Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12239922073600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 4x^{4} - 32x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.2 | ||
Root | \(1.89639 - 0.635381i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.q.451.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89639 | + | 0.635381i | −0.948194 | + | 0.317690i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.19258 | − | 2.40986i | 0.798146 | − | 0.602465i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.1035i | 1.44336i | 0.692226 | + | 0.721681i | \(0.256630\pi\) | ||||
−0.692226 | + | 0.721681i | \(0.743370\pi\) | |||||||
\(8\) | −4.52320 | + | 6.59853i | −0.565400 | + | 0.824817i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.6555i | − | 0.968686i | −0.874878 | − | 0.484343i | \(-0.839059\pi\) | ||
0.874878 | − | 0.484343i | \(-0.160941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.7703 | 0.905410 | 0.452705 | − | 0.891660i | \(-0.350459\pi\) | ||||
0.452705 | + | 0.891660i | \(0.350459\pi\) | |||||||
\(14\) | −6.41959 | − | 19.1602i | −0.458542 | − | 1.36859i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.38516 | − | 15.3873i | 0.274073 | − | 0.961709i | ||||
\(17\) | 16.6320 | 0.978350 | 0.489175 | − | 0.872186i | \(-0.337298\pi\) | ||||
0.489175 | + | 0.872186i | \(0.337298\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.464096i | 0.0244261i | 0.999925 | + | 0.0122131i | \(0.00388763\pi\) | ||||
−0.999925 | + | 0.0122131i | \(0.996112\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.77033 | + | 20.2071i | 0.307742 | + | 0.918503i | ||||
\(23\) | − | 42.1327i | − | 1.83186i | −0.401340 | − | 0.915929i | \(-0.631456\pi\) | ||
0.401340 | − | 0.915929i | \(-0.368544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −22.3211 | + | 7.47864i | −0.858505 | + | 0.287640i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 24.3481 | + | 32.2564i | 0.869574 | + | 1.15201i | ||||
\(29\) | −19.5536 | −0.674264 | −0.337132 | − | 0.941457i | \(-0.609457\pi\) | ||||
−0.337132 | + | 0.941457i | \(0.609457\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.17534i | 0.295979i | 0.988989 | + | 0.147989i | \(0.0472801\pi\) | ||||
−0.988989 | + | 0.147989i | \(0.952720\pi\) | |||||||
\(32\) | 1.46084 | + | 31.9666i | 0.0456514 | + | 0.998957i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −31.5407 | + | 10.5676i | −0.927666 | + | 0.310813i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 23.5407 | 0.636234 | 0.318117 | − | 0.948051i | \(-0.396950\pi\) | ||||
0.318117 | + | 0.948051i | \(0.396950\pi\) | |||||||
\(38\) | −0.294878 | − | 0.880107i | −0.00775994 | − | 0.0231607i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.0525 | 1.07445 | 0.537226 | − | 0.843439i | \(-0.319472\pi\) | ||||
0.537226 | + | 0.843439i | \(0.319472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 58.3007i | 1.35583i | 0.735140 | + | 0.677915i | \(0.237116\pi\) | ||||
−0.735140 | + | 0.677915i | \(0.762884\pi\) | |||||||
\(44\) | −25.6784 | − | 34.0187i | −0.583599 | − | 0.773152i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 26.7703 | + | 79.9000i | 0.581964 | + | 1.73696i | ||||
\(47\) | 41.6433i | 0.886027i | 0.896515 | + | 0.443014i | \(0.146091\pi\) | ||||
−0.896515 | + | 0.443014i | \(0.853909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −53.0813 | −1.08329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 37.5777 | − | 28.3648i | 0.722649 | − | 0.545477i | ||||
\(53\) | −80.2381 | −1.51393 | −0.756963 | − | 0.653458i | \(-0.773318\pi\) | ||||
−0.756963 | + | 0.653458i | \(0.773318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −66.6685 | − | 45.7003i | −1.19051 | − | 0.816077i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 37.0813 | − | 12.4240i | 0.639333 | − | 0.214207i | ||||
\(59\) | − | 63.9333i | − | 1.08361i | −0.840503 | − | 0.541807i | \(-0.817740\pi\) | ||
0.840503 | − | 0.541807i | \(-0.182260\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 80.3923 | 1.31791 | 0.658953 | − | 0.752184i | \(-0.270999\pi\) | ||||
0.658953 | + | 0.752184i | \(0.270999\pi\) | |||||||
\(62\) | −5.82983 | − | 17.4000i | −0.0940296 | − | 0.280645i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −23.0813 | − | 59.6930i | −0.360646 | − | 0.932703i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 22.5275i | − | 0.336232i | −0.985767 | − | 0.168116i | \(-0.946232\pi\) | ||
0.985767 | − | 0.168116i | \(-0.0537683\pi\) | |||||||
\(68\) | 53.0989 | − | 40.0807i | 0.780866 | − | 0.589421i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61.4860i | 0.866000i | 0.901394 | + | 0.433000i | \(0.142545\pi\) | ||||
−0.901394 | + | 0.433000i | \(0.857455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 137.703 | 1.88635 | 0.943173 | − | 0.332301i | \(-0.107825\pi\) | ||||
0.943173 | + | 0.332301i | \(0.107825\pi\) | |||||||
\(74\) | −44.6422 | + | 14.9573i | −0.603274 | + | 0.202125i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.11841 | + | 1.48167i | 0.0147159 | + | 0.0194956i | ||||
\(77\) | 107.659 | 1.39816 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 138.665i | − | 1.75525i | −0.479347 | − | 0.877626i | \(-0.659126\pi\) | ||
0.479347 | − | 0.877626i | \(-0.340874\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −83.5407 | + | 27.9901i | −1.01879 | + | 0.341343i | ||||
\(83\) | 86.2233i | 1.03883i | 0.854521 | + | 0.519417i | \(0.173851\pi\) | ||||
−0.854521 | + | 0.519417i | \(0.826149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −37.0431 | − | 110.561i | −0.430734 | − | 1.28559i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 70.3110 | + | 48.1972i | 0.798989 | + | 0.547695i | ||||
\(89\) | 127.212 | 1.42935 | 0.714676 | − | 0.699456i | \(-0.246574\pi\) | ||||
0.714676 | + | 0.699456i | \(0.246574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 118.922i | 1.30683i | ||||||||
\(92\) | −101.534 | − | 134.512i | −1.10363 | − | 1.46209i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −26.4593 | − | 78.9719i | −0.281482 | − | 0.840126i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0000 | 0.154639 | 0.0773196 | − | 0.997006i | \(-0.475364\pi\) | ||||
0.0773196 | + | 0.997006i | \(0.475364\pi\) | |||||||
\(98\) | 100.663 | − | 33.7269i | 1.02717 | − | 0.344152i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 195.764 | 1.93825 | 0.969127 | − | 0.246563i | \(-0.0793012\pi\) | ||||
0.969127 | + | 0.246563i | \(0.0793012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5661i | 0.151127i | 0.997141 | + | 0.0755636i | \(0.0240756\pi\) | ||||
−0.997141 | + | 0.0755636i | \(0.975924\pi\) | |||||||
\(104\) | −53.2396 | + | 77.6669i | −0.511919 | + | 0.746797i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 152.163 | − | 50.9817i | 1.43550 | − | 0.480960i | ||||
\(107\) | 51.3199i | 0.479625i | 0.970819 | + | 0.239813i | \(0.0770860\pi\) | ||||
−0.970819 | + | 0.239813i | \(0.922914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −46.8516 | −0.429832 | −0.214916 | − | 0.976633i | \(-0.568948\pi\) | ||||
−0.214916 | + | 0.976633i | \(0.568948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 155.466 | + | 44.3056i | 1.38809 | + | 0.395586i | ||||
\(113\) | −115.526 | −1.02235 | −0.511175 | − | 0.859477i | \(-0.670790\pi\) | ||||
−0.511175 | + | 0.859477i | \(0.670790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −62.4266 | + | 47.1215i | −0.538161 | + | 0.406220i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 40.6220 | + | 121.242i | 0.344254 | + | 1.02748i | ||||
\(119\) | 168.041i | 1.41211i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.45934 | 0.0616474 | ||||||||
\(122\) | −152.455 | + | 51.0797i | −1.24963 | + | 0.418686i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 22.1113 | + | 29.2930i | 0.178317 | + | 0.236234i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 161.656i | 1.27289i | 0.771324 | + | 0.636443i | \(0.219595\pi\) | ||||
−0.771324 | + | 0.636443i | \(0.780405\pi\) | |||||||
\(128\) | 81.6989 | + | 98.5357i | 0.638273 | + | 0.769810i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 197.561i | 1.50810i | 0.656818 | + | 0.754049i | \(0.271902\pi\) | ||||
−0.656818 | + | 0.754049i | \(0.728098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.68901 | −0.0352557 | ||||||||
\(134\) | 14.3136 | + | 42.7210i | 0.106818 | + | 0.318813i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −75.2297 | + | 109.747i | −0.553159 | + | 0.806960i | ||||
\(137\) | 76.4182 | 0.557797 | 0.278899 | − | 0.960321i | \(-0.410031\pi\) | ||||
0.278899 | + | 0.960321i | \(0.410031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 223.206i | 1.60580i | 0.596115 | + | 0.802899i | \(0.296710\pi\) | ||||
−0.596115 | + | 0.802899i | \(0.703290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −39.0670 | − | 116.601i | −0.275120 | − | 0.821137i | ||||
\(143\) | − | 125.419i | − | 0.877058i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −261.139 | + | 87.4940i | −1.78862 | + | 0.599274i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 75.1555 | − | 56.7297i | 0.507807 | − | 0.383308i | ||||
\(149\) | 166.320 | 1.11624 | 0.558119 | − | 0.829761i | \(-0.311523\pi\) | ||||
0.558119 | + | 0.829761i | \(0.311523\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 112.995i | − | 0.748313i | −0.927366 | − | 0.374156i | \(-0.877932\pi\) | ||
0.927366 | − | 0.374156i | \(-0.122068\pi\) | |||||||
\(152\) | −3.06236 | − | 2.09920i | −0.0201471 | − | 0.0138105i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −204.163 | + | 68.4042i | −1.32573 | + | 0.444183i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 75.9330 | 0.483649 | 0.241825 | − | 0.970320i | \(-0.422254\pi\) | ||||
0.241825 | + | 0.970320i | \(0.422254\pi\) | |||||||
\(158\) | 88.1050 | + | 262.962i | 0.557626 | + | 1.66432i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 425.689 | 2.64403 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 184.184i | 1.12996i | 0.825103 | + | 0.564982i | \(0.191117\pi\) | ||||
−0.825103 | + | 0.564982i | \(0.808883\pi\) | |||||||
\(164\) | 140.641 | − | 106.160i | 0.857568 | − | 0.647319i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −54.7846 | − | 163.513i | −0.330028 | − | 0.985017i | ||||
\(167\) | − | 193.268i | − | 1.15729i | −0.815578 | − | 0.578647i | \(-0.803581\pi\) | ||
0.815578 | − | 0.578647i | \(-0.196419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30.4593 | −0.180233 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 140.496 | + | 186.130i | 0.816840 | + | 1.08215i | ||||
\(173\) | −56.8646 | −0.328697 | −0.164348 | − | 0.986402i | \(-0.552552\pi\) | ||||
−0.164348 | + | 0.986402i | \(0.552552\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −163.961 | − | 46.7263i | −0.931594 | − | 0.265490i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −241.244 | + | 80.8282i | −1.35530 | + | 0.454091i | ||||
\(179\) | 272.150i | 1.52039i | 0.649695 | + | 0.760195i | \(0.274896\pi\) | ||||
−0.649695 | + | 0.760195i | \(0.725104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −50.2297 | −0.277512 | −0.138756 | − | 0.990327i | \(-0.544310\pi\) | ||||
−0.138756 | + | 0.990327i | \(0.544310\pi\) | |||||||
\(182\) | −75.5607 | − | 225.522i | −0.415169 | − | 1.23913i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 278.014 | + | 190.575i | 1.51095 | + | 1.03573i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 177.223i | − | 0.947714i | ||||||
\(188\) | 100.354 | + | 132.950i | 0.533800 | + | 0.707179i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 194.247i | − | 1.01700i | −0.861062 | − | 0.508500i | \(-0.830200\pi\) | ||
0.861062 | − | 0.508500i | \(-0.169800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.7033 | −0.117634 | −0.0588168 | − | 0.998269i | \(-0.518733\pi\) | ||||
−0.0588168 | + | 0.998269i | \(0.518733\pi\) | |||||||
\(194\) | −28.4458 | + | 9.53071i | −0.146628 | + | 0.0491274i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −169.466 | + | 127.918i | −0.864625 | + | 0.652645i | ||||
\(197\) | 154.633 | 0.784938 | 0.392469 | − | 0.919765i | \(-0.371621\pi\) | ||||
0.392469 | + | 0.919765i | \(0.371621\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 236.094i | − | 1.18640i | −0.805054 | − | 0.593201i | \(-0.797864\pi\) | ||
0.805054 | − | 0.593201i | \(-0.202136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −371.244 | + | 124.384i | −1.83784 | + | 0.615765i | ||||
\(203\) | − | 197.561i | − | 0.973206i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.89040 | − | 29.5194i | −0.0480116 | − | 0.143298i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 51.6148 | − | 181.114i | 0.248148 | − | 0.870741i | ||||
\(209\) | 4.94520 | 0.0236612 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 115.209i | − | 0.546015i | −0.962012 | − | 0.273007i | \(-0.911982\pi\) | ||
0.962012 | − | 0.273007i | \(-0.0880183\pi\) | |||||||
\(212\) | −256.167 | + | 193.362i | −1.20833 | + | 0.912087i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −32.6077 | − | 97.3225i | −0.152372 | − | 0.454778i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −92.7033 | −0.427204 | ||||||||
\(218\) | 88.8489 | − | 29.7686i | 0.407564 | − | 0.136553i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 195.764 | 0.885808 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 425.170i | − | 1.90659i | −0.302039 | − | 0.953296i | \(-0.597667\pi\) | ||
0.302039 | − | 0.953296i | \(-0.402333\pi\) | |||||||
\(224\) | −322.976 | + | 14.7597i | −1.44186 | + | 0.0658915i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 219.081 | − | 73.4027i | 0.969386 | − | 0.324791i | ||||
\(227\) | 178.208i | 0.785055i | 0.919740 | + | 0.392528i | \(0.128399\pi\) | ||||
−0.919740 | + | 0.392528i | \(0.871601\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 331.636 | 1.44819 | 0.724097 | − | 0.689699i | \(-0.242257\pi\) | ||||
0.724097 | + | 0.689699i | \(0.242257\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 88.4451 | − | 129.025i | 0.381229 | − | 0.556144i | ||||
\(233\) | −182.952 | −0.785200 | −0.392600 | − | 0.919709i | \(-0.628424\pi\) | ||||
−0.392600 | + | 0.919709i | \(0.628424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −154.070 | − | 204.112i | −0.652840 | − | 0.864882i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −106.770 | − | 318.672i | −0.448615 | − | 1.33896i | ||||
\(239\) | − | 210.664i | − | 0.881438i | −0.897645 | − | 0.440719i | \(-0.854724\pi\) | ||
0.897645 | − | 0.440719i | \(-0.145276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.62198 | −0.0150290 | −0.00751448 | − | 0.999972i | \(-0.502392\pi\) | ||||
−0.00751448 | + | 0.999972i | \(0.502392\pi\) | |||||||
\(242\) | −14.1458 | + | 4.73952i | −0.0584538 | + | 0.0195848i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 256.659 | − | 193.734i | 1.05188 | − | 0.793992i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.46257i | 0.0221157i | ||||||||
\(248\) | −60.5438 | − | 41.5019i | −0.244128 | − | 0.167346i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 250.839i | 0.999357i | 0.866211 | + | 0.499678i | \(0.166548\pi\) | ||||
−0.866211 | + | 0.499678i | \(0.833452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −448.947 | −1.77450 | ||||||||
\(254\) | −102.713 | − | 306.564i | −0.404384 | − | 1.20694i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −217.541 | − | 134.952i | −0.849768 | − | 0.527157i | ||||
\(257\) | 360.060 | 1.40101 | 0.700505 | − | 0.713647i | \(-0.252958\pi\) | ||||
0.700505 | + | 0.713647i | \(0.252958\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 237.844i | 0.918316i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −125.526 | − | 374.652i | −0.479108 | − | 1.42997i | ||||
\(263\) | 191.310i | 0.727416i | 0.931513 | + | 0.363708i | \(0.118489\pi\) | ||||
−0.931513 | + | 0.363708i | \(0.881511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.89219 | − | 2.97931i | 0.0334293 | − | 0.0112004i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −54.2882 | − | 71.9210i | −0.202568 | − | 0.268362i | ||||
\(269\) | 156.656 | 0.582365 | 0.291183 | − | 0.956667i | \(-0.405951\pi\) | ||||
0.291183 | + | 0.956667i | \(0.405951\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.4172i | 0.112241i | 0.998424 | + | 0.0561203i | \(0.0178730\pi\) | ||||
−0.998424 | + | 0.0561203i | \(0.982127\pi\) | |||||||
\(272\) | 72.9339 | − | 255.922i | 0.268139 | − | 0.940888i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −144.919 | + | 48.5547i | −0.528900 | + | 0.177207i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −438.421 | −1.58275 | −0.791373 | − | 0.611333i | \(-0.790634\pi\) | ||||
−0.791373 | + | 0.611333i | \(0.790634\pi\) | |||||||
\(278\) | −141.821 | − | 423.285i | −0.510146 | − | 1.52261i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −239.589 | −0.852630 | −0.426315 | − | 0.904575i | \(-0.640188\pi\) | ||||
−0.426315 | + | 0.904575i | \(0.640188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 235.523i | − | 0.832238i | −0.909310 | − | 0.416119i | \(-0.863390\pi\) | ||
0.909310 | − | 0.416119i | \(-0.136610\pi\) | |||||||
\(284\) | 148.173 | + | 196.299i | 0.521734 | + | 0.691194i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 79.6890 | + | 237.844i | 0.278633 | + | 0.831622i | ||||
\(287\) | 445.086i | 1.55082i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3780 | −0.0428305 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 439.629 | − | 331.845i | 1.50558 | − | 1.13646i | ||||
\(293\) | −271.955 | −0.928173 | −0.464086 | − | 0.885790i | \(-0.653617\pi\) | ||||
−0.464086 | + | 0.885790i | \(0.653617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −106.479 | + | 155.334i | −0.359727 | + | 0.524777i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −315.407 | + | 105.676i | −1.05841 | + | 0.354618i | ||||
\(299\) | − | 495.916i | − | 1.65858i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −589.043 | −1.95695 | ||||||||
\(302\) | 71.7950 | + | 214.283i | 0.237732 | + | 0.709546i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.14121 | + | 2.03514i | 0.0234908 | + | 0.00669454i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 316.352i | − | 1.03046i | −0.857052 | − | 0.515230i | \(-0.827706\pi\) | ||
0.857052 | − | 0.515230i | \(-0.172294\pi\) | |||||||
\(308\) | 343.709 | − | 259.442i | 1.11594 | − | 0.842344i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 298.355i | 0.959342i | 0.877448 | + | 0.479671i | \(0.159244\pi\) | ||||
−0.877448 | + | 0.479671i | \(0.840756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −191.651 | −0.612302 | −0.306151 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(314\) | −143.998 | + | 48.2464i | −0.458594 | + | 0.153651i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −334.163 | − | 442.699i | −1.05748 | − | 1.40095i | ||||
\(317\) | −232.847 | −0.734534 | −0.367267 | − | 0.930115i | \(-0.619707\pi\) | ||||
−0.367267 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 208.355i | 0.653150i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −807.273 | + | 270.475i | −2.50706 | + | 0.839984i | ||||
\(323\) | 7.71883i | 0.0238973i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −117.027 | − | 349.285i | −0.358979 | − | 1.07143i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −199.258 | + | 290.682i | −0.607495 | + | 0.886225i | ||||
\(329\) | −420.744 | −1.27886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 200.214i | 0.604877i | 0.953169 | + | 0.302438i | \(0.0978007\pi\) | ||||
−0.953169 | + | 0.302438i | \(0.902199\pi\) | |||||||
\(332\) | 207.786 | + | 275.275i | 0.625861 | + | 0.829141i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 122.799 | + | 366.512i | 0.367661 | + | 1.09734i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 451.029 | 1.33836 | 0.669182 | − | 0.743099i | \(-0.266645\pi\) | ||||
0.669182 | + | 0.743099i | \(0.266645\pi\) | |||||||
\(338\) | 57.7628 | − | 19.3533i | 0.170896 | − | 0.0572582i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 97.7682 | 0.286710 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 41.2357i | − | 0.120221i | ||||||
\(344\) | −384.699 | − | 263.706i | −1.11831 | − | 0.766586i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 107.837 | − | 36.1307i | 0.311669 | − | 0.104424i | ||||
\(347\) | − | 128.845i | − | 0.371313i | −0.982615 | − | 0.185656i | \(-0.940559\pi\) | ||
0.982615 | − | 0.185656i | \(-0.0594411\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.756045 | 0.00216632 | 0.00108316 | − | 0.999999i | \(-0.499655\pi\) | ||||
0.00108316 | + | 0.999999i | \(0.499655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 340.622 | − | 15.5661i | 0.967676 | − | 0.0442219i | ||||
\(353\) | −55.7392 | −0.157902 | −0.0789508 | − | 0.996879i | \(-0.525157\pi\) | ||||
−0.0789508 | + | 0.996879i | \(0.525157\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 406.136 | − | 306.564i | 1.14083 | − | 0.861134i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −172.919 | − | 516.102i | −0.483013 | − | 1.44162i | ||||
\(359\) | − | 194.247i | − | 0.541078i | −0.962709 | − | 0.270539i | \(-0.912798\pi\) | ||
0.962709 | − | 0.270539i | \(-0.0872019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 360.785 | 0.999403 | ||||||||
\(362\) | 95.2550 | − | 31.9150i | 0.263135 | − | 0.0881629i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 286.585 | + | 379.668i | 0.787321 | + | 1.04304i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.0264i | 0.0654671i | 0.999464 | + | 0.0327335i | \(0.0104213\pi\) | ||||
−0.999464 | + | 0.0327335i | \(0.989579\pi\) | |||||||
\(368\) | −648.311 | − | 184.759i | −1.76171 | − | 0.502062i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 810.688i | − | 2.18514i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −136.986 | −0.367254 | −0.183627 | − | 0.982996i | \(-0.558784\pi\) | ||||
−0.183627 | + | 0.982996i | \(0.558784\pi\) | |||||||
\(374\) | 112.604 | + | 336.083i | 0.301080 | + | 0.898617i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −274.785 | − | 188.361i | −0.730810 | − | 0.500960i | ||||
\(377\) | −230.153 | −0.610485 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 103.356i | 0.272707i | 0.990660 | + | 0.136353i | \(0.0435382\pi\) | ||||
−0.990660 | + | 0.136353i | \(0.956462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 123.421 | + | 368.368i | 0.323091 | + | 0.964314i | ||||
\(383\) | − | 19.3533i | − | 0.0505308i | −0.999681 | − | 0.0252654i | \(-0.991957\pi\) | ||
0.999681 | − | 0.0252654i | \(-0.00804308\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 43.0543 | − | 14.4252i | 0.111540 | − | 0.0373711i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 47.8887 | − | 36.1479i | 0.123425 | − | 0.0931646i | ||||
\(389\) | −273.978 | −0.704314 | −0.352157 | − | 0.935941i | \(-0.614552\pi\) | ||||
−0.352157 | + | 0.935941i | \(0.614552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 700.750i | − | 1.79220i | ||||||
\(392\) | 240.097 | − | 350.259i | 0.612493 | − | 0.893518i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −293.244 | + | 98.2507i | −0.744274 | + | 0.249367i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −218.230 | −0.549697 | −0.274848 | − | 0.961488i | \(-0.588628\pi\) | ||||
−0.274848 | + | 0.961488i | \(0.588628\pi\) | |||||||
\(398\) | 150.010 | + | 447.726i | 0.376908 | + | 1.12494i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −396.472 | −0.988709 | −0.494355 | − | 0.869260i | \(-0.664596\pi\) | ||||
−0.494355 | + | 0.869260i | \(0.664596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 107.997i | 0.267982i | ||||||||
\(404\) | 624.991 | − | 471.763i | 1.54701 | − | 1.16773i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 125.526 | + | 374.652i | 0.309178 | + | 0.922789i | ||||
\(407\) | − | 250.839i | − | 0.616311i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 301.976 | 0.738327 | 0.369164 | − | 0.929364i | \(-0.379644\pi\) | ||||
0.369164 | + | 0.929364i | \(0.379644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 37.5121 | + | 49.6960i | 0.0910488 | + | 0.120621i | ||||
\(413\) | 645.952 | 1.56405 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.1946 | + | 376.258i | 0.0413332 | + | 0.904466i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.37802 | + | 3.14209i | −0.0224355 | + | 0.00751695i | ||||
\(419\) | 420.461i | 1.00349i | 0.865017 | + | 0.501743i | \(0.167308\pi\) | ||||
−0.865017 | + | 0.501743i | \(0.832692\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −197.378 | −0.468831 | −0.234416 | − | 0.972136i | \(-0.575318\pi\) | ||||
−0.234416 | + | 0.972136i | \(0.575318\pi\) | |||||||
\(422\) | 73.2017 | + | 218.481i | 0.173464 | + | 0.517728i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 362.933 | − | 529.454i | 0.855974 | − | 1.24871i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 812.246i | 1.90222i | ||||||||
\(428\) | 123.674 | + | 163.843i | 0.288957 | + | 0.382811i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 236.869i | 0.549581i | 0.961504 | + | 0.274790i | \(0.0886084\pi\) | ||||
−0.961504 | + | 0.274790i | \(0.911392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 364.378 | 0.841520 | 0.420760 | − | 0.907172i | \(-0.361764\pi\) | ||||
0.420760 | + | 0.907172i | \(0.361764\pi\) | |||||||
\(434\) | 175.802 | − | 58.9019i | 0.405073 | − | 0.135719i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −149.578 | + | 112.906i | −0.343068 | + | 0.258958i | ||||
\(437\) | 19.5536 | 0.0447452 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 72.3679i | − | 0.164847i | −0.996597 | − | 0.0824236i | \(-0.973734\pi\) | ||
0.996597 | − | 0.0824236i | \(-0.0262660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −371.244 | + | 124.384i | −0.839918 | + | 0.281413i | ||||
\(443\) | − | 240.295i | − | 0.542428i | −0.962519 | − | 0.271214i | \(-0.912575\pi\) | ||
0.962519 | − | 0.271214i | \(-0.0874250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 270.145 | + | 806.287i | 0.605706 | + | 1.80782i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 603.110 | − | 233.203i | 1.34623 | − | 0.520542i | ||||
\(449\) | 498.959 | 1.11127 | 0.555633 | − | 0.831427i | \(-0.312476\pi\) | ||||
0.555633 | + | 0.831427i | \(0.312476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 469.403i | − | 1.04081i | ||||||
\(452\) | −368.825 | + | 278.400i | −0.815984 | + | 0.615930i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −113.230 | − | 337.951i | −0.249405 | − | 0.744385i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −171.866 | −0.376074 | −0.188037 | − | 0.982162i | \(-0.560213\pi\) | ||||
−0.188037 | + | 0.982162i | \(0.560213\pi\) | |||||||
\(458\) | −628.911 | + | 210.715i | −1.37317 | + | 0.460077i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −831.825 | −1.80439 | −0.902196 | − | 0.431326i | \(-0.858046\pi\) | ||||
−0.902196 | + | 0.431326i | \(0.858046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 370.011i | 0.799160i | 0.916698 | + | 0.399580i | \(0.130844\pi\) | ||||
−0.916698 | + | 0.399580i | \(0.869156\pi\) | |||||||
\(464\) | −85.7460 | + | 300.879i | −0.184797 | + | 0.648445i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 346.947 | − | 116.244i | 0.744522 | − | 0.249450i | ||||
\(467\) | − | 527.770i | − | 1.13013i | −0.825047 | − | 0.565065i | \(-0.808851\pi\) | ||
0.825047 | − | 0.565065i | \(-0.191149\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 227.608 | 0.485304 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 421.866 | + | 289.183i | 0.893784 | + | 0.612676i | ||||
\(473\) | 621.226 | 1.31337 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 404.956 | + | 536.486i | 0.850748 | + | 1.12707i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 133.852 | + | 399.500i | 0.280024 | + | 0.835775i | ||||
\(479\) | 532.777i | 1.11227i | 0.831092 | + | 0.556135i | \(0.187716\pi\) | ||||
−0.831092 | + | 0.556135i | \(0.812284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 277.081 | 0.576053 | ||||||||
\(482\) | 6.86868 | − | 2.30134i | 0.0142504 | − | 0.00477455i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 23.8146 | − | 17.9760i | 0.0492036 | − | 0.0371404i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 495.073i | − | 1.01658i | −0.861187 | − | 0.508288i | \(-0.830278\pi\) | ||
0.861187 | − | 0.508288i | \(-0.169722\pi\) | |||||||
\(488\) | −363.631 | + | 530.471i | −0.745144 | + | 1.08703i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 518.094i | − | 1.05518i | −0.849499 | − | 0.527590i | \(-0.823096\pi\) | ||
0.849499 | − | 0.527590i | \(-0.176904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −325.215 | −0.659666 | ||||||||
\(494\) | −3.47081 | − | 10.3592i | −0.00702593 | − | 0.0209699i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 141.184 | + | 40.2354i | 0.284645 | + | 0.0811197i | ||||
\(497\) | −621.226 | −1.24995 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 676.579i | − | 1.35587i | −0.735122 | − | 0.677935i | \(-0.762875\pi\) | ||
0.735122 | − | 0.677935i | \(-0.237125\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −159.378 | − | 475.688i | −0.317486 | − | 0.947585i | ||||
\(503\) | 35.2804i | 0.0701399i | 0.999385 | + | 0.0350700i | \(0.0111654\pi\) | ||||
−0.999385 | + | 0.0350700i | \(0.988835\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 851.379 | − | 285.252i | 1.68257 | − | 0.563740i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 389.569 | + | 516.102i | 0.766869 | + | 1.01595i | ||||
\(509\) | −538.520 | −1.05800 | −0.528998 | − | 0.848623i | \(-0.677432\pi\) | ||||
−0.528998 | + | 0.848623i | \(0.677432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1391.29i | 2.72268i | ||||||||
\(512\) | 498.288 | + | 117.700i | 0.973218 | + | 0.229884i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −682.813 | + | 228.775i | −1.32843 | + | 0.445088i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 443.732 | 0.858282 | ||||||||
\(518\) | −151.121 | − | 451.044i | −0.291740 | − | 0.870742i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −73.7237 | −0.141504 | −0.0707521 | − | 0.997494i | \(-0.522540\pi\) | ||||
−0.0707521 | + | 0.997494i | \(0.522540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 465.440i | − | 0.889942i | −0.895545 | − | 0.444971i | \(-0.853214\pi\) | ||
0.895545 | − | 0.444971i | \(-0.146786\pi\) | |||||||
\(524\) | 476.094 | + | 630.729i | 0.908576 | + | 1.20368i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −121.555 | − | 362.799i | −0.231093 | − | 0.689732i | ||||
\(527\) | 152.604i | 0.289571i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1246.17 | −2.35570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.9701 | + | 11.2999i | −0.0281392 | + | 0.0212403i | ||||
\(533\) | 518.512 | 0.972819 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 148.649 | + | 101.897i | 0.277330 | + | 0.190106i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −297.081 | + | 99.5364i | −0.552196 | + | 0.185012i | ||||
\(539\) | 565.610i | 1.04937i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −48.9857 | −0.0905466 | −0.0452733 | − | 0.998975i | \(-0.514416\pi\) | ||||
−0.0452733 | + | 0.998975i | \(0.514416\pi\) | |||||||
\(542\) | −19.3265 | − | 57.6828i | −0.0356577 | − | 0.106426i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24.2967 | + | 531.668i | 0.0446631 | + | 0.977330i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 500.536i | − | 0.915056i | −0.889195 | − | 0.457528i | \(-0.848735\pi\) | ||
0.889195 | − | 0.457528i | \(-0.151265\pi\) | |||||||
\(548\) | 243.971 | − | 184.157i | 0.445203 | − | 0.336053i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.07478i | − | 0.0164696i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1401.00 | 2.53346 | ||||||||
\(554\) | 831.417 | − | 278.564i | 1.50075 | − | 0.502824i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 537.895 | + | 712.603i | 0.967436 | + | 1.28166i | ||||
\(557\) | −771.368 | −1.38486 | −0.692431 | − | 0.721484i | \(-0.743460\pi\) | ||||
−0.692431 | + | 0.721484i | \(0.743460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 686.218i | 1.22758i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 454.354 | − | 152.230i | 0.808459 | − | 0.270872i | ||||
\(563\) | 535.602i | 0.951335i | 0.879625 | + | 0.475667i | \(0.157793\pi\) | ||||
−0.879625 | + | 0.475667i | \(0.842207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 149.647 | + | 446.644i | 0.264394 | + | 0.789123i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −405.718 | − | 278.114i | −0.714292 | − | 0.489637i | ||||
\(569\) | −102.941 | −0.180915 | −0.0904575 | − | 0.995900i | \(-0.528833\pi\) | ||||
−0.0904575 | + | 0.995900i | \(0.528833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 642.662i | 1.12550i | 0.826626 | + | 0.562752i | \(0.190257\pi\) | ||||
−0.826626 | + | 0.562752i | \(0.809743\pi\) | |||||||
\(572\) | −302.243 | − | 400.411i | −0.528396 | − | 0.700020i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −282.799 | − | 844.056i | −0.492681 | − | 1.47048i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 397.919 | 0.689634 | 0.344817 | − | 0.938670i | \(-0.387941\pi\) | ||||
0.344817 | + | 0.938670i | \(0.387941\pi\) | |||||||
\(578\) | 23.4735 | − | 7.86476i | 0.0406117 | − | 0.0136068i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −871.159 | −1.49941 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 854.981i | 1.46652i | ||||||||
\(584\) | −622.860 | + | 908.640i | −1.06654 | + | 1.55589i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 515.732 | − | 172.795i | 0.880089 | − | 0.294872i | ||||
\(587\) | − | 813.625i | − | 1.38607i | −0.720903 | − | 0.693036i | \(-0.756273\pi\) | ||
0.720903 | − | 0.693036i | \(-0.243727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.25824 | −0.00722961 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 103.230 | − | 362.228i | 0.174374 | − | 0.611872i | ||||
\(593\) | 731.362 | 1.23333 | 0.616663 | − | 0.787227i | \(-0.288484\pi\) | ||||
0.616663 | + | 0.787227i | \(0.288484\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 530.989 | − | 400.807i | 0.890921 | − | 0.672494i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 315.096 | + | 940.450i | 0.526916 | + | 1.57266i | ||||
\(599\) | − | 752.516i | − | 1.25629i | −0.778098 | − | 0.628143i | \(-0.783815\pi\) | ||
0.778098 | − | 0.628143i | \(-0.216185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1013.81 | 1.68688 | 0.843439 | − | 0.537226i | \(-0.180528\pi\) | ||||
0.843439 | + | 0.537226i | \(0.180528\pi\) | |||||||
\(602\) | 1117.05 | − | 374.267i | 1.85557 | − | 0.621705i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −272.302 | − | 360.747i | −0.450832 | − | 0.597262i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 432.276i | 0.712151i | 0.934457 | + | 0.356075i | \(0.115885\pi\) | ||||
−0.934457 | + | 0.356075i | \(0.884115\pi\) | |||||||
\(608\) | −14.8356 | + | 0.677973i | −0.0244007 | + | 0.00111509i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 490.155i | 0.802218i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −213.971 | −0.349056 | −0.174528 | − | 0.984652i | \(-0.555840\pi\) | ||||
−0.174528 | + | 0.984652i | \(0.555840\pi\) | |||||||
\(614\) | 201.004 | + | 599.926i | 0.327368 | + | 0.977077i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −486.962 | + | 710.389i | −0.790522 | + | 1.15323i | ||||
\(617\) | −814.966 | −1.32085 | −0.660426 | − | 0.750891i | \(-0.729624\pi\) | ||||
−0.660426 | + | 0.750891i | \(0.729624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1035.45i | − | 1.67278i | −0.548133 | − | 0.836391i | \(-0.684661\pi\) | ||
0.548133 | − | 0.836391i | \(-0.315339\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −189.569 | − | 565.798i | −0.304774 | − | 0.909643i | ||||
\(623\) | 1285.29i | 2.06307i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 363.444 | − | 121.771i | 0.580581 | − | 0.194522i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 242.422 | − | 182.988i | 0.386023 | − | 0.291382i | ||||
\(629\) | 391.527 | 0.622460 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 67.7270i | 0.107333i | 0.998559 | + | 0.0536664i | \(0.0170907\pi\) | ||||
−0.998559 | + | 0.0536664i | \(0.982909\pi\) | |||||||
\(632\) | 914.985 | + | 627.209i | 1.44776 | + | 0.992419i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 441.569 | − | 147.947i | 0.696481 | − | 0.233355i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −624.785 | −0.980824 | ||||||||
\(638\) | −132.385 | − | 395.122i | −0.207499 | − | 0.619313i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −851.379 | −1.32820 | −0.664102 | − | 0.747642i | \(-0.731186\pi\) | ||||
−0.664102 | + | 0.747642i | \(0.731186\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 562.800i | 0.875272i | 0.899152 | + | 0.437636i | \(0.144184\pi\) | ||||
−0.899152 | + | 0.437636i | \(0.855816\pi\) | |||||||
\(644\) | 1359.05 | − | 1025.85i | 2.11032 | − | 1.59294i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.90440 | − | 14.6379i | −0.00759195 | − | 0.0226593i | ||||
\(647\) | − | 331.188i | − | 0.511883i | −0.966692 | − | 0.255942i | \(-0.917615\pi\) | ||
0.966692 | − | 0.255942i | \(-0.0823855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −681.244 | −1.04968 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 443.857 | + | 588.023i | 0.680763 | + | 0.901875i | ||||
\(653\) | −804.177 | −1.23151 | −0.615756 | − | 0.787937i | \(-0.711149\pi\) | ||||
−0.615756 | + | 0.787937i | \(0.711149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 193.177 | − | 677.851i | 0.294478 | − | 1.03331i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 797.895 | − | 267.333i | 1.21261 | − | 0.406281i | ||||
\(659\) | − | 1061.53i | − | 1.61081i | −0.592722 | − | 0.805407i | \(-0.701947\pi\) | ||
0.592722 | − | 0.805407i | \(-0.298053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −117.646 | −0.177982 | −0.0889910 | − | 0.996032i | \(-0.528364\pi\) | ||||
−0.0889910 | + | 0.996032i | \(0.528364\pi\) | |||||||
\(662\) | −127.212 | − | 379.684i | −0.192164 | − | 0.573541i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −568.947 | − | 390.005i | −0.856848 | − | 0.587357i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 823.848i | 1.23516i | ||||||||
\(668\) | −465.749 | − | 617.025i | −0.697229 | − | 0.923690i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 856.624i | − | 1.27664i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 984.785 | 1.46328 | 0.731638 | − | 0.681693i | \(-0.238756\pi\) | ||||
0.731638 | + | 0.681693i | \(0.238756\pi\) | |||||||
\(674\) | −855.326 | + | 286.575i | −1.26903 | + | 0.425185i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −97.2440 | + | 73.4027i | −0.143852 | + | 0.108584i | ||||
\(677\) | 99.5646 | 0.147067 | 0.0735337 | − | 0.997293i | \(-0.476572\pi\) | ||||
0.0735337 | + | 0.997293i | \(0.476572\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 151.553i | 0.223200i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −185.407 | + | 62.1201i | −0.271857 | + | 0.0910851i | ||||
\(683\) | 434.807i | 0.636614i | 0.947988 | + | 0.318307i | \(0.103114\pi\) | ||||
−0.947988 | + | 0.318307i | \(0.896886\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.2004 | + | 78.1990i | 0.0381930 | + | 0.113993i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 897.093 | + | 255.658i | 1.30391 | + | 0.371596i | ||||
\(689\) | −944.429 | −1.37072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1153.87i | − | 1.66986i | −0.550358 | − | 0.834929i | \(-0.685509\pi\) | ||
0.550358 | − | 0.834929i | \(-0.314491\pi\) | |||||||
\(692\) | −181.545 | + | 137.036i | −0.262348 | + | 0.198028i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 81.8659 | + | 244.341i | 0.117962 | + | 0.352077i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 732.679 | 1.05119 | ||||||||
\(698\) | −1.43375 | + | 0.480376i | −0.00205409 | + | 0.000688218i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −479.405 | −0.683887 | −0.341944 | − | 0.939720i | \(-0.611085\pi\) | ||||
−0.341944 | + | 0.939720i | \(0.611085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9251i | 0.0155407i | ||||||||
\(704\) | −636.061 | + | 245.944i | −0.903496 | + | 0.349352i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 105.703 | − | 35.4156i | 0.149721 | − | 0.0501638i | ||||
\(707\) | 1977.90i | 2.79760i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 932.880 | 1.31577 | 0.657884 | − | 0.753119i | \(-0.271451\pi\) | ||||
0.657884 | + | 0.753119i | \(0.271451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −575.407 | + | 839.415i | −0.808155 | + | 1.17895i | ||||
\(713\) | 386.582 | 0.542191 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 655.842 | + | 868.860i | 0.915981 | + | 1.21349i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 123.421 | + | 368.368i | 0.171895 | + | 0.513047i | ||||
\(719\) | 141.836i | 0.197268i | 0.995124 | + | 0.0986341i | \(0.0314473\pi\) | ||||
−0.995124 | + | 0.0986341i | \(0.968553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −157.273 | −0.218131 | ||||||||
\(722\) | −684.188 | + | 229.236i | −0.947629 | + | 0.317501i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −160.362 | + | 121.046i | −0.221495 | + | 0.167191i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 891.575i | − | 1.22638i | −0.789937 | − | 0.613188i | \(-0.789887\pi\) | ||
0.789937 | − | 0.613188i | \(-0.210113\pi\) | |||||||
\(728\) | −784.710 | − | 537.907i | −1.07790 | − | 0.738884i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 969.655i | 1.32648i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −614.593 | −0.838463 | −0.419232 | − | 0.907879i | \(-0.637700\pi\) | ||||
−0.419232 | + | 0.907879i | \(0.637700\pi\) | |||||||
\(734\) | −15.2659 | − | 45.5634i | −0.0207983 | − | 0.0620755i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1346.84 | − | 61.5494i | 1.82995 | − | 0.0836269i | ||||
\(737\) | −240.043 | −0.325703 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 817.138i | − | 1.10573i | −0.833269 | − | 0.552867i | \(-0.813534\pi\) | ||
0.833269 | − | 0.552867i | \(-0.186466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 515.096 | + | 1537.38i | 0.694199 | + | 2.07194i | ||||
\(743\) | − | 868.860i | − | 1.16939i | −0.811252 | − | 0.584697i | \(-0.801213\pi\) | ||
0.811252 | − | 0.584697i | \(-0.198787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 259.778 | − | 87.0381i | 0.348228 | − | 0.116673i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −427.081 | − | 565.798i | −0.570964 | − | 0.756414i | ||||
\(749\) | −518.512 | −0.692273 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 100.822i | − | 0.134250i | −0.997745 | − | 0.0671252i | \(-0.978617\pi\) | ||
0.997745 | − | 0.0671252i | \(-0.0213827\pi\) | |||||||
\(752\) | 640.779 | + | 182.613i | 0.852100 | + | 0.242836i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 436.459 | − | 146.235i | 0.578859 | − | 0.193945i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.6363 | 0.0444336 | 0.0222168 | − | 0.999753i | \(-0.492928\pi\) | ||||
0.0222168 | + | 0.999753i | \(0.492928\pi\) | |||||||
\(758\) | −65.6703 | − | 196.003i | −0.0866363 | − | 0.258579i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −685.059 | −0.900209 | −0.450105 | − | 0.892976i | \(-0.648613\pi\) | ||||
−0.450105 | + | 0.892976i | \(0.648613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 473.367i | − | 0.620402i | ||||||
\(764\) | −468.108 | − | 620.150i | −0.612707 | − | 0.811714i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.2967 | + | 36.7013i | 0.0160531 | + | 0.0479130i | ||||
\(767\) | − | 752.516i | − | 0.981116i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.6505 | 0.0307549 | 0.0153775 | − | 0.999882i | \(-0.495105\pi\) | ||||
0.0153775 | + | 0.999882i | \(0.495105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −72.4821 | + | 54.7117i | −0.0938888 | + | 0.0708701i | ||||
\(773\) | 947.350 | 1.22555 | 0.612775 | − | 0.790257i | \(-0.290053\pi\) | ||||
0.612775 | + | 0.790257i | \(0.290053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −67.8480 | + | 98.9780i | −0.0874330 | + | 0.127549i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 519.569 | − | 174.080i | 0.667827 | − | 0.223754i | ||||
\(779\) | 20.4446i | 0.0262447i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 655.167 | 0.838882 | ||||||||
\(782\) | 445.243 | + | 1328.89i | 0.569364 | + | 1.69935i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −232.770 | + | 816.780i | −0.296901 | + | 1.04181i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1054.73i | 1.34019i | 0.742275 | + | 0.670096i | \(0.233747\pi\) | ||||
−0.742275 | + | 0.670096i | \(0.766253\pi\) | |||||||
\(788\) | 493.678 | − | 372.643i | 0.626495 | − | 0.472897i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1167.22i | − | 1.47562i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 946.244 | 1.19325 | ||||||||
\(794\) | 413.848 | − | 138.659i | 0.521220 | − | 0.174633i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −568.953 | − | 753.749i | −0.714765 | − | 0.946921i | ||||
\(797\) | 810.475 | 1.01691 | 0.508454 | − | 0.861089i | \(-0.330217\pi\) | ||||
0.508454 | + | 0.861089i | \(0.330217\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 692.609i | 0.866845i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 751.866 | − | 251.911i | 0.937489 | − | 0.314103i | ||||
\(803\) | − | 1467.30i | − | 1.82728i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −68.6191 | − | 204.804i | −0.0851353 | − | 0.254099i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −885.478 | + | 1291.75i | −1.09589 | + | 1.59870i | ||||
\(809\) | 768.673 | 0.950152 | 0.475076 | − | 0.879945i | \(-0.342421\pi\) | ||||
0.475076 | + | 0.879945i | \(0.342421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 744.199i | 0.917632i | 0.888531 | + | 0.458816i | \(0.151726\pi\) | ||||
−0.888531 | + | 0.458816i | \(0.848274\pi\) | |||||||
\(812\) | −476.094 | − | 630.729i | −0.586322 | − | 0.776760i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 159.378 | + | 475.688i | 0.195796 | + | 0.584383i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.0571 | −0.0331177 | ||||||||
\(818\) | −572.664 | + | 191.870i | −0.700078 | + | 0.234559i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 205.427 | 0.250215 | 0.125108 | − | 0.992143i | \(-0.460072\pi\) | ||||
0.125108 | + | 0.992143i | \(0.460072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1287.79i | 1.56475i | 0.622808 | + | 0.782375i | \(0.285992\pi\) | ||||
−0.622808 | + | 0.782375i | \(0.714008\pi\) | |||||||
\(824\) | −102.713 | − | 70.4086i | −0.124652 | − | 0.0854473i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1224.98 | + | 410.425i | −1.48302 | + | 0.496883i | ||||
\(827\) | − | 255.621i | − | 0.309094i | −0.987985 | − | 0.154547i | \(-0.950608\pi\) | ||
0.987985 | − | 0.154547i | \(-0.0493918\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0286 | −0.0169223 | −0.00846114 | − | 0.999964i | \(-0.502693\pi\) | ||||
−0.00846114 | + | 0.999964i | \(0.502693\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −271.675 | − | 702.606i | −0.326532 | − | 0.844479i | ||||
\(833\) | −882.846 | −1.05984 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.7880 | − | 11.9172i | 0.0188851 | − | 0.0142551i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −267.153 | − | 797.357i | −0.318798 | − | 0.951500i | ||||
\(839\) | − | 333.636i | − | 0.397659i | −0.980034 | − | 0.198829i | \(-0.936286\pi\) | ||
0.980034 | − | 0.198829i | \(-0.0637140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −458.655 | −0.545369 | ||||||||
\(842\) | 374.306 | − | 125.410i | 0.444543 | − | 0.148943i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −277.638 | − | 367.815i | −0.328955 | − | 0.435799i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 75.3657i | 0.0889795i | ||||||||
\(848\) | −351.857 | + | 1234.65i | −0.414926 | + | 1.45596i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 991.832i | − | 1.16549i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1563.83 | −1.83333 | −0.916663 | − | 0.399661i | \(-0.869128\pi\) | ||||
−0.916663 | + | 0.399661i | \(0.869128\pi\) | |||||||
\(854\) | −516.086 | − | 1540.33i | −0.604316 | − | 1.80367i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −338.636 | − | 232.130i | −0.395603 | − | 0.271180i | ||||
\(857\) | 1283.36 | 1.49750 | 0.748749 | − | 0.662854i | \(-0.230655\pi\) | ||||
0.748749 | + | 0.662854i | \(0.230655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1448.91i | 1.68674i | 0.537330 | + | 0.843372i | \(0.319433\pi\) | ||||
−0.537330 | + | 0.843372i | \(0.680567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −150.502 | − | 449.196i | −0.174597 | − | 0.521109i | ||||
\(863\) | − | 755.677i | − | 0.875640i | −0.899063 | − | 0.437820i | \(-0.855751\pi\) | ||
0.899063 | − | 0.437820i | \(-0.144249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −691.002 | + | 231.519i | −0.797924 | + | 0.267343i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −295.963 | + | 223.402i | −0.340971 | + | 0.257375i | ||||
\(869\) | −1477.55 | −1.70029 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 265.157i | − | 0.304428i | ||||||
\(872\) | 211.919 | − | 309.152i | 0.243027 | − | 0.354532i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −37.0813 | + | 12.4240i | −0.0424271 | + | 0.0142151i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 248.612 | 0.283480 | 0.141740 | − | 0.989904i | \(-0.454730\pi\) | ||||
0.141740 | + | 0.989904i | \(0.454730\pi\) | |||||||
\(878\) | 45.9812 | + | 137.238i | 0.0523704 | + | 0.156307i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 460.306 | 0.522481 | 0.261240 | − | 0.965274i | \(-0.415868\pi\) | ||||
0.261240 | + | 0.965274i | \(0.415868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 554.195i | − | 0.627628i | −0.949485 | − | 0.313814i | \(-0.898393\pi\) | ||
0.949485 | − | 0.313814i | \(-0.101607\pi\) | |||||||
\(884\) | 624.991 | − | 471.763i | 0.707004 | − | 0.533668i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 152.679 | + | 455.694i | 0.172324 | + | 0.514327i | ||||
\(887\) | 251.593i | 0.283644i | 0.989892 | + | 0.141822i | \(0.0452961\pi\) | ||||
−0.989892 | + | 0.141822i | \(0.954704\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1633.30 | −1.83723 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1024.60 | − | 1357.39i | −1.14865 | − | 1.52174i | ||||
\(893\) | −19.3265 | −0.0216422 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −995.558 | + | 825.448i | −1.11111 | + | 0.921259i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −946.220 | + | 317.029i | −1.05370 | + | 0.353039i | ||||
\(899\) | − | 179.411i | − | 0.199568i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1334.52 | −1.48115 | ||||||||
\(902\) | 298.250 | + | 890.171i | 0.330654 | + | 0.986886i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 522.545 | − | 762.299i | 0.578037 | − | 0.843251i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 447.842i | − | 0.493762i | −0.969046 | − | 0.246881i | \(-0.920594\pi\) | ||
0.969046 | − | 0.246881i | \(-0.0794056\pi\) | |||||||
\(908\) | 429.455 | + | 568.942i | 0.472968 | + | 0.626588i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 96.7664i | 0.106220i | 0.998589 | + | 0.0531100i | \(0.0169134\pi\) | ||||
−0.998589 | + | 0.0531100i | \(0.983087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 918.756 | 1.00630 | ||||||||
\(914\) | 325.925 | − | 109.200i | 0.356592 | − | 0.119475i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1058.78 | − | 799.196i | 1.15587 | − | 0.872485i | ||||
\(917\) | −1996.06 | −2.17673 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 234.739i | 0.255429i | 0.991811 | + | 0.127715i | \(0.0407641\pi\) | ||||
−0.991811 | + | 0.127715i | \(0.959236\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1577.46 | − | 528.526i | 1.71092 | − | 0.573238i | ||||
\(923\) | 723.711i | 0.784085i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −235.098 | − | 701.685i | −0.253886 | − | 0.757759i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28.5648 | − | 625.064i | −0.0307811 | − | 0.673561i | ||||
\(929\) | −552.902 | −0.595158 | −0.297579 | − | 0.954697i | \(-0.596179\pi\) | ||||
−0.297579 | + | 0.954697i | \(0.596179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 24.6348i | − | 0.0264606i | ||||||
\(932\) | −584.088 | + | 440.887i | −0.626704 | + | 0.473055i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 335.335 | + | 1000.86i | 0.359031 | + | 1.07158i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −957.870 | −1.02227 | −0.511137 | − | 0.859499i | \(-0.670775\pi\) | ||||
−0.511137 | + | 0.859499i | \(0.670775\pi\) | |||||||
\(938\) | −431.633 | + | 144.618i | −0.460163 | + | 0.154177i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1125.13 | 1.19567 | 0.597837 | − | 0.801618i | \(-0.296027\pi\) | ||||
0.597837 | + | 0.801618i | \(0.296027\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1856.05i | − | 1.96824i | ||||||
\(944\) | −983.763 | − | 280.358i | −1.04212 | − | 0.296989i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1178.09 | + | 394.715i | −1.24533 | + | 0.417246i | ||||
\(947\) | − | 256.824i | − | 0.271198i | −0.990764 | − | 0.135599i | \(-0.956704\pi\) | ||
0.990764 | − | 0.135599i | \(-0.0432959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1620.81 | 1.70792 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1108.83 | − | 760.085i | −1.16473 | − | 0.798409i | ||||
\(953\) | −575.377 | −0.603753 | −0.301877 | − | 0.953347i | \(-0.597613\pi\) | ||||
−0.301877 | + | 0.953347i | \(0.597613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −507.670 | − | 672.561i | −0.531035 | − | 0.703516i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −338.516 | − | 1010.35i | −0.353357 | − | 1.05465i | ||||
\(959\) | 772.094i | 0.805103i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 876.813 | 0.912397 | ||||||||
\(962\) | −525.454 | + | 176.052i | −0.546210 | + | 0.183006i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.5635 | + | 8.72845i | −0.0119953 | + | 0.00905441i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 860.976i | − | 0.890358i | −0.895442 | − | 0.445179i | \(-0.853140\pi\) | ||
0.895442 | − | 0.445179i | \(-0.146860\pi\) | |||||||
\(968\) | −33.7401 | + | 49.2207i | −0.0348555 | + | 0.0508478i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 177.116i | 0.182406i | 0.995832 | + | 0.0912030i | \(0.0290712\pi\) | ||||
−0.995832 | + | 0.0912030i | \(0.970929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2255.17 | −2.31775 | ||||||||
\(974\) | 314.560 | + | 938.851i | 0.322957 | + | 0.963913i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 352.534 | − | 1237.02i | 0.361202 | − | 1.26744i | ||||
\(977\) | 755.634 | 0.773423 | 0.386711 | − | 0.922201i | \(-0.373611\pi\) | ||||
0.386711 | + | 0.922201i | \(0.373611\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1355.52i | − | 1.38459i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 329.187 | + | 982.507i | 0.335221 | + | 1.00052i | ||||
\(983\) | − | 1108.93i | − | 1.12811i | −0.825738 | − | 0.564054i | \(-0.809241\pi\) | ||
0.825738 | − | 0.564054i | \(-0.190759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 616.735 | − | 206.636i | 0.625492 | − | 0.209570i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.1640 | + | 17.4397i | 0.0133239 | + | 0.0176515i | ||||
\(989\) | 2456.37 | 2.48369 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 516.421i | 0.521111i | 0.965459 | + | 0.260556i | \(0.0839058\pi\) | ||||
−0.965459 | + | 0.260556i | \(0.916094\pi\) | |||||||
\(992\) | −293.305 | + | 13.4037i | −0.295670 | + | 0.0135118i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1178.09 | − | 394.715i | 1.18520 | − | 0.397098i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1127.03 | −1.13042 | −0.565212 | − | 0.824946i | \(-0.691206\pi\) | ||||
−0.565212 | + | 0.824946i | \(0.691206\pi\) | |||||||
\(998\) | 429.885 | + | 1283.06i | 0.430747 | + | 1.28563i | ||||
\(999\) | 0 | 0 |
(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 | 900.3.c.q.451.2 | yes | 8 | |
3.2 | odd | 2 | inner | 900.3.c.q.451.7 | yes | 8 | |
4.3 | odd | 2 | inner | 900.3.c.q.451.1 | yes | 8 | |
5.2 | odd | 4 | 900.3.f.g.199.5 | 16 | |||
5.3 | odd | 4 | 900.3.f.g.199.12 | 16 | |||
5.4 | even | 2 | 900.3.c.p.451.7 | yes | 8 | ||
12.11 | even | 2 | inner | 900.3.c.q.451.8 | yes | 8 | |
15.2 | even | 4 | 900.3.f.g.199.11 | 16 | |||
15.8 | even | 4 | 900.3.f.g.199.6 | 16 | |||
15.14 | odd | 2 | 900.3.c.p.451.2 | yes | 8 | ||
20.3 | even | 4 | 900.3.f.g.199.7 | 16 | |||
20.7 | even | 4 | 900.3.f.g.199.10 | 16 | |||
20.19 | odd | 2 | 900.3.c.p.451.8 | yes | 8 | ||
60.23 | odd | 4 | 900.3.f.g.199.9 | 16 | |||
60.47 | odd | 4 | 900.3.f.g.199.8 | 16 | |||
60.59 | even | 2 | 900.3.c.p.451.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.c.p.451.1 | ✓ | 8 | 60.59 | even | 2 | ||
900.3.c.p.451.2 | yes | 8 | 15.14 | odd | 2 | ||
900.3.c.p.451.7 | yes | 8 | 5.4 | even | 2 | ||
900.3.c.p.451.8 | yes | 8 | 20.19 | odd | 2 | ||
900.3.c.q.451.1 | yes | 8 | 4.3 | odd | 2 | inner | |
900.3.c.q.451.2 | yes | 8 | 1.1 | even | 1 | trivial | |
900.3.c.q.451.7 | yes | 8 | 3.2 | odd | 2 | inner | |
900.3.c.q.451.8 | yes | 8 | 12.11 | even | 2 | inner | |
900.3.f.g.199.5 | 16 | 5.2 | odd | 4 | |||
900.3.f.g.199.6 | 16 | 15.8 | even | 4 | |||
900.3.f.g.199.7 | 16 | 20.3 | even | 4 | |||
900.3.f.g.199.8 | 16 | 60.47 | odd | 4 | |||
900.3.f.g.199.9 | 16 | 60.23 | odd | 4 | |||
900.3.f.g.199.10 | 16 | 20.7 | even | 4 | |||
900.3.f.g.199.11 | 16 | 15.2 | even | 4 | |||
900.3.f.g.199.12 | 16 | 5.3 | odd | 4 |