Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,2,Mod(65,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.e (of order \(4\), degree \(2\), 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: | \(2.04417029174\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.193 |
Dual form | 256.2.e.b.65.2 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.517638 | + | 0.517638i | −0.298858 | + | 0.298858i | −0.840567 | − | 0.541708i | \(-0.817778\pi\) |
0.541708 | + | 0.840567i | \(0.317778\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205 | + | 1.73205i | 0.774597 | + | 0.774597i | 0.978906 | − | 0.204310i | \(-0.0654949\pi\) |
−0.204310 | + | 0.978906i | \(0.565495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.86370i | − | 1.46034i | −0.683264 | − | 0.730171i | \(-0.739440\pi\) | ||
0.683264 | − | 0.730171i | \(-0.260560\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.46410i | 0.821367i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.34607 | + | 3.34607i | 1.00888 | + | 1.00888i | 0.999960 | + | 0.00891637i | \(0.00283821\pi\) |
0.00891637 | + | 0.999960i | \(0.497162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.267949 | − | 0.267949i | 0.0743157 | − | 0.0743157i | −0.668972 | − | 0.743288i | \(-0.733265\pi\) |
0.743288 | + | 0.668972i | \(0.233265\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.79315 | −0.462990 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.34607 | + | 3.34607i | −0.767640 | + | 0.767640i | −0.977691 | − | 0.210051i | \(-0.932637\pi\) |
0.210051 | + | 0.977691i | \(0.432637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 2.00000i | 0.436436 | + | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.79315i | 0.373898i | 0.982370 | + | 0.186949i | \(0.0598599\pi\) | ||||
−0.982370 | + | 0.186949i | \(0.940140\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.82843 | − | 2.82843i | −0.544331 | − | 0.544331i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.73205 | − | 1.73205i | 0.321634 | − | 0.321634i | −0.527760 | − | 0.849394i | \(-0.676968\pi\) |
0.849394 | + | 0.527760i | \(0.176968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.46410 | −0.603023 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.69213 | − | 6.69213i | 1.13118 | − | 1.13118i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.73205 | − | 3.73205i | −0.613545 | − | 0.613545i | 0.330323 | − | 0.943868i | \(-0.392842\pi\) |
−0.943868 | + | 0.330323i | \(0.892842\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.277401i | 0.0444198i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.55291 | − | 1.55291i | −0.236817 | − | 0.236817i | 0.578714 | − | 0.815531i | \(-0.303555\pi\) |
−0.815531 | + | 0.578714i | \(0.803555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.26795 | + | 4.26795i | −0.636228 | + | 0.636228i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.79796 | −1.42918 | −0.714590 | − | 0.699544i | \(-0.753387\pi\) | ||||
−0.714590 | + | 0.699544i | \(0.753387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.92820 | −1.13260 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.79315 | + | 1.79315i | −0.251091 | + | 0.251091i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.73205 | − | 7.73205i | −1.06208 | − | 1.06208i | −0.997941 | − | 0.0641378i | \(-0.979570\pi\) |
−0.0641378 | − | 0.997941i | \(-0.520430\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5911i | 1.56294i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.46410i | − | 0.458831i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.13922 | − | 5.13922i | −0.669069 | − | 0.669069i | 0.288432 | − | 0.957501i | \(-0.406866\pi\) |
−0.957501 | + | 0.288432i | \(0.906866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.73205 | + | 3.73205i | −0.477840 | + | 0.477840i | −0.904440 | − | 0.426600i | \(-0.859711\pi\) |
0.426600 | + | 0.904440i | \(0.359711\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.52056 | 1.19948 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.928203 | 0.115129 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.38134 | − | 4.38134i | 0.535266 | − | 0.535266i | −0.386869 | − | 0.922135i | \(-0.626443\pi\) |
0.922135 | + | 0.386869i | \(0.126443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.928203 | − | 0.928203i | −0.111743 | − | 0.111743i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.79315i | 0.212808i | 0.994323 | + | 0.106404i | \(0.0339337\pi\) | ||||
−0.994323 | + | 0.106404i | \(0.966066\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.53590i | 0.296804i | 0.988927 | + | 0.148402i | \(0.0474130\pi\) | ||||
−0.988927 | + | 0.148402i | \(0.952587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.517638 | − | 0.517638i | −0.0597717 | − | 0.0597717i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9282 | − | 12.9282i | 1.47331 | − | 1.47331i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.14110 | 0.465911 | 0.232955 | − | 0.972487i | \(-0.425160\pi\) | ||||
0.232955 | + | 0.972487i | \(0.425160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.46410 | −0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.55291 | − | 1.55291i | 0.170454 | − | 0.170454i | −0.616725 | − | 0.787179i | \(-0.711541\pi\) |
0.787179 | + | 0.616725i | \(0.211541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | + | 6.00000i | 0.650791 | + | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.79315i | 0.192246i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.53590i | − | 0.268805i | −0.990927 | − | 0.134402i | \(-0.957089\pi\) | ||
0.990927 | − | 0.134402i | \(-0.0429115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03528 | − | 1.03528i | −0.108526 | − | 0.108526i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.92820 | + | 2.92820i | −0.303641 | + | 0.303641i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.5911 | −1.18922 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.46410 | 0.351726 | 0.175863 | − | 0.984415i | \(-0.443728\pi\) | ||||
0.175863 | + | 0.984415i | \(0.443728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.24504 | + | 8.24504i | −0.828658 | + | 0.828658i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.803848 | − | 0.803848i | −0.0799858 | − | 0.0799858i | 0.665982 | − | 0.745968i | \(-0.268013\pi\) |
−0.745968 | + | 0.665982i | \(0.768013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.52056i | − | 0.938088i | −0.883175 | − | 0.469044i | \(-0.844598\pi\) | ||
0.883175 | − | 0.469044i | \(-0.155402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.92820i | 0.676123i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1440 | + | 13.1440i | 1.27068 | + | 1.27068i | 0.945731 | + | 0.324949i | \(0.105347\pi\) |
0.324949 | + | 0.945731i | \(0.394653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1962 | + | 13.1962i | −1.26396 | + | 1.26396i | −0.314806 | + | 0.949156i | \(0.601940\pi\) |
−0.949156 | + | 0.314806i | \(0.898060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.86370 | 0.366726 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9282 | 1.21618 | 0.608092 | − | 0.793867i | \(-0.291935\pi\) | ||||
0.608092 | + | 0.793867i | \(0.291935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.10583 | + | 3.10583i | −0.289620 | + | 0.289620i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.660254 | + | 0.660254i | 0.0610405 | + | 0.0610405i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 13.3843i | − | 1.22693i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923i | 1.03566i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.58630 | + | 3.58630i | 0.323366 | + | 0.323366i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | − | 6.92820i | 0.619677 | − | 0.619677i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65685 | −0.501965 | −0.250982 | − | 0.967992i | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.60770 | 0.141550 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.240237 | − | 0.240237i | 0.0209896 | − | 0.0209896i | −0.696534 | − | 0.717524i | \(-0.745276\pi\) |
0.717524 | + | 0.696534i | \(0.245276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9282 | + | 12.9282i | 1.12102 | + | 1.12102i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 9.79796i | − | 0.843274i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.0000i | − | 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.20977 | − | 7.20977i | −0.611525 | − | 0.611525i | 0.331819 | − | 0.943343i | \(-0.392338\pi\) |
−0.943343 | + | 0.331819i | \(0.892338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.07180 | − | 5.07180i | 0.427122 | − | 0.427122i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.79315 | 0.149951 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.10394 | − | 4.10394i | 0.338487 | − | 0.338487i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7321 | + | 13.7321i | 1.12497 | + | 1.12497i | 0.990983 | + | 0.133991i | \(0.0427793\pi\) |
0.133991 | + | 0.990983i | \(0.457221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.52056i | − | 0.774772i | −0.921918 | − | 0.387386i | \(-0.873378\pi\) | ||
0.921918 | − | 0.387386i | \(-0.126622\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.53590i | 0.690086i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.79796 | + | 9.79796i | 0.786991 | + | 0.786991i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.19615 | − | 7.19615i | 0.574315 | − | 0.574315i | −0.359016 | − | 0.933331i | \(-0.616888\pi\) |
0.933331 | + | 0.359016i | \(0.116888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.00481 | 0.634823 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.8313 | + | 11.8313i | −0.926703 | + | 0.926703i | −0.997491 | − | 0.0707887i | \(-0.977448\pi\) |
0.0707887 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | − | 6.00000i | −0.467099 | − | 0.467099i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7637i | 1.45198i | 0.687705 | + | 0.725990i | \(0.258618\pi\) | ||||
−0.687705 | + | 0.725990i | \(0.741382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8564i | 0.988954i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.24504 | − | 8.24504i | −0.630514 | − | 0.630514i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.73205 | + | 7.73205i | −0.587857 | + | 0.587857i | −0.937051 | − | 0.349194i | \(-0.886456\pi\) |
0.349194 | + | 0.937051i | \(0.386456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.86370 | 0.292069 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.32051 | 0.399914 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.55291 | − | 1.55291i | 0.116070 | − | 0.116070i | −0.646686 | − | 0.762756i | \(-0.723846\pi\) |
0.762756 | + | 0.646686i | \(0.223846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.1244 | − | 16.1244i | −1.19851 | − | 1.19851i | −0.974612 | − | 0.223902i | \(-0.928120\pi\) |
−0.223902 | − | 0.974612i | \(-0.571880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.86370i | − | 0.285613i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.9282i | − | 0.950500i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.5911 | + | 11.5911i | 0.847626 | + | 0.847626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.9282 | + | 10.9282i | −0.794910 | + | 0.794910i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.3923 | −1.32391 | −0.661954 | − | 0.749545i | \(-0.730272\pi\) | ||||
−0.661954 | + | 0.749545i | \(0.730272\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.480473 | + | 0.480473i | −0.0344074 | + | 0.0344074i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.73205 | + | 1.73205i | 0.123404 | + | 0.123404i | 0.766111 | − | 0.642708i | \(-0.222189\pi\) |
−0.642708 | + | 0.766111i | \(0.722189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7322i | 1.11523i | 0.830101 | + | 0.557614i | \(0.188283\pi\) | ||||
−0.830101 | + | 0.557614i | \(0.811717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.53590i | 0.319938i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.69213 | − | 6.69213i | −0.469695 | − | 0.469695i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | − | 12.0000i | 0.838116 | − | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.41851 | −0.307107 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.3923 | −1.54891 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.20977 | − | 7.20977i | 0.496341 | − | 0.496341i | −0.413956 | − | 0.910297i | \(-0.635853\pi\) |
0.910297 | + | 0.413956i | \(0.135853\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.928203 | − | 0.928203i | −0.0635994 | − | 0.0635994i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 5.37945i | − | 0.366876i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 21.8564i | − | 1.48371i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.31268 | − | 1.31268i | −0.0887025 | − | 0.0887025i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.928203 | − | 0.928203i | 0.0624377 | − | 0.0624377i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65685 | 0.378811 | 0.189405 | − | 0.981899i | \(-0.439344\pi\) | ||||
0.189405 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.9372 | − | 14.9372i | 0.991415 | − | 0.991415i | −0.00854833 | − | 0.999963i | \(-0.502721\pi\) |
0.999963 | + | 0.00854833i | \(0.00272105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.19615 | − | 9.19615i | −0.607699 | − | 0.607699i | 0.334645 | − | 0.942344i | \(-0.391383\pi\) |
−0.942344 | + | 0.334645i | \(0.891383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.3843i | 0.880620i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.53590i | 0.166132i | 0.996544 | + | 0.0830661i | \(0.0264713\pi\) | ||||
−0.996544 | + | 0.0830661i | \(0.973529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.9706 | − | 16.9706i | −1.10704 | − | 1.10704i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.14359 | + | 2.14359i | −0.139241 | + | 0.139241i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.7685 | 1.73151 | 0.865756 | − | 0.500467i | \(-0.166838\pi\) | ||||
0.865756 | + | 0.500467i | \(0.166838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.39230 | −0.154102 | −0.0770510 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770510 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7961 | − | 10.7961i | 0.692568 | − | 0.692568i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.7321 | − | 13.7321i | −0.877309 | − | 0.877309i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.79315i | 0.114095i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.60770i | 0.101884i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9372 | − | 14.9372i | −0.942826 | − | 0.942826i | 0.0556256 | − | 0.998452i | \(-0.482285\pi\) |
−0.998452 | + | 0.0556256i | \(0.982285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | + | 6.00000i | −0.377217 | + | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.21166 | −0.388989 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9282 | 0.806439 | 0.403220 | − | 0.915103i | \(-0.367891\pi\) | ||||
0.403220 | + | 0.915103i | \(0.367891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4195 | + | 14.4195i | −0.895986 | + | 0.895986i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.26795 | + | 4.26795i | 0.264179 | + | 0.264179i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.3891i | 1.31891i | 0.751746 | + | 0.659453i | \(0.229212\pi\) | ||||
−0.751746 | + | 0.659453i | \(0.770788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 26.7846i | − | 1.64537i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.31268 | + | 1.31268i | 0.0803346 | + | 0.0803346i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.19615 | + | 5.19615i | −0.316815 | + | 0.316815i | −0.847543 | − | 0.530728i | \(-0.821919\pi\) |
0.530728 | + | 0.847543i | \(0.321919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.51575 | 0.0920752 | 0.0460376 | − | 0.998940i | \(-0.485341\pi\) | ||||
0.0460376 | + | 0.998940i | \(0.485341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.07180 | 0.0648681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.34607 | + | 3.34607i | −0.201775 | + | 0.201775i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.19615 | + | 3.19615i | 0.192038 | + | 0.192038i | 0.796576 | − | 0.604538i | \(-0.206642\pi\) |
−0.604538 | + | 0.796576i | \(0.706642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.9391i | 0.834510i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3923i | 0.977883i | 0.872317 | + | 0.488941i | \(0.162617\pi\) | ||||
−0.872317 | + | 0.488941i | \(0.837383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.27551 | + | 1.27551i | 0.0758214 | + | 0.0758214i | 0.744000 | − | 0.668179i | \(-0.232926\pi\) |
−0.668179 | + | 0.744000i | \(0.732926\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00000 | − | 6.00000i | 0.355409 | − | 0.355409i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.7685 | −1.58010 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.79315 | + | 1.79315i | −0.105116 | + | 0.105116i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.1244 | − | 12.1244i | −0.708312 | − | 0.708312i | 0.257868 | − | 0.966180i | \(-0.416980\pi\) |
−0.966180 | + | 0.257868i | \(0.916980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 17.8028i | − | 1.03652i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 18.9282i | − | 1.09833i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.480473 | + | 0.480473i | 0.0277865 | + | 0.0277865i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | + | 6.00000i | −0.345834 | + | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.832204 | 0.0478089 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.9282 | −0.740267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.9067 | − | 21.9067i | 1.25028 | − | 1.25028i | 0.294688 | − | 0.955593i | \(-0.404784\pi\) |
0.955593 | − | 0.294688i | \(-0.0952159\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.92820 | + | 4.92820i | 0.280356 | + | 0.280356i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.1774i | − | 0.860632i | −0.902678 | − | 0.430316i | \(-0.858402\pi\) | ||
0.902678 | − | 0.430316i | \(-0.141598\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7846i | 0.722629i | 0.932444 | + | 0.361314i | \(0.117672\pi\) | ||||
−0.932444 | + | 0.361314i | \(0.882328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.4901 | + | 16.4901i | 0.929111 | + | 0.929111i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.80385 | − | 6.80385i | 0.382142 | − | 0.382142i | −0.489731 | − | 0.871873i | \(-0.662905\pi\) |
0.871873 | + | 0.489731i | \(0.162905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5911 | 0.648978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.6077 | −0.759507 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.5911 | + | 11.5911i | −0.644947 | + | 0.644947i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.267949 | + | 0.267949i | 0.0148631 | + | 0.0148631i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 13.6617i | − | 0.755492i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 37.8564i | 2.08709i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.8009 | + | 18.8009i | 1.03339 | + | 1.03339i | 0.999423 | + | 0.0339668i | \(0.0108140\pi\) |
0.0339668 | + | 0.999423i | \(0.489186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.19615 | − | 9.19615i | 0.503946 | − | 0.503946i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.1774 | 0.829231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7128 | 1.18277 | 0.591386 | − | 0.806389i | \(-0.298581\pi\) | ||||
0.591386 | + | 0.806389i | \(0.298581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.69213 | + | 6.69213i | −0.363467 | + | 0.363467i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.9282 | + | 18.9282i | 1.02502 | + | 1.02502i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.58630i | 0.193642i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 3.21539i | − | 0.173111i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.13922 | − | 5.13922i | −0.275888 | − | 0.275888i | 0.555577 | − | 0.831465i | \(-0.312497\pi\) |
−0.831465 | + | 0.555577i | \(0.812497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.12436 | + | 4.12436i | −0.220772 | + | 0.220772i | −0.808823 | − | 0.588052i | \(-0.799895\pi\) |
0.588052 | + | 0.808823i | \(0.299895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.51575 | −0.0809047 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.928203 | −0.0494033 | −0.0247016 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247016 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.10583 | + | 3.10583i | −0.164840 | + | 0.164840i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.92820 | + | 6.92820i | 0.366679 | + | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.8028i | − | 0.939594i | −0.882774 | − | 0.469797i | \(-0.844327\pi\) | ||
0.882774 | − | 0.469797i | \(-0.155673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 3.39230i | − | 0.178542i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.89709 | − | 5.89709i | −0.309517 | − | 0.309517i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.39230 | + | 4.39230i | −0.229904 | + | 0.229904i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.4254 | −1.69259 | −0.846295 | − | 0.532714i | \(-0.821172\pi\) | ||||
−0.846295 | + | 0.532714i | \(0.821172\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.0718 | 0.888722 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.8744 | + | 29.8744i | −1.55100 | + | 1.55100i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.1244 | + | 14.1244i | 0.731331 | + | 0.731331i | 0.970884 | − | 0.239552i | \(-0.0770006\pi\) |
−0.239552 | + | 0.970884i | \(0.577001\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.17260i | 0.370392i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.928203i | − | 0.0478049i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.03339 | + | 2.03339i | 0.104448 | + | 0.104448i | 0.757400 | − | 0.652952i | \(-0.226469\pi\) |
−0.652952 | + | 0.757400i | \(0.726469\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.92820 | − | 2.92820i | 0.150016 | − | 0.150016i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.5959 | 1.00130 | 0.500652 | − | 0.865648i | \(-0.333094\pi\) | ||||
0.500652 | + | 0.865648i | \(0.333094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 44.7846 | 2.28244 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.82654 | − | 3.82654i | 0.194514 | − | 0.194514i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.26795 | + | 4.26795i | 0.216394 | + | 0.216394i | 0.806977 | − | 0.590583i | \(-0.201102\pi\) |
−0.590583 | + | 0.806977i | \(0.701102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.21166i | 0.314137i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.248711i | 0.0125458i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.17260 | + | 7.17260i | 0.360893 | + | 0.360893i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5885 | − | 19.5885i | 0.983116 | − | 0.983116i | −0.0167433 | − | 0.999860i | \(-0.505330\pi\) |
0.999860 | + | 0.0167433i | \(0.00532982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.3843 | −0.670051 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6077 | 0.679536 | 0.339768 | − | 0.940509i | \(-0.389651\pi\) | ||||
0.339768 | + | 0.940509i | \(0.389651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51575 | − | 1.51575i | 0.0755049 | − | 0.0755049i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.73205 | − | 7.73205i | −0.384209 | − | 0.384209i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 24.9754i | − | 1.23798i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0718i | 0.844146i | 0.906562 | + | 0.422073i | \(0.138697\pi\) | ||||
−0.906562 | + | 0.422073i | \(0.861303\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.21166 | + | 6.21166i | 0.306398 | + | 0.306398i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.8564 | + | 19.8564i | −0.977070 | + | 0.977070i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.37945 | 0.264067 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.46410 | 0.365519 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0382 | − | 10.0382i | 0.490398 | − | 0.490398i | −0.418034 | − | 0.908432i | \(-0.637281\pi\) |
0.908432 | + | 0.418034i | \(0.137281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5167 | + | 18.5167i | 0.902447 | + | 0.902447i | 0.995647 | − | 0.0932005i | \(-0.0297098\pi\) |
−0.0932005 | + | 0.995647i | \(0.529710\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 24.1432i | − | 1.17388i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410i | 0.168034i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4195 | + | 14.4195i | 0.697810 | + | 0.697810i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.928203 | + | 0.928203i | −0.0448141 | + | 0.0448141i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.7685 | 1.28939 | 0.644697 | − | 0.764438i | \(-0.276983\pi\) | ||||
0.644697 | + | 0.764438i | \(0.276983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.3923 | −1.65279 | −0.826394 | − | 0.563092i | \(-0.809612\pi\) | ||||
−0.826394 | + | 0.563092i | \(0.809612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.10583 | + | 3.10583i | −0.148913 | + | 0.148913i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.00000 | − | 6.00000i | −0.287019 | − | 0.287019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 12.1459i | − | 0.579693i | −0.957073 | − | 0.289846i | \(-0.906396\pi\) | ||
0.957073 | − | 0.289846i | \(-0.0936042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 19.5359i | − | 0.930281i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0382 | − | 10.0382i | −0.476929 | − | 0.476929i | 0.427219 | − | 0.904148i | \(-0.359493\pi\) |
−0.904148 | + | 0.427219i | \(0.859493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.39230 | − | 4.39230i | 0.208215 | − | 0.208215i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.2165 | −0.672416 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.2487 | −1.14437 | −0.572184 | − | 0.820125i | \(-0.693904\pi\) | ||||
−0.572184 | + | 0.820125i | \(0.693904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.1822 | − | 23.1822i | 1.09161 | − | 1.09161i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.92820 | + | 4.92820i | 0.231547 | + | 0.231547i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.58630i | − | 0.168128i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7846i | 0.972263i | 0.873886 | + | 0.486132i | \(0.161592\pi\) | ||||
−0.873886 | + | 0.486132i | \(0.838408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.79796 | − | 9.79796i | −0.457330 | − | 0.457330i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.1244 | + | 24.1244i | −1.12358 | + | 1.12358i | −0.132385 | + | 0.991198i | \(0.542263\pi\) |
−0.991198 | + | 0.132385i | \(0.957737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.0822 | −1.76983 | −0.884916 | − | 0.465751i | \(-0.845784\pi\) | ||||
−0.884916 | + | 0.465751i | \(0.845784\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.1436 | −0.470398 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.3166 | + | 20.3166i | −0.940141 | + | 0.940141i | −0.998307 | − | 0.0581655i | \(-0.981475\pi\) |
0.0581655 | + | 0.998307i | \(0.481475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.9282 | − | 16.9282i | −0.781672 | − | 0.781672i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.45001i | 0.343278i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.3923i | − | 0.477839i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.34607 | − | 3.34607i | −0.153528 | − | 0.153528i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.0526 | − | 19.0526i | 0.872357 | − | 0.872357i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.5665 | 1.67077 | 0.835383 | − | 0.549669i | \(-0.185246\pi\) | ||||
0.835383 | + | 0.549669i | \(0.185246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.58630 | + | 3.58630i | −0.163182 | + | 0.163182i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | + | 6.00000i | 0.272446 | + | 0.272446i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.0459i | 1.22557i | 0.790251 | + | 0.612784i | \(0.209950\pi\) | ||||
−0.790251 | + | 0.612784i | \(0.790050\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.2487i | − | 0.553906i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.4176 | + | 15.4176i | 0.695789 | + | 0.695789i | 0.963499 | − | 0.267711i | \(-0.0862671\pi\) |
−0.267711 | + | 0.963499i | \(0.586267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | − | 6.00000i | 0.270226 | − | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.5617 | −1.28375 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.92820 | 0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.10394 | + | 4.10394i | −0.183718 | + | 0.183718i | −0.792974 | − | 0.609256i | \(-0.791468\pi\) |
0.609256 | + | 0.792974i | \(0.291468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.71281 | − | 9.71281i | −0.433936 | − | 0.433936i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.9850i | 1.82743i | 0.406355 | + | 0.913715i | \(0.366800\pi\) | ||||
−0.406355 | + | 0.913715i | \(0.633200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.78461i | − | 0.123914i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.65497 | − | 6.65497i | −0.295557 | − | 0.295557i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.58846 | + | 9.58846i | −0.425001 | + | 0.425001i | −0.886921 | − | 0.461920i | \(-0.847161\pi\) |
0.461920 | + | 0.886921i | \(0.347161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | 0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9282 | 0.835701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.4901 | − | 16.4901i | 0.726640 | − | 0.726640i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.7846 | − | 32.7846i | −1.44187 | − | 1.44187i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.00481i | − | 0.351372i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.0000i | − | 0.525730i | −0.964833 | − | 0.262865i | \(-0.915333\pi\) | ||
0.964833 | − | 0.262865i | \(-0.0846673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6245 | − | 13.6245i | −0.595758 | − | 0.595758i | 0.343423 | − | 0.939181i | \(-0.388414\pi\) |
−0.939181 | + | 0.343423i | \(0.888414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00000 | + | 2.00000i | −0.0872872 | + | 0.0872872i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.5959 | 0.853612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.7846 | 0.860200 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6636 | − | 12.6636i | 0.549551 | − | 0.549551i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.85641 | − | 1.85641i | −0.0804099 | − | 0.0804099i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45.5322i | 1.96853i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.60770i | 0.0693772i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.5283 | − | 26.5283i | −1.14265 | − | 1.14265i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.1244 | − | 10.1244i | 0.435280 | − | 0.435280i | −0.455140 | − | 0.890420i | \(-0.650411\pi\) |
0.890420 | + | 0.455140i | \(0.150411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.6932 | 0.716372 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −45.7128 | −1.95812 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.240237 | − | 0.240237i | 0.0102718 | − | 0.0102718i | −0.701952 | − | 0.712224i | \(-0.747688\pi\) |
0.712224 | + | 0.701952i | \(0.247688\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.19615 | − | 9.19615i | −0.392482 | − | 0.392482i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5911i | 0.493798i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 16.0000i | − | 0.680389i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.69213 | + | 6.69213i | 0.284065 | + | 0.284065i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1962 | − | 11.1962i | 0.474396 | − | 0.474396i | −0.428938 | − | 0.903334i | \(-0.641112\pi\) |
0.903334 | + | 0.428938i | \(0.141112\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.832204 | −0.0351985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.5187 | + | 10.5187i | −0.443309 | + | 0.443309i | −0.893123 | − | 0.449813i | \(-0.851490\pi\) |
0.449813 | + | 0.893123i | \(0.351490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.3923 | + | 22.3923i | 0.942051 | + | 0.942051i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.2480i | 0.724346i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000i | 0.503066i | 0.967849 | + | 0.251533i | \(0.0809347\pi\) | ||||
−0.967849 | + | 0.251533i | \(0.919065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.3519 | − | 21.3519i | −0.893549 | − | 0.893549i | 0.101306 | − | 0.994855i | \(-0.467698\pi\) |
−0.994855 | + | 0.101306i | \(0.967698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.78461 | − | 8.78461i | 0.366982 | − | 0.366982i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.79315 | −0.0747796 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.8564 | −1.82577 | −0.912883 | − | 0.408221i | \(-0.866149\pi\) | ||||
−0.912883 | + | 0.408221i | \(0.866149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.52056 | − | 9.52056i | 0.395661 | − | 0.395661i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | − | 6.00000i | −0.248922 | − | 0.248922i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 51.7439i | − | 2.14301i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.28719i | 0.0945635i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.45189 | − | 6.45189i | −0.266298 | − | 0.266298i | 0.561308 | − | 0.827607i | \(-0.310298\pi\) |
−0.827607 | + | 0.561308i | \(0.810298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.9282 | + | 18.9282i | −0.779923 | + | 0.779923i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.79315 | −0.0737604 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.8564 | −0.815405 | −0.407702 | − | 0.913115i | \(-0.633670\pi\) | ||||
−0.407702 | + | 0.913115i | \(0.633670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.1822 | − | 23.1822i | 0.950378 | − | 0.950378i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.14359 | − | 8.14359i | −0.333295 | − | 0.333295i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.41851i | 0.180535i | 0.995918 | + | 0.0902676i | \(0.0287722\pi\) | ||||
−0.995918 | + | 0.0902676i | \(0.971228\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 40.3923i | − | 1.64764i | −0.566854 | − | 0.823818i | \(-0.691840\pi\) | ||
0.566854 | − | 0.823818i | \(-0.308160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.7961 | + | 10.7961i | 0.439650 | + | 0.439650i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.7321 | + | 19.7321i | −0.802222 | + | 0.802222i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.28221 | −0.336165 | −0.168082 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168082 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.92820 | 0.280745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.62536 | + | 2.62536i | −0.106211 | + | 0.106211i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0526 | − | 15.0526i | −0.607967 | − | 0.607967i | 0.334447 | − | 0.942414i | \(-0.391450\pi\) |
−0.942414 | + | 0.334447i | \(0.891450\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.4233i | 0.500956i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.3205i | 0.455746i | 0.973691 | + | 0.227873i | \(0.0731772\pi\) | ||||
−0.973691 | + | 0.227873i | \(0.926823\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.8009 | + | 18.8009i | 0.755671 | + | 0.755671i | 0.975531 | − | 0.219860i | \(-0.0705601\pi\) |
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.07180 | − | 5.07180i | 0.203524 | − | 0.203524i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.79796 | −0.392547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.0000 | 1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.5911 | − | 11.5911i | 0.462904 | − | 0.462904i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.9282 | − | 12.9282i | −0.515481 | − | 0.515481i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.23835i | − | 0.0492979i | −0.999696 | − | 0.0246489i | \(-0.992153\pi\) | ||
0.999696 | − | 0.0246489i | \(-0.00784679\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.46410i | 0.296671i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.79796 | − | 9.79796i | −0.388820 | − | 0.388820i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.12436 | + | 2.12436i | −0.0841700 | + | 0.0841700i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.41851 | −0.174793 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6077 | 0.537472 | 0.268736 | − | 0.963214i | \(-0.413394\pi\) | ||||
0.268736 | + | 0.963214i | \(0.413394\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.93237 | + | 6.93237i | −0.273386 | + | 0.273386i | −0.830462 | − | 0.557076i | \(-0.811923\pi\) |
0.557076 | + | 0.830462i | \(0.311923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.78461 | + | 2.78461i | 0.109644 | + | 0.109644i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.79315i | 0.0704960i | 0.999379 | + | 0.0352480i | \(0.0112221\pi\) | ||||
−0.999379 | + | 0.0352480i | \(0.988778\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 34.3923i | − | 1.35002i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3137 | + | 11.3137i | 0.443419 | + | 0.443419i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.3397 | + | 15.3397i | −0.600291 | + | 0.600291i | −0.940390 | − | 0.340099i | \(-0.889539\pi\) |
0.340099 | + | 0.940390i | \(0.389539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.832204 | 0.0325169 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.24871 | −0.243785 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0430 | + | 18.0430i | −0.702856 | + | 0.702856i | −0.965023 | − | 0.262167i | \(-0.915563\pi\) |
0.262167 | + | 0.965023i | \(0.415563\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.2679 | − | 18.2679i | −0.710541 | − | 0.710541i | 0.256107 | − | 0.966648i | \(-0.417560\pi\) |
−0.966648 | + | 0.256107i | \(0.917560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.960947i | 0.0373201i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 44.7846i | 1.73667i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.10583 | + | 3.10583i | 0.120258 | + | 0.120258i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.92820 | + | 2.92820i | −0.113211 | + | 0.113211i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.9754 | −0.964163 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.3205 | 1.59279 | 0.796394 | − | 0.604778i | \(-0.206738\pi\) | ||||
0.796394 | + | 0.604778i | \(0.206738\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.82843 | − | 2.82843i | 0.108866 | − | 0.108866i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.2679 | + | 28.2679i | 1.08643 | + | 1.08643i | 0.995894 | + | 0.0905320i | \(0.0288567\pi\) |
0.0905320 | + | 0.995894i | \(0.471143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.3843i | − | 0.513641i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.4641i | 0.592586i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.72552 | − | 8.72552i | −0.333873 | − | 0.333873i | 0.520182 | − | 0.854055i | \(-0.325864\pi\) |
−0.854055 | + | 0.520182i | \(0.825864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7846 | − | 20.7846i | 0.794139 | − | 0.794139i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.52056 | 0.363232 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.14359 | −0.157858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.8410 | + | 27.8410i | −1.05912 | + | 1.05912i | −0.0609812 | + | 0.998139i | \(0.519423\pi\) |
−0.998139 | + | 0.0609812i | \(0.980577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31.8564 | + | 31.8564i | 1.21012 | + | 1.21012i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 24.9754i | − | 0.947370i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 24.0000i | − | 0.909065i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.31268 | − | 1.31268i | −0.0496500 | − | 0.0496500i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.33975 | − | 9.33975i | 0.352757 | − | 0.352757i | −0.508377 | − | 0.861135i | \(-0.669754\pi\) |
0.861135 | + | 0.508377i | \(0.169754\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9754 | 0.941964 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.5692 | 0.661695 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.10583 | + | 3.10583i | −0.116807 | + | 0.116807i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.0526 | + | 29.0526i | 1.09109 | + | 1.09109i | 0.995412 | + | 0.0956796i | \(0.0305024\pi\) |
0.0956796 | + | 0.995412i | \(0.469498\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.2041i | 0.382684i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1436i | 0.379881i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.10583 | + | 3.10583i | 0.116151 | + | 0.116151i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.8564 | + | 13.8564i | −0.517477 | + | 0.517477i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.4233 | 0.463311 | 0.231656 | − | 0.972798i | \(-0.425586\pi\) | ||||
0.231656 | + | 0.972798i | \(0.425586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.7846 | −1.36993 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.23835 | − | 1.23835i | 0.0460547 | − | 0.0460547i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.73205 | + | 1.73205i | 0.0643268 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.4596i | − | 0.870069i | −0.900414 | − | 0.435035i | \(-0.856736\pi\) | ||
0.900414 | − | 0.435035i | \(-0.143264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 2.21539i | − | 0.0820515i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.37945 | − | 5.37945i | −0.198966 | − | 0.198966i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8038 | − | 14.8038i | 0.546793 | − | 0.546793i | −0.378719 | − | 0.925512i | \(-0.623635\pi\) |
0.925512 | + | 0.378719i | \(0.123635\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.2165 | 0.524382 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.3205 | 1.08003 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.10772 | − | 2.10772i | 0.0775336 | − | 0.0775336i | −0.667276 | − | 0.744810i | \(-0.732540\pi\) |
0.744810 | + | 0.667276i | \(0.232540\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.928203 | − | 0.928203i | −0.0340984 | − | 0.0340984i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 15.1774i | − | 0.556805i | −0.960464 | − | 0.278403i | \(-0.910195\pi\) | ||
0.960464 | − | 0.278403i | \(-0.0898050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.5692i | 1.74280i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.82654 | + | 3.82654i | 0.140006 | + | 0.140006i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.7846 | − | 50.7846i | 1.85563 | − | 1.85563i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.14110 | −0.151111 | −0.0755555 | − | 0.997142i | \(-0.524073\pi\) | ||||
−0.0755555 | + | 0.997142i | \(0.524073\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.4641 | 0.563543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.4901 | − | 16.4901i | 0.600136 | − | 0.600136i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.7321 | + | 21.7321i | 0.789865 | + | 0.789865i | 0.981472 | − | 0.191607i | \(-0.0613699\pi\) |
−0.191607 | + | 0.981472i | \(0.561370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 6.21166i | − | 0.225469i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6410i | 1.25574i | 0.778320 | + | 0.627868i | \(0.216072\pi\) | ||||
−0.778320 | + | 0.627868i | \(0.783928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.9860 | + | 50.9860i | 1.84582 | + | 1.84582i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.7846 | + | 14.7846i | −0.534539 | + | 0.534539i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.75410 | −0.0994447 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.39230 | −0.0862687 | −0.0431344 | − | 0.999069i | \(-0.513734\pi\) | ||||
−0.0431344 | + | 0.999069i | \(0.513734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.69213 | + | 6.69213i | −0.241011 | + | 0.241011i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.6603 | − | 14.6603i | −0.527293 | − | 0.527293i | 0.392471 | − | 0.919764i | \(-0.371620\pi\) |
−0.919764 | + | 0.392471i | \(0.871620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685i | 0.203200i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 14.9282i | − | 0.535546i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.1822 | + | 23.1822i | 0.830589 | + | 0.830589i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | + | 6.00000i | −0.214697 | + | 0.214697i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.79796 | −0.350150 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.9282 | 0.889726 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.2156 | + | 25.2156i | −0.898839 | + | 0.898839i | −0.995334 | − | 0.0964942i | \(-0.969237\pi\) |
0.0964942 | + | 0.995334i | \(0.469237\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0718 | − | 11.0718i | −0.394166 | − | 0.394166i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 49.9507i | − | 1.77604i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000i | 0.0710221i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.8647 | + | 13.8647i | 0.491731 | + | 0.491731i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.5885 | + | 33.5885i | −1.18976 | + | 1.18976i | −0.212632 | + | 0.977132i | \(0.568203\pi\) |
−0.977132 | + | 0.212632i | \(0.931797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.9411 | −1.20075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.24871 | 0.220787 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.48528 | + | 8.48528i | −0.299439 | + | 0.299439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | + | 12.0000i | 0.422944 | + | 0.422944i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 5.37945i | − | 0.189366i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.0718i | − | 0.600212i | −0.953906 | − | 0.300106i | \(-0.902978\pi\) | ||
0.953906 | − | 0.300106i | \(-0.0970221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.2204 | − | 33.2204i | −1.16653 | − | 1.16653i | −0.983018 | − | 0.183508i | \(-0.941255\pi\) |
−0.183508 | − | 0.983018i | \(-0.558745\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.784610 | + | 0.784610i | −0.0275175 | + | 0.0275175i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.9850 | −1.43564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3923 | 0.363581 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.55103 | − | 2.55103i | 0.0891401 | − | 0.0891401i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.9808 | + | 19.9808i | 0.697333 | + | 0.697333i | 0.963835 | − | 0.266501i | \(-0.0858676\pi\) |
−0.266501 | + | 0.963835i | \(0.585868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.7322i | 0.548391i | 0.961674 | + | 0.274195i | \(0.0884115\pi\) | ||||
−0.961674 | + | 0.274195i | \(0.911589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.46410i | − | 0.120605i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.7303 | + | 16.7303i | 0.581770 | + | 0.581770i | 0.935390 | − | 0.353619i | \(-0.115049\pi\) |
−0.353619 | + | 0.935390i | \(0.615049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.12436 | − | 2.12436i | 0.0737819 | − | 0.0737819i | −0.669253 | − | 0.743035i | \(-0.733386\pi\) |
0.743035 | + | 0.669253i | \(0.233386\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.30890 | −0.114784 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.4641 | −0.951575 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.4997 | + | 32.4997i | −1.12470 | + | 1.12470i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | − | 16.0000i | −0.553041 | − | 0.553041i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.3596i | 1.32432i | 0.749362 | + | 0.662161i | \(0.230360\pi\) | ||||
−0.749362 | + | 0.662161i | \(0.769640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000i | 0.793103i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.48528 | − | 8.48528i | −0.292249 | − | 0.292249i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.2679 | + | 22.2679i | −0.766041 | + | 0.766041i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.0165 | 1.51242 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.32051 | −0.0453197 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.69213 | − | 6.69213i | 0.229403 | − | 0.229403i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.87564 | − | 9.87564i | −0.338136 | − | 0.338136i | 0.517530 | − | 0.855665i | \(-0.326852\pi\) |
−0.855665 | + | 0.517530i | \(0.826852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 28.5617i | − | 0.976789i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 25.8564i | − | 0.883238i | −0.897203 | − | 0.441619i | \(-0.854404\pi\) | ||
0.897203 | − | 0.441619i | \(-0.145596\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4567 | + | 14.4567i | 0.493256 | + | 0.493256i | 0.909331 | − | 0.416074i | \(-0.136594\pi\) |
−0.416074 | + | 0.909331i | \(0.636594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.8564 | − | 13.8564i | 0.472225 | − | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.62536 | −0.0893681 | −0.0446841 | − | 0.999001i | \(-0.514228\pi\) | ||||
−0.0446841 | + | 0.999001i | \(0.514228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.7846 | −0.910704 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.58819 | − | 2.58819i | 0.0878996 | − | 0.0878996i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.8564 | + | 13.8564i | 0.470046 | + | 0.470046i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.34795i | − | 0.0795574i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.53590i | 0.288896i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.7685 | − | 26.7685i | −0.904941 | − | 0.904941i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1244 | + | 16.1244i | −0.544481 | + | 0.544481i | −0.924839 | − | 0.380358i | \(-0.875801\pi\) |
0.380358 | + | 0.924839i | \(0.375801\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.5521 | 0.423370 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.8564 | 1.07327 | 0.536635 | − | 0.843815i | \(-0.319695\pi\) | ||||
0.536635 | + | 0.843815i | \(0.319695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.3930 | − | 40.3930i | 1.35933 | − | 1.35933i | 0.484594 | − | 0.874739i | \(-0.338967\pi\) |
0.874739 | − | 0.484594i | \(-0.161033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.21539 | + | 9.21539i | 0.309772 | + | 0.309772i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 15.1774i | − | 0.509608i | −0.966993 | − | 0.254804i | \(-0.917989\pi\) | ||
0.966993 | − | 0.254804i | \(-0.0820109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.8564i | 0.733040i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.9372 | − | 14.9372i | −0.500414 | − | 0.500414i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.7846 | − | 32.7846i | 1.09710 | − | 1.09710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.37945 | 0.179815 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.497423 | −0.0166085 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.79796 | − | 9.79796i | 0.326780 | − | 0.326780i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.7846 | − | 26.7846i | −0.892325 | − | 0.892325i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6.21166i | − | 0.206711i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 55.8564i | − | 1.85673i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.1488 | − | 21.1488i | −0.702235 | − | 0.702235i | 0.262655 | − | 0.964890i | \(-0.415402\pi\) |
−0.964890 | + | 0.262655i | \(0.915402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.98076 | − | 1.98076i | 0.0656977 | − | 0.0656977i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.1432 | 0.799899 | 0.399949 | − | 0.916537i | \(-0.369028\pi\) | ||||
0.399949 | + | 0.916537i | \(0.369028\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.3923 | 0.343935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.69213 | − | 6.69213i | 0.221235 | − | 0.221235i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.928203 | − | 0.928203i | −0.0306520 | − | 0.0306520i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.3576i | 0.605560i | 0.953060 | + | 0.302780i | \(0.0979148\pi\) | ||||
−0.953060 | + | 0.302780i | \(0.902085\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.6795i | 0.747315i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.480473 | + | 0.480473i | 0.0158150 | + | 0.0158150i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.73205 | − | 3.73205i | 0.122709 | − | 0.122709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.4596 | 0.770515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.46410 | 0.113653 | 0.0568267 | − | 0.998384i | \(-0.481902\pi\) | ||||
0.0568267 | + | 0.998384i | \(0.481902\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.5283 | − | 26.5283i | 0.869429 | − | 0.869429i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.85641 | + | 7.85641i | 0.257207 | + | 0.257207i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.1528i | 1.31314i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9.17691i | − | 0.299797i | −0.988701 | − | 0.149898i | \(-0.952105\pi\) | ||
0.988701 | − | 0.149898i | \(-0.0478946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.61780 | − | 6.61780i | −0.215964 | − | 0.215964i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8038 | − | 18.8038i | 0.612988 | − | 0.612988i | −0.330736 | − | 0.943723i | \(-0.607297\pi\) |
0.943723 | + | 0.330736i | \(0.107297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.4233 | 0.404559 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −37.8564 | −1.23147 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.6245 | − | 13.6245i | 0.442737 | − | 0.442737i | −0.450194 | − | 0.892931i | \(-0.648645\pi\) |
0.892931 | + | 0.450194i | \(0.148645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.679492 | + | 0.679492i | 0.0220572 | + | 0.0220572i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.04386i | 0.228413i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 53.5692i | − | 1.73528i | −0.497195 | − | 0.867639i | \(-0.665637\pi\) | ||
0.497195 | − | 0.867639i | \(-0.334363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.3939 | − | 29.3939i | −0.951164 | − | 0.951164i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.00000 | + | 6.00000i | −0.193952 | + | 0.193952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.3644 | −1.49719 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.3882 | + | 32.3882i | −1.04370 | + | 1.04370i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.8564 | − | 31.8564i | −1.02549 | − | 1.02549i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.0459i | 0.869738i | 0.900494 | + | 0.434869i | \(0.143205\pi\) | ||||
−0.900494 | + | 0.434869i | \(0.856795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 12.0000i | − | 0.385496i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.8410 | + | 27.8410i | 0.893459 | + | 0.893459i | 0.994847 | − | 0.101388i | \(-0.0323283\pi\) |
−0.101388 | + | 0.994847i | \(0.532328\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.8564 | + | 27.8564i | −0.893035 | + | 0.893035i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.277401 | −0.00888396 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.5359 | −1.42483 | −0.712415 | − | 0.701759i | \(-0.752399\pi\) | ||||
−0.712415 | + | 0.701759i | \(0.752399\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.48528 | − | 8.48528i | 0.271191 | − | 0.271191i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.5167 | − | 32.5167i | −1.03818 | − | 1.03818i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.7048i | 1.68102i | 0.541793 | + | 0.840512i | \(0.317745\pi\) | ||||
−0.541793 | + | 0.840512i | \(0.682255\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000i | 0.191176i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.5959 | − | 19.5959i | −0.623745 | − | 0.623745i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.78461 | − | 2.78461i | 0.0885454 | − | 0.0885454i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.8193 | −1.96375 | −0.981877 | − | 0.189521i | \(-0.939306\pi\) | ||||
−0.981877 | + | 0.189521i | \(0.939306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.4641 | −0.617675 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.2490 | + | 27.2490i | −0.863851 | + | 0.863851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.1962 | + | 15.1962i | 0.481267 | + | 0.481267i | 0.905536 | − | 0.424269i | \(-0.139469\pi\) |
−0.424269 | + | 0.905536i | \(0.639469\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.1117i | 0.667944i |
(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 | 256.2.e.b.193.2 | yes | 8 | |
3.2 | odd | 2 | 2304.2.k.k.1729.1 | 8 | |||
4.3 | odd | 2 | inner | 256.2.e.b.193.3 | yes | 8 | |
8.3 | odd | 2 | 256.2.e.a.193.2 | yes | 8 | ||
8.5 | even | 2 | 256.2.e.a.193.3 | yes | 8 | ||
12.11 | even | 2 | 2304.2.k.k.1729.2 | 8 | |||
16.3 | odd | 4 | inner | 256.2.e.b.65.3 | yes | 8 | |
16.5 | even | 4 | 256.2.e.a.65.3 | yes | 8 | ||
16.11 | odd | 4 | 256.2.e.a.65.2 | ✓ | 8 | ||
16.13 | even | 4 | inner | 256.2.e.b.65.2 | yes | 8 | |
24.5 | odd | 2 | 2304.2.k.f.1729.3 | 8 | |||
24.11 | even | 2 | 2304.2.k.f.1729.4 | 8 | |||
32.3 | odd | 8 | 1024.2.a.g.1.3 | 4 | |||
32.5 | even | 8 | 1024.2.b.h.513.4 | 8 | |||
32.11 | odd | 8 | 1024.2.b.h.513.3 | 8 | |||
32.13 | even | 8 | 1024.2.a.g.1.4 | 4 | |||
32.19 | odd | 8 | 1024.2.a.j.1.2 | 4 | |||
32.21 | even | 8 | 1024.2.b.h.513.5 | 8 | |||
32.27 | odd | 8 | 1024.2.b.h.513.6 | 8 | |||
32.29 | even | 8 | 1024.2.a.j.1.1 | 4 | |||
48.5 | odd | 4 | 2304.2.k.f.577.4 | 8 | |||
48.11 | even | 4 | 2304.2.k.f.577.3 | 8 | |||
48.29 | odd | 4 | 2304.2.k.k.577.2 | 8 | |||
48.35 | even | 4 | 2304.2.k.k.577.1 | 8 | |||
96.29 | odd | 8 | 9216.2.a.bb.1.3 | 4 | |||
96.35 | even | 8 | 9216.2.a.bk.1.4 | 4 | |||
96.77 | odd | 8 | 9216.2.a.bk.1.1 | 4 | |||
96.83 | even | 8 | 9216.2.a.bb.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
256.2.e.a.65.2 | ✓ | 8 | 16.11 | odd | 4 | ||
256.2.e.a.65.3 | yes | 8 | 16.5 | even | 4 | ||
256.2.e.a.193.2 | yes | 8 | 8.3 | odd | 2 | ||
256.2.e.a.193.3 | yes | 8 | 8.5 | even | 2 | ||
256.2.e.b.65.2 | yes | 8 | 16.13 | even | 4 | inner | |
256.2.e.b.65.3 | yes | 8 | 16.3 | odd | 4 | inner | |
256.2.e.b.193.2 | yes | 8 | 1.1 | even | 1 | trivial | |
256.2.e.b.193.3 | yes | 8 | 4.3 | odd | 2 | inner | |
1024.2.a.g.1.3 | 4 | 32.3 | odd | 8 | |||
1024.2.a.g.1.4 | 4 | 32.13 | even | 8 | |||
1024.2.a.j.1.1 | 4 | 32.29 | even | 8 | |||
1024.2.a.j.1.2 | 4 | 32.19 | odd | 8 | |||
1024.2.b.h.513.3 | 8 | 32.11 | odd | 8 | |||
1024.2.b.h.513.4 | 8 | 32.5 | even | 8 | |||
1024.2.b.h.513.5 | 8 | 32.21 | even | 8 | |||
1024.2.b.h.513.6 | 8 | 32.27 | odd | 8 | |||
2304.2.k.f.577.3 | 8 | 48.11 | even | 4 | |||
2304.2.k.f.577.4 | 8 | 48.5 | odd | 4 | |||
2304.2.k.f.1729.3 | 8 | 24.5 | odd | 2 | |||
2304.2.k.f.1729.4 | 8 | 24.11 | even | 2 | |||
2304.2.k.k.577.1 | 8 | 48.35 | even | 4 | |||
2304.2.k.k.577.2 | 8 | 48.29 | odd | 4 | |||
2304.2.k.k.1729.1 | 8 | 3.2 | odd | 2 | |||
2304.2.k.k.1729.2 | 8 | 12.11 | even | 2 | |||
9216.2.a.bb.1.2 | 4 | 96.83 | even | 8 | |||
9216.2.a.bb.1.3 | 4 | 96.29 | odd | 8 | |||
9216.2.a.bk.1.1 | 4 | 96.77 | odd | 8 | |||
9216.2.a.bk.1.4 | 4 | 96.35 | even | 8 |