 0.0939610 | ||||||||
\(781\) | −0.219445 | −0.00785234 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.59969 | 0.0571683 | ||||||||
\(784\) | −58.4542 | −2.08765 | ||||||||
\(785\) | −9.41222 | −0.335937 | ||||||||
\(786\) | −10.1674 | −0.362659 | ||||||||
\(787\) | 19.8384 | 0.707161 | 0.353581 | − | 0.935404i | \(-0.384964\pi\) | ||||
0.353581 | + | 0.935404i | \(0.384964\pi\) | |||||||
\(788\) | 22.9966 | 0.819221 | ||||||||
\(789\) | 14.9471 | 0.532130 | ||||||||
\(790\) | 18.0275 | 0.641391 | ||||||||
\(791\) | 13.0836 | 0.465198 | ||||||||
\(792\) | −0.177026 | −0.00629035 | ||||||||
\(793\) | 18.0616 | 0.641387 | ||||||||
\(794\) | 7.02499 | 0.249308 | ||||||||
\(795\) | −8.29826 | −0.294309 | ||||||||
\(796\) | 33.6285 | 1.19193 | ||||||||
\(797\) | 5.56111 | 0.196984 | 0.0984922 | − | 0.995138i | \(-0.468598\pi\) | ||||
0.0984922 | + | 0.995138i | \(0.468598\pi\) | |||||||
\(798\) | 42.1819 | 1.49322 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 6.23717 | 0.220517 | ||||||||
\(801\) | −25.8133 | −0.912068 | ||||||||
\(802\) | 66.3436 | 2.34267 | ||||||||
\(803\) | 0.283008 | 0.00998714 | ||||||||
\(804\) | 0.794645 | 0.0280250 | ||||||||
\(805\) | 4.52415 | 0.159455 | ||||||||
\(806\) | 7.56207 | 0.266363 | ||||||||
\(807\) | 15.9405 | 0.561132 | ||||||||
\(808\) | 17.7385 | 0.624040 | ||||||||
\(809\) | −31.0442 | −1.09146 | −0.545729 | − | 0.837962i | \(-0.683747\pi\) | ||||
−0.545729 | + | 0.837962i | \(0.683747\pi\) | |||||||
\(810\) | 8.96572 | 0.315023 | ||||||||
\(811\) | 46.9708 | 1.64937 | 0.824683 | − | 0.565595i | \(-0.191353\pi\) | ||||
0.824683 | + | 0.565595i | \(0.191353\pi\) | |||||||
\(812\) | 2.30374 | 0.0808455 | ||||||||
\(813\) | −2.72136 | −0.0954424 | ||||||||
\(814\) | 0.0319451 | 0.00111968 | ||||||||
\(815\) | −12.4453 | −0.435941 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −78.1626 | −2.73456 | ||||||||
\(818\) | 40.3656 | 1.41135 | ||||||||
\(819\) | −33.1883 | −1.15969 | ||||||||
\(820\) | −8.31351 | −0.290320 | ||||||||
\(821\) | 16.7433 | 0.584346 | 0.292173 | − | 0.956366i | \(-0.405622\pi\) | ||||
0.292173 | + | 0.956366i | \(0.405622\pi\) | |||||||
\(822\) | −2.77505 | −0.0967908 | ||||||||
\(823\) | −26.5996 | −0.927205 | −0.463602 | − | 0.886043i | \(-0.653443\pi\) | ||||
−0.463602 | + | 0.886043i | \(0.653443\pi\) | |||||||
\(824\) | −9.22517 | −0.321374 | ||||||||
\(825\) | −0.0361159 | −0.00125740 | ||||||||
\(826\) | 39.9707 | 1.39076 | ||||||||
\(827\) | 34.4855 | 1.19918 | 0.599590 | − | 0.800307i | \(-0.295330\pi\) | ||||
0.599590 | + | 0.800307i | \(0.295330\pi\) | |||||||
\(828\) | 3.32004 | 0.115379 | ||||||||
\(829\) | −7.29346 | −0.253312 | −0.126656 | − | 0.991947i | \(-0.540424\pi\) | ||||
−0.126656 | + | 0.991947i | \(0.540424\pi\) | |||||||
\(830\) | 11.7922 | 0.409314 | ||||||||
\(831\) | 11.6326 | 0.403531 | ||||||||
\(832\) | −4.23372 | −0.146778 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 24.5170 | 0.848956 | ||||||||
\(835\) | −12.6025 | −0.436128 | ||||||||
\(836\) | 0.517745 | 0.0179066 | ||||||||
\(837\) | −5.26302 | −0.181917 | ||||||||
\(838\) | −39.4859 | −1.36402 | ||||||||
\(839\) | 35.5082 | 1.22588 | 0.612940 | − | 0.790129i | \(-0.289987\pi\) | ||||
0.612940 | + | 0.790129i | \(0.289987\pi\) | |||||||
\(840\) | 3.98591 | 0.137527 | ||||||||
\(841\) | −28.8230 | −0.993895 | ||||||||
\(842\) | −37.2202 | −1.28269 | ||||||||
\(843\) | −3.21248 | −0.110644 | ||||||||
\(844\) | 9.84311 | 0.338814 | ||||||||
\(845\) | 3.84890 | 0.132406 | ||||||||
\(846\) | −27.9784 | −0.961916 | ||||||||
\(847\) | −47.7492 | −1.64068 | ||||||||
\(848\) | 59.4925 | 2.04298 | ||||||||
\(849\) | 5.98513 | 0.205409 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.351091 | 0.0120352 | ||||||||
\(852\) | 3.62594 | 0.124223 | ||||||||
\(853\) | −0.238822 | −0.00817712 | −0.00408856 | − | 0.999992i | \(-0.501301\pi\) | ||||
−0.00408856 | + | 0.999992i | \(0.501301\pi\) | |||||||
\(854\) | −46.8144 | −1.60196 | ||||||||
\(855\) | 19.7604 | 0.675793 | ||||||||
\(856\) | 19.6711 | 0.672343 | ||||||||
\(857\) | −18.1950 | −0.621528 | −0.310764 | − | 0.950487i | \(-0.600585\pi\) | ||||
−0.310764 | + | 0.950487i | \(0.600585\pi\) | |||||||
\(858\) | 0.197293 | 0.00673548 | ||||||||
\(859\) | −20.1560 | −0.687715 | −0.343857 | − | 0.939022i | \(-0.611734\pi\) | ||||
−0.343857 | + | 0.939022i | \(0.611734\pi\) | |||||||
\(860\) | 12.6035 | 0.429775 | ||||||||
\(861\) | −19.6916 | −0.671088 | ||||||||
\(862\) | 40.2795 | 1.37192 | ||||||||
\(863\) | 14.7597 | 0.502424 | 0.251212 | − | 0.967932i | \(-0.419171\pi\) | ||||
0.251212 | + | 0.967932i | \(0.419171\pi\) | |||||||
\(864\) | 23.7135 | 0.806749 | ||||||||
\(865\) | 12.1965 | 0.414694 | ||||||||
\(866\) | −16.1284 | −0.548064 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.57936 | −0.257260 | ||||||||
\(869\) | 0.524110 | 0.0177792 | ||||||||
\(870\) | −0.522687 | −0.0177207 | ||||||||
\(871\) | −2.77109 | −0.0938949 | ||||||||
\(872\) | −6.33644 | −0.214579 | ||||||||
\(873\) | −48.5741 | −1.64398 | ||||||||
\(874\) | 14.7151 | 0.497745 | ||||||||
\(875\) | −4.34193 | −0.146784 | ||||||||
\(876\) | −4.67622 | −0.157995 | ||||||||
\(877\) | −42.7577 | −1.44382 | −0.721912 | − | 0.691984i | \(-0.756737\pi\) | ||||
−0.721912 | + | 0.691984i | \(0.756737\pi\) | |||||||
\(878\) | −40.2055 | −1.35687 | ||||||||
\(879\) | −0.508439 | −0.0171492 | ||||||||
\(880\) | 0.258925 | 0.00872837 | ||||||||
\(881\) | −43.6832 | −1.47172 | −0.735862 | − | 0.677131i | \(-0.763223\pi\) | ||||
−0.735862 | + | 0.677131i | \(0.763223\pi\) | |||||||
\(882\) | 54.0813 | 1.82101 | ||||||||
\(883\) | −41.4824 | −1.39599 | −0.697997 | − | 0.716101i | \(-0.745925\pi\) | ||||
−0.697997 | + | 0.716101i | \(0.745925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.50686 | −0.117882 | ||||||||
\(886\) | 11.1496 | 0.374577 | ||||||||
\(887\) | −32.8798 | −1.10400 | −0.551998 | − | 0.833845i | \(-0.686134\pi\) | ||||
−0.551998 | + | 0.833845i | \(0.686134\pi\) | |||||||
\(888\) | 0.309321 | 0.0103801 | ||||||||
\(889\) | −0.0359818 | −0.00120679 | ||||||||
\(890\) | 18.4482 | 0.618386 | ||||||||
\(891\) | 0.260658 | 0.00873238 | ||||||||
\(892\) | 6.01370 | 0.201354 | ||||||||
\(893\) | −47.9524 | −1.60467 | ||||||||
\(894\) | 12.6505 | 0.423097 | ||||||||
\(895\) | −13.8608 | −0.463315 | ||||||||
\(896\) | −43.1892 | −1.44285 | ||||||||
\(897\) | 2.16834 | 0.0723988 | ||||||||
\(898\) | −54.7140 | −1.82583 | ||||||||
\(899\) | −0.582447 | −0.0194257 | ||||||||
\(900\) | −3.18631 | −0.106210 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.625031 | −0.0208113 | ||||||||
\(903\) | 29.8529 | 0.993443 | ||||||||
\(904\) | 4.02116 | 0.133742 | ||||||||
\(905\) | −2.04424 | −0.0679528 | ||||||||
\(906\) | −19.0667 | −0.633448 | ||||||||
\(907\) | −36.4475 | −1.21022 | −0.605110 | − | 0.796142i | \(-0.706871\pi\) | ||||
−0.605110 | + | 0.796142i | \(0.706871\pi\) | |||||||
\(908\) | 14.1374 | 0.469166 | ||||||||
\(909\) | −33.5873 | −1.11402 | ||||||||
\(910\) | 23.7190 | 0.786277 | ||||||||
\(911\) | 29.8739 | 0.989767 | 0.494883 | − | 0.868959i | \(-0.335211\pi\) | ||||
0.494883 | + | 0.868959i | \(0.335211\pi\) | |||||||
\(912\) | 26.5325 | 0.878579 | ||||||||
\(913\) | 0.342832 | 0.0113461 | ||||||||
\(914\) | 46.1852 | 1.52767 | ||||||||
\(915\) | 4.10730 | 0.135783 | ||||||||
\(916\) | 26.0381 | 0.860324 | ||||||||
\(917\) | −35.5369 | −1.17353 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6218 | 0.383368 | 0.191684 | − | 0.981457i | \(-0.438605\pi\) | ||||
0.191684 | + | 0.981457i | \(0.438605\pi\) | |||||||
\(920\) | 1.39048 | 0.0458426 | ||||||||
\(921\) | 1.96818 | 0.0648539 | ||||||||
\(922\) | 25.3837 | 0.835966 | ||||||||
\(923\) | −12.6444 | −0.416196 | ||||||||
\(924\) | −0.197744 | −0.00650531 | ||||||||
\(925\) | −0.336949 | −0.0110788 | ||||||||
\(926\) | 45.3684 | 1.49090 | ||||||||
\(927\) | 17.4675 | 0.573709 | ||||||||
\(928\) | 2.62432 | 0.0861475 | ||||||||
\(929\) | −5.04232 | −0.165433 | −0.0827165 | − | 0.996573i | \(-0.526360\pi\) | ||||
−0.0827165 | + | 0.996573i | \(0.526360\pi\) | |||||||
\(930\) | 1.71965 | 0.0563896 | ||||||||
\(931\) | 92.6904 | 3.03781 | ||||||||
\(932\) | 3.85685 | 0.126335 | ||||||||
\(933\) | −14.1009 | −0.461643 | ||||||||
\(934\) | −40.2520 | −1.31709 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.2003 | −0.333406 | ||||||||
\(937\) | 34.9116 | 1.14051 | 0.570257 | − | 0.821466i | \(-0.306844\pi\) | ||||
0.570257 | + | 0.821466i | \(0.306844\pi\) | |||||||
\(938\) | 7.18248 | 0.234516 | ||||||||
\(939\) | −5.82351 | −0.190043 | ||||||||
\(940\) | 7.73218 | 0.252196 | ||||||||
\(941\) | −11.0586 | −0.360502 | −0.180251 | − | 0.983621i | \(-0.557691\pi\) | ||||
−0.180251 | + | 0.983621i | \(0.557691\pi\) | |||||||
\(942\) | 11.6924 | 0.380960 | ||||||||
\(943\) | −6.86937 | −0.223697 | ||||||||
\(944\) | 25.1416 | 0.818290 | ||||||||
\(945\) | −16.5078 | −0.537000 | ||||||||
\(946\) | 0.947562 | 0.0308079 | ||||||||
\(947\) | −11.4918 | −0.373435 | −0.186717 | − | 0.982414i | \(-0.559785\pi\) | ||||
−0.186717 | + | 0.982414i | \(0.559785\pi\) | |||||||
\(948\) | −8.66000 | −0.281264 | ||||||||
\(949\) | 16.3069 | 0.529346 | ||||||||
\(950\) | −14.1224 | −0.458190 | ||||||||
\(951\) | 14.5094 | 0.470500 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.704896 | −0.0228338 | −0.0114169 | − | 0.999935i | \(-0.503634\pi\) | ||||
−0.0114169 | + | 0.999935i | \(0.503634\pi\) | |||||||
\(954\) | −55.0419 | −1.78205 | ||||||||
\(955\) | 3.08056 | 0.0996847 | ||||||||
\(956\) | 6.23035 | 0.201504 | ||||||||
\(957\) | −0.0151959 | −0.000491215 0 | ||||||||
\(958\) | 48.3053 | 1.56067 | ||||||||
\(959\) | −9.69929 | −0.313206 | ||||||||
\(960\) | −0.962768 | −0.0310732 | ||||||||
\(961\) | −29.0837 | −0.938185 | ||||||||
\(962\) | 1.84068 | 0.0593459 | ||||||||
\(963\) | −37.2465 | −1.20025 | ||||||||
\(964\) | −2.09552 | −0.0674920 | ||||||||
\(965\) | 20.6419 | 0.664486 | ||||||||
\(966\) | −5.62018 | −0.180826 | ||||||||
\(967\) | −39.9545 | −1.28485 | −0.642425 | − | 0.766348i | \(-0.722072\pi\) | ||||
−0.642425 | + | 0.766348i | \(0.722072\pi\) | |||||||
\(968\) | −14.6755 | −0.471688 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.7149 | 1.11463 | ||||||||
\(971\) | 43.2538 | 1.38808 | 0.694040 | − | 0.719936i | \(-0.255829\pi\) | ||||
0.694040 | + | 0.719936i | \(0.255829\pi\) | |||||||
\(972\) | −18.6900 | −0.599481 | ||||||||
\(973\) | 85.6915 | 2.74714 | ||||||||
\(974\) | 41.7978 | 1.33929 | ||||||||
\(975\) | −2.08100 | −0.0666454 | ||||||||
\(976\) | −29.4464 | −0.942555 | ||||||||
\(977\) | 48.8671 | 1.56340 | 0.781699 | − | 0.623656i | \(-0.214353\pi\) | ||||
0.781699 | + | 0.623656i | \(0.214353\pi\) | |||||||
\(978\) | 15.4603 | 0.494367 | ||||||||
\(979\) | 0.536340 | 0.0171415 | ||||||||
\(980\) | −14.9461 | −0.477434 | ||||||||
\(981\) | 11.9978 | 0.383061 | ||||||||
\(982\) | −14.0671 | −0.448898 | ||||||||
\(983\) | −48.8832 | −1.55913 | −0.779565 | − | 0.626321i | \(-0.784560\pi\) | ||||
−0.779565 | + | 0.626321i | \(0.784560\pi\) | |||||||
\(984\) | −6.05211 | −0.192934 | ||||||||
\(985\) | −18.2365 | −0.581063 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.3146 | 0.582961 | ||||||||
\(988\) | 29.8325 | 0.949099 | ||||||||
\(989\) | 10.4141 | 0.331150 | ||||||||
\(990\) | −0.239555 | −0.00761356 | ||||||||
\(991\) | 14.5340 | 0.461687 | 0.230843 | − | 0.972991i | \(-0.425851\pi\) | ||||
0.230843 | + | 0.972991i | \(0.425851\pi\) | |||||||
\(992\) | −8.63407 | −0.274132 | ||||||||
\(993\) | 10.4743 | 0.332392 | ||||||||
\(994\) | 32.7734 | 1.03951 | ||||||||
\(995\) | −26.6677 | −0.845422 | ||||||||
\(996\) | −5.66470 | −0.179493 | ||||||||
\(997\) | −44.2040 | −1.39995 | −0.699977 | − | 0.714165i | \(-0.746807\pi\) | ||||
−0.699977 | + | 0.714165i | \(0.746807\pi\) | |||||||
\(998\) | −15.8870 | −0.502896 | ||||||||
\(999\) | −1.28107 | −0.0405312 |
(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 | 1445.2.a.q.1.3 | 12 | ||
5.4 | even | 2 | 7225.2.a.bq.1.10 | 12 | |||
17.4 | even | 4 | 1445.2.d.j.866.19 | 24 | |||
17.11 | odd | 16 | 85.2.l.a.36.2 | yes | 24 | ||
17.13 | even | 4 | 1445.2.d.j.866.20 | 24 | |||
17.14 | odd | 16 | 85.2.l.a.26.2 | ✓ | 24 | ||
17.16 | even | 2 | 1445.2.a.p.1.3 | 12 | |||
51.11 | even | 16 | 765.2.be.b.631.5 | 24 | |||
51.14 | even | 16 | 765.2.be.b.451.5 | 24 | |||
85.14 | odd | 16 | 425.2.m.b.26.5 | 24 | |||
85.28 | even | 16 | 425.2.n.f.274.2 | 24 | |||
85.48 | even | 16 | 425.2.n.c.349.5 | 24 | |||
85.62 | even | 16 | 425.2.n.c.274.5 | 24 | |||
85.79 | odd | 16 | 425.2.m.b.376.5 | 24 | |||
85.82 | even | 16 | 425.2.n.f.349.2 | 24 | |||
85.84 | even | 2 | 7225.2.a.bs.1.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
85.2.l.a.26.2 | ✓ | 24 | 17.14 | odd | 16 | ||
85.2.l.a.36.2 | yes | 24 | 17.11 | odd | 16 | ||
425.2.m.b.26.5 | 24 | 85.14 | odd | 16 | |||
425.2.m.b.376.5 | 24 | 85.79 | odd | 16 | |||
425.2.n.c.274.5 | 24 | 85.62 | even | 16 | |||
425.2.n.c.349.5 | 24 | 85.48 | even | 16 | |||
425.2.n.f.274.2 | 24 | 85.28 | even | 16 | |||
425.2.n.f.349.2 | 24 | 85.82 | even | 16 | |||
765.2.be.b.451.5 | 24 | 51.14 | even | 16 | |||
765.2.be.b.631.5 | 24 | 51.11 | even | 16 | |||
1445.2.a.p.1.3 | 12 | 17.16 | even | 2 | |||
1445.2.a.q.1.3 | 12 | 1.1 | even | 1 | trivial | ||
1445.2.d.j.866.19 | 24 | 17.4 | even | 4 | |||
1445.2.d.j.866.20 | 24 | 17.13 | even | 4 | |||
7225.2.a.bq.1.10 | 12 | 5.4 | even | 2 | |||
7225.2.a.bs.1.10 | 12 | 85.84 | even | 2 |