Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(145,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.be (of order \(6\), 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: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 51 x^{18} + 314 x^{17} + 631 x^{16} - 7264 x^{15} + 8030 x^{14} + 12664 x^{13} + \cdots + 26753228352 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Root | \(-2.00924 + 3.91523i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.145 |
Dual form | 912.3.be.i.673.3 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.33973 | − | 4.05253i | −0.467946 | − | 0.810506i | 0.531383 | − | 0.847132i | \(-0.321672\pi\) |
−0.999329 | + | 0.0366255i | \(0.988339\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.94782 | −0.563974 | −0.281987 | − | 0.959418i | \(-0.590994\pi\) | ||||
−0.281987 | + | 0.959418i | \(0.590994\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.3784 | 1.76168 | 0.880838 | − | 0.473418i | \(-0.156980\pi\) | ||||
0.880838 | + | 0.473418i | \(0.156980\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.2230 | − | 7.63431i | −1.01715 | − | 0.587254i | −0.103876 | − | 0.994590i | \(-0.533124\pi\) |
−0.913278 | + | 0.407336i | \(0.866458\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.01919 | + | 4.05253i | 0.467946 | + | 0.270169i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.802147 | + | 1.38936i | 0.0471851 | + | 0.0817270i | 0.888653 | − | 0.458580i | \(-0.151642\pi\) |
−0.841468 | + | 0.540307i | \(0.818308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.1147 | + | 16.0839i | −0.532354 | + | 0.846522i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.92173 | − | 3.41891i | 0.281987 | − | 0.162805i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 15.9684 | − | 27.6580i | 0.694276 | − | 1.20252i | −0.276148 | − | 0.961115i | \(-0.589058\pi\) |
0.970424 | − | 0.241407i | \(-0.0776088\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.55133 | − | 2.68698i | 0.0620532 | − | 0.107479i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.68452 | − | 2.12726i | −0.127052 | − | 0.0733537i | 0.435127 | − | 0.900369i | \(-0.356704\pi\) |
−0.562179 | + | 0.827015i | \(0.690037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.43590i | − | 0.239868i | −0.992782 | − | 0.119934i | \(-0.961732\pi\) | ||
0.992782 | − | 0.119934i | \(-0.0382682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −29.0677 | + | 16.7822i | −0.880838 | + | 0.508552i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.23684 | + | 15.9987i | 0.263910 | + | 0.457105i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.72980i | − | 0.100805i | −0.998729 | − | 0.0504026i | \(-0.983950\pi\) | ||
0.998729 | − | 0.0504026i | \(-0.0160505\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 26.4460 | 0.678103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −53.4137 | + | 30.8384i | −1.30277 | + | 0.752157i | −0.980879 | − | 0.194618i | \(-0.937653\pi\) |
−0.321895 | + | 0.946775i | \(0.604320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 28.1611 | + | 48.7764i | 0.654909 | + | 1.13434i | 0.981917 | + | 0.189314i | \(0.0606264\pi\) |
−0.327008 | + | 0.945022i | \(0.606040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.0384 | −0.311964 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −23.2709 | + | 40.3064i | −0.495126 | + | 0.857584i | −0.999984 | − | 0.00561857i | \(-0.998212\pi\) |
0.504858 | + | 0.863202i | \(0.331545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.4147 | −0.681933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.40644 | − | 1.38936i | −0.0471851 | − | 0.0272423i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −50.8905 | − | 29.3816i | −0.960198 | − | 0.554370i | −0.0639637 | − | 0.997952i | \(-0.520374\pi\) |
−0.896234 | + | 0.443582i | \(0.853708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −45.3403 | − | 78.5317i | −0.824369 | − | 1.42785i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.24302 | − | 32.8855i | 0.0218074 | − | 0.576938i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −55.0501 | + | 31.7832i | −0.933052 | + | 0.538698i | −0.887775 | − | 0.460277i | \(-0.847750\pi\) |
−0.0452763 | + | 0.998975i | \(0.514417\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.5481 | − | 23.4660i | 0.222100 | − | 0.384689i | −0.733345 | − | 0.679856i | \(-0.762042\pi\) |
0.955446 | + | 0.295167i | \(0.0953754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.92173 | + | 10.2567i | −0.0939957 | + | 0.162805i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 71.4489i | 1.09921i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −53.4750 | − | 30.8738i | −0.798134 | − | 0.460803i | 0.0446842 | − | 0.999001i | \(-0.485772\pi\) |
−0.842818 | + | 0.538198i | \(0.819105\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 55.3160i | 0.801681i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −62.4861 | + | 36.0763i | −0.880085 | + | 0.508118i | −0.870687 | − | 0.491838i | \(-0.836325\pi\) |
−0.00939883 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18.7010 | − | 32.3912i | −0.256179 | − | 0.443715i | 0.709036 | − | 0.705172i | \(-0.249130\pi\) |
−0.965215 | + | 0.261457i | \(0.915797\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.37396i | 0.0716528i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −76.5026 | −0.993540 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −55.7126 | + | 32.1657i | −0.705223 | + | 0.407160i | −0.809290 | − | 0.587410i | \(-0.800148\pi\) |
0.104067 | + | 0.994570i | \(0.466814\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.24425 | −0.0872801 | −0.0436400 | − | 0.999047i | \(-0.513895\pi\) | ||||
−0.0436400 | + | 0.999047i | \(0.513895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.75361 | − | 6.50145i | 0.0441602 | − | 0.0764877i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.36904 | 0.0847016 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −56.2548 | − | 32.4787i | −0.632076 | − | 0.364929i | 0.149480 | − | 0.988765i | \(-0.452240\pi\) |
−0.781556 | + | 0.623836i | \(0.785573\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 52.2021 | + | 30.1389i | 0.573649 | + | 0.331196i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.43968 | + | 11.1538i | 0.0692438 | + | 0.119934i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 88.8463 | + | 3.35826i | 0.935224 | + | 0.0353501i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 127.071 | − | 73.3643i | 1.31001 | − | 0.756333i | 0.327910 | − | 0.944709i | \(-0.393656\pi\) |
0.982097 | + | 0.188376i | \(0.0603225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29.0677 | − | 50.3467i | 0.293613 | − | 0.508552i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −60.9597 | + | 105.585i | −0.603561 | + | 1.04540i | 0.388716 | + | 0.921358i | \(0.372919\pi\) |
−0.992277 | + | 0.124041i | \(0.960415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 157.182i | − | 1.52604i | −0.646374 | − | 0.763020i | \(-0.723716\pi\) | ||
0.646374 | − | 0.763020i | \(-0.276284\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −27.7105 | − | 15.9987i | −0.263910 | − | 0.152368i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 173.040i | 1.61719i | 0.588364 | + | 0.808597i | \(0.299772\pi\) | ||||
−0.588364 | + | 0.808597i | \(0.700228\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −91.1417 | + | 52.6207i | −0.836163 | + | 0.482759i | −0.855958 | − | 0.517045i | \(-0.827032\pi\) |
0.0197954 | + | 0.999804i | \(0.493699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.23010 | + | 5.59469i | 0.0291000 | + | 0.0504026i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 57.5510i | − | 0.509301i | −0.967033 | − | 0.254650i | \(-0.918040\pi\) | ||
0.967033 | − | 0.254650i | \(-0.0819603\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −149.447 | −1.29954 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −39.6690 | + | 22.9029i | −0.339051 | + | 0.195751i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.16673 | − | 5.48494i | −0.0266112 | − | 0.0460920i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 254.524 | 2.10350 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 53.4137 | − | 92.5153i | 0.434258 | − | 0.752157i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −131.505 | −1.05204 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −65.9889 | − | 38.0987i | −0.519597 | − | 0.299990i | 0.217173 | − | 0.976133i | \(-0.430317\pi\) |
−0.736770 | + | 0.676144i | \(0.763650\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −84.4833 | − | 48.7764i | −0.654909 | − | 0.378112i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −113.903 | − | 197.286i | −0.869491 | − | 1.50600i | −0.862518 | − | 0.506027i | \(-0.831114\pi\) |
−0.00697352 | − | 0.999976i | \(-0.502220\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 39.9312 | − | 63.4964i | 0.300234 | − | 0.477417i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.0576 | − | 12.1576i | 0.155982 | − | 0.0900562i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 51.4290 | − | 89.0777i | 0.375394 | − | 0.650202i | −0.614992 | − | 0.788534i | \(-0.710841\pi\) |
0.990386 | + | 0.138331i | \(0.0441739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −119.474 | + | 206.935i | −0.859523 | + | 1.48874i | 0.0128609 | + | 0.999917i | \(0.495906\pi\) |
−0.872384 | + | 0.488821i | \(0.837427\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 80.6129i | − | 0.571723i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −256.241 | − | 147.941i | −1.79190 | − | 1.03455i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.9088i | 0.137302i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 50.1221 | − | 28.9380i | 0.340966 | − | 0.196857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 61.0326 | + | 105.712i | 0.409615 | + | 0.709473i | 0.994846 | − | 0.101393i | \(-0.0323299\pi\) |
−0.585232 | + | 0.810866i | \(0.698997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 27.9696i | 0.185229i | 0.995702 | + | 0.0926146i | \(0.0295224\pi\) | ||||
−0.995702 | + | 0.0926146i | \(0.970478\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.81288 | 0.0314567 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.1342 | + | 17.3980i | −0.194414 | + | 0.112245i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 140.481 | + | 243.321i | 0.894785 | + | 1.54981i | 0.834071 | + | 0.551657i | \(0.186004\pi\) |
0.0607139 | + | 0.998155i | \(0.480662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 101.781 | 0.640132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −63.0402 | + | 109.189i | −0.391554 | + | 0.678192i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −156.155 | −0.958009 | −0.479004 | − | 0.877813i | \(-0.659002\pi\) | ||||
−0.479004 | + | 0.877813i | \(0.659002\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 136.021 | + | 78.5317i | 0.824369 | + | 0.475950i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −165.655 | − | 95.6412i | −0.991949 | − | 0.572702i | −0.0860926 | − | 0.996287i | \(-0.527438\pi\) |
−0.905856 | + | 0.423585i | \(0.860771\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.0653 | + | 55.5386i | 0.189735 | + | 0.328631i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.6151 | + | 50.4047i | 0.155644 | + | 0.294764i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 79.9046 | − | 46.1329i | 0.461876 | − | 0.266664i | −0.250957 | − | 0.967998i | \(-0.580745\pi\) |
0.712833 | + | 0.701334i | \(0.247412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.12437 | + | 10.6077i | −0.0349964 | + | 0.0606156i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 55.0501 | − | 95.3495i | 0.311017 | − | 0.538698i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 239.687i | 1.33904i | 0.742796 | + | 0.669518i | \(0.233499\pi\) | ||||
−0.742796 | + | 0.669518i | \(0.766501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −164.571 | − | 95.0153i | −0.909234 | − | 0.524946i | −0.0290491 | − | 0.999578i | \(-0.509248\pi\) |
−0.880184 | + | 0.474632i | \(0.842581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 46.9321i | 0.256459i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.1151 | + | 8.72671i | −0.0817033 | + | 0.0471714i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.5444 | + | 26.9236i | 0.0831249 | + | 0.143977i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 20.5135i | − | 0.108537i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 276.040 | 1.44523 | 0.722617 | − | 0.691249i | \(-0.242939\pi\) | ||||
0.722617 | + | 0.691249i | \(0.242939\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 144.476 | − | 83.4131i | 0.748579 | − | 0.432192i | −0.0766010 | − | 0.997062i | \(-0.524407\pi\) |
0.825180 | + | 0.564869i | \(0.191073\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −61.8765 | − | 107.173i | −0.317315 | − | 0.549607i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.7356 | 0.0798761 | 0.0399381 | − | 0.999202i | \(-0.487284\pi\) | ||||
0.0399381 | + | 0.999202i | \(0.487284\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −33.1412 | + | 57.4022i | −0.166539 | + | 0.288453i | −0.937201 | − | 0.348791i | \(-0.886592\pi\) |
0.770662 | + | 0.637244i | \(0.219926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 106.950 | 0.532089 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.5458 | + | 8.39803i | 0.0716543 | + | 0.0413696i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 249.947 | + | 144.307i | 1.21926 | + | 0.703938i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −47.9051 | − | 82.9740i | −0.231425 | − | 0.400841i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −196.008 | + | 311.681i | −0.937836 | + | 1.49130i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.26033 | − | 3.03705i | 0.0249305 | − | 0.0143936i | −0.487483 | − | 0.873132i | \(-0.662085\pi\) |
0.512413 | + | 0.858739i | \(0.328752\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 62.4861 | − | 108.229i | 0.293362 | − | 0.508118i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 131.779 | − | 228.247i | 0.612924 | − | 1.06162i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.3556i | 0.135279i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 56.1031 | + | 32.3912i | 0.256179 | + | 0.147905i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 24.4953i | − | 0.110839i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 200.656 | − | 115.849i | 0.899801 | − | 0.519500i | 0.0226655 | − | 0.999743i | \(-0.492785\pi\) |
0.877136 | + | 0.480243i | \(0.159451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65399 | − | 8.06094i | −0.0206844 | − | 0.0358264i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 159.880i | 0.704316i | 0.935941 | + | 0.352158i | \(0.114552\pi\) | ||||
−0.935941 | + | 0.352158i | \(0.885448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −50.8060 | −0.221860 | −0.110930 | − | 0.993828i | \(-0.535383\pi\) | ||||
−0.110930 | + | 0.993828i | \(0.535383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 114.754 | − | 66.2532i | 0.496770 | − | 0.286810i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 89.4791 | + | 154.982i | 0.384031 | + | 0.665160i | 0.991634 | − | 0.129080i | \(-0.0412024\pi\) |
−0.607604 | + | 0.794240i | \(0.707869\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 217.791 | 0.926769 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 55.7126 | − | 96.4970i | 0.235074 | − | 0.407160i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 230.403 | 0.964029 | 0.482015 | − | 0.876163i | \(-0.339905\pi\) | ||||
0.482015 | + | 0.876163i | \(0.339905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 49.3942 | + | 28.5178i | 0.204955 | + | 0.118331i | 0.598965 | − | 0.800775i | \(-0.295579\pi\) |
−0.394009 | + | 0.919106i | \(0.628912\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 78.1814 | + | 135.414i | 0.319108 | + | 0.552711i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 256.537 | − | 135.459i | 1.03861 | − | 0.548416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.8664 | − | 6.27370i | 0.0436400 | − | 0.0251956i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −132.396 | + | 229.317i | −0.527475 | + | 0.913613i | 0.472012 | + | 0.881592i | \(0.343528\pi\) |
−0.999487 | + | 0.0320214i | \(0.989806\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 309.442 | − | 535.969i | 1.22309 | − | 2.11845i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.0029i | 0.0509918i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −336.523 | − | 194.291i | −1.30943 | − | 0.755998i | −0.327426 | − | 0.944877i | \(-0.606181\pi\) |
−0.982000 | + | 0.188879i | \(0.939515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.7246i | 0.0568516i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.0536 | + | 6.38177i | −0.0423508 | + | 0.0244512i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 178.514 | + | 309.195i | 0.678759 | + | 1.17565i | 0.975355 | + | 0.220642i | \(0.0708152\pi\) |
−0.296596 | + | 0.955003i | \(0.595851\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 274.980i | 1.03766i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 112.510 | 0.421384 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 57.3739 | − | 33.1249i | 0.213286 | − | 0.123141i | −0.389552 | − | 0.921005i | \(-0.627370\pi\) |
0.602838 | + | 0.797864i | \(0.294037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 104.603 | + | 181.178i | 0.385990 | + | 0.668554i | 0.991906 | − | 0.126975i | \(-0.0405267\pi\) |
−0.605916 | + | 0.795528i | \(0.707193\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −104.404 | −0.382433 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.0623 | − | 52.0695i | 0.109318 | − | 0.189344i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −378.194 | −1.36532 | −0.682662 | − | 0.730735i | \(-0.739178\pi\) | ||||
−0.682662 | + | 0.730735i | \(0.739178\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.3190 | − | 11.1538i | −0.0692438 | − | 0.0399780i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 130.762 | + | 75.4952i | 0.465343 | + | 0.268666i | 0.714288 | − | 0.699851i | \(-0.246750\pi\) |
−0.248945 | + | 0.968518i | \(0.580084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.64143 | − | 9.77125i | −0.0199344 | − | 0.0345274i | 0.855886 | − | 0.517164i | \(-0.173012\pi\) |
−0.875821 | + | 0.482637i | \(0.839679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −136.178 | + | 71.9058i | −0.477817 | + | 0.252301i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 210.868 | − | 121.745i | 0.734731 | − | 0.424197i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 143.213 | − | 248.052i | 0.495547 | − | 0.858313i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −127.071 | + | 220.093i | −0.436669 | + | 0.756333i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 284.454i | − | 0.970834i | −0.874283 | − | 0.485417i | \(-0.838668\pi\) | ||
0.874283 | − | 0.485417i | \(-0.161332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 257.604 | + | 148.728i | 0.873236 | + | 0.504163i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 100.693i | 0.339035i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −422.299 | + | 243.815i | −1.41237 | + | 0.815434i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −111.175 | − | 192.561i | −0.369352 | − | 0.639736i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 211.171i | − | 0.696933i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −126.796 | −0.415724 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 470.039 | − | 271.377i | 1.53107 | − | 0.883964i | 0.531757 | − | 0.846897i | \(-0.321532\pi\) |
0.999313 | − | 0.0370670i | \(-0.0118015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 136.124 | + | 235.773i | 0.440530 | + | 0.763020i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −462.767 | −1.48800 | −0.743998 | − | 0.668182i | \(-0.767073\pi\) | ||||
−0.743998 | + | 0.668182i | \(0.767073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 77.0082 | − | 133.382i | 0.246033 | − | 0.426141i | −0.716389 | − | 0.697701i | \(-0.754206\pi\) |
0.962421 | + | 0.271560i | \(0.0875396\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 55.4210 | 0.175940 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −62.9859 | − | 36.3649i | −0.198694 | − | 0.114716i | 0.397352 | − | 0.917666i | \(-0.369929\pi\) |
−0.596046 | + | 0.802950i | \(0.703262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −71.4002 | − | 41.2229i | −0.223825 | − | 0.129225i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −149.857 | − | 259.559i | −0.466843 | − | 0.808597i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.4598 | − | 1.15134i | −0.0943029 | − | 0.00356451i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −41.0265 | + | 23.6866i | −0.126235 | + | 0.0728820i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 91.1417 | − | 157.862i | 0.278721 | − | 0.482759i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 91.8695 | − | 159.123i | 0.279239 | − | 0.483655i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 538.875i | − | 1.62802i | −0.580850 | − | 0.814011i | \(-0.697280\pi\) | ||
0.580850 | − | 0.814011i | \(-0.302720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.69029 | − | 5.59469i | −0.0291000 | − | 0.0168009i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 288.945i | 0.862523i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −163.217 | + | 94.2337i | −0.484325 | + | 0.279625i | −0.722217 | − | 0.691666i | \(-0.756877\pi\) |
0.237892 | + | 0.971292i | \(0.423544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 49.8406 | + | 86.3264i | 0.147022 | + | 0.254650i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 144.096i | − | 0.422569i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 325.359 | 0.948567 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 224.170 | − | 129.425i | 0.649768 | − | 0.375144i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 50.2667 | + | 87.0645i | 0.144861 | + | 0.250906i | 0.929321 | − | 0.369273i | \(-0.120393\pi\) |
−0.784460 | + | 0.620179i | \(0.787060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −94.2449 | −0.270043 | −0.135021 | − | 0.990843i | \(-0.543110\pi\) | ||||
−0.135021 | + | 0.990843i | \(0.543110\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 39.6690 | − | 68.7088i | 0.113017 | − | 0.195751i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 218.637 | 0.619368 | 0.309684 | − | 0.950840i | \(-0.399777\pi\) | ||||
0.309684 | + | 0.950840i | \(0.399777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 292.401 | + | 168.818i | 0.823665 | + | 0.475543i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.50020 | + | 5.48494i | 0.0266112 | + | 0.0153640i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −142.528 | − | 246.866i | −0.397014 | − | 0.687648i | 0.596342 | − | 0.802730i | \(-0.296620\pi\) |
−0.993356 | + | 0.115082i | \(0.963287\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −156.384 | − | 325.369i | −0.433198 | − | 0.901299i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −381.786 | + | 220.424i | −1.05175 | + | 0.607229i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −87.5108 | + | 151.573i | −0.239756 | + | 0.415269i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 211.429 | − | 366.206i | 0.576101 | − | 0.997836i | −0.419820 | − | 0.907607i | \(-0.637907\pi\) |
0.995921 | − | 0.0902289i | \(-0.0287599\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 185.031i | 0.501438i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 200.906 | + | 115.993i | 0.541527 | + | 0.312651i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 112.822i | − | 0.302473i | −0.988498 | − | 0.151237i | \(-0.951674\pi\) | ||
0.988498 | − | 0.151237i | \(-0.0483255\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 197.258 | − | 113.887i | 0.526021 | − | 0.303698i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.4803 | + | 56.2575i | 0.0861546 | + | 0.149224i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 149.551i | − | 0.394594i | −0.980344 | − | 0.197297i | \(-0.936784\pi\) | ||
0.980344 | − | 0.197297i | \(-0.0632164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 131.978 | 0.346398 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 391.265 | − | 225.897i | 1.02158 | − | 0.589809i | 0.107019 | − | 0.994257i | \(-0.465870\pi\) |
0.914561 | + | 0.404448i | \(0.132536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 178.995 | + | 310.029i | 0.464923 | + | 0.805271i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 168.967 | 0.436606 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 126.626 | − | 219.322i | 0.325516 | − | 0.563811i | −0.656100 | − | 0.754674i | \(-0.727795\pi\) |
0.981617 | + | 0.190863i | \(0.0611285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.2359 | 0.131038 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 341.710 | + | 197.286i | 0.869491 | + | 0.502001i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 260.705 | + | 150.518i | 0.660012 | + | 0.381058i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 150.685 | + | 260.994i | 0.379559 | + | 0.657416i | 0.990998 | − | 0.133876i | \(-0.0427424\pi\) |
−0.611439 | + | 0.791292i | \(0.709409\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.90723 | + | 129.826i | −0.0122988 | + | 0.325378i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −561.563 | + | 324.219i | −1.40041 | + | 0.808526i | −0.994434 | − | 0.105359i | \(-0.966401\pi\) |
−0.405973 | + | 0.913885i | \(0.633067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −56.7679 | + | 98.3249i | −0.140863 | + | 0.243982i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.0576 | + | 36.4728i | −0.0519940 | + | 0.0900562i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 72.2776i | − | 0.177586i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −212.163 | − | 122.493i | −0.518737 | − | 0.299493i | 0.217681 | − | 0.976020i | \(-0.430151\pi\) |
−0.736418 | + | 0.676527i | \(0.763484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 178.155i | 0.433468i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 217.328 | − | 125.474i | 0.526217 | − | 0.303812i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.9496 | + | 29.3575i | 0.0408424 | + | 0.0707410i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 413.869i | − | 0.992492i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.9585 | 0.0357004 | 0.0178502 | − | 0.999841i | \(-0.494318\pi\) | ||||
0.0178502 | + | 0.999841i | \(0.494318\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −139.721 | + | 80.6681i | −0.331879 | + | 0.191611i | −0.656675 | − | 0.754173i | \(-0.728038\pi\) |
0.324796 | + | 0.945784i | \(0.394704\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 69.8128 | + | 120.919i | 0.165042 | + | 0.285861i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.97758 | 0.0117119 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −53.4856 | + | 92.6397i | −0.125259 | + | 0.216955i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 512.482 | 1.19460 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −681.099 | − | 393.233i | −1.58028 | − | 0.912373i | −0.994818 | − | 0.101670i | \(-0.967581\pi\) |
−0.585458 | − | 0.810703i | \(-0.699085\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −566.404 | − | 327.014i | −1.30809 | − | 0.755228i | −0.326315 | − | 0.945261i | \(-0.605807\pi\) |
−0.981778 | + | 0.190033i | \(0.939140\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.2416 | − | 29.8633i | −0.0396358 | − | 0.0686512i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 283.333 | + | 536.587i | 0.648360 | + | 1.22789i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 445.258 | − | 257.070i | 1.01426 | − | 0.585581i | 0.101820 | − | 0.994803i | \(-0.467533\pi\) |
0.912435 | + | 0.409222i | \(0.134200\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −50.1221 | + | 86.8140i | −0.113655 | + | 0.196857i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −96.8769 | + | 167.796i | −0.218684 | + | 0.378771i | −0.954406 | − | 0.298512i | \(-0.903510\pi\) |
0.735722 | + | 0.677284i | \(0.236843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 303.966i | 0.683069i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −183.098 | − | 105.712i | −0.409615 | − | 0.236491i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 133.827i | − | 0.298056i | −0.988833 | − | 0.149028i | \(-0.952386\pi\) | ||
0.988833 | − | 0.149028i | \(-0.0476145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1035.07 | + | 597.601i | −2.29507 | + | 1.32506i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.2224 | − | 41.9544i | −0.0534710 | − | 0.0926146i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 282.067i | − | 0.619928i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −523.362 | −1.14521 | −0.572606 | − | 0.819831i | \(-0.694068\pi\) | ||||
−0.572606 | + | 0.819831i | \(0.694068\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.21932 | + | 4.16808i | −0.0157284 | + | 0.00908078i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −50.7350 | − | 87.8756i | −0.110054 | − | 0.190620i | 0.805738 | − | 0.592273i | \(-0.201769\pi\) |
−0.915792 | + | 0.401653i | \(0.868436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −847.358 | −1.83015 | −0.915074 | − | 0.403286i | \(-0.867868\pi\) | ||||
−0.915074 | + | 0.403286i | \(0.867868\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.1342 | − | 52.1940i | 0.0648048 | − | 0.112245i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 75.6277 | 0.161944 | 0.0809718 | − | 0.996716i | \(-0.474198\pi\) | ||||
0.0809718 | + | 0.996716i | \(0.474198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 211.110 | + | 121.884i | 0.450127 | + | 0.259881i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −421.444 | − | 243.321i | −0.894785 | − | 0.516604i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 545.718 | + | 945.211i | 1.15374 | + | 1.99833i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.5259 | + | 52.1295i | 0.0579492 | + | 0.109746i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −152.671 | + | 88.1449i | −0.320066 | + | 0.184790i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −246.600 | + | 427.125i | −0.514824 | + | 0.891701i | 0.485028 | + | 0.874498i | \(0.338809\pi\) |
−0.999852 | + | 0.0172022i | \(0.994524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.4744 | + | 49.3191i | −0.0591983 | + | 0.102535i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 218.378i | − | 0.452128i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −594.622 | − | 343.305i | −1.22602 | − | 0.707846i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 431.748i | − | 0.886546i | −0.896387 | − | 0.443273i | \(-0.853817\pi\) | ||
0.896387 | − | 0.443273i | \(-0.146183\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 234.233 | − | 135.235i | 0.479004 | − | 0.276553i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0053 | + | 65.8272i | 0.0774040 | + | 0.134068i | 0.902129 | − | 0.431466i | \(-0.142004\pi\) |
−0.824725 | + | 0.565534i | \(0.808670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.82549i | − | 0.0138448i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −272.042 | −0.549579 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 246.684 | − | 142.423i | 0.496346 | − | 0.286565i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 458.229 | + | 793.676i | 0.918295 | + | 1.59053i | 0.802005 | + | 0.597318i | \(0.203767\pi\) |
0.116290 | + | 0.993215i | \(0.462900\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 331.311 | 0.661299 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −164.601 | + | 285.098i | −0.327240 | + | 0.566795i | −0.981963 | − | 0.189073i | \(-0.939452\pi\) |
0.654724 | + | 0.755868i | \(0.272785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 570.517 | 1.12974 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −96.1958 | − | 55.5386i | −0.189735 | − | 0.109544i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −520.177 | − | 300.324i | −1.02196 | − | 0.590028i | −0.107287 | − | 0.994228i | \(-0.534216\pi\) |
−0.914670 | + | 0.404200i | \(0.867550\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 73.8284 | + | 127.875i | 0.144478 | + | 0.250244i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −83.5745 | − | 52.5577i | −0.162913 | − | 0.102452i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −636.986 | + | 367.764i | −1.23687 | + | 0.714105i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −450.954 | + | 781.076i | −0.872252 | + | 1.51078i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −79.9046 | + | 138.399i | −0.153959 | + | 0.266664i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 960.062i | 1.84273i | 0.388698 | + | 0.921365i | \(0.372925\pi\) | ||||
−0.388698 | + | 0.921365i | \(0.627075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 580.646 | + | 335.236i | 1.11022 | + | 0.640986i | 0.938887 | − | 0.344227i | \(-0.111859\pi\) |
0.171334 | + | 0.985213i | \(0.445192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 21.2154i | − | 0.0404104i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3311 | − | 5.96468i | 0.0196037 | − | 0.0113182i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −245.477 | − | 425.179i | −0.464040 | − | 0.803740i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 190.699i | 0.359132i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 941.720 | 1.76683 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 701.249 | − | 404.866i | 1.31074 | − | 0.756759i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −207.575 | − | 359.531i | −0.386546 | − | 0.669518i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −647.525 | −1.20134 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 381.031 | − | 659.964i | 0.704308 | − | 1.21990i | −0.262633 | − | 0.964896i | \(-0.584591\pi\) |
0.966941 | − | 0.255001i | \(-0.0820759\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 329.143 | 0.606156 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 426.494 | + | 246.236i | 0.782558 | + | 0.451810i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 246.215 | + | 142.152i | 0.450119 | + | 0.259876i | 0.707880 | − | 0.706332i | \(-0.249652\pi\) |
−0.257762 | + | 0.966209i | \(0.582985\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.6444 | − | 70.3981i | −0.0740334 | − | 0.128230i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 71.4825 | − | 37.7448i | 0.129732 | − | 0.0685024i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 219.943 | − | 126.984i | 0.397728 | − | 0.229628i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.1151 | − | 26.1801i | 0.0272344 | − | 0.0471714i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 366.164 | − | 634.214i | 0.657386 | − | 1.13863i | −0.323904 | − | 0.946090i | \(-0.604996\pi\) |
0.981290 | − | 0.192536i | \(-0.0616711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 859.961i | − | 1.53839i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −46.6331 | − | 26.9236i | −0.0831249 | − | 0.0479922i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 420.289i | − | 0.746516i | −0.927728 | − | 0.373258i | \(-0.878241\pi\) | ||
0.927728 | − | 0.373258i | \(-0.121759\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −233.227 | + | 134.654i | −0.412791 | + | 0.238325i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.7652 | + | 30.7702i | 0.0313319 | + | 0.0542685i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 75.1265i | − | 0.132033i | −0.997819 | − | 0.0660163i | \(-0.978971\pi\) | ||
0.997819 | − | 0.0660163i | \(-0.0210289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 166.499 | 0.291592 | 0.145796 | − | 0.989315i | \(-0.453426\pi\) | ||||
0.145796 | + | 0.989315i | \(0.453426\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −414.059 | + | 239.057i | −0.722617 | + | 0.417203i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −49.5444 | − | 85.8134i | −0.0861641 | − | 0.149241i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −663.313 | −1.14959 | −0.574795 | − | 0.818298i | \(-0.694918\pi\) | ||||
−0.574795 | + | 0.818298i | \(0.694918\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −144.476 | + | 250.239i | −0.249526 | + | 0.432192i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.5990 | 0.0492237 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −986.178 | − | 569.370i | −1.69156 | − | 0.976621i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 185.630 | + | 107.173i | 0.317315 | + | 0.183202i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −418.538 | − | 724.929i | −0.713012 | − | 1.23497i | −0.963721 | − | 0.266910i | \(-0.913997\pi\) |
0.250710 | − | 0.968062i | \(-0.419336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 119.598 | + | 75.2121i | 0.203053 | + | 0.127695i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.6034 | + | 13.6274i | −0.0399381 | + | 0.0230583i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.7134 | + | 75.7139i | −0.0737157 | + | 0.127679i | −0.900527 | − | 0.434800i | \(-0.856819\pi\) |
0.826811 | + | 0.562479i | \(0.190152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.8186 | + | 25.6666i | −0.0249052 | + | 0.0431371i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 114.804i | − | 0.192302i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −252.242 | − | 145.632i | −0.421105 | − | 0.243125i | 0.274445 | − | 0.961603i | \(-0.411506\pi\) |
−0.695550 | + | 0.718478i | \(0.744839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 103.857i | 0.172808i | 0.996260 | + | 0.0864038i | \(0.0275375\pi\) | ||||
−0.996260 | + | 0.0864038i | \(0.972462\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −160.425 | + | 92.6214i | −0.266045 | + | 0.153601i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −595.517 | − | 1031.47i | −0.984325 | − | 1.70490i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 655.928i | 1.08061i | 0.841471 | + | 0.540303i | \(0.181690\pi\) | ||||
−0.841471 | + | 0.540303i | \(0.818310\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.0916 | −0.0477695 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 615.423 | − | 355.315i | 1.00724 | − | 0.581530i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 436.652 | + | 756.304i | 0.712320 | + | 1.23378i | 0.963984 | + | 0.265960i | \(0.0856890\pi\) |
−0.251664 | + | 0.967815i | \(0.580978\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −499.895 | −0.812837 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −246.350 | + | 426.690i | −0.399270 | + | 0.691556i | −0.993636 | − | 0.112639i | \(-0.964070\pi\) |
0.594366 | + | 0.804195i | \(0.297403\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −404.540 | −0.653537 | −0.326769 | − | 0.945104i | \(-0.605960\pi\) | ||||
−0.326769 | + | 0.945104i | \(0.605960\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 143.715 | + | 82.9740i | 0.231425 | + | 0.133614i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 222.084 | + | 128.220i | 0.356475 | + | 0.205811i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 268.904 | + | 465.755i | 0.430246 | + | 0.745207i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0878 | − | 637.269i | 0.0384176 | − | 1.01638i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.18203 | − | 2.99184i | 0.00823852 | − | 0.00475651i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 270.126 | − | 467.872i | 0.428092 | − | 0.741477i | −0.568611 | − | 0.822606i | \(-0.692519\pi\) |
0.996704 | + | 0.0811289i | \(0.0258525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.26033 | + | 9.11116i | −0.00831016 | + | 0.0143936i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 356.563i | 0.561516i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 441.843 | + | 255.098i | 0.693631 | + | 0.400468i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 216.458i | 0.338745i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 872.388 | − | 503.673i | 1.36098 | − | 0.785762i | 0.371225 | − | 0.928543i | \(-0.378938\pi\) |
0.989754 | + | 0.142781i | \(0.0456046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −383.801 | − | 664.763i | −0.596891 | − | 1.03385i | −0.993277 | − | 0.115762i | \(-0.963069\pi\) |
0.396386 | − | 0.918084i | \(-0.370264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 456.495i | 0.707744i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −962.536 | −1.48769 | −0.743846 | − | 0.668352i | \(-0.767000\pi\) | ||||
−0.743846 | + | 0.668352i | \(0.767000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1066.78 | + | 615.908i | −1.64373 | + | 0.949011i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.4227 | − | 44.0334i | −0.0390518 | − | 0.0676396i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1020.58 | −1.56291 | −0.781455 | − | 0.623961i | \(-0.785522\pi\) | ||||
−0.781455 | + | 0.623961i | \(0.785522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −533.006 | + | 923.194i | −0.813750 | + | 1.40946i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −112.206 | −0.170786 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.6046 | − | 14.7828i | −0.0388538 | − | 0.0224322i | 0.480447 | − | 0.877024i | \(-0.340474\pi\) |
−0.519301 | + | 0.854591i | \(0.673808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.61074 | + | 4.97141i | 0.0130268 | + | 0.00752104i | 0.506499 | − | 0.862240i | \(-0.330939\pi\) |
−0.493472 | + | 0.869761i | \(0.664273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.2136 | + | 36.7430i | 0.0319964 | + | 0.0554193i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −350.749 | − | 13.2578i | −0.527443 | − | 0.0199365i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −117.671 | + | 67.9376i | −0.176419 | + | 0.101856i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −200.656 | + | 347.546i | −0.299934 | + | 0.519500i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 262.541 | − | 454.735i | 0.391269 | − | 0.677697i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 914.332i | − | 1.35859i | −0.733864 | − | 0.679296i | \(-0.762285\pi\) | ||
0.733864 | − | 0.679296i | \(-0.237715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.9620 | + | 8.06094i | 0.0206844 | + | 0.0119421i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.92519i | − | 0.00875213i | −0.999990 | − | 0.00437606i | \(-0.998607\pi\) | ||
0.999990 | − | 0.00437606i | \(-0.00139295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −501.652 | + | 289.629i | −0.738810 | + | 0.426552i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −138.460 | − | 239.820i | −0.203319 | − | 0.352158i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 264.458i | 0.387201i | 0.981080 | + | 0.193601i | \(0.0620166\pi\) | ||||
−0.981080 | + | 0.193601i | \(0.937983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −481.320 | −0.702657 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 76.2089 | − | 43.9993i | 0.110930 | − | 0.0640455i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 448.617 | + | 777.027i | 0.651113 | + | 1.12776i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −788.543 | −1.14116 | −0.570581 | − | 0.821241i | \(-0.693282\pi\) | ||||
−0.570581 | + | 0.821241i | \(0.693282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −114.754 | + | 198.760i | −0.165590 | + | 0.286810i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1118.15 | 1.60884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −85.6913 | − | 49.4739i | −0.122943 | − | 0.0709812i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −268.437 | − | 154.982i | −0.384031 | − | 0.221720i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −515.363 | − | 892.635i | −0.735183 | − | 1.27337i | −0.954643 | − | 0.297752i | \(-0.903763\pi\) |
0.219460 | − | 0.975621i | \(-0.429570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.9897 | + | 37.7259i | 0.0853339 | + | 0.0536641i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −326.686 | + | 188.612i | −0.463385 | + | 0.267535i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 240.658 | − | 416.832i | 0.340393 | − | 0.589578i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 369.792 | − | 640.498i | 0.521568 | − | 0.903383i | −0.478117 | − | 0.878296i | \(-0.658681\pi\) |
0.999685 | − | 0.0250866i | \(-0.00798616\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 192.994i | 0.271440i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −205.662 | − | 118.739i | −0.288446 | − | 0.166534i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1384.57i | 1.93646i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −345.604 | + | 199.535i | −0.482015 | + | 0.278291i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 286.874 | + | 496.881i | 0.398991 | + | 0.691072i | 0.993602 | − | 0.112942i | \(-0.0360273\pi\) |
−0.594611 | + | 0.804013i | \(0.702694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 620.527i | 0.860648i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −98.7884 | −0.136637 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.4318 | + | 6.60015i | −0.0157680 | + | 0.00910366i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 132.019 | + | 228.664i | 0.181595 | + | 0.314531i | 0.942424 | − | 0.334421i | \(-0.108541\pi\) |
−0.760829 | + | 0.648952i | \(0.775207\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45.1787 | + | 78.2517i | −0.0618039 | + | 0.107048i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −626.432 | −0.854614 | −0.427307 | − | 0.904107i | \(-0.640538\pi\) | ||||
−0.427307 | + | 0.904107i | \(0.640538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −234.544 | − | 135.414i | −0.319108 | − | 0.184237i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1036.26 | − | 598.286i | −1.40605 | − | 0.811785i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −304.320 | − | 527.098i | −0.411800 | − | 0.713259i | 0.583286 | − | 0.812267i | \(-0.301767\pi\) |
−0.995087 | + | 0.0990076i | \(0.968433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −267.494 | + | 425.355i | −0.360991 | + | 0.574029i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.7871 | + | 6.22796i | −0.0145184 | + | 0.00838218i | −0.507242 | − | 0.861804i | \(-0.669335\pi\) |
0.492723 | + | 0.870186i | \(0.336001\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 285.599 | − | 494.673i | 0.383355 | − | 0.663990i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.8664 | + | 18.8211i | −0.0145467 | + | 0.0251956i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 683.130i | − | 0.912056i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 158.562 | + | 91.5457i | 0.211134 | + | 0.121898i | 0.601838 | − | 0.798618i | \(-0.294435\pi\) |
−0.390704 | + | 0.920516i | \(0.627768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 458.634i | − | 0.609076i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 113.348 | − | 65.4413i | 0.150129 | − | 0.0866772i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 574.146 | + | 994.450i | 0.758449 | + | 1.31367i | 0.943641 | + | 0.330970i | \(0.107376\pi\) |
−0.185193 | + | 0.982702i | \(0.559291\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1071.94i | 1.41230i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 872.192 | 1.14611 | 0.573056 | − | 0.819516i | \(-0.305758\pi\) | ||||
0.573056 | + | 0.819516i | \(0.305758\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 359.811 | − | 207.737i | 0.471574 | − | 0.272264i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.2608 | − | 19.5044i | −0.0147201 | − | 0.0254959i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 970.570 | 1.26541 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 516.956 | − | 895.394i | 0.672244 | − | 1.16436i | −0.305022 | − | 0.952345i | \(-0.598664\pi\) |
0.977266 | − | 0.212016i | \(-0.0680029\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 673.045 | 0.872951 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 388.981 | + | 224.578i | 0.503210 | + | 0.290528i | 0.730038 | − | 0.683407i | \(-0.239502\pi\) |
−0.226828 | + | 0.973935i | \(0.572836\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.9801 | − | 11.5355i | −0.0257808 | − | 0.0148846i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.7518 | − | 22.0869i | −0.0164116 | − | 0.0284258i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.2630 | − | 1171.02i | 0.0568203 | − | 1.50324i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1210.88 | + | 699.103i | −1.55043 | + | 0.895138i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.0536 | − | 19.1453i | 0.0141169 | − | 0.0244512i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 657.376 | − | 1138.61i | 0.837422 | − | 1.45046i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 141.308i | 0.179552i | 0.995962 | + | 0.0897762i | \(0.0286152\pi\) | ||||
−0.995962 | + | 0.0897762i | \(0.971385\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −535.541 | − | 309.195i | −0.678759 | − | 0.391882i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 227.201i | 0.287232i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −358.294 | + | 206.861i | −0.451821 | + | 0.260859i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −238.140 | − | 412.470i | −0.299547 | − | 0.518831i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1074.10i | 1.34768i | 0.738878 | + | 0.673839i | \(0.235356\pi\) | ||||
−0.738878 | + | 0.673839i | \(0.764644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −74.6668 | −0.0934504 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −168.764 | + | 97.4361i | −0.210692 | + | 0.121643i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −362.397 | − | 627.690i | −0.451304 | − | 0.781681i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 589.988 | 0.732905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −57.3739 | + | 99.3746i | −0.0710954 | + | 0.123141i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 242.419 | 0.299653 | 0.149827 | − | 0.988712i | \(-0.452128\pi\) | ||||
0.149827 | + | 0.988712i | \(0.452128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −179.138 | − | 103.426i | −0.220886 | − | 0.127528i | 0.385475 | − | 0.922718i | \(-0.374038\pi\) |
−0.606360 | + | 0.795190i | \(0.707371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −313.810 | − | 181.178i | −0.385990 | − | 0.222851i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 365.361 | + | 632.825i | 0.448296 | + | 0.776472i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1069.36 | − | 40.4201i | −1.30888 | − | 0.0494739i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 156.606 | − | 90.4166i | 0.191216 | − | 0.110399i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 703.143 | − | 1217.88i | 0.856447 | − | 1.48341i | −0.0188483 | − | 0.999822i | \(-0.506000\pi\) |
0.875296 | − | 0.483588i | \(-0.160667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −273.933 | + | 474.465i | −0.332846 | + | 0.576507i | −0.983069 | − | 0.183237i | \(-0.941342\pi\) |
0.650222 | + | 0.759744i | \(0.274676\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 104.139i | 0.126229i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1057.69 | + | 610.656i | 1.27894 | + | 0.738399i | 0.976654 | − | 0.214817i | \(-0.0689155\pi\) |
0.302290 | + | 0.953216i | \(0.402249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 173.838i | 0.209696i | 0.994488 | + | 0.104848i | \(0.0334356\pi\) | ||||
−0.994488 | + | 0.104848i | \(0.966564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 567.292 | − | 327.526i | 0.682662 | − | 0.394135i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.8035 | − | 46.4250i | −0.0321771 | − | 0.0557323i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 895.098i | 1.07197i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.6381 | 0.0461626 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.4785 | − | 22.2156i | 0.0458624 | − | 0.0264787i | −0.476894 | − | 0.878961i | \(-0.658237\pi\) |
0.522756 | + | 0.852482i | \(0.324904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −411.450 | − | 712.652i | −0.489238 | − | 0.847386i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −261.523 | −0.310229 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 150.048 | − | 259.891i | 0.177572 | − | 0.307563i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1004.81 | −1.18632 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9243 | + | 9.77125i | 0.0199344 | + | 0.0115091i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −103.159 | − | 59.5587i | −0.121221 | − | 0.0699867i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 251.377 | + | 435.398i | 0.294698 | + | 0.510432i | 0.974915 | − | 0.222579i | \(-0.0714477\pi\) |
−0.680217 | + | 0.733011i | \(0.738114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 141.994 | − | 225.792i | 0.166075 | − | 0.264084i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −912.584 | + | 526.881i | −1.06486 | + | 0.614796i | −0.926772 | − | 0.375624i | \(-0.877428\pi\) |
−0.138086 | + | 0.990420i | \(0.544095\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 73.4561 | − | 127.230i | 0.0855136 | − | 0.148114i | −0.820096 | − | 0.572225i | \(-0.806080\pi\) |
0.905610 | + | 0.424112i | \(0.139414\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −210.868 | + | 365.234i | −0.244910 | + | 0.424197i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 290.509i | − | 0.336627i | −0.985734 | − | 0.168314i | \(-0.946168\pi\) | ||
0.985734 | − | 0.168314i | \(-0.0538321\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −373.910 | − | 215.877i | −0.432266 | − | 0.249569i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 496.105i | 0.572209i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1079.62 | + | 623.320i | −1.24237 | + | 0.717285i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 471.400 | + | 816.489i | 0.541217 | + | 0.937415i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 440.186i | − | 0.504222i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 519.159 | 0.593325 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1225.93 | + | 707.789i | −1.39786 | + | 0.807056i | −0.994169 | − | 0.107837i | \(-0.965607\pi\) |
−0.403694 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 246.345 | + | 426.682i | 0.280256 | + | 0.485417i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 107.877 | 0.122449 | 0.0612243 | − | 0.998124i | \(-0.480500\pi\) | ||||
0.0612243 | + | 0.998124i | \(0.480500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 390.301 | − | 676.021i | 0.442017 | − | 0.765596i | −0.555822 | − | 0.831301i | \(-0.687596\pi\) |
0.997839 | + | 0.0657056i | \(0.0209298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −515.209 | −0.582157 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 320.543 | + | 185.066i | 0.361379 | + | 0.208642i | 0.669686 | − | 0.742645i | \(-0.266429\pi\) |
−0.308306 | + | 0.951287i | \(0.599762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 260.512 | + | 150.407i | 0.293040 | + | 0.169187i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −87.2030 | − | 151.040i | −0.0978709 | − | 0.169517i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −412.906 | − | 781.977i | −0.462381 | − | 0.875674i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 971.341 | − | 560.804i | 1.08530 | − | 0.626596i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 422.299 | − | 731.444i | 0.470791 | − | 0.815434i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.8181 | + | 27.3977i | −0.0175952 | + | 0.0304758i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 94.2735i | − | 0.104632i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 333.525 | + | 192.561i | 0.369352 | + | 0.213245i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 889.240i | 0.982586i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −288.815 | + | 166.747i | −0.318429 | + | 0.183845i | −0.650692 | − | 0.759342i | \(-0.725521\pi\) |
0.332263 | + | 0.943187i | \(0.392188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 182.879 | + | 316.756i | 0.201187 | + | 0.348466i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 326.591i | 0.358498i | 0.983804 | + | 0.179249i | \(0.0573667\pi\) | ||||
−0.983804 | + | 0.179249i | \(0.942633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −140.382 | −0.153759 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 190.194 | − | 109.808i | 0.207862 | − | 0.120009i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 449.670 | + | 778.851i | 0.490371 | + | 0.849347i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −874.662 | −0.951755 | −0.475877 | − | 0.879512i | \(-0.657869\pi\) | ||||
−0.475877 | + | 0.879512i | \(0.657869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −470.039 | + | 814.131i | −0.510357 | + | 0.883964i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1101.67 | 1.19358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0219 | − | 5.78614i | −0.0108345 | − | 0.00625529i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −408.371 | − | 235.773i | −0.440530 | − | 0.254340i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 124.288 | + | 215.274i | 0.133787 | + | 0.231727i | 0.925134 | − | 0.379642i | \(-0.123953\pi\) |
−0.791346 | + | 0.611368i | \(0.790619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 337.981 | − | 537.439i | 0.363030 | − | 0.577271i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 694.150 | − | 400.768i | 0.743998 | − | 0.429547i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 72.7392 | − | 125.988i | 0.0777959 | − | 0.134746i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 913.478 | − | 1582.19i | 0.974897 | − | 1.68857i | 0.294620 | − | 0.955614i | \(-0.404807\pi\) |
0.680276 | − | 0.732956i | \(-0.261860\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 266.764i | 0.284094i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1174.62 | − | 678.166i | −1.24827 | − | 0.720687i | −0.277502 | − | 0.960725i | \(-0.589507\pi\) |
−0.970763 | + | 0.240038i | \(0.922840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1969.76i | 2.08882i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −83.1315 | + | 47.9960i | −0.0879699 | + | 0.0507894i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −478.965 | − | 829.592i | −0.505771 | − | 0.876021i | −0.999978 | − | 0.00667692i | \(-0.997875\pi\) |
0.494206 | − | 0.869345i | \(-0.335459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 571.078i | 0.601768i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 125.972 | 0.132463 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 136.474 | − | 78.7933i | 0.143205 | − | 0.0826793i | −0.426686 | − | 0.904400i | \(-0.640319\pi\) |
0.569890 | + | 0.821721i | \(0.306986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −645.858 | − | 1118.66i | −0.676291 | − | 1.17137i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 142.800 | 0.149217 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −203.033 | + | 351.663i | −0.211713 | + | 0.366698i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 905.707 | 0.942463 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 449.570 | + | 259.559i | 0.466843 | + | 0.269532i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −676.069 | − | 390.328i | −0.700589 | − | 0.404485i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −359.447 | − | 622.581i | −0.371714 | − | 0.643827i | 0.618115 | − | 0.786087i | \(-0.287896\pi\) |
−0.989829 | + | 0.142260i | \(0.954563\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 46.6868 | − | 24.6520i | 0.0481804 | − | 0.0254406i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1159.84 | − | 669.635i | 1.19448 | − | 0.689635i | 0.235163 | − | 0.971956i | \(-0.424438\pi\) |
0.959320 | + | 0.282321i | \(0.0911044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 471.661 | − | 816.941i | 0.484749 | − | 0.839610i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41.0265 | − | 71.0599i | 0.0420784 | − | 0.0728820i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1527.02i | 1.56297i | 0.623926 | + | 0.781483i | \(0.285537\pi\) | ||||
−0.623926 | + | 0.781483i | \(0.714463\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1090.13 | − | 629.386i | −1.11351 | − | 0.642887i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 315.724i | 0.321839i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 524.286 | − | 302.697i | 0.533353 | − | 0.307932i | −0.209028 | − | 0.977910i | \(-0.567030\pi\) |
0.742381 | + | 0.669978i | \(0.233697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.8170 | − | 63.7690i | −0.0373777 | − | 0.0647401i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 318.245i | 0.322437i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1798.75 | 1.81875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1423.50 | + | 821.857i | −1.43643 | + | 0.829321i | −0.997599 | − | 0.0692508i | \(-0.977939\pi\) |
−0.438827 | + | 0.898572i | \(0.644606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 466.680 | + | 808.313i | 0.469969 | + | 0.814011i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 310.166 | 0.311724 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 671.544 | − | 1163.15i | 0.673565 | − | 1.16665i | −0.303322 | − | 0.952888i | \(-0.598096\pi\) |
0.976886 | − | 0.213760i | \(-0.0685710\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.3806 | 0.0194000 |
(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 | 912.3.be.i.145.3 | 20 | ||
4.3 | odd | 2 | 456.3.w.b.145.3 | ✓ | 20 | ||
12.11 | even | 2 | 1368.3.bv.b.145.8 | 20 | |||
19.8 | odd | 6 | inner | 912.3.be.i.673.3 | 20 | ||
76.27 | even | 6 | 456.3.w.b.217.3 | yes | 20 | ||
228.179 | odd | 6 | 1368.3.bv.b.217.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.3.w.b.145.3 | ✓ | 20 | 4.3 | odd | 2 | ||
456.3.w.b.217.3 | yes | 20 | 76.27 | even | 6 | ||
912.3.be.i.145.3 | 20 | 1.1 | even | 1 | trivial | ||
912.3.be.i.673.3 | 20 | 19.8 | odd | 6 | inner | ||
1368.3.bv.b.145.8 | 20 | 12.11 | even | 2 | |||
1368.3.bv.b.217.8 | 20 | 228.179 | odd | 6 |