Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(107,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.s (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(-1.08900 - 0.902261i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.107 |
Dual form | 400.2.s.d.243.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41267 | + | 0.0660953i | −0.998907 | + | 0.0467365i | ||||
\(3\) | 0.496487 | 0.286647 | 0.143324 | − | 0.989676i | \(-0.454221\pi\) | ||||
0.143324 | + | 0.989676i | \(0.454221\pi\) | |||||||
\(4\) | 1.99126 | − | 0.186742i | 0.995631 | − | 0.0933708i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.701372 | + | 0.0328155i | −0.286334 | + | 0.0133969i | ||||
\(7\) | −1.55426 | − | 1.55426i | −0.587453 | − | 0.587453i | 0.349488 | − | 0.936941i | \(-0.386356\pi\) |
−0.936941 | + | 0.349488i | \(0.886356\pi\) | |||||||
\(8\) | −2.80065 | + | 0.395417i | −0.990180 | + | 0.139801i | ||||
\(9\) | −2.75350 | −0.917833 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.19607 | + | 4.19607i | −1.26516 | + | 1.26516i | −0.316604 | + | 0.948558i | \(0.602543\pi\) |
−0.948558 | + | 0.316604i | \(0.897457\pi\) | |||||||
\(12\) | 0.988637 | − | 0.0927148i | 0.285395 | − | 0.0267645i | ||||
\(13\) | 5.09530i | 1.41318i | 0.707622 | + | 0.706591i | \(0.249768\pi\) | ||||
−0.707622 | + | 0.706591i | \(0.750232\pi\) | |||||||
\(14\) | 2.29838 | + | 2.09292i | 0.614267 | + | 0.559356i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.93026 | − | 0.743703i | 0.982564 | − | 0.185926i | ||||
\(17\) | −0.213542 | − | 0.213542i | −0.0517916 | − | 0.0517916i | 0.680737 | − | 0.732528i | \(-0.261660\pi\) |
−0.732528 | + | 0.680737i | \(0.761660\pi\) | |||||||
\(18\) | 3.88978 | − | 0.181993i | 0.916830 | − | 0.0428963i | ||||
\(19\) | 0.844754 | − | 0.844754i | 0.193800 | − | 0.193800i | −0.603536 | − | 0.797336i | \(-0.706242\pi\) |
0.797336 | + | 0.603536i | \(0.206242\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.771668 | − | 0.771668i | −0.168392 | − | 0.168392i | ||||
\(22\) | 5.65031 | − | 6.20499i | 1.20465 | − | 1.32291i | ||||
\(23\) | −1.70744 | + | 1.70744i | −0.356027 | + | 0.356027i | −0.862346 | − | 0.506319i | \(-0.831006\pi\) |
0.506319 | + | 0.862346i | \(0.331006\pi\) | |||||||
\(24\) | −1.39049 | + | 0.196320i | −0.283832 | + | 0.0400736i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.336775 | − | 7.19797i | −0.0660471 | − | 1.41164i | ||||
\(27\) | −2.85654 | −0.549741 | ||||||||
\(28\) | −3.38518 | − | 2.80469i | −0.639738 | − | 0.530036i | ||||
\(29\) | 2.24750 | + | 2.24750i | 0.417350 | + | 0.417350i | 0.884289 | − | 0.466939i | \(-0.154643\pi\) |
−0.466939 | + | 0.884289i | \(0.654643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.818209i | 0.146955i | 0.997297 | + | 0.0734773i | \(0.0234097\pi\) | ||||
−0.997297 | + | 0.0734773i | \(0.976590\pi\) | |||||||
\(32\) | −5.50299 | + | 1.31038i | −0.972801 | + | 0.231644i | ||||
\(33\) | −2.08329 | + | 2.08329i | −0.362655 | + | 0.362655i | ||||
\(34\) | 0.315778 | + | 0.287550i | 0.0541556 | + | 0.0493144i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.48294 | + | 0.514193i | −0.913824 | + | 0.0856988i | ||||
\(37\) | 5.12639i | 0.842774i | 0.906881 | + | 0.421387i | \(0.138457\pi\) | ||||
−0.906881 | + | 0.421387i | \(0.861543\pi\) | |||||||
\(38\) | −1.13752 | + | 1.24919i | −0.184531 | + | 0.202646i | ||||
\(39\) | 2.52975i | 0.405084i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.34727i | 0.522756i | 0.965237 | + | 0.261378i | \(0.0841769\pi\) | ||||
−0.965237 | + | 0.261378i | \(0.915823\pi\) | |||||||
\(42\) | 1.14111 | + | 1.03911i | 0.176078 | + | 0.160338i | ||||
\(43\) | − | 4.49131i | − | 0.684919i | −0.939533 | − | 0.342460i | \(-0.888740\pi\) | ||
0.939533 | − | 0.342460i | \(-0.111260\pi\) | |||||||
\(44\) | −7.57189 | + | 9.13905i | −1.14151 | + | 1.37776i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.29920 | − | 2.52490i | 0.338998 | − | 0.372277i | ||||
\(47\) | −4.29355 | + | 4.29355i | −0.626278 | + | 0.626278i | −0.947130 | − | 0.320851i | \(-0.896031\pi\) |
0.320851 | + | 0.947130i | \(0.396031\pi\) | |||||||
\(48\) | 1.95132 | − | 0.369239i | 0.281649 | − | 0.0532951i | ||||
\(49\) | − | 2.16858i | − | 0.309797i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.106021 | − | 0.106021i | −0.0148459 | − | 0.0148459i | ||||
\(52\) | 0.951504 | + | 10.1461i | 0.131950 | + | 1.40701i | ||||
\(53\) | 1.00653 | 0.138258 | 0.0691291 | − | 0.997608i | \(-0.477978\pi\) | ||||
0.0691291 | + | 0.997608i | \(0.477978\pi\) | |||||||
\(54\) | 4.03534 | − | 0.188804i | 0.549141 | − | 0.0256930i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.96751 | + | 3.73835i | 0.663811 | + | 0.499558i | ||||
\(57\) | 0.419410 | − | 0.419410i | 0.0555521 | − | 0.0555521i | ||||
\(58\) | −3.32352 | − | 3.02642i | −0.436399 | − | 0.397388i | ||||
\(59\) | −7.65005 | − | 7.65005i | −0.995952 | − | 0.995952i | 0.00404030 | − | 0.999992i | \(-0.498714\pi\) |
−0.999992 | + | 0.00404030i | \(0.998714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.90291 | + | 1.90291i | −0.243643 | + | 0.243643i | −0.818355 | − | 0.574712i | \(-0.805114\pi\) |
0.574712 | + | 0.818355i | \(0.305114\pi\) | |||||||
\(62\) | −0.0540798 | − | 1.15586i | −0.00686814 | − | 0.146794i | ||||
\(63\) | 4.27964 | + | 4.27964i | 0.539184 | + | 0.539184i | ||||
\(64\) | 7.68729 | − | 2.21485i | 0.960911 | − | 0.276856i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.80531 | − | 3.08070i | 0.345310 | − | 0.379208i | ||||
\(67\) | − | 11.0221i | − | 1.34656i | −0.739387 | − | 0.673280i | \(-0.764885\pi\) | ||
0.739387 | − | 0.673280i | \(-0.235115\pi\) | |||||||
\(68\) | −0.465096 | − | 0.385341i | −0.0564012 | − | 0.0467295i | ||||
\(69\) | −0.847724 | + | 0.847724i | −0.102054 | + | 0.102054i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.5331 | −1.25005 | −0.625027 | − | 0.780604i | \(-0.714912\pi\) | ||||
−0.625027 | + | 0.780604i | \(0.714912\pi\) | |||||||
\(72\) | 7.71159 | − | 1.08878i | 0.908820 | − | 0.128314i | ||||
\(73\) | −2.70854 | − | 2.70854i | −0.317010 | − | 0.317010i | 0.530607 | − | 0.847618i | \(-0.321964\pi\) |
−0.847618 | + | 0.530607i | \(0.821964\pi\) | |||||||
\(74\) | −0.338831 | − | 7.24189i | −0.0393883 | − | 0.841853i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.52438 | − | 1.83988i | 0.174858 | − | 0.211048i | ||||
\(77\) | 13.0435 | 1.48645 | ||||||||
\(78\) | −0.167205 | − | 3.57370i | −0.0189322 | − | 0.404642i | ||||
\(79\) | −8.32010 | −0.936085 | −0.468042 | − | 0.883706i | \(-0.655041\pi\) | ||||
−0.468042 | + | 0.883706i | \(0.655041\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.84226 | 0.760252 | ||||||||
\(82\) | −0.221239 | − | 4.72858i | −0.0244317 | − | 0.522185i | ||||
\(83\) | 9.17237 | 1.00680 | 0.503399 | − | 0.864054i | \(-0.332083\pi\) | ||||
0.503399 | + | 0.864054i | \(0.332083\pi\) | |||||||
\(84\) | −1.68070 | − | 1.39249i | −0.183379 | − | 0.151933i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.296855 | + | 6.34474i | 0.0320107 | + | 0.684171i | ||||
\(87\) | 1.11585 | + | 1.11585i | 0.119632 | + | 0.119632i | ||||
\(88\) | 10.0925 | − | 13.4109i | 1.07587 | − | 1.42961i | ||||
\(89\) | −4.25101 | −0.450606 | −0.225303 | − | 0.974289i | \(-0.572337\pi\) | ||||
−0.225303 | + | 0.974289i | \(0.572337\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.91940 | − | 7.91940i | 0.830178 | − | 0.830178i | ||||
\(92\) | −3.08112 | + | 3.71882i | −0.321229 | + | 0.387714i | ||||
\(93\) | 0.406230i | 0.0421241i | ||||||||
\(94\) | 5.78157 | − | 6.34914i | 0.596324 | − | 0.654864i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.73217 | + | 0.650586i | −0.278850 | + | 0.0664001i | ||||
\(97\) | 7.16000 | + | 7.16000i | 0.726987 | + | 0.726987i | 0.970019 | − | 0.243031i | \(-0.0781417\pi\) |
−0.243031 | + | 0.970019i | \(0.578142\pi\) | |||||||
\(98\) | 0.143333 | + | 3.06348i | 0.0144788 | + | 0.309458i | ||||
\(99\) | 11.5539 | − | 11.5539i | 1.16121 | − | 1.16121i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.38846 | + | 8.38846i | 0.834683 | + | 0.834683i | 0.988153 | − | 0.153470i | \(-0.0490448\pi\) |
−0.153470 | + | 0.988153i | \(0.549045\pi\) | |||||||
\(102\) | 0.156780 | + | 0.142765i | 0.0155235 | + | 0.0141358i | ||||
\(103\) | 5.16478 | − | 5.16478i | 0.508901 | − | 0.508901i | −0.405288 | − | 0.914189i | \(-0.632829\pi\) |
0.914189 | + | 0.405288i | \(0.132829\pi\) | |||||||
\(104\) | −2.01477 | − | 14.2702i | −0.197564 | − | 1.39930i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.42190 | + | 0.0665272i | −0.138107 | + | 0.00646169i | ||||
\(107\) | −8.97973 | −0.868103 | −0.434052 | − | 0.900888i | \(-0.642916\pi\) | ||||
−0.434052 | + | 0.900888i | \(0.642916\pi\) | |||||||
\(108\) | −5.68812 | + | 0.533435i | −0.547340 | + | 0.0513298i | ||||
\(109\) | 10.9081 | + | 10.9081i | 1.04481 | + | 1.04481i | 0.998948 | + | 0.0458592i | \(0.0146025\pi\) |
0.0458592 | + | 0.998948i | \(0.485397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.54519i | 0.241579i | ||||||||
\(112\) | −7.26453 | − | 4.95272i | −0.686433 | − | 0.467988i | ||||
\(113\) | 4.29684 | − | 4.29684i | 0.404212 | − | 0.404212i | −0.475502 | − | 0.879715i | \(-0.657734\pi\) |
0.879715 | + | 0.475502i | \(0.157734\pi\) | |||||||
\(114\) | −0.564765 | + | 0.620208i | −0.0528951 | + | 0.0580878i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.89506 | + | 4.05566i | 0.454495 | + | 0.376558i | ||||
\(117\) | − | 14.0299i | − | 1.29707i | ||||||
\(118\) | 11.3126 | + | 10.3013i | 1.04141 | + | 0.948316i | ||||
\(119\) | 0.663798i | 0.0608503i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 24.2140i | − | 2.20127i | ||||||
\(122\) | 2.56241 | − | 2.81396i | 0.231990 | − | 0.254764i | ||||
\(123\) | 1.66188i | 0.149846i | ||||||||
\(124\) | 0.152794 | + | 1.62927i | 0.0137213 | + | 0.146313i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.32858 | − | 5.76285i | −0.563795 | − | 0.513396i | ||||
\(127\) | −0.759686 | + | 0.759686i | −0.0674112 | + | 0.0674112i | −0.740009 | − | 0.672597i | \(-0.765179\pi\) |
0.672597 | + | 0.740009i | \(0.265179\pi\) | |||||||
\(128\) | −10.7132 | + | 3.63694i | −0.946922 | + | 0.321463i | ||||
\(129\) | − | 2.22988i | − | 0.196330i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.59995 | + | 7.59995i | 0.664010 | + | 0.664010i | 0.956323 | − | 0.292312i | \(-0.0944247\pi\) |
−0.292312 | + | 0.956323i | \(0.594425\pi\) | |||||||
\(132\) | −3.75935 | + | 4.53742i | −0.327209 | + | 0.394932i | ||||
\(133\) | −2.62593 | −0.227697 | ||||||||
\(134\) | 0.728507 | + | 15.5705i | 0.0629335 | + | 1.34509i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.682495 | + | 0.513619i | 0.0585235 | + | 0.0440425i | ||||
\(137\) | −12.7789 | + | 12.7789i | −1.09178 | + | 1.09178i | −0.0964376 | + | 0.995339i | \(0.530745\pi\) |
−0.995339 | + | 0.0964376i | \(0.969255\pi\) | |||||||
\(138\) | 1.14152 | − | 1.25358i | 0.0971728 | − | 0.106712i | ||||
\(139\) | 7.74227 | + | 7.74227i | 0.656691 | + | 0.656691i | 0.954596 | − | 0.297905i | \(-0.0962877\pi\) |
−0.297905 | + | 0.954596i | \(0.596288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.13169 | + | 2.13169i | −0.179521 | + | 0.179521i | ||||
\(142\) | 14.8798 | − | 0.696191i | 1.24869 | − | 0.0584230i | ||||
\(143\) | −21.3802 | − | 21.3802i | −1.78790 | − | 1.78790i | ||||
\(144\) | −10.8220 | + | 2.04779i | −0.901830 | + | 0.170649i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00529 | + | 3.64724i | 0.331480 | + | 0.301848i | ||||
\(147\) | − | 1.07667i | − | 0.0888024i | ||||||
\(148\) | 0.957310 | + | 10.2080i | 0.0786904 | + | 0.839092i | ||||
\(149\) | 9.57165 | − | 9.57165i | 0.784140 | − | 0.784140i | −0.196386 | − | 0.980527i | \(-0.562921\pi\) |
0.980527 | + | 0.196386i | \(0.0629207\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.68791 | −0.788391 | −0.394195 | − | 0.919027i | \(-0.628977\pi\) | ||||
−0.394195 | + | 0.919027i | \(0.628977\pi\) | |||||||
\(152\) | −2.03183 | + | 2.69989i | −0.164803 | + | 0.218990i | ||||
\(153\) | 0.587989 | + | 0.587989i | 0.0475361 | + | 0.0475361i | ||||
\(154\) | −18.4262 | + | 0.862116i | −1.48482 | + | 0.0694713i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.472410 | + | 5.03740i | 0.0378230 | + | 0.403315i | ||||
\(157\) | 9.97637 | 0.796201 | 0.398101 | − | 0.917342i | \(-0.369669\pi\) | ||||
0.398101 | + | 0.917342i | \(0.369669\pi\) | |||||||
\(158\) | 11.7535 | − | 0.549920i | 0.935062 | − | 0.0437493i | ||||
\(159\) | 0.499732 | 0.0396313 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.30761 | 0.418298 | ||||||||
\(162\) | −9.66585 | + | 0.452242i | −0.759421 | + | 0.0355315i | ||||
\(163\) | −9.48267 | −0.742740 | −0.371370 | − | 0.928485i | \(-0.621112\pi\) | ||||
−0.371370 | + | 0.928485i | \(0.621112\pi\) | |||||||
\(164\) | 0.625074 | + | 6.66529i | 0.0488101 | + | 0.520472i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.9575 | + | 0.606250i | −1.00570 | + | 0.0470542i | ||||
\(167\) | 9.43528 | + | 9.43528i | 0.730124 | + | 0.730124i | 0.970644 | − | 0.240520i | \(-0.0773180\pi\) |
−0.240520 | + | 0.970644i | \(0.577318\pi\) | |||||||
\(168\) | 2.46630 | + | 1.85604i | 0.190279 | + | 0.143197i | ||||
\(169\) | −12.9621 | −0.997082 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.32603 | + | 2.32603i | −0.177876 | + | 0.177876i | ||||
\(172\) | −0.838715 | − | 8.94339i | −0.0639514 | − | 0.681927i | ||||
\(173\) | 8.94716i | 0.680240i | 0.940382 | + | 0.340120i | \(0.110468\pi\) | ||||
−0.940382 | + | 0.340120i | \(0.889532\pi\) | |||||||
\(174\) | −1.65008 | − | 1.50258i | −0.125093 | − | 0.113910i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.3710 | + | 19.6122i | −1.00788 | + | 1.47833i | ||||
\(177\) | −3.79815 | − | 3.79815i | −0.285487 | − | 0.285487i | ||||
\(178\) | 6.00526 | − | 0.280972i | 0.450114 | − | 0.0210597i | ||||
\(179\) | −3.02430 | + | 3.02430i | −0.226047 | + | 0.226047i | −0.811039 | − | 0.584992i | \(-0.801098\pi\) |
0.584992 | + | 0.811039i | \(0.301098\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.54845 | − | 1.54845i | −0.115095 | − | 0.115095i | 0.647213 | − | 0.762309i | \(-0.275934\pi\) |
−0.762309 | + | 0.647213i | \(0.775934\pi\) | |||||||
\(182\) | −10.6640 | + | 11.7109i | −0.790472 | + | 0.868071i | ||||
\(183\) | −0.944773 | + | 0.944773i | −0.0698396 | + | 0.0698396i | ||||
\(184\) | 4.10680 | − | 5.45710i | 0.302757 | − | 0.402303i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0268499 | − | 0.573869i | −0.00196873 | − | 0.0420781i | ||||
\(187\) | 1.79208 | 0.131050 | ||||||||
\(188\) | −7.74779 | + | 9.35136i | −0.565066 | + | 0.682018i | ||||
\(189\) | 4.43979 | + | 4.43979i | 0.322947 | + | 0.322947i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.1005i | − | 1.45442i | −0.686415 | − | 0.727210i | \(-0.740817\pi\) | ||
0.686415 | − | 0.727210i | \(-0.259183\pi\) | |||||||
\(192\) | 3.81664 | − | 1.09964i | 0.275442 | − | 0.0793600i | ||||
\(193\) | −3.82483 | + | 3.82483i | −0.275317 | + | 0.275317i | −0.831236 | − | 0.555919i | \(-0.812366\pi\) |
0.555919 | + | 0.831236i | \(0.312366\pi\) | |||||||
\(194\) | −10.5879 | − | 9.64146i | −0.760170 | − | 0.692216i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.404964 | − | 4.31821i | −0.0289260 | − | 0.308444i | ||||
\(197\) | 1.11758i | 0.0796246i | 0.999207 | + | 0.0398123i | \(0.0126760\pi\) | ||||
−0.999207 | + | 0.0398123i | \(0.987324\pi\) | |||||||
\(198\) | −15.5581 | + | 17.0854i | −1.10567 | + | 1.21421i | ||||
\(199\) | 25.5830i | 1.81353i | 0.421635 | + | 0.906766i | \(0.361456\pi\) | ||||
−0.421635 | + | 0.906766i | \(0.638544\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.47232i | − | 0.385988i | ||||||
\(202\) | −12.4046 | − | 11.2957i | −0.872781 | − | 0.794761i | ||||
\(203\) | − | 6.98637i | − | 0.490347i | ||||||
\(204\) | −0.230914 | − | 0.191317i | −0.0161672 | − | 0.0133949i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.95475 | + | 7.63749i | −0.484560 | + | 0.532129i | ||||
\(207\) | 4.70145 | − | 4.70145i | 0.326773 | − | 0.326773i | ||||
\(208\) | 3.78939 | + | 20.0258i | 0.262747 | + | 1.38854i | ||||
\(209\) | 7.08929i | 0.490376i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.411613 | + | 0.411613i | 0.0283366 | + | 0.0283366i | 0.721133 | − | 0.692797i | \(-0.243622\pi\) |
−0.692797 | + | 0.721133i | \(0.743622\pi\) | |||||||
\(212\) | 2.00427 | − | 0.187962i | 0.137654 | − | 0.0129093i | ||||
\(213\) | −5.22957 | −0.358324 | ||||||||
\(214\) | 12.6854 | − | 0.593518i | 0.867155 | − | 0.0405721i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.00017 | − | 1.12952i | 0.544343 | − | 0.0768544i | ||||
\(217\) | 1.27171 | − | 1.27171i | 0.0863290 | − | 0.0863290i | ||||
\(218\) | −16.1305 | − | 14.6886i | −1.09250 | − | 0.994835i | ||||
\(219\) | −1.34475 | − | 1.34475i | −0.0908701 | − | 0.0908701i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.08806 | − | 1.08806i | 0.0731909 | − | 0.0731909i | ||||
\(222\) | −0.168225 | − | 3.59551i | −0.0112905 | − | 0.241315i | ||||
\(223\) | 16.7466 | + | 16.7466i | 1.12143 | + | 1.12143i | 0.991526 | + | 0.129908i | \(0.0414682\pi\) |
0.129908 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(224\) | 10.5897 | + | 6.51639i | 0.707555 | + | 0.435395i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.78600 | + | 6.35401i | −0.384879 | + | 0.422662i | ||||
\(227\) | − | 13.7807i | − | 0.914659i | −0.889297 | − | 0.457330i | \(-0.848806\pi\) | ||
0.889297 | − | 0.457330i | \(-0.151194\pi\) | |||||||
\(228\) | 0.756833 | − | 0.913476i | 0.0501225 | − | 0.0604964i | ||||
\(229\) | −7.90971 | + | 7.90971i | −0.522688 | + | 0.522688i | −0.918382 | − | 0.395694i | \(-0.870504\pi\) |
0.395694 | + | 0.918382i | \(0.370504\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.47594 | 0.426086 | ||||||||
\(232\) | −7.18315 | − | 5.40576i | −0.471597 | − | 0.354905i | ||||
\(233\) | 1.67997 | + | 1.67997i | 0.110058 | + | 0.110058i | 0.759991 | − | 0.649933i | \(-0.225203\pi\) |
−0.649933 | + | 0.759991i | \(0.725203\pi\) | |||||||
\(234\) | 0.927311 | + | 19.8196i | 0.0606202 | + | 1.29565i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −16.6618 | − | 13.8047i | −1.08459 | − | 0.898608i | ||||
\(237\) | −4.13083 | −0.268326 | ||||||||
\(238\) | −0.0438740 | − | 0.937727i | −0.00284393 | − | 0.0607838i | ||||
\(239\) | 11.7685 | 0.761241 | 0.380620 | − | 0.924731i | \(-0.375710\pi\) | ||||
0.380620 | + | 0.924731i | \(0.375710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2730 | −0.854991 | −0.427495 | − | 0.904018i | \(-0.640604\pi\) | ||||
−0.427495 | + | 0.904018i | \(0.640604\pi\) | |||||||
\(242\) | 1.60043 | + | 34.2063i | 0.102880 | + | 2.19886i | ||||
\(243\) | 11.9667 | 0.767665 | ||||||||
\(244\) | −3.43385 | + | 4.14455i | −0.219830 | + | 0.265328i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.109842 | − | 2.34768i | −0.00700329 | − | 0.149683i | ||||
\(247\) | 4.30427 | + | 4.30427i | 0.273874 | + | 0.273874i | ||||
\(248\) | −0.323534 | − | 2.29152i | −0.0205444 | − | 0.145511i | ||||
\(249\) | 4.55396 | 0.288596 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3795 | − | 10.3795i | 0.655149 | − | 0.655149i | −0.299079 | − | 0.954228i | \(-0.596679\pi\) |
0.954228 | + | 0.299079i | \(0.0966795\pi\) | |||||||
\(252\) | 9.32108 | + | 7.72271i | 0.587173 | + | 0.486485i | ||||
\(253\) | − | 14.3291i | − | 0.900863i | ||||||
\(254\) | 1.02297 | − | 1.12340i | 0.0641870 | − | 0.0704881i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.8938 | − | 5.84588i | 0.930863 | − | 0.365368i | ||||
\(257\) | −20.4353 | − | 20.4353i | −1.27472 | − | 1.27472i | −0.943582 | − | 0.331140i | \(-0.892567\pi\) |
−0.331140 | − | 0.943582i | \(-0.607433\pi\) | |||||||
\(258\) | 0.147385 | + | 3.15008i | 0.00917577 | + | 0.196116i | ||||
\(259\) | 7.96772 | − | 7.96772i | 0.495090 | − | 0.495090i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.18848 | − | 6.18848i | −0.383058 | − | 0.383058i | ||||
\(262\) | −11.2385 | − | 10.2339i | −0.694318 | − | 0.632251i | ||||
\(263\) | −14.0611 | + | 14.0611i | −0.867047 | + | 0.867047i | −0.992144 | − | 0.125098i | \(-0.960076\pi\) |
0.125098 | + | 0.992144i | \(0.460076\pi\) | |||||||
\(264\) | 5.01081 | − | 6.65835i | 0.308394 | − | 0.409793i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.70956 | − | 0.173561i | 0.227448 | − | 0.0106417i | ||||
\(267\) | −2.11057 | −0.129165 | ||||||||
\(268\) | −2.05828 | − | 21.9478i | −0.125729 | − | 1.34068i | ||||
\(269\) | −6.61443 | − | 6.61443i | −0.403289 | − | 0.403289i | 0.476101 | − | 0.879390i | \(-0.342050\pi\) |
−0.879390 | + | 0.476101i | \(0.842050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6219i | 0.645237i | 0.946529 | + | 0.322619i | \(0.104563\pi\) | ||||
−0.946529 | + | 0.322619i | \(0.895437\pi\) | |||||||
\(272\) | −0.998087 | − | 0.680463i | −0.0605179 | − | 0.0412592i | ||||
\(273\) | 3.93188 | − | 3.93188i | 0.237968 | − | 0.237968i | ||||
\(274\) | 17.2077 | − | 18.8970i | 1.03956 | − | 1.14161i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.52974 | + | 1.84635i | −0.0920793 | + | 0.111137i | ||||
\(277\) | 8.28511i | 0.497804i | 0.968529 | + | 0.248902i | \(0.0800697\pi\) | ||||
−0.968529 | + | 0.248902i | \(0.919930\pi\) | |||||||
\(278\) | −11.4490 | − | 10.4255i | −0.686665 | − | 0.625282i | ||||
\(279\) | − | 2.25294i | − | 0.134880i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.0176i | 1.25380i | 0.779098 | + | 0.626902i | \(0.215677\pi\) | ||||
−0.779098 | + | 0.626902i | \(0.784323\pi\) | |||||||
\(282\) | 2.87048 | − | 3.15227i | 0.170934 | − | 0.187715i | ||||
\(283\) | 14.4748i | 0.860436i | 0.902725 | + | 0.430218i | \(0.141563\pi\) | ||||
−0.902725 | + | 0.430218i | \(0.858437\pi\) | |||||||
\(284\) | −20.9742 | + | 1.96697i | −1.24459 | + | 0.116718i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 31.6163 | + | 28.7900i | 1.86951 | + | 1.70239i | ||||
\(287\) | 5.20251 | − | 5.20251i | 0.307095 | − | 0.307095i | ||||
\(288\) | 15.1525 | − | 3.60812i | 0.892869 | − | 0.212611i | ||||
\(289\) | − | 16.9088i | − | 0.994635i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.55485 | + | 3.55485i | 0.208389 | + | 0.208389i | ||||
\(292\) | −5.89921 | − | 4.88761i | −0.345225 | − | 0.286026i | ||||
\(293\) | 11.9165 | 0.696171 | 0.348086 | − | 0.937463i | \(-0.386832\pi\) | ||||
0.348086 | + | 0.937463i | \(0.386832\pi\) | |||||||
\(294\) | 0.0711630 | + | 1.52098i | 0.00415031 | + | 0.0887054i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.02706 | − | 14.3572i | −0.117821 | − | 0.834497i | ||||
\(297\) | 11.9862 | − | 11.9862i | 0.695512 | − | 0.695512i | ||||
\(298\) | −12.8889 | + | 14.1542i | −0.746635 | + | 0.819931i | ||||
\(299\) | −8.69993 | − | 8.69993i | −0.503130 | − | 0.503130i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.98065 | + | 6.98065i | −0.402358 | + | 0.402358i | ||||
\(302\) | 13.6858 | − | 0.640325i | 0.787529 | − | 0.0368466i | ||||
\(303\) | 4.16477 | + | 4.16477i | 0.239260 | + | 0.239260i | ||||
\(304\) | 2.69185 | − | 3.94834i | 0.154388 | − | 0.226453i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.869496 | − | 0.791769i | −0.0497058 | − | 0.0452624i | ||||
\(307\) | 25.4511i | 1.45257i | 0.687392 | + | 0.726287i | \(0.258755\pi\) | ||||
−0.687392 | + | 0.726287i | \(0.741245\pi\) | |||||||
\(308\) | 25.9731 | − | 2.43577i | 1.47995 | − | 0.138791i | ||||
\(309\) | 2.56425 | − | 2.56425i | 0.145875 | − | 0.145875i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.4775 | 1.21788 | 0.608939 | − | 0.793217i | \(-0.291596\pi\) | ||||
0.608939 | + | 0.793217i | \(0.291596\pi\) | |||||||
\(312\) | −1.00031 | − | 7.08495i | −0.0566312 | − | 0.401106i | ||||
\(313\) | −18.7965 | − | 18.7965i | −1.06244 | − | 1.06244i | −0.997916 | − | 0.0645277i | \(-0.979446\pi\) |
−0.0645277 | − | 0.997916i | \(-0.520554\pi\) | |||||||
\(314\) | −14.0933 | + | 0.659392i | −0.795331 | + | 0.0372116i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.5675 | + | 1.55371i | −0.931995 | + | 0.0874029i | ||||
\(317\) | −16.2531 | −0.912864 | −0.456432 | − | 0.889758i | \(-0.650873\pi\) | ||||
−0.456432 | + | 0.889758i | \(0.650873\pi\) | |||||||
\(318\) | −0.705955 | + | 0.0330299i | −0.0395880 | + | 0.00185223i | ||||
\(319\) | −18.8613 | −1.05603 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.45832 | −0.248839 | ||||||||
\(322\) | −7.49789 | + | 0.350808i | −0.417841 | + | 0.0195498i | ||||
\(323\) | −0.360781 | −0.0200744 | ||||||||
\(324\) | 13.6247 | − | 1.27773i | 0.756930 | − | 0.0709853i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.3959 | − | 0.626760i | 0.741928 | − | 0.0347130i | ||||
\(327\) | 5.41574 | + | 5.41574i | 0.299491 | + | 0.299491i | ||||
\(328\) | −1.32357 | − | 9.37453i | −0.0730818 | − | 0.517622i | ||||
\(329\) | 13.3465 | 0.735818 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.71558 | + | 8.71558i | −0.479052 | + | 0.479052i | −0.904828 | − | 0.425777i | \(-0.860001\pi\) |
0.425777 | + | 0.904828i | \(0.360001\pi\) | |||||||
\(332\) | 18.2646 | − | 1.71286i | 1.00240 | − | 0.0940055i | ||||
\(333\) | − | 14.1155i | − | 0.773526i | ||||||
\(334\) | −13.9526 | − | 12.7053i | −0.763450 | − | 0.695203i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.60674 | − | 2.45896i | −0.196764 | − | 0.134147i | ||||
\(337\) | −0.0406874 | − | 0.0406874i | −0.00221638 | − | 0.00221638i | 0.705998 | − | 0.708214i | \(-0.250499\pi\) |
−0.708214 | + | 0.705998i | \(0.750499\pi\) | |||||||
\(338\) | 18.3111 | − | 0.856732i | 0.995993 | − | 0.0466001i | ||||
\(339\) | 2.13333 | − | 2.13333i | 0.115866 | − | 0.115866i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.43326 | − | 3.43326i | −0.185921 | − | 0.185921i | ||||
\(342\) | 3.13217 | − | 3.43965i | 0.169368 | − | 0.185995i | ||||
\(343\) | −14.2503 | + | 14.2503i | −0.769445 | + | 0.769445i | ||||
\(344\) | 1.77594 | + | 12.5786i | 0.0957524 | + | 0.678193i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.591366 | − | 12.6394i | −0.0317920 | − | 0.679497i | ||||
\(347\) | 35.7094 | 1.91698 | 0.958491 | − | 0.285124i | \(-0.0920348\pi\) | ||||
0.958491 | + | 0.285124i | \(0.0920348\pi\) | |||||||
\(348\) | 2.43033 | + | 2.01358i | 0.130280 | + | 0.107939i | ||||
\(349\) | −0.274452 | − | 0.274452i | −0.0146911 | − | 0.0146911i | 0.699723 | − | 0.714414i | \(-0.253307\pi\) |
−0.714414 | + | 0.699723i | \(0.753307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 14.5549i | − | 0.776884i | ||||||
\(352\) | 17.5925 | − | 28.5894i | 0.937683 | − | 1.52382i | ||||
\(353\) | 15.6215 | − | 15.6215i | 0.831446 | − | 0.831446i | −0.156268 | − | 0.987715i | \(-0.549946\pi\) |
0.987715 | + | 0.156268i | \(0.0499464\pi\) | |||||||
\(354\) | 5.61657 | + | 5.11449i | 0.298517 | + | 0.271832i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.46487 | + | 0.793840i | −0.448637 | + | 0.0420734i | ||||
\(357\) | 0.329567i | 0.0174426i | ||||||||
\(358\) | 4.07244 | − | 4.47222i | 0.215235 | − | 0.236364i | ||||
\(359\) | − | 0.768787i | − | 0.0405750i | −0.999794 | − | 0.0202875i | \(-0.993542\pi\) | ||
0.999794 | − | 0.0202875i | \(-0.00645816\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.5728i | 0.924883i | ||||||||
\(362\) | 2.28979 | + | 2.08510i | 0.120349 | + | 0.109591i | ||||
\(363\) | − | 12.0219i | − | 0.630988i | ||||||
\(364\) | 14.2907 | − | 17.2485i | 0.749037 | − | 0.904066i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.27221 | − | 1.39710i | 0.0664992 | − | 0.0730273i | ||||
\(367\) | −13.7849 | + | 13.7849i | −0.719568 | + | 0.719568i | −0.968517 | − | 0.248949i | \(-0.919915\pi\) |
0.248949 | + | 0.968517i | \(0.419915\pi\) | |||||||
\(368\) | −5.44086 | + | 7.98052i | −0.283624 | + | 0.416013i | ||||
\(369\) | − | 9.21671i | − | 0.479803i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.56441 | − | 1.56441i | −0.0812202 | − | 0.0812202i | ||||
\(372\) | 0.0758601 | + | 0.808911i | 0.00393316 | + | 0.0419401i | ||||
\(373\) | 21.4003 | 1.10806 | 0.554031 | − | 0.832496i | \(-0.313089\pi\) | ||||
0.554031 | + | 0.832496i | \(0.313089\pi\) | |||||||
\(374\) | −2.53161 | + | 0.118448i | −0.130906 | + | 0.00612479i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3270 | − | 13.7225i | 0.532573 | − | 0.707682i | ||||
\(377\) | −11.4517 | + | 11.4517i | −0.589791 | + | 0.589791i | ||||
\(378\) | −6.56540 | − | 5.97851i | −0.337688 | − | 0.307501i | ||||
\(379\) | 11.3922 | + | 11.3922i | 0.585180 | + | 0.585180i | 0.936322 | − | 0.351142i | \(-0.114207\pi\) |
−0.351142 | + | 0.936322i | \(0.614207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.377174 | + | 0.377174i | −0.0193232 | + | 0.0193232i | ||||
\(382\) | 1.32855 | + | 28.3953i | 0.0679744 | + | 1.45283i | ||||
\(383\) | −4.42635 | − | 4.42635i | −0.226176 | − | 0.226176i | 0.584917 | − | 0.811093i | \(-0.301127\pi\) |
−0.811093 | + | 0.584917i | \(0.801127\pi\) | |||||||
\(384\) | −5.31897 | + | 1.80570i | −0.271432 | + | 0.0921465i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.15041 | − | 5.65602i | 0.262149 | − | 0.287884i | ||||
\(387\) | 12.3668i | 0.628642i | ||||||||
\(388\) | 15.5945 | + | 12.9204i | 0.791691 | + | 0.655932i | ||||
\(389\) | 12.3502 | − | 12.3502i | 0.626180 | − | 0.626180i | −0.320924 | − | 0.947105i | \(-0.603994\pi\) |
0.947105 | + | 0.320924i | \(0.103994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.729222 | 0.0368784 | ||||||||
\(392\) | 0.857493 | + | 6.07343i | 0.0433099 | + | 0.306755i | ||||
\(393\) | 3.77328 | + | 3.77328i | 0.190337 | + | 0.190337i | ||||
\(394\) | −0.0738671 | − | 1.57878i | −0.00372137 | − | 0.0795376i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 20.8492 | − | 25.1644i | 1.04771 | − | 1.26456i | ||||
\(397\) | −17.9832 | −0.902551 | −0.451275 | − | 0.892385i | \(-0.649031\pi\) | ||||
−0.451275 | + | 0.892385i | \(0.649031\pi\) | |||||||
\(398\) | −1.69092 | − | 36.1403i | −0.0847580 | − | 1.81155i | ||||
\(399\) | −1.30374 | −0.0652686 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.06570 | 0.452720 | 0.226360 | − | 0.974044i | \(-0.427317\pi\) | ||||
0.226360 | + | 0.974044i | \(0.427317\pi\) | |||||||
\(402\) | 0.361695 | + | 7.73057i | 0.0180397 | + | 0.385566i | ||||
\(403\) | −4.16902 | −0.207674 | ||||||||
\(404\) | 18.2701 | + | 15.1372i | 0.908972 | + | 0.753102i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.461766 | + | 9.86942i | 0.0229171 | + | 0.489811i | ||||
\(407\) | −21.5107 | − | 21.5107i | −1.06625 | − | 1.06625i | ||||
\(408\) | 0.338850 | + | 0.255005i | 0.0167756 | + | 0.0126246i | ||||
\(409\) | −30.0616 | −1.48645 | −0.743226 | − | 0.669040i | \(-0.766705\pi\) | ||||
−0.743226 | + | 0.669040i | \(0.766705\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.34457 | + | 6.34457i | −0.312955 | + | 0.312955i | ||||
\(412\) | 9.31995 | − | 11.2489i | 0.459161 | − | 0.554194i | ||||
\(413\) | 23.7803i | 1.17015i | ||||||||
\(414\) | −6.33084 | + | 6.95233i | −0.311144 | + | 0.341688i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.67676 | − | 28.0394i | −0.327355 | − | 1.37474i | ||||
\(417\) | 3.84394 | + | 3.84394i | 0.188239 | + | 0.188239i | ||||
\(418\) | −0.468569 | − | 10.0148i | −0.0229184 | − | 0.489840i | ||||
\(419\) | −15.3986 | + | 15.3986i | −0.752271 | + | 0.752271i | −0.974903 | − | 0.222631i | \(-0.928535\pi\) |
0.222631 | + | 0.974903i | \(0.428535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.86468 | − | 3.86468i | −0.188353 | − | 0.188353i | 0.606631 | − | 0.794984i | \(-0.292521\pi\) |
−0.794984 | + | 0.606631i | \(0.792521\pi\) | |||||||
\(422\) | −0.608679 | − | 0.554267i | −0.0296300 | − | 0.0269813i | ||||
\(423\) | 11.8223 | − | 11.8223i | 0.574819 | − | 0.574819i | ||||
\(424\) | −2.81895 | + | 0.398001i | −0.136900 | + | 0.0193286i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.38764 | − | 0.345650i | 0.357933 | − | 0.0167468i | ||||
\(427\) | 5.91523 | 0.286258 | ||||||||
\(428\) | −17.8810 | + | 1.67689i | −0.864311 | + | 0.0810555i | ||||
\(429\) | −10.6150 | − | 10.6150i | −0.512497 | − | 0.512497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.2692i | 1.31351i | 0.754103 | + | 0.656756i | \(0.228072\pi\) | ||||
−0.754103 | + | 0.656756i | \(0.771928\pi\) | |||||||
\(432\) | −11.2269 | + | 2.12442i | −0.540156 | + | 0.102211i | ||||
\(433\) | −19.1435 | + | 19.1435i | −0.919978 | + | 0.919978i | −0.997027 | − | 0.0770497i | \(-0.975450\pi\) |
0.0770497 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(434\) | −1.71244 | + | 1.88055i | −0.0821999 | + | 0.0902694i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.7579 | + | 19.6839i | 1.13780 | + | 0.942688i | ||||
\(437\) | 2.88474i | 0.137996i | ||||||||
\(438\) | 1.98857 | + | 1.81081i | 0.0950177 | + | 0.0865238i | ||||
\(439\) | − | 30.1995i | − | 1.44134i | −0.693276 | − | 0.720672i | \(-0.743833\pi\) | ||
0.693276 | − | 0.720672i | \(-0.256167\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.97118i | 0.284342i | ||||||||
\(442\) | −1.46515 | + | 1.60899i | −0.0696903 | + | 0.0765316i | ||||
\(443\) | 27.7051i | 1.31631i | 0.752884 | + | 0.658153i | \(0.228662\pi\) | ||||
−0.752884 | + | 0.658153i | \(0.771338\pi\) | |||||||
\(444\) | 0.475292 | + | 5.06814i | 0.0225564 | + | 0.240523i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.7642 | − | 22.5505i | −1.17262 | − | 1.06780i | ||||
\(447\) | 4.75220 | − | 4.75220i | 0.224772 | − | 0.224772i | ||||
\(448\) | −15.3905 | − | 8.50557i | −0.727131 | − | 0.401851i | ||||
\(449\) | 9.78315i | 0.461695i | 0.972990 | + | 0.230848i | \(0.0741499\pi\) | ||||
−0.972990 | + | 0.230848i | \(0.925850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0454 | − | 14.0454i | −0.661371 | − | 0.661371i | ||||
\(452\) | 7.75373 | − | 9.35853i | 0.364705 | − | 0.440188i | ||||
\(453\) | −4.80992 | −0.225990 | ||||||||
\(454\) | 0.910842 | + | 19.4676i | 0.0427479 | + | 0.913660i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00878 | + | 1.34046i | −0.0472404 | + | 0.0627729i | ||||
\(457\) | 0.557108 | − | 0.557108i | 0.0260604 | − | 0.0260604i | −0.693957 | − | 0.720017i | \(-0.744134\pi\) |
0.720017 | + | 0.693957i | \(0.244134\pi\) | |||||||
\(458\) | 10.6510 | − | 11.6966i | 0.497689 | − | 0.546546i | ||||
\(459\) | 0.609992 | + | 0.609992i | 0.0284720 | + | 0.0284720i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.5791 | + | 12.5791i | −0.585865 | + | 0.585865i | −0.936509 | − | 0.350644i | \(-0.885963\pi\) |
0.350644 | + | 0.936509i | \(0.385963\pi\) | |||||||
\(462\) | −9.14836 | + | 0.428030i | −0.425620 | + | 0.0199137i | ||||
\(463\) | 3.29549 | + | 3.29549i | 0.153154 | + | 0.153154i | 0.779525 | − | 0.626371i | \(-0.215460\pi\) |
−0.626371 | + | 0.779525i | \(0.715460\pi\) | |||||||
\(464\) | 10.5047 | + | 7.16177i | 0.487669 | + | 0.332477i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.48427 | − | 2.26220i | −0.115082 | − | 0.104794i | ||||
\(467\) | − | 10.1995i | − | 0.471979i | −0.971756 | − | 0.235989i | \(-0.924167\pi\) | ||
0.971756 | − | 0.235989i | \(-0.0758331\pi\) | |||||||
\(468\) | −2.61997 | − | 27.9372i | −0.121108 | − | 1.29140i | ||||
\(469\) | −17.1311 | + | 17.1311i | −0.791042 | + | 0.791042i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.95314 | 0.228229 | ||||||||
\(472\) | 24.4501 | + | 18.4002i | 1.12541 | + | 0.846936i | ||||
\(473\) | 18.8459 | + | 18.8459i | 0.866534 | + | 0.866534i | ||||
\(474\) | 5.83549 | − | 0.273028i | 0.268033 | − | 0.0125406i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.123959 | + | 1.32180i | 0.00568164 | + | 0.0605845i | ||||
\(477\) | −2.77149 | −0.126898 | ||||||||
\(478\) | −16.6250 | + | 0.777843i | −0.760409 | + | 0.0355777i | ||||
\(479\) | 5.65795 | 0.258518 | 0.129259 | − | 0.991611i | \(-0.458740\pi\) | ||||
0.129259 | + | 0.991611i | \(0.458740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1205 | −1.19099 | ||||||||
\(482\) | 18.7504 | − | 0.877285i | 0.854057 | − | 0.0399592i | ||||
\(483\) | 2.63516 | 0.119904 | ||||||||
\(484\) | −4.52175 | − | 48.2164i | −0.205534 | − | 2.19165i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −16.9050 | + | 0.790944i | −0.766826 | + | 0.0358780i | ||||
\(487\) | 19.7470 | + | 19.7470i | 0.894823 | + | 0.894823i | 0.994972 | − | 0.100149i | \(-0.0319321\pi\) |
−0.100149 | + | 0.994972i | \(0.531932\pi\) | |||||||
\(488\) | 4.57695 | − | 6.08184i | 0.207189 | − | 0.275312i | ||||
\(489\) | −4.70802 | −0.212904 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.21405 | + | 4.21405i | −0.190177 | + | 0.190177i | −0.795773 | − | 0.605595i | \(-0.792935\pi\) |
0.605595 | + | 0.795773i | \(0.292935\pi\) | |||||||
\(492\) | 0.310341 | + | 3.30923i | 0.0139913 | + | 0.149192i | ||||
\(493\) | − | 0.959871i | − | 0.0432304i | ||||||
\(494\) | −6.36500 | − | 5.79602i | −0.286375 | − | 0.260775i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.608504 | + | 3.21577i | 0.0273226 | + | 0.144392i | ||||
\(497\) | 16.3712 | + | 16.3712i | 0.734348 | + | 0.734348i | ||||
\(498\) | −6.43324 | + | 0.300996i | −0.288280 | + | 0.0134879i | ||||
\(499\) | −16.8862 | + | 16.8862i | −0.755928 | + | 0.755928i | −0.975579 | − | 0.219650i | \(-0.929508\pi\) |
0.219650 | + | 0.975579i | \(0.429508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.68450 | + | 4.68450i | 0.209288 | + | 0.209288i | ||||
\(502\) | −13.9768 | + | 15.3488i | −0.623814 | + | 0.685053i | ||||
\(503\) | 20.3714 | − | 20.3714i | 0.908317 | − | 0.908317i | −0.0878190 | − | 0.996136i | \(-0.527990\pi\) |
0.996136 | + | 0.0878190i | \(0.0279897\pi\) | |||||||
\(504\) | −13.6780 | − | 10.2935i | −0.609268 | − | 0.458511i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.947086 | + | 20.2423i | 0.0421031 | + | 0.899878i | ||||
\(507\) | −6.43550 | −0.285811 | ||||||||
\(508\) | −1.37087 | + | 1.65460i | −0.0608225 | + | 0.0734110i | ||||
\(509\) | −20.6309 | − | 20.6309i | −0.914448 | − | 0.914448i | 0.0821701 | − | 0.996618i | \(-0.473815\pi\) |
−0.996618 | + | 0.0821701i | \(0.973815\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.41952i | 0.372458i | ||||||||
\(512\) | −20.6536 | + | 9.24271i | −0.912770 | + | 0.408474i | ||||
\(513\) | −2.41307 | + | 2.41307i | −0.106540 | + | 0.106540i | ||||
\(514\) | 30.2190 | + | 27.5177i | 1.33290 | + | 1.21375i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.416411 | − | 4.44028i | −0.0183315 | − | 0.195472i | ||||
\(517\) | − | 36.0320i | − | 1.58469i | ||||||
\(518\) | −10.7291 | + | 11.7824i | −0.471411 | + | 0.517688i | ||||
\(519\) | 4.44215i | 0.194989i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.0433i | − | 0.834300i | −0.908838 | − | 0.417150i | \(-0.863029\pi\) | ||
0.908838 | − | 0.417150i | \(-0.136971\pi\) | |||||||
\(522\) | 9.15131 | + | 8.33325i | 0.400542 | + | 0.364736i | ||||
\(523\) | − | 19.1782i | − | 0.838603i | −0.907847 | − | 0.419301i | \(-0.862275\pi\) | ||
0.907847 | − | 0.419301i | \(-0.137725\pi\) | |||||||
\(524\) | 16.5527 | + | 13.7143i | 0.723109 | + | 0.599110i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.9343 | − | 20.7931i | 0.825577 | − | 0.906622i | ||||
\(527\) | 0.174722 | − | 0.174722i | 0.00761101 | − | 0.00761101i | ||||
\(528\) | −6.63853 | + | 9.73723i | −0.288905 | + | 0.423759i | ||||
\(529\) | 17.1693i | 0.746490i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.0644 | + | 21.0644i | 0.914118 | + | 0.914118i | ||||
\(532\) | −5.22891 | + | 0.490369i | −0.226702 | + | 0.0212602i | ||||
\(533\) | −17.0553 | −0.738749 | ||||||||
\(534\) | 2.98154 | − | 0.139499i | 0.129024 | − | 0.00603671i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.35831 | + | 30.8690i | 0.188251 | + | 1.33334i | ||||
\(537\) | −1.50153 | + | 1.50153i | −0.0647957 | + | 0.0647957i | ||||
\(538\) | 9.78118 | + | 8.90681i | 0.421697 | + | 0.384000i | ||||
\(539\) | 9.09950 | + | 9.09950i | 0.391943 | + | 0.391943i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5231 | − | 14.5231i | 0.624398 | − | 0.624398i | −0.322255 | − | 0.946653i | \(-0.604441\pi\) |
0.946653 | + | 0.322255i | \(0.104441\pi\) | |||||||
\(542\) | −0.702061 | − | 15.0053i | −0.0301561 | − | 0.644532i | ||||
\(543\) | −0.768787 | − | 0.768787i | −0.0329918 | − | 0.0329918i | ||||
\(544\) | 1.45494 | + | 0.895300i | 0.0623801 | + | 0.0383857i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.29456 | + | 5.81432i | −0.226586 | + | 0.248830i | ||||
\(547\) | 9.97058i | 0.426311i | 0.977018 | + | 0.213156i | \(0.0683742\pi\) | ||||
−0.977018 | + | 0.213156i | \(0.931626\pi\) | |||||||
\(548\) | −23.0598 | + | 27.8325i | −0.985067 | + | 1.18895i | ||||
\(549\) | 5.23967 | − | 5.23967i | 0.223624 | − | 0.223624i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.79716 | 0.161765 | ||||||||
\(552\) | 2.03897 | − | 2.70938i | 0.0867845 | − | 0.115319i | ||||
\(553\) | 12.9316 | + | 12.9316i | 0.549906 | + | 0.549906i | ||||
\(554\) | −0.547607 | − | 11.7041i | −0.0232656 | − | 0.497260i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8627 | + | 13.9711i | 0.715138 | + | 0.592506i | ||||
\(557\) | −11.4424 | −0.484831 | −0.242416 | − | 0.970173i | \(-0.577940\pi\) | ||||
−0.242416 | + | 0.970173i | \(0.577940\pi\) | |||||||
\(558\) | 0.148909 | + | 3.18265i | 0.00630381 | + | 0.134732i | ||||
\(559\) | 22.8846 | 0.967915 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.889743 | 0.0375650 | ||||||||
\(562\) | −1.38916 | − | 29.6909i | −0.0585984 | − | 1.25243i | ||||
\(563\) | −47.0585 | −1.98328 | −0.991640 | − | 0.129034i | \(-0.958812\pi\) | ||||
−0.991640 | + | 0.129034i | \(0.958812\pi\) | |||||||
\(564\) | −3.84668 | + | 4.64283i | −0.161975 | + | 0.195499i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.956715 | − | 20.4481i | −0.0402137 | − | 0.859496i | ||||
\(567\) | −10.6346 | − | 10.6346i | −0.446612 | − | 0.446612i | ||||
\(568\) | 29.4996 | − | 4.16498i | 1.23778 | − | 0.174759i | ||||
\(569\) | 41.4684 | 1.73845 | 0.869224 | − | 0.494419i | \(-0.164619\pi\) | ||||
0.869224 | + | 0.494419i | \(0.164619\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.1745 | − | 16.1745i | 0.676881 | − | 0.676881i | −0.282412 | − | 0.959293i | \(-0.591135\pi\) |
0.959293 | + | 0.282412i | \(0.0911347\pi\) | |||||||
\(572\) | −46.5662 | − | 38.5811i | −1.94703 | − | 1.61316i | ||||
\(573\) | − | 9.97963i | − | 0.416905i | ||||||
\(574\) | −7.00556 | + | 7.69329i | −0.292407 | + | 0.321112i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −21.1670 | + | 6.09859i | −0.881957 | + | 0.254108i | ||||
\(577\) | −20.0316 | − | 20.0316i | −0.833926 | − | 0.833926i | 0.154125 | − | 0.988051i | \(-0.450744\pi\) |
−0.988051 | + | 0.154125i | \(0.950744\pi\) | |||||||
\(578\) | 1.11759 | + | 23.8865i | 0.0464857 | + | 0.993548i | ||||
\(579\) | −1.89898 | + | 1.89898i | −0.0789189 | + | 0.0789189i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.2562 | − | 14.2562i | −0.591447 | − | 0.591447i | ||||
\(582\) | −5.25678 | − | 4.78686i | −0.217900 | − | 0.198422i | ||||
\(583\) | −4.22349 | + | 4.22349i | −0.174919 | + | 0.174919i | ||||
\(584\) | 8.65667 | + | 6.51467i | 0.358215 | + | 0.269579i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.8341 | + | 0.787627i | −0.695411 | + | 0.0325366i | ||||
\(587\) | −29.1190 | −1.20187 | −0.600935 | − | 0.799298i | \(-0.705205\pi\) | ||||
−0.600935 | + | 0.799298i | \(0.705205\pi\) | |||||||
\(588\) | −0.201059 | − | 2.14394i | −0.00829155 | − | 0.0884145i | ||||
\(589\) | 0.691185 | + | 0.691185i | 0.0284798 | + | 0.0284798i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.554866i | 0.0228242i | ||||||||
\(592\) | 3.81251 | + | 20.1480i | 0.156693 | + | 0.828079i | ||||
\(593\) | 10.3431 | − | 10.3431i | 0.424740 | − | 0.424740i | −0.462092 | − | 0.886832i | \(-0.652901\pi\) |
0.886832 | + | 0.462092i | \(0.152901\pi\) | |||||||
\(594\) | −16.1403 | + | 17.7248i | −0.662246 | + | 0.727258i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.2722 | − | 20.8471i | 0.707499 | − | 0.853930i | ||||
\(597\) | 12.7016i | 0.519843i | ||||||||
\(598\) | 12.8651 | + | 11.7151i | 0.526095 | + | 0.479066i | ||||
\(599\) | − | 2.59479i | − | 0.106020i | −0.998594 | − | 0.0530101i | \(-0.983118\pi\) | ||
0.998594 | − | 0.0530101i | \(-0.0168816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.4092i | 0.587765i | 0.955842 | + | 0.293882i | \(0.0949474\pi\) | ||||
−0.955842 | + | 0.293882i | \(0.905053\pi\) | |||||||
\(602\) | 9.39996 | − | 10.3227i | 0.383114 | − | 0.420723i | ||||
\(603\) | 30.3493i | 1.23592i | ||||||||
\(604\) | −19.2912 | + | 1.80913i | −0.784946 | + | 0.0736126i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.15870 | − | 5.60816i | −0.250180 | − | 0.227816i | ||||
\(607\) | 11.8502 | − | 11.8502i | 0.480985 | − | 0.480985i | −0.424461 | − | 0.905446i | \(-0.639536\pi\) |
0.905446 | + | 0.424461i | \(0.139536\pi\) | |||||||
\(608\) | −3.54173 | + | 5.75562i | −0.143636 | + | 0.233421i | ||||
\(609\) | − | 3.46864i | − | 0.140557i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.8769 | − | 21.8769i | −0.885045 | − | 0.885045i | ||||
\(612\) | 1.28064 | + | 1.06104i | 0.0517669 | + | 0.0428899i | ||||
\(613\) | −16.8256 | −0.679579 | −0.339789 | − | 0.940502i | \(-0.610356\pi\) | ||||
−0.339789 | + | 0.940502i | \(0.610356\pi\) | |||||||
\(614\) | −1.68220 | − | 35.9540i | −0.0678881 | − | 1.45099i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −36.5304 | + | 5.15763i | −1.47185 | + | 0.207807i | ||||
\(617\) | 22.4849 | − | 22.4849i | 0.905209 | − | 0.905209i | −0.0906720 | − | 0.995881i | \(-0.528902\pi\) |
0.995881 | + | 0.0906720i | \(0.0289015\pi\) | |||||||
\(618\) | −3.45295 | + | 3.79191i | −0.138898 | + | 0.152533i | ||||
\(619\) | −14.1269 | − | 14.1269i | −0.567809 | − | 0.567809i | 0.363705 | − | 0.931514i | \(-0.381512\pi\) |
−0.931514 | + | 0.363705i | \(0.881512\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.87738 | − | 4.87738i | 0.195723 | − | 0.195723i | ||||
\(622\) | −30.3406 | + | 1.41956i | −1.21655 | + | 0.0569193i | ||||
\(623\) | 6.60715 | + | 6.60715i | 0.264710 | + | 0.264710i | ||||
\(624\) | 1.88138 | + | 9.94257i | 0.0753156 | + | 0.398021i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.7956 | + | 25.3109i | 1.11094 | + | 1.01163i | ||||
\(627\) | 3.51974i | 0.140565i | ||||||||
\(628\) | 19.8656 | − | 1.86300i | 0.792723 | − | 0.0743419i | ||||
\(629\) | 1.09470 | − | 1.09470i | 0.0436486 | − | 0.0436486i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.9235 | −1.35047 | −0.675236 | − | 0.737601i | \(-0.735958\pi\) | ||||
−0.675236 | + | 0.737601i | \(0.735958\pi\) | |||||||
\(632\) | 23.3017 | − | 3.28991i | 0.926892 | − | 0.130866i | ||||
\(633\) | 0.204361 | + | 0.204361i | 0.00812261 | + | 0.00812261i | ||||
\(634\) | 22.9602 | − | 1.07425i | 0.911867 | − | 0.0426640i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.995097 | − | 0.0933206i | 0.0394582 | − | 0.00370040i | ||||
\(637\) | 11.0496 | 0.437799 | ||||||||
\(638\) | 26.6448 | − | 1.24664i | 1.05488 | − | 0.0493551i | ||||
\(639\) | 29.0030 | 1.14734 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8495 | 0.744509 | 0.372254 | − | 0.928131i | \(-0.378585\pi\) | ||||
0.372254 | + | 0.928131i | \(0.378585\pi\) | |||||||
\(642\) | 6.29813 | − | 0.294674i | 0.248567 | − | 0.0116299i | ||||
\(643\) | 16.4916 | 0.650364 | 0.325182 | − | 0.945652i | \(-0.394574\pi\) | ||||
0.325182 | + | 0.945652i | \(0.394574\pi\) | |||||||
\(644\) | 10.5688 | − | 0.991150i | 0.416471 | − | 0.0390568i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.509664 | − | 0.0238459i | 0.0200525 | − | 0.000938206i | ||||
\(647\) | 0.316870 | + | 0.316870i | 0.0124574 | + | 0.0124574i | 0.713308 | − | 0.700851i | \(-0.247196\pi\) |
−0.700851 | + | 0.713308i | \(0.747196\pi\) | |||||||
\(648\) | −19.1628 | + | 2.70555i | −0.752786 | + | 0.106284i | ||||
\(649\) | 64.2002 | 2.52008 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.631386 | − | 0.631386i | 0.0247460 | − | 0.0247460i | ||||
\(652\) | −18.8825 | + | 1.77081i | −0.739495 | + | 0.0693502i | ||||
\(653\) | − | 17.0751i | − | 0.668200i | −0.942538 | − | 0.334100i | \(-0.891568\pi\) | ||
0.942538 | − | 0.334100i | \(-0.108432\pi\) | |||||||
\(654\) | −8.00859 | − | 7.29268i | −0.313161 | − | 0.285167i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.48937 | + | 13.1556i | 0.0971937 | + | 0.513641i | ||||
\(657\) | 7.45796 | + | 7.45796i | 0.290963 | + | 0.290963i | ||||
\(658\) | −18.8542 | + | 0.882144i | −0.735014 | + | 0.0343895i | ||||
\(659\) | −7.42245 | + | 7.42245i | −0.289138 | + | 0.289138i | −0.836739 | − | 0.547601i | \(-0.815541\pi\) |
0.547601 | + | 0.836739i | \(0.315541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.7614 | + | 31.7614i | 1.23538 | + | 1.23538i | 0.961870 | + | 0.273507i | \(0.0881837\pi\) |
0.273507 | + | 0.961870i | \(0.411816\pi\) | |||||||
\(662\) | 11.7362 | − | 12.8883i | 0.456139 | − | 0.500917i | ||||
\(663\) | 0.540209 | − | 0.540209i | 0.0209800 | − | 0.0209800i | ||||
\(664\) | −25.6886 | + | 3.62691i | −0.996911 | + | 0.140751i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.932970 | + | 19.9406i | 0.0361519 | + | 0.772681i | ||||
\(667\) | −7.67495 | −0.297175 | ||||||||
\(668\) | 20.5501 | + | 17.0262i | 0.795107 | + | 0.658762i | ||||
\(669\) | 8.31446 | + | 8.31446i | 0.321456 | + | 0.321456i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 15.9695i | − | 0.616496i | ||||||
\(672\) | 5.25766 | + | 3.23531i | 0.202819 | + | 0.124805i | ||||
\(673\) | −4.14672 | + | 4.14672i | −0.159844 | + | 0.159844i | −0.782498 | − | 0.622653i | \(-0.786055\pi\) |
0.622653 | + | 0.782498i | \(0.286055\pi\) | |||||||
\(674\) | 0.0601670 | + | 0.0547885i | 0.00231755 | + | 0.00211037i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.8109 | + | 2.42056i | −0.992727 | + | 0.0930983i | ||||
\(677\) | 25.2618i | 0.970890i | 0.874267 | + | 0.485445i | \(0.161342\pi\) | ||||
−0.874267 | + | 0.485445i | \(0.838658\pi\) | |||||||
\(678\) | −2.87268 | + | 3.15468i | −0.110325 | + | 0.121155i | ||||
\(679\) | − | 22.2569i | − | 0.854143i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.84196i | − | 0.262184i | ||||||
\(682\) | 5.07698 | + | 4.62313i | 0.194408 | + | 0.177029i | ||||
\(683\) | − | 8.20306i | − | 0.313881i | −0.987608 | − | 0.156941i | \(-0.949837\pi\) | ||
0.987608 | − | 0.156941i | \(-0.0501631\pi\) | |||||||
\(684\) | −4.19737 | + | 5.06610i | −0.160490 | + | 0.193707i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.1891 | − | 21.0728i | 0.732643 | − | 0.804565i | ||||
\(687\) | −3.92707 | + | 3.92707i | −0.149827 | + | 0.149827i | ||||
\(688\) | −3.34020 | − | 17.6520i | −0.127344 | − | 0.672977i | ||||
\(689\) | 5.12859i | 0.195384i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.89158 | − | 7.89158i | −0.300210 | − | 0.300210i | 0.540886 | − | 0.841096i | \(-0.318089\pi\) |
−0.841096 | + | 0.540886i | \(0.818089\pi\) | |||||||
\(692\) | 1.67081 | + | 17.8162i | 0.0635145 | + | 0.677268i | ||||
\(693\) | −35.9153 | −1.36431 | ||||||||
\(694\) | −50.4455 | + | 2.36022i | −1.91489 | + | 0.0895929i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.56635 | − | 2.68389i | −0.135182 | − | 0.101733i | ||||
\(697\) | 0.714783 | − | 0.714783i | 0.0270744 | − | 0.0270744i | ||||
\(698\) | 0.405850 | + | 0.369570i | 0.0153616 | + | 0.0139884i | ||||
\(699\) | 0.834083 | + | 0.834083i | 0.0315479 | + | 0.0315479i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.50228 | − | 1.50228i | 0.0567405 | − | 0.0567405i | −0.678167 | − | 0.734908i | \(-0.737225\pi\) |
0.734908 | + | 0.678167i | \(0.237225\pi\) | |||||||
\(702\) | 0.962012 | + | 20.5613i | 0.0363088 | + | 0.776036i | ||||
\(703\) | 4.33054 | + | 4.33054i | 0.163329 | + | 0.163329i | ||||
\(704\) | −22.9627 | + | 41.5501i | −0.865441 | + | 1.56598i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.0354 | + | 23.1004i | −0.791679 | + | 0.869397i | ||||
\(707\) | − | 26.0756i | − | 0.980675i | ||||||
\(708\) | −8.27239 | − | 6.85385i | −0.310896 | − | 0.257583i | ||||
\(709\) | −36.0738 | + | 36.0738i | −1.35478 | + | 1.35478i | −0.474551 | + | 0.880228i | \(0.657390\pi\) |
−0.880228 | + | 0.474551i | \(0.842610\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.9094 | 0.859170 | ||||||||
\(712\) | 11.9056 | − | 1.68092i | 0.446181 | − | 0.0629952i | ||||
\(713\) | −1.39704 | − | 1.39704i | −0.0523197 | − | 0.0523197i | ||||
\(714\) | −0.0217829 | − | 0.465570i | −0.000815203 | − | 0.0174235i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.45741 | + | 6.58694i | −0.203953 | + | 0.246165i | ||||
\(717\) | 5.84291 | 0.218207 | ||||||||
\(718\) | 0.0508132 | + | 1.08604i | 0.00189633 | + | 0.0405307i | ||||
\(719\) | −35.0340 | −1.30655 | −0.653274 | − | 0.757121i | \(-0.726605\pi\) | ||||
−0.653274 | + | 0.757121i | \(0.726605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0548 | −0.597911 | ||||||||
\(722\) | −1.16148 | − | 24.8245i | −0.0432258 | − | 0.923873i | ||||
\(723\) | −6.58989 | −0.245081 | ||||||||
\(724\) | −3.37253 | − | 2.79421i | −0.125339 | − | 0.103846i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.794593 | + | 16.9830i | 0.0294901 | + | 0.630298i | ||||
\(727\) | −25.4241 | − | 25.4241i | −0.942928 | − | 0.942928i | 0.0555295 | − | 0.998457i | \(-0.482315\pi\) |
−0.998457 | + | 0.0555295i | \(0.982315\pi\) | |||||||
\(728\) | −19.0480 | + | 25.3109i | −0.705966 | + | 0.938085i | ||||
\(729\) | −14.5855 | −0.540203 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.959085 | + | 0.959085i | −0.0354731 | + | 0.0354731i | ||||
\(732\) | −1.70486 | + | 2.05772i | −0.0630135 | + | 0.0760555i | ||||
\(733\) | − | 7.37554i | − | 0.272422i | −0.990680 | − | 0.136211i | \(-0.956508\pi\) | ||
0.990680 | − | 0.136211i | \(-0.0434925\pi\) | |||||||
\(734\) | 18.5624 | − | 20.3847i | 0.685151 | − | 0.752411i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.15865 | − | 11.6334i | 0.263871 | − | 0.428814i | ||||
\(737\) | 46.2494 | + | 46.2494i | 1.70362 | + | 1.70362i | ||||
\(738\) | 0.609181 | + | 13.0202i | 0.0224243 | + | 0.479278i | ||||
\(739\) | 5.55025 | − | 5.55025i | 0.204169 | − | 0.204169i | −0.597614 | − | 0.801784i | \(-0.703885\pi\) |
0.801784 | + | 0.597614i | \(0.203885\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.13702 | + | 2.13702i | 0.0785053 | + | 0.0785053i | ||||
\(742\) | 2.31339 | + | 2.10659i | 0.0849274 | + | 0.0773355i | ||||
\(743\) | 6.78835 | − | 6.78835i | 0.249040 | − | 0.249040i | −0.571536 | − | 0.820577i | \(-0.693652\pi\) |
0.820577 | + | 0.571536i | \(0.193652\pi\) | |||||||
\(744\) | −0.160630 | − | 1.13771i | −0.00588899 | − | 0.0417104i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.2315 | + | 1.41446i | −1.10685 | + | 0.0517869i | ||||
\(747\) | −25.2561 | −0.924073 | ||||||||
\(748\) | 3.56849 | − | 0.334655i | 0.130477 | − | 0.0122362i | ||||
\(749\) | 13.9568 | + | 13.9568i | 0.509970 | + | 0.509970i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.93385i | 0.143548i | 0.997421 | + | 0.0717742i | \(0.0228661\pi\) | ||||
−0.997421 | + | 0.0717742i | \(0.977134\pi\) | |||||||
\(752\) | −13.6816 | + | 20.0679i | −0.498917 | + | 0.731799i | ||||
\(753\) | 5.15330 | − | 5.15330i | 0.187797 | − | 0.187797i | ||||
\(754\) | 15.4205 | − | 16.9343i | 0.561582 | − | 0.616711i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.66989 | + | 8.01170i | 0.351690 | + | 0.291383i | ||||
\(757\) | 21.8327i | 0.793525i | 0.917921 | + | 0.396762i | \(0.129866\pi\) | ||||
−0.917921 | + | 0.396762i | \(0.870134\pi\) | |||||||
\(758\) | −16.8464 | − | 15.3405i | −0.611890 | − | 0.557191i | ||||
\(759\) | − | 7.11421i | − | 0.258230i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.27291i | − | 0.154893i | −0.996997 | − | 0.0774464i | \(-0.975323\pi\) | ||
0.996997 | − | 0.0774464i | \(-0.0246767\pi\) | |||||||
\(762\) | 0.507893 | − | 0.557752i | 0.0183990 | − | 0.0202052i | ||||
\(763\) | − | 33.9080i | − | 1.22755i | ||||||
\(764\) | −3.75359 | − | 40.0253i | −0.135800 | − | 1.44807i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.54552 | + | 5.96040i | 0.236499 | + | 0.215358i | ||||
\(767\) | 38.9793 | − | 38.9793i | 1.40746 | − | 1.40746i | ||||
\(768\) | 7.39459 | − | 2.90241i | 0.266829 | − | 0.104732i | ||||
\(769\) | 26.1800i | 0.944074i | 0.881579 | + | 0.472037i | \(0.156481\pi\) | ||||
−0.881579 | + | 0.472037i | \(0.843519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.1459 | − | 10.1459i | −0.365395 | − | 0.365395i | ||||
\(772\) | −6.90198 | + | 8.33049i | −0.248408 | + | 0.299821i | ||||
\(773\) | 15.0077 | 0.539791 | 0.269895 | − | 0.962890i | \(-0.413011\pi\) | ||||
0.269895 | + | 0.962890i | \(0.413011\pi\) | |||||||
\(774\) | −0.817390 | − | 17.4702i | −0.0293805 | − | 0.627955i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −22.8838 | − | 17.2215i | −0.821482 | − | 0.618215i | ||||
\(777\) | 3.95587 | − | 3.95587i | 0.141916 | − | 0.141916i | ||||
\(778\) | −16.6305 | + | 18.2630i | −0.596231 | + | 0.654762i | ||||
\(779\) | 2.82762 | + | 2.82762i | 0.101310 | + | 0.101310i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.1977 | − | 44.1977i | 1.58152 | − | 1.58152i | ||||
\(782\) | −1.03015 | + | 0.0481982i | −0.0368381 | + | 0.00172356i | ||||
\(783\) | −6.42007 | − | 6.42007i | −0.229434 | − | 0.229434i | ||||
\(784\) | −1.61278 | − | 8.52307i | −0.0575992 | − | 0.304395i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.57978 | − | 5.08099i | −0.199024 | − | 0.181233i | ||||
\(787\) | 42.9223i | 1.53001i | 0.644022 | + | 0.765007i | \(0.277264\pi\) | ||||
−0.644022 | + | 0.765007i | \(0.722736\pi\) | |||||||
\(788\) | 0.208699 | + | 2.22540i | 0.00743461 | + | 0.0792767i | ||||
\(789\) | −6.98118 | + | 6.98118i | −0.248536 | + | 0.248536i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.3568 | −0.474912 | ||||||||
\(792\) | −27.7898 | + | 36.9270i | −0.987466 | + | 1.31214i | ||||
\(793\) | −9.69591 | − | 9.69591i | −0.344312 | − | 0.344312i | ||||
\(794\) | 25.4043 | − | 1.18861i | 0.901565 | − | 0.0421820i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.77741 | + | 50.9425i | 0.169331 | + | 1.80561i | ||||
\(797\) | −0.280831 | −0.00994753 | −0.00497377 | − | 0.999988i | \(-0.501583\pi\) | ||||
−0.00497377 | + | 0.999988i | \(0.501583\pi\) | |||||||
\(798\) | 1.84175 | − | 0.0861711i | 0.0651973 | − | 0.00305042i | ||||
\(799\) | 1.83371 | 0.0648719 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.7052 | 0.413581 | ||||||||
\(802\) | −12.8068 | + | 0.599200i | −0.452225 | + | 0.0211585i | ||||
\(803\) | 22.7304 | 0.802139 | ||||||||
\(804\) | −1.02191 | − | 10.8968i | −0.0360400 | − | 0.384301i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.88944 | − | 0.275553i | 0.207447 | − | 0.00970593i | ||||
\(807\) | −3.28398 | − | 3.28398i | −0.115602 | − | 0.115602i | ||||
\(808\) | −26.8101 | − | 20.1762i | −0.943176 | − | 0.709797i | ||||
\(809\) | −16.5787 | −0.582876 | −0.291438 | − | 0.956590i | \(-0.594134\pi\) | ||||
−0.291438 | + | 0.956590i | \(0.594134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.25384 | − | 7.25384i | 0.254717 | − | 0.254717i | −0.568184 | − | 0.822901i | \(-0.692354\pi\) |
0.822901 | + | 0.568184i | \(0.192354\pi\) | |||||||
\(812\) | −1.30465 | − | 13.9117i | −0.0457841 | − | 0.488205i | ||||
\(813\) | 5.27366i | 0.184955i | ||||||||
\(814\) | 31.8092 | + | 28.9657i | 1.11491 | + | 1.01525i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.495538 | − | 0.337841i | −0.0173473 | − | 0.0118268i | ||||
\(817\) | −3.79405 | − | 3.79405i | −0.132737 | − | 0.132737i | ||||
\(818\) | 42.4671 | − | 1.98693i | 1.48483 | − | 0.0694715i | ||||
\(819\) | −21.8061 | + | 21.8061i | −0.761965 | + | 0.761965i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.3525 | − | 15.3525i | −0.535806 | − | 0.535806i | 0.386489 | − | 0.922294i | \(-0.373688\pi\) |
−0.922294 | + | 0.386489i | \(0.873688\pi\) | |||||||
\(822\) | 8.54343 | − | 9.38212i | 0.297986 | − | 0.327239i | ||||
\(823\) | 26.7794 | − | 26.7794i | 0.933472 | − | 0.933472i | −0.0644492 | − | 0.997921i | \(-0.520529\pi\) |
0.997921 | + | 0.0644492i | \(0.0205290\pi\) | |||||||
\(824\) | −12.4225 | + | 16.5070i | −0.432758 | + | 0.575048i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.57176 | − | 33.5936i | −0.0546887 | − | 1.16887i | ||||
\(827\) | 39.4186 | 1.37072 | 0.685359 | − | 0.728205i | \(-0.259645\pi\) | ||||
0.685359 | + | 0.728205i | \(0.259645\pi\) | |||||||
\(828\) | 8.48386 | − | 10.2398i | 0.294834 | − | 0.355857i | ||||
\(829\) | −20.7102 | − | 20.7102i | −0.719296 | − | 0.719296i | 0.249165 | − | 0.968461i | \(-0.419844\pi\) |
−0.968461 | + | 0.249165i | \(0.919844\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.11345i | 0.142694i | ||||||||
\(832\) | 11.2853 | + | 39.1690i | 0.391248 | + | 1.35794i | ||||
\(833\) | −0.463083 | + | 0.463083i | −0.0160449 | + | 0.0160449i | ||||
\(834\) | −5.68428 | − | 5.17615i | −0.196830 | − | 0.179235i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.32386 | + | 14.1166i | 0.0457868 | + | 0.488234i | ||||
\(837\) | − | 2.33725i | − | 0.0807870i | ||||||
\(838\) | 20.7354 | − | 22.7709i | 0.716291 | − | 0.786608i | ||||
\(839\) | − | 31.8706i | − | 1.10029i | −0.835068 | − | 0.550147i | \(-0.814572\pi\) | ||
0.835068 | − | 0.550147i | \(-0.185428\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 18.8975i | − | 0.651638i | ||||||
\(842\) | 5.71495 | + | 5.20408i | 0.196950 | + | 0.179344i | ||||
\(843\) | 10.4350i | 0.359399i | ||||||||
\(844\) | 0.896495 | + | 0.742765i | 0.0308586 | + | 0.0255670i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15.9196 | + | 17.4824i | −0.547326 | + | 0.601056i | ||||
\(847\) | −37.6347 | + | 37.6347i | −1.29314 | + | 1.29314i | ||||
\(848\) | 3.95594 | − | 0.748562i | 0.135847 | − | 0.0257057i | ||||
\(849\) | 7.18654i | 0.246642i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.75302 | − | 8.75302i | −0.300050 | − | 0.300050i | ||||
\(852\) | −10.4134 | + | 0.976577i | −0.356759 | + | 0.0334570i | ||||
\(853\) | 26.5538 | 0.909185 | 0.454592 | − | 0.890700i | \(-0.349785\pi\) | ||||
0.454592 | + | 0.890700i | \(0.349785\pi\) | |||||||
\(854\) | −8.35626 | + | 0.390969i | −0.285945 | + | 0.0133787i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.1491 | − | 3.55074i | 0.859578 | − | 0.121362i | ||||
\(857\) | 20.7249 | − | 20.7249i | 0.707951 | − | 0.707951i | −0.258153 | − | 0.966104i | \(-0.583114\pi\) |
0.966104 | + | 0.258153i | \(0.0831140\pi\) | |||||||
\(858\) | 15.6971 | + | 14.2939i | 0.535890 | + | 0.487985i | ||||
\(859\) | 35.9248 | + | 35.9248i | 1.22574 | + | 1.22574i | 0.965561 | + | 0.260176i | \(0.0837807\pi\) |
0.260176 | + | 0.965561i | \(0.416219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.58298 | − | 2.58298i | 0.0880278 | − | 0.0880278i | ||||
\(862\) | −1.80237 | − | 38.5224i | −0.0613889 | − | 1.31208i | ||||
\(863\) | −9.19232 | − | 9.19232i | −0.312910 | − | 0.312910i | 0.533126 | − | 0.846036i | \(-0.321017\pi\) |
−0.846036 | + | 0.533126i | \(0.821017\pi\) | |||||||
\(864\) | 15.7195 | − | 3.74314i | 0.534789 | − | 0.127344i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.7781 | − | 28.3087i | 0.875976 | − | 0.961969i | ||||
\(867\) | − | 8.39500i | − | 0.285109i | ||||||
\(868\) | 2.29482 | − | 2.76978i | 0.0778913 | − | 0.0940125i | ||||
\(869\) | 34.9117 | − | 34.9117i | 1.18430 | − | 1.18430i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.1608 | 1.90293 | ||||||||
\(872\) | −34.8630 | − | 26.2365i | −1.18061 | − | 0.888482i | ||||
\(873\) | −19.7151 | − | 19.7151i | −0.667253 | − | 0.667253i | ||||
\(874\) | −0.190668 | − | 4.07518i | −0.00644943 | − | 0.137845i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.92888 | − | 2.42664i | −0.0989577 | − | 0.0819885i | ||||
\(877\) | 17.9106 | 0.604799 | 0.302399 | − | 0.953181i | \(-0.402212\pi\) | ||||
0.302399 | + | 0.953181i | \(0.402212\pi\) | |||||||
\(878\) | 1.99605 | + | 42.6619i | 0.0673633 | + | 1.43977i | ||||
\(879\) | 5.91641 | 0.199556 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.01537 | 0.202663 | 0.101332 | − | 0.994853i | \(-0.467690\pi\) | ||||
0.101332 | + | 0.994853i | \(0.467690\pi\) | |||||||
\(882\) | −0.394667 | − | 8.43530i | −0.0132891 | − | 0.284031i | ||||
\(883\) | −19.8374 | −0.667580 | −0.333790 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333790 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(884\) | 1.96343 | − | 2.36980i | 0.0660373 | − | 0.0797051i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.83117 | − | 39.1381i | −0.0615195 | − | 1.31487i | ||||
\(887\) | −14.3740 | − | 14.3740i | −0.482632 | − | 0.482632i | 0.423339 | − | 0.905971i | \(-0.360858\pi\) |
−0.905971 | + | 0.423339i | \(0.860858\pi\) | |||||||
\(888\) | −1.00641 | − | 7.12819i | −0.0337729 | − | 0.239206i | ||||
\(889\) | 2.36149 | 0.0792019 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.7106 | + | 28.7106i | −0.961842 | + | 0.961842i | ||||
\(892\) | 36.4741 | + | 30.2196i | 1.22124 | + | 1.01183i | ||||
\(893\) | 7.25398i | 0.242745i | ||||||||
\(894\) | −6.39919 | + | 7.02739i | −0.214021 | + | 0.235031i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 22.3038 | + | 10.9983i | 0.745117 | + | 0.367428i | ||||
\(897\) | −4.31941 | − | 4.31941i | −0.144221 | − | 0.144221i | ||||
\(898\) | −0.646620 | − | 13.8203i | −0.0215780 | − | 0.461191i | ||||
\(899\) | −1.83892 | + | 1.83892i | −0.0613315 | + | 0.0613315i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.214938 | − | 0.214938i | −0.00716061 | − | 0.00716061i | ||||
\(902\) | 20.7698 | + | 18.9131i | 0.691558 | + | 0.629738i | ||||
\(903\) | −3.46580 | + | 3.46580i | −0.115335 | + | 0.115335i | ||||
\(904\) | −10.3349 | + | 13.7330i | −0.343734 | + | 0.456752i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.79482 | − | 0.317913i | 0.225743 | − | 0.0105620i | ||||
\(907\) | 39.0417 | 1.29636 | 0.648180 | − | 0.761487i | \(-0.275531\pi\) | ||||
0.648180 | + | 0.761487i | \(0.275531\pi\) | |||||||
\(908\) | −2.57343 | − | 27.4411i | −0.0854024 | − | 0.910663i | ||||
\(909\) | −23.0976 | − | 23.0976i | −0.766100 | − | 0.766100i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14.0166i | − | 0.464392i | −0.972669 | − | 0.232196i | \(-0.925409\pi\) | ||
0.972669 | − | 0.232196i | \(-0.0745911\pi\) | |||||||
\(912\) | 1.33647 | − | 1.96030i | 0.0442550 | − | 0.0649121i | ||||
\(913\) | −38.4879 | + | 38.4879i | −1.27376 | + | 1.27376i | ||||
\(914\) | −0.750187 | + | 0.823831i | −0.0248140 | + | 0.0272499i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.2732 | + | 17.2274i | −0.471601 | + | 0.569209i | ||||
\(917\) | − | 23.6245i | − | 0.780150i | ||||||
\(918\) | −0.902034 | − | 0.821399i | −0.0297716 | − | 0.0271102i | ||||
\(919\) | − | 8.15149i | − | 0.268893i | −0.990921 | − | 0.134446i | \(-0.957074\pi\) | ||
0.990921 | − | 0.134446i | \(-0.0429256\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6362i | 0.416376i | ||||||||
\(922\) | 16.9386 | − | 18.6015i | 0.557844 | − | 0.612606i | ||||
\(923\) | − | 53.6695i | − | 1.76655i | ||||||
\(924\) | 12.8953 | − | 1.20933i | 0.424224 | − | 0.0397840i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.87325 | − | 4.43762i | −0.160145 | − | 0.145829i | ||||
\(927\) | −14.2212 | + | 14.2212i | −0.467086 | + | 0.467086i | ||||
\(928\) | −15.3130 | − | 9.42289i | −0.502675 | − | 0.309322i | ||||
\(929\) | − | 13.4779i | − | 0.442196i | −0.975252 | − | 0.221098i | \(-0.929036\pi\) | ||
0.975252 | − | 0.221098i | \(-0.0709641\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.83192 | − | 1.83192i | −0.0600386 | − | 0.0600386i | ||||
\(932\) | 3.65898 | + | 3.03154i | 0.119854 | + | 0.0993013i | ||||
\(933\) | 10.6633 | 0.349101 | ||||||||
\(934\) | 0.674142 | + | 14.4086i | 0.0220586 | + | 0.471463i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.54766 | + | 39.2929i | 0.181331 | + | 1.28433i | ||||
\(937\) | 15.8564 | − | 15.8564i | 0.518005 | − | 0.518005i | −0.398963 | − | 0.916967i | \(-0.630630\pi\) |
0.916967 | + | 0.398963i | \(0.130630\pi\) | |||||||
\(938\) | 23.0683 | − | 25.3329i | 0.753207 | − | 0.827148i | ||||
\(939\) | −9.33225 | − | 9.33225i | −0.304546 | − | 0.304546i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.7073 | − | 15.7073i | 0.512044 | − | 0.512044i | −0.403108 | − | 0.915152i | \(-0.632070\pi\) |
0.915152 | + | 0.403108i | \(0.132070\pi\) | |||||||
\(942\) | −6.99715 | + | 0.327380i | −0.227979 | + | 0.0106666i | ||||
\(943\) | −5.71527 | − | 5.71527i | −0.186115 | − | 0.186115i | ||||
\(944\) | −35.7560 | − | 24.3773i | −1.16376 | − | 0.793413i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.8686 | − | 25.3773i | −0.906085 | − | 0.825088i | ||||
\(947\) | 33.6925i | 1.09486i | 0.836852 | + | 0.547430i | \(0.184394\pi\) | ||||
−0.836852 | + | 0.547430i | \(0.815606\pi\) | |||||||
\(948\) | −8.22556 | + | 0.771397i | −0.267154 | + | 0.0250538i | ||||
\(949\) | 13.8008 | − | 13.8008i | 0.447993 | − | 0.447993i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.06945 | −0.261670 | ||||||||
\(952\) | −0.262477 | − | 1.85907i | −0.00850693 | − | 0.0602527i | ||||
\(953\) | 33.5702 | + | 33.5702i | 1.08745 | + | 1.08745i | 0.995791 | + | 0.0916550i | \(0.0292157\pi\) |
0.0916550 | + | 0.995791i | \(0.470784\pi\) | |||||||
\(954\) | 3.91520 | − | 0.183183i | 0.126759 | − | 0.00593076i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 23.4342 | − | 2.19767i | 0.757915 | − | 0.0710776i | ||||
\(957\) | −9.36440 | −0.302708 | ||||||||
\(958\) | −7.99281 | + | 0.373964i | −0.258236 | + | 0.0120822i | ||||
\(959\) | 39.7234 | 1.28274 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3305 | 0.978404 | ||||||||
\(962\) | 36.8996 | − | 1.72644i | 1.18969 | − | 0.0556628i | ||||
\(963\) | 24.7257 | 0.796774 | ||||||||
\(964\) | −26.4301 | + | 2.47863i | −0.851256 | + | 0.0798311i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.72261 | + | 0.174172i | −0.119773 | + | 0.00560388i | ||||
\(967\) | −28.6436 | − | 28.6436i | −0.921115 | − | 0.921115i | 0.0759933 | − | 0.997108i | \(-0.475787\pi\) |
−0.997108 | + | 0.0759933i | \(0.975787\pi\) | |||||||
\(968\) | 9.57461 | + | 67.8149i | 0.307740 | + | 2.17965i | ||||
\(969\) | −0.179123 | −0.00575427 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.7115 | + | 35.7115i | −1.14604 | + | 1.14604i | −0.158713 | + | 0.987325i | \(0.550734\pi\) |
−0.987325 | + | 0.158713i | \(0.949266\pi\) | |||||||
\(972\) | 23.8289 | − | 2.23468i | 0.764312 | − | 0.0716775i | ||||
\(973\) | − | 24.0669i | − | 0.771551i | ||||||
\(974\) | −29.2012 | − | 26.5908i | −0.935666 | − | 0.852024i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.06373 | + | 8.89414i | −0.194095 | + | 0.284694i | ||||
\(977\) | −7.12822 | − | 7.12822i | −0.228052 | − | 0.228052i | 0.583826 | − | 0.811879i | \(-0.301555\pi\) |
−0.811879 | + | 0.583826i | \(0.801555\pi\) | |||||||
\(978\) | 6.65088 | − | 0.311178i | 0.212672 | − | 0.00995039i | ||||
\(979\) | 17.8375 | − | 17.8375i | 0.570090 | − | 0.570090i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0355 | − | 30.0355i | −0.958959 | − | 0.958959i | ||||
\(982\) | 5.67452 | − | 6.23158i | 0.181081 | − | 0.198858i | ||||
\(983\) | 23.9941 | − | 23.9941i | 0.765292 | − | 0.765292i | −0.211982 | − | 0.977274i | \(-0.567992\pi\) |
0.977274 | + | 0.211982i | \(0.0679918\pi\) | |||||||
\(984\) | −0.657134 | − | 4.65434i | −0.0209487 | − | 0.148375i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.0634430 | + | 1.35598i | 0.00202044 | + | 0.0431832i | ||||
\(987\) | 6.62639 | 0.210920 | ||||||||
\(988\) | 9.37472 | + | 7.76715i | 0.298250 | + | 0.247106i | ||||
\(989\) | 7.66866 | + | 7.66866i | 0.243849 | + | 0.243849i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.6040i | 1.28983i | 0.764255 | + | 0.644914i | \(0.223107\pi\) | ||||
−0.764255 | + | 0.644914i | \(0.776893\pi\) | |||||||
\(992\) | −1.07216 | − | 4.50260i | −0.0340412 | − | 0.142958i | ||||
\(993\) | −4.32718 | + | 4.32718i | −0.137319 | + | 0.137319i | ||||
\(994\) | −24.2091 | − | 22.0450i | −0.767866 | − | 0.699225i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.06814 | − | 0.850414i | 0.287335 | − | 0.0269464i | ||||
\(997\) | 54.9087i | 1.73898i | 0.493953 | + | 0.869488i | \(0.335551\pi\) | ||||
−0.493953 | + | 0.869488i | \(0.664449\pi\) | |||||||
\(998\) | 22.7384 | − | 24.9706i | 0.719773 | − | 0.790431i | ||||
\(999\) | − | 14.6437i | − | 0.463308i |
(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 | 400.2.s.d.107.1 | 18 | ||
4.3 | odd | 2 | 1600.2.s.d.207.4 | 18 | |||
5.2 | odd | 4 | 80.2.j.b.43.6 | ✓ | 18 | ||
5.3 | odd | 4 | 400.2.j.d.43.4 | 18 | |||
5.4 | even | 2 | 80.2.s.b.27.9 | yes | 18 | ||
15.2 | even | 4 | 720.2.bd.g.523.4 | 18 | |||
15.14 | odd | 2 | 720.2.z.g.667.1 | 18 | |||
16.3 | odd | 4 | 400.2.j.d.307.4 | 18 | |||
16.13 | even | 4 | 1600.2.j.d.1007.6 | 18 | |||
20.3 | even | 4 | 1600.2.j.d.143.4 | 18 | |||
20.7 | even | 4 | 320.2.j.b.143.6 | 18 | |||
20.19 | odd | 2 | 320.2.s.b.207.6 | 18 | |||
40.19 | odd | 2 | 640.2.s.c.287.4 | 18 | |||
40.27 | even | 4 | 640.2.j.c.543.4 | 18 | |||
40.29 | even | 2 | 640.2.s.d.287.6 | 18 | |||
40.37 | odd | 4 | 640.2.j.d.543.6 | 18 | |||
80.3 | even | 4 | inner | 400.2.s.d.243.1 | 18 | ||
80.13 | odd | 4 | 1600.2.s.d.943.4 | 18 | |||
80.19 | odd | 4 | 80.2.j.b.67.6 | yes | 18 | ||
80.27 | even | 4 | 640.2.s.d.223.6 | 18 | |||
80.29 | even | 4 | 320.2.j.b.47.4 | 18 | |||
80.37 | odd | 4 | 640.2.s.c.223.4 | 18 | |||
80.59 | odd | 4 | 640.2.j.d.607.4 | 18 | |||
80.67 | even | 4 | 80.2.s.b.3.9 | yes | 18 | ||
80.69 | even | 4 | 640.2.j.c.607.6 | 18 | |||
80.77 | odd | 4 | 320.2.s.b.303.6 | 18 | |||
240.179 | even | 4 | 720.2.bd.g.307.4 | 18 | |||
240.227 | odd | 4 | 720.2.z.g.163.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.6 | ✓ | 18 | 5.2 | odd | 4 | ||
80.2.j.b.67.6 | yes | 18 | 80.19 | odd | 4 | ||
80.2.s.b.3.9 | yes | 18 | 80.67 | even | 4 | ||
80.2.s.b.27.9 | yes | 18 | 5.4 | even | 2 | ||
320.2.j.b.47.4 | 18 | 80.29 | even | 4 | |||
320.2.j.b.143.6 | 18 | 20.7 | even | 4 | |||
320.2.s.b.207.6 | 18 | 20.19 | odd | 2 | |||
320.2.s.b.303.6 | 18 | 80.77 | odd | 4 | |||
400.2.j.d.43.4 | 18 | 5.3 | odd | 4 | |||
400.2.j.d.307.4 | 18 | 16.3 | odd | 4 | |||
400.2.s.d.107.1 | 18 | 1.1 | even | 1 | trivial | ||
400.2.s.d.243.1 | 18 | 80.3 | even | 4 | inner | ||
640.2.j.c.543.4 | 18 | 40.27 | even | 4 | |||
640.2.j.c.607.6 | 18 | 80.69 | even | 4 | |||
640.2.j.d.543.6 | 18 | 40.37 | odd | 4 | |||
640.2.j.d.607.4 | 18 | 80.59 | odd | 4 | |||
640.2.s.c.223.4 | 18 | 80.37 | odd | 4 | |||
640.2.s.c.287.4 | 18 | 40.19 | odd | 2 | |||
640.2.s.d.223.6 | 18 | 80.27 | even | 4 | |||
640.2.s.d.287.6 | 18 | 40.29 | even | 2 | |||
720.2.z.g.163.1 | 18 | 240.227 | odd | 4 | |||
720.2.z.g.667.1 | 18 | 15.14 | odd | 2 | |||
720.2.bd.g.307.4 | 18 | 240.179 | even | 4 | |||
720.2.bd.g.523.4 | 18 | 15.2 | even | 4 | |||
1600.2.j.d.143.4 | 18 | 20.3 | even | 4 | |||
1600.2.j.d.1007.6 | 18 | 16.13 | even | 4 | |||
1600.2.s.d.207.4 | 18 | 4.3 | odd | 2 | |||
1600.2.s.d.943.4 | 18 | 80.13 | odd | 4 |