Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.61803 | 1.85123 | 0.925615 | − | 0.378467i | \(-0.123549\pi\) | ||||
0.925615 | + | 0.378467i | \(0.123549\pi\) | |||||||
\(3\) | 2.61803 | 1.51152 | 0.755761 | − | 0.654847i | \(-0.227267\pi\) | ||||
0.755761 | + | 0.654847i | \(0.227267\pi\) | |||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 6.85410 | 2.79818 | ||||||||
\(7\) | 0.236068 | 0.0892253 | 0.0446127 | − | 0.999004i | \(-0.485795\pi\) | ||||
0.0446127 | + | 0.999004i | \(0.485795\pi\) | |||||||
\(8\) | 7.47214 | 2.64180 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | −2.61803 | −0.827895 | ||||||||
\(11\) | −4.61803 | −1.39239 | −0.696195 | − | 0.717853i | \(-0.745125\pi\) | ||||
−0.696195 | + | 0.717853i | \(0.745125\pi\) | |||||||
\(12\) | 12.7082 | 3.66854 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0.618034 | 0.165177 | ||||||||
\(15\) | −2.61803 | −0.675973 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 10.0902 | 2.37828 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −4.85410 | −1.08541 | ||||||||
\(21\) | 0.618034 | 0.134866 | ||||||||
\(22\) | −12.0902 | −2.57763 | ||||||||
\(23\) | −1.61803 | −0.337383 | −0.168692 | − | 0.985669i | \(-0.553954\pi\) | ||||
−0.168692 | + | 0.985669i | \(0.553954\pi\) | |||||||
\(24\) | 19.5623 | 3.99314 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 13.0902 | 2.56719 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 1.14590 | 0.216554 | ||||||||
\(29\) | −1.85410 | −0.344298 | −0.172149 | − | 0.985071i | \(-0.555071\pi\) | ||||
−0.172149 | + | 0.985071i | \(0.555071\pi\) | |||||||
\(30\) | −6.85410 | −1.25138 | ||||||||
\(31\) | 4.14590 | 0.744625 | 0.372313 | − | 0.928107i | \(-0.378565\pi\) | ||||
0.372313 | + | 0.928107i | \(0.378565\pi\) | |||||||
\(32\) | 10.8541 | 1.91875 | ||||||||
\(33\) | −12.0902 | −2.10463 | ||||||||
\(34\) | −15.7082 | −2.69393 | ||||||||
\(35\) | −0.236068 | −0.0399028 | ||||||||
\(36\) | 18.7082 | 3.11803 | ||||||||
\(37\) | −1.85410 | −0.304812 | −0.152406 | − | 0.988318i | \(-0.548702\pi\) | ||||
−0.152406 | + | 0.988318i | \(0.548702\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.0902 | 2.09610 | ||||||||
\(40\) | −7.47214 | −1.18145 | ||||||||
\(41\) | 11.1803 | 1.74608 | 0.873038 | − | 0.487652i | \(-0.162147\pi\) | ||||
0.873038 | + | 0.487652i | \(0.162147\pi\) | |||||||
\(42\) | 1.61803 | 0.249668 | ||||||||
\(43\) | −2.85410 | −0.435246 | −0.217623 | − | 0.976033i | \(-0.569830\pi\) | ||||
−0.217623 | + | 0.976033i | \(0.569830\pi\) | |||||||
\(44\) | −22.4164 | −3.37940 | ||||||||
\(45\) | −3.85410 | −0.574536 | ||||||||
\(46\) | −4.23607 | −0.624574 | ||||||||
\(47\) | −10.2361 | −1.49308 | −0.746542 | − | 0.665338i | \(-0.768287\pi\) | ||||
−0.746542 | + | 0.665338i | \(0.768287\pi\) | |||||||
\(48\) | 25.7984 | 3.72367 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | 2.61803 | 0.370246 | ||||||||
\(51\) | −15.7082 | −2.19959 | ||||||||
\(52\) | 24.2705 | 3.36571 | ||||||||
\(53\) | 5.61803 | 0.771696 | 0.385848 | − | 0.922562i | \(-0.373909\pi\) | ||||
0.385848 | + | 0.922562i | \(0.373909\pi\) | |||||||
\(54\) | 5.85410 | 0.796642 | ||||||||
\(55\) | 4.61803 | 0.622696 | ||||||||
\(56\) | 1.76393 | 0.235715 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.85410 | −0.637375 | ||||||||
\(59\) | 0.0901699 | 0.0117391 | 0.00586956 | − | 0.999983i | \(-0.498132\pi\) | ||||
0.00586956 | + | 0.999983i | \(0.498132\pi\) | |||||||
\(60\) | −12.7082 | −1.64062 | ||||||||
\(61\) | −3.00000 | −0.384111 | −0.192055 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(62\) | 10.8541 | 1.37847 | ||||||||
\(63\) | 0.909830 | 0.114628 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | −5.00000 | −0.620174 | ||||||||
\(66\) | −31.6525 | −3.89615 | ||||||||
\(67\) | −4.70820 | −0.575199 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(68\) | −29.1246 | −3.53188 | ||||||||
\(69\) | −4.23607 | −0.509963 | ||||||||
\(70\) | −0.618034 | −0.0738692 | ||||||||
\(71\) | 3.76393 | 0.446697 | 0.223348 | − | 0.974739i | \(-0.428301\pi\) | ||||
0.223348 | + | 0.974739i | \(0.428301\pi\) | |||||||
\(72\) | 28.7984 | 3.39392 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −4.85410 | −0.564278 | ||||||||
\(75\) | 2.61803 | 0.302305 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.09017 | −0.124236 | ||||||||
\(78\) | 34.2705 | 3.88037 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −9.85410 | −1.10172 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | 29.2705 | 3.23239 | ||||||||
\(83\) | 4.47214 | 0.490881 | 0.245440 | − | 0.969412i | \(-0.421067\pi\) | ||||
0.245440 | + | 0.969412i | \(0.421067\pi\) | |||||||
\(84\) | 3.00000 | 0.327327 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | −7.47214 | −0.805741 | ||||||||
\(87\) | −4.85410 | −0.520414 | ||||||||
\(88\) | −34.5066 | −3.67841 | ||||||||
\(89\) | −6.70820 | −0.711068 | −0.355534 | − | 0.934663i | \(-0.615701\pi\) | ||||
−0.355534 | + | 0.934663i | \(0.615701\pi\) | |||||||
\(90\) | −10.0902 | −1.06360 | ||||||||
\(91\) | 1.18034 | 0.123733 | ||||||||
\(92\) | −7.85410 | −0.818847 | ||||||||
\(93\) | 10.8541 | 1.12552 | ||||||||
\(94\) | −26.7984 | −2.76404 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 28.4164 | 2.90024 | ||||||||
\(97\) | 6.09017 | 0.618363 | 0.309182 | − | 0.951003i | \(-0.399945\pi\) | ||||
0.309182 | + | 0.951003i | \(0.399945\pi\) | |||||||
\(98\) | −18.1803 | −1.83649 | ||||||||
\(99\) | −17.7984 | −1.78880 | ||||||||
\(100\) | 4.85410 | 0.485410 | ||||||||
\(101\) | −11.9443 | −1.18850 | −0.594250 | − | 0.804281i | \(-0.702551\pi\) | ||||
−0.594250 | + | 0.804281i | \(0.702551\pi\) | |||||||
\(102\) | −41.1246 | −4.07194 | ||||||||
\(103\) | 17.3262 | 1.70720 | 0.853602 | − | 0.520925i | \(-0.174413\pi\) | ||||
0.853602 | + | 0.520925i | \(0.174413\pi\) | |||||||
\(104\) | 37.3607 | 3.66352 | ||||||||
\(105\) | −0.618034 | −0.0603139 | ||||||||
\(106\) | 14.7082 | 1.42859 | ||||||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | 10.8541 | 1.04444 | ||||||||
\(109\) | 6.23607 | 0.597307 | 0.298653 | − | 0.954362i | \(-0.403463\pi\) | ||||
0.298653 | + | 0.954362i | \(0.403463\pi\) | |||||||
\(110\) | 12.0902 | 1.15275 | ||||||||
\(111\) | −4.85410 | −0.460731 | ||||||||
\(112\) | 2.32624 | 0.219809 | ||||||||
\(113\) | 2.94427 | 0.276974 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.61803 | 0.150882 | ||||||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | 19.2705 | 1.78156 | ||||||||
\(118\) | 0.236068 | 0.0217318 | ||||||||
\(119\) | −1.41641 | −0.129842 | ||||||||
\(120\) | −19.5623 | −1.78579 | ||||||||
\(121\) | 10.3262 | 0.938749 | ||||||||
\(122\) | −7.85410 | −0.711077 | ||||||||
\(123\) | 29.2705 | 2.63923 | ||||||||
\(124\) | 20.1246 | 1.80724 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.38197 | 0.212202 | ||||||||
\(127\) | −2.70820 | −0.240314 | −0.120157 | − | 0.992755i | \(-0.538340\pi\) | ||||
−0.120157 | + | 0.992755i | \(0.538340\pi\) | |||||||
\(128\) | 1.09017 | 0.0963583 | ||||||||
\(129\) | −7.47214 | −0.657885 | ||||||||
\(130\) | −13.0902 | −1.14808 | ||||||||
\(131\) | −1.14590 | −0.100118 | −0.0500588 | − | 0.998746i | \(-0.515941\pi\) | ||||
−0.0500588 | + | 0.998746i | \(0.515941\pi\) | |||||||
\(132\) | −58.6869 | −5.10804 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.3262 | −1.06482 | ||||||||
\(135\) | −2.23607 | −0.192450 | ||||||||
\(136\) | −44.8328 | −3.84438 | ||||||||
\(137\) | −21.1803 | −1.80956 | −0.904779 | − | 0.425881i | \(-0.859964\pi\) | ||||
−0.904779 | + | 0.425881i | \(0.859964\pi\) | |||||||
\(138\) | −11.0902 | −0.944058 | ||||||||
\(139\) | 14.8541 | 1.25991 | 0.629954 | − | 0.776632i | \(-0.283074\pi\) | ||||
0.629954 | + | 0.776632i | \(0.283074\pi\) | |||||||
\(140\) | −1.14590 | −0.0968461 | ||||||||
\(141\) | −26.7984 | −2.25683 | ||||||||
\(142\) | 9.85410 | 0.826938 | ||||||||
\(143\) | −23.0902 | −1.93090 | ||||||||
\(144\) | 37.9787 | 3.16489 | ||||||||
\(145\) | 1.85410 | 0.153975 | ||||||||
\(146\) | −2.61803 | −0.216670 | ||||||||
\(147\) | −18.1803 | −1.49949 | ||||||||
\(148\) | −9.00000 | −0.739795 | ||||||||
\(149\) | −5.38197 | −0.440908 | −0.220454 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220454 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(150\) | 6.85410 | 0.559635 | ||||||||
\(151\) | −9.61803 | −0.782705 | −0.391352 | − | 0.920241i | \(-0.627993\pi\) | ||||
−0.391352 | + | 0.920241i | \(0.627993\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −23.1246 | −1.86951 | ||||||||
\(154\) | −2.85410 | −0.229990 | ||||||||
\(155\) | −4.14590 | −0.333007 | ||||||||
\(156\) | 63.5410 | 5.08735 | ||||||||
\(157\) | 5.03444 | 0.401792 | 0.200896 | − | 0.979613i | \(-0.435615\pi\) | ||||
0.200896 | + | 0.979613i | \(0.435615\pi\) | |||||||
\(158\) | 20.9443 | 1.66624 | ||||||||
\(159\) | 14.7082 | 1.16644 | ||||||||
\(160\) | −10.8541 | −0.858092 | ||||||||
\(161\) | −0.381966 | −0.0301031 | ||||||||
\(162\) | −14.9443 | −1.17413 | ||||||||
\(163\) | 17.4721 | 1.36852 | 0.684262 | − | 0.729237i | \(-0.260125\pi\) | ||||
0.684262 | + | 0.729237i | \(0.260125\pi\) | |||||||
\(164\) | 54.2705 | 4.23781 | ||||||||
\(165\) | 12.0902 | 0.941218 | ||||||||
\(166\) | 11.7082 | 0.908733 | ||||||||
\(167\) | 3.76393 | 0.291262 | 0.145631 | − | 0.989339i | \(-0.453479\pi\) | ||||
0.145631 | + | 0.989339i | \(0.453479\pi\) | |||||||
\(168\) | 4.61803 | 0.356289 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 15.7082 | 1.20476 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.8541 | −1.05637 | ||||||||
\(173\) | −21.8885 | −1.66416 | −0.832078 | − | 0.554659i | \(-0.812849\pi\) | ||||
−0.832078 | + | 0.554659i | \(0.812849\pi\) | |||||||
\(174\) | −12.7082 | −0.963406 | ||||||||
\(175\) | 0.236068 | 0.0178451 | ||||||||
\(176\) | −45.5066 | −3.43019 | ||||||||
\(177\) | 0.236068 | 0.0177440 | ||||||||
\(178\) | −17.5623 | −1.31635 | ||||||||
\(179\) | 19.4721 | 1.45542 | 0.727708 | − | 0.685887i | \(-0.240586\pi\) | ||||
0.727708 | + | 0.685887i | \(0.240586\pi\) | |||||||
\(180\) | −18.7082 | −1.39443 | ||||||||
\(181\) | 21.7082 | 1.61356 | 0.806779 | − | 0.590853i | \(-0.201209\pi\) | ||||
0.806779 | + | 0.590853i | \(0.201209\pi\) | |||||||
\(182\) | 3.09017 | 0.229059 | ||||||||
\(183\) | −7.85410 | −0.580592 | ||||||||
\(184\) | −12.0902 | −0.891299 | ||||||||
\(185\) | 1.85410 | 0.136316 | ||||||||
\(186\) | 28.4164 | 2.08359 | ||||||||
\(187\) | 27.7082 | 2.02622 | ||||||||
\(188\) | −49.6869 | −3.62379 | ||||||||
\(189\) | 0.527864 | 0.0383965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.9443 | 1.73255 | 0.866273 | − | 0.499570i | \(-0.166509\pi\) | ||||
0.866273 | + | 0.499570i | \(0.166509\pi\) | |||||||
\(192\) | 22.7984 | 1.64533 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | 15.9443 | 1.14473 | ||||||||
\(195\) | −13.0902 | −0.937407 | ||||||||
\(196\) | −33.7082 | −2.40773 | ||||||||
\(197\) | 25.4721 | 1.81481 | 0.907407 | − | 0.420252i | \(-0.138058\pi\) | ||||
0.907407 | + | 0.420252i | \(0.138058\pi\) | |||||||
\(198\) | −46.5967 | −3.31149 | ||||||||
\(199\) | −13.4164 | −0.951064 | −0.475532 | − | 0.879698i | \(-0.657744\pi\) | ||||
−0.475532 | + | 0.879698i | \(0.657744\pi\) | |||||||
\(200\) | 7.47214 | 0.528360 | ||||||||
\(201\) | −12.3262 | −0.869426 | ||||||||
\(202\) | −31.2705 | −2.20019 | ||||||||
\(203\) | −0.437694 | −0.0307201 | ||||||||
\(204\) | −76.2492 | −5.33851 | ||||||||
\(205\) | −11.1803 | −0.780869 | ||||||||
\(206\) | 45.3607 | 3.16043 | ||||||||
\(207\) | −6.23607 | −0.433437 | ||||||||
\(208\) | 49.2705 | 3.41630 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.61803 | −0.111655 | ||||||||
\(211\) | −18.0902 | −1.24538 | −0.622689 | − | 0.782469i | \(-0.713960\pi\) | ||||
−0.622689 | + | 0.782469i | \(0.713960\pi\) | |||||||
\(212\) | 27.2705 | 1.87295 | ||||||||
\(213\) | 9.85410 | 0.675192 | ||||||||
\(214\) | 7.85410 | 0.536895 | ||||||||
\(215\) | 2.85410 | 0.194648 | ||||||||
\(216\) | 16.7082 | 1.13685 | ||||||||
\(217\) | 0.978714 | 0.0664394 | ||||||||
\(218\) | 16.3262 | 1.10575 | ||||||||
\(219\) | −2.61803 | −0.176910 | ||||||||
\(220\) | 22.4164 | 1.51131 | ||||||||
\(221\) | −30.0000 | −2.01802 | ||||||||
\(222\) | −12.7082 | −0.852919 | ||||||||
\(223\) | 5.76393 | 0.385981 | 0.192991 | − | 0.981201i | \(-0.438181\pi\) | ||||
0.192991 | + | 0.981201i | \(0.438181\pi\) | |||||||
\(224\) | 2.56231 | 0.171201 | ||||||||
\(225\) | 3.85410 | 0.256940 | ||||||||
\(226\) | 7.70820 | 0.512742 | ||||||||
\(227\) | −13.6525 | −0.906147 | −0.453073 | − | 0.891473i | \(-0.649672\pi\) | ||||
−0.453073 | + | 0.891473i | \(0.649672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.3820 | −1.28080 | −0.640398 | − | 0.768043i | \(-0.721231\pi\) | ||||
−0.640398 | + | 0.768043i | \(0.721231\pi\) | |||||||
\(230\) | 4.23607 | 0.279318 | ||||||||
\(231\) | −2.85410 | −0.187786 | ||||||||
\(232\) | −13.8541 | −0.909566 | ||||||||
\(233\) | −29.1803 | −1.91167 | −0.955834 | − | 0.293908i | \(-0.905044\pi\) | ||||
−0.955834 | + | 0.293908i | \(0.905044\pi\) | |||||||
\(234\) | 50.4508 | 3.29808 | ||||||||
\(235\) | 10.2361 | 0.667727 | ||||||||
\(236\) | 0.437694 | 0.0284915 | ||||||||
\(237\) | 20.9443 | 1.36048 | ||||||||
\(238\) | −3.70820 | −0.240367 | ||||||||
\(239\) | 3.43769 | 0.222366 | 0.111183 | − | 0.993800i | \(-0.464536\pi\) | ||||
0.111183 | + | 0.993800i | \(0.464536\pi\) | |||||||
\(240\) | −25.7984 | −1.66528 | ||||||||
\(241\) | −22.1246 | −1.42517 | −0.712586 | − | 0.701585i | \(-0.752476\pi\) | ||||
−0.712586 | + | 0.701585i | \(0.752476\pi\) | |||||||
\(242\) | 27.0344 | 1.73784 | ||||||||
\(243\) | −21.6525 | −1.38901 | ||||||||
\(244\) | −14.5623 | −0.932256 | ||||||||
\(245\) | 6.94427 | 0.443653 | ||||||||
\(246\) | 76.6312 | 4.88583 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 30.9787 | 1.96715 | ||||||||
\(249\) | 11.7082 | 0.741977 | ||||||||
\(250\) | −2.61803 | −0.165579 | ||||||||
\(251\) | −7.18034 | −0.453219 | −0.226610 | − | 0.973986i | \(-0.572764\pi\) | ||||
−0.226610 | + | 0.973986i | \(0.572764\pi\) | |||||||
\(252\) | 4.41641 | 0.278208 | ||||||||
\(253\) | 7.47214 | 0.469769 | ||||||||
\(254\) | −7.09017 | −0.444877 | ||||||||
\(255\) | 15.7082 | 0.983686 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | 22.4721 | 1.40177 | 0.700887 | − | 0.713273i | \(-0.252788\pi\) | ||||
0.700887 | + | 0.713273i | \(0.252788\pi\) | |||||||
\(258\) | −19.5623 | −1.21790 | ||||||||
\(259\) | −0.437694 | −0.0271970 | ||||||||
\(260\) | −24.2705 | −1.50519 | ||||||||
\(261\) | −7.14590 | −0.442320 | ||||||||
\(262\) | −3.00000 | −0.185341 | ||||||||
\(263\) | 15.8885 | 0.979730 | 0.489865 | − | 0.871798i | \(-0.337046\pi\) | ||||
0.489865 | + | 0.871798i | \(0.337046\pi\) | |||||||
\(264\) | −90.3394 | −5.56001 | ||||||||
\(265\) | −5.61803 | −0.345113 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.5623 | −1.07480 | ||||||||
\(268\) | −22.8541 | −1.39604 | ||||||||
\(269\) | 17.3262 | 1.05640 | 0.528200 | − | 0.849120i | \(-0.322867\pi\) | ||||
0.528200 | + | 0.849120i | \(0.322867\pi\) | |||||||
\(270\) | −5.85410 | −0.356269 | ||||||||
\(271\) | 18.6180 | 1.13097 | 0.565483 | − | 0.824760i | \(-0.308690\pi\) | ||||
0.565483 | + | 0.824760i | \(0.308690\pi\) | |||||||
\(272\) | −59.1246 | −3.58496 | ||||||||
\(273\) | 3.09017 | 0.187026 | ||||||||
\(274\) | −55.4508 | −3.34991 | ||||||||
\(275\) | −4.61803 | −0.278478 | ||||||||
\(276\) | −20.5623 | −1.23771 | ||||||||
\(277\) | 1.41641 | 0.0851037 | 0.0425519 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425519 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(278\) | 38.8885 | 2.33238 | ||||||||
\(279\) | 15.9787 | 0.956621 | ||||||||
\(280\) | −1.76393 | −0.105415 | ||||||||
\(281\) | −10.5066 | −0.626770 | −0.313385 | − | 0.949626i | \(-0.601463\pi\) | ||||
−0.313385 | + | 0.949626i | \(0.601463\pi\) | |||||||
\(282\) | −70.1591 | −4.17791 | ||||||||
\(283\) | 2.38197 | 0.141593 | 0.0707966 | − | 0.997491i | \(-0.477446\pi\) | ||||
0.0707966 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(284\) | 18.2705 | 1.08416 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −60.4508 | −3.57453 | ||||||||
\(287\) | 2.63932 | 0.155794 | ||||||||
\(288\) | 41.8328 | 2.46502 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 4.85410 | 0.285043 | ||||||||
\(291\) | 15.9443 | 0.934670 | ||||||||
\(292\) | −4.85410 | −0.284065 | ||||||||
\(293\) | −7.03444 | −0.410956 | −0.205478 | − | 0.978662i | \(-0.565875\pi\) | ||||
−0.205478 | + | 0.978662i | \(0.565875\pi\) | |||||||
\(294\) | −47.5967 | −2.77590 | ||||||||
\(295\) | −0.0901699 | −0.00524990 | ||||||||
\(296\) | −13.8541 | −0.805253 | ||||||||
\(297\) | −10.3262 | −0.599189 | ||||||||
\(298\) | −14.0902 | −0.816222 | ||||||||
\(299\) | −8.09017 | −0.467867 | ||||||||
\(300\) | 12.7082 | 0.733708 | ||||||||
\(301\) | −0.673762 | −0.0388350 | ||||||||
\(302\) | −25.1803 | −1.44897 | ||||||||
\(303\) | −31.2705 | −1.79644 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | 0.171780 | ||||||||
\(306\) | −60.5410 | −3.46090 | ||||||||
\(307\) | 21.2705 | 1.21397 | 0.606986 | − | 0.794712i | \(-0.292378\pi\) | ||||
0.606986 | + | 0.794712i | \(0.292378\pi\) | |||||||
\(308\) | −5.29180 | −0.301528 | ||||||||
\(309\) | 45.3607 | 2.58048 | ||||||||
\(310\) | −10.8541 | −0.616472 | ||||||||
\(311\) | −24.9443 | −1.41446 | −0.707230 | − | 0.706984i | \(-0.750055\pi\) | ||||
−0.707230 | + | 0.706984i | \(0.750055\pi\) | |||||||
\(312\) | 97.8115 | 5.53749 | ||||||||
\(313\) | 14.7984 | 0.836454 | 0.418227 | − | 0.908343i | \(-0.362652\pi\) | ||||
0.418227 | + | 0.908343i | \(0.362652\pi\) | |||||||
\(314\) | 13.1803 | 0.743810 | ||||||||
\(315\) | −0.909830 | −0.0512631 | ||||||||
\(316\) | 38.8328 | 2.18452 | ||||||||
\(317\) | −8.76393 | −0.492231 | −0.246116 | − | 0.969240i | \(-0.579154\pi\) | ||||
−0.246116 | + | 0.969240i | \(0.579154\pi\) | |||||||
\(318\) | 38.5066 | 2.15934 | ||||||||
\(319\) | 8.56231 | 0.479397 | ||||||||
\(320\) | −8.70820 | −0.486803 | ||||||||
\(321\) | 7.85410 | 0.438373 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −27.7082 | −1.53934 | ||||||||
\(325\) | 5.00000 | 0.277350 | ||||||||
\(326\) | 45.7426 | 2.53345 | ||||||||
\(327\) | 16.3262 | 0.902843 | ||||||||
\(328\) | 83.5410 | 4.61278 | ||||||||
\(329\) | −2.41641 | −0.133221 | ||||||||
\(330\) | 31.6525 | 1.74241 | ||||||||
\(331\) | −13.7082 | −0.753471 | −0.376736 | − | 0.926321i | \(-0.622953\pi\) | ||||
−0.376736 | + | 0.926321i | \(0.622953\pi\) | |||||||
\(332\) | 21.7082 | 1.19139 | ||||||||
\(333\) | −7.14590 | −0.391593 | ||||||||
\(334\) | 9.85410 | 0.539192 | ||||||||
\(335\) | 4.70820 | 0.257237 | ||||||||
\(336\) | 6.09017 | 0.332246 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 31.4164 | 1.70883 | ||||||||
\(339\) | 7.70820 | 0.418652 | ||||||||
\(340\) | 29.1246 | 1.57950 | ||||||||
\(341\) | −19.1459 | −1.03681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.29180 | −0.177740 | ||||||||
\(344\) | −21.3262 | −1.14983 | ||||||||
\(345\) | 4.23607 | 0.228062 | ||||||||
\(346\) | −57.3050 | −3.08073 | ||||||||
\(347\) | 15.8885 | 0.852942 | 0.426471 | − | 0.904501i | \(-0.359757\pi\) | ||||
0.426471 | + | 0.904501i | \(0.359757\pi\) | |||||||
\(348\) | −23.5623 | −1.26307 | ||||||||
\(349\) | −20.7426 | −1.11033 | −0.555164 | − | 0.831741i | \(-0.687345\pi\) | ||||
−0.555164 | + | 0.831741i | \(0.687345\pi\) | |||||||
\(350\) | 0.618034 | 0.0330353 | ||||||||
\(351\) | 11.1803 | 0.596762 | ||||||||
\(352\) | −50.1246 | −2.67165 | ||||||||
\(353\) | 33.1591 | 1.76488 | 0.882439 | − | 0.470427i | \(-0.155900\pi\) | ||||
0.882439 | + | 0.470427i | \(0.155900\pi\) | |||||||
\(354\) | 0.618034 | 0.0328481 | ||||||||
\(355\) | −3.76393 | −0.199769 | ||||||||
\(356\) | −32.5623 | −1.72580 | ||||||||
\(357\) | −3.70820 | −0.196259 | ||||||||
\(358\) | 50.9787 | 2.69431 | ||||||||
\(359\) | 28.6180 | 1.51040 | 0.755201 | − | 0.655493i | \(-0.227539\pi\) | ||||
0.755201 | + | 0.655493i | \(0.227539\pi\) | |||||||
\(360\) | −28.7984 | −1.51781 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 56.8328 | 2.98707 | ||||||||
\(363\) | 27.0344 | 1.41894 | ||||||||
\(364\) | 5.72949 | 0.300307 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −20.5623 | −1.07481 | ||||||||
\(367\) | −29.6525 | −1.54785 | −0.773923 | − | 0.633279i | \(-0.781708\pi\) | ||||
−0.773923 | + | 0.633279i | \(0.781708\pi\) | |||||||
\(368\) | −15.9443 | −0.831153 | ||||||||
\(369\) | 43.0902 | 2.24318 | ||||||||
\(370\) | 4.85410 | 0.252353 | ||||||||
\(371\) | 1.32624 | 0.0688548 | ||||||||
\(372\) | 52.6869 | 2.73169 | ||||||||
\(373\) | 6.70820 | 0.347338 | 0.173669 | − | 0.984804i | \(-0.444438\pi\) | ||||
0.173669 | + | 0.984804i | \(0.444438\pi\) | |||||||
\(374\) | 72.5410 | 3.75101 | ||||||||
\(375\) | −2.61803 | −0.135195 | ||||||||
\(376\) | −76.4853 | −3.94443 | ||||||||
\(377\) | −9.27051 | −0.477456 | ||||||||
\(378\) | 1.38197 | 0.0710807 | ||||||||
\(379\) | 26.8328 | 1.37831 | 0.689155 | − | 0.724614i | \(-0.257982\pi\) | ||||
0.689155 | + | 0.724614i | \(0.257982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.09017 | −0.363240 | ||||||||
\(382\) | 62.6869 | 3.20734 | ||||||||
\(383\) | −31.9230 | −1.63119 | −0.815594 | − | 0.578624i | \(-0.803590\pi\) | ||||
−0.815594 | + | 0.578624i | \(0.803590\pi\) | |||||||
\(384\) | 2.85410 | 0.145648 | ||||||||
\(385\) | 1.09017 | 0.0555602 | ||||||||
\(386\) | 10.4721 | 0.533018 | ||||||||
\(387\) | −11.0000 | −0.559161 | ||||||||
\(388\) | 29.5623 | 1.50080 | ||||||||
\(389\) | −8.67376 | −0.439777 | −0.219889 | − | 0.975525i | \(-0.570569\pi\) | ||||
−0.219889 | + | 0.975525i | \(0.570569\pi\) | |||||||
\(390\) | −34.2705 | −1.73535 | ||||||||
\(391\) | 9.70820 | 0.490965 | ||||||||
\(392\) | −51.8885 | −2.62077 | ||||||||
\(393\) | −3.00000 | −0.151330 | ||||||||
\(394\) | 66.6869 | 3.35964 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | −86.3951 | −4.34152 | ||||||||
\(397\) | 18.8885 | 0.947989 | 0.473994 | − | 0.880528i | \(-0.342812\pi\) | ||||
0.473994 | + | 0.880528i | \(0.342812\pi\) | |||||||
\(398\) | −35.1246 | −1.76064 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.85410 | 0.492705 | ||||||||
\(401\) | 11.2361 | 0.561102 | 0.280551 | − | 0.959839i | \(-0.409483\pi\) | ||||
0.280551 | + | 0.959839i | \(0.409483\pi\) | |||||||
\(402\) | −32.2705 | −1.60951 | ||||||||
\(403\) | 20.7295 | 1.03261 | ||||||||
\(404\) | −57.9787 | −2.88455 | ||||||||
\(405\) | 5.70820 | 0.283643 | ||||||||
\(406\) | −1.14590 | −0.0568700 | ||||||||
\(407\) | 8.56231 | 0.424418 | ||||||||
\(408\) | −117.374 | −5.81087 | ||||||||
\(409\) | 11.7082 | 0.578933 | 0.289467 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289467 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(410\) | −29.2705 | −1.44557 | ||||||||
\(411\) | −55.4508 | −2.73519 | ||||||||
\(412\) | 84.1033 | 4.14347 | ||||||||
\(413\) | 0.0212862 | 0.00104743 | ||||||||
\(414\) | −16.3262 | −0.802391 | ||||||||
\(415\) | −4.47214 | −0.219529 | ||||||||
\(416\) | 54.2705 | 2.66083 | ||||||||
\(417\) | 38.8885 | 1.90438 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.9443 | 0.925488 | 0.462744 | − | 0.886492i | \(-0.346865\pi\) | ||||
0.462744 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(420\) | −3.00000 | −0.146385 | ||||||||
\(421\) | −14.1246 | −0.688391 | −0.344196 | − | 0.938898i | \(-0.611848\pi\) | ||||
−0.344196 | + | 0.938898i | \(0.611848\pi\) | |||||||
\(422\) | −47.3607 | −2.30548 | ||||||||
\(423\) | −39.4508 | −1.91817 | ||||||||
\(424\) | 41.9787 | 2.03867 | ||||||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | 25.7984 | 1.24994 | ||||||||
\(427\) | −0.708204 | −0.0342724 | ||||||||
\(428\) | 14.5623 | 0.703896 | ||||||||
\(429\) | −60.4508 | −2.91859 | ||||||||
\(430\) | 7.47214 | 0.360338 | ||||||||
\(431\) | −2.81966 | −0.135818 | −0.0679091 | − | 0.997692i | \(-0.521633\pi\) | ||||
−0.0679091 | + | 0.997692i | \(0.521633\pi\) | |||||||
\(432\) | 22.0344 | 1.06013 | ||||||||
\(433\) | 22.2148 | 1.06757 | 0.533787 | − | 0.845619i | \(-0.320768\pi\) | ||||
0.533787 | + | 0.845619i | \(0.320768\pi\) | |||||||
\(434\) | 2.56231 | 0.122995 | ||||||||
\(435\) | 4.85410 | 0.232736 | ||||||||
\(436\) | 30.2705 | 1.44969 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.85410 | −0.327502 | ||||||||
\(439\) | −5.47214 | −0.261171 | −0.130585 | − | 0.991437i | \(-0.541686\pi\) | ||||
−0.130585 | + | 0.991437i | \(0.541686\pi\) | |||||||
\(440\) | 34.5066 | 1.64504 | ||||||||
\(441\) | −26.7639 | −1.27447 | ||||||||
\(442\) | −78.5410 | −3.73582 | ||||||||
\(443\) | 15.3607 | 0.729808 | 0.364904 | − | 0.931045i | \(-0.381102\pi\) | ||||
0.364904 | + | 0.931045i | \(0.381102\pi\) | |||||||
\(444\) | −23.5623 | −1.11822 | ||||||||
\(445\) | 6.70820 | 0.317999 | ||||||||
\(446\) | 15.0902 | 0.714540 | ||||||||
\(447\) | −14.0902 | −0.666442 | ||||||||
\(448\) | 2.05573 | 0.0971240 | ||||||||
\(449\) | 32.5279 | 1.53508 | 0.767542 | − | 0.640998i | \(-0.221479\pi\) | ||||
0.767542 | + | 0.640998i | \(0.221479\pi\) | |||||||
\(450\) | 10.0902 | 0.475655 | ||||||||
\(451\) | −51.6312 | −2.43122 | ||||||||
\(452\) | 14.2918 | 0.672230 | ||||||||
\(453\) | −25.1803 | −1.18308 | ||||||||
\(454\) | −35.7426 | −1.67749 | ||||||||
\(455\) | −1.18034 | −0.0553352 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | −50.7426 | −2.37105 | ||||||||
\(459\) | −13.4164 | −0.626224 | ||||||||
\(460\) | 7.85410 | 0.366199 | ||||||||
\(461\) | −18.9443 | −0.882323 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(462\) | −7.47214 | −0.347635 | ||||||||
\(463\) | 3.96556 | 0.184295 | 0.0921476 | − | 0.995745i | \(-0.470627\pi\) | ||||
0.0921476 | + | 0.995745i | \(0.470627\pi\) | |||||||
\(464\) | −18.2705 | −0.848187 | ||||||||
\(465\) | −10.8541 | −0.503347 | ||||||||
\(466\) | −76.3951 | −3.53894 | ||||||||
\(467\) | −11.2918 | −0.522522 | −0.261261 | − | 0.965268i | \(-0.584138\pi\) | ||||
−0.261261 | + | 0.965268i | \(0.584138\pi\) | |||||||
\(468\) | 93.5410 | 4.32394 | ||||||||
\(469\) | −1.11146 | −0.0513223 | ||||||||
\(470\) | 26.7984 | 1.23612 | ||||||||
\(471\) | 13.1803 | 0.607318 | ||||||||
\(472\) | 0.673762 | 0.0310124 | ||||||||
\(473\) | 13.1803 | 0.606033 | ||||||||
\(474\) | 54.8328 | 2.51855 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.87539 | −0.315133 | ||||||||
\(477\) | 21.6525 | 0.991399 | ||||||||
\(478\) | 9.00000 | 0.411650 | ||||||||
\(479\) | −8.38197 | −0.382982 | −0.191491 | − | 0.981494i | \(-0.561332\pi\) | ||||
−0.191491 | + | 0.981494i | \(0.561332\pi\) | |||||||
\(480\) | −28.4164 | −1.29703 | ||||||||
\(481\) | −9.27051 | −0.422699 | ||||||||
\(482\) | −57.9230 | −2.63832 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 50.1246 | 2.27839 | ||||||||
\(485\) | −6.09017 | −0.276540 | ||||||||
\(486\) | −56.6869 | −2.57137 | ||||||||
\(487\) | −8.58359 | −0.388960 | −0.194480 | − | 0.980907i | \(-0.562302\pi\) | ||||
−0.194480 | + | 0.980907i | \(0.562302\pi\) | |||||||
\(488\) | −22.4164 | −1.01474 | ||||||||
\(489\) | 45.7426 | 2.06855 | ||||||||
\(490\) | 18.1803 | 0.821304 | ||||||||
\(491\) | 24.3262 | 1.09783 | 0.548914 | − | 0.835879i | \(-0.315041\pi\) | ||||
0.548914 | + | 0.835879i | \(0.315041\pi\) | |||||||
\(492\) | 142.082 | 6.40555 | ||||||||
\(493\) | 11.1246 | 0.501027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.7984 | 0.799977 | ||||||||
\(496\) | 40.8541 | 1.83440 | ||||||||
\(497\) | 0.888544 | 0.0398566 | ||||||||
\(498\) | 30.6525 | 1.37357 | ||||||||
\(499\) | −4.65248 | −0.208273 | −0.104137 | − | 0.994563i | \(-0.533208\pi\) | ||||
−0.104137 | + | 0.994563i | \(0.533208\pi\) | |||||||
\(500\) | −4.85410 | −0.217082 | ||||||||
\(501\) | 9.85410 | 0.440249 | ||||||||
\(502\) | −18.7984 | −0.839012 | ||||||||
\(503\) | −19.9443 | −0.889271 | −0.444636 | − | 0.895712i | \(-0.646667\pi\) | ||||
−0.444636 | + | 0.895712i | \(0.646667\pi\) | |||||||
\(504\) | 6.79837 | 0.302824 | ||||||||
\(505\) | 11.9443 | 0.531513 | ||||||||
\(506\) | 19.5623 | 0.869651 | ||||||||
\(507\) | 31.4164 | 1.39525 | ||||||||
\(508\) | −13.1459 | −0.583255 | ||||||||
\(509\) | −13.7984 | −0.611602 | −0.305801 | − | 0.952095i | \(-0.598924\pi\) | ||||
−0.305801 | + | 0.952095i | \(0.598924\pi\) | |||||||
\(510\) | 41.1246 | 1.82103 | ||||||||
\(511\) | −0.236068 | −0.0104430 | ||||||||
\(512\) | −40.3050 | −1.78124 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 58.8328 | 2.59500 | ||||||||
\(515\) | −17.3262 | −0.763485 | ||||||||
\(516\) | −36.2705 | −1.59672 | ||||||||
\(517\) | 47.2705 | 2.07895 | ||||||||
\(518\) | −1.14590 | −0.0503479 | ||||||||
\(519\) | −57.3050 | −2.51541 | ||||||||
\(520\) | −37.3607 | −1.63837 | ||||||||
\(521\) | −2.61803 | −0.114698 | −0.0573491 | − | 0.998354i | \(-0.518265\pi\) | ||||
−0.0573491 | + | 0.998354i | \(0.518265\pi\) | |||||||
\(522\) | −18.7082 | −0.818836 | ||||||||
\(523\) | −38.5967 | −1.68772 | −0.843859 | − | 0.536565i | \(-0.819722\pi\) | ||||
−0.843859 | + | 0.536565i | \(0.819722\pi\) | |||||||
\(524\) | −5.56231 | −0.242990 | ||||||||
\(525\) | 0.618034 | 0.0269732 | ||||||||
\(526\) | 41.5967 | 1.81370 | ||||||||
\(527\) | −24.8754 | −1.08359 | ||||||||
\(528\) | −119.138 | −5.18481 | ||||||||
\(529\) | −20.3820 | −0.886172 | ||||||||
\(530\) | −14.7082 | −0.638884 | ||||||||
\(531\) | 0.347524 | 0.0150813 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 55.9017 | 2.42137 | ||||||||
\(534\) | −45.9787 | −1.98969 | ||||||||
\(535\) | −3.00000 | −0.129701 | ||||||||
\(536\) | −35.1803 | −1.51956 | ||||||||
\(537\) | 50.9787 | 2.19989 | ||||||||
\(538\) | 45.3607 | 1.95564 | ||||||||
\(539\) | 32.0689 | 1.38130 | ||||||||
\(540\) | −10.8541 | −0.467086 | ||||||||
\(541\) | −16.5967 | −0.713550 | −0.356775 | − | 0.934190i | \(-0.616124\pi\) | ||||
−0.356775 | + | 0.934190i | \(0.616124\pi\) | |||||||
\(542\) | 48.7426 | 2.09368 | ||||||||
\(543\) | 56.8328 | 2.43893 | ||||||||
\(544\) | −65.1246 | −2.79219 | ||||||||
\(545\) | −6.23607 | −0.267124 | ||||||||
\(546\) | 8.09017 | 0.346227 | ||||||||
\(547\) | −8.97871 | −0.383902 | −0.191951 | − | 0.981405i | \(-0.561481\pi\) | ||||
−0.191951 | + | 0.981405i | \(0.561481\pi\) | |||||||
\(548\) | −102.812 | −4.39189 | ||||||||
\(549\) | −11.5623 | −0.493467 | ||||||||
\(550\) | −12.0902 | −0.515527 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −31.6525 | −1.34722 | ||||||||
\(553\) | 1.88854 | 0.0803091 | ||||||||
\(554\) | 3.70820 | 0.157546 | ||||||||
\(555\) | 4.85410 | 0.206045 | ||||||||
\(556\) | 72.1033 | 3.05786 | ||||||||
\(557\) | −12.5279 | −0.530823 | −0.265411 | − | 0.964135i | \(-0.585508\pi\) | ||||
−0.265411 | + | 0.964135i | \(0.585508\pi\) | |||||||
\(558\) | 41.8328 | 1.77092 | ||||||||
\(559\) | −14.2705 | −0.603578 | ||||||||
\(560\) | −2.32624 | −0.0983015 | ||||||||
\(561\) | 72.5410 | 3.06268 | ||||||||
\(562\) | −27.5066 | −1.16029 | ||||||||
\(563\) | −7.81966 | −0.329559 | −0.164780 | − | 0.986330i | \(-0.552691\pi\) | ||||
−0.164780 | + | 0.986330i | \(0.552691\pi\) | |||||||
\(564\) | −130.082 | −5.47744 | ||||||||
\(565\) | −2.94427 | −0.123866 | ||||||||
\(566\) | 6.23607 | 0.262121 | ||||||||
\(567\) | −1.34752 | −0.0565907 | ||||||||
\(568\) | 28.1246 | 1.18008 | ||||||||
\(569\) | −20.5623 | −0.862017 | −0.431008 | − | 0.902348i | \(-0.641842\pi\) | ||||
−0.431008 | + | 0.902348i | \(0.641842\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.1459 | 0.843080 | 0.421540 | − | 0.906810i | \(-0.361490\pi\) | ||||
0.421540 | + | 0.906810i | \(0.361490\pi\) | |||||||
\(572\) | −112.082 | −4.68639 | ||||||||
\(573\) | 62.6869 | 2.61878 | ||||||||
\(574\) | 6.90983 | 0.288411 | ||||||||
\(575\) | −1.61803 | −0.0674767 | ||||||||
\(576\) | 33.5623 | 1.39843 | ||||||||
\(577\) | 24.2361 | 1.00896 | 0.504480 | − | 0.863423i | \(-0.331684\pi\) | ||||
0.504480 | + | 0.863423i | \(0.331684\pi\) | |||||||
\(578\) | 49.7426 | 2.06902 | ||||||||
\(579\) | 10.4721 | 0.435207 | ||||||||
\(580\) | 9.00000 | 0.373705 | ||||||||
\(581\) | 1.05573 | 0.0437990 | ||||||||
\(582\) | 41.7426 | 1.73029 | ||||||||
\(583\) | −25.9443 | −1.07450 | ||||||||
\(584\) | −7.47214 | −0.309199 | ||||||||
\(585\) | −19.2705 | −0.796738 | ||||||||
\(586\) | −18.4164 | −0.760775 | ||||||||
\(587\) | −37.7639 | −1.55868 | −0.779342 | − | 0.626599i | \(-0.784447\pi\) | ||||
−0.779342 | + | 0.626599i | \(0.784447\pi\) | |||||||
\(588\) | −88.2492 | −3.63934 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.236068 | −0.00971876 | ||||||||
\(591\) | 66.6869 | 2.74313 | ||||||||
\(592\) | −18.2705 | −0.750913 | ||||||||
\(593\) | 15.6525 | 0.642770 | 0.321385 | − | 0.946949i | \(-0.395852\pi\) | ||||
0.321385 | + | 0.946949i | \(0.395852\pi\) | |||||||
\(594\) | −27.0344 | −1.10924 | ||||||||
\(595\) | 1.41641 | 0.0580671 | ||||||||
\(596\) | −26.1246 | −1.07011 | ||||||||
\(597\) | −35.1246 | −1.43755 | ||||||||
\(598\) | −21.1803 | −0.866129 | ||||||||
\(599\) | −37.3607 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(600\) | 19.5623 | 0.798628 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | −1.76393 | −0.0718925 | ||||||||
\(603\) | −18.1459 | −0.738958 | ||||||||
\(604\) | −46.6869 | −1.89966 | ||||||||
\(605\) | −10.3262 | −0.419821 | ||||||||
\(606\) | −81.8673 | −3.32563 | ||||||||
\(607\) | 3.56231 | 0.144590 | 0.0722948 | − | 0.997383i | \(-0.476968\pi\) | ||||
0.0722948 | + | 0.997383i | \(0.476968\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.14590 | −0.0464341 | ||||||||
\(610\) | 7.85410 | 0.318003 | ||||||||
\(611\) | −51.1803 | −2.07053 | ||||||||
\(612\) | −112.249 | −4.53741 | ||||||||
\(613\) | 21.9443 | 0.886321 | 0.443160 | − | 0.896442i | \(-0.353857\pi\) | ||||
0.443160 | + | 0.896442i | \(0.353857\pi\) | |||||||
\(614\) | 55.6869 | 2.24734 | ||||||||
\(615\) | −29.2705 | −1.18030 | ||||||||
\(616\) | −8.14590 | −0.328208 | ||||||||
\(617\) | −24.0902 | −0.969834 | −0.484917 | − | 0.874560i | \(-0.661150\pi\) | ||||
−0.484917 | + | 0.874560i | \(0.661150\pi\) | |||||||
\(618\) | 118.756 | 4.77706 | ||||||||
\(619\) | −25.9443 | −1.04279 | −0.521394 | − | 0.853316i | \(-0.674588\pi\) | ||||
−0.521394 | + | 0.853316i | \(0.674588\pi\) | |||||||
\(620\) | −20.1246 | −0.808224 | ||||||||
\(621\) | −3.61803 | −0.145187 | ||||||||
\(622\) | −65.3050 | −2.61849 | ||||||||
\(623\) | −1.58359 | −0.0634453 | ||||||||
\(624\) | 128.992 | 5.16381 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 38.7426 | 1.54847 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.4377 | 0.975170 | ||||||||
\(629\) | 11.1246 | 0.443567 | ||||||||
\(630\) | −2.38197 | −0.0948998 | ||||||||
\(631\) | 15.0000 | 0.597141 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(632\) | 59.7771 | 2.37780 | ||||||||
\(633\) | −47.3607 | −1.88242 | ||||||||
\(634\) | −22.9443 | −0.911233 | ||||||||
\(635\) | 2.70820 | 0.107472 | ||||||||
\(636\) | 71.3951 | 2.83100 | ||||||||
\(637\) | −34.7214 | −1.37571 | ||||||||
\(638\) | 22.4164 | 0.887474 | ||||||||
\(639\) | 14.5066 | 0.573871 | ||||||||
\(640\) | −1.09017 | −0.0430928 | ||||||||
\(641\) | 39.2705 | 1.55109 | 0.775546 | − | 0.631291i | \(-0.217475\pi\) | ||||
0.775546 | + | 0.631291i | \(0.217475\pi\) | |||||||
\(642\) | 20.5623 | 0.811529 | ||||||||
\(643\) | −17.5967 | −0.693948 | −0.346974 | − | 0.937875i | \(-0.612791\pi\) | ||||
−0.346974 | + | 0.937875i | \(0.612791\pi\) | |||||||
\(644\) | −1.85410 | −0.0730619 | ||||||||
\(645\) | 7.47214 | 0.294215 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.3050 | −1.03415 | −0.517077 | − | 0.855939i | \(-0.672980\pi\) | ||||
−0.517077 | + | 0.855939i | \(0.672980\pi\) | |||||||
\(648\) | −42.6525 | −1.67555 | ||||||||
\(649\) | −0.416408 | −0.0163454 | ||||||||
\(650\) | 13.0902 | 0.513439 | ||||||||
\(651\) | 2.56231 | 0.100425 | ||||||||
\(652\) | 84.8115 | 3.32148 | ||||||||
\(653\) | 1.14590 | 0.0448425 | 0.0224212 | − | 0.999749i | \(-0.492863\pi\) | ||||
0.0224212 | + | 0.999749i | \(0.492863\pi\) | |||||||
\(654\) | 42.7426 | 1.67137 | ||||||||
\(655\) | 1.14590 | 0.0447739 | ||||||||
\(656\) | 110.172 | 4.30150 | ||||||||
\(657\) | −3.85410 | −0.150363 | ||||||||
\(658\) | −6.32624 | −0.246622 | ||||||||
\(659\) | 33.5279 | 1.30606 | 0.653030 | − | 0.757332i | \(-0.273498\pi\) | ||||
0.653030 | + | 0.757332i | \(0.273498\pi\) | |||||||
\(660\) | 58.6869 | 2.28439 | ||||||||
\(661\) | 9.70820 | 0.377605 | 0.188803 | − | 0.982015i | \(-0.439539\pi\) | ||||
0.188803 | + | 0.982015i | \(0.439539\pi\) | |||||||
\(662\) | −35.8885 | −1.39485 | ||||||||
\(663\) | −78.5410 | −3.05028 | ||||||||
\(664\) | 33.4164 | 1.29681 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.7082 | −0.724928 | ||||||||
\(667\) | 3.00000 | 0.116160 | ||||||||
\(668\) | 18.2705 | 0.706907 | ||||||||
\(669\) | 15.0902 | 0.583420 | ||||||||
\(670\) | 12.3262 | 0.476204 | ||||||||
\(671\) | 13.8541 | 0.534832 | ||||||||
\(672\) | 6.70820 | 0.258775 | ||||||||
\(673\) | −46.8885 | −1.80742 | −0.903710 | − | 0.428145i | \(-0.859167\pi\) | ||||
−0.903710 | + | 0.428145i | \(0.859167\pi\) | |||||||
\(674\) | 73.3050 | 2.82360 | ||||||||
\(675\) | 2.23607 | 0.0860663 | ||||||||
\(676\) | 58.2492 | 2.24035 | ||||||||
\(677\) | −10.6180 | −0.408084 | −0.204042 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204042 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(678\) | 20.1803 | 0.775021 | ||||||||
\(679\) | 1.43769 | 0.0551736 | ||||||||
\(680\) | 44.8328 | 1.71926 | ||||||||
\(681\) | −35.7426 | −1.36966 | ||||||||
\(682\) | −50.1246 | −1.91937 | ||||||||
\(683\) | 14.5279 | 0.555893 | 0.277947 | − | 0.960597i | \(-0.410346\pi\) | ||||
0.277947 | + | 0.960597i | \(0.410346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.1803 | 0.809259 | ||||||||
\(686\) | −8.61803 | −0.329038 | ||||||||
\(687\) | −50.7426 | −1.93595 | ||||||||
\(688\) | −28.1246 | −1.07224 | ||||||||
\(689\) | 28.0902 | 1.07015 | ||||||||
\(690\) | 11.0902 | 0.422196 | ||||||||
\(691\) | 12.5279 | 0.476582 | 0.238291 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238291 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(692\) | −106.249 | −4.03899 | ||||||||
\(693\) | −4.20163 | −0.159607 | ||||||||
\(694\) | 41.5967 | 1.57899 | ||||||||
\(695\) | −14.8541 | −0.563448 | ||||||||
\(696\) | −36.2705 | −1.37483 | ||||||||
\(697\) | −67.0820 | −2.54091 | ||||||||
\(698\) | −54.3050 | −2.05547 | ||||||||
\(699\) | −76.3951 | −2.88953 | ||||||||
\(700\) | 1.14590 | 0.0433109 | ||||||||
\(701\) | −47.5755 | −1.79690 | −0.898450 | − | 0.439075i | \(-0.855306\pi\) | ||||
−0.898450 | + | 0.439075i | \(0.855306\pi\) | |||||||
\(702\) | 29.2705 | 1.10474 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −40.2148 | −1.51565 | ||||||||
\(705\) | 26.7984 | 1.00929 | ||||||||
\(706\) | 86.8115 | 3.26720 | ||||||||
\(707\) | −2.81966 | −0.106044 | ||||||||
\(708\) | 1.14590 | 0.0430655 | ||||||||
\(709\) | −2.29180 | −0.0860702 | −0.0430351 | − | 0.999074i | \(-0.513703\pi\) | ||||
−0.0430351 | + | 0.999074i | \(0.513703\pi\) | |||||||
\(710\) | −9.85410 | −0.369818 | ||||||||
\(711\) | 30.8328 | 1.15632 | ||||||||
\(712\) | −50.1246 | −1.87850 | ||||||||
\(713\) | −6.70820 | −0.251224 | ||||||||
\(714\) | −9.70820 | −0.363320 | ||||||||
\(715\) | 23.0902 | 0.863523 | ||||||||
\(716\) | 94.5197 | 3.53237 | ||||||||
\(717\) | 9.00000 | 0.336111 | ||||||||
\(718\) | 74.9230 | 2.79610 | ||||||||
\(719\) | 36.7984 | 1.37235 | 0.686174 | − | 0.727438i | \(-0.259289\pi\) | ||||
0.686174 | + | 0.727438i | \(0.259289\pi\) | |||||||
\(720\) | −37.9787 | −1.41538 | ||||||||
\(721\) | 4.09017 | 0.152326 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −57.9230 | −2.15418 | ||||||||
\(724\) | 105.374 | 3.91619 | ||||||||
\(725\) | −1.85410 | −0.0688596 | ||||||||
\(726\) | 70.7771 | 2.62678 | ||||||||
\(727\) | −37.4164 | −1.38770 | −0.693849 | − | 0.720121i | \(-0.744086\pi\) | ||||
−0.693849 | + | 0.720121i | \(0.744086\pi\) | |||||||
\(728\) | 8.81966 | 0.326878 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 2.61803 | 0.0968978 | ||||||||
\(731\) | 17.1246 | 0.633377 | ||||||||
\(732\) | −38.1246 | −1.40913 | ||||||||
\(733\) | −4.23607 | −0.156463 | −0.0782314 | − | 0.996935i | \(-0.524927\pi\) | ||||
−0.0782314 | + | 0.996935i | \(0.524927\pi\) | |||||||
\(734\) | −77.6312 | −2.86542 | ||||||||
\(735\) | 18.1803 | 0.670592 | ||||||||
\(736\) | −17.5623 | −0.647355 | ||||||||
\(737\) | 21.7426 | 0.800901 | ||||||||
\(738\) | 112.812 | 4.15265 | ||||||||
\(739\) | 31.8328 | 1.17099 | 0.585495 | − | 0.810676i | \(-0.300900\pi\) | ||||
0.585495 | + | 0.810676i | \(0.300900\pi\) | |||||||
\(740\) | 9.00000 | 0.330847 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.47214 | 0.127466 | ||||||||
\(743\) | 31.7639 | 1.16531 | 0.582653 | − | 0.812721i | \(-0.302015\pi\) | ||||
0.582653 | + | 0.812721i | \(0.302015\pi\) | |||||||
\(744\) | 81.1033 | 2.97339 | ||||||||
\(745\) | 5.38197 | 0.197180 | ||||||||
\(746\) | 17.5623 | 0.643002 | ||||||||
\(747\) | 17.2361 | 0.630635 | ||||||||
\(748\) | 134.498 | 4.91775 | ||||||||
\(749\) | 0.708204 | 0.0258772 | ||||||||
\(750\) | −6.85410 | −0.250276 | ||||||||
\(751\) | 17.5623 | 0.640858 | 0.320429 | − | 0.947273i | \(-0.396173\pi\) | ||||
0.320429 | + | 0.947273i | \(0.396173\pi\) | |||||||
\(752\) | −100.867 | −3.67825 | ||||||||
\(753\) | −18.7984 | −0.685051 | ||||||||
\(754\) | −24.2705 | −0.883880 | ||||||||
\(755\) | 9.61803 | 0.350036 | ||||||||
\(756\) | 2.56231 | 0.0931902 | ||||||||
\(757\) | −16.6180 | −0.603993 | −0.301996 | − | 0.953309i | \(-0.597653\pi\) | ||||
−0.301996 | + | 0.953309i | \(0.597653\pi\) | |||||||
\(758\) | 70.2492 | 2.55157 | ||||||||
\(759\) | 19.5623 | 0.710067 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.36068 | −0.266824 | −0.133412 | − | 0.991061i | \(-0.542593\pi\) | ||||
−0.133412 | + | 0.991061i | \(0.542593\pi\) | |||||||
\(762\) | −18.5623 | −0.672441 | ||||||||
\(763\) | 1.47214 | 0.0532949 | ||||||||
\(764\) | 116.228 | 4.20498 | ||||||||
\(765\) | 23.1246 | 0.836072 | ||||||||
\(766\) | −83.5755 | −3.01970 | ||||||||
\(767\) | 0.450850 | 0.0162792 | ||||||||
\(768\) | −38.1246 | −1.37570 | ||||||||
\(769\) | −46.6869 | −1.68357 | −0.841787 | − | 0.539810i | \(-0.818496\pi\) | ||||
−0.841787 | + | 0.539810i | \(0.818496\pi\) | |||||||
\(770\) | 2.85410 | 0.102855 | ||||||||
\(771\) | 58.8328 | 2.11881 | ||||||||
\(772\) | 19.4164 | 0.698812 | ||||||||
\(773\) | 2.74265 | 0.0986461 | 0.0493231 | − | 0.998783i | \(-0.484294\pi\) | ||||
0.0493231 | + | 0.998783i | \(0.484294\pi\) | |||||||
\(774\) | −28.7984 | −1.03514 | ||||||||
\(775\) | 4.14590 | 0.148925 | ||||||||
\(776\) | 45.5066 | 1.63359 | ||||||||
\(777\) | −1.14590 | −0.0411089 | ||||||||
\(778\) | −22.7082 | −0.814129 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −63.5410 | −2.27513 | ||||||||
\(781\) | −17.3820 | −0.621976 | ||||||||
\(782\) | 25.4164 | 0.908889 | ||||||||
\(783\) | −4.14590 | −0.148162 | ||||||||
\(784\) | −68.4296 | −2.44391 | ||||||||
\(785\) | −5.03444 | −0.179687 | ||||||||
\(786\) | −7.85410 | −0.280147 | ||||||||
\(787\) | 49.4853 | 1.76396 | 0.881980 | − | 0.471287i | \(-0.156210\pi\) | ||||
0.881980 | + | 0.471287i | \(0.156210\pi\) | |||||||
\(788\) | 123.644 | 4.40465 | ||||||||
\(789\) | 41.5967 | 1.48088 | ||||||||
\(790\) | −20.9443 | −0.745164 | ||||||||
\(791\) | 0.695048 | 0.0247131 | ||||||||
\(792\) | −132.992 | −4.72566 | ||||||||
\(793\) | −15.0000 | −0.532666 | ||||||||
\(794\) | 49.4508 | 1.75494 | ||||||||
\(795\) | −14.7082 | −0.521646 | ||||||||
\(796\) | −65.1246 | −2.30828 | ||||||||
\(797\) | 20.1803 | 0.714824 | 0.357412 | − | 0.933947i | \(-0.383659\pi\) | ||||
0.357412 | + | 0.933947i | \(0.383659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.4164 | 2.17276 | ||||||||
\(800\) | 10.8541 | 0.383750 | ||||||||
\(801\) | −25.8541 | −0.913510 | ||||||||
\(802\) | 29.4164 | 1.03873 | ||||||||
\(803\) | 4.61803 | 0.162967 | ||||||||
\(804\) | −59.8328 | −2.11014 | ||||||||
\(805\) | 0.381966 | 0.0134625 | ||||||||
\(806\) | 54.2705 | 1.91160 | ||||||||
\(807\) | 45.3607 | 1.59677 | ||||||||
\(808\) | −89.2492 | −3.13978 | ||||||||
\(809\) | 40.0902 | 1.40950 | 0.704748 | − | 0.709458i | \(-0.251060\pi\) | ||||
0.704748 | + | 0.709458i | \(0.251060\pi\) | |||||||
\(810\) | 14.9443 | 0.525088 | ||||||||
\(811\) | 24.6738 | 0.866413 | 0.433206 | − | 0.901295i | \(-0.357382\pi\) | ||||
0.433206 | + | 0.901295i | \(0.357382\pi\) | |||||||
\(812\) | −2.12461 | −0.0745593 | ||||||||
\(813\) | 48.7426 | 1.70948 | ||||||||
\(814\) | 22.4164 | 0.785695 | ||||||||
\(815\) | −17.4721 | −0.612022 | ||||||||
\(816\) | −154.790 | −5.41874 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 30.6525 | 1.07174 | ||||||||
\(819\) | 4.54915 | 0.158960 | ||||||||
\(820\) | −54.2705 | −1.89521 | ||||||||
\(821\) | 14.6180 | 0.510173 | 0.255086 | − | 0.966918i | \(-0.417896\pi\) | ||||
0.255086 | + | 0.966918i | \(0.417896\pi\) | |||||||
\(822\) | −145.172 | −5.06346 | ||||||||
\(823\) | −36.3607 | −1.26745 | −0.633727 | − | 0.773557i | \(-0.718476\pi\) | ||||
−0.633727 | + | 0.773557i | \(0.718476\pi\) | |||||||
\(824\) | 129.464 | 4.51009 | ||||||||
\(825\) | −12.0902 | −0.420926 | ||||||||
\(826\) | 0.0557281 | 0.00193903 | ||||||||
\(827\) | 17.8328 | 0.620108 | 0.310054 | − | 0.950719i | \(-0.399653\pi\) | ||||
0.310054 | + | 0.950719i | \(0.399653\pi\) | |||||||
\(828\) | −30.2705 | −1.05197 | ||||||||
\(829\) | −30.3951 | −1.05567 | −0.527833 | − | 0.849348i | \(-0.676995\pi\) | ||||
−0.527833 | + | 0.849348i | \(0.676995\pi\) | |||||||
\(830\) | −11.7082 | −0.406398 | ||||||||
\(831\) | 3.70820 | 0.128636 | ||||||||
\(832\) | 43.5410 | 1.50951 | ||||||||
\(833\) | 41.6656 | 1.44363 | ||||||||
\(834\) | 101.812 | 3.52544 | ||||||||
\(835\) | −3.76393 | −0.130256 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.27051 | 0.320436 | ||||||||
\(838\) | 49.5967 | 1.71329 | ||||||||
\(839\) | −15.6180 | −0.539194 | −0.269597 | − | 0.962973i | \(-0.586891\pi\) | ||||
−0.269597 | + | 0.962973i | \(0.586891\pi\) | |||||||
\(840\) | −4.61803 | −0.159337 | ||||||||
\(841\) | −25.5623 | −0.881459 | ||||||||
\(842\) | −36.9787 | −1.27437 | ||||||||
\(843\) | −27.5066 | −0.947377 | ||||||||
\(844\) | −87.8115 | −3.02260 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | −103.284 | −3.55097 | ||||||||
\(847\) | 2.43769 | 0.0837602 | ||||||||
\(848\) | 55.3607 | 1.90109 | ||||||||
\(849\) | 6.23607 | 0.214021 | ||||||||
\(850\) | −15.7082 | −0.538787 | ||||||||
\(851\) | 3.00000 | 0.102839 | ||||||||
\(852\) | 47.8328 | 1.63873 | ||||||||
\(853\) | −40.9574 | −1.40236 | −0.701178 | − | 0.712986i | \(-0.747342\pi\) | ||||
−0.701178 | + | 0.712986i | \(0.747342\pi\) | |||||||
\(854\) | −1.85410 | −0.0634461 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.4164 | 0.766177 | ||||||||
\(857\) | −30.3820 | −1.03783 | −0.518914 | − | 0.854826i | \(-0.673664\pi\) | ||||
−0.518914 | + | 0.854826i | \(0.673664\pi\) | |||||||
\(858\) | −158.262 | −5.40299 | ||||||||
\(859\) | −35.5967 | −1.21455 | −0.607273 | − | 0.794493i | \(-0.707736\pi\) | ||||
−0.607273 | + | 0.794493i | \(0.707736\pi\) | |||||||
\(860\) | 13.8541 | 0.472421 | ||||||||
\(861\) | 6.90983 | 0.235486 | ||||||||
\(862\) | −7.38197 | −0.251431 | ||||||||
\(863\) | 26.6525 | 0.907261 | 0.453630 | − | 0.891190i | \(-0.350129\pi\) | ||||
0.453630 | + | 0.891190i | \(0.350129\pi\) | |||||||
\(864\) | 24.2705 | 0.825700 | ||||||||
\(865\) | 21.8885 | 0.744233 | ||||||||
\(866\) | 58.1591 | 1.97633 | ||||||||
\(867\) | 49.7426 | 1.68935 | ||||||||
\(868\) | 4.75078 | 0.161252 | ||||||||
\(869\) | −36.9443 | −1.25325 | ||||||||
\(870\) | 12.7082 | 0.430848 | ||||||||
\(871\) | −23.5410 | −0.797657 | ||||||||
\(872\) | 46.5967 | 1.57796 | ||||||||
\(873\) | 23.4721 | 0.794411 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.236068 | −0.00798055 | ||||||||
\(876\) | −12.7082 | −0.429370 | ||||||||
\(877\) | −30.1803 | −1.01912 | −0.509559 | − | 0.860436i | \(-0.670191\pi\) | ||||
−0.509559 | + | 0.860436i | \(0.670191\pi\) | |||||||
\(878\) | −14.3262 | −0.483487 | ||||||||
\(879\) | −18.4164 | −0.621170 | ||||||||
\(880\) | 45.5066 | 1.53403 | ||||||||
\(881\) | −4.03444 | −0.135924 | −0.0679619 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679619 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(882\) | −70.0689 | −2.35934 | ||||||||
\(883\) | −17.9230 | −0.603156 | −0.301578 | − | 0.953441i | \(-0.597513\pi\) | ||||
−0.301578 | + | 0.953441i | \(0.597513\pi\) | |||||||
\(884\) | −145.623 | −4.89783 | ||||||||
\(885\) | −0.236068 | −0.00793534 | ||||||||
\(886\) | 40.2148 | 1.35104 | ||||||||
\(887\) | 3.52786 | 0.118454 | 0.0592270 | − | 0.998245i | \(-0.481136\pi\) | ||||
0.0592270 | + | 0.998245i | \(0.481136\pi\) | |||||||
\(888\) | −36.2705 | −1.21716 | ||||||||
\(889\) | −0.639320 | −0.0214421 | ||||||||
\(890\) | 17.5623 | 0.588690 | ||||||||
\(891\) | 26.3607 | 0.883116 | ||||||||
\(892\) | 27.9787 | 0.936797 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −36.8885 | −1.23374 | ||||||||
\(895\) | −19.4721 | −0.650882 | ||||||||
\(896\) | 0.257354 | 0.00859760 | ||||||||
\(897\) | −21.1803 | −0.707191 | ||||||||
\(898\) | 85.1591 | 2.84179 | ||||||||
\(899\) | −7.68692 | −0.256373 | ||||||||
\(900\) | 18.7082 | 0.623607 | ||||||||
\(901\) | −33.7082 | −1.12298 | ||||||||
\(902\) | −135.172 | −4.50074 | ||||||||
\(903\) | −1.76393 | −0.0587000 | ||||||||
\(904\) | 22.0000 | 0.731709 | ||||||||
\(905\) | −21.7082 | −0.721605 | ||||||||
\(906\) | −65.9230 | −2.19014 | ||||||||
\(907\) | 48.2492 | 1.60209 | 0.801045 | − | 0.598605i | \(-0.204278\pi\) | ||||
0.801045 | + | 0.598605i | \(0.204278\pi\) | |||||||
\(908\) | −66.2705 | −2.19926 | ||||||||
\(909\) | −46.0344 | −1.52687 | ||||||||
\(910\) | −3.09017 | −0.102438 | ||||||||
\(911\) | −51.1033 | −1.69313 | −0.846564 | − | 0.532286i | \(-0.821333\pi\) | ||||
−0.846564 | + | 0.532286i | \(0.821333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.6525 | −0.683497 | ||||||||
\(914\) | −15.7082 | −0.519581 | ||||||||
\(915\) | 7.85410 | 0.259649 | ||||||||
\(916\) | −94.0820 | −3.10856 | ||||||||
\(917\) | −0.270510 | −0.00893302 | ||||||||
\(918\) | −35.1246 | −1.15928 | ||||||||
\(919\) | −12.8885 | −0.425154 | −0.212577 | − | 0.977144i | \(-0.568186\pi\) | ||||
−0.212577 | + | 0.977144i | \(0.568186\pi\) | |||||||
\(920\) | 12.0902 | 0.398601 | ||||||||
\(921\) | 55.6869 | 1.83495 | ||||||||
\(922\) | −49.5967 | −1.63338 | ||||||||
\(923\) | 18.8197 | 0.619457 | ||||||||
\(924\) | −13.8541 | −0.455766 | ||||||||
\(925\) | −1.85410 | −0.0609625 | ||||||||
\(926\) | 10.3820 | 0.341173 | ||||||||
\(927\) | 66.7771 | 2.19325 | ||||||||
\(928\) | −20.1246 | −0.660623 | ||||||||
\(929\) | 9.38197 | 0.307812 | 0.153906 | − | 0.988085i | \(-0.450815\pi\) | ||||
0.153906 | + | 0.988085i | \(0.450815\pi\) | |||||||
\(930\) | −28.4164 | −0.931811 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −141.644 | −4.63971 | ||||||||
\(933\) | −65.3050 | −2.13799 | ||||||||
\(934\) | −29.5623 | −0.967308 | ||||||||
\(935\) | −27.7082 | −0.906155 | ||||||||
\(936\) | 143.992 | 4.70652 | ||||||||
\(937\) | −17.5623 | −0.573736 | −0.286868 | − | 0.957970i | \(-0.592614\pi\) | ||||
−0.286868 | + | 0.957970i | \(0.592614\pi\) | |||||||
\(938\) | −2.90983 | −0.0950093 | ||||||||
\(939\) | 38.7426 | 1.26432 | ||||||||
\(940\) | 49.6869 | 1.62061 | ||||||||
\(941\) | −27.5066 | −0.896689 | −0.448344 | − | 0.893861i | \(-0.647986\pi\) | ||||
−0.448344 | + | 0.893861i | \(0.647986\pi\) | |||||||
\(942\) | 34.5066 | 1.12429 | ||||||||
\(943\) | −18.0902 | −0.589097 | ||||||||
\(944\) | 0.888544 | 0.0289196 | ||||||||
\(945\) | −0.527864 | −0.0171714 | ||||||||
\(946\) | 34.5066 | 1.12191 | ||||||||
\(947\) | 48.0000 | 1.55979 | 0.779895 | − | 0.625910i | \(-0.215272\pi\) | ||||
0.779895 | + | 0.625910i | \(0.215272\pi\) | |||||||
\(948\) | 101.666 | 3.30195 | ||||||||
\(949\) | −5.00000 | −0.162307 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.9443 | −0.744019 | ||||||||
\(952\) | −10.5836 | −0.343016 | ||||||||
\(953\) | 41.8328 | 1.35510 | 0.677549 | − | 0.735478i | \(-0.263042\pi\) | ||||
0.677549 | + | 0.735478i | \(0.263042\pi\) | |||||||
\(954\) | 56.6869 | 1.83531 | ||||||||
\(955\) | −23.9443 | −0.774818 | ||||||||
\(956\) | 16.6869 | 0.539693 | ||||||||
\(957\) | 22.4164 | 0.724620 | ||||||||
\(958\) | −21.9443 | −0.708987 | ||||||||
\(959\) | −5.00000 | −0.161458 | ||||||||
\(960\) | −22.7984 | −0.735814 | ||||||||
\(961\) | −13.8115 | −0.445533 | ||||||||
\(962\) | −24.2705 | −0.782513 | ||||||||
\(963\) | 11.5623 | 0.372590 | ||||||||
\(964\) | −107.395 | −3.45896 | ||||||||
\(965\) | −4.00000 | −0.128765 | ||||||||
\(966\) | −2.61803 | −0.0842339 | ||||||||
\(967\) | 33.2361 | 1.06880 | 0.534400 | − | 0.845232i | \(-0.320538\pi\) | ||||
0.534400 | + | 0.845232i | \(0.320538\pi\) | |||||||
\(968\) | 77.1591 | 2.47999 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.9443 | −0.511940 | ||||||||
\(971\) | −13.2016 | −0.423660 | −0.211830 | − | 0.977306i | \(-0.567942\pi\) | ||||
−0.211830 | + | 0.977306i | \(0.567942\pi\) | |||||||
\(972\) | −105.103 | −3.37119 | ||||||||
\(973\) | 3.50658 | 0.112416 | ||||||||
\(974\) | −22.4721 | −0.720054 | ||||||||
\(975\) | 13.0902 | 0.419221 | ||||||||
\(976\) | −29.5623 | −0.946266 | ||||||||
\(977\) | 22.3475 | 0.714961 | 0.357480 | − | 0.933921i | \(-0.383636\pi\) | ||||
0.357480 | + | 0.933921i | \(0.383636\pi\) | |||||||
\(978\) | 119.756 | 3.82937 | ||||||||
\(979\) | 30.9787 | 0.990084 | ||||||||
\(980\) | 33.7082 | 1.07677 | ||||||||
\(981\) | 24.0344 | 0.767361 | ||||||||
\(982\) | 63.6869 | 2.03233 | ||||||||
\(983\) | 7.14590 | 0.227919 | 0.113959 | − | 0.993485i | \(-0.463647\pi\) | ||||
0.113959 | + | 0.993485i | \(0.463647\pi\) | |||||||
\(984\) | 218.713 | 6.97232 | ||||||||
\(985\) | −25.4721 | −0.811610 | ||||||||
\(986\) | 29.1246 | 0.927517 | ||||||||
\(987\) | −6.32624 | −0.201366 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.61803 | 0.146845 | ||||||||
\(990\) | 46.5967 | 1.48094 | ||||||||
\(991\) | 24.8541 | 0.789517 | 0.394758 | − | 0.918785i | \(-0.370828\pi\) | ||||
0.394758 | + | 0.918785i | \(0.370828\pi\) | |||||||
\(992\) | 45.0000 | 1.42875 | ||||||||
\(993\) | −35.8885 | −1.13889 | ||||||||
\(994\) | 2.32624 | 0.0737838 | ||||||||
\(995\) | 13.4164 | 0.425329 | ||||||||
\(996\) | 56.8328 | 1.80082 | ||||||||
\(997\) | 1.23607 | 0.0391467 | 0.0195733 | − | 0.999808i | \(-0.493769\pi\) | ||||
0.0195733 | + | 0.999808i | \(0.493769\pi\) | |||||||
\(998\) | −12.1803 | −0.385562 | ||||||||
\(999\) | −4.14590 | −0.131170 |
(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 | 1805.2.a.e.1.2 | yes | 2 | |
5.4 | even | 2 | 9025.2.a.k.1.1 | 2 | |||
19.18 | odd | 2 | 1805.2.a.c.1.1 | ✓ | 2 | ||
95.94 | odd | 2 | 9025.2.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.c.1.1 | ✓ | 2 | 19.18 | odd | 2 | ||
1805.2.a.e.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
9025.2.a.k.1.1 | 2 | 5.4 | even | 2 | |||
9025.2.a.v.1.2 | 2 | 95.94 | odd | 2 |