Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.7 | ||
Character | \(\chi\) | \(=\) | 1008.529 |
Dual form | 1008.2.q.l.625.7 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0.704143 | + | 1.58246i | 0.406537 | + | 0.913634i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.05220 | + | 1.82246i | −0.470558 | + | 0.815030i | −0.999433 | − | 0.0336699i | \(-0.989281\pi\) |
0.528876 | + | 0.848699i | \(0.322614\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.58382 | − | 0.569079i | −0.976594 | − | 0.215092i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00837 | + | 2.22856i | −0.669455 | + | 0.742852i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.199532 | + | 0.345600i | 0.0601612 | + | 0.104202i | 0.894537 | − | 0.446993i | \(-0.147505\pi\) |
−0.834376 | + | 0.551195i | \(0.814172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44292 | + | 2.49921i | 0.400194 | + | 0.693157i | 0.993749 | − | 0.111637i | \(-0.0356093\pi\) |
−0.593555 | + | 0.804794i | \(0.702276\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.62487 | − | 0.381790i | −0.935938 | − | 0.0985778i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.176596 | + | 0.305873i | −0.0428308 | + | 0.0741851i | −0.886646 | − | 0.462449i | \(-0.846971\pi\) |
0.843815 | + | 0.536634i | \(0.180304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.84888 | − | 4.93440i | −0.653578 | − | 1.13203i | −0.982248 | − | 0.187585i | \(-0.939934\pi\) |
0.328670 | − | 0.944445i | \(-0.393399\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.918837 | − | 4.48951i | −0.200507 | − | 0.979692i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.438682 | + | 0.759820i | −0.0914716 | + | 0.158433i | −0.908131 | − | 0.418687i | \(-0.862490\pi\) |
0.816659 | + | 0.577121i | \(0.195824\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.285756 | + | 0.494945i | 0.0571513 | + | 0.0989889i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.94078 | − | 1.60894i | −0.950854 | − | 0.309640i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.874997 | − | 1.51554i | 0.162483 | − | 0.281429i | −0.773276 | − | 0.634070i | \(-0.781383\pi\) |
0.935759 | + | 0.352641i | \(0.114716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.13490 | −1.64068 | −0.820339 | − | 0.571878i | \(-0.806215\pi\) | ||||
−0.820339 | + | 0.571878i | \(0.806215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.406399 | + | 0.559103i | −0.0707450 | + | 0.0973274i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.75582 | − | 4.11014i | 0.634850 | − | 0.694740i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.39555 | − | 5.88127i | −0.558225 | − | 0.966874i | −0.997645 | − | 0.0685922i | \(-0.978149\pi\) |
0.439420 | − | 0.898282i | \(-0.355184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.93888 | + | 4.04317i | −0.470598 | + | 0.647425i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.20377 | + | 2.08499i | 0.187997 | + | 0.325621i | 0.944582 | − | 0.328274i | \(-0.106467\pi\) |
−0.756585 | + | 0.653895i | \(0.773134\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.276745 | + | 0.479336i | −0.0422032 | + | 0.0730981i | −0.886355 | − | 0.463005i | \(-0.846771\pi\) |
0.844152 | + | 0.536104i | \(0.180104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.94826 | − | 6.00505i | −0.290429 | − | 0.895181i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7372 | −1.71205 | −0.856023 | − | 0.516939i | \(-0.827072\pi\) | ||||
−0.856023 | + | 0.516939i | \(0.827072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.35230 | + | 2.94080i | 0.907471 | + | 0.420114i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.608381 | − | 0.0640778i | −0.0851904 | − | 0.00897269i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.07821 | + | 3.59956i | −0.285464 | + | 0.494437i | −0.972721 | − | 0.231976i | \(-0.925481\pi\) |
0.687258 | + | 0.726413i | \(0.258814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.839790 | −0.113237 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.80248 | − | 7.98277i | 0.768558 | − | 1.05734i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.32421 | 1.21391 | 0.606954 | − | 0.794737i | \(-0.292391\pi\) | ||||
0.606954 | + | 0.794737i | \(0.292391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0720 | −1.28959 | −0.644795 | − | 0.764356i | \(-0.723057\pi\) | ||||
−0.644795 | + | 0.764356i | \(0.723057\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.45749 | − | 4.61528i | 0.813567 | − | 0.581471i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.07296 | −0.753258 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.20241 | −0.146898 | −0.0734488 | − | 0.997299i | \(-0.523401\pi\) | ||||
−0.0734488 | + | 0.997299i | \(0.523401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.51128 | − | 0.159176i | −0.181937 | − | 0.0191625i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.6826 | 1.74250 | 0.871250 | − | 0.490840i | \(-0.163310\pi\) | ||||
0.871250 | + | 0.490840i | \(0.163310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.315636 | − | 0.546697i | 0.0369423 | − | 0.0639860i | −0.846963 | − | 0.531652i | \(-0.821572\pi\) |
0.883905 | + | 0.467666i | \(0.154905\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.582017 | + | 0.800710i | −0.0672056 | + | 0.0924580i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.318883 | − | 1.00652i | −0.0363400 | − | 0.114703i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.48729 | 0.279842 | 0.139921 | − | 0.990163i | \(-0.455315\pi\) | ||||
0.139921 | + | 0.990163i | \(0.455315\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.932933 | − | 8.95152i | −0.103659 | − | 0.994613i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.59366 | − | 7.95645i | 0.504219 | − | 0.873333i | −0.495769 | − | 0.868455i | \(-0.665114\pi\) |
0.999988 | − | 0.00487885i | \(-0.00155299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.371628 | − | 0.643678i | −0.0403087 | − | 0.0698167i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.01440 | + | 0.317493i | 0.323178 | + | 0.0340388i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.29358 | + | 12.6328i | 0.773118 | + | 1.33908i | 0.935846 | + | 0.352408i | \(0.114637\pi\) |
−0.162729 | + | 0.986671i | \(0.552029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.30601 | − | 7.27866i | −0.241735 | − | 0.763011i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.43228 | − | 14.4556i | −0.666996 | − | 1.49898i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.9903 | 1.23018 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.84245 | + | 13.5835i | −0.796280 | + | 1.37920i | 0.125744 | + | 0.992063i | \(0.459868\pi\) |
−0.922023 | + | 0.387134i | \(0.873465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.17092 | − | 0.249422i | −0.117682 | − | 0.0250679i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0464285 | + | 0.0804166i | 0.00461981 | + | 0.00800175i | 0.868326 | − | 0.495994i | \(-0.165196\pi\) |
−0.863706 | + | 0.503996i | \(0.831863\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.95769 | + | 17.2472i | −0.981161 | + | 1.69942i | −0.323270 | + | 0.946307i | \(0.604782\pi\) |
−0.657891 | + | 0.753113i | \(0.728551\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.14877 | + | 3.04932i | 0.892828 | + | 0.297583i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.89225 | + | 5.00953i | 0.279605 | + | 0.484290i | 0.971287 | − | 0.237913i | \(-0.0764633\pi\) |
−0.691682 | + | 0.722202i | \(0.743130\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.25516 | + | 10.8343i | −0.599136 | + | 1.03773i | 0.393813 | + | 0.919191i | \(0.371156\pi\) |
−0.992949 | + | 0.118543i | \(0.962178\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.91592 | − | 9.51458i | 0.656430 | − | 0.903084i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.69411 | + | 2.93428i | 0.159368 | + | 0.276034i | 0.934641 | − | 0.355593i | \(-0.115721\pi\) |
−0.775273 | + | 0.631627i | \(0.782388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.923161 | − | 1.59896i | −0.0860853 | − | 0.149104i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.46755 | − | 1.80370i | −0.782826 | − | 0.166752i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.630359 | − | 0.689825i | 0.0577849 | − | 0.0632362i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.42037 | − | 9.38836i | 0.492761 | − | 0.853488i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.45179 | + | 3.37305i | −0.221071 | + | 0.304138i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7247 | −1.04869 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7348 | −1.30750 | −0.653752 | − | 0.756709i | \(-0.726806\pi\) | ||||
−0.653752 | + | 0.756709i | \(0.726806\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.953399 | − | 0.100417i | −0.0839421 | − | 0.00884122i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.95392 | + | 12.0445i | −0.607567 | + | 1.05234i | 0.384073 | + | 0.923303i | \(0.374521\pi\) |
−0.991640 | + | 0.129034i | \(0.958812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.55294 | + | 14.3709i | 0.394790 | + | 1.24611i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.13091 | − | 7.31146i | 0.699797 | − | 0.629270i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.27874 | − | 12.6072i | −0.621865 | − | 1.07710i | −0.989138 | − | 0.146989i | \(-0.953042\pi\) |
0.367273 | − | 0.930113i | \(-0.380291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.63996 | + | 6.30460i | 0.308737 | + | 0.534749i | 0.978086 | − | 0.208199i | \(-0.0667603\pi\) |
−0.669349 | + | 0.742948i | \(0.733427\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.26466 | − | 18.5736i | −0.696010 | − | 1.56418i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.575818 | + | 0.997347i | −0.0481523 | + | 0.0834023i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.84134 | + | 3.18930i | 0.152915 | + | 0.264857i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.180775 | + | 12.1230i | −0.0149100 | + | 0.999889i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.360832 | − | 0.624979i | 0.0295605 | − | 0.0512003i | −0.850867 | − | 0.525382i | \(-0.823923\pi\) |
0.880427 | + | 0.474181i | \(0.157256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9022 | + | 18.8831i | 0.887207 | + | 1.53669i | 0.843163 | + | 0.537657i | \(0.180691\pi\) |
0.0440432 | + | 0.999030i | \(0.485976\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.326986 | − | 1.00786i | −0.0264353 | − | 0.0814806i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.61173 | − | 16.6480i | 0.772033 | − | 1.33720i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.17973 | 0.413387 | 0.206694 | − | 0.978406i | \(-0.433730\pi\) | ||||
0.206694 | + | 0.978406i | \(0.433730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.15951 | − | 0.754077i | −0.567786 | − | 0.0598022i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.56588 | − | 1.71360i | 0.123408 | − | 0.135050i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.63906 | − | 4.57098i | −0.206707 | − | 0.358027i | 0.743968 | − | 0.668215i | \(-0.232941\pi\) |
−0.950675 | + | 0.310188i | \(0.899608\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.591332 | − | 1.32893i | −0.0460351 | − | 0.103457i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.83710 | + | 11.8422i | 0.529071 | + | 0.916378i | 0.999425 | + | 0.0339001i | \(0.0107928\pi\) |
−0.470354 | + | 0.882478i | \(0.655874\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.33596 | − | 4.04599i | 0.179689 | − | 0.311230i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.7182 | + | 3.56120i | 1.27847 | + | 0.272332i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.1824 | 1.53444 | 0.767218 | − | 0.641386i | \(-0.221640\pi\) | ||||
0.767218 | + | 0.641386i | \(0.221640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.456682 | − | 1.44147i | −0.0345219 | − | 0.108965i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.56557 | + | 14.7552i | 0.493499 | + | 1.10907i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5968 | + | 21.8183i | −0.941528 | + | 1.63077i | −0.178971 | + | 0.983854i | \(0.557277\pi\) |
−0.762557 | + | 0.646921i | \(0.776056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.2815 | −1.28453 | −0.642263 | − | 0.766485i | \(-0.722004\pi\) | ||||
−0.642263 | + | 0.766485i | \(0.722004\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.09214 | − | 15.9386i | −0.524266 | − | 1.17821i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.2912 | 1.05071 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.140946 | −0.0103070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.8505 | + | 6.96891i | 0.861997 | + | 0.506913i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.01898 | 0.363161 | 0.181580 | − | 0.983376i | \(-0.441879\pi\) | ||||
0.181580 | + | 0.983376i | \(0.441879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.43765 | −0.391411 | −0.195705 | − | 0.980663i | \(-0.562700\pi\) | ||||
−0.195705 | + | 0.980663i | \(0.562700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.27623 | − | 9.61022i | −0.306227 | − | 0.688202i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.95839 | 0.424517 | 0.212259 | − | 0.977214i | \(-0.431918\pi\) | ||||
0.212259 | + | 0.977214i | \(0.431918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.62062 | + | 9.73520i | −0.398435 | + | 0.690110i | −0.993533 | − | 0.113543i | \(-0.963780\pi\) |
0.595098 | + | 0.803653i | \(0.297113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.846668 | − | 1.90277i | −0.0597193 | − | 0.134211i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.12330 | + | 3.41795i | −0.219213 | + | 0.239893i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.06643 | −0.353855 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.812267 | − | 2.50362i | −0.0564565 | − | 0.174014i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.13689 | − | 1.96914i | 0.0786401 | − | 0.136209i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.381084 | − | 0.660057i | −0.0262349 | − | 0.0454402i | 0.852610 | − | 0.522548i | \(-0.175018\pi\) |
−0.878845 | + | 0.477108i | \(0.841685\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.3386 | + | 23.2346i | 0.708391 | + | 1.59201i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.582381 | − | 1.00871i | −0.0397181 | − | 0.0687937i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.6030 | + | 5.19848i | 1.60228 | + | 0.352896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.08738 | + | 0.114528i | 0.0734783 | + | 0.00773911i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.01926 | −0.0685626 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.80556 | − | 10.0555i | 0.388769 | − | 0.673368i | −0.603515 | − | 0.797352i | \(-0.706234\pi\) |
0.992284 | + | 0.123984i | \(0.0395670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.67692 | − | 0.357205i | −0.111794 | − | 0.0238137i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.16624 | − | 8.94818i | −0.342895 | − | 0.593912i | 0.642074 | − | 0.766643i | \(-0.278074\pi\) |
−0.984969 | + | 0.172731i | \(0.944741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.86191 | − | 3.22493i | 0.123039 | − | 0.213109i | −0.797926 | − | 0.602756i | \(-0.794069\pi\) |
0.920965 | + | 0.389646i | \(0.127403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.36824 | − | 1.21335i | 0.0900234 | − | 0.0798327i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3649 | + | 23.1488i | 0.875566 | + | 1.51653i | 0.856158 | + | 0.516714i | \(0.172845\pi\) |
0.0194083 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3499 | − | 21.3906i | 0.805616 | − | 1.39537i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.75141 | + | 3.93604i | 0.113766 | + | 0.255673i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.94164 | − | 12.0233i | −0.449018 | − | 0.777721i | 0.549305 | − | 0.835622i | \(-0.314893\pi\) |
−0.998322 | + | 0.0579007i | \(0.981559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.45280 | − | 12.9086i | −0.480077 | − | 0.831518i | 0.519662 | − | 0.854372i | \(-0.326058\pi\) |
−0.999739 | + | 0.0228542i | \(0.992725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5085 | − | 7.77948i | 0.866571 | − | 0.499054i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.0434 | + | 8.48251i | −0.769423 | + | 0.541928i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.22142 | − | 14.2399i | 0.523116 | − | 0.906064i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.8254 | + | 1.66681i | 1.00289 | + | 0.105630i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5515 | −1.42344 | −0.711720 | − | 0.702464i | \(-0.752083\pi\) | ||||
−0.711720 | + | 0.702464i | \(0.752083\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.350125 | −0.0220122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.756917 | − | 1.04133i | 0.0474000 | − | 0.0652105i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.94765 | + | 10.3016i | −0.371004 | + | 0.642598i | −0.989720 | − | 0.143017i | \(-0.954320\pi\) |
0.618716 | + | 0.785615i | \(0.287653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.42660 | + | 17.1285i | 0.337193 | + | 1.06431i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.62015 | + | 4.99374i | 0.100285 | + | 0.309105i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3030 | + | 21.3094i | 0.758633 | + | 1.31399i | 0.943548 | + | 0.331236i | \(0.107466\pi\) |
−0.184915 | + | 0.982755i | \(0.559201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.37337 | − | 7.57490i | −0.268654 | − | 0.465322i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.8553 | + | 20.4371i | −0.909128 | + | 1.25073i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.75722 | − | 11.7039i | 0.411995 | − | 0.713597i | −0.583113 | − | 0.812391i | \(-0.698165\pi\) |
0.995108 | + | 0.0987947i | \(0.0314987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.34195 | + | 2.32433i | 0.0815177 | + | 0.141193i | 0.903902 | − | 0.427740i | \(-0.140690\pi\) |
−0.822384 | + | 0.568932i | \(0.807357\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.89444 | − | 8.77438i | 0.598839 | − | 0.531050i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.114035 | + | 0.197515i | −0.00687658 | + | 0.0119106i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.52618 | − | 16.4998i | −0.572373 | − | 0.991379i | −0.996322 | − | 0.0856928i | \(-0.972690\pi\) |
0.423949 | − | 0.905686i | \(-0.360644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.3462 | − | 20.3577i | 1.09836 | − | 1.21878i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.2006 | − | 24.5962i | 0.847139 | − | 1.46729i | −0.0366118 | − | 0.999330i | \(-0.511657\pi\) |
0.883751 | − | 0.467958i | \(-0.155010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4221 | 0.916749 | 0.458374 | − | 0.888759i | \(-0.348432\pi\) | ||||
0.458374 | + | 0.888759i | \(0.348432\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.44292 | + | 18.9743i | 0.500115 | + | 1.12394i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.92381 | − | 6.07230i | −0.113559 | − | 0.358436i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.43763 | + | 14.6144i | 0.496331 | + | 0.859671i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.0176 | − | 2.84563i | −1.58380 | − | 0.166814i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.02253 | + | 15.6275i | 0.527102 | + | 0.912967i | 0.999501 | + | 0.0315825i | \(0.0100547\pi\) |
−0.472399 | + | 0.881385i | \(0.656612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.81092 | + | 16.9930i | −0.571214 | + | 0.989371i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.429796 | − | 2.02857i | −0.0249393 | − | 0.117709i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.53194 | −0.146426 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.987841 | − | 1.08103i | 0.0569382 | − | 0.0623096i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.0945638 | + | 0.130096i | −0.00543255 | + | 0.00747383i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.5978 | − | 18.3559i | 0.606826 | − | 1.05105i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.30860 | 0.417124 | 0.208562 | − | 0.978009i | \(-0.433122\pi\) | ||||
0.208562 | + | 0.978009i | \(0.433122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.3047 | − | 3.61315i | −1.95153 | − | 0.205545i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7792 | 1.34839 | 0.674197 | − | 0.738551i | \(-0.264490\pi\) | ||||
0.674197 | + | 0.738551i | \(0.264490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2907 | −1.03385 | −0.516925 | − | 0.856031i | \(-0.672923\pi\) | ||||
−0.516925 | + | 0.856031i | \(0.672923\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.61661 | + | 16.6247i | 0.0910858 | + | 0.936697i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.68988 | −0.263410 | −0.131705 | − | 0.991289i | \(-0.542045\pi\) | ||||
−0.131705 | + | 0.991289i | \(0.542045\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.698360 | 0.0391007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.89083 | + | 8.10430i | −0.328794 | + | 0.452338i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.01240 | 0.111973 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.824648 | + | 1.42833i | −0.0457432 | + | 0.0792296i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.5493 | − | 2.26969i | −1.19168 | − | 0.125514i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.3268 | + | 6.67938i | 1.67197 | + | 0.368246i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4287 | 0.628176 | 0.314088 | − | 0.949394i | \(-0.398301\pi\) | ||||
0.314088 | + | 0.949394i | \(0.398301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.9262 | + | 4.24456i | 1.09195 | + | 0.232600i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.26517 | − | 2.19134i | 0.0691238 | − | 0.119726i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.74160 | + | 15.1409i | 0.476185 | + | 0.824777i | 0.999628 | − | 0.0272840i | \(-0.00868584\pi\) |
−0.523442 | + | 0.852061i | \(0.675353\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.45049 | + | 4.74702i | −0.187405 | + | 0.257823i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.82271 | − | 3.15702i | −0.0987051 | − | 0.170962i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.7397 | − | 11.2135i | −0.795868 | − | 0.605470i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.88026 | − | 2.58677i | 0.101230 | − | 0.139267i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.1186 | −0.757925 | −0.378962 | − | 0.925412i | \(-0.623719\pi\) | ||||
−0.378962 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.7216 | − | 18.5704i | 0.573916 | − | 0.994052i | −0.422242 | − | 0.906483i | \(-0.638757\pi\) |
0.996158 | − | 0.0875692i | \(-0.0279099\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.10808 | − | 14.6696i | −0.165897 | − | 0.783007i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6880 | + | 27.1724i | 0.834987 | + | 1.44624i | 0.894041 | + | 0.447985i | \(0.147858\pi\) |
−0.0590538 | + | 0.998255i | \(0.518808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4490 | + | 26.7584i | −0.819946 | + | 1.42019i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.53548 | + | 0.511782i | 0.0812664 | + | 0.0270864i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.313156 | − | 0.542402i | −0.0165277 | − | 0.0286269i | 0.857643 | − | 0.514245i | \(-0.171928\pi\) |
−0.874171 | + | 0.485618i | \(0.838595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.73223 | + | 11.6606i | −0.354328 | + | 0.613714i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.6734 | + | 1.96678i | 0.980101 | + | 0.103229i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.664223 | + | 1.15047i | 0.0347670 | + | 0.0602182i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.62199 | − | 2.80936i | −0.0846670 | − | 0.146648i | 0.820582 | − | 0.571528i | \(-0.193649\pi\) |
−0.905249 | + | 0.424881i | \(0.860316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.06414 | − | 1.50476i | −0.367744 | − | 0.0783345i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.41815 | − | 8.11796i | 0.385131 | − | 0.421464i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8013 | − | 23.9046i | 0.714606 | − | 1.23773i | −0.248506 | − | 0.968630i | \(-0.579939\pi\) |
0.963111 | − | 0.269103i | \(-0.0867272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.25585 | − | 18.5538i | −0.426330 | − | 0.958116i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.05021 | 0.260099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.7800 | 0.656463 | 0.328231 | − | 0.944597i | \(-0.393547\pi\) | ||||
0.328231 | + | 0.944597i | \(0.393547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.3754 | − | 23.3173i | −0.531549 | − | 1.19458i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.58278 | + | 4.47351i | −0.131974 | + | 0.228586i | −0.924437 | − | 0.381334i | \(-0.875465\pi\) |
0.792463 | + | 0.609919i | \(0.208798\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.16987 | + | 0.477906i | 0.110587 | + | 0.0243564i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.512423 | − | 1.57943i | −0.0260479 | − | 0.0802867i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.4707 | − | 28.5280i | −0.835095 | − | 1.44643i | −0.893953 | − | 0.448161i | \(-0.852079\pi\) |
0.0588576 | − | 0.998266i | \(-0.481254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.154939 | − | 0.268362i | −0.00783560 | − | 0.0135717i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.9566 | − | 2.52323i | −1.20845 | − | 0.127280i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.61712 | + | 4.53299i | −0.131682 | + | 0.228079i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.411705 | − | 0.713095i | −0.0206629 | − | 0.0357892i | 0.855509 | − | 0.517788i | \(-0.173244\pi\) |
−0.876172 | + | 0.481999i | \(0.839911\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.5354 | + | 17.3240i | −0.977995 | + | 0.867285i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.86923 | − | 17.0940i | 0.492846 | − | 0.853634i | −0.507120 | − | 0.861875i | \(-0.669290\pi\) |
0.999966 | + | 0.00824153i | \(0.00262339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.1809 | − | 22.8301i | −0.656590 | − | 1.13725i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.2954 | + | 7.71854i | 0.859416 | + | 0.383537i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.35504 | − | 2.34700i | 0.0671670 | − | 0.116337i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.2551 | −1.24879 | −0.624393 | − | 0.781110i | \(-0.714654\pi\) | ||||
−0.624393 | + | 0.781110i | \(0.714654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.8251 | − | 20.3956i | 0.731266 | − | 1.00604i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0921 | − | 5.30621i | −1.18550 | − | 0.261101i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.66688 | + | 16.7435i | 0.474528 | + | 0.821907i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.41372 | + | 10.1994i | −0.363052 | + | 0.499468i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.406717 | − | 0.704455i | −0.0198694 | − | 0.0344149i | 0.855920 | − | 0.517109i | \(-0.172992\pi\) |
−0.875789 | + | 0.482694i | \(0.839658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.12114 | − | 8.87008i | 0.249589 | − | 0.432301i | −0.713823 | − | 0.700326i | \(-0.753038\pi\) |
0.963412 | + | 0.268025i | \(0.0863711\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.5726 | − | 26.1570i | 1.14614 | − | 1.27180i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.201854 | −0.00979134 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.0243 | + | 5.73177i | 1.25941 | + | 0.277380i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.98372 | − | 0.208936i | −0.0957749 | − | 0.0100875i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3348 | + | 28.2928i | −0.786822 | + | 1.36281i | 0.141083 | + | 0.989998i | \(0.454941\pi\) |
−0.927905 | + | 0.372817i | \(0.878392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.3151 | −0.687941 | −0.343970 | − | 0.938980i | \(-0.611772\pi\) | ||||
−0.343970 | + | 0.938980i | \(0.611772\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.75037 | + | 5.15957i | −0.179817 | + | 0.247382i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.99901 | 0.239135 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.86660 | 0.470907 | 0.235453 | − | 0.971886i | \(-0.424342\pi\) | ||||
0.235453 | + | 0.971886i | \(0.424342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.3115 | + | 8.25026i | −0.919594 | + | 0.392870i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.2801 | −1.77123 | −0.885615 | − | 0.464419i | \(-0.846263\pi\) | ||||
−0.885615 | + | 0.464419i | \(0.846263\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.6972 | −1.45519 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.24308 | + | 0.130928i | 0.0587958 | + | 0.00619267i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.2926 | −1.71276 | −0.856378 | − | 0.516350i | \(-0.827290\pi\) | ||||
−0.856378 | + | 0.516350i | \(0.827290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.480382 | + | 0.832046i | −0.0226203 | + | 0.0391795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.2051 | + | 30.5487i | −1.04329 | + | 1.43530i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.6915 | + | 3.45599i | 0.735627 | + | 0.162019i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1943 | −0.617205 | −0.308602 | − | 0.951191i | \(-0.599861\pi\) | ||||
−0.308602 | + | 0.951191i | \(0.599861\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.36465 | − | 1.22712i | 0.0636965 | − | 0.0572771i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1326 | − | 17.5502i | 0.471924 | − | 0.817396i | −0.527560 | − | 0.849518i | \(-0.676893\pi\) |
0.999484 | + | 0.0321215i | \(0.0102263\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7106 | − | 22.0154i | −0.590712 | − | 1.02314i | −0.994137 | − | 0.108131i | \(-0.965513\pi\) |
0.403424 | − | 0.915013i | \(-0.367820\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 33.1129 | + | 3.48762i | 1.53557 | + | 0.161734i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.40661 | + | 7.63248i | 0.203914 | + | 0.353189i | 0.949786 | − | 0.312900i | \(-0.101300\pi\) |
−0.745872 | + | 0.666089i | \(0.767967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.10681 | + | 0.684265i | 0.143459 | + | 0.0315964i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.64727 | + | 8.19671i | 0.168057 | + | 0.377685i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.220878 | −0.0101560 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.62817 | − | 2.82008i | 0.0747056 | − | 0.129394i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.84802 | − | 11.8606i | −0.176189 | − | 0.543061i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.1343 | + | 21.0173i | 0.554433 | + | 0.960305i | 0.997947 | + | 0.0640383i | \(0.0203980\pi\) |
−0.443515 | + | 0.896267i | \(0.646269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.79902 | − | 16.9724i | 0.446797 | − | 0.773875i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.81430 | + | 1.27132i | 0.173557 | + | 0.0578470i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.5036 | − | 28.5851i | −0.749391 | − | 1.29798i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.37220 | − | 9.30492i | 0.243438 | − | 0.421646i | −0.718254 | − | 0.695781i | \(-0.755058\pi\) |
0.961691 | + | 0.274135i | \(0.0883916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.37513 | − | 7.39483i | 0.243072 | − | 0.334406i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.3934 | − | 19.7340i | −0.514179 | − | 0.890584i | −0.999865 | − | 0.0164507i | \(-0.994763\pi\) |
0.485686 | − | 0.874134i | \(-0.338570\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.309042 | + | 0.535276i | 0.0139185 | + | 0.0241076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.68660 | − | 1.87152i | 0.0758073 | − | 0.0841185i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.9372 | − | 8.35553i | −1.70171 | − | 0.374797i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.5755 | − | 20.0493i | 0.518189 | − | 0.897530i | −0.481588 | − | 0.876398i | \(-0.659940\pi\) |
0.999777 | − | 0.0211317i | \(-0.00672693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.9255 | + | 19.1581i | −0.622147 | + | 0.855919i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.43360 | −0.420623 | −0.210312 | − | 0.977634i | \(-0.567448\pi\) | ||||
−0.210312 | + | 0.977634i | \(0.567448\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.195408 | −0.00869555 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.04747 | + | 0.847601i | 0.357401 | + | 0.0376433i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.72981 | − | 8.19228i | 0.209645 | − | 0.363116i | −0.741957 | − | 0.670447i | \(-0.766102\pi\) |
0.951603 | + | 0.307331i | \(0.0994357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.12666 | + | 1.23295i | −0.0498405 | + | 0.0545424i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.13654 | + | 28.9635i | 0.270935 | + | 1.27877i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.9549 | − | 36.2950i | −0.923385 | − | 1.59935i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.34195 | − | 4.05637i | −0.102999 | − | 0.178399i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.2113 | + | 31.9378i | 0.623805 | + | 1.40191i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.3368 | + | 24.8320i | −0.628105 | + | 1.08791i | 0.359826 | + | 0.933019i | \(0.382836\pi\) |
−0.987932 | + | 0.154891i | \(0.950497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5104 | + | 23.4006i | 0.590767 | + | 1.02324i | 0.994129 | + | 0.108198i | \(0.0345081\pi\) |
−0.403362 | + | 0.915040i | \(0.632159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.95950 | − | 1.73768i | 0.0855195 | − | 0.0758386i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.61319 | − | 2.79412i | 0.0702715 | − | 0.121714i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1151 | + | 19.2519i | 0.483266 | + | 0.837041i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.7264 | + | 20.7795i | −0.812658 | + | 0.901755i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.47389 | + | 6.01696i | −0.150471 | + | 0.260624i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.1729 | −0.526280 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −43.3965 | − | 4.57075i | −1.87270 | − | 0.197242i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.251148 | + | 2.78214i | 0.0108177 | + | 0.119835i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.52907 | − | 2.64842i | −0.0657397 | − | 0.113864i | 0.831282 | − | 0.555851i | \(-0.187607\pi\) |
−0.897022 | + | 0.441986i | \(0.854274\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.1687 | − | 27.3473i | −0.522207 | − | 1.17359i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.1633 | − | 22.7996i | −0.563856 | − | 0.976627i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.58144 | + | 6.20323i | −0.153131 | + | 0.265231i | −0.932377 | − | 0.361487i | \(-0.882269\pi\) |
0.779246 | + | 0.626719i | \(0.215602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.2283 | − | 22.4461i | 0.863322 | − | 0.957974i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.97105 | −0.424781 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.42672 | − | 1.41546i | −0.273292 | − | 0.0601916i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.0630 | + | 22.6152i | 0.427152 | + | 0.959963i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.3518 | + | 24.8580i | −0.608104 | + | 1.05327i | 0.383449 | + | 0.923562i | \(0.374736\pi\) |
−0.991553 | + | 0.129704i | \(0.958597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.59729 | −0.0675580 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0992463 | − | 0.223042i | −0.00419018 | − | 0.00941684i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.7719 | −1.50761 | −0.753803 | − | 0.657101i | \(-0.771782\pi\) | ||||
−0.753803 | + | 0.657101i | \(0.771782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.13016 | −0.299968 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.68358 | + | 23.6601i | −0.112700 | + | 0.993629i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.2002 | −1.05645 | −0.528223 | − | 0.849106i | \(-0.677142\pi\) | ||||
−0.528223 | + | 0.849106i | \(0.677142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.04938 | 0.253159 | 0.126579 | − | 0.991956i | \(-0.459600\pi\) | ||||
0.126579 | + | 0.991956i | \(0.459600\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.53408 | + | 7.94234i | 0.147638 | + | 0.331796i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.501425 | −0.0209109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.57977 | − | 16.5926i | 0.398811 | − | 0.690761i | −0.594768 | − | 0.803897i | \(-0.702756\pi\) |
0.993580 | + | 0.113136i | \(0.0360896\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.82888 | − | 8.60487i | −0.159123 | − | 0.357606i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.3970 | + | 17.9439i | −0.680264 | + | 0.744439i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.65868 | −0.0686953 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.1967 | − | 13.5339i | 0.504272 | − | 0.559559i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.4147 | + | 31.8953i | −0.760058 | + | 1.31646i | 0.182763 | + | 0.983157i | \(0.441496\pi\) |
−0.942820 | + | 0.333301i | \(0.891837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.0242 | + | 45.0753i | 1.07231 | + | 1.85730i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.19555 | + | 9.42891i | 0.172582 | + | 0.387854i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.97285 | + | 15.5414i | 0.368471 | + | 0.638210i | 0.989327 | − | 0.145715i | \(-0.0465481\pi\) |
−0.620856 | + | 0.783925i | \(0.713215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.593918 | + | 1.87464i | 0.0243482 | + | 0.0768526i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.3633 | − | 2.03944i | −0.792487 | − | 0.0834688i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.4913 | 1.65443 | 0.827215 | − | 0.561885i | \(-0.189924\pi\) | ||||
0.827215 | + | 0.561885i | \(0.189924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.2589 | − | 22.9651i | 0.540841 | − | 0.936765i | −0.458015 | − | 0.888945i | \(-0.651439\pi\) |
0.998856 | − | 0.0478200i | \(-0.0152274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.41488 | − | 2.67964i | 0.0983414 | − | 0.109123i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.4066 | + | 19.7568i | 0.463745 | + | 0.803230i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.0848 | + | 36.5200i | −0.855806 | + | 1.48230i | 0.0200897 | + | 0.999798i | \(0.493605\pi\) |
−0.875895 | + | 0.482501i | \(0.839729\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.60802 | − | 2.53578i | −0.308292 | − | 0.102755i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.9358 | − | 29.3337i | −0.685151 | − | 1.18672i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.700827 | + | 1.21387i | −0.0283061 | + | 0.0490277i | −0.879831 | − | 0.475286i | \(-0.842345\pi\) |
0.851525 | + | 0.524313i | \(0.175678\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.56749 | − | 8.01742i | −0.143855 | − | 0.323294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.76787 | − | 11.7223i | −0.272464 | − | 0.471922i | 0.697028 | − | 0.717044i | \(-0.254505\pi\) |
−0.969492 | + | 0.245122i | \(0.921172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9122 | − | 25.8288i | −0.599374 | − | 1.03815i | −0.992914 | − | 0.118838i | \(-0.962083\pi\) |
0.393540 | − | 0.919308i | \(-0.371250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.38994 | − | 3.04829i | 0.136033 | − | 0.122324i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.6562 | − | 36.7917i | −0.466997 | − | 1.47403i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.9079 | − | 18.8930i | 0.436316 | − | 0.755722i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.91662 | + | 0.412519i | 0.156415 | + | 0.0164744i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.39856 | 0.0956369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.84708 | −0.272578 | −0.136289 | − | 0.990669i | \(-0.543518\pi\) | ||||
−0.136289 | + | 0.990669i | \(0.543518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.776177 | − | 1.06782i | 0.0308503 | − | 0.0424422i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.5040 | − | 26.8536i | 0.615256 | − | 1.06565i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.81618 | + | 20.1191i | 0.0719598 | + | 0.797147i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.4880 | + | 32.7209i | −1.16653 | + | 1.29442i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1209 | − | 27.9221i | −0.636735 | − | 1.10286i | −0.986145 | − | 0.165888i | \(-0.946951\pi\) |
0.349409 | − | 0.936970i | \(-0.386382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.16002 | − | 2.00921i | −0.0457465 | − | 0.0792353i | 0.842245 | − | 0.539094i | \(-0.181233\pi\) |
−0.887992 | + | 0.459859i | \(0.847900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.18617 | − | 1.63187i | 0.0467055 | − | 0.0642550i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.06813 | + | 1.85005i | −0.0419924 | + | 0.0727329i | −0.886258 | − | 0.463193i | \(-0.846704\pi\) |
0.844265 | + | 0.535925i | \(0.180037\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.86048 | + | 3.22244i | 0.0730302 | + | 0.126492i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.39348 | + | 41.0113i | 0.328967 | + | 1.60736i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.51932 | + | 2.63155i | −0.0594558 | + | 0.102980i | −0.894221 | − | 0.447625i | \(-0.852270\pi\) |
0.834765 | + | 0.550606i | \(0.185603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.6338 | − | 25.3465i | −0.571790 | − | 0.990370i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.584433 | + | 1.80138i | 0.0228009 | + | 0.0702785i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.8000 | − | 34.2946i | 0.771298 | − | 1.33593i | −0.165554 | − | 0.986201i | \(-0.552941\pi\) |
0.936852 | − | 0.349726i | \(-0.113725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.12398 | 0.238195 | 0.119098 | − | 0.992883i | \(-0.462000\pi\) | ||||
0.119098 | + | 0.992883i | \(0.462000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.717702 | − | 1.61293i | −0.0278732 | − | 0.0626411i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30.9810 | − | 6.82345i | −1.20139 | − | 0.264602i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.767691 | + | 1.32968i | 0.0297251 | + | 0.0514854i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.0004 | + | 2.10655i | 0.773261 | + | 0.0814439i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00969 | − | 3.48089i | −0.0775832 | − | 0.134378i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.36248 | + | 7.55603i | −0.168161 | + | 0.291264i | −0.937773 | − | 0.347248i | \(-0.887116\pi\) |
0.769612 | + | 0.638512i | \(0.220450\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.615524 | − | 2.90518i | −0.0236915 | − | 0.111820i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.9601 | 0.574965 | 0.287482 | − | 0.957786i | \(-0.407182\pi\) | ||||
0.287482 | + | 0.957786i | \(0.407182\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.9936 | − | 30.6345i | 1.07430 | − | 1.17564i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5224 | − | 14.4762i | 0.403219 | − | 0.554728i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.89558 | − | 15.4076i | 0.340380 | − | 0.589555i | −0.644123 | − | 0.764922i | \(-0.722778\pi\) |
0.984503 | + | 0.175366i | \(0.0561110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.6347 | 1.17049 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.41437 | + | 0.675595i | 0.244724 | + | 0.0257756i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.9948 | −0.456964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.5389 | 1.12371 | 0.561856 | − | 0.827235i | \(-0.310087\pi\) | ||||
0.561856 | + | 0.827235i | \(0.310087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.88352 | + | 1.31081i | 0.109536 | + | 0.0497935i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.3198 | −0.581115 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.850324 | −0.0322083 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.2212 | + | 37.4495i | −1.02960 | + | 1.41647i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7740 | 1.04901 | 0.524504 | − | 0.851408i | \(-0.324251\pi\) | ||||
0.524504 | + | 0.851408i | \(0.324251\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.3470 | + | 33.5100i | −0.729687 | + | 1.26385i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 42.5458 | + | 4.48114i | 1.60237 | + | 0.168770i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0741998 | − | 0.234204i | −0.00279057 | − | 0.00880814i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.0984 | 1.76882 | 0.884409 | − | 0.466712i | \(-0.154562\pi\) | ||||
0.884409 | + | 0.466712i | \(0.154562\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.99539 | + | 5.54307i | −0.187342 | + | 0.207881i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00732 | − | 6.94088i | 0.150075 | − | 0.259938i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.21175 | − | 2.09881i | −0.0453169 | − | 0.0784912i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.1385 | − | 19.4510i | 0.528011 | − | 0.726411i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.63394 | − | 2.83007i | −0.0609357 | − | 0.105544i | 0.833948 | − | 0.551843i | \(-0.186075\pi\) |
−0.894884 | + | 0.446299i | \(0.852742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.5440 | − | 38.8971i | 1.32373 | − | 1.44860i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.1796 | − | 20.8833i | 0.564534 | − | 0.776658i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00014 | 0.0371444 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.37047 | − | 11.0340i | 0.236268 | − | 0.409228i | −0.723373 | − | 0.690458i | \(-0.757409\pi\) |
0.959640 | + | 0.281230i | \(0.0907424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8226 | + | 15.8988i | 0.808246 | + | 0.588845i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0977441 | − | 0.169298i | −0.00361520 | − | 0.00626170i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.58858 | + | 7.94765i | −0.169483 | + | 0.293553i | −0.938238 | − | 0.345990i | \(-0.887543\pi\) |
0.768755 | + | 0.639543i | \(0.220876\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.9035 | − | 13.0853i | −0.807923 | − | 0.482657i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.239919 | − | 0.415552i | −0.00883754 | − | 0.0153071i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.3467 | − | 40.4377i | 0.858823 | − | 1.48752i | −0.0142303 | − | 0.999899i | \(-0.504530\pi\) |
0.873053 | − | 0.487626i | \(-0.162137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.3232 | + | 2.98314i | 1.04048 | + | 0.109588i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.62654 | + | 13.2095i | 0.279790 | + | 0.484611i | 0.971333 | − | 0.237725i | \(-0.0764017\pi\) |
−0.691542 | + | 0.722336i | \(0.743068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.759333 | + | 1.31520i | 0.0278198 | + | 0.0481853i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.50565 | + | 26.2167i | 0.311205 | + | 0.959218i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.62226 | − | 14.5897i | −0.168894 | − | 0.533095i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.17443 | − | 5.49828i | 0.115837 | − | 0.200635i | −0.802277 | − | 0.596952i | \(-0.796378\pi\) |
0.918114 | + | 0.396317i | \(0.129712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.8795 | − | 35.6869i | −0.578681 | − | 1.30050i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.8850 | −1.66993 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4278 | 1.03323 | 0.516614 | − | 0.856219i | \(-0.327192\pi\) | ||||
0.516614 | + | 0.856219i | \(0.327192\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.246538 | − | 0.554059i | −0.00894876 | − | 0.0201111i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.03437 | − | 15.6480i | 0.327496 | − | 0.567239i | −0.654519 | − | 0.756046i | \(-0.727129\pi\) |
0.982014 | + | 0.188807i | \(0.0604620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.3278 | − | 24.4341i | 0.808320 | − | 0.884575i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.18084 | + | 0.464548i | 0.0788484 | + | 0.0167958i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.4541 | + | 23.3032i | 0.485799 | + | 0.841429i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.72471 | − | 2.98728i | −0.0621946 | − | 0.107724i | 0.833252 | − | 0.552894i | \(-0.186477\pi\) |
−0.895446 | + | 0.445170i | \(0.853143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.4899 | − | 2.15810i | −0.737926 | − | 0.0777222i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.1837 | + | 34.9592i | −0.725957 | + | 1.25740i | 0.232621 | + | 0.972567i | \(0.425270\pi\) |
−0.958579 | + | 0.284828i | \(0.908064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.61036 | − | 4.52127i | −0.0937668 | − | 0.162409i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.2841 | + | 20.6483i | −0.835311 | + | 0.740753i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.85880 | − | 11.8798i | 0.245742 | − | 0.425638i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.92964 | + | 5.07429i | 0.104831 | + | 0.181572i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.76158 | + | 6.08013i | −0.241639 | + | 0.217286i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.45010 | + | 9.43985i | −0.194522 | + | 0.336923i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.3206 | −0.653060 | −0.326530 | − | 0.945187i | \(-0.605879\pi\) | ||||
−0.326530 | + | 0.945187i | \(0.605879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.0582 | + | 34.4738i | −0.892095 | + | 1.22730i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.70744 | − | 8.54575i | −0.0962656 | − | 0.303852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.5331 | − | 25.1721i | −0.516086 | − | 0.893888i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.90751 | − | 12.2545i | 0.315917 | − | 0.434622i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.86884 | − | 8.43307i | −0.172463 | − | 0.298715i | 0.766817 | − | 0.641865i | \(-0.221839\pi\) |
−0.939280 | + | 0.343151i | \(0.888506\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.07274 | − | 3.59009i | 0.0733283 | − | 0.127008i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42.8012 | − | 9.11723i | −1.51231 | − | 0.322141i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.251918 | 0.00888998 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.47535 | + | 4.65679i | 0.0519993 | + | 0.164130i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.2789 | + | 2.45186i | 0.819458 | + | 0.0863095i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.98714 | + | 10.3700i | −0.210497 | + | 0.364591i | −0.951870 | − | 0.306502i | \(-0.900841\pi\) |
0.741373 | + | 0.671093i | \(0.234175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.05517 | −0.142396 | −0.0711982 | − | 0.997462i | \(-0.522682\pi\) | ||||
−0.0711982 | + | 0.997462i | \(0.522682\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.73323 | + | 3.76024i | −0.0958586 | + | 0.131877i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.1072 | 0.389070 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.15365 | 0.110332 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.8522 | + | 9.47915i | 0.728636 | + | 0.331228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.98513 | 0.278683 | 0.139341 | − | 0.990244i | \(-0.455501\pi\) | ||||
0.139341 | + | 0.990244i | \(0.455501\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.5802 | −1.65854 | −0.829270 | − | 0.558847i | \(-0.811244\pi\) | ||||
−0.829270 | + | 0.558847i | \(0.811244\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.392856 | − | 0.0413776i | −0.0136775 | − | 0.00144058i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2725 | 1.01790 | 0.508952 | − | 0.860795i | \(-0.330033\pi\) | ||||
0.508952 | + | 0.860795i | \(0.330033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.15249 | − | 5.46028i | 0.109491 | − | 0.189643i | −0.806073 | − | 0.591816i | \(-0.798411\pi\) |
0.915564 | + | 0.402172i | \(0.131745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.4026 | − | 26.6931i | 0.673067 | − | 0.925972i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.02130 | + | 1.42366i | −0.0700339 | + | 0.0493270i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.7760 | −0.995833 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.1336 | + | 14.6975i | 1.56004 | + | 0.508020i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.501711 | − | 0.868989i | 0.0173210 | − | 0.0300008i | −0.857235 | − | 0.514925i | \(-0.827820\pi\) |
0.874556 | + | 0.484925i | \(0.161153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9688 | + | 22.4626i | 0.447199 | + | 0.774571i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.9218 | + | 5.15270i | 1.68496 | + | 0.177468i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.91578 | + | 8.51438i | 0.169108 | + | 0.292904i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.3480 | + | 21.1733i | −0.664806 | + | 0.727522i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.8594 | + | 24.4049i | 0.372692 | + | 0.837573i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.95827 | 0.204247 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.0519 | − | 34.7309i | 0.686565 | − | 1.18916i | −0.286378 | − | 0.958117i | \(-0.592451\pi\) |
0.972942 | − | 0.231048i | \(-0.0742154\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.0810 | + | 26.7212i | −0.823553 | + | 0.913845i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.7388 | + | 32.4566i | 0.640106 | + | 1.10870i | 0.985409 | + | 0.170205i | \(0.0544428\pi\) |
−0.345303 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.2516 | − | 21.2204i | 0.418019 | − | 0.724031i | −0.577721 | − | 0.816234i | \(-0.696058\pi\) |
0.995740 | + | 0.0922036i | \(0.0293911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.25454 | − | 7.32012i | 0.281314 | − | 0.249469i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.79806 | − | 16.9707i | −0.333530 | − | 0.577691i | 0.649671 | − | 0.760215i | \(-0.274906\pi\) |
−0.983201 | + | 0.182524i | \(0.941573\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.2359 | + | 36.7816i | −0.722041 | + | 1.25061i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.1854 | + | 23.6428i | −0.583648 | + | 0.802953i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.496294 | + | 0.859607i | 0.0168356 | + | 0.0291602i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.73498 | − | 3.00508i | −0.0587876 | − | 0.101823i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.5211 | − | 44.7580i | −0.491466 | − | 1.51483i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.2945 | + | 6.67226i | 1.02414 | + | 0.225564i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.1134 | + | 29.6414i | −0.577880 | + | 1.00092i | 0.417842 | + | 0.908520i | \(0.362786\pi\) |
−0.995722 | + | 0.0923977i | \(0.970547\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.3767 | + | 25.2818i | −0.619832 | + | 0.852733i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.2818 | −0.851764 | −0.425882 | − | 0.904779i | \(-0.640036\pi\) | ||||
−0.425882 | + | 0.904779i | \(0.640036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.4688 | 1.53015 | 0.765073 | − | 0.643943i | \(-0.222703\pi\) | ||||
0.765073 | + | 0.643943i | \(0.222703\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.7991 | − | 3.55989i | −1.13614 | − | 0.119664i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.41504 | − | 9.37912i | 0.181819 | − | 0.314920i | −0.760681 | − | 0.649126i | \(-0.775135\pi\) |
0.942500 | + | 0.334206i | \(0.108468\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.0722 | + | 8.38527i | 1.27690 | + | 0.281233i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.90749 | − | 2.10854i | 0.0974046 | − | 0.0706386i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.4378 | + | 57.9160i | 1.11895 | + | 1.93809i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.5087 | − | 45.9143i | −0.886086 | − | 1.53475i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.78284 | − | 4.00669i | −0.0595274 | − | 0.133779i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.99301 | + | 13.8443i | −0.266582 | + | 0.461733i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.734005 | − | 1.27133i | −0.0244533 | − | 0.0423543i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.40627 | + | 0.802019i | 0.0800757 | + | 0.0266895i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.1836 | − | 31.4949i | 0.604443 | − | 1.04693i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.00841 | + | 3.47868i | 0.0666883 | + | 0.115508i | 0.897442 | − | 0.441133i | \(-0.145423\pi\) |
−0.830753 | + | 0.556641i | \(0.812090\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.272458 | − | 0.0580373i | −0.00903688 | − | 0.00192498i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.43681 | − | 14.6130i | 0.279524 | − | 0.484150i | −0.691743 | − | 0.722144i | \(-0.743157\pi\) |
0.971266 | + | 0.237995i | \(0.0764901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.66633 | 0.121338 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.5098 | + | 3.84540i | 1.20698 | + | 0.127125i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.8220 | − | 27.1637i | 0.819695 | − | 0.897023i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9485 | + | 29.3557i | 0.559081 | + | 0.968356i | 0.997573 | + | 0.0696214i | \(0.0221791\pi\) |
−0.438493 | + | 0.898735i | \(0.644488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.14630 | + | 11.5656i | 0.169576 | + | 0.381099i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.1858 | + | 36.6949i | 0.697339 | + | 1.20783i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.94060 | − | 3.36122i | 0.0638065 | − | 0.110516i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.4377 | − | 56.8300i | −0.605575 | − | 1.86654i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.6100 | −1.26675 | −0.633377 | − | 0.773843i | \(-0.718332\pi\) | ||||
−0.633377 | + | 0.773843i | \(0.718332\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.58584 | − | 39.7228i | −0.117521 | − | 1.30186i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.7440 | + | 37.6297i | 0.548172 | + | 1.23194i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.148303 | − | 0.256869i | 0.00485004 | − | 0.00840052i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.4955 | −1.48627 | −0.743136 | − | 0.669140i | \(-0.766663\pi\) | ||||
−0.743136 | + | 0.669140i | \(0.766663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.8793 | − | 28.9443i | −0.420298 | − | 0.944561i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.9892 | −0.586431 | −0.293216 | − | 0.956046i | \(-0.594725\pi\) | ||||
−0.293216 | + | 0.956046i | \(0.594725\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.11229 | −0.0687857 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.1696 | + | 14.2644i | −0.818769 | + | 0.464021i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.5224 | −0.536906 | −0.268453 | − | 0.963293i | \(-0.586512\pi\) | ||||
−0.268453 | + | 0.963293i | \(0.586512\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.82175 | 0.0591365 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.30234 | − | 7.42155i | −0.107086 | − | 0.240660i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.6799 | −0.507922 | −0.253961 | − | 0.967214i | \(-0.581734\pi\) | ||||
−0.253961 | + | 0.967214i | \(0.581734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.28096 | + | 9.14690i | −0.170888 | + | 0.295987i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.491745 | + | 1.10513i | 0.0158959 | + | 0.0357237i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.6325 | + | 36.7168i | 0.375634 | + | 1.18565i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.4465 | 1.69182 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.9727 | − | 3.61542i | −0.546938 | − | 0.116505i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.72149 | − | 9.90991i | 0.184181 | − | 0.319011i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.3908 | + | 43.9782i | 0.816513 | + | 1.41424i | 0.908236 | + | 0.418458i | \(0.137429\pi\) |
−0.0917230 | + | 0.995785i | \(0.529237\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.41702 | + | 3.18455i | 0.0455212 | + | 0.102302i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.23027 | + | 15.9873i | 0.296214 | + | 0.513057i | 0.975266 | − | 0.221032i | \(-0.0709427\pi\) |
−0.679053 | + | 0.734089i | \(0.737609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.81721 | − | 18.3614i | −0.186491 | − | 0.588639i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.84095 | − | 0.299223i | −0.0909832 | − | 0.00958282i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.6302 | 1.01194 | 0.505970 | − | 0.862551i | \(-0.331135\pi\) | ||||
0.505970 | + | 0.862551i | \(0.331135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.91061 | + | 5.04132i | −0.0930234 | + | 0.161121i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.5821 | − | 35.6991i | −0.369788 | − | 1.13979i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.2066 | + | 34.9988i | 0.644490 | + | 1.11629i | 0.984419 | + | 0.175838i | \(0.0562635\pi\) |
−0.339929 | + | 0.940451i | \(0.610403\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.26940 | + | 10.8589i | −0.199760 | + | 0.345994i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.7846 | + | 52.6943i | 0.343276 | + | 1.67728i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.242806 | − | 0.420553i | −0.00772079 | − | 0.0133728i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.6187 | + | 28.7845i | −0.527911 | + | 0.914368i | 0.471560 | + | 0.881834i | \(0.343691\pi\) |
−0.999471 | + | 0.0325343i | \(0.989642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.04741 | + | 18.0854i | 0.255377 | + | 0.573923i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.8280 | − | 20.4867i | −0.374973 | − | 0.649473i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5592 | + | 35.6096i | 0.651117 | + | 1.12777i | 0.982852 | + | 0.184396i | \(0.0590328\pi\) |
−0.331735 | + | 0.943373i | \(0.607634\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.31408 | + | 34.5213i | 0.231407 | + | 1.09220i |
(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 | 1008.2.q.l.529.7 | 22 | ||
3.2 | odd | 2 | 3024.2.q.l.2881.8 | 22 | |||
4.3 | odd | 2 | 504.2.q.c.25.5 | ✓ | 22 | ||
7.2 | even | 3 | 1008.2.t.l.961.1 | 22 | |||
9.4 | even | 3 | 1008.2.t.l.193.1 | 22 | |||
9.5 | odd | 6 | 3024.2.t.k.1873.4 | 22 | |||
12.11 | even | 2 | 1512.2.q.d.1369.8 | 22 | |||
21.2 | odd | 6 | 3024.2.t.k.289.4 | 22 | |||
28.23 | odd | 6 | 504.2.t.c.457.11 | yes | 22 | ||
36.23 | even | 6 | 1512.2.t.c.361.4 | 22 | |||
36.31 | odd | 6 | 504.2.t.c.193.11 | yes | 22 | ||
63.23 | odd | 6 | 3024.2.q.l.2305.8 | 22 | |||
63.58 | even | 3 | inner | 1008.2.q.l.625.7 | 22 | ||
84.23 | even | 6 | 1512.2.t.c.289.4 | 22 | |||
252.23 | even | 6 | 1512.2.q.d.793.8 | 22 | |||
252.247 | odd | 6 | 504.2.q.c.121.5 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.5 | ✓ | 22 | 4.3 | odd | 2 | ||
504.2.q.c.121.5 | yes | 22 | 252.247 | odd | 6 | ||
504.2.t.c.193.11 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.c.457.11 | yes | 22 | 28.23 | odd | 6 | ||
1008.2.q.l.529.7 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.q.l.625.7 | 22 | 63.58 | even | 3 | inner | ||
1008.2.t.l.193.1 | 22 | 9.4 | even | 3 | |||
1008.2.t.l.961.1 | 22 | 7.2 | even | 3 | |||
1512.2.q.d.793.8 | 22 | 252.23 | even | 6 | |||
1512.2.q.d.1369.8 | 22 | 12.11 | even | 2 | |||
1512.2.t.c.289.4 | 22 | 84.23 | even | 6 | |||
1512.2.t.c.361.4 | 22 | 36.23 | even | 6 | |||
3024.2.q.l.2305.8 | 22 | 63.23 | odd | 6 | |||
3024.2.q.l.2881.8 | 22 | 3.2 | odd | 2 | |||
3024.2.t.k.289.4 | 22 | 21.2 | odd | 6 | |||
3024.2.t.k.1873.4 | 22 | 9.5 | odd | 6 |