Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(211,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.j (of order \(3\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.211 |
Dual form | 630.2.j.f.421.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | − | 1.50000i | −0.500000 | − | 0.866025i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.866025 | − | 1.50000i | 0.353553 | − | 0.612372i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.86603 | − | 3.23205i | −0.562628 | − | 0.974500i | −0.997266 | − | 0.0738948i | \(-0.976457\pi\) |
0.434638 | − | 0.900605i | \(-0.356876\pi\) | |||||||
\(12\) | 1.73205 | 0.500000 | ||||||||
\(13\) | −2.36603 | + | 4.09808i | −0.656217 | + | 1.13660i | 0.325370 | + | 0.945587i | \(0.394511\pi\) |
−0.981587 | + | 0.191015i | \(0.938822\pi\) | |||||||
\(14\) | −0.500000 | + | 0.866025i | −0.133631 | + | 0.231455i | ||||
\(15\) | 1.73205 | 0.447214 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | −6.46410 | −1.48297 | −0.741483 | − | 0.670971i | \(-0.765877\pi\) | ||||
−0.741483 | + | 0.670971i | \(0.765877\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 0.866025 | − | 1.50000i | 0.188982 | − | 0.327327i | ||||
\(22\) | 1.86603 | − | 3.23205i | 0.397838 | − | 0.689076i | ||||
\(23\) | −0.633975 | + | 1.09808i | −0.132193 | + | 0.228965i | −0.924522 | − | 0.381130i | \(-0.875535\pi\) |
0.792329 | + | 0.610094i | \(0.208868\pi\) | |||||||
\(24\) | 0.866025 | + | 1.50000i | 0.176777 | + | 0.306186i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −4.73205 | −0.928032 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.09808 | + | 7.09808i | 0.760994 | + | 1.31808i | 0.942339 | + | 0.334660i | \(0.108622\pi\) |
−0.181345 | + | 0.983419i | \(0.558045\pi\) | |||||||
\(30\) | 0.866025 | + | 1.50000i | 0.158114 | + | 0.273861i | ||||
\(31\) | −4.46410 | + | 7.73205i | −0.801776 | + | 1.38872i | 0.116670 | + | 0.993171i | \(0.462778\pi\) |
−0.918446 | + | 0.395547i | \(0.870555\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −3.23205 | + | 5.59808i | −0.562628 | + | 0.974500i | ||||
\(34\) | 0.500000 | + | 0.866025i | 0.0857493 | + | 0.148522i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.50000 | − | 2.59808i | −0.250000 | − | 0.433013i | ||||
\(37\) | −9.66025 | −1.58814 | −0.794068 | − | 0.607829i | \(-0.792041\pi\) | ||||
−0.794068 | + | 0.607829i | \(0.792041\pi\) | |||||||
\(38\) | −3.23205 | − | 5.59808i | −0.524308 | − | 0.908128i | ||||
\(39\) | 8.19615 | 1.31243 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −2.86603 | + | 4.96410i | −0.447598 | + | 0.775262i | −0.998229 | − | 0.0594862i | \(-0.981054\pi\) |
0.550631 | + | 0.834749i | \(0.314387\pi\) | |||||||
\(42\) | 1.73205 | 0.267261 | ||||||||
\(43\) | −5.69615 | − | 9.86603i | −0.868655 | − | 1.50455i | −0.863372 | − | 0.504569i | \(-0.831652\pi\) |
−0.00528357 | − | 0.999986i | \(-0.501682\pi\) | |||||||
\(44\) | 3.73205 | 0.562628 | ||||||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | −1.26795 | −0.186949 | ||||||||
\(47\) | −2.00000 | − | 3.46410i | −0.291730 | − | 0.505291i | 0.682489 | − | 0.730896i | \(-0.260898\pi\) |
−0.974219 | + | 0.225605i | \(0.927564\pi\) | |||||||
\(48\) | −0.866025 | + | 1.50000i | −0.125000 | + | 0.216506i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | −0.866025 | − | 1.50000i | −0.121268 | − | 0.210042i | ||||
\(52\) | −2.36603 | − | 4.09808i | −0.328109 | − | 0.568301i | ||||
\(53\) | 10.1962 | 1.40055 | 0.700275 | − | 0.713874i | \(-0.253061\pi\) | ||||
0.700275 | + | 0.713874i | \(0.253061\pi\) | |||||||
\(54\) | 2.59808 | + | 4.50000i | 0.353553 | + | 0.612372i | ||||
\(55\) | 3.73205 | 0.503230 | ||||||||
\(56\) | −0.500000 | − | 0.866025i | −0.0668153 | − | 0.115728i | ||||
\(57\) | 5.59808 | + | 9.69615i | 0.741483 | + | 1.28429i | ||||
\(58\) | −4.09808 | + | 7.09808i | −0.538104 | + | 0.932023i | ||||
\(59\) | −4.23205 | + | 7.33013i | −0.550966 | + | 0.954301i | 0.447239 | + | 0.894414i | \(0.352407\pi\) |
−0.998205 | + | 0.0598868i | \(0.980926\pi\) | |||||||
\(60\) | −0.866025 | + | 1.50000i | −0.111803 | + | 0.193649i | ||||
\(61\) | 0.366025 | + | 0.633975i | 0.0468648 | + | 0.0811721i | 0.888506 | − | 0.458865i | \(-0.151744\pi\) |
−0.841641 | + | 0.540037i | \(0.818410\pi\) | |||||||
\(62\) | −8.92820 | −1.13388 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.36603 | − | 4.09808i | −0.293469 | − | 0.508304i | ||||
\(66\) | −6.46410 | −0.795676 | ||||||||
\(67\) | 4.50000 | − | 7.79423i | 0.549762 | − | 0.952217i | −0.448528 | − | 0.893769i | \(-0.648052\pi\) |
0.998290 | − | 0.0584478i | \(-0.0186151\pi\) | |||||||
\(68\) | −0.500000 | + | 0.866025i | −0.0606339 | + | 0.105021i | ||||
\(69\) | 2.19615 | 0.264386 | ||||||||
\(70\) | −0.500000 | − | 0.866025i | −0.0597614 | − | 0.103510i | ||||
\(71\) | 8.73205 | 1.03630 | 0.518152 | − | 0.855289i | \(-0.326620\pi\) | ||||
0.518152 | + | 0.855289i | \(0.326620\pi\) | |||||||
\(72\) | 1.50000 | − | 2.59808i | 0.176777 | − | 0.306186i | ||||
\(73\) | −1.92820 | −0.225679 | −0.112840 | − | 0.993613i | \(-0.535995\pi\) | ||||
−0.112840 | + | 0.993613i | \(0.535995\pi\) | |||||||
\(74\) | −4.83013 | − | 8.36603i | −0.561491 | − | 0.972531i | ||||
\(75\) | −0.866025 | + | 1.50000i | −0.100000 | + | 0.173205i | ||||
\(76\) | 3.23205 | − | 5.59808i | 0.370742 | − | 0.642143i | ||||
\(77\) | 1.86603 | − | 3.23205i | 0.212653 | − | 0.368326i | ||||
\(78\) | 4.09808 | + | 7.09808i | 0.464016 | + | 0.803699i | ||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −5.73205 | −0.632999 | ||||||||
\(83\) | −0.732051 | − | 1.26795i | −0.0803530 | − | 0.139176i | 0.823049 | − | 0.567971i | \(-0.192271\pi\) |
−0.903402 | + | 0.428795i | \(0.858938\pi\) | |||||||
\(84\) | 0.866025 | + | 1.50000i | 0.0944911 | + | 0.163663i | ||||
\(85\) | −0.500000 | + | 0.866025i | −0.0542326 | + | 0.0939336i | ||||
\(86\) | 5.69615 | − | 9.86603i | 0.614232 | − | 1.06388i | ||||
\(87\) | 7.09808 | − | 12.2942i | 0.760994 | − | 1.31808i | ||||
\(88\) | 1.86603 | + | 3.23205i | 0.198919 | + | 0.344538i | ||||
\(89\) | −0.535898 | −0.0568051 | −0.0284026 | − | 0.999597i | \(-0.509042\pi\) | ||||
−0.0284026 | + | 0.999597i | \(0.509042\pi\) | |||||||
\(90\) | 1.50000 | − | 2.59808i | 0.158114 | − | 0.273861i | ||||
\(91\) | −4.73205 | −0.496054 | ||||||||
\(92\) | −0.633975 | − | 1.09808i | −0.0660964 | − | 0.114482i | ||||
\(93\) | 15.4641 | 1.60355 | ||||||||
\(94\) | 2.00000 | − | 3.46410i | 0.206284 | − | 0.357295i | ||||
\(95\) | 3.23205 | − | 5.59808i | 0.331601 | − | 0.574351i | ||||
\(96\) | −1.73205 | −0.176777 | ||||||||
\(97\) | 0.500000 | + | 0.866025i | 0.0507673 | + | 0.0879316i | 0.890292 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543321i | \(0.817167\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 11.1962 | 1.12526 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −4.73205 | − | 8.19615i | −0.470857 | − | 0.815548i | 0.528588 | − | 0.848879i | \(-0.322722\pi\) |
−0.999444 | + | 0.0333310i | \(0.989388\pi\) | |||||||
\(102\) | 0.866025 | − | 1.50000i | 0.0857493 | − | 0.148522i | ||||
\(103\) | 3.36603 | − | 5.83013i | 0.331664 | − | 0.574459i | −0.651174 | − | 0.758928i | \(-0.725723\pi\) |
0.982838 | + | 0.184469i | \(0.0590565\pi\) | |||||||
\(104\) | 2.36603 | − | 4.09808i | 0.232008 | − | 0.401849i | ||||
\(105\) | 0.866025 | + | 1.50000i | 0.0845154 | + | 0.146385i | ||||
\(106\) | 5.09808 | + | 8.83013i | 0.495169 | + | 0.857658i | ||||
\(107\) | 18.4641 | 1.78499 | 0.892496 | − | 0.451055i | \(-0.148952\pi\) | ||||
0.892496 | + | 0.451055i | \(0.148952\pi\) | |||||||
\(108\) | −2.59808 | + | 4.50000i | −0.250000 | + | 0.433013i | ||||
\(109\) | −4.73205 | −0.453248 | −0.226624 | − | 0.973982i | \(-0.572769\pi\) | ||||
−0.226624 | + | 0.973982i | \(0.572769\pi\) | |||||||
\(110\) | 1.86603 | + | 3.23205i | 0.177919 | + | 0.308164i | ||||
\(111\) | 8.36603 | + | 14.4904i | 0.794068 | + | 1.37537i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | 4.92820 | − | 8.53590i | 0.463606 | − | 0.802990i | −0.535531 | − | 0.844516i | \(-0.679889\pi\) |
0.999137 | + | 0.0415258i | \(0.0132219\pi\) | |||||||
\(114\) | −5.59808 | + | 9.69615i | −0.524308 | + | 0.908128i | ||||
\(115\) | −0.633975 | − | 1.09808i | −0.0591184 | − | 0.102396i | ||||
\(116\) | −8.19615 | −0.760994 | ||||||||
\(117\) | −7.09808 | − | 12.2942i | −0.656217 | − | 1.13660i | ||||
\(118\) | −8.46410 | −0.779184 | ||||||||
\(119\) | 0.500000 | + | 0.866025i | 0.0458349 | + | 0.0793884i | ||||
\(120\) | −1.73205 | −0.158114 | ||||||||
\(121\) | −1.46410 | + | 2.53590i | −0.133100 | + | 0.230536i | ||||
\(122\) | −0.366025 | + | 0.633975i | −0.0331384 | + | 0.0573974i | ||||
\(123\) | 9.92820 | 0.895196 | ||||||||
\(124\) | −4.46410 | − | 7.73205i | −0.400888 | − | 0.694359i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.50000 | − | 2.59808i | −0.133631 | − | 0.231455i | ||||
\(127\) | −1.66025 | −0.147324 | −0.0736619 | − | 0.997283i | \(-0.523469\pi\) | ||||
−0.0736619 | + | 0.997283i | \(0.523469\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −9.86603 | + | 17.0885i | −0.868655 | + | 1.50455i | ||||
\(130\) | 2.36603 | − | 4.09808i | 0.207514 | − | 0.359425i | ||||
\(131\) | 7.92820 | − | 13.7321i | 0.692690 | − | 1.19977i | −0.278263 | − | 0.960505i | \(-0.589759\pi\) |
0.970953 | − | 0.239270i | \(-0.0769081\pi\) | |||||||
\(132\) | −3.23205 | − | 5.59808i | −0.281314 | − | 0.487250i | ||||
\(133\) | −3.23205 | − | 5.59808i | −0.280254 | − | 0.485415i | ||||
\(134\) | 9.00000 | 0.777482 | ||||||||
\(135\) | −2.59808 | + | 4.50000i | −0.223607 | + | 0.387298i | ||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −2.13397 | − | 3.69615i | −0.182318 | − | 0.315784i | 0.760352 | − | 0.649512i | \(-0.225027\pi\) |
−0.942669 | + | 0.333728i | \(0.891693\pi\) | |||||||
\(138\) | 1.09808 | + | 1.90192i | 0.0934745 | + | 0.161903i | ||||
\(139\) | 1.23205 | − | 2.13397i | 0.104501 | − | 0.181001i | −0.809033 | − | 0.587763i | \(-0.800009\pi\) |
0.913534 | + | 0.406762i | \(0.133342\pi\) | |||||||
\(140\) | 0.500000 | − | 0.866025i | 0.0422577 | − | 0.0731925i | ||||
\(141\) | −3.46410 | + | 6.00000i | −0.291730 | + | 0.505291i | ||||
\(142\) | 4.36603 | + | 7.56218i | 0.366389 | + | 0.634604i | ||||
\(143\) | 17.6603 | 1.47682 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −8.19615 | −0.680653 | ||||||||
\(146\) | −0.964102 | − | 1.66987i | −0.0797896 | − | 0.138200i | ||||
\(147\) | 1.73205 | 0.142857 | ||||||||
\(148\) | 4.83013 | − | 8.36603i | 0.397034 | − | 0.687683i | ||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | −1.73205 | −0.141421 | ||||||||
\(151\) | 5.92820 | + | 10.2679i | 0.482430 | + | 0.835594i | 0.999797 | − | 0.0201702i | \(-0.00642082\pi\) |
−0.517366 | + | 0.855764i | \(0.673087\pi\) | |||||||
\(152\) | 6.46410 | 0.524308 | ||||||||
\(153\) | −1.50000 | + | 2.59808i | −0.121268 | + | 0.210042i | ||||
\(154\) | 3.73205 | 0.300737 | ||||||||
\(155\) | −4.46410 | − | 7.73205i | −0.358565 | − | 0.621053i | ||||
\(156\) | −4.09808 | + | 7.09808i | −0.328109 | + | 0.568301i | ||||
\(157\) | −10.0263 | + | 17.3660i | −0.800184 | + | 1.38596i | 0.119310 | + | 0.992857i | \(0.461932\pi\) |
−0.919495 | + | 0.393103i | \(0.871402\pi\) | |||||||
\(158\) | −7.00000 | + | 12.1244i | −0.556890 | + | 0.964562i | ||||
\(159\) | −8.83013 | − | 15.2942i | −0.700275 | − | 1.21291i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −1.26795 | −0.0999284 | ||||||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | −2.39230 | −0.187380 | −0.0936899 | − | 0.995601i | \(-0.529866\pi\) | ||||
−0.0936899 | + | 0.995601i | \(0.529866\pi\) | |||||||
\(164\) | −2.86603 | − | 4.96410i | −0.223799 | − | 0.387631i | ||||
\(165\) | −3.23205 | − | 5.59808i | −0.251615 | − | 0.435810i | ||||
\(166\) | 0.732051 | − | 1.26795i | 0.0568182 | − | 0.0984119i | ||||
\(167\) | −4.56218 | + | 7.90192i | −0.353032 | + | 0.611469i | −0.986779 | − | 0.162071i | \(-0.948183\pi\) |
0.633747 | + | 0.773540i | \(0.281516\pi\) | |||||||
\(168\) | −0.866025 | + | 1.50000i | −0.0668153 | + | 0.115728i | ||||
\(169\) | −4.69615 | − | 8.13397i | −0.361242 | − | 0.625690i | ||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | 9.69615 | − | 16.7942i | 0.741483 | − | 1.28429i | ||||
\(172\) | 11.3923 | 0.868655 | ||||||||
\(173\) | −1.53590 | − | 2.66025i | −0.116772 | − | 0.202255i | 0.801715 | − | 0.597707i | \(-0.203921\pi\) |
−0.918487 | + | 0.395452i | \(0.870588\pi\) | |||||||
\(174\) | 14.1962 | 1.07621 | ||||||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −1.86603 | + | 3.23205i | −0.140657 | + | 0.243625i | ||||
\(177\) | 14.6603 | 1.10193 | ||||||||
\(178\) | −0.267949 | − | 0.464102i | −0.0200836 | − | 0.0347859i | ||||
\(179\) | −24.2487 | −1.81243 | −0.906217 | − | 0.422813i | \(-0.861043\pi\) | ||||
−0.906217 | + | 0.422813i | \(0.861043\pi\) | |||||||
\(180\) | 3.00000 | 0.223607 | ||||||||
\(181\) | 17.8564 | 1.32726 | 0.663628 | − | 0.748063i | \(-0.269016\pi\) | ||||
0.663628 | + | 0.748063i | \(0.269016\pi\) | |||||||
\(182\) | −2.36603 | − | 4.09808i | −0.175381 | − | 0.303770i | ||||
\(183\) | 0.633975 | − | 1.09808i | 0.0468648 | − | 0.0811721i | ||||
\(184\) | 0.633975 | − | 1.09808i | 0.0467372 | − | 0.0809513i | ||||
\(185\) | 4.83013 | − | 8.36603i | 0.355118 | − | 0.615082i | ||||
\(186\) | 7.73205 | + | 13.3923i | 0.566941 | + | 0.981971i | ||||
\(187\) | −1.86603 | − | 3.23205i | −0.136457 | − | 0.236351i | ||||
\(188\) | 4.00000 | 0.291730 | ||||||||
\(189\) | 2.59808 | + | 4.50000i | 0.188982 | + | 0.327327i | ||||
\(190\) | 6.46410 | 0.468955 | ||||||||
\(191\) | 1.26795 | + | 2.19615i | 0.0917456 | + | 0.158908i | 0.908246 | − | 0.418437i | \(-0.137422\pi\) |
−0.816500 | + | 0.577345i | \(0.804089\pi\) | |||||||
\(192\) | −0.866025 | − | 1.50000i | −0.0625000 | − | 0.108253i | ||||
\(193\) | −13.0622 | + | 22.6244i | −0.940236 | + | 1.62854i | −0.175216 | + | 0.984530i | \(0.556062\pi\) |
−0.765020 | + | 0.644007i | \(0.777271\pi\) | |||||||
\(194\) | −0.500000 | + | 0.866025i | −0.0358979 | + | 0.0621770i | ||||
\(195\) | −4.09808 | + | 7.09808i | −0.293469 | + | 0.508304i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | 2.73205 | 0.194651 | 0.0973253 | − | 0.995253i | \(-0.468971\pi\) | ||||
0.0973253 | + | 0.995253i | \(0.468971\pi\) | |||||||
\(198\) | 5.59808 | + | 9.69615i | 0.397838 | + | 0.689076i | ||||
\(199\) | −11.2679 | −0.798764 | −0.399382 | − | 0.916785i | \(-0.630775\pi\) | ||||
−0.399382 | + | 0.916785i | \(0.630775\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −15.5885 | −1.09952 | ||||||||
\(202\) | 4.73205 | − | 8.19615i | 0.332946 | − | 0.576679i | ||||
\(203\) | −4.09808 | + | 7.09808i | −0.287629 | + | 0.498187i | ||||
\(204\) | 1.73205 | 0.121268 | ||||||||
\(205\) | −2.86603 | − | 4.96410i | −0.200172 | − | 0.346708i | ||||
\(206\) | 6.73205 | 0.469044 | ||||||||
\(207\) | −1.90192 | − | 3.29423i | −0.132193 | − | 0.228965i | ||||
\(208\) | 4.73205 | 0.328109 | ||||||||
\(209\) | 12.0622 | + | 20.8923i | 0.834358 | + | 1.44515i | ||||
\(210\) | −0.866025 | + | 1.50000i | −0.0597614 | + | 0.103510i | ||||
\(211\) | −4.19615 | + | 7.26795i | −0.288875 | + | 0.500346i | −0.973542 | − | 0.228510i | \(-0.926615\pi\) |
0.684666 | + | 0.728857i | \(0.259948\pi\) | |||||||
\(212\) | −5.09808 | + | 8.83013i | −0.350137 | + | 0.606456i | ||||
\(213\) | −7.56218 | − | 13.0981i | −0.518152 | − | 0.897465i | ||||
\(214\) | 9.23205 | + | 15.9904i | 0.631090 | + | 1.09308i | ||||
\(215\) | 11.3923 | 0.776949 | ||||||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | −8.92820 | −0.606086 | ||||||||
\(218\) | −2.36603 | − | 4.09808i | −0.160247 | − | 0.277557i | ||||
\(219\) | 1.66987 | + | 2.89230i | 0.112840 | + | 0.195444i | ||||
\(220\) | −1.86603 | + | 3.23205i | −0.125807 | + | 0.217905i | ||||
\(221\) | −2.36603 | + | 4.09808i | −0.159156 | + | 0.275666i | ||||
\(222\) | −8.36603 | + | 14.4904i | −0.561491 | + | 0.972531i | ||||
\(223\) | 13.2942 | + | 23.0263i | 0.890247 | + | 1.54195i | 0.839579 | + | 0.543238i | \(0.182802\pi\) |
0.0506688 | + | 0.998716i | \(0.483865\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 9.85641 | 0.655638 | ||||||||
\(227\) | −3.66987 | − | 6.35641i | −0.243578 | − | 0.421890i | 0.718153 | − | 0.695885i | \(-0.244988\pi\) |
−0.961731 | + | 0.273996i | \(0.911655\pi\) | |||||||
\(228\) | −11.1962 | −0.741483 | ||||||||
\(229\) | −6.09808 | + | 10.5622i | −0.402972 | + | 0.697968i | −0.994083 | − | 0.108622i | \(-0.965356\pi\) |
0.591111 | + | 0.806590i | \(0.298690\pi\) | |||||||
\(230\) | 0.633975 | − | 1.09808i | 0.0418030 | − | 0.0724050i | ||||
\(231\) | −6.46410 | −0.425307 | ||||||||
\(232\) | −4.09808 | − | 7.09808i | −0.269052 | − | 0.466012i | ||||
\(233\) | 27.5885 | 1.80738 | 0.903690 | − | 0.428187i | \(-0.140848\pi\) | ||||
0.903690 | + | 0.428187i | \(0.140848\pi\) | |||||||
\(234\) | 7.09808 | − | 12.2942i | 0.464016 | − | 0.803699i | ||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | −4.23205 | − | 7.33013i | −0.275483 | − | 0.477151i | ||||
\(237\) | 12.1244 | − | 21.0000i | 0.787562 | − | 1.36410i | ||||
\(238\) | −0.500000 | + | 0.866025i | −0.0324102 | + | 0.0561361i | ||||
\(239\) | −3.19615 | + | 5.53590i | −0.206742 | + | 0.358087i | −0.950686 | − | 0.310154i | \(-0.899619\pi\) |
0.743944 | + | 0.668242i | \(0.232953\pi\) | |||||||
\(240\) | −0.866025 | − | 1.50000i | −0.0559017 | − | 0.0968246i | ||||
\(241\) | 9.25833 | + | 16.0359i | 0.596381 | + | 1.03296i | 0.993350 | + | 0.115131i | \(0.0367288\pi\) |
−0.396969 | + | 0.917832i | \(0.629938\pi\) | |||||||
\(242\) | −2.92820 | −0.188232 | ||||||||
\(243\) | −7.79423 | + | 13.5000i | −0.500000 | + | 0.866025i | ||||
\(244\) | −0.732051 | −0.0468648 | ||||||||
\(245\) | −0.500000 | − | 0.866025i | −0.0319438 | − | 0.0553283i | ||||
\(246\) | 4.96410 | + | 8.59808i | 0.316500 | + | 0.548193i | ||||
\(247\) | 15.2942 | − | 26.4904i | 0.973148 | − | 1.68554i | ||||
\(248\) | 4.46410 | − | 7.73205i | 0.283471 | − | 0.490986i | ||||
\(249\) | −1.26795 | + | 2.19615i | −0.0803530 | + | 0.139176i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −10.8564 | −0.685250 | −0.342625 | − | 0.939472i | \(-0.611316\pi\) | ||||
−0.342625 | + | 0.939472i | \(0.611316\pi\) | |||||||
\(252\) | 1.50000 | − | 2.59808i | 0.0944911 | − | 0.163663i | ||||
\(253\) | 4.73205 | 0.297501 | ||||||||
\(254\) | −0.830127 | − | 1.43782i | −0.0520868 | − | 0.0902170i | ||||
\(255\) | 1.73205 | 0.108465 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.03590 | + | 5.25833i | −0.189374 | + | 0.328006i | −0.945042 | − | 0.326950i | \(-0.893979\pi\) |
0.755668 | + | 0.654955i | \(0.227313\pi\) | |||||||
\(258\) | −19.7321 | −1.22846 | ||||||||
\(259\) | −4.83013 | − | 8.36603i | −0.300129 | − | 0.519840i | ||||
\(260\) | 4.73205 | 0.293469 | ||||||||
\(261\) | −24.5885 | −1.52199 | ||||||||
\(262\) | 15.8564 | 0.979612 | ||||||||
\(263\) | −6.90192 | − | 11.9545i | −0.425591 | − | 0.737145i | 0.570885 | − | 0.821030i | \(-0.306600\pi\) |
−0.996475 | + | 0.0838854i | \(0.973267\pi\) | |||||||
\(264\) | 3.23205 | − | 5.59808i | 0.198919 | − | 0.344538i | ||||
\(265\) | −5.09808 | + | 8.83013i | −0.313172 | + | 0.542430i | ||||
\(266\) | 3.23205 | − | 5.59808i | 0.198170 | − | 0.343240i | ||||
\(267\) | 0.464102 | + | 0.803848i | 0.0284026 | + | 0.0491947i | ||||
\(268\) | 4.50000 | + | 7.79423i | 0.274881 | + | 0.476108i | ||||
\(269\) | −19.2679 | −1.17479 | −0.587394 | − | 0.809301i | \(-0.699846\pi\) | ||||
−0.587394 | + | 0.809301i | \(0.699846\pi\) | |||||||
\(270\) | −5.19615 | −0.316228 | ||||||||
\(271\) | 16.0526 | 0.975124 | 0.487562 | − | 0.873089i | \(-0.337886\pi\) | ||||
0.487562 | + | 0.873089i | \(0.337886\pi\) | |||||||
\(272\) | −0.500000 | − | 0.866025i | −0.0303170 | − | 0.0525105i | ||||
\(273\) | 4.09808 | + | 7.09808i | 0.248027 | + | 0.429595i | ||||
\(274\) | 2.13397 | − | 3.69615i | 0.128918 | − | 0.223293i | ||||
\(275\) | −1.86603 | + | 3.23205i | −0.112526 | + | 0.194900i | ||||
\(276\) | −1.09808 | + | 1.90192i | −0.0660964 | + | 0.114482i | ||||
\(277\) | −15.9282 | − | 27.5885i | −0.957033 | − | 1.65763i | −0.729646 | − | 0.683825i | \(-0.760315\pi\) |
−0.227387 | − | 0.973804i | \(-0.573018\pi\) | |||||||
\(278\) | 2.46410 | 0.147787 | ||||||||
\(279\) | −13.3923 | − | 23.1962i | −0.801776 | − | 1.38872i | ||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −10.1962 | − | 17.6603i | −0.608251 | − | 1.05352i | −0.991529 | − | 0.129889i | \(-0.958538\pi\) |
0.383277 | − | 0.923633i | \(-0.374795\pi\) | |||||||
\(282\) | −6.92820 | −0.412568 | ||||||||
\(283\) | 12.3923 | − | 21.4641i | 0.736646 | − | 1.27591i | −0.217351 | − | 0.976093i | \(-0.569742\pi\) |
0.953997 | − | 0.299815i | \(-0.0969249\pi\) | |||||||
\(284\) | −4.36603 | + | 7.56218i | −0.259076 | + | 0.448733i | ||||
\(285\) | −11.1962 | −0.663203 | ||||||||
\(286\) | 8.83013 | + | 15.2942i | 0.522136 | + | 0.904367i | ||||
\(287\) | −5.73205 | −0.338352 | ||||||||
\(288\) | 1.50000 | + | 2.59808i | 0.0883883 | + | 0.153093i | ||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −4.09808 | − | 7.09808i | −0.240647 | − | 0.416813i | ||||
\(291\) | 0.866025 | − | 1.50000i | 0.0507673 | − | 0.0879316i | ||||
\(292\) | 0.964102 | − | 1.66987i | 0.0564198 | − | 0.0977219i | ||||
\(293\) | −10.2942 | + | 17.8301i | −0.601395 | + | 1.04165i | 0.391215 | + | 0.920299i | \(0.372055\pi\) |
−0.992610 | + | 0.121348i | \(0.961278\pi\) | |||||||
\(294\) | 0.866025 | + | 1.50000i | 0.0505076 | + | 0.0874818i | ||||
\(295\) | −4.23205 | − | 7.33013i | −0.246400 | − | 0.426776i | ||||
\(296\) | 9.66025 | 0.561491 | ||||||||
\(297\) | −9.69615 | − | 16.7942i | −0.562628 | − | 0.974500i | ||||
\(298\) | −12.0000 | −0.695141 | ||||||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | −0.866025 | − | 1.50000i | −0.0500000 | − | 0.0866025i | ||||
\(301\) | 5.69615 | − | 9.86603i | 0.328321 | − | 0.568668i | ||||
\(302\) | −5.92820 | + | 10.2679i | −0.341130 | + | 0.590854i | ||||
\(303\) | −8.19615 | + | 14.1962i | −0.470857 | + | 0.815548i | ||||
\(304\) | 3.23205 | + | 5.59808i | 0.185371 | + | 0.321072i | ||||
\(305\) | −0.732051 | −0.0419171 | ||||||||
\(306\) | −3.00000 | −0.171499 | ||||||||
\(307\) | −6.26795 | −0.357731 | −0.178865 | − | 0.983874i | \(-0.557243\pi\) | ||||
−0.178865 | + | 0.983874i | \(0.557243\pi\) | |||||||
\(308\) | 1.86603 | + | 3.23205i | 0.106327 | + | 0.184163i | ||||
\(309\) | −11.6603 | −0.663329 | ||||||||
\(310\) | 4.46410 | − | 7.73205i | 0.253544 | − | 0.439151i | ||||
\(311\) | −4.26795 | + | 7.39230i | −0.242013 | + | 0.419179i | −0.961288 | − | 0.275547i | \(-0.911141\pi\) |
0.719274 | + | 0.694726i | \(0.244474\pi\) | |||||||
\(312\) | −8.19615 | −0.464016 | ||||||||
\(313\) | −8.50000 | − | 14.7224i | −0.480448 | − | 0.832161i | 0.519300 | − | 0.854592i | \(-0.326193\pi\) |
−0.999748 | + | 0.0224310i | \(0.992859\pi\) | |||||||
\(314\) | −20.0526 | −1.13163 | ||||||||
\(315\) | 1.50000 | − | 2.59808i | 0.0845154 | − | 0.146385i | ||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | −4.63397 | − | 8.02628i | −0.260270 | − | 0.450801i | 0.706044 | − | 0.708168i | \(-0.250478\pi\) |
−0.966314 | + | 0.257368i | \(0.917145\pi\) | |||||||
\(318\) | 8.83013 | − | 15.2942i | 0.495169 | − | 0.857658i | ||||
\(319\) | 15.2942 | − | 26.4904i | 0.856312 | − | 1.48318i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −15.9904 | − | 27.6962i | −0.892496 | − | 1.54585i | ||||
\(322\) | −0.633975 | − | 1.09808i | −0.0353300 | − | 0.0611934i | ||||
\(323\) | −6.46410 | −0.359672 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 4.73205 | 0.262487 | ||||||||
\(326\) | −1.19615 | − | 2.07180i | −0.0662488 | − | 0.114746i | ||||
\(327\) | 4.09808 | + | 7.09808i | 0.226624 | + | 0.392525i | ||||
\(328\) | 2.86603 | − | 4.96410i | 0.158250 | − | 0.274097i | ||||
\(329\) | 2.00000 | − | 3.46410i | 0.110264 | − | 0.190982i | ||||
\(330\) | 3.23205 | − | 5.59808i | 0.177919 | − | 0.308164i | ||||
\(331\) | 11.2679 | + | 19.5167i | 0.619343 | + | 1.07273i | 0.989606 | + | 0.143806i | \(0.0459341\pi\) |
−0.370263 | + | 0.928927i | \(0.620733\pi\) | |||||||
\(332\) | 1.46410 | 0.0803530 | ||||||||
\(333\) | 14.4904 | − | 25.0981i | 0.794068 | − | 1.37537i | ||||
\(334\) | −9.12436 | −0.499263 | ||||||||
\(335\) | 4.50000 | + | 7.79423i | 0.245861 | + | 0.425844i | ||||
\(336\) | −1.73205 | −0.0944911 | ||||||||
\(337\) | −9.66987 | + | 16.7487i | −0.526752 | + | 0.912360i | 0.472763 | + | 0.881190i | \(0.343257\pi\) |
−0.999514 | + | 0.0311706i | \(0.990076\pi\) | |||||||
\(338\) | 4.69615 | − | 8.13397i | 0.255437 | − | 0.442430i | ||||
\(339\) | −17.0718 | −0.927213 | ||||||||
\(340\) | −0.500000 | − | 0.866025i | −0.0271163 | − | 0.0469668i | ||||
\(341\) | 33.3205 | 1.80441 | ||||||||
\(342\) | 19.3923 | 1.04862 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.69615 | + | 9.86603i | 0.307116 | + | 0.531940i | ||||
\(345\) | −1.09808 | + | 1.90192i | −0.0591184 | + | 0.102396i | ||||
\(346\) | 1.53590 | − | 2.66025i | 0.0825704 | − | 0.143016i | ||||
\(347\) | −13.3564 | + | 23.1340i | −0.717009 | + | 1.24190i | 0.245170 | + | 0.969480i | \(0.421156\pi\) |
−0.962179 | + | 0.272417i | \(0.912177\pi\) | |||||||
\(348\) | 7.09808 | + | 12.2942i | 0.380497 | + | 0.659040i | ||||
\(349\) | 4.29423 | + | 7.43782i | 0.229865 | + | 0.398137i | 0.957768 | − | 0.287543i | \(-0.0928383\pi\) |
−0.727903 | + | 0.685680i | \(0.759505\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −12.2942 | + | 21.2942i | −0.656217 | + | 1.13660i | ||||
\(352\) | −3.73205 | −0.198919 | ||||||||
\(353\) | 10.9641 | + | 18.9904i | 0.583560 | + | 1.01076i | 0.995053 | + | 0.0993431i | \(0.0316741\pi\) |
−0.411493 | + | 0.911413i | \(0.634993\pi\) | |||||||
\(354\) | 7.33013 | + | 12.6962i | 0.389592 | + | 0.674793i | ||||
\(355\) | −4.36603 | + | 7.56218i | −0.231725 | + | 0.401359i | ||||
\(356\) | 0.267949 | − | 0.464102i | 0.0142013 | − | 0.0245973i | ||||
\(357\) | 0.866025 | − | 1.50000i | 0.0458349 | − | 0.0793884i | ||||
\(358\) | −12.1244 | − | 21.0000i | −0.640792 | − | 1.10988i | ||||
\(359\) | 14.0526 | 0.741666 | 0.370833 | − | 0.928700i | \(-0.379072\pi\) | ||||
0.370833 | + | 0.928700i | \(0.379072\pi\) | |||||||
\(360\) | 1.50000 | + | 2.59808i | 0.0790569 | + | 0.136931i | ||||
\(361\) | 22.7846 | 1.19919 | ||||||||
\(362\) | 8.92820 | + | 15.4641i | 0.469256 | + | 0.812775i | ||||
\(363\) | 5.07180 | 0.266200 | ||||||||
\(364\) | 2.36603 | − | 4.09808i | 0.124013 | − | 0.214798i | ||||
\(365\) | 0.964102 | − | 1.66987i | 0.0504634 | − | 0.0874051i | ||||
\(366\) | 1.26795 | 0.0662768 | ||||||||
\(367\) | −7.36603 | − | 12.7583i | −0.384503 | − | 0.665979i | 0.607197 | − | 0.794551i | \(-0.292294\pi\) |
−0.991700 | + | 0.128572i | \(0.958961\pi\) | |||||||
\(368\) | 1.26795 | 0.0660964 | ||||||||
\(369\) | −8.59808 | − | 14.8923i | −0.447598 | − | 0.775262i | ||||
\(370\) | 9.66025 | 0.502213 | ||||||||
\(371\) | 5.09808 | + | 8.83013i | 0.264679 | + | 0.458437i | ||||
\(372\) | −7.73205 | + | 13.3923i | −0.400888 | + | 0.694359i | ||||
\(373\) | −3.19615 | + | 5.53590i | −0.165490 | + | 0.286638i | −0.936829 | − | 0.349787i | \(-0.886254\pi\) |
0.771339 | + | 0.636425i | \(0.219587\pi\) | |||||||
\(374\) | 1.86603 | − | 3.23205i | 0.0964899 | − | 0.167125i | ||||
\(375\) | −0.866025 | − | 1.50000i | −0.0447214 | − | 0.0774597i | ||||
\(376\) | 2.00000 | + | 3.46410i | 0.103142 | + | 0.178647i | ||||
\(377\) | −38.7846 | −1.99751 | ||||||||
\(378\) | −2.59808 | + | 4.50000i | −0.133631 | + | 0.231455i | ||||
\(379\) | 0.803848 | 0.0412909 | 0.0206454 | − | 0.999787i | \(-0.493428\pi\) | ||||
0.0206454 | + | 0.999787i | \(0.493428\pi\) | |||||||
\(380\) | 3.23205 | + | 5.59808i | 0.165801 | + | 0.287175i | ||||
\(381\) | 1.43782 | + | 2.49038i | 0.0736619 | + | 0.127586i | ||||
\(382\) | −1.26795 | + | 2.19615i | −0.0648739 | + | 0.112365i | ||||
\(383\) | 1.26795 | − | 2.19615i | 0.0647892 | − | 0.112218i | −0.831811 | − | 0.555059i | \(-0.812696\pi\) |
0.896600 | + | 0.442840i | \(0.146029\pi\) | |||||||
\(384\) | 0.866025 | − | 1.50000i | 0.0441942 | − | 0.0765466i | ||||
\(385\) | 1.86603 | + | 3.23205i | 0.0951015 | + | 0.164721i | ||||
\(386\) | −26.1244 | −1.32969 | ||||||||
\(387\) | 34.1769 | 1.73731 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | −4.53590 | − | 7.85641i | −0.229979 | − | 0.398336i | 0.727822 | − | 0.685766i | \(-0.240532\pi\) |
−0.957802 | + | 0.287430i | \(0.907199\pi\) | |||||||
\(390\) | −8.19615 | −0.415028 | ||||||||
\(391\) | −0.633975 | + | 1.09808i | −0.0320615 | + | 0.0555321i | ||||
\(392\) | 0.500000 | − | 0.866025i | 0.0252538 | − | 0.0437409i | ||||
\(393\) | −27.4641 | −1.38538 | ||||||||
\(394\) | 1.36603 | + | 2.36603i | 0.0688194 | + | 0.119199i | ||||
\(395\) | −14.0000 | −0.704416 | ||||||||
\(396\) | −5.59808 | + | 9.69615i | −0.281314 | + | 0.487250i | ||||
\(397\) | 4.33975 | 0.217806 | 0.108903 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108903 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(398\) | −5.63397 | − | 9.75833i | −0.282406 | − | 0.489141i | ||||
\(399\) | −5.59808 | + | 9.69615i | −0.280254 | + | 0.485415i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 10.4282 | − | 18.0622i | 0.520760 | − | 0.901982i | −0.478949 | − | 0.877843i | \(-0.658982\pi\) |
0.999709 | − | 0.0241394i | \(-0.00768455\pi\) | |||||||
\(402\) | −7.79423 | − | 13.5000i | −0.388741 | − | 0.673319i | ||||
\(403\) | −21.1244 | − | 36.5885i | −1.05228 | − | 1.82260i | ||||
\(404\) | 9.46410 | 0.470857 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | −8.19615 | −0.406768 | ||||||||
\(407\) | 18.0263 | + | 31.2224i | 0.893529 | + | 1.54764i | ||||
\(408\) | 0.866025 | + | 1.50000i | 0.0428746 | + | 0.0742611i | ||||
\(409\) | −14.1340 | + | 24.4808i | −0.698880 | + | 1.21050i | 0.269975 | + | 0.962867i | \(0.412985\pi\) |
−0.968855 | + | 0.247628i | \(0.920349\pi\) | |||||||
\(410\) | 2.86603 | − | 4.96410i | 0.141543 | − | 0.245160i | ||||
\(411\) | −3.69615 | + | 6.40192i | −0.182318 | + | 0.315784i | ||||
\(412\) | 3.36603 | + | 5.83013i | 0.165832 | + | 0.287230i | ||||
\(413\) | −8.46410 | −0.416491 | ||||||||
\(414\) | 1.90192 | − | 3.29423i | 0.0934745 | − | 0.161903i | ||||
\(415\) | 1.46410 | 0.0718699 | ||||||||
\(416\) | 2.36603 | + | 4.09808i | 0.116004 | + | 0.200925i | ||||
\(417\) | −4.26795 | −0.209002 | ||||||||
\(418\) | −12.0622 | + | 20.8923i | −0.589980 | + | 1.02188i | ||||
\(419\) | −2.66025 | + | 4.60770i | −0.129962 | + | 0.225101i | −0.923662 | − | 0.383209i | \(-0.874819\pi\) |
0.793700 | + | 0.608310i | \(0.208152\pi\) | |||||||
\(420\) | −1.73205 | −0.0845154 | ||||||||
\(421\) | 11.7583 | + | 20.3660i | 0.573066 | + | 0.992579i | 0.996249 | + | 0.0865350i | \(0.0275795\pi\) |
−0.423183 | + | 0.906044i | \(0.639087\pi\) | |||||||
\(422\) | −8.39230 | −0.408531 | ||||||||
\(423\) | 12.0000 | 0.583460 | ||||||||
\(424\) | −10.1962 | −0.495169 | ||||||||
\(425\) | −0.500000 | − | 0.866025i | −0.0242536 | − | 0.0420084i | ||||
\(426\) | 7.56218 | − | 13.0981i | 0.366389 | − | 0.634604i | ||||
\(427\) | −0.366025 | + | 0.633975i | −0.0177132 | + | 0.0306802i | ||||
\(428\) | −9.23205 | + | 15.9904i | −0.446248 | + | 0.772924i | ||||
\(429\) | −15.2942 | − | 26.4904i | −0.738412 | − | 1.27897i | ||||
\(430\) | 5.69615 | + | 9.86603i | 0.274693 | + | 0.475782i | ||||
\(431\) | −18.2487 | −0.879009 | −0.439505 | − | 0.898240i | \(-0.644846\pi\) | ||||
−0.439505 | + | 0.898240i | \(0.644846\pi\) | |||||||
\(432\) | −2.59808 | − | 4.50000i | −0.125000 | − | 0.216506i | ||||
\(433\) | 22.3205 | 1.07266 | 0.536328 | − | 0.844010i | \(-0.319811\pi\) | ||||
0.536328 | + | 0.844010i | \(0.319811\pi\) | |||||||
\(434\) | −4.46410 | − | 7.73205i | −0.214284 | − | 0.371150i | ||||
\(435\) | 7.09808 | + | 12.2942i | 0.340327 | + | 0.589463i | ||||
\(436\) | 2.36603 | − | 4.09808i | 0.113312 | − | 0.196262i | ||||
\(437\) | 4.09808 | − | 7.09808i | 0.196038 | − | 0.339547i | ||||
\(438\) | −1.66987 | + | 2.89230i | −0.0797896 | + | 0.138200i | ||||
\(439\) | −8.63397 | − | 14.9545i | −0.412077 | − | 0.713739i | 0.583040 | − | 0.812444i | \(-0.301863\pi\) |
−0.995117 | + | 0.0987052i | \(0.968530\pi\) | |||||||
\(440\) | −3.73205 | −0.177919 | ||||||||
\(441\) | −1.50000 | − | 2.59808i | −0.0714286 | − | 0.123718i | ||||
\(442\) | −4.73205 | −0.225081 | ||||||||
\(443\) | 15.6244 | + | 27.0622i | 0.742336 | + | 1.28576i | 0.951429 | + | 0.307867i | \(0.0996153\pi\) |
−0.209094 | + | 0.977896i | \(0.567051\pi\) | |||||||
\(444\) | −16.7321 | −0.794068 | ||||||||
\(445\) | 0.267949 | − | 0.464102i | 0.0127020 | − | 0.0220005i | ||||
\(446\) | −13.2942 | + | 23.0263i | −0.629500 | + | 1.09033i | ||||
\(447\) | 20.7846 | 0.983078 | ||||||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | 23.7846 | 1.12247 | 0.561233 | − | 0.827658i | \(-0.310327\pi\) | ||||
0.561233 | + | 0.827658i | \(0.310327\pi\) | |||||||
\(450\) | 1.50000 | + | 2.59808i | 0.0707107 | + | 0.122474i | ||||
\(451\) | 21.3923 | 1.00732 | ||||||||
\(452\) | 4.92820 | + | 8.53590i | 0.231803 | + | 0.401495i | ||||
\(453\) | 10.2679 | − | 17.7846i | 0.482430 | − | 0.835594i | ||||
\(454\) | 3.66987 | − | 6.35641i | 0.172236 | − | 0.298321i | ||||
\(455\) | 2.36603 | − | 4.09808i | 0.110921 | − | 0.192121i | ||||
\(456\) | −5.59808 | − | 9.69615i | −0.262154 | − | 0.454064i | ||||
\(457\) | −8.99038 | − | 15.5718i | −0.420552 | − | 0.728418i | 0.575441 | − | 0.817843i | \(-0.304830\pi\) |
−0.995994 | + | 0.0894252i | \(0.971497\pi\) | |||||||
\(458\) | −12.1962 | −0.569889 | ||||||||
\(459\) | 5.19615 | 0.242536 | ||||||||
\(460\) | 1.26795 | 0.0591184 | ||||||||
\(461\) | −3.36603 | − | 5.83013i | −0.156771 | − | 0.271536i | 0.776931 | − | 0.629585i | \(-0.216775\pi\) |
−0.933703 | + | 0.358049i | \(0.883442\pi\) | |||||||
\(462\) | −3.23205 | − | 5.59808i | −0.150369 | − | 0.260446i | ||||
\(463\) | 0.392305 | − | 0.679492i | 0.0182320 | − | 0.0315787i | −0.856765 | − | 0.515706i | \(-0.827530\pi\) |
0.874997 | + | 0.484128i | \(0.160863\pi\) | |||||||
\(464\) | 4.09808 | − | 7.09808i | 0.190248 | − | 0.329520i | ||||
\(465\) | −7.73205 | + | 13.3923i | −0.358565 | + | 0.621053i | ||||
\(466\) | 13.7942 | + | 23.8923i | 0.639005 | + | 1.10679i | ||||
\(467\) | 2.26795 | 0.104948 | 0.0524741 | − | 0.998622i | \(-0.483289\pi\) | ||||
0.0524741 | + | 0.998622i | \(0.483289\pi\) | |||||||
\(468\) | 14.1962 | 0.656217 | ||||||||
\(469\) | 9.00000 | 0.415581 | ||||||||
\(470\) | 2.00000 | + | 3.46410i | 0.0922531 | + | 0.159787i | ||||
\(471\) | 34.7321 | 1.60037 | ||||||||
\(472\) | 4.23205 | − | 7.33013i | 0.194796 | − | 0.337396i | ||||
\(473\) | −21.2583 | + | 36.8205i | −0.977459 | + | 1.69301i | ||||
\(474\) | 24.2487 | 1.11378 | ||||||||
\(475\) | 3.23205 | + | 5.59808i | 0.148297 | + | 0.256857i | ||||
\(476\) | −1.00000 | −0.0458349 | ||||||||
\(477\) | −15.2942 | + | 26.4904i | −0.700275 | + | 1.21291i | ||||
\(478\) | −6.39230 | −0.292377 | ||||||||
\(479\) | 13.5622 | + | 23.4904i | 0.619672 | + | 1.07330i | 0.989546 | + | 0.144221i | \(0.0460676\pi\) |
−0.369874 | + | 0.929082i | \(0.620599\pi\) | |||||||
\(480\) | 0.866025 | − | 1.50000i | 0.0395285 | − | 0.0684653i | ||||
\(481\) | 22.8564 | − | 39.5885i | 1.04216 | − | 1.80508i | ||||
\(482\) | −9.25833 | + | 16.0359i | −0.421705 | + | 0.730415i | ||||
\(483\) | 1.09808 | + | 1.90192i | 0.0499642 | + | 0.0865405i | ||||
\(484\) | −1.46410 | − | 2.53590i | −0.0665501 | − | 0.115268i | ||||
\(485\) | −1.00000 | −0.0454077 | ||||||||
\(486\) | −15.5885 | −0.707107 | ||||||||
\(487\) | −14.3923 | −0.652178 | −0.326089 | − | 0.945339i | \(-0.605731\pi\) | ||||
−0.326089 | + | 0.945339i | \(0.605731\pi\) | |||||||
\(488\) | −0.366025 | − | 0.633975i | −0.0165692 | − | 0.0286987i | ||||
\(489\) | 2.07180 | + | 3.58846i | 0.0936899 | + | 0.162276i | ||||
\(490\) | 0.500000 | − | 0.866025i | 0.0225877 | − | 0.0391230i | ||||
\(491\) | −12.8660 | + | 22.2846i | −0.580636 | + | 1.00569i | 0.414769 | + | 0.909927i | \(0.363863\pi\) |
−0.995404 | + | 0.0957634i | \(0.969471\pi\) | |||||||
\(492\) | −4.96410 | + | 8.59808i | −0.223799 | + | 0.387631i | ||||
\(493\) | 4.09808 | + | 7.09808i | 0.184568 | + | 0.319681i | ||||
\(494\) | 30.5885 | 1.37624 | ||||||||
\(495\) | −5.59808 | + | 9.69615i | −0.251615 | + | 0.435810i | ||||
\(496\) | 8.92820 | 0.400888 | ||||||||
\(497\) | 4.36603 | + | 7.56218i | 0.195843 | + | 0.339210i | ||||
\(498\) | −2.53590 | −0.113636 | ||||||||
\(499\) | −5.59808 | + | 9.69615i | −0.250604 | + | 0.434059i | −0.963692 | − | 0.267015i | \(-0.913963\pi\) |
0.713088 | + | 0.701074i | \(0.247296\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 15.8038 | 0.706064 | ||||||||
\(502\) | −5.42820 | − | 9.40192i | −0.242273 | − | 0.419628i | ||||
\(503\) | −21.7128 | −0.968126 | −0.484063 | − | 0.875033i | \(-0.660840\pi\) | ||||
−0.484063 | + | 0.875033i | \(0.660840\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | 9.46410 | 0.421147 | ||||||||
\(506\) | 2.36603 | + | 4.09808i | 0.105183 | + | 0.182182i | ||||
\(507\) | −8.13397 | + | 14.0885i | −0.361242 | + | 0.625690i | ||||
\(508\) | 0.830127 | − | 1.43782i | 0.0368309 | − | 0.0637930i | ||||
\(509\) | 8.63397 | − | 14.9545i | 0.382694 | − | 0.662846i | −0.608752 | − | 0.793360i | \(-0.708330\pi\) |
0.991446 | + | 0.130515i | \(0.0416630\pi\) | |||||||
\(510\) | 0.866025 | + | 1.50000i | 0.0383482 | + | 0.0664211i | ||||
\(511\) | −0.964102 | − | 1.66987i | −0.0426493 | − | 0.0738708i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −33.5885 | −1.48297 | ||||||||
\(514\) | −6.07180 | −0.267815 | ||||||||
\(515\) | 3.36603 | + | 5.83013i | 0.148325 | + | 0.256906i | ||||
\(516\) | −9.86603 | − | 17.0885i | −0.434328 | − | 0.752277i | ||||
\(517\) | −7.46410 | + | 12.9282i | −0.328271 | + | 0.568582i | ||||
\(518\) | 4.83013 | − | 8.36603i | 0.212224 | − | 0.367582i | ||||
\(519\) | −2.66025 | + | 4.60770i | −0.116772 | + | 0.202255i | ||||
\(520\) | 2.36603 | + | 4.09808i | 0.103757 | + | 0.179713i | ||||
\(521\) | 23.7321 | 1.03972 | 0.519860 | − | 0.854251i | \(-0.325984\pi\) | ||||
0.519860 | + | 0.854251i | \(0.325984\pi\) | |||||||
\(522\) | −12.2942 | − | 21.2942i | −0.538104 | − | 0.932023i | ||||
\(523\) | 24.5359 | 1.07288 | 0.536440 | − | 0.843938i | \(-0.319769\pi\) | ||||
0.536440 | + | 0.843938i | \(0.319769\pi\) | |||||||
\(524\) | 7.92820 | + | 13.7321i | 0.346345 | + | 0.599887i | ||||
\(525\) | −1.73205 | −0.0755929 | ||||||||
\(526\) | 6.90192 | − | 11.9545i | 0.300938 | − | 0.521240i | ||||
\(527\) | −4.46410 | + | 7.73205i | −0.194459 | + | 0.336813i | ||||
\(528\) | 6.46410 | 0.281314 | ||||||||
\(529\) | 10.6962 | + | 18.5263i | 0.465050 | + | 0.805490i | ||||
\(530\) | −10.1962 | −0.442893 | ||||||||
\(531\) | −12.6962 | − | 21.9904i | −0.550966 | − | 0.954301i | ||||
\(532\) | 6.46410 | 0.280254 | ||||||||
\(533\) | −13.5622 | − | 23.4904i | −0.587443 | − | 1.01748i | ||||
\(534\) | −0.464102 | + | 0.803848i | −0.0200836 | + | 0.0347859i | ||||
\(535\) | −9.23205 | + | 15.9904i | −0.399136 | + | 0.691324i | ||||
\(536\) | −4.50000 | + | 7.79423i | −0.194370 | + | 0.336659i | ||||
\(537\) | 21.0000 | + | 36.3731i | 0.906217 | + | 1.56961i | ||||
\(538\) | −9.63397 | − | 16.6865i | −0.415350 | − | 0.719408i | ||||
\(539\) | 3.73205 | 0.160751 | ||||||||
\(540\) | −2.59808 | − | 4.50000i | −0.111803 | − | 0.193649i | ||||
\(541\) | −16.3923 | −0.704760 | −0.352380 | − | 0.935857i | \(-0.614628\pi\) | ||||
−0.352380 | + | 0.935857i | \(0.614628\pi\) | |||||||
\(542\) | 8.02628 | + | 13.9019i | 0.344758 | + | 0.597139i | ||||
\(543\) | −15.4641 | − | 26.7846i | −0.663628 | − | 1.14944i | ||||
\(544\) | 0.500000 | − | 0.866025i | 0.0214373 | − | 0.0371305i | ||||
\(545\) | 2.36603 | − | 4.09808i | 0.101349 | − | 0.175542i | ||||
\(546\) | −4.09808 | + | 7.09808i | −0.175381 | + | 0.303770i | ||||
\(547\) | −14.0885 | − | 24.4019i | −0.602379 | − | 1.04335i | −0.992460 | − | 0.122570i | \(-0.960886\pi\) |
0.390081 | − | 0.920781i | \(-0.372447\pi\) | |||||||
\(548\) | 4.26795 | 0.182318 | ||||||||
\(549\) | −2.19615 | −0.0937295 | ||||||||
\(550\) | −3.73205 | −0.159135 | ||||||||
\(551\) | −26.4904 | − | 45.8827i | −1.12853 | − | 1.95467i | ||||
\(552\) | −2.19615 | −0.0934745 | ||||||||
\(553\) | −7.00000 | + | 12.1244i | −0.297670 | + | 0.515580i | ||||
\(554\) | 15.9282 | − | 27.5885i | 0.676725 | − | 1.17212i | ||||
\(555\) | −16.7321 | −0.710236 | ||||||||
\(556\) | 1.23205 | + | 2.13397i | 0.0522506 | + | 0.0905007i | ||||
\(557\) | 40.7846 | 1.72810 | 0.864050 | − | 0.503407i | \(-0.167920\pi\) | ||||
0.864050 | + | 0.503407i | \(0.167920\pi\) | |||||||
\(558\) | 13.3923 | − | 23.1962i | 0.566941 | − | 0.981971i | ||||
\(559\) | 53.9090 | 2.28011 | ||||||||
\(560\) | 0.500000 | + | 0.866025i | 0.0211289 | + | 0.0365963i | ||||
\(561\) | −3.23205 | + | 5.59808i | −0.136457 | + | 0.236351i | ||||
\(562\) | 10.1962 | − | 17.6603i | 0.430099 | − | 0.744953i | ||||
\(563\) | 6.93782 | − | 12.0167i | 0.292394 | − | 0.506442i | −0.681981 | − | 0.731370i | \(-0.738881\pi\) |
0.974375 | + | 0.224928i | \(0.0722147\pi\) | |||||||
\(564\) | −3.46410 | − | 6.00000i | −0.145865 | − | 0.252646i | ||||
\(565\) | 4.92820 | + | 8.53590i | 0.207331 | + | 0.359108i | ||||
\(566\) | 24.7846 | 1.04177 | ||||||||
\(567\) | 4.50000 | − | 7.79423i | 0.188982 | − | 0.327327i | ||||
\(568\) | −8.73205 | −0.366389 | ||||||||
\(569\) | 8.89230 | + | 15.4019i | 0.372785 | + | 0.645682i | 0.989993 | − | 0.141118i | \(-0.0450696\pi\) |
−0.617208 | + | 0.786800i | \(0.711736\pi\) | |||||||
\(570\) | −5.59808 | − | 9.69615i | −0.234478 | − | 0.406127i | ||||
\(571\) | 3.06218 | − | 5.30385i | 0.128148 | − | 0.221959i | −0.794811 | − | 0.606857i | \(-0.792430\pi\) |
0.922959 | + | 0.384898i | \(0.125763\pi\) | |||||||
\(572\) | −8.83013 | + | 15.2942i | −0.369206 | + | 0.639484i | ||||
\(573\) | 2.19615 | − | 3.80385i | 0.0917456 | − | 0.158908i | ||||
\(574\) | −2.86603 | − | 4.96410i | −0.119626 | − | 0.207198i | ||||
\(575\) | 1.26795 | 0.0528771 | ||||||||
\(576\) | −1.50000 | + | 2.59808i | −0.0625000 | + | 0.108253i | ||||
\(577\) | −11.2487 | −0.468290 | −0.234145 | − | 0.972202i | \(-0.575229\pi\) | ||||
−0.234145 | + | 0.972202i | \(0.575229\pi\) | |||||||
\(578\) | −8.00000 | − | 13.8564i | −0.332756 | − | 0.576351i | ||||
\(579\) | 45.2487 | 1.88047 | ||||||||
\(580\) | 4.09808 | − | 7.09808i | 0.170163 | − | 0.294732i | ||||
\(581\) | 0.732051 | − | 1.26795i | 0.0303706 | − | 0.0526034i | ||||
\(582\) | 1.73205 | 0.0717958 | ||||||||
\(583\) | −19.0263 | − | 32.9545i | −0.787988 | − | 1.36484i | ||||
\(584\) | 1.92820 | 0.0797896 | ||||||||
\(585\) | 14.1962 | 0.586939 | ||||||||
\(586\) | −20.5885 | −0.850501 | ||||||||
\(587\) | −2.99038 | − | 5.17949i | −0.123426 | − | 0.213781i | 0.797690 | − | 0.603067i | \(-0.206055\pi\) |
−0.921117 | + | 0.389287i | \(0.872722\pi\) | |||||||
\(588\) | −0.866025 | + | 1.50000i | −0.0357143 | + | 0.0618590i | ||||
\(589\) | 28.8564 | − | 49.9808i | 1.18901 | − | 2.05942i | ||||
\(590\) | 4.23205 | − | 7.33013i | 0.174231 | − | 0.301777i | ||||
\(591\) | −2.36603 | − | 4.09808i | −0.0973253 | − | 0.168572i | ||||
\(592\) | 4.83013 | + | 8.36603i | 0.198517 | + | 0.343842i | ||||
\(593\) | 2.53590 | 0.104137 | 0.0520684 | − | 0.998644i | \(-0.483419\pi\) | ||||
0.0520684 | + | 0.998644i | \(0.483419\pi\) | |||||||
\(594\) | 9.69615 | − | 16.7942i | 0.397838 | − | 0.689076i | ||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | −6.00000 | − | 10.3923i | −0.245770 | − | 0.425685i | ||||
\(597\) | 9.75833 | + | 16.9019i | 0.399382 | + | 0.691750i | ||||
\(598\) | 3.00000 | − | 5.19615i | 0.122679 | − | 0.212486i | ||||
\(599\) | −17.3205 | + | 30.0000i | −0.707697 | + | 1.22577i | 0.258013 | + | 0.966142i | \(0.416932\pi\) |
−0.965709 | + | 0.259625i | \(0.916401\pi\) | |||||||
\(600\) | 0.866025 | − | 1.50000i | 0.0353553 | − | 0.0612372i | ||||
\(601\) | 3.06218 | + | 5.30385i | 0.124909 | + | 0.216348i | 0.921697 | − | 0.387910i | \(-0.126803\pi\) |
−0.796788 | + | 0.604258i | \(0.793469\pi\) | |||||||
\(602\) | 11.3923 | 0.464316 | ||||||||
\(603\) | 13.5000 | + | 23.3827i | 0.549762 | + | 0.952217i | ||||
\(604\) | −11.8564 | −0.482430 | ||||||||
\(605\) | −1.46410 | − | 2.53590i | −0.0595242 | − | 0.103099i | ||||
\(606\) | −16.3923 | −0.665892 | ||||||||
\(607\) | −21.8564 | + | 37.8564i | −0.887124 | + | 1.53654i | −0.0438647 | + | 0.999037i | \(0.513967\pi\) |
−0.843260 | + | 0.537507i | \(0.819366\pi\) | |||||||
\(608\) | −3.23205 | + | 5.59808i | −0.131077 | + | 0.227032i | ||||
\(609\) | 14.1962 | 0.575257 | ||||||||
\(610\) | −0.366025 | − | 0.633975i | −0.0148199 | − | 0.0256689i | ||||
\(611\) | 18.9282 | 0.765753 | ||||||||
\(612\) | −1.50000 | − | 2.59808i | −0.0606339 | − | 0.105021i | ||||
\(613\) | 30.0000 | 1.21169 | 0.605844 | − | 0.795583i | \(-0.292835\pi\) | ||||
0.605844 | + | 0.795583i | \(0.292835\pi\) | |||||||
\(614\) | −3.13397 | − | 5.42820i | −0.126477 | − | 0.219064i | ||||
\(615\) | −4.96410 | + | 8.59808i | −0.200172 | + | 0.346708i | ||||
\(616\) | −1.86603 | + | 3.23205i | −0.0751843 | + | 0.130223i | ||||
\(617\) | −7.13397 | + | 12.3564i | −0.287203 | + | 0.497450i | −0.973141 | − | 0.230210i | \(-0.926059\pi\) |
0.685938 | + | 0.727660i | \(0.259392\pi\) | |||||||
\(618\) | −5.83013 | − | 10.0981i | −0.234522 | − | 0.406204i | ||||
\(619\) | −22.3564 | − | 38.7224i | −0.898580 | − | 1.55639i | −0.829311 | − | 0.558788i | \(-0.811267\pi\) |
−0.0692693 | − | 0.997598i | \(-0.522067\pi\) | |||||||
\(620\) | 8.92820 | 0.358565 | ||||||||
\(621\) | −3.29423 | + | 5.70577i | −0.132193 | + | 0.228965i | ||||
\(622\) | −8.53590 | −0.342258 | ||||||||
\(623\) | −0.267949 | − | 0.464102i | −0.0107352 | − | 0.0185938i | ||||
\(624\) | −4.09808 | − | 7.09808i | −0.164054 | − | 0.284150i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 8.50000 | − | 14.7224i | 0.339728 | − | 0.588427i | ||||
\(627\) | 20.8923 | − | 36.1865i | 0.834358 | − | 1.44515i | ||||
\(628\) | −10.0263 | − | 17.3660i | −0.400092 | − | 0.692980i | ||||
\(629\) | −9.66025 | −0.385180 | ||||||||
\(630\) | 3.00000 | 0.119523 | ||||||||
\(631\) | −27.6603 | −1.10114 | −0.550569 | − | 0.834790i | \(-0.685589\pi\) | ||||
−0.550569 | + | 0.834790i | \(0.685589\pi\) | |||||||
\(632\) | −7.00000 | − | 12.1244i | −0.278445 | − | 0.482281i | ||||
\(633\) | 14.5359 | 0.577750 | ||||||||
\(634\) | 4.63397 | − | 8.02628i | 0.184039 | − | 0.318764i | ||||
\(635\) | 0.830127 | − | 1.43782i | 0.0329426 | − | 0.0570582i | ||||
\(636\) | 17.6603 | 0.700275 | ||||||||
\(637\) | −2.36603 | − | 4.09808i | −0.0937453 | − | 0.162372i | ||||
\(638\) | 30.5885 | 1.21101 | ||||||||
\(639\) | −13.0981 | + | 22.6865i | −0.518152 | + | 0.897465i | ||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −9.50000 | − | 16.4545i | −0.375227 | − | 0.649913i | 0.615134 | − | 0.788423i | \(-0.289102\pi\) |
−0.990361 | + | 0.138510i | \(0.955769\pi\) | |||||||
\(642\) | 15.9904 | − | 27.6962i | 0.631090 | − | 1.09308i | ||||
\(643\) | 10.0622 | − | 17.4282i | 0.396814 | − | 0.687301i | −0.596517 | − | 0.802600i | \(-0.703449\pi\) |
0.993331 | + | 0.115299i | \(0.0367826\pi\) | |||||||
\(644\) | 0.633975 | − | 1.09808i | 0.0249821 | − | 0.0432703i | ||||
\(645\) | −9.86603 | − | 17.0885i | −0.388474 | − | 0.672857i | ||||
\(646\) | −3.23205 | − | 5.59808i | −0.127163 | − | 0.220253i | ||||
\(647\) | 10.1962 | 0.400852 | 0.200426 | − | 0.979709i | \(-0.435767\pi\) | ||||
0.200426 | + | 0.979709i | \(0.435767\pi\) | |||||||
\(648\) | 4.50000 | + | 7.79423i | 0.176777 | + | 0.306186i | ||||
\(649\) | 31.5885 | 1.23996 | ||||||||
\(650\) | 2.36603 | + | 4.09808i | 0.0928032 | + | 0.160740i | ||||
\(651\) | 7.73205 | + | 13.3923i | 0.303043 | + | 0.524886i | ||||
\(652\) | 1.19615 | − | 2.07180i | 0.0468449 | − | 0.0811378i | ||||
\(653\) | 13.9282 | − | 24.1244i | 0.545053 | − | 0.944059i | −0.453551 | − | 0.891230i | \(-0.649843\pi\) |
0.998604 | − | 0.0528286i | \(-0.0168237\pi\) | |||||||
\(654\) | −4.09808 | + | 7.09808i | −0.160247 | + | 0.277557i | ||||
\(655\) | 7.92820 | + | 13.7321i | 0.309781 | + | 0.536556i | ||||
\(656\) | 5.73205 | 0.223799 | ||||||||
\(657\) | 2.89230 | − | 5.00962i | 0.112840 | − | 0.195444i | ||||
\(658\) | 4.00000 | 0.155936 | ||||||||
\(659\) | 0.732051 | + | 1.26795i | 0.0285167 | + | 0.0493923i | 0.879932 | − | 0.475101i | \(-0.157588\pi\) |
−0.851415 | + | 0.524493i | \(0.824255\pi\) | |||||||
\(660\) | 6.46410 | 0.251615 | ||||||||
\(661\) | −4.19615 | + | 7.26795i | −0.163211 | + | 0.282690i | −0.936019 | − | 0.351950i | \(-0.885519\pi\) |
0.772807 | + | 0.634641i | \(0.218852\pi\) | |||||||
\(662\) | −11.2679 | + | 19.5167i | −0.437941 | + | 0.758537i | ||||
\(663\) | 8.19615 | 0.318312 | ||||||||
\(664\) | 0.732051 | + | 1.26795i | 0.0284091 | + | 0.0492060i | ||||
\(665\) | 6.46410 | 0.250667 | ||||||||
\(666\) | 28.9808 | 1.12298 | ||||||||
\(667\) | −10.3923 | −0.402392 | ||||||||
\(668\) | −4.56218 | − | 7.90192i | −0.176516 | − | 0.305735i | ||||
\(669\) | 23.0263 | − | 39.8827i | 0.890247 | − | 1.54195i | ||||
\(670\) | −4.50000 | + | 7.79423i | −0.173850 | + | 0.301117i | ||||
\(671\) | 1.36603 | − | 2.36603i | 0.0527348 | − | 0.0913394i | ||||
\(672\) | −0.866025 | − | 1.50000i | −0.0334077 | − | 0.0578638i | ||||
\(673\) | 2.85641 | + | 4.94744i | 0.110106 | + | 0.190710i | 0.915813 | − | 0.401605i | \(-0.131548\pi\) |
−0.805707 | + | 0.592315i | \(0.798214\pi\) | |||||||
\(674\) | −19.3397 | −0.744939 | ||||||||
\(675\) | −2.59808 | − | 4.50000i | −0.100000 | − | 0.173205i | ||||
\(676\) | 9.39230 | 0.361242 | ||||||||
\(677\) | 8.70577 | + | 15.0788i | 0.334590 | + | 0.579527i | 0.983406 | − | 0.181418i | \(-0.0580689\pi\) |
−0.648816 | + | 0.760945i | \(0.724736\pi\) | |||||||
\(678\) | −8.53590 | − | 14.7846i | −0.327819 | − | 0.567800i | ||||
\(679\) | −0.500000 | + | 0.866025i | −0.0191882 | + | 0.0332350i | ||||
\(680\) | 0.500000 | − | 0.866025i | 0.0191741 | − | 0.0332106i | ||||
\(681\) | −6.35641 | + | 11.0096i | −0.243578 | + | 0.421890i | ||||
\(682\) | 16.6603 | + | 28.8564i | 0.637954 | + | 1.10497i | ||||
\(683\) | −10.3205 | −0.394903 | −0.197452 | − | 0.980313i | \(-0.563267\pi\) | ||||
−0.197452 | + | 0.980313i | \(0.563267\pi\) | |||||||
\(684\) | 9.69615 | + | 16.7942i | 0.370742 | + | 0.642143i | ||||
\(685\) | 4.26795 | 0.163070 | ||||||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | 21.1244 | 0.805944 | ||||||||
\(688\) | −5.69615 | + | 9.86603i | −0.217164 | + | 0.376139i | ||||
\(689\) | −24.1244 | + | 41.7846i | −0.919065 | + | 1.59187i | ||||
\(690\) | −2.19615 | −0.0836061 | ||||||||
\(691\) | −5.46410 | − | 9.46410i | −0.207864 | − | 0.360031i | 0.743177 | − | 0.669095i | \(-0.233318\pi\) |
−0.951042 | + | 0.309063i | \(0.899985\pi\) | |||||||
\(692\) | 3.07180 | 0.116772 | ||||||||
\(693\) | 5.59808 | + | 9.69615i | 0.212653 | + | 0.368326i | ||||
\(694\) | −26.7128 | −1.01400 | ||||||||
\(695\) | 1.23205 | + | 2.13397i | 0.0467344 | + | 0.0809463i | ||||
\(696\) | −7.09808 | + | 12.2942i | −0.269052 | + | 0.466012i | ||||
\(697\) | −2.86603 | + | 4.96410i | −0.108558 | + | 0.188029i | ||||
\(698\) | −4.29423 | + | 7.43782i | −0.162539 | + | 0.281526i | ||||
\(699\) | −23.8923 | − | 41.3827i | −0.903690 | − | 1.56524i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | 13.6603 | 0.515941 | 0.257970 | − | 0.966153i | \(-0.416946\pi\) | ||||
0.257970 | + | 0.966153i | \(0.416946\pi\) | |||||||
\(702\) | −24.5885 | −0.928032 | ||||||||
\(703\) | 62.4449 | 2.35515 | ||||||||
\(704\) | −1.86603 | − | 3.23205i | −0.0703285 | − | 0.121812i | ||||
\(705\) | −3.46410 | − | 6.00000i | −0.130466 | − | 0.225973i | ||||
\(706\) | −10.9641 | + | 18.9904i | −0.412639 | + | 0.714712i | ||||
\(707\) | 4.73205 | − | 8.19615i | 0.177967 | − | 0.308248i | ||||
\(708\) | −7.33013 | + | 12.6962i | −0.275483 | + | 0.477151i | ||||
\(709\) | −0.437822 | − | 0.758330i | −0.0164428 | − | 0.0284797i | 0.857687 | − | 0.514172i | \(-0.171901\pi\) |
−0.874130 | + | 0.485693i | \(0.838567\pi\) | |||||||
\(710\) | −8.73205 | −0.327708 | ||||||||
\(711\) | −42.0000 | −1.57512 | ||||||||
\(712\) | 0.535898 | 0.0200836 | ||||||||
\(713\) | −5.66025 | − | 9.80385i | −0.211978 | − | 0.367157i | ||||
\(714\) | 1.73205 | 0.0648204 | ||||||||
\(715\) | −8.83013 | + | 15.2942i | −0.330228 | + | 0.571972i | ||||
\(716\) | 12.1244 | − | 21.0000i | 0.453108 | − | 0.784807i | ||||
\(717\) | 11.0718 | 0.413484 | ||||||||
\(718\) | 7.02628 | + | 12.1699i | 0.262218 | + | 0.454176i | ||||
\(719\) | −34.9808 | −1.30456 | −0.652281 | − | 0.757977i | \(-0.726188\pi\) | ||||
−0.652281 | + | 0.757977i | \(0.726188\pi\) | |||||||
\(720\) | −1.50000 | + | 2.59808i | −0.0559017 | + | 0.0968246i | ||||
\(721\) | 6.73205 | 0.250715 | ||||||||
\(722\) | 11.3923 | + | 19.7321i | 0.423978 | + | 0.734351i | ||||
\(723\) | 16.0359 | − | 27.7750i | 0.596381 | − | 1.03296i | ||||
\(724\) | −8.92820 | + | 15.4641i | −0.331814 | + | 0.574719i | ||||
\(725\) | 4.09808 | − | 7.09808i | 0.152199 | − | 0.263616i | ||||
\(726\) | 2.53590 | + | 4.39230i | 0.0941160 | + | 0.163014i | ||||
\(727\) | 23.0263 | + | 39.8827i | 0.853997 | + | 1.47917i | 0.877572 | + | 0.479445i | \(0.159162\pi\) |
−0.0235746 | + | 0.999722i | \(0.507505\pi\) | |||||||
\(728\) | 4.73205 | 0.175381 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 1.92820 | 0.0713660 | ||||||||
\(731\) | −5.69615 | − | 9.86603i | −0.210680 | − | 0.364908i | ||||
\(732\) | 0.633975 | + | 1.09808i | 0.0234324 | + | 0.0405861i | ||||
\(733\) | −9.09808 | + | 15.7583i | −0.336045 | + | 0.582047i | −0.983685 | − | 0.179899i | \(-0.942423\pi\) |
0.647640 | + | 0.761947i | \(0.275756\pi\) | |||||||
\(734\) | 7.36603 | − | 12.7583i | 0.271885 | − | 0.470919i | ||||
\(735\) | −0.866025 | + | 1.50000i | −0.0319438 | + | 0.0553283i | ||||
\(736\) | 0.633975 | + | 1.09808i | 0.0233686 | + | 0.0404756i | ||||
\(737\) | −33.5885 | −1.23725 | ||||||||
\(738\) | 8.59808 | − | 14.8923i | 0.316500 | − | 0.548193i | ||||
\(739\) | 22.1244 | 0.813858 | 0.406929 | − | 0.913460i | \(-0.366600\pi\) | ||||
0.406929 | + | 0.913460i | \(0.366600\pi\) | |||||||
\(740\) | 4.83013 | + | 8.36603i | 0.177559 | + | 0.307541i | ||||
\(741\) | −52.9808 | −1.94630 | ||||||||
\(742\) | −5.09808 | + | 8.83013i | −0.187156 | + | 0.324164i | ||||
\(743\) | 13.3923 | − | 23.1962i | 0.491316 | − | 0.850984i | −0.508634 | − | 0.860983i | \(-0.669849\pi\) |
0.999950 | + | 0.00999854i | \(0.00318269\pi\) | |||||||
\(744\) | −15.4641 | −0.566941 | ||||||||
\(745\) | −6.00000 | − | 10.3923i | −0.219823 | − | 0.380745i | ||||
\(746\) | −6.39230 | −0.234039 | ||||||||
\(747\) | 4.39230 | 0.160706 | ||||||||
\(748\) | 3.73205 | 0.136457 | ||||||||
\(749\) | 9.23205 | + | 15.9904i | 0.337332 | + | 0.584276i | ||||
\(750\) | 0.866025 | − | 1.50000i | 0.0316228 | − | 0.0547723i | ||||
\(751\) | 16.8301 | − | 29.1506i | 0.614140 | − | 1.06372i | −0.376395 | − | 0.926459i | \(-0.622836\pi\) |
0.990535 | − | 0.137262i | \(-0.0438303\pi\) | |||||||
\(752\) | −2.00000 | + | 3.46410i | −0.0729325 | + | 0.126323i | ||||
\(753\) | 9.40192 | + | 16.2846i | 0.342625 | + | 0.593444i | ||||
\(754\) | −19.3923 | − | 33.5885i | −0.706226 | − | 1.22322i | ||||
\(755\) | −11.8564 | −0.431499 | ||||||||
\(756\) | −5.19615 | −0.188982 | ||||||||
\(757\) | 15.6603 | 0.569182 | 0.284591 | − | 0.958649i | \(-0.408142\pi\) | ||||
0.284591 | + | 0.958649i | \(0.408142\pi\) | |||||||
\(758\) | 0.401924 | + | 0.696152i | 0.0145985 | + | 0.0252854i | ||||
\(759\) | −4.09808 | − | 7.09808i | −0.148751 | − | 0.257644i | ||||
\(760\) | −3.23205 | + | 5.59808i | −0.117239 | + | 0.203064i | ||||
\(761\) | 1.39230 | − | 2.41154i | 0.0504710 | − | 0.0874184i | −0.839686 | − | 0.543072i | \(-0.817261\pi\) |
0.890157 | + | 0.455654i | \(0.150594\pi\) | |||||||
\(762\) | −1.43782 | + | 2.49038i | −0.0520868 | + | 0.0902170i | ||||
\(763\) | −2.36603 | − | 4.09808i | −0.0856559 | − | 0.148360i | ||||
\(764\) | −2.53590 | −0.0917456 | ||||||||
\(765\) | −1.50000 | − | 2.59808i | −0.0542326 | − | 0.0939336i | ||||
\(766\) | 2.53590 | 0.0916257 | ||||||||
\(767\) | −20.0263 | − | 34.6865i | −0.723107 | − | 1.25246i | ||||
\(768\) | 1.73205 | 0.0625000 | ||||||||
\(769\) | −15.8564 | + | 27.4641i | −0.571797 | + | 0.990381i | 0.424585 | + | 0.905388i | \(0.360420\pi\) |
−0.996382 | + | 0.0849927i | \(0.972913\pi\) | |||||||
\(770\) | −1.86603 | + | 3.23205i | −0.0672469 | + | 0.116475i | ||||
\(771\) | 10.5167 | 0.378748 | ||||||||
\(772\) | −13.0622 | − | 22.6244i | −0.470118 | − | 0.814268i | ||||
\(773\) | −21.3731 | −0.768736 | −0.384368 | − | 0.923180i | \(-0.625581\pi\) | ||||
−0.384368 | + | 0.923180i | \(0.625581\pi\) | |||||||
\(774\) | 17.0885 | + | 29.5981i | 0.614232 | + | 1.06388i | ||||
\(775\) | 8.92820 | 0.320711 | ||||||||
\(776\) | −0.500000 | − | 0.866025i | −0.0179490 | − | 0.0310885i | ||||
\(777\) | −8.36603 | + | 14.4904i | −0.300129 | + | 0.519840i | ||||
\(778\) | 4.53590 | − | 7.85641i | 0.162620 | − | 0.281666i | ||||
\(779\) | 18.5263 | − | 32.0885i | 0.663773 | − | 1.14969i | ||||
\(780\) | −4.09808 | − | 7.09808i | −0.146735 | − | 0.254152i | ||||
\(781\) | −16.2942 | − | 28.2224i | −0.583053 | − | 1.00988i | ||||
\(782\) | −1.26795 | −0.0453418 | ||||||||
\(783\) | 21.2942 | + | 36.8827i | 0.760994 | + | 1.31808i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −10.0263 | − | 17.3660i | −0.357853 | − | 0.619820i | ||||
\(786\) | −13.7321 | − | 23.7846i | −0.489806 | − | 0.848369i | ||||
\(787\) | −14.9282 | + | 25.8564i | −0.532133 | + | 0.921681i | 0.467163 | + | 0.884171i | \(0.345276\pi\) |
−0.999296 | + | 0.0375103i | \(0.988057\pi\) | |||||||
\(788\) | −1.36603 | + | 2.36603i | −0.0486626 | + | 0.0842862i | ||||
\(789\) | −11.9545 | + | 20.7058i | −0.425591 | + | 0.737145i | ||||
\(790\) | −7.00000 | − | 12.1244i | −0.249049 | − | 0.431365i | ||||
\(791\) | 9.85641 | 0.350453 | ||||||||
\(792\) | −11.1962 | −0.397838 | ||||||||
\(793\) | −3.46410 | −0.123014 | ||||||||
\(794\) | 2.16987 | + | 3.75833i | 0.0770059 | + | 0.133378i | ||||
\(795\) | 17.6603 | 0.626345 | ||||||||
\(796\) | 5.63397 | − | 9.75833i | 0.199691 | − | 0.345875i | ||||
\(797\) | 9.46410 | − | 16.3923i | 0.335236 | − | 0.580645i | −0.648294 | − | 0.761390i | \(-0.724517\pi\) |
0.983530 | + | 0.180745i | \(0.0578507\pi\) | |||||||
\(798\) | −11.1962 | −0.396339 | ||||||||
\(799\) | −2.00000 | − | 3.46410i | −0.0707549 | − | 0.122551i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0.803848 | − | 1.39230i | 0.0284026 | − | 0.0491947i | ||||
\(802\) | 20.8564 | 0.736465 | ||||||||
\(803\) | 3.59808 | + | 6.23205i | 0.126973 | + | 0.219924i | ||||
\(804\) | 7.79423 | − | 13.5000i | 0.274881 | − | 0.476108i | ||||
\(805\) | 0.633975 | − | 1.09808i | 0.0223447 | − | 0.0387021i | ||||
\(806\) | 21.1244 | − | 36.5885i | 0.744074 | − | 1.28877i | ||||
\(807\) | 16.6865 | + | 28.9019i | 0.587394 | + | 1.01740i | ||||
\(808\) | 4.73205 | + | 8.19615i | 0.166473 | + | 0.288340i | ||||
\(809\) | 22.6077 | 0.794844 | 0.397422 | − | 0.917636i | \(-0.369905\pi\) | ||||
0.397422 | + | 0.917636i | \(0.369905\pi\) | |||||||
\(810\) | 4.50000 | + | 7.79423i | 0.158114 | + | 0.273861i | ||||
\(811\) | −26.6077 | −0.934323 | −0.467161 | − | 0.884172i | \(-0.654723\pi\) | ||||
−0.467161 | + | 0.884172i | \(0.654723\pi\) | |||||||
\(812\) | −4.09808 | − | 7.09808i | −0.143814 | − | 0.249094i | ||||
\(813\) | −13.9019 | − | 24.0788i | −0.487562 | − | 0.844482i | ||||
\(814\) | −18.0263 | + | 31.2224i | −0.631821 | + | 1.09435i | ||||
\(815\) | 1.19615 | − | 2.07180i | 0.0418994 | − | 0.0725719i | ||||
\(816\) | −0.866025 | + | 1.50000i | −0.0303170 | + | 0.0525105i | ||||
\(817\) | 36.8205 | + | 63.7750i | 1.28819 | + | 2.23120i | ||||
\(818\) | −28.2679 | −0.988366 | ||||||||
\(819\) | 7.09808 | − | 12.2942i | 0.248027 | − | 0.429595i | ||||
\(820\) | 5.73205 | 0.200172 | ||||||||
\(821\) | −6.16987 | − | 10.6865i | −0.215330 | − | 0.372963i | 0.738045 | − | 0.674752i | \(-0.235749\pi\) |
−0.953375 | + | 0.301789i | \(0.902416\pi\) | |||||||
\(822\) | −7.39230 | −0.257836 | ||||||||
\(823\) | −8.16987 | + | 14.1506i | −0.284784 | + | 0.493260i | −0.972557 | − | 0.232666i | \(-0.925255\pi\) |
0.687773 | + | 0.725926i | \(0.258588\pi\) | |||||||
\(824\) | −3.36603 | + | 5.83013i | −0.117261 | + | 0.203102i | ||||
\(825\) | 6.46410 | 0.225051 | ||||||||
\(826\) | −4.23205 | − | 7.33013i | −0.147252 | − | 0.255048i | ||||
\(827\) | −12.1436 | −0.422274 | −0.211137 | − | 0.977456i | \(-0.567717\pi\) | ||||
−0.211137 | + | 0.977456i | \(0.567717\pi\) | |||||||
\(828\) | 3.80385 | 0.132193 | ||||||||
\(829\) | −20.3923 | −0.708254 | −0.354127 | − | 0.935197i | \(-0.615222\pi\) | ||||
−0.354127 | + | 0.935197i | \(0.615222\pi\) | |||||||
\(830\) | 0.732051 | + | 1.26795i | 0.0254099 | + | 0.0440112i | ||||
\(831\) | −27.5885 | + | 47.7846i | −0.957033 | + | 1.65763i | ||||
\(832\) | −2.36603 | + | 4.09808i | −0.0820272 | + | 0.142075i | ||||
\(833\) | −0.500000 | + | 0.866025i | −0.0173240 | + | 0.0300060i | ||||
\(834\) | −2.13397 | − | 3.69615i | −0.0738935 | − | 0.127987i | ||||
\(835\) | −4.56218 | − | 7.90192i | −0.157881 | − | 0.273457i | ||||
\(836\) | −24.1244 | −0.834358 | ||||||||
\(837\) | −23.1962 | + | 40.1769i | −0.801776 | + | 1.38872i | ||||
\(838\) | −5.32051 | −0.183794 | ||||||||
\(839\) | −28.1506 | − | 48.7583i | −0.971868 | − | 1.68332i | −0.689906 | − | 0.723899i | \(-0.742348\pi\) |
−0.281962 | − | 0.959426i | \(-0.590985\pi\) | |||||||
\(840\) | −0.866025 | − | 1.50000i | −0.0298807 | − | 0.0517549i | ||||
\(841\) | −19.0885 | + | 33.0622i | −0.658223 | + | 1.14008i | ||||
\(842\) | −11.7583 | + | 20.3660i | −0.405219 | + | 0.701860i | ||||
\(843\) | −17.6603 | + | 30.5885i | −0.608251 | + | 1.05352i | ||||
\(844\) | −4.19615 | − | 7.26795i | −0.144438 | − | 0.250173i | ||||
\(845\) | 9.39230 | 0.323105 | ||||||||
\(846\) | 6.00000 | + | 10.3923i | 0.206284 | + | 0.357295i | ||||
\(847\) | −2.92820 | −0.100614 | ||||||||
\(848\) | −5.09808 | − | 8.83013i | −0.175069 | − | 0.303228i | ||||
\(849\) | −42.9282 | −1.47329 | ||||||||
\(850\) | 0.500000 | − | 0.866025i | 0.0171499 | − | 0.0297044i | ||||
\(851\) | 6.12436 | − | 10.6077i | 0.209940 | − | 0.363627i | ||||
\(852\) | 15.1244 | 0.518152 | ||||||||
\(853\) | 8.58846 | + | 14.8756i | 0.294063 | + | 0.509332i | 0.974767 | − | 0.223227i | \(-0.0716591\pi\) |
−0.680703 | + | 0.732559i | \(0.738326\pi\) | |||||||
\(854\) | −0.732051 | −0.0250503 | ||||||||
\(855\) | 9.69615 | + | 16.7942i | 0.331601 | + | 0.574351i | ||||
\(856\) | −18.4641 | −0.631090 | ||||||||
\(857\) | 21.4641 | + | 37.1769i | 0.733200 | + | 1.26994i | 0.955509 | + | 0.294963i | \(0.0953073\pi\) |
−0.222309 | + | 0.974976i | \(0.571359\pi\) | |||||||
\(858\) | 15.2942 | − | 26.4904i | 0.522136 | − | 0.904367i | ||||
\(859\) | 1.96410 | − | 3.40192i | 0.0670143 | − | 0.116072i | −0.830571 | − | 0.556912i | \(-0.811986\pi\) |
0.897586 | + | 0.440840i | \(0.145319\pi\) | |||||||
\(860\) | −5.69615 | + | 9.86603i | −0.194237 | + | 0.336429i | ||||
\(861\) | 4.96410 | + | 8.59808i | 0.169176 | + | 0.293022i | ||||
\(862\) | −9.12436 | − | 15.8038i | −0.310777 | − | 0.538281i | ||||
\(863\) | 1.32051 | 0.0449506 | 0.0224753 | − | 0.999747i | \(-0.492845\pi\) | ||||
0.0224753 | + | 0.999747i | \(0.492845\pi\) | |||||||
\(864\) | 2.59808 | − | 4.50000i | 0.0883883 | − | 0.153093i | ||||
\(865\) | 3.07180 | 0.104444 | ||||||||
\(866\) | 11.1603 | + | 19.3301i | 0.379241 | + | 0.656864i | ||||
\(867\) | 13.8564 | + | 24.0000i | 0.470588 | + | 0.815083i | ||||
\(868\) | 4.46410 | − | 7.73205i | 0.151521 | − | 0.262443i | ||||
\(869\) | 26.1244 | − | 45.2487i | 0.886208 | − | 1.53496i | ||||
\(870\) | −7.09808 | + | 12.2942i | −0.240647 | + | 0.416813i | ||||
\(871\) | 21.2942 | + | 36.8827i | 0.721527 | + | 1.24972i | ||||
\(872\) | 4.73205 | 0.160247 | ||||||||
\(873\) | −3.00000 | −0.101535 | ||||||||
\(874\) | 8.19615 | 0.277239 | ||||||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | −3.33975 | −0.112840 | ||||||||
\(877\) | 8.75833 | − | 15.1699i | 0.295748 | − | 0.512250i | −0.679411 | − | 0.733758i | \(-0.737765\pi\) |
0.975159 | + | 0.221508i | \(0.0710979\pi\) | |||||||
\(878\) | 8.63397 | − | 14.9545i | 0.291383 | − | 0.504689i | ||||
\(879\) | 35.6603 | 1.20279 | ||||||||
\(880\) | −1.86603 | − | 3.23205i | −0.0629037 | − | 0.108952i | ||||
\(881\) | −11.2154 | −0.377856 | −0.188928 | − | 0.981991i | \(-0.560501\pi\) | ||||
−0.188928 | + | 0.981991i | \(0.560501\pi\) | |||||||
\(882\) | 1.50000 | − | 2.59808i | 0.0505076 | − | 0.0874818i | ||||
\(883\) | −30.4641 | −1.02520 | −0.512599 | − | 0.858628i | \(-0.671317\pi\) | ||||
−0.512599 | + | 0.858628i | \(0.671317\pi\) | |||||||
\(884\) | −2.36603 | − | 4.09808i | −0.0795780 | − | 0.137833i | ||||
\(885\) | −7.33013 | + | 12.6962i | −0.246400 | + | 0.426776i | ||||
\(886\) | −15.6244 | + | 27.0622i | −0.524910 | + | 0.909172i | ||||
\(887\) | 28.7128 | − | 49.7321i | 0.964082 | − | 1.66984i | 0.252020 | − | 0.967722i | \(-0.418905\pi\) |
0.712062 | − | 0.702117i | \(-0.247762\pi\) | |||||||
\(888\) | −8.36603 | − | 14.4904i | −0.280745 | − | 0.486265i | ||||
\(889\) | −0.830127 | − | 1.43782i | −0.0278416 | − | 0.0482230i | ||||
\(890\) | 0.535898 | 0.0179634 | ||||||||
\(891\) | −16.7942 | + | 29.0885i | −0.562628 | + | 0.974500i | ||||
\(892\) | −26.5885 | −0.890247 | ||||||||
\(893\) | 12.9282 | + | 22.3923i | 0.432626 | + | 0.749330i | ||||
\(894\) | 10.3923 | + | 18.0000i | 0.347571 | + | 0.602010i | ||||
\(895\) | 12.1244 | − | 21.0000i | 0.405273 | − | 0.701953i | ||||
\(896\) | −0.500000 | + | 0.866025i | −0.0167038 | + | 0.0289319i | ||||
\(897\) | −5.19615 | + | 9.00000i | −0.173494 | + | 0.300501i | ||||
\(898\) | 11.8923 | + | 20.5981i | 0.396851 | + | 0.687367i | ||||
\(899\) | −73.1769 | −2.44059 | ||||||||
\(900\) | −1.50000 | + | 2.59808i | −0.0500000 | + | 0.0866025i | ||||
\(901\) | 10.1962 | 0.339683 | ||||||||
\(902\) | 10.6962 | + | 18.5263i | 0.356143 | + | 0.616858i | ||||
\(903\) | −19.7321 | −0.656642 | ||||||||
\(904\) | −4.92820 | + | 8.53590i | −0.163910 | + | 0.283900i | ||||
\(905\) | −8.92820 | + | 15.4641i | −0.296784 | + | 0.514044i | ||||
\(906\) | 20.5359 | 0.682260 | ||||||||
\(907\) | 13.4282 | + | 23.2583i | 0.445876 | + | 0.772280i | 0.998113 | − | 0.0614072i | \(-0.0195588\pi\) |
−0.552237 | + | 0.833687i | \(0.686226\pi\) | |||||||
\(908\) | 7.33975 | 0.243578 | ||||||||
\(909\) | 28.3923 | 0.941713 | ||||||||
\(910\) | 4.73205 | 0.156866 | ||||||||
\(911\) | −7.68653 | − | 13.3135i | −0.254666 | − | 0.441095i | 0.710139 | − | 0.704062i | \(-0.248632\pi\) |
−0.964805 | + | 0.262967i | \(0.915299\pi\) | |||||||
\(912\) | 5.59808 | − | 9.69615i | 0.185371 | − | 0.321072i | ||||
\(913\) | −2.73205 | + | 4.73205i | −0.0904177 | + | 0.156608i | ||||
\(914\) | 8.99038 | − | 15.5718i | 0.297375 | − | 0.515069i | ||||
\(915\) | 0.633975 | + | 1.09808i | 0.0209586 | + | 0.0363013i | ||||
\(916\) | −6.09808 | − | 10.5622i | −0.201486 | − | 0.348984i | ||||
\(917\) | 15.8564 | 0.523625 | ||||||||
\(918\) | 2.59808 | + | 4.50000i | 0.0857493 | + | 0.148522i | ||||
\(919\) | −44.0526 | −1.45316 | −0.726580 | − | 0.687082i | \(-0.758891\pi\) | ||||
−0.726580 | + | 0.687082i | \(0.758891\pi\) | |||||||
\(920\) | 0.633975 | + | 1.09808i | 0.0209015 | + | 0.0362025i | ||||
\(921\) | 5.42820 | + | 9.40192i | 0.178865 | + | 0.309804i | ||||
\(922\) | 3.36603 | − | 5.83013i | 0.110854 | − | 0.192005i | ||||
\(923\) | −20.6603 | + | 35.7846i | −0.680041 | + | 1.17786i | ||||
\(924\) | 3.23205 | − | 5.59808i | 0.106327 | − | 0.184163i | ||||
\(925\) | 4.83013 | + | 8.36603i | 0.158814 | + | 0.275073i | ||||
\(926\) | 0.784610 | 0.0257839 | ||||||||
\(927\) | 10.0981 | + | 17.4904i | 0.331664 | + | 0.574459i | ||||
\(928\) | 8.19615 | 0.269052 | ||||||||
\(929\) | 0.607695 | + | 1.05256i | 0.0199378 | + | 0.0345333i | 0.875822 | − | 0.482634i | \(-0.160320\pi\) |
−0.855884 | + | 0.517167i | \(0.826987\pi\) | |||||||
\(930\) | −15.4641 | −0.507088 | ||||||||
\(931\) | 3.23205 | − | 5.59808i | 0.105926 | − | 0.183470i | ||||
\(932\) | −13.7942 | + | 23.8923i | −0.451845 | + | 0.782618i | ||||
\(933\) | 14.7846 | 0.484026 | ||||||||
\(934\) | 1.13397 | + | 1.96410i | 0.0371048 | + | 0.0642674i | ||||
\(935\) | 3.73205 | 0.122051 | ||||||||
\(936\) | 7.09808 | + | 12.2942i | 0.232008 | + | 0.401849i | ||||
\(937\) | −25.4641 | −0.831876 | −0.415938 | − | 0.909393i | \(-0.636547\pi\) | ||||
−0.415938 | + | 0.909393i | \(0.636547\pi\) | |||||||
\(938\) | 4.50000 | + | 7.79423i | 0.146930 | + | 0.254491i | ||||
\(939\) | −14.7224 | + | 25.5000i | −0.480448 | + | 0.832161i | ||||
\(940\) | −2.00000 | + | 3.46410i | −0.0652328 | + | 0.112987i | ||||
\(941\) | 14.7321 | − | 25.5167i | 0.480251 | − | 0.831819i | −0.519492 | − | 0.854475i | \(-0.673879\pi\) |
0.999743 | + | 0.0226558i | \(0.00721219\pi\) | |||||||
\(942\) | 17.3660 | + | 30.0788i | 0.565816 | + | 0.980022i | ||||
\(943\) | −3.63397 | − | 6.29423i | −0.118338 | − | 0.204968i | ||||
\(944\) | 8.46410 | 0.275483 | ||||||||
\(945\) | −5.19615 | −0.169031 | ||||||||
\(946\) | −42.5167 | −1.38234 | ||||||||
\(947\) | −11.3564 | − | 19.6699i | −0.369034 | − | 0.639185i | 0.620381 | − | 0.784301i | \(-0.286978\pi\) |
−0.989415 | + | 0.145116i | \(0.953645\pi\) | |||||||
\(948\) | 12.1244 | + | 21.0000i | 0.393781 | + | 0.682048i | ||||
\(949\) | 4.56218 | − | 7.90192i | 0.148095 | − | 0.256507i | ||||
\(950\) | −3.23205 | + | 5.59808i | −0.104862 | + | 0.181626i | ||||
\(951\) | −8.02628 | + | 13.9019i | −0.260270 | + | 0.450801i | ||||
\(952\) | −0.500000 | − | 0.866025i | −0.0162051 | − | 0.0280680i | ||||
\(953\) | −11.8756 | −0.384690 | −0.192345 | − | 0.981327i | \(-0.561609\pi\) | ||||
−0.192345 | + | 0.981327i | \(0.561609\pi\) | |||||||
\(954\) | −30.5885 | −0.990338 | ||||||||
\(955\) | −2.53590 | −0.0820597 | ||||||||
\(956\) | −3.19615 | − | 5.53590i | −0.103371 | − | 0.179044i | ||||
\(957\) | −52.9808 | −1.71262 | ||||||||
\(958\) | −13.5622 | + | 23.4904i | −0.438174 | + | 0.758940i | ||||
\(959\) | 2.13397 | − | 3.69615i | 0.0689096 | − | 0.119355i | ||||
\(960\) | 1.73205 | 0.0559017 | ||||||||
\(961\) | −24.3564 | − | 42.1865i | −0.785691 | − | 1.36086i | ||||
\(962\) | 45.7128 | 1.47384 | ||||||||
\(963\) | −27.6962 | + | 47.9711i | −0.892496 | + | 1.54585i | ||||
\(964\) | −18.5167 | −0.596381 | ||||||||
\(965\) | −13.0622 | − | 22.6244i | −0.420486 | − | 0.728304i | ||||
\(966\) | −1.09808 | + | 1.90192i | −0.0353300 | + | 0.0611934i | ||||
\(967\) | 16.4641 | − | 28.5167i | 0.529450 | − | 0.917034i | −0.469960 | − | 0.882688i | \(-0.655732\pi\) |
0.999410 | − | 0.0343464i | \(-0.0109349\pi\) | |||||||
\(968\) | 1.46410 | − | 2.53590i | 0.0470580 | − | 0.0815069i | ||||
\(969\) | 5.59808 | + | 9.69615i | 0.179836 | + | 0.311485i | ||||
\(970\) | −0.500000 | − | 0.866025i | −0.0160540 | − | 0.0278064i | ||||
\(971\) | 25.8564 | 0.829772 | 0.414886 | − | 0.909873i | \(-0.363822\pi\) | ||||
0.414886 | + | 0.909873i | \(0.363822\pi\) | |||||||
\(972\) | −7.79423 | − | 13.5000i | −0.250000 | − | 0.433013i | ||||
\(973\) | 2.46410 | 0.0789955 | ||||||||
\(974\) | −7.19615 | − | 12.4641i | −0.230580 | − | 0.399376i | ||||
\(975\) | −4.09808 | − | 7.09808i | −0.131243 | − | 0.227320i | ||||
\(976\) | 0.366025 | − | 0.633975i | 0.0117162 | − | 0.0202930i | ||||
\(977\) | 9.52628 | − | 16.5000i | 0.304773 | − | 0.527882i | −0.672438 | − | 0.740153i | \(-0.734753\pi\) |
0.977211 | + | 0.212272i | \(0.0680862\pi\) | |||||||
\(978\) | −2.07180 | + | 3.58846i | −0.0662488 | + | 0.114746i | ||||
\(979\) | 1.00000 | + | 1.73205i | 0.0319601 | + | 0.0553566i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 7.09808 | − | 12.2942i | 0.226624 | − | 0.392525i | ||||
\(982\) | −25.7321 | −0.821143 | ||||||||
\(983\) | −6.39230 | − | 11.0718i | −0.203883 | − | 0.353135i | 0.745893 | − | 0.666065i | \(-0.232023\pi\) |
−0.949776 | + | 0.312930i | \(0.898690\pi\) | |||||||
\(984\) | −9.92820 | −0.316500 | ||||||||
\(985\) | −1.36603 | + | 2.36603i | −0.0435252 | + | 0.0753878i | ||||
\(986\) | −4.09808 | + | 7.09808i | −0.130509 | + | 0.226049i | ||||
\(987\) | −6.92820 | −0.220527 | ||||||||
\(988\) | 15.2942 | + | 26.4904i | 0.486574 | + | 0.842771i | ||||
\(989\) | 14.4449 | 0.459320 | ||||||||
\(990\) | −11.1962 | −0.355837 | ||||||||
\(991\) | −17.4641 | −0.554765 | −0.277383 | − | 0.960760i | \(-0.589467\pi\) | ||||
−0.277383 | + | 0.960760i | \(0.589467\pi\) | |||||||
\(992\) | 4.46410 | + | 7.73205i | 0.141735 | + | 0.245493i | ||||
\(993\) | 19.5167 | − | 33.8038i | 0.619343 | − | 1.07273i | ||||
\(994\) | −4.36603 | + | 7.56218i | −0.138482 | + | 0.239858i | ||||
\(995\) | 5.63397 | − | 9.75833i | 0.178609 | − | 0.309360i | ||||
\(996\) | −1.26795 | − | 2.19615i | −0.0401765 | − | 0.0695878i | ||||
\(997\) | 1.53590 | + | 2.66025i | 0.0486424 | + | 0.0842511i | 0.889321 | − | 0.457283i | \(-0.151177\pi\) |
−0.840679 | + | 0.541534i | \(0.817844\pi\) | |||||||
\(998\) | −11.1962 | −0.354408 | ||||||||
\(999\) | −50.1962 | −1.58814 |
(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 | 630.2.j.f.211.1 | ✓ | 4 | |
3.2 | odd | 2 | 1890.2.j.h.631.2 | 4 | |||
9.2 | odd | 6 | 1890.2.j.h.1261.2 | 4 | |||
9.4 | even | 3 | 5670.2.a.z.1.2 | 2 | |||
9.5 | odd | 6 | 5670.2.a.be.1.1 | 2 | |||
9.7 | even | 3 | inner | 630.2.j.f.421.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.f.211.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
630.2.j.f.421.1 | yes | 4 | 9.7 | even | 3 | inner | |
1890.2.j.h.631.2 | 4 | 3.2 | odd | 2 | |||
1890.2.j.h.1261.2 | 4 | 9.2 | odd | 6 | |||
5670.2.a.z.1.2 | 2 | 9.4 | even | 3 | |||
5670.2.a.be.1.1 | 2 | 9.5 | odd | 6 |