Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(424,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.424");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.r (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 15x^{14} + 158x^{12} - 843x^{10} + 3258x^{8} - 4947x^{6} + 5489x^{4} - 1296x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.8 | ||
Root | \(2.34074 + 1.35143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.499 |
Dual form | 525.2.r.h.424.8 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34074 | + | 1.35143i | 1.65515 | + | 0.955603i | 0.974905 | + | 0.222621i | \(0.0714613\pi\) |
0.680248 | + | 0.732982i | \(0.261872\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 2.65271 | + | 4.59463i | 1.32635 | + | 2.29731i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.70285 | −1.10344 | ||||||||
\(7\) | 2.06605 | + | 1.65271i | 0.780893 | + | 0.624665i | ||||
\(8\) | 8.93406i | 3.15867i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41275 | − | 2.44696i | −0.425960 | − | 0.737785i | 0.570549 | − | 0.821263i | \(-0.306730\pi\) |
−0.996510 | + | 0.0834785i | \(0.973397\pi\) | |||||||
\(12\) | −4.59463 | − | 2.65271i | −1.32635 | − | 0.765771i | ||||
\(13\) | − | 4.47992i | − | 1.24251i | −0.783610 | − | 0.621253i | \(-0.786624\pi\) | ||
0.783610 | − | 0.621253i | \(-0.213376\pi\) | |||||||
\(14\) | 2.60256 | + | 6.66067i | 0.695565 | + | 1.78014i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.76831 | + | 11.7231i | −1.69208 | + | 2.93077i | ||||
\(17\) | −3.66433 | + | 2.11560i | −0.888732 | + | 0.513109i | −0.873527 | − | 0.486775i | \(-0.838173\pi\) |
−0.0152042 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(18\) | 2.34074 | − | 1.35143i | 0.551718 | − | 0.318534i | ||||
\(19\) | 1.05014 | − | 1.81890i | 0.240920 | − | 0.417285i | −0.720057 | − | 0.693915i | \(-0.755884\pi\) |
0.960977 | + | 0.276630i | \(0.0892176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.61560 | − | 0.398264i | −0.570772 | − | 0.0869084i | ||||
\(22\) | − | 7.63692i | − | 1.62820i | ||||||
\(23\) | 5.72515 | + | 3.30542i | 1.19378 | + | 0.689227i | 0.959161 | − | 0.282861i | \(-0.0912835\pi\) |
0.234616 | + | 0.972088i | \(0.424617\pi\) | |||||||
\(24\) | −4.46703 | − | 7.73712i | −0.911829 | − | 1.57933i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.05428 | − | 10.4863i | 1.18734 | − | 2.05654i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.11296 | + | 13.8769i | −0.399312 | + | 2.62248i | ||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.66575 | − | 8.08131i | −0.837993 | − | 1.45145i | −0.891570 | − | 0.452883i | \(-0.850395\pi\) |
0.0535767 | − | 0.998564i | \(-0.482938\pi\) | |||||||
\(32\) | −16.2115 | + | 9.35970i | −2.86581 | + | 1.65458i | ||||
\(33\) | 2.44696 | + | 1.41275i | 0.425960 | + | 0.245928i | ||||
\(34\) | −11.4363 | −1.96132 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.30542 | 0.884236 | ||||||||
\(37\) | 3.64175 | + | 2.10256i | 0.598700 | + | 0.345659i | 0.768530 | − | 0.639814i | \(-0.220989\pi\) |
−0.169830 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(38\) | 4.91623 | − | 2.83839i | 0.797518 | − | 0.460447i | ||||
\(39\) | 2.23996 | + | 3.87972i | 0.358680 | + | 0.621253i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.37963 | 0.371635 | 0.185818 | − | 0.982584i | \(-0.440507\pi\) | ||||
0.185818 | + | 0.982584i | \(0.440507\pi\) | |||||||
\(42\) | −5.58422 | − | 4.46703i | −0.861665 | − | 0.689278i | ||||
\(43\) | − | 3.13092i | − | 0.477461i | −0.971086 | − | 0.238730i | \(-0.923269\pi\) | ||
0.971086 | − | 0.238730i | \(-0.0767312\pi\) | |||||||
\(44\) | 7.49523 | − | 12.9821i | 1.12995 | − | 1.95713i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.93406 | + | 15.4742i | 1.31726 | + | 2.28155i | ||||
\(47\) | 6.74230 | + | 3.89267i | 0.983465 | + | 0.567804i | 0.903315 | − | 0.428979i | \(-0.141126\pi\) |
0.0801507 | + | 0.996783i | \(0.474460\pi\) | |||||||
\(48\) | − | 13.5366i | − | 1.95384i | ||||||
\(49\) | 1.53710 | + | 6.82915i | 0.219586 | + | 0.975593i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.11560 | − | 3.66433i | 0.296244 | − | 0.513109i | ||||
\(52\) | 20.5835 | − | 11.8839i | 2.85442 | − | 1.64800i | ||||
\(53\) | 2.23452 | − | 1.29010i | 0.306936 | − | 0.177209i | −0.338619 | − | 0.940924i | \(-0.609960\pi\) |
0.645554 | + | 0.763714i | \(0.276626\pi\) | |||||||
\(54\) | −1.35143 | + | 2.34074i | −0.183906 | + | 0.318534i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14.7654 | + | 18.4582i | −1.97311 | + | 2.46658i | ||||
\(57\) | 2.10029i | 0.278190i | ||||||||
\(58\) | −9.36296 | − | 5.40571i | −1.22942 | − | 0.709804i | ||||
\(59\) | −1.89267 | − | 3.27820i | −0.246404 | − | 0.426785i | 0.716121 | − | 0.697976i | \(-0.245916\pi\) |
−0.962526 | + | 0.271191i | \(0.912582\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | − | 25.2217i | − | 3.20316i | ||||||
\(63\) | 2.46431 | − | 0.962895i | 0.310474 | − | 0.121313i | ||||
\(64\) | −23.5225 | −2.94032 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.81846 | + | 6.61376i | 0.470020 | + | 0.814098i | ||||
\(67\) | 2.86258 | − | 1.65271i | 0.349719 | − | 0.201911i | −0.314842 | − | 0.949144i | \(-0.601952\pi\) |
0.664562 | + | 0.747233i | \(0.268618\pi\) | |||||||
\(68\) | −19.4408 | − | 11.2242i | −2.35755 | − | 1.36113i | ||||
\(69\) | −6.61084 | −0.795851 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4223 | −1.35557 | −0.677786 | − | 0.735259i | \(-0.737060\pi\) | ||||
−0.677786 | + | 0.735259i | \(0.737060\pi\) | |||||||
\(72\) | 7.73712 | + | 4.46703i | 0.911829 | + | 0.526445i | ||||
\(73\) | 2.29584 | − | 1.32550i | 0.268707 | − | 0.155138i | −0.359593 | − | 0.933109i | \(-0.617084\pi\) |
0.628300 | + | 0.777971i | \(0.283751\pi\) | |||||||
\(74\) | 5.68292 | + | 9.84311i | 0.660627 | + | 1.14424i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.1429 | 1.27818 | ||||||||
\(77\) | 1.12530 | − | 7.39039i | 0.128239 | − | 0.842213i | ||||
\(78\) | 12.1086i | 1.37102i | ||||||||
\(79\) | 6.31846 | − | 10.9439i | 0.710882 | − | 1.23128i | −0.253644 | − | 0.967298i | \(-0.581629\pi\) |
0.964526 | − | 0.263986i | \(-0.0850374\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 5.57009 | + | 3.21589i | 0.615114 | + | 0.355136i | ||||
\(83\) | − | 3.02608i | − | 0.332155i | −0.986113 | − | 0.166078i | \(-0.946890\pi\) | ||
0.986113 | − | 0.166078i | \(-0.0531102\pi\) | |||||||
\(84\) | −5.10856 | − | 13.0742i | −0.557390 | − | 1.42651i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.23121 | − | 7.32867i | 0.456263 | − | 0.790271i | ||||
\(87\) | 3.46410 | − | 2.00000i | 0.371391 | − | 0.214423i | ||||
\(88\) | 21.8613 | − | 12.6216i | 2.33042 | − | 1.34547i | ||||
\(89\) | −4.11560 | + | 7.12844i | −0.436253 | + | 0.755613i | −0.997397 | − | 0.0721056i | \(-0.977028\pi\) |
0.561144 | + | 0.827718i | \(0.310361\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.40400 | − | 9.25572i | 0.776150 | − | 0.970263i | ||||
\(92\) | 35.0733i | 3.65664i | ||||||||
\(93\) | 8.08131 | + | 4.66575i | 0.837993 | + | 0.483816i | ||||
\(94\) | 10.5213 | + | 18.2234i | 1.08519 | + | 1.87960i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.35970 | − | 16.2115i | 0.955270 | − | 1.65458i | ||||
\(97\) | 15.0165i | 1.52470i | 0.647166 | + | 0.762350i | \(0.275954\pi\) | ||||
−0.647166 | + | 0.762350i | \(0.724046\pi\) | |||||||
\(98\) | −5.63114 | + | 18.0626i | −0.568831 | + | 1.82459i | ||||
\(99\) | −2.82550 | −0.283974 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.11560 | + | 1.93228i | 0.111007 | + | 0.192269i | 0.916176 | − | 0.400775i | \(-0.131259\pi\) |
−0.805170 | + | 0.593045i | \(0.797926\pi\) | |||||||
\(102\) | 9.90416 | − | 5.71817i | 0.980658 | − | 0.566183i | ||||
\(103\) | −6.79141 | − | 3.92102i | −0.669178 | − | 0.386350i | 0.126587 | − | 0.991955i | \(-0.459598\pi\) |
−0.795765 | + | 0.605606i | \(0.792931\pi\) | |||||||
\(104\) | 40.0239 | 3.92466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.97392 | 0.677367 | ||||||||
\(107\) | −13.5420 | − | 7.81846i | −1.30915 | − | 0.755839i | −0.327197 | − | 0.944956i | \(-0.606104\pi\) |
−0.981954 | + | 0.189117i | \(0.939437\pi\) | |||||||
\(108\) | −4.59463 | + | 2.65271i | −0.442118 | + | 0.255257i | ||||
\(109\) | 1.53710 | + | 2.66234i | 0.147228 | + | 0.255006i | 0.930202 | − | 0.367048i | \(-0.119632\pi\) |
−0.782974 | + | 0.622054i | \(0.786298\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.20513 | −0.399133 | ||||||||
\(112\) | −33.3585 | + | 13.0344i | −3.15208 | + | 1.23163i | ||||
\(113\) | 0.348998i | 0.0328310i | 0.999865 | + | 0.0164155i | \(0.00522545\pi\) | ||||
−0.999865 | + | 0.0164155i | \(0.994775\pi\) | |||||||
\(114\) | −2.83839 | + | 4.91623i | −0.265839 | + | 0.460447i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.6108 | − | 18.3785i | −0.985191 | − | 1.70640i | ||||
\(117\) | −3.87972 | − | 2.23996i | −0.358680 | − | 0.207084i | ||||
\(118\) | − | 10.2312i | − | 0.941859i | ||||||
\(119\) | −11.0672 | − | 1.68514i | −1.01453 | − | 0.154476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.50827 | − | 2.61240i | 0.137116 | − | 0.237491i | ||||
\(122\) | 11.7037 | − | 6.75713i | 1.05960 | − | 0.611762i | ||||
\(123\) | −2.06082 | + | 1.18981i | −0.185818 | + | 0.107282i | ||||
\(124\) | 24.7537 | − | 42.8748i | 2.22295 | − | 3.85027i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.06960 | + | 1.07645i | 0.629810 | + | 0.0958978i | ||||
\(127\) | 2.27137i | 0.201552i | 0.994909 | + | 0.100776i | \(0.0321325\pi\) | ||||
−0.994909 | + | 0.100776i | \(0.967867\pi\) | |||||||
\(128\) | −22.6372 | − | 13.0696i | −2.00087 | − | 1.15520i | ||||
\(129\) | 1.56546 | + | 2.71146i | 0.137831 | + | 0.238730i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.61084 | + | 16.6465i | −0.839703 | + | 1.45441i | 0.0504406 | + | 0.998727i | \(0.483937\pi\) |
−0.890143 | + | 0.455681i | \(0.849396\pi\) | |||||||
\(132\) | 14.9905i | 1.30475i | ||||||||
\(133\) | 5.17577 | − | 2.02236i | 0.448796 | − | 0.175361i | ||||
\(134\) | 8.93406 | 0.771785 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −18.9009 | − | 32.7374i | −1.62074 | − | 2.80721i | ||||
\(137\) | −7.15496 | + | 4.13092i | −0.611290 | + | 0.352928i | −0.773470 | − | 0.633833i | \(-0.781481\pi\) |
0.162180 | + | 0.986761i | \(0.448147\pi\) | |||||||
\(138\) | −15.4742 | − | 8.93406i | −1.31726 | − | 0.760518i | ||||
\(139\) | −0.985914 | −0.0836241 | −0.0418121 | − | 0.999125i | \(-0.513313\pi\) | ||||
−0.0418121 | + | 0.999125i | \(0.513313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.78534 | −0.655644 | ||||||||
\(142\) | −26.7365 | − | 15.4363i | −2.24368 | − | 1.29539i | ||||
\(143\) | −10.9622 | + | 6.32901i | −0.916702 | + | 0.529258i | ||||
\(144\) | 6.76831 | + | 11.7231i | 0.564026 | + | 0.976922i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.16527 | 0.593002 | ||||||||
\(147\) | −4.74575 | − | 5.14567i | −0.391423 | − | 0.424407i | ||||
\(148\) | 22.3100i | 1.83387i | ||||||||
\(149\) | 3.91048 | − | 6.77314i | 0.320359 | − | 0.554877i | −0.660203 | − | 0.751087i | \(-0.729530\pi\) |
0.980562 | + | 0.196209i | \(0.0628633\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.56717 | + | 2.71441i | 0.127534 | + | 0.220896i | 0.922721 | − | 0.385469i | \(-0.125960\pi\) |
−0.795186 | + | 0.606365i | \(0.792627\pi\) | |||||||
\(152\) | 16.2502 | + | 9.38206i | 1.31807 | + | 0.760985i | ||||
\(153\) | 4.23121i | 0.342073i | ||||||||
\(154\) | 12.6216 | − | 15.7782i | 1.01708 | − | 1.27145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.8839 | + | 20.5835i | −0.951475 | + | 1.64800i | ||||
\(157\) | −20.3334 | + | 11.7395i | −1.62278 | + | 0.936913i | −0.636608 | + | 0.771187i | \(0.719663\pi\) |
−0.986172 | + | 0.165725i | \(0.947004\pi\) | |||||||
\(158\) | 29.5797 | − | 17.0779i | 2.35324 | − | 1.35864i | ||||
\(159\) | −1.29010 | + | 2.23452i | −0.102312 | + | 0.177209i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.36554 | + | 16.2912i | 0.501675 | + | 1.28392i | ||||
\(162\) | − | 2.70285i | − | 0.212356i | ||||||
\(163\) | −10.7702 | − | 6.21817i | −0.843586 | − | 0.487045i | 0.0148956 | − | 0.999889i | \(-0.495258\pi\) |
−0.858482 | + | 0.512844i | \(0.828592\pi\) | |||||||
\(164\) | 6.31246 | + | 10.9335i | 0.492920 | + | 0.853763i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.08952 | − | 7.08326i | 0.317409 | − | 0.549768i | ||||
\(167\) | 18.4483i | 1.42757i | 0.700362 | + | 0.713787i | \(0.253022\pi\) | ||||
−0.700362 | + | 0.713787i | \(0.746978\pi\) | |||||||
\(168\) | 3.55812 | − | 23.3680i | 0.274515 | − | 1.80288i | ||||
\(169\) | −7.06966 | −0.543820 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.05014 | − | 1.81890i | −0.0803066 | − | 0.139095i | ||||
\(172\) | 14.3854 | − | 8.30542i | 1.09688 | − | 0.633282i | ||||
\(173\) | 6.62596 | + | 3.82550i | 0.503763 | + | 0.290847i | 0.730266 | − | 0.683163i | \(-0.239396\pi\) |
−0.226503 | + | 0.974010i | \(0.572729\pi\) | |||||||
\(174\) | 10.8114 | 0.819611 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 38.2478 | 2.88303 | ||||||||
\(177\) | 3.27820 | + | 1.89267i | 0.246404 | + | 0.142262i | ||||
\(178\) | −19.2671 | + | 11.1239i | −1.44413 | + | 0.833770i | ||||
\(179\) | −1.20513 | − | 2.08734i | −0.0900756 | − | 0.156015i | 0.817467 | − | 0.575975i | \(-0.195378\pi\) |
−0.907543 | + | 0.419960i | \(0.862044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6970 | −1.01809 | −0.509046 | − | 0.860739i | \(-0.670002\pi\) | ||||
−0.509046 | + | 0.860739i | \(0.670002\pi\) | |||||||
\(182\) | 29.8393 | − | 11.6593i | 2.21183 | − | 0.864243i | ||||
\(183\) | 5.00000i | 0.369611i | ||||||||
\(184\) | −29.5308 | + | 51.1489i | −2.17704 | + | 3.77074i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.6108 | + | 21.8426i | 0.924671 | + | 1.60158i | ||||
\(187\) | 10.3536 | + | 5.97764i | 0.757129 | + | 0.437128i | ||||
\(188\) | 41.3045i | 3.01244i | ||||||||
\(189\) | −1.65271 | + | 2.06605i | −0.120217 | + | 0.150283i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.06717 | − | 10.5086i | 0.439005 | − | 0.760379i | −0.558608 | − | 0.829432i | \(-0.688664\pi\) |
0.997613 | + | 0.0690531i | \(0.0219978\pi\) | |||||||
\(192\) | 20.3711 | − | 11.7613i | 1.47016 | − | 0.848797i | ||||
\(193\) | −10.3280 | + | 5.96290i | −0.743428 | + | 0.429219i | −0.823315 | − | 0.567585i | \(-0.807878\pi\) |
0.0798861 | + | 0.996804i | \(0.474544\pi\) | |||||||
\(194\) | −20.2938 | + | 35.1498i | −1.45701 | + | 2.52361i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −27.2999 | + | 25.1782i | −1.94999 | + | 1.79844i | ||||
\(197\) | − | 5.50258i | − | 0.392043i | −0.980600 | − | 0.196021i | \(-0.937198\pi\) | ||
0.980600 | − | 0.196021i | \(-0.0628022\pi\) | |||||||
\(198\) | −6.61376 | − | 3.81846i | −0.470020 | − | 0.271366i | ||||
\(199\) | −5.66404 | − | 9.81041i | −0.401513 | − | 0.695441i | 0.592396 | − | 0.805647i | \(-0.298182\pi\) |
−0.993909 | + | 0.110206i | \(0.964849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.65271 | + | 2.86258i | −0.116573 | + | 0.201911i | ||||
\(202\) | 6.03063i | 0.424314i | ||||||||
\(203\) | −8.26419 | − | 6.61084i | −0.580032 | − | 0.463990i | ||||
\(204\) | 22.4483 | 1.57170 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.5980 | − | 18.3562i | −0.738394 | − | 1.27894i | ||||
\(207\) | 5.72515 | − | 3.30542i | 0.397926 | − | 0.229742i | ||||
\(208\) | 52.5184 | + | 30.3215i | 3.64149 | + | 2.10242i | ||||
\(209\) | −5.93437 | −0.410489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.82095 | 0.607259 | 0.303630 | − | 0.952790i | \(-0.401801\pi\) | ||||
0.303630 | + | 0.952790i | \(0.401801\pi\) | |||||||
\(212\) | 11.8551 | + | 6.84454i | 0.814211 | + | 0.470085i | ||||
\(213\) | 9.89196 | − | 5.71113i | 0.677786 | − | 0.391320i | ||||
\(214\) | −21.1321 | − | 36.6020i | −1.44456 | − | 2.50206i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.93406 | −0.607886 | ||||||||
\(217\) | 3.71640 | − | 24.4075i | 0.252286 | − | 1.65689i | ||||
\(218\) | 8.30914i | 0.562766i | ||||||||
\(219\) | −1.32550 | + | 2.29584i | −0.0895691 | + | 0.155138i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.47773 | + | 16.4159i | 0.637541 | + | 1.10425i | ||||
\(222\) | −9.84311 | − | 5.68292i | −0.660627 | − | 0.381413i | ||||
\(223\) | − | 26.4885i | − | 1.77380i | −0.461961 | − | 0.886900i | \(-0.652854\pi\) | ||
0.461961 | − | 0.886900i | \(-0.347146\pi\) | |||||||
\(224\) | −48.9625 | − | 7.45527i | −3.27145 | − | 0.498126i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.471645 | + | 0.816914i | −0.0313734 | + | 0.0543403i | ||||
\(227\) | −15.3904 | + | 8.88562i | −1.02149 | + | 0.589760i | −0.914536 | − | 0.404504i | \(-0.867444\pi\) |
−0.106957 | + | 0.994264i | \(0.534111\pi\) | |||||||
\(228\) | −9.65005 | + | 5.57146i | −0.639090 | + | 0.368979i | ||||
\(229\) | 9.32244 | − | 16.1469i | 0.616044 | − | 1.06702i | −0.374156 | − | 0.927366i | \(-0.622068\pi\) |
0.990200 | − | 0.139654i | \(-0.0445991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.72066 | + | 6.96292i | 0.179006 | + | 0.458126i | ||||
\(232\) | − | 35.7362i | − | 2.34620i | ||||||
\(233\) | −8.46002 | − | 4.88440i | −0.554234 | − | 0.319987i | 0.196594 | − | 0.980485i | \(-0.437012\pi\) |
−0.750828 | + | 0.660498i | \(0.770345\pi\) | |||||||
\(234\) | −6.05428 | − | 10.4863i | −0.395781 | − | 0.685512i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.0414 | − | 17.3922i | 0.653639 | − | 1.13214i | ||||
\(237\) | 12.6369i | 0.820856i | ||||||||
\(238\) | −23.6280 | − | 18.9009i | −1.53158 | − | 1.22517i | ||||
\(239\) | 6.20058 | 0.401082 | 0.200541 | − | 0.979685i | \(-0.435730\pi\) | ||||
0.200541 | + | 0.979685i | \(0.435730\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1191 | + | 17.5268i | 0.651829 | + | 1.12900i | 0.982679 | + | 0.185318i | \(0.0593314\pi\) |
−0.330850 | + | 0.943684i | \(0.607335\pi\) | |||||||
\(242\) | 7.06095 | − | 4.07664i | 0.453895 | − | 0.262056i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 26.5271 | 1.69822 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.43179 | −0.410076 | ||||||||
\(247\) | −8.14854 | − | 4.70456i | −0.518479 | − | 0.299344i | ||||
\(248\) | 72.1990 | − | 41.6841i | 4.58464 | − | 2.64694i | ||||
\(249\) | 1.51304 | + | 2.62066i | 0.0958850 | + | 0.166078i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.21466 | −0.392266 | −0.196133 | − | 0.980577i | \(-0.562838\pi\) | ||||
−0.196133 | + | 0.980577i | \(0.562838\pi\) | |||||||
\(252\) | 10.9612 | + | 8.76831i | 0.690494 | + | 0.552352i | ||||
\(253\) | − | 18.6789i | − | 1.17433i | ||||||
\(254\) | −3.06960 | + | 5.31670i | −0.192604 | + | 0.333599i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.8027 | − | 20.4428i | −0.737667 | − | 1.27768i | ||||
\(257\) | −4.89604 | − | 2.82673i | −0.305407 | − | 0.176327i | 0.339463 | − | 0.940620i | \(-0.389755\pi\) |
−0.644869 | + | 0.764293i | \(0.723088\pi\) | |||||||
\(258\) | 8.46242i | 0.526847i | ||||||||
\(259\) | 4.04910 | + | 10.3627i | 0.251599 | + | 0.643910i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | + | 3.46410i | −0.123797 | + | 0.214423i | ||||
\(262\) | −44.9929 | + | 25.9767i | −2.77967 | + | 1.60484i | ||||
\(263\) | −21.6610 | + | 12.5060i | −1.33568 | + | 0.771153i | −0.986163 | − | 0.165779i | \(-0.946986\pi\) |
−0.349513 | + | 0.936932i | \(0.613653\pi\) | |||||||
\(264\) | −12.6216 | + | 21.8613i | −0.776806 | + | 1.34547i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.8482 | + | 2.26086i | 0.910401 | + | 0.138622i | ||||
\(267\) | − | 8.23121i | − | 0.503742i | ||||||
\(268\) | 15.1872 | + | 8.76831i | 0.927704 | + | 0.535610i | ||||
\(269\) | −3.94111 | − | 6.82619i | −0.240293 | − | 0.416200i | 0.720504 | − | 0.693450i | \(-0.243910\pi\) |
−0.960798 | + | 0.277250i | \(0.910577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.37136 | + | 4.10731i | −0.144050 | + | 0.249501i | −0.929018 | − | 0.370035i | \(-0.879346\pi\) |
0.784968 | + | 0.619536i | \(0.212679\pi\) | |||||||
\(272\) | − | 57.2763i | − | 3.47289i | ||||||
\(273\) | −1.78419 | + | 11.7177i | −0.107984 | + | 0.709187i | ||||
\(274\) | −22.3305 | −1.34904 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.5366 | − | 30.3743i | −1.05558 | − | 1.82832i | ||||
\(277\) | 6.70062 | − | 3.86860i | 0.402601 | − | 0.232442i | −0.285005 | − | 0.958526i | \(-0.591995\pi\) |
0.687606 | + | 0.726084i | \(0.258662\pi\) | |||||||
\(278\) | −2.30777 | − | 1.33239i | −0.138411 | − | 0.0799115i | ||||
\(279\) | −9.33150 | −0.558662 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.11779 | 0.126337 | 0.0631684 | − | 0.998003i | \(-0.479879\pi\) | ||||
0.0631684 | + | 0.998003i | \(0.479879\pi\) | |||||||
\(282\) | −18.2234 | − | 10.5213i | −1.08519 | − | 0.626535i | ||||
\(283\) | −3.80856 | + | 2.19887i | −0.226395 | + | 0.130709i | −0.608908 | − | 0.793241i | \(-0.708392\pi\) |
0.382513 | + | 0.923950i | \(0.375059\pi\) | |||||||
\(284\) | −30.2999 | − | 52.4810i | −1.79797 | − | 3.11417i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −34.2128 | −2.02304 | ||||||||
\(287\) | 4.91642 | + | 3.93283i | 0.290207 | + | 0.232148i | ||||
\(288\) | 18.7194i | 1.10305i | ||||||||
\(289\) | 0.451563 | − | 0.782129i | 0.0265625 | − | 0.0460076i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.50827 | − | 13.0047i | −0.440143 | − | 0.762350i | ||||
\(292\) | 12.1804 | + | 7.03234i | 0.712802 | + | 0.411536i | ||||
\(293\) | 14.2006i | 0.829607i | 0.909911 | + | 0.414803i | \(0.136150\pi\) | ||||
−0.909911 | + | 0.414803i | \(0.863850\pi\) | |||||||
\(294\) | −4.15457 | − | 18.4582i | −0.242299 | − | 1.07650i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.7844 | + | 32.5356i | −1.09182 | + | 1.89109i | ||||
\(297\) | 2.44696 | − | 1.41275i | 0.141987 | − | 0.0819761i | ||||
\(298\) | 18.3068 | − | 10.5694i | 1.06049 | − | 0.612271i | ||||
\(299\) | 14.8080 | − | 25.6482i | 0.856369 | − | 1.48327i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.17450 | − | 6.46863i | 0.298253 | − | 0.372846i | ||||
\(302\) | 8.47165i | 0.487488i | ||||||||
\(303\) | −1.93228 | − | 1.11560i | −0.111007 | − | 0.0640898i | ||||
\(304\) | 14.2154 | + | 24.6218i | 0.815310 | + | 1.41216i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.71817 | + | 9.90416i | −0.326886 | + | 0.566183i | ||||
\(307\) | − | 13.9423i | − | 0.795731i | −0.917444 | − | 0.397866i | \(-0.869751\pi\) | ||
0.917444 | − | 0.397866i | \(-0.130249\pi\) | |||||||
\(308\) | 36.9412 | − | 14.4342i | 2.10492 | − | 0.822467i | ||||
\(309\) | 7.84205 | 0.446118 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.89971 | + | 3.29040i | 0.107723 | + | 0.186581i | 0.914847 | − | 0.403800i | \(-0.132311\pi\) |
−0.807125 | + | 0.590381i | \(0.798977\pi\) | |||||||
\(312\) | −34.6617 | + | 20.0119i | −1.96233 | + | 1.13295i | ||||
\(313\) | 24.1600 | + | 13.9488i | 1.36561 | + | 0.788433i | 0.990363 | − | 0.138493i | \(-0.0442259\pi\) |
0.375243 | + | 0.926926i | \(0.377559\pi\) | |||||||
\(314\) | −63.4602 | −3.58127 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 67.0441 | 3.77153 | ||||||||
\(317\) | −29.8740 | − | 17.2478i | −1.67789 | − | 0.968730i | −0.963003 | − | 0.269490i | \(-0.913145\pi\) |
−0.714887 | − | 0.699240i | \(-0.753522\pi\) | |||||||
\(318\) | −6.03959 | + | 3.48696i | −0.338684 | + | 0.195539i | ||||
\(319\) | 5.65100 | + | 9.78782i | 0.316395 | + | 0.548013i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.6369 | 0.872768 | ||||||||
\(322\) | −7.11624 | + | 46.7359i | −0.396572 | + | 2.60449i | ||||
\(323\) | 8.88676i | 0.494473i | ||||||||
\(324\) | 2.65271 | − | 4.59463i | 0.147373 | − | 0.255257i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.8068 | − | 29.1102i | −0.930843 | − | 1.61227i | ||||
\(327\) | −2.66234 | − | 1.53710i | −0.147228 | − | 0.0850021i | ||||
\(328\) | 21.2597i | 1.17387i | ||||||||
\(329\) | 7.49646 | + | 19.1855i | 0.413293 | + | 1.05773i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9471 | − | 25.8891i | 0.821567 | − | 1.42300i | −0.0829479 | − | 0.996554i | \(-0.526434\pi\) |
0.904515 | − | 0.426442i | \(-0.140233\pi\) | |||||||
\(332\) | 13.9037 | − | 8.02731i | 0.763065 | − | 0.440556i | ||||
\(333\) | 3.64175 | − | 2.10256i | 0.199567 | − | 0.115220i | ||||
\(334\) | −24.9316 | + | 43.1827i | −1.36419 | + | 2.36285i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 22.3721 | − | 27.9673i | 1.22050 | − | 1.52574i | ||||
\(337\) | 19.3480i | 1.05395i | 0.849879 | + | 0.526977i | \(0.176675\pi\) | ||||
−0.849879 | + | 0.526977i | \(0.823325\pi\) | |||||||
\(338\) | −16.5482 | − | 9.55413i | −0.900105 | − | 0.519676i | ||||
\(339\) | −0.174499 | − | 0.302241i | −0.00947748 | − | 0.0164155i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.1831 | + | 22.8338i | −0.713904 | + | 1.23652i | ||||
\(342\) | − | 5.67677i | − | 0.306965i | ||||||
\(343\) | −8.11087 | + | 16.6497i | −0.437946 | + | 0.899001i | ||||
\(344\) | 27.9718 | 1.50814 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.3398 | + | 17.9090i | 0.555869 | + | 0.962794i | ||||
\(347\) | 22.7764 | − | 13.1500i | 1.22270 | − | 0.705927i | 0.257208 | − | 0.966356i | \(-0.417197\pi\) |
0.965493 | + | 0.260429i | \(0.0838642\pi\) | |||||||
\(348\) | 18.3785 | + | 10.6108i | 0.985191 | + | 0.568801i | ||||
\(349\) | 14.9083 | 0.798022 | 0.399011 | − | 0.916946i | \(-0.369353\pi\) | ||||
0.399011 | + | 0.916946i | \(0.369353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47992 | 0.239120 | ||||||||
\(352\) | 45.8055 | + | 26.4458i | 2.44144 | + | 1.40957i | ||||
\(353\) | 13.7013 | − | 7.91048i | 0.729249 | − | 0.421032i | −0.0888984 | − | 0.996041i | \(-0.528335\pi\) |
0.818147 | + | 0.575009i | \(0.195001\pi\) | |||||||
\(354\) | 5.11560 | + | 8.86049i | 0.271891 | + | 0.470930i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −43.6700 | −2.31451 | ||||||||
\(357\) | 10.4270 | − | 4.07421i | 0.551856 | − | 0.215630i | ||||
\(358\) | − | 6.51458i | − | 0.344306i | ||||||
\(359\) | 8.33854 | − | 14.4428i | 0.440091 | − | 0.762261i | −0.557604 | − | 0.830107i | \(-0.688279\pi\) |
0.997696 | + | 0.0678462i | \(0.0216127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.29439 | + | 12.6343i | 0.383915 | + | 0.664961i | ||||
\(362\) | −32.0612 | − | 18.5105i | −1.68510 | − | 0.972893i | ||||
\(363\) | 3.01654i | 0.158328i | ||||||||
\(364\) | 62.1673 | + | 9.46588i | 3.25845 | + | 0.496147i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.75713 | + | 11.7037i | −0.353201 | + | 0.611762i | ||||
\(367\) | 24.4112 | − | 14.0938i | 1.27425 | − | 0.735691i | 0.298469 | − | 0.954419i | \(-0.403524\pi\) |
0.975786 | + | 0.218728i | \(0.0701908\pi\) | |||||||
\(368\) | −77.4993 | + | 44.7442i | −4.03993 | + | 2.33245i | ||||
\(369\) | 1.18981 | − | 2.06082i | 0.0619392 | − | 0.107282i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.74880 | + | 1.02760i | 0.350380 | + | 0.0533506i | ||||
\(372\) | 49.5075i | 2.56684i | ||||||||
\(373\) | 20.7838 | + | 11.9995i | 1.07614 | + | 0.621312i | 0.929853 | − | 0.367930i | \(-0.119933\pi\) |
0.146290 | + | 0.989242i | \(0.453267\pi\) | |||||||
\(374\) | 16.1567 | + | 27.9842i | 0.835443 | + | 1.44703i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −34.7773 | + | 60.2361i | −1.79350 | + | 3.10644i | ||||
\(377\) | 17.9197i | 0.922910i | ||||||||
\(378\) | −6.66067 | + | 2.60256i | −0.342588 | + | 0.133861i | ||||
\(379\) | −13.8550 | −0.711683 | −0.355842 | − | 0.934546i | \(-0.615806\pi\) | ||||
−0.355842 | + | 0.934546i | \(0.615806\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.13569 | − | 1.96707i | −0.0581830 | − | 0.100776i | ||||
\(382\) | 28.4033 | − | 16.3987i | 1.45324 | − | 0.839029i | ||||
\(383\) | −26.6532 | − | 15.3882i | −1.36191 | − | 0.786301i | −0.372034 | − | 0.928219i | \(-0.621340\pi\) |
−0.989878 | + | 0.141918i | \(0.954673\pi\) | |||||||
\(384\) | 26.1392 | 1.33391 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.2337 | −1.64065 | ||||||||
\(387\) | −2.71146 | − | 1.56546i | −0.137831 | − | 0.0795768i | ||||
\(388\) | −68.9954 | + | 39.8345i | −3.50271 | + | 2.02229i | ||||
\(389\) | 19.2064 | + | 33.2664i | 0.973801 | + | 1.68667i | 0.683836 | + | 0.729636i | \(0.260310\pi\) |
0.289965 | + | 0.957037i | \(0.406356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.9718 | −1.41460 | ||||||||
\(392\) | −61.0121 | + | 13.7326i | −3.08157 | + | 0.693601i | ||||
\(393\) | − | 19.2217i | − | 0.969605i | ||||||
\(394\) | 7.43634 | − | 12.8801i | 0.374637 | − | 0.648891i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.49523 | − | 12.9821i | −0.376650 | − | 0.652376i | ||||
\(397\) | 28.9785 | + | 16.7307i | 1.45439 | + | 0.839691i | 0.998726 | − | 0.0504616i | \(-0.0160693\pi\) |
0.455662 | + | 0.890153i | \(0.349403\pi\) | |||||||
\(398\) | − | 30.6182i | − | 1.53475i | ||||||
\(399\) | −3.47117 | + | 4.33930i | −0.173776 | + | 0.217237i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.42102 | + | 12.8536i | −0.370588 | + | 0.641878i | −0.989656 | − | 0.143460i | \(-0.954177\pi\) |
0.619068 | + | 0.785337i | \(0.287511\pi\) | |||||||
\(402\) | −7.73712 | + | 4.46703i | −0.385893 | + | 0.222795i | ||||
\(403\) | −36.2036 | + | 20.9022i | −1.80343 | + | 1.04121i | ||||
\(404\) | −5.91875 | + | 10.2516i | −0.294469 | + | 0.510035i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.4103 | − | 26.6427i | −0.516652 | − | 1.32225i | ||||
\(407\) | − | 11.8816i | − | 0.588949i | ||||||
\(408\) | 32.7374 | + | 18.9009i | 1.62074 | + | 0.935736i | ||||
\(409\) | 4.22246 | + | 7.31351i | 0.208787 | + | 0.361630i | 0.951333 | − | 0.308166i | \(-0.0997151\pi\) |
−0.742546 | + | 0.669796i | \(0.766382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.13092 | − | 7.15496i | 0.203763 | − | 0.352928i | ||||
\(412\) | − | 41.6053i | − | 2.04975i | ||||||
\(413\) | 1.50756 | − | 9.90094i | 0.0741824 | − | 0.487193i | ||||
\(414\) | 17.8681 | 0.878170 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 41.9307 | + | 72.6261i | 2.05582 | + | 3.56079i | ||||
\(417\) | 0.853827 | − | 0.492957i | 0.0418121 | − | 0.0241402i | ||||
\(418\) | −13.8908 | − | 8.01987i | −0.679422 | − | 0.392264i | ||||
\(419\) | 18.8427 | 0.920524 | 0.460262 | − | 0.887783i | \(-0.347755\pi\) | ||||
0.460262 | + | 0.887783i | \(0.347755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.09687 | −0.443355 | −0.221677 | − | 0.975120i | \(-0.571153\pi\) | ||||
−0.221677 | + | 0.975120i | \(0.571153\pi\) | |||||||
\(422\) | 20.6476 | + | 11.9209i | 1.00511 | + | 0.580299i | ||||
\(423\) | 6.74230 | − | 3.89267i | 0.327822 | − | 0.189268i | ||||
\(424\) | 11.5259 | + | 19.9634i | 0.559745 | + | 0.969507i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 30.8727 | 1.49579 | ||||||||
\(427\) | 12.3216 | − | 4.81448i | 0.596282 | − | 0.232989i | ||||
\(428\) | − | 82.9604i | − | 4.01004i | ||||||
\(429\) | 6.32901 | − | 10.9622i | 0.305567 | − | 0.529258i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.47992 | + | 4.29534i | 0.119453 | + | 0.206899i | 0.919551 | − | 0.392970i | \(-0.128552\pi\) |
−0.800098 | + | 0.599870i | \(0.795219\pi\) | |||||||
\(432\) | −11.7231 | − | 6.76831i | −0.564026 | − | 0.325641i | ||||
\(433\) | 2.61696i | 0.125763i | 0.998021 | + | 0.0628815i | \(0.0200290\pi\) | ||||
−0.998021 | + | 0.0628815i | \(0.979971\pi\) | |||||||
\(434\) | 41.6841 | − | 52.1092i | 2.00090 | − | 2.50132i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.15498 | + | 14.1248i | −0.390553 | + | 0.676458i | ||||
\(437\) | 12.0245 | − | 6.94233i | 0.575209 | − | 0.332097i | ||||
\(438\) | −6.20531 | + | 3.58264i | −0.296501 | + | 0.171185i | ||||
\(439\) | −13.2525 | + | 22.9540i | −0.632508 | + | 1.09554i | 0.354529 | + | 0.935045i | \(0.384641\pi\) |
−0.987037 | + | 0.160491i | \(0.948692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.68277 | + | 2.08340i | 0.318227 | + | 0.0992097i | ||||
\(442\) | 51.2338i | 2.43695i | ||||||||
\(443\) | 34.1996 | + | 19.7452i | 1.62487 | + | 0.938121i | 0.985590 | + | 0.169150i | \(0.0541023\pi\) |
0.639284 | + | 0.768971i | \(0.279231\pi\) | |||||||
\(444\) | −11.1550 | − | 19.3210i | −0.529392 | − | 0.916934i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 35.7973 | − | 62.0027i | 1.69505 | − | 2.93591i | ||||
\(447\) | 7.82095i | 0.369918i | ||||||||
\(448\) | −48.5987 | − | 38.8759i | −2.29607 | − | 1.83671i | ||||
\(449\) | −21.3045 | −1.00542 | −0.502710 | − | 0.864455i | \(-0.667664\pi\) | ||||
−0.502710 | + | 0.864455i | \(0.667664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.36182 | − | 5.82284i | −0.158302 | − | 0.274187i | ||||
\(452\) | −1.60352 | + | 0.925790i | −0.0754230 | + | 0.0435455i | ||||
\(453\) | −2.71441 | − | 1.56717i | −0.127534 | − | 0.0736319i | ||||
\(454\) | −48.0331 | −2.25430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.7641 | −0.878710 | ||||||||
\(457\) | −24.1449 | − | 13.9401i | −1.12945 | − | 0.652088i | −0.185654 | − | 0.982615i | \(-0.559440\pi\) |
−0.943797 | + | 0.330527i | \(0.892774\pi\) | |||||||
\(458\) | 43.6428 | − | 25.1972i | 2.03929 | − | 1.17739i | ||||
\(459\) | −2.11560 | − | 3.66433i | −0.0987479 | − | 0.171036i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.5237 | 1.04903 | 0.524516 | − | 0.851401i | \(-0.324246\pi\) | ||||
0.524516 | + | 0.851401i | \(0.324246\pi\) | |||||||
\(462\) | −3.04151 | + | 19.9751i | −0.141504 | + | 0.929328i | ||||
\(463\) | 1.69301i | 0.0786809i | 0.999226 | + | 0.0393405i | \(0.0125257\pi\) | ||||
−0.999226 | + | 0.0393405i | \(0.987474\pi\) | |||||||
\(464\) | 27.0733 | − | 46.8923i | 1.25684 | − | 2.17692i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.2018 | − | 22.8662i | −0.611562 | − | 1.05926i | ||||
\(467\) | 0.0695685 | + | 0.0401654i | 0.00321925 | + | 0.00185863i | 0.501609 | − | 0.865095i | \(-0.332742\pi\) |
−0.498390 | + | 0.866953i | \(0.666075\pi\) | |||||||
\(468\) | − | 23.7678i | − | 1.09867i | ||||||
\(469\) | 8.64567 | + | 1.31643i | 0.399220 | + | 0.0607871i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.7395 | − | 20.3334i | 0.540927 | − | 0.936913i | ||||
\(472\) | 29.2876 | − | 16.9092i | 1.34807 | − | 0.778310i | ||||
\(473\) | −7.66122 | + | 4.42321i | −0.352263 | + | 0.203379i | ||||
\(474\) | −17.0779 | + | 29.5797i | −0.784412 | + | 1.35864i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −21.6154 | − | 55.3197i | −0.990740 | − | 2.53557i | ||||
\(477\) | − | 2.58021i | − | 0.118140i | ||||||
\(478\) | 14.5139 | + | 8.37963i | 0.663852 | + | 0.383275i | ||||
\(479\) | −19.3891 | − | 33.5830i | −0.885912 | − | 1.53444i | −0.844665 | − | 0.535295i | \(-0.820200\pi\) |
−0.0412471 | − | 0.999149i | \(-0.513133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.41932 | − | 16.3147i | 0.429484 | − | 0.743888i | ||||
\(482\) | 54.7009i | 2.49156i | ||||||||
\(483\) | −13.6583 | − | 10.9258i | −0.621474 | − | 0.497141i | ||||
\(484\) | 16.0040 | 0.727456 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.35143 | + | 2.34074i | 0.0613020 | + | 0.106178i | ||||
\(487\) | −23.4961 | + | 13.5655i | −1.06471 | + | 0.614710i | −0.926731 | − | 0.375726i | \(-0.877393\pi\) |
−0.137977 | + | 0.990435i | \(0.544060\pi\) | |||||||
\(488\) | 38.6856 | + | 22.3352i | 1.75122 | + | 1.01106i | ||||
\(489\) | 12.4363 | 0.562391 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7243 | 0.754755 | 0.377378 | − | 0.926059i | \(-0.376826\pi\) | ||||
0.377378 | + | 0.926059i | \(0.376826\pi\) | |||||||
\(492\) | −10.9335 | − | 6.31246i | −0.492920 | − | 0.284588i | ||||
\(493\) | 14.6573 | − | 8.46242i | 0.660133 | − | 0.381128i | ||||
\(494\) | −12.7157 | − | 22.0243i | −0.572108 | − | 0.990920i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 126.317 | 5.67180 | ||||||||
\(497\) | −23.5989 | − | 18.8777i | −1.05856 | − | 0.846779i | ||||
\(498\) | 8.17905i | 0.366512i | ||||||||
\(499\) | 9.89219 | − | 17.1338i | 0.442835 | − | 0.767013i | −0.555063 | − | 0.831808i | \(-0.687306\pi\) |
0.997899 | + | 0.0647949i | \(0.0206393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.22417 | − | 15.9767i | −0.412105 | − | 0.713787i | ||||
\(502\) | −14.5469 | − | 8.39866i | −0.649261 | − | 0.374851i | ||||
\(503\) | 6.75015i | 0.300975i | 0.988612 | + | 0.150487i | \(0.0480843\pi\) | ||||
−0.988612 | + | 0.150487i | \(0.951916\pi\) | |||||||
\(504\) | 8.60256 | + | 22.0163i | 0.383189 | + | 0.980685i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 25.2432 | − | 43.7225i | 1.12220 | − | 1.94370i | ||||
\(507\) | 6.12250 | − | 3.53483i | 0.271910 | − | 0.156987i | ||||
\(508\) | −10.4361 | + | 6.02529i | −0.463028 | + | 0.267329i | ||||
\(509\) | −20.1735 | + | 34.9416i | −0.894177 | + | 1.54876i | −0.0593561 | + | 0.998237i | \(0.518905\pi\) |
−0.834820 | + | 0.550522i | \(0.814429\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.93397 | + | 1.05580i | 0.306741 | + | 0.0467058i | ||||
\(512\) | − | 11.5234i | − | 0.509266i | ||||||
\(513\) | 1.81890 | + | 1.05014i | 0.0803066 | + | 0.0463650i | ||||
\(514\) | −7.64024 | − | 13.2333i | −0.336996 | − | 0.583695i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.30542 | + | 14.3854i | −0.365626 | + | 0.633282i | ||||
\(517\) | − | 21.9975i | − | 0.967448i | ||||||
\(518\) | −4.52661 | + | 29.7286i | −0.198888 | + | 1.30620i | ||||
\(519\) | −7.65100 | −0.335842 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.8019 | − | 32.5658i | −0.823725 | − | 1.42673i | −0.902890 | − | 0.429872i | \(-0.858559\pi\) |
0.0791643 | − | 0.996862i | \(-0.474775\pi\) | |||||||
\(522\) | −9.36296 | + | 5.40571i | −0.409806 | + | 0.236601i | ||||
\(523\) | 34.0456 | + | 19.6562i | 1.48871 | + | 0.859506i | 0.999917 | − | 0.0128944i | \(-0.00410453\pi\) |
0.488792 | + | 0.872401i | \(0.337438\pi\) | |||||||
\(524\) | −101.979 | −4.45497 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −67.6038 | −2.94766 | ||||||||
\(527\) | 34.1937 | + | 19.7418i | 1.48950 | + | 0.859964i | ||||
\(528\) | −33.1235 | + | 19.1239i | −1.44152 | + | 0.832260i | ||||
\(529\) | 10.3516 | + | 17.9295i | 0.450069 | + | 0.779542i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.78534 | −0.164270 | ||||||||
\(532\) | 23.0218 | + | 18.4160i | 0.998121 | + | 0.798435i | ||||
\(533\) | − | 10.6605i | − | 0.461759i | ||||||
\(534\) | 11.1239 | − | 19.2671i | 0.481377 | − | 0.833770i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.7654 | + | 25.5744i | 0.637768 | + | 1.10465i | ||||
\(537\) | 2.08734 | + | 1.20513i | 0.0900756 | + | 0.0520052i | ||||
\(538\) | − | 21.3045i | − | 0.918501i | ||||||
\(539\) | 14.5391 | − | 13.4091i | 0.626243 | − | 0.577571i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.7861 | + | 18.6821i | −0.463732 | + | 0.803207i | −0.999143 | − | 0.0413846i | \(-0.986823\pi\) |
0.535412 | + | 0.844591i | \(0.320156\pi\) | |||||||
\(542\) | −11.1015 | + | 6.40943i | −0.476848 | + | 0.275309i | ||||
\(543\) | 11.8620 | − | 6.84852i | 0.509046 | − | 0.293898i | ||||
\(544\) | 39.6028 | − | 68.5941i | 1.69796 | − | 2.94095i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −20.0119 | + | 25.0169i | −0.856432 | + | 1.07062i | ||||
\(547\) | − | 21.3707i | − | 0.913745i | −0.889532 | − | 0.456873i | \(-0.848969\pi\) | ||
0.889532 | − | 0.456873i | \(-0.151031\pi\) | |||||||
\(548\) | −37.9601 | − | 21.9163i | −1.62157 | − | 0.936216i | ||||
\(549\) | −2.50000 | − | 4.33013i | −0.106697 | − | 0.184805i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.20058 | + | 7.27562i | −0.178951 | + | 0.309952i | ||||
\(552\) | − | 59.0616i | − | 2.51383i | ||||||
\(553\) | 31.1413 | − | 12.1680i | 1.32426 | − | 0.517437i | ||||
\(554\) | 20.9125 | 0.888488 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.61534 | − | 4.52991i | −0.110915 | − | 0.192111i | ||||
\(557\) | 12.3511 | − | 7.13092i | 0.523334 | − | 0.302147i | −0.214964 | − | 0.976622i | \(-0.568963\pi\) |
0.738297 | + | 0.674475i | \(0.235630\pi\) | |||||||
\(558\) | −21.8426 | − | 12.6108i | −0.924671 | − | 0.533859i | ||||
\(559\) | −14.0263 | −0.593248 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.9553 | −0.504752 | ||||||||
\(562\) | 4.95719 | + | 2.86204i | 0.209107 | + | 0.120728i | ||||
\(563\) | 2.04649 | − | 1.18154i | 0.0862493 | − | 0.0497961i | −0.456255 | − | 0.889849i | \(-0.650810\pi\) |
0.542504 | + | 0.840053i | \(0.317476\pi\) | |||||||
\(564\) | −20.6522 | − | 35.7707i | −0.869616 | − | 1.50622i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.8865 | −0.499625 | ||||||||
\(567\) | 0.398264 | − | 2.61560i | 0.0167255 | − | 0.109845i | ||||
\(568\) | − | 102.047i | − | 4.28180i | ||||||
\(569\) | −6.37289 | + | 11.0382i | −0.267166 | + | 0.462744i | −0.968129 | − | 0.250453i | \(-0.919420\pi\) |
0.700963 | + | 0.713197i | \(0.252754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.180757 | − | 0.313080i | −0.00756444 | − | 0.0131020i | 0.862218 | − | 0.506537i | \(-0.169075\pi\) |
−0.869783 | + | 0.493435i | \(0.835741\pi\) | |||||||
\(572\) | −58.1588 | − | 33.5780i | −2.43174 | − | 1.40397i | ||||
\(573\) | 12.1343i | 0.506919i | ||||||||
\(574\) | 6.19314 | + | 15.8499i | 0.258496 | + | 0.661563i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.7613 | + | 20.3711i | −0.490053 | + | 0.848797i | ||||
\(577\) | 8.30807 | − | 4.79667i | 0.345870 | − | 0.199688i | −0.316995 | − | 0.948427i | \(-0.602674\pi\) |
0.662865 | + | 0.748739i | \(0.269341\pi\) | |||||||
\(578\) | 2.11398 | − | 1.22051i | 0.0879300 | − | 0.0507664i | ||||
\(579\) | 5.96290 | − | 10.3280i | 0.247809 | − | 0.429219i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.00123 | − | 6.25202i | 0.207486 | − | 0.259378i | ||||
\(582\) | − | 40.5875i | − | 1.68241i | ||||||
\(583\) | −6.31365 | − | 3.64519i | −0.261485 | − | 0.150968i | ||||
\(584\) | 11.8421 | + | 20.5111i | 0.490030 | + | 0.848757i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.1910 | + | 33.2399i | −0.792775 | + | 1.37313i | ||||
\(587\) | 19.2217i | 0.793363i | 0.917956 | + | 0.396682i | \(0.129838\pi\) | ||||
−0.917956 | + | 0.396682i | \(0.870162\pi\) | |||||||
\(588\) | 11.0533 | − | 35.4549i | 0.455832 | − | 1.46214i | ||||
\(589\) | −19.5988 | −0.807556 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.75129 | + | 4.76538i | 0.113173 | + | 0.196021i | ||||
\(592\) | −49.2970 | + | 28.4616i | −2.02609 | + | 1.16977i | ||||
\(593\) | 10.2186 | + | 5.89971i | 0.419628 | + | 0.242272i | 0.694918 | − | 0.719089i | \(-0.255441\pi\) |
−0.275290 | + | 0.961361i | \(0.588774\pi\) | |||||||
\(594\) | 7.63692 | 0.313346 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 41.4934 | 1.69964 | ||||||||
\(597\) | 9.81041 | + | 5.66404i | 0.401513 | + | 0.231814i | ||||
\(598\) | 69.3234 | − | 40.0239i | 2.83484 | − | 1.63670i | ||||
\(599\) | 20.1981 | + | 34.9841i | 0.825271 | + | 1.42941i | 0.901712 | + | 0.432338i | \(0.142311\pi\) |
−0.0764403 | + | 0.997074i | \(0.524355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9073 | −0.852828 | −0.426414 | − | 0.904528i | \(-0.640223\pi\) | ||||
−0.426414 | + | 0.904528i | \(0.640223\pi\) | |||||||
\(602\) | 20.8540 | − | 8.14842i | 0.849947 | − | 0.332105i | ||||
\(603\) | − | 3.30542i | − | 0.134607i | ||||||
\(604\) | −8.31448 | + | 14.4011i | −0.338311 | + | 0.585972i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.01532 | − | 5.22268i | −0.122489 | − | 0.212157i | ||||
\(607\) | 3.64388 | + | 2.10379i | 0.147900 | + | 0.0853903i | 0.572124 | − | 0.820167i | \(-0.306120\pi\) |
−0.424224 | + | 0.905557i | \(0.639453\pi\) | |||||||
\(608\) | 39.3161i | 1.59448i | ||||||||
\(609\) | 10.4624 | + | 1.59306i | 0.423959 | + | 0.0645539i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.4388 | − | 30.2049i | 0.705500 | − | 1.22196i | ||||
\(612\) | −19.4408 | + | 11.2242i | −0.785849 | + | 0.453710i | ||||
\(613\) | 14.2260 | − | 8.21340i | 0.574584 | − | 0.331736i | −0.184394 | − | 0.982852i | \(-0.559032\pi\) |
0.758978 | + | 0.651116i | \(0.225699\pi\) | |||||||
\(614\) | 18.8420 | − | 32.6354i | 0.760403 | − | 1.31706i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 66.0262 | + | 10.0535i | 2.66027 | + | 0.405066i | ||||
\(617\) | − | 21.9037i | − | 0.881811i | −0.897553 | − | 0.440906i | \(-0.854657\pi\) | ||
0.897553 | − | 0.440906i | \(-0.145343\pi\) | |||||||
\(618\) | 18.3562 | + | 10.5980i | 0.738394 | + | 0.426312i | ||||
\(619\) | 0.159752 | + | 0.276699i | 0.00642098 | + | 0.0111215i | 0.869218 | − | 0.494429i | \(-0.164623\pi\) |
−0.862797 | + | 0.505550i | \(0.831289\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.30542 | + | 5.72515i | −0.132642 | + | 0.229742i | ||||
\(622\) | 10.2693i | 0.411761i | ||||||||
\(623\) | −20.2843 | + | 7.92579i | −0.812672 | + | 0.317540i | ||||
\(624\) | −60.6430 | −2.42766 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 37.7016 | + | 65.3011i | 1.50686 | + | 2.60996i | ||||
\(627\) | 5.13931 | − | 2.96718i | 0.205244 | − | 0.118498i | ||||
\(628\) | −107.877 | − | 62.2829i | −4.30476 | − | 2.48536i | ||||
\(629\) | −17.7928 | −0.709445 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3090 | 0.689061 | 0.344530 | − | 0.938775i | \(-0.388038\pi\) | ||||
0.344530 | + | 0.938775i | \(0.388038\pi\) | |||||||
\(632\) | 97.7734 | + | 56.4495i | 3.88922 | + | 2.24544i | ||||
\(633\) | −7.63917 | + | 4.41048i | −0.303630 | + | 0.175301i | ||||
\(634\) | −46.6182 | − | 80.7450i | −1.85144 | − | 3.20679i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.6891 | −0.542807 | ||||||||
\(637\) | 30.5940 | − | 6.88610i | 1.21218 | − | 0.272837i | ||||
\(638\) | 30.5477i | 1.20939i | ||||||||
\(639\) | −5.71113 | + | 9.89196i | −0.225929 | + | 0.391320i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.1429 | − | 41.8168i | −0.953588 | − | 1.65166i | −0.737567 | − | 0.675273i | \(-0.764026\pi\) |
−0.216020 | − | 0.976389i | \(-0.569308\pi\) | |||||||
\(642\) | 36.6020 | + | 21.1321i | 1.44456 | + | 0.834019i | ||||
\(643\) | 12.6460i | 0.498710i | 0.968412 | + | 0.249355i | \(0.0802186\pi\) | ||||
−0.968412 | + | 0.249355i | \(0.919781\pi\) | |||||||
\(644\) | −57.9659 | + | 72.4630i | −2.28418 | + | 2.85544i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0098 | + | 20.8016i | −0.472520 | + | 0.818428i | ||||
\(647\) | 13.7295 | − | 7.92671i | 0.539761 | − | 0.311631i | −0.205221 | − | 0.978716i | \(-0.565791\pi\) |
0.744982 | + | 0.667084i | \(0.232458\pi\) | |||||||
\(648\) | 7.73712 | − | 4.46703i | 0.303943 | − | 0.175482i | ||||
\(649\) | −5.34773 | + | 9.26255i | −0.209917 | + | 0.363587i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.98525 | + | 22.9957i | 0.352160 | + | 0.901273i | ||||
\(652\) | − | 65.9800i | − | 2.58398i | ||||||
\(653\) | −1.00282 | − | 0.578977i | −0.0392433 | − | 0.0226571i | 0.480250 | − | 0.877132i | \(-0.340546\pi\) |
−0.519493 | + | 0.854475i | \(0.673879\pi\) | |||||||
\(654\) | −4.15457 | − | 7.19593i | −0.162457 | − | 0.281383i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16.1061 | + | 27.8965i | −0.628836 | + | 1.08918i | ||||
\(657\) | − | 2.65100i | − | 0.103425i | ||||||
\(658\) | −8.38053 | + | 55.0392i | −0.326707 | + | 2.14565i | ||||
\(659\) | 34.5617 | 1.34633 | 0.673167 | − | 0.739490i | \(-0.264933\pi\) | ||||
0.673167 | + | 0.739490i | \(0.264933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.640148 | + | 1.10877i | 0.0248989 | + | 0.0431261i | 0.878206 | − | 0.478282i | \(-0.158740\pi\) |
−0.853307 | + | 0.521408i | \(0.825407\pi\) | |||||||
\(662\) | 69.9746 | − | 40.3998i | 2.71964 | − | 1.57018i | ||||
\(663\) | −16.4159 | − | 9.47773i | −0.637541 | − | 0.368085i | ||||
\(664\) | 27.0352 | 1.04917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.3658 | 0.440418 | ||||||||
\(667\) | −22.9006 | − | 13.2217i | −0.886715 | − | 0.511945i | ||||
\(668\) | −84.7632 | + | 48.9381i | −3.27959 | + | 1.89347i | ||||
\(669\) | 13.2442 | + | 22.9397i | 0.512052 | + | 0.886900i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1275 | −0.545386 | ||||||||
\(672\) | 46.1304 | − | 18.0248i | 1.77952 | − | 0.695322i | ||||
\(673\) | 45.9058i | 1.76954i | 0.466031 | + | 0.884769i | \(0.345684\pi\) | ||||
−0.466031 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(674\) | −26.1475 | + | 45.2887i | −1.00716 | + | 1.74446i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.7537 | − | 32.4824i | −0.721298 | − | 1.24932i | ||||
\(677\) | 17.0694 | + | 9.85499i | 0.656028 | + | 0.378758i | 0.790762 | − | 0.612124i | \(-0.209685\pi\) |
−0.134734 | + | 0.990882i | \(0.543018\pi\) | |||||||
\(678\) | − | 0.943291i | − | 0.0362269i | ||||||
\(679\) | −24.8180 | + | 31.0249i | −0.952427 | + | 1.19063i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.88562 | − | 15.3904i | 0.340498 | − | 0.589760i | ||||
\(682\) | −61.7163 | + | 35.6319i | −2.36324 | + | 1.36442i | ||||
\(683\) | 1.24982 | − | 0.721583i | 0.0478230 | − | 0.0276106i | −0.475898 | − | 0.879501i | \(-0.657877\pi\) |
0.523721 | + | 0.851890i | \(0.324543\pi\) | |||||||
\(684\) | 5.57146 | − | 9.65005i | 0.213030 | − | 0.368979i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −41.4863 | + | 28.0115i | −1.58396 | + | 1.06948i | ||||
\(687\) | 18.6449i | 0.711347i | ||||||||
\(688\) | 36.7040 | + | 21.1910i | 1.39933 | + | 0.807901i | ||||
\(689\) | −5.77956 | − | 10.0105i | −0.220184 | − | 0.381369i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4611 | − | 26.7793i | 0.588167 | − | 1.01873i | −0.406306 | − | 0.913737i | \(-0.633183\pi\) |
0.994473 | − | 0.104997i | \(-0.0334834\pi\) | |||||||
\(692\) | 40.5918i | 1.54307i | ||||||||
\(693\) | −5.83762 | − | 4.66973i | −0.221753 | − | 0.177388i | ||||
\(694\) | 71.0848 | 2.69834 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 17.8681 | + | 30.9485i | 0.677290 | + | 1.17310i | ||||
\(697\) | −8.71975 | + | 5.03435i | −0.330284 | + | 0.190690i | ||||
\(698\) | 34.8964 | + | 20.1475i | 1.32085 | + | 0.762593i | ||||
\(699\) | 9.76879 | 0.369490 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.6746 | 1.91395 | 0.956976 | − | 0.290168i | \(-0.0937111\pi\) | ||||
0.956976 | + | 0.290168i | \(0.0937111\pi\) | |||||||
\(702\) | 10.4863 | + | 6.05428i | 0.395781 | + | 0.228504i | ||||
\(703\) | 7.64873 | − | 4.41599i | 0.288477 | − | 0.166552i | ||||
\(704\) | 33.2315 | + | 57.5586i | 1.25246 | + | 2.16932i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 42.7617 | 1.60936 | ||||||||
\(707\) | −0.888611 | + | 5.83596i | −0.0334196 | + | 0.219484i | ||||
\(708\) | 20.0828i | 0.754757i | ||||||||
\(709\) | −10.0885 | + | 17.4738i | −0.378881 | + | 0.656241i | −0.990900 | − | 0.134602i | \(-0.957024\pi\) |
0.612019 | + | 0.790843i | \(0.290358\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.31846 | − | 10.9439i | −0.236961 | − | 0.410428i | ||||
\(712\) | −63.6859 | − | 36.7691i | −2.38673 | − | 1.37798i | ||||
\(713\) | − | 61.6890i | − | 2.31027i | ||||||
\(714\) | 29.9129 | + | 4.55469i | 1.11946 | + | 0.170455i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.39371 | − | 11.0742i | 0.238944 | − | 0.413864i | ||||
\(717\) | −5.36986 | + | 3.10029i | −0.200541 | + | 0.115782i | ||||
\(718\) | 39.0367 | − | 22.5379i | 1.45684 | − | 0.841105i | ||||
\(719\) | 22.6639 | − | 39.2551i | 0.845221 | − | 1.46397i | −0.0402072 | − | 0.999191i | \(-0.512802\pi\) |
0.885429 | − | 0.464775i | \(-0.153865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.55107 | − | 19.3252i | −0.281216 | − | 0.719710i | ||||
\(722\) | 39.4314i | 1.46748i | ||||||||
\(723\) | −17.5268 | − | 10.1191i | −0.651829 | − | 0.376334i | ||||
\(724\) | −36.3343 | − | 62.9328i | −1.35035 | − | 2.33888i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.07664 | + | 7.06095i | −0.151298 | + | 0.262056i | ||||
\(727\) | 16.9117i | 0.627220i | 0.949552 | + | 0.313610i | \(0.101539\pi\) | ||||
−0.949552 | + | 0.313610i | \(0.898461\pi\) | |||||||
\(728\) | 82.6912 | + | 66.1478i | 3.06474 | + | 2.45160i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.62379 | + | 11.4727i | 0.244990 | + | 0.424334i | ||||
\(732\) | −22.9731 | + | 13.2635i | −0.849112 | + | 0.490235i | ||||
\(733\) | 6.20557 | + | 3.58279i | 0.229208 | + | 0.132333i | 0.610207 | − | 0.792242i | \(-0.291086\pi\) |
−0.380999 | + | 0.924576i | \(0.624420\pi\) | |||||||
\(734\) | 76.1870 | 2.81211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −123.751 | −4.56152 | ||||||||
\(737\) | −8.08821 | − | 4.66973i | −0.297933 | − | 0.172012i | ||||
\(738\) | 5.57009 | − | 3.21589i | 0.205038 | − | 0.118379i | ||||
\(739\) | −10.1924 | − | 17.6537i | −0.374933 | − | 0.649404i | 0.615384 | − | 0.788228i | \(-0.289001\pi\) |
−0.990317 | + | 0.138824i | \(0.955668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.40912 | 0.345653 | ||||||||
\(742\) | 14.4085 | + | 11.5259i | 0.528951 | + | 0.423128i | ||||
\(743\) | − | 16.9267i | − | 0.620982i | −0.950576 | − | 0.310491i | \(-0.899507\pi\) | ||
0.950576 | − | 0.310491i | \(-0.100493\pi\) | |||||||
\(744\) | −41.6841 | + | 72.1990i | −1.52821 | + | 2.64694i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.4330 | + | 56.1755i | 1.18745 | + | 2.05673i | ||||
\(747\) | −2.62066 | − | 1.51304i | −0.0958850 | − | 0.0553592i | ||||
\(748\) | 63.4278i | 2.31915i | ||||||||
\(749\) | −15.0567 | − | 38.5342i | −0.550160 | − | 1.40801i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.5439 | + | 33.8509i | −0.713165 | + | 1.23524i | 0.250498 | + | 0.968117i | \(0.419406\pi\) |
−0.963663 | + | 0.267121i | \(0.913928\pi\) | |||||||
\(752\) | −91.2680 | + | 52.6936i | −3.32820 | + | 1.92154i | ||||
\(753\) | 5.38206 | − | 3.10733i | 0.196133 | − | 0.113237i | ||||
\(754\) | −24.2171 | + | 41.9453i | −0.881936 | + | 1.52756i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.8769 | − | 2.11296i | −0.504697 | − | 0.0768476i | ||||
\(757\) | − | 22.6675i | − | 0.823866i | −0.911214 | − | 0.411933i | \(-0.864854\pi\) | ||
0.911214 | − | 0.411933i | \(-0.135146\pi\) | |||||||
\(758\) | −32.4309 | − | 18.7240i | −1.17794 | − | 0.680087i | ||||
\(759\) | 9.33946 | + | 16.1764i | 0.339001 | + | 0.587167i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.16373 | + | 8.94385i | −0.187185 | + | 0.324214i | −0.944311 | − | 0.329055i | \(-0.893270\pi\) |
0.757125 | + | 0.653269i | \(0.226603\pi\) | |||||||
\(762\) | − | 6.13919i | − | 0.222399i | ||||||
\(763\) | −1.22435 | + | 8.04092i | −0.0443244 | + | 0.291101i | ||||
\(764\) | 64.3777 | 2.32910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.5921 | − | 72.0396i | −1.50278 | − | 2.60290i | ||||
\(767\) | −14.6861 | + | 8.47900i | −0.530283 | + | 0.306159i | ||||
\(768\) | 20.4428 | + | 11.8027i | 0.737667 | + | 0.425892i | ||||
\(769\) | 25.8785 | 0.933204 | 0.466602 | − | 0.884467i | \(-0.345478\pi\) | ||||
0.466602 | + | 0.884467i | \(0.345478\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.65346 | 0.203604 | ||||||||
\(772\) | −54.7946 | − | 31.6357i | −1.97210 | − | 1.13859i | ||||
\(773\) | −8.10094 | + | 4.67708i | −0.291371 | + | 0.168223i | −0.638560 | − | 0.769572i | \(-0.720470\pi\) |
0.347189 | + | 0.937795i | \(0.387136\pi\) | |||||||
\(774\) | −4.23121 | − | 7.32867i | −0.152088 | − | 0.263424i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −134.159 | −4.81602 | ||||||||
\(777\) | −8.68800 | − | 6.94986i | −0.311680 | − | 0.249325i | ||||
\(778\) | 103.824i | 3.72227i | ||||||||
\(779\) | 2.49895 | − | 4.32831i | 0.0895343 | − | 0.155078i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.1368 | + | 27.9497i | 0.577420 | + | 1.00012i | ||||
\(782\) | −65.4748 | − | 37.8019i | −2.34137 | − | 1.35179i | ||||
\(783\) | − | 4.00000i | − | 0.142948i | ||||||
\(784\) | −90.4622 | − | 28.2023i | −3.23079 | − | 1.00722i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 25.9767 | − | 44.9929i | 0.926558 | − | 1.60484i | ||||
\(787\) | −2.42650 | + | 1.40094i | −0.0864953 | + | 0.0499381i | −0.542624 | − | 0.839976i | \(-0.682569\pi\) |
0.456128 | + | 0.889914i | \(0.349236\pi\) | |||||||
\(788\) | 25.2823 | − | 14.5968i | 0.900645 | − | 0.519988i | ||||
\(789\) | 12.5060 | − | 21.6610i | 0.445225 | − | 0.771153i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.576792 | + | 0.721046i | −0.0205084 | + | 0.0256375i | ||||
\(792\) | − | 25.2432i | − | 0.896978i | ||||||
\(793\) | −19.3986 | − | 11.1998i | −0.688865 | − | 0.397716i | ||||
\(794\) | 45.2207 | + | 78.3246i | 1.60482 | + | 2.77964i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30.0501 | − | 52.0483i | 1.06510 | − | 1.84480i | ||||
\(797\) | 13.0211i | 0.461231i | 0.973045 | + | 0.230615i | \(0.0740739\pi\) | ||||
−0.973045 | + | 0.230615i | \(0.925926\pi\) | |||||||
\(798\) | −13.9893 | + | 5.46614i | −0.495217 | + | 0.193499i | ||||
\(799\) | −32.9414 | −1.16538 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.11560 | + | 7.12844i | 0.145418 | + | 0.251871i | ||||
\(802\) | −34.7414 | + | 20.0579i | −1.22676 | + | 0.708270i | ||||
\(803\) | −6.48688 | − | 3.74520i | −0.228917 | − | 0.132165i | ||||
\(804\) | −17.5366 | −0.618469 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −112.991 | −3.97994 | ||||||||
\(807\) | 6.82619 | + | 3.94111i | 0.240293 | + | 0.138733i | ||||
\(808\) | −17.2631 | + | 9.96688i | −0.607315 | + | 0.350634i | ||||
\(809\) | 10.5105 | + | 18.2048i | 0.369531 | + | 0.640047i | 0.989492 | − | 0.144586i | \(-0.0461850\pi\) |
−0.619961 | + | 0.784633i | \(0.712852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.2591 | −1.62438 | −0.812189 | − | 0.583395i | \(-0.801724\pi\) | ||||
−0.812189 | + | 0.583395i | \(0.801724\pi\) | |||||||
\(812\) | 8.45184 | − | 55.5075i | 0.296601 | − | 1.94793i | ||||
\(813\) | − | 4.74271i | − | 0.166334i | ||||||
\(814\) | 16.0571 | − | 27.8117i | 0.562801 | − | 0.974801i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 28.6381 | + | 49.6027i | 1.00254 | + | 1.73644i | ||||
\(817\) | −5.69484 | − | 3.28792i | −0.199237 | − | 0.115030i | ||||
\(818\) | 22.8254i | 0.798070i | ||||||||
\(819\) | −4.31369 | − | 11.0399i | −0.150733 | − | 0.385766i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.46915 | + | 14.6690i | −0.295575 | + | 0.511952i | −0.975119 | − | 0.221684i | \(-0.928845\pi\) |
0.679543 | + | 0.733636i | \(0.262178\pi\) | |||||||
\(822\) | 19.3388 | − | 11.1653i | 0.674519 | − | 0.389434i | ||||
\(823\) | −16.0502 | + | 9.26661i | −0.559476 | + | 0.323014i | −0.752935 | − | 0.658095i | \(-0.771363\pi\) |
0.193459 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(824\) | 35.0307 | − | 60.6749i | 1.22035 | − | 2.11371i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.9092 | − | 21.1382i | 0.588347 | − | 0.735491i | ||||
\(827\) | − | 32.5496i | − | 1.13186i | −0.824453 | − | 0.565930i | \(-0.808517\pi\) | ||
0.824453 | − | 0.565930i | \(-0.191483\pi\) | |||||||
\(828\) | 30.3743 | + | 17.5366i | 1.05558 | + | 0.609440i | ||||
\(829\) | −5.47764 | − | 9.48755i | −0.190246 | − | 0.329516i | 0.755085 | − | 0.655626i | \(-0.227595\pi\) |
−0.945332 | + | 0.326110i | \(0.894262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.86860 | + | 6.70062i | −0.134200 | + | 0.232442i | ||||
\(832\) | 105.379i | 3.65336i | ||||||||
\(833\) | −20.0802 | − | 21.7724i | −0.695739 | − | 0.754368i | ||||
\(834\) | 2.66478 | 0.0922738 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.7422 | − | 27.2662i | −0.544454 | − | 0.943022i | ||||
\(837\) | 8.08131 | − | 4.66575i | 0.279331 | − | 0.161272i | ||||
\(838\) | 44.1058 | + | 25.4645i | 1.52361 | + | 0.879656i | ||||
\(839\) | −1.24074 | −0.0428352 | −0.0214176 | − | 0.999771i | \(-0.506818\pi\) | ||||
−0.0214176 | + | 0.999771i | \(0.506818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −21.2934 | − | 12.2938i | −0.733820 | − | 0.423671i | ||||
\(843\) | −1.83406 | + | 1.05889i | −0.0631684 | + | 0.0364703i | ||||
\(844\) | 23.3994 | + | 40.5290i | 0.805441 | + | 1.39506i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 21.0426 | 0.723460 | ||||||||
\(847\) | 7.43371 | − | 2.90462i | 0.255425 | − | 0.0998038i | ||||
\(848\) | 34.9273i | 1.19941i | ||||||||
\(849\) | 2.19887 | − | 3.80856i | 0.0754651 | − | 0.130709i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.8997 | + | 24.0750i | 0.476476 | + | 0.825281i | ||||
\(852\) | 52.4810 | + | 30.2999i | 1.79797 | + | 1.03806i | ||||
\(853\) | 44.8500i | 1.53564i | 0.640669 | + | 0.767818i | \(0.278657\pi\) | ||||
−0.640669 | + | 0.767818i | \(0.721343\pi\) | |||||||
\(854\) | 35.3480 | + | 5.38225i | 1.20958 | + | 0.184177i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 69.8506 | − | 120.985i | 2.38744 | − | 4.13517i | ||||
\(857\) | −33.4380 | + | 19.3054i | −1.14222 | + | 0.659461i | −0.946979 | − | 0.321295i | \(-0.895882\pi\) |
−0.195240 | + | 0.980756i | \(0.562549\pi\) | |||||||
\(858\) | 29.6291 | − | 17.1064i | 1.01152 | − | 0.584002i | ||||
\(859\) | 17.5541 | − | 30.4046i | 0.598939 | − | 1.03739i | −0.394039 | − | 0.919094i | \(-0.628922\pi\) |
0.992978 | − | 0.118299i | \(-0.0377442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.22417 | − | 0.947721i | −0.212119 | − | 0.0322982i | ||||
\(862\) | 13.4057i | 0.456600i | ||||||||
\(863\) | −4.28314 | − | 2.47287i | −0.145800 | − | 0.0841776i | 0.425325 | − | 0.905040i | \(-0.360160\pi\) |
−0.571125 | + | 0.820863i | \(0.693493\pi\) | |||||||
\(864\) | −9.35970 | − | 16.2115i | −0.318423 | − | 0.551526i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.53663 | + | 6.12562i | −0.120179 | + | 0.208157i | ||||
\(867\) | 0.903125i | 0.0306717i | ||||||||
\(868\) | 122.002 | − | 47.6705i | 4.14101 | − | 1.61804i | ||||
\(869\) | −35.7056 | −1.21123 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.40400 | − | 12.8241i | −0.250875 | − | 0.434528i | ||||
\(872\) | −23.7855 | + | 13.7326i | −0.805480 | + | 0.465044i | ||||
\(873\) | 13.0047 | + | 7.50827i | 0.440143 | + | 0.254117i | ||||
\(874\) | 37.5282 | 1.26941 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.0647 | −0.475201 | ||||||||
\(877\) | −9.27709 | − | 5.35613i | −0.313265 | − | 0.180864i | 0.335122 | − | 0.942175i | \(-0.391223\pi\) |
−0.648387 | + | 0.761311i | \(0.724556\pi\) | |||||||
\(878\) | −62.0414 | + | 35.8196i | −2.09380 | + | 1.20885i | ||||
\(879\) | −7.10029 | − | 12.2981i | −0.239487 | − | 0.414803i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.2527 | 1.35615 | 0.678075 | − | 0.734993i | \(-0.262815\pi\) | ||||
0.678075 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(882\) | 12.8271 | + | 13.9080i | 0.431910 | + | 0.468306i | ||||
\(883\) | − | 26.2228i | − | 0.882468i | −0.897392 | − | 0.441234i | \(-0.854541\pi\) | ||
0.897392 | − | 0.441234i | \(-0.145459\pi\) | |||||||
\(884\) | −50.2833 | + | 87.0933i | −1.69121 | + | 2.92926i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 53.3683 | + | 92.4366i | 1.79294 | + | 3.10547i | ||||
\(887\) | 42.7785 | + | 24.6982i | 1.43636 | + | 0.829284i | 0.997595 | − | 0.0693174i | \(-0.0220821\pi\) |
0.438767 | + | 0.898601i | \(0.355415\pi\) | |||||||
\(888\) | − | 37.5689i | − | 1.26073i | ||||||
\(889\) | −3.75392 | + | 4.69277i | −0.125902 | + | 0.157390i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.41275 | + | 2.44696i | −0.0473289 | + | 0.0819761i | ||||
\(892\) | 121.705 | − | 70.2663i | 4.07498 | − | 2.35269i | ||||
\(893\) | 14.1608 | − | 8.17573i | 0.473872 | − | 0.273590i | ||||
\(894\) | −10.5694 | + | 18.3068i | −0.353495 | + | 0.612271i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.1693 | − | 64.4151i | −0.840847 | − | 2.15196i | ||||
\(897\) | 29.6160i | 0.988850i | ||||||||
\(898\) | −49.8682 | − | 28.7914i | −1.66412 | − | 0.960782i | ||||
\(899\) | 18.6630 | + | 32.3253i | 0.622446 | + | 1.07811i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.45870 | + | 9.45474i | −0.181856 | + | 0.314983i | ||||
\(902\) | − | 18.1730i | − | 0.605095i | ||||||
\(903\) | −1.24693 | + | 8.18925i | −0.0414953 | + | 0.272521i | ||||
\(904\) | −3.11797 | −0.103702 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.23582 | − | 7.33666i | −0.140726 | − | 0.243744i | ||||
\(907\) | −48.6385 | + | 28.0814i | −1.61501 | + | 0.932429i | −0.626830 | + | 0.779156i | \(0.715648\pi\) |
−0.988184 | + | 0.153273i | \(0.951019\pi\) | |||||||
\(908\) | −81.6523 | − | 47.1420i | −2.70973 | − | 1.56446i | ||||
\(909\) | 2.23121 | 0.0740045 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.9981 | −1.19267 | −0.596335 | − | 0.802736i | \(-0.703377\pi\) | ||||
−0.596335 | + | 0.802736i | \(0.703377\pi\) | |||||||
\(912\) | −24.6218 | − | 14.2154i | −0.815310 | − | 0.470719i | ||||
\(913\) | −7.40468 | + | 4.27510i | −0.245059 | + | 0.141485i | ||||
\(914\) | −37.6779 | − | 65.2601i | −1.24628 | − | 2.15861i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 98.9189 | 3.26837 | ||||||||
\(917\) | −47.3682 | + | 18.5085i | −1.56424 | + | 0.611203i | ||||
\(918\) | − | 11.4363i | − | 0.377455i | ||||||
\(919\) | −3.77400 | + | 6.53677i | −0.124493 | + | 0.215628i | −0.921535 | − | 0.388296i | \(-0.873064\pi\) |
0.797042 | + | 0.603924i | \(0.206397\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.97117 | + | 12.0744i | 0.229708 | + | 0.397866i | ||||
\(922\) | 52.7221 | + | 30.4391i | 1.73631 | + | 1.00246i | ||||
\(923\) | 51.1707i | 1.68431i | ||||||||
\(924\) | −24.7749 | + | 30.9710i | −0.815034 | + | 1.01887i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.28798 | + | 3.96290i | −0.0751877 | + | 0.130229i | ||||
\(927\) | −6.79141 | + | 3.92102i | −0.223059 | + | 0.128783i | ||||
\(928\) | 64.8459 | − | 37.4388i | 2.12867 | − | 1.22899i | ||||
\(929\) | 2.59552 | − | 4.49558i | 0.0851563 | − | 0.147495i | −0.820302 | − | 0.571931i | \(-0.806194\pi\) |
0.905458 | + | 0.424436i | \(0.139528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0358 | + | 4.37575i | 0.460003 | + | 0.143409i | ||||
\(932\) | − | 51.8275i | − | 1.69767i | ||||||
\(933\) | −3.29040 | − | 1.89971i | −0.107723 | − | 0.0621937i | ||||
\(934\) | 0.108561 | + | 0.188034i | 0.00355223 | + | 0.00615264i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.0119 | − | 34.6617i | 0.654110 | − | 1.13295i | ||||
\(937\) | 5.23690i | 0.171082i | 0.996335 | + | 0.0855410i | \(0.0272619\pi\) | ||||
−0.996335 | + | 0.0855410i | \(0.972738\pi\) | |||||||
\(938\) | 18.4582 | + | 14.7654i | 0.602682 | + | 0.482108i | ||||
\(939\) | −27.8976 | −0.910404 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.47195 | + | 11.2098i | 0.210980 | + | 0.365427i | 0.952021 | − | 0.306032i | \(-0.0990013\pi\) |
−0.741042 | + | 0.671459i | \(0.765668\pi\) | |||||||
\(942\) | 54.9581 | − | 31.7301i | 1.79063 | − | 1.03382i | ||||
\(943\) | 13.6237 | + | 7.86567i | 0.443650 | + | 0.256141i | ||||
\(944\) | 51.2407 | 1.66774 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.9106 | −0.777400 | ||||||||
\(947\) | −19.9309 | − | 11.5071i | −0.647669 | − | 0.373932i | 0.139894 | − | 0.990167i | \(-0.455324\pi\) |
−0.787562 | + | 0.616235i | \(0.788657\pi\) | |||||||
\(948\) | −58.0619 | + | 33.5221i | −1.88576 | + | 1.08875i | ||||
\(949\) | −5.93813 | − | 10.2852i | −0.192760 | − | 0.333870i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.4955 | 1.11859 | ||||||||
\(952\) | 15.0551 | − | 98.8748i | 0.487940 | − | 3.20455i | ||||
\(953\) | − | 15.1560i | − | 0.490952i | −0.969403 | − | 0.245476i | \(-0.921056\pi\) | ||
0.969403 | − | 0.245476i | \(-0.0789443\pi\) | |||||||
\(954\) | 3.48696 | − | 6.03959i | 0.112895 | − | 0.195539i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.4483 | + | 28.4893i | 0.531977 | + | 0.921411i | ||||
\(957\) | −9.78782 | − | 5.65100i | −0.316395 | − | 0.182671i | ||||
\(958\) | − | 104.812i | − | 3.38632i | ||||||
\(959\) | −21.6097 | − | 3.29040i | −0.697814 | − | 0.106252i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0384 | + | 48.5640i | −0.904465 | + | 1.56658i | ||||
\(962\) | 44.0963 | − | 25.4590i | 1.42172 | − | 0.820832i | ||||
\(963\) | −13.5420 | + | 7.81846i | −0.436384 | + | 0.251946i | ||||
\(964\) | −53.6861 | + | 92.9871i | −1.72911 | + | 2.99491i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.2051 | − | 44.0326i | −0.553566 | − | 1.41673i | ||||
\(967\) | 45.5145i | 1.46365i | 0.681494 | + | 0.731824i | \(0.261331\pi\) | ||||
−0.681494 | + | 0.731824i | \(0.738669\pi\) | |||||||
\(968\) | 23.3394 | + | 13.4750i | 0.750156 | + | 0.433103i | ||||
\(969\) | −4.44338 | − | 7.69616i | −0.142742 | − | 0.247236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.80096 | − | 6.58345i | 0.121979 | − | 0.211273i | −0.798569 | − | 0.601903i | \(-0.794409\pi\) |
0.920548 | + | 0.390630i | \(0.127743\pi\) | |||||||
\(972\) | 5.30542i | 0.170171i | ||||||||
\(973\) | −2.03695 | − | 1.62943i | −0.0653015 | − | 0.0522371i | ||||
\(974\) | −73.3309 | −2.34967 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33.8416 | + | 58.6153i | 1.08324 | + | 1.87623i | ||||
\(977\) | 30.0456 | − | 17.3468i | 0.961243 | − | 0.554974i | 0.0646874 | − | 0.997906i | \(-0.479395\pi\) |
0.896555 | + | 0.442932i | \(0.146062\pi\) | |||||||
\(978\) | 29.1102 | + | 16.8068i | 0.930843 | + | 0.537422i | ||||
\(979\) | 23.2573 | 0.743306 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.07421 | 0.0981520 | ||||||||
\(982\) | 39.1471 | + | 22.6016i | 1.24924 | + | 0.721246i | ||||
\(983\) | 13.4909 | − | 7.78896i | 0.430292 | − | 0.248429i | −0.269179 | − | 0.963090i | \(-0.586752\pi\) |
0.699471 | + | 0.714661i | \(0.253419\pi\) | |||||||
\(984\) | −10.6299 | − | 18.4115i | −0.338868 | − | 0.586937i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 45.7454 | 1.45683 | ||||||||
\(987\) | −16.0849 | − | 12.8669i | −0.511987 | − | 0.409558i | ||||
\(988\) | − | 49.9193i | − | 1.58815i | ||||||
\(989\) | 10.3490 | − | 17.9250i | 0.329079 | − | 0.569982i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.9794 | + | 39.8016i | 0.729966 | + | 1.26434i | 0.956897 | + | 0.290427i | \(0.0937974\pi\) |
−0.226931 | + | 0.973911i | \(0.572869\pi\) | |||||||
\(992\) | 151.277 | + | 87.3400i | 4.80306 | + | 2.77305i | ||||
\(993\) | 29.8942i | 0.948664i | ||||||||
\(994\) | −29.7271 | − | 76.0799i | −0.942888 | − | 2.41311i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.02731 | + | 13.9037i | −0.254355 | + | 0.440556i | ||||
\(997\) | −35.5665 | + | 20.5344i | −1.12640 | + | 0.650329i | −0.943028 | − | 0.332713i | \(-0.892036\pi\) |
−0.183376 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(998\) | 46.3101 | − | 26.7371i | 1.46592 | − | 0.846349i | ||||
\(999\) | −2.10256 | + | 3.64175i | −0.0665222 | + | 0.115220i |
(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 | 525.2.r.h.499.8 | 16 | ||
5.2 | odd | 4 | 525.2.i.i.226.1 | yes | 8 | ||
5.3 | odd | 4 | 525.2.i.j.226.4 | yes | 8 | ||
5.4 | even | 2 | inner | 525.2.r.h.499.1 | 16 | ||
7.4 | even | 3 | inner | 525.2.r.h.424.1 | 16 | ||
35.2 | odd | 12 | 3675.2.a.bw.1.4 | 4 | |||
35.4 | even | 6 | inner | 525.2.r.h.424.8 | 16 | ||
35.12 | even | 12 | 3675.2.a.bx.1.4 | 4 | |||
35.18 | odd | 12 | 525.2.i.j.151.4 | yes | 8 | ||
35.23 | odd | 12 | 3675.2.a.br.1.1 | 4 | |||
35.32 | odd | 12 | 525.2.i.i.151.1 | ✓ | 8 | ||
35.33 | even | 12 | 3675.2.a.bq.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.i.i.151.1 | ✓ | 8 | 35.32 | odd | 12 | ||
525.2.i.i.226.1 | yes | 8 | 5.2 | odd | 4 | ||
525.2.i.j.151.4 | yes | 8 | 35.18 | odd | 12 | ||
525.2.i.j.226.4 | yes | 8 | 5.3 | odd | 4 | ||
525.2.r.h.424.1 | 16 | 7.4 | even | 3 | inner | ||
525.2.r.h.424.8 | 16 | 35.4 | even | 6 | inner | ||
525.2.r.h.499.1 | 16 | 5.4 | even | 2 | inner | ||
525.2.r.h.499.8 | 16 | 1.1 | even | 1 | trivial | ||
3675.2.a.bq.1.1 | 4 | 35.33 | even | 12 | |||
3675.2.a.br.1.1 | 4 | 35.23 | odd | 12 | |||
3675.2.a.bw.1.4 | 4 | 35.2 | odd | 12 | |||
3675.2.a.bx.1.4 | 4 | 35.12 | even | 12 |