Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 533.9 | ||
Character | \(\chi\) | \(=\) | 570.533 |
Dual form | 570.2.k.a.77.9 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.65263 | − | 0.518471i | 0.954147 | − | 0.299339i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.11139 | + | 0.736229i | 0.944242 | + | 0.329251i | ||||
\(6\) | −1.53520 | − | 0.801972i | −0.626743 | − | 0.327404i | ||||
\(7\) | −2.44114 | + | 2.44114i | −0.922665 | + | 0.922665i | −0.997217 | − | 0.0745524i | \(-0.976247\pi\) |
0.0745524 | + | 0.997217i | \(0.476247\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 2.46238 | − | 1.71368i | 0.820792 | − | 0.571227i | ||||
\(10\) | −0.972386 | − | 2.01357i | −0.307495 | − | 0.636747i | ||||
\(11\) | 5.62118i | 1.69485i | 0.530916 | + | 0.847424i | \(0.321848\pi\) | ||||
−0.530916 | + | 0.847424i | \(0.678152\pi\) | |||||||
\(12\) | 0.518471 | + | 1.65263i | 0.149670 | + | 0.477073i | ||||
\(13\) | 0.933851 | + | 0.933851i | 0.259004 | + | 0.259004i | 0.824649 | − | 0.565645i | \(-0.191373\pi\) |
−0.565645 | + | 0.824649i | \(0.691373\pi\) | |||||||
\(14\) | 3.45230 | 0.922665 | ||||||||
\(15\) | 3.87106 | + | 0.122020i | 0.999504 | + | 0.0315055i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.0532613 | − | 0.0532613i | −0.0129178 | − | 0.0129178i | 0.700618 | − | 0.713536i | \(-0.252908\pi\) |
−0.713536 | + | 0.700618i | \(0.752908\pi\) | |||||||
\(18\) | −2.95292 | − | 0.529408i | −0.696010 | − | 0.124783i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −0.736229 | + | 2.11139i | −0.164626 | + | 0.472121i | ||||
\(21\) | −2.76865 | + | 5.29997i | −0.604168 | + | 1.15655i | ||||
\(22\) | 3.97477 | − | 3.97477i | 0.847424 | − | 0.847424i | ||||
\(23\) | 0.841693 | − | 0.841693i | 0.175505 | − | 0.175505i | −0.613888 | − | 0.789393i | \(-0.710395\pi\) |
0.789393 | + | 0.613888i | \(0.210395\pi\) | |||||||
\(24\) | 0.801972 | − | 1.53520i | 0.163702 | − | 0.313371i | ||||
\(25\) | 3.91593 | + | 3.10893i | 0.783187 | + | 0.621786i | ||||
\(26\) | − | 1.32067i | − | 0.259004i | ||||||
\(27\) | 3.18091 | − | 4.10875i | 0.612166 | − | 0.790730i | ||||
\(28\) | −2.44114 | − | 2.44114i | −0.461332 | − | 0.461332i | ||||
\(29\) | 6.56484 | 1.21906 | 0.609530 | − | 0.792763i | \(-0.291358\pi\) | ||||
0.609530 | + | 0.792763i | \(0.291358\pi\) | |||||||
\(30\) | −2.65097 | − | 2.82353i | −0.483999 | − | 0.515505i | ||||
\(31\) | −5.11218 | −0.918175 | −0.459087 | − | 0.888391i | \(-0.651824\pi\) | ||||
−0.459087 | + | 0.888391i | \(0.651824\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 2.91441 | + | 9.28973i | 0.507335 | + | 1.61713i | ||||
\(34\) | 0.0753229i | 0.0129178i | ||||||||
\(35\) | −6.95144 | + | 3.35696i | −1.17501 | + | 0.567430i | ||||
\(36\) | 1.71368 | + | 2.46238i | 0.285614 | + | 0.410396i | ||||
\(37\) | −5.88633 | + | 5.88633i | −0.967707 | + | 0.967707i | −0.999495 | − | 0.0317880i | \(-0.989880\pi\) |
0.0317880 | + | 0.999495i | \(0.489880\pi\) | |||||||
\(38\) | −0.707107 | + | 0.707107i | −0.114708 | + | 0.114708i | ||||
\(39\) | 2.02749 | + | 1.05914i | 0.324658 | + | 0.169598i | ||||
\(40\) | 2.01357 | − | 0.972386i | 0.318373 | − | 0.153748i | ||||
\(41\) | − | 5.75913i | − | 0.899426i | −0.893173 | − | 0.449713i | \(-0.851526\pi\) | ||
0.893173 | − | 0.449713i | \(-0.148474\pi\) | |||||||
\(42\) | 5.70537 | − | 1.78991i | 0.880358 | − | 0.276190i | ||||
\(43\) | −7.57828 | − | 7.57828i | −1.15568 | − | 1.15568i | −0.985395 | − | 0.170282i | \(-0.945532\pi\) |
−0.170282 | − | 0.985395i | \(-0.554468\pi\) | |||||||
\(44\) | −5.62118 | −0.847424 | ||||||||
\(45\) | 6.46070 | − | 1.80538i | 0.963104 | − | 0.269130i | ||||
\(46\) | −1.19033 | −0.175505 | ||||||||
\(47\) | −2.64154 | − | 2.64154i | −0.385308 | − | 0.385308i | 0.487702 | − | 0.873010i | \(-0.337835\pi\) |
−0.873010 | + | 0.487702i | \(0.837835\pi\) | |||||||
\(48\) | −1.65263 | + | 0.518471i | −0.238537 | + | 0.0748348i | ||||
\(49\) | − | 4.91834i | − | 0.702620i | ||||||
\(50\) | −0.570637 | − | 4.96733i | −0.0807003 | − | 0.702487i | ||||
\(51\) | −0.115636 | − | 0.0604069i | −0.0161922 | − | 0.00845865i | ||||
\(52\) | −0.933851 | + | 0.933851i | −0.129502 | + | 0.129502i | ||||
\(53\) | 9.67459 | − | 9.67459i | 1.32891 | − | 1.32891i | 0.422583 | − | 0.906324i | \(-0.361124\pi\) |
0.906324 | − | 0.422583i | \(-0.138876\pi\) | |||||||
\(54\) | −5.15457 | + | 0.656086i | −0.701448 | + | 0.0892821i | ||||
\(55\) | −4.13847 | + | 11.8685i | −0.558031 | + | 1.60035i | ||||
\(56\) | 3.45230i | 0.461332i | ||||||||
\(57\) | −0.518471 | − | 1.65263i | −0.0686731 | − | 0.218896i | ||||
\(58\) | −4.64204 | − | 4.64204i | −0.609530 | − | 0.609530i | ||||
\(59\) | 11.0697 | 1.44116 | 0.720579 | − | 0.693373i | \(-0.243876\pi\) | ||||
0.720579 | + | 0.693373i | \(0.243876\pi\) | |||||||
\(60\) | −0.122020 | + | 3.87106i | −0.0157528 | + | 0.499752i | ||||
\(61\) | 9.82484 | 1.25794 | 0.628971 | − | 0.777429i | \(-0.283476\pi\) | ||||
0.628971 | + | 0.777429i | \(0.283476\pi\) | |||||||
\(62\) | 3.61486 | + | 3.61486i | 0.459087 | + | 0.459087i | ||||
\(63\) | −1.82767 | + | 10.1943i | −0.230265 | + | 1.28437i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 1.28420 | + | 2.65925i | 0.159285 | + | 0.329840i | ||||
\(66\) | 4.50803 | − | 8.62963i | 0.554900 | − | 1.06223i | ||||
\(67\) | 6.27631 | − | 6.27631i | 0.766774 | − | 0.766774i | −0.210764 | − | 0.977537i | \(-0.567595\pi\) |
0.977537 | + | 0.210764i | \(0.0675950\pi\) | |||||||
\(68\) | 0.0532613 | − | 0.0532613i | 0.00645888 | − | 0.00645888i | ||||
\(69\) | 0.954615 | − | 1.82740i | 0.114922 | − | 0.219993i | ||||
\(70\) | 7.28914 | + | 2.54168i | 0.871219 | + | 0.303789i | ||||
\(71\) | 2.29302i | 0.272131i | 0.990700 | + | 0.136066i | \(0.0434458\pi\) | ||||
−0.990700 | + | 0.136066i | \(0.956554\pi\) | |||||||
\(72\) | 0.529408 | − | 2.95292i | 0.0623913 | − | 0.348005i | ||||
\(73\) | −7.35442 | − | 7.35442i | −0.860770 | − | 0.860770i | 0.130658 | − | 0.991428i | \(-0.458291\pi\) |
−0.991428 | + | 0.130658i | \(0.958291\pi\) | |||||||
\(74\) | 8.32453 | 0.967707 | ||||||||
\(75\) | 8.08348 | + | 3.10762i | 0.933400 | + | 0.358837i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −13.7221 | − | 13.7221i | −1.56378 | − | 1.56378i | ||||
\(78\) | −0.684726 | − | 2.18257i | −0.0775300 | − | 0.247128i | ||||
\(79\) | − | 3.41806i | − | 0.384561i | −0.981340 | − | 0.192281i | \(-0.938412\pi\) | ||
0.981340 | − | 0.192281i | \(-0.0615884\pi\) | |||||||
\(80\) | −2.11139 | − | 0.736229i | −0.236061 | − | 0.0823129i | ||||
\(81\) | 3.12659 | − | 8.43946i | 0.347399 | − | 0.937717i | ||||
\(82\) | −4.07232 | + | 4.07232i | −0.449713 | + | 0.449713i | ||||
\(83\) | −4.84479 | + | 4.84479i | −0.531785 | + | 0.531785i | −0.921103 | − | 0.389318i | \(-0.872711\pi\) |
0.389318 | + | 0.921103i | \(0.372711\pi\) | |||||||
\(84\) | −5.29997 | − | 2.76865i | −0.578274 | − | 0.302084i | ||||
\(85\) | −0.0732429 | − | 0.151668i | −0.00794431 | − | 0.0164507i | ||||
\(86\) | 10.7173i | 1.15568i | ||||||||
\(87\) | 10.8493 | − | 3.40368i | 1.16316 | − | 0.364912i | ||||
\(88\) | 3.97477 | + | 3.97477i | 0.423712 | + | 0.423712i | ||||
\(89\) | −4.69409 | −0.497572 | −0.248786 | − | 0.968558i | \(-0.580032\pi\) | ||||
−0.248786 | + | 0.968558i | \(0.580032\pi\) | |||||||
\(90\) | −5.84500 | − | 3.29181i | −0.616117 | − | 0.346987i | ||||
\(91\) | −4.55933 | −0.477947 | ||||||||
\(92\) | 0.841693 | + | 0.841693i | 0.0877526 | + | 0.0877526i | ||||
\(93\) | −8.44855 | + | 2.65052i | −0.876073 | + | 0.274846i | ||||
\(94\) | 3.73570i | 0.385308i | ||||||||
\(95\) | 0.736229 | − | 2.11139i | 0.0755355 | − | 0.216624i | ||||
\(96\) | 1.53520 | + | 0.801972i | 0.156686 | + | 0.0818509i | ||||
\(97\) | −4.18214 | + | 4.18214i | −0.424632 | + | 0.424632i | −0.886795 | − | 0.462163i | \(-0.847073\pi\) |
0.462163 | + | 0.886795i | \(0.347073\pi\) | |||||||
\(98\) | −3.47779 | + | 3.47779i | −0.351310 | + | 0.351310i | ||||
\(99\) | 9.63290 | + | 13.8415i | 0.968143 | + | 1.39112i | ||||
\(100\) | −3.10893 | + | 3.91593i | −0.310893 | + | 0.391593i | ||||
\(101\) | − | 0.845280i | − | 0.0841085i | −0.999115 | − | 0.0420543i | \(-0.986610\pi\) | ||
0.999115 | − | 0.0420543i | \(-0.0133902\pi\) | |||||||
\(102\) | 0.0390527 | + | 0.124481i | 0.00386679 | + | 0.0123254i | ||||
\(103\) | 1.72028 | + | 1.72028i | 0.169505 | + | 0.169505i | 0.786762 | − | 0.617257i | \(-0.211756\pi\) |
−0.617257 | + | 0.786762i | \(0.711756\pi\) | |||||||
\(104\) | 1.32067 | 0.129502 | ||||||||
\(105\) | −9.74768 | + | 9.15194i | −0.951276 | + | 0.893138i | ||||
\(106\) | −13.6819 | −1.32891 | ||||||||
\(107\) | −6.17999 | − | 6.17999i | −0.597442 | − | 0.597442i | 0.342189 | − | 0.939631i | \(-0.388832\pi\) |
−0.939631 | + | 0.342189i | \(0.888832\pi\) | |||||||
\(108\) | 4.10875 | + | 3.18091i | 0.395365 | + | 0.306083i | ||||
\(109\) | 13.7634i | 1.31830i | 0.752012 | + | 0.659149i | \(0.229083\pi\) | ||||
−0.752012 | + | 0.659149i | \(0.770917\pi\) | |||||||
\(110\) | 11.3186 | − | 5.46595i | 1.07919 | − | 0.521158i | ||||
\(111\) | −6.67604 | + | 12.7798i | −0.633662 | + | 1.21301i | ||||
\(112\) | 2.44114 | − | 2.44114i | 0.230666 | − | 0.230666i | ||||
\(113\) | 13.5833 | − | 13.5833i | 1.27781 | − | 1.27781i | 0.335915 | − | 0.941892i | \(-0.390955\pi\) |
0.941892 | − | 0.335915i | \(-0.109045\pi\) | |||||||
\(114\) | −0.801972 | + | 1.53520i | −0.0751116 | + | 0.143785i | ||||
\(115\) | 2.39682 | − | 1.15746i | 0.223505 | − | 0.107934i | ||||
\(116\) | 6.56484i | 0.609530i | ||||||||
\(117\) | 3.89982 | + | 0.699170i | 0.360538 | + | 0.0646383i | ||||
\(118\) | −7.82749 | − | 7.82749i | −0.720579 | − | 0.720579i | ||||
\(119\) | 0.260037 | 0.0238375 | ||||||||
\(120\) | 2.82353 | − | 2.65097i | 0.257752 | − | 0.242000i | ||||
\(121\) | −20.5976 | −1.87251 | ||||||||
\(122\) | −6.94721 | − | 6.94721i | −0.628971 | − | 0.628971i | ||||
\(123\) | −2.98594 | − | 9.51772i | −0.269233 | − | 0.858184i | ||||
\(124\) | − | 5.11218i | − | 0.459087i | ||||||
\(125\) | 5.97918 | + | 9.44719i | 0.534794 | + | 0.844982i | ||||
\(126\) | 8.50085 | − | 5.91613i | 0.757316 | − | 0.527051i | ||||
\(127\) | −4.84183 | + | 4.84183i | −0.429643 | + | 0.429643i | −0.888507 | − | 0.458864i | \(-0.848257\pi\) |
0.458864 | + | 0.888507i | \(0.348257\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −16.4532 | − | 8.59499i | −1.44863 | − | 0.756746i | ||||
\(130\) | 0.972312 | − | 2.78844i | 0.0852774 | − | 0.244562i | ||||
\(131\) | 0.132969i | 0.0116176i | 0.999983 | + | 0.00580880i | \(0.00184901\pi\) | ||||
−0.999983 | + | 0.00580880i | \(0.998151\pi\) | |||||||
\(132\) | −9.28973 | + | 2.91441i | −0.808567 | + | 0.253667i | ||||
\(133\) | 2.44114 | + | 2.44114i | 0.211674 | + | 0.211674i | ||||
\(134\) | −8.87605 | −0.766774 | ||||||||
\(135\) | 9.74111 | − | 6.33330i | 0.838381 | − | 0.545084i | ||||
\(136\) | −0.0753229 | −0.00645888 | ||||||||
\(137\) | −11.8447 | − | 11.8447i | −1.01196 | − | 1.01196i | −0.999928 | − | 0.0120322i | \(-0.996170\pi\) |
−0.0120322 | − | 0.999928i | \(-0.503830\pi\) | |||||||
\(138\) | −1.96718 | + | 0.617153i | −0.167458 | + | 0.0525356i | ||||
\(139\) | 11.4478i | 0.970986i | 0.874241 | + | 0.485493i | \(0.161360\pi\) | ||||
−0.874241 | + | 0.485493i | \(0.838640\pi\) | |||||||
\(140\) | −3.35696 | − | 6.95144i | −0.283715 | − | 0.587504i | ||||
\(141\) | −5.73505 | − | 2.99593i | −0.482978 | − | 0.252303i | ||||
\(142\) | 1.62141 | − | 1.62141i | 0.136066 | − | 0.136066i | ||||
\(143\) | −5.24934 | + | 5.24934i | −0.438972 | + | 0.438972i | ||||
\(144\) | −2.46238 | + | 1.71368i | −0.205198 | + | 0.142807i | ||||
\(145\) | 13.8609 | + | 4.83322i | 1.15109 | + | 0.401377i | ||||
\(146\) | 10.4007i | 0.860770i | ||||||||
\(147\) | −2.55002 | − | 8.12820i | −0.210322 | − | 0.670403i | ||||
\(148\) | −5.88633 | − | 5.88633i | −0.483853 | − | 0.483853i | ||||
\(149\) | −21.7749 | −1.78387 | −0.891934 | − | 0.452165i | \(-0.850652\pi\) | ||||
−0.891934 | + | 0.452165i | \(0.850652\pi\) | |||||||
\(150\) | −3.51847 | − | 7.91330i | −0.287282 | − | 0.646119i | ||||
\(151\) | −12.9880 | −1.05694 | −0.528472 | − | 0.848951i | \(-0.677235\pi\) | ||||
−0.528472 | + | 0.848951i | \(0.677235\pi\) | |||||||
\(152\) | −0.707107 | − | 0.707107i | −0.0573539 | − | 0.0573539i | ||||
\(153\) | −0.222422 | − | 0.0398765i | −0.0179818 | − | 0.00322382i | ||||
\(154\) | 19.4060i | 1.56378i | ||||||||
\(155\) | −10.7938 | − | 3.76373i | −0.866979 | − | 0.302310i | ||||
\(156\) | −1.05914 | + | 2.02749i | −0.0847988 | + | 0.162329i | ||||
\(157\) | 10.2762 | − | 10.2762i | 0.820131 | − | 0.820131i | −0.165995 | − | 0.986127i | \(-0.553084\pi\) |
0.986127 | + | 0.165995i | \(0.0530837\pi\) | |||||||
\(158\) | −2.41693 | + | 2.41693i | −0.192281 | + | 0.192281i | ||||
\(159\) | 10.9725 | − | 21.0045i | 0.870178 | − | 1.66577i | ||||
\(160\) | 0.972386 | + | 2.01357i | 0.0768738 | + | 0.159187i | ||||
\(161\) | 4.10938i | 0.323865i | ||||||||
\(162\) | −8.17843 | + | 3.75676i | −0.642558 | + | 0.295159i | ||||
\(163\) | 4.97451 | + | 4.97451i | 0.389634 | + | 0.389634i | 0.874557 | − | 0.484923i | \(-0.161152\pi\) |
−0.484923 | + | 0.874557i | \(0.661152\pi\) | |||||||
\(164\) | 5.75913 | 0.449713 | ||||||||
\(165\) | −0.685899 | + | 21.7599i | −0.0533971 | + | 1.69401i | ||||
\(166\) | 6.85157 | 0.531785 | ||||||||
\(167\) | −11.3116 | − | 11.3116i | −0.875319 | − | 0.875319i | 0.117727 | − | 0.993046i | \(-0.462439\pi\) |
−0.993046 | + | 0.117727i | \(0.962439\pi\) | |||||||
\(168\) | 1.78991 | + | 5.70537i | 0.138095 | + | 0.440179i | ||||
\(169\) | − | 11.2558i | − | 0.865834i | ||||||
\(170\) | −0.0554549 | + | 0.159036i | −0.00425319 | + | 0.0121975i | ||||
\(171\) | −1.71368 | − | 2.46238i | −0.131048 | − | 0.188303i | ||||
\(172\) | 7.57828 | − | 7.57828i | 0.577839 | − | 0.577839i | ||||
\(173\) | −16.5624 | + | 16.5624i | −1.25921 | + | 1.25921i | −0.307746 | + | 0.951468i | \(0.599575\pi\) |
−0.951468 | + | 0.307746i | \(0.900425\pi\) | |||||||
\(174\) | −10.0783 | − | 5.26482i | −0.764037 | − | 0.399125i | ||||
\(175\) | −17.1487 | + | 1.97001i | −1.29632 | + | 0.148919i | ||||
\(176\) | − | 5.62118i | − | 0.423712i | ||||||
\(177\) | 18.2942 | − | 5.73934i | 1.37508 | − | 0.431395i | ||||
\(178\) | 3.31922 | + | 3.31922i | 0.248786 | + | 0.248786i | ||||
\(179\) | 13.4740 | 1.00710 | 0.503549 | − | 0.863967i | \(-0.332027\pi\) | ||||
0.503549 | + | 0.863967i | \(0.332027\pi\) | |||||||
\(180\) | 1.80538 | + | 6.46070i | 0.134565 | + | 0.481552i | ||||
\(181\) | 10.4967 | 0.780217 | 0.390108 | − | 0.920769i | \(-0.372438\pi\) | ||||
0.390108 | + | 0.920769i | \(0.372438\pi\) | |||||||
\(182\) | 3.22393 | + | 3.22393i | 0.238974 | + | 0.238974i | ||||
\(183\) | 16.2368 | − | 5.09389i | 1.20026 | − | 0.376551i | ||||
\(184\) | − | 1.19033i | − | 0.0877526i | ||||||
\(185\) | −16.7620 | + | 8.09465i | −1.23237 | + | 0.595131i | ||||
\(186\) | 7.84822 | + | 4.09983i | 0.575460 | + | 0.300614i | ||||
\(187\) | 0.299391 | − | 0.299391i | 0.0218937 | − | 0.0218937i | ||||
\(188\) | 2.64154 | − | 2.64154i | 0.192654 | − | 0.192654i | ||||
\(189\) | 2.26500 | + | 17.7951i | 0.164755 | + | 1.29440i | ||||
\(190\) | −2.01357 | + | 0.972386i | −0.146080 | + | 0.0705443i | ||||
\(191\) | 16.2464i | 1.17555i | 0.809024 | + | 0.587775i | \(0.199996\pi\) | ||||
−0.809024 | + | 0.587775i | \(0.800004\pi\) | |||||||
\(192\) | −0.518471 | − | 1.65263i | −0.0374174 | − | 0.119268i | ||||
\(193\) | −2.23569 | − | 2.23569i | −0.160928 | − | 0.160928i | 0.622049 | − | 0.782978i | \(-0.286300\pi\) |
−0.782978 | + | 0.622049i | \(0.786300\pi\) | |||||||
\(194\) | 5.91443 | 0.424632 | ||||||||
\(195\) | 3.50105 | + | 3.72894i | 0.250715 | + | 0.267035i | ||||
\(196\) | 4.91834 | 0.351310 | ||||||||
\(197\) | 5.51445 | + | 5.51445i | 0.392889 | + | 0.392889i | 0.875716 | − | 0.482827i | \(-0.160390\pi\) |
−0.482827 | + | 0.875716i | \(0.660390\pi\) | |||||||
\(198\) | 2.97589 | − | 16.5989i | 0.211488 | − | 1.17963i | ||||
\(199\) | 22.3312i | 1.58302i | 0.611159 | + | 0.791508i | \(0.290703\pi\) | ||||
−0.611159 | + | 0.791508i | \(0.709297\pi\) | |||||||
\(200\) | 4.96733 | − | 0.570637i | 0.351243 | − | 0.0403501i | ||||
\(201\) | 7.11834 | − | 13.6265i | 0.502089 | − | 0.961140i | ||||
\(202\) | −0.597703 | + | 0.597703i | −0.0420543 | + | 0.0420543i | ||||
\(203\) | −16.0257 | + | 16.0257i | −1.12478 | + | 1.12478i | ||||
\(204\) | 0.0604069 | − | 0.115636i | 0.00422933 | − | 0.00809612i | ||||
\(205\) | 4.24004 | − | 12.1598i | 0.296137 | − | 0.849276i | ||||
\(206\) | − | 2.43285i | − | 0.169505i | ||||||
\(207\) | 0.630172 | − | 3.51496i | 0.0438000 | − | 0.244307i | ||||
\(208\) | −0.933851 | − | 0.933851i | −0.0647509 | − | 0.0647509i | ||||
\(209\) | 5.62118 | 0.388825 | ||||||||
\(210\) | 13.3640 | + | 0.421251i | 0.922207 | + | 0.0290691i | ||||
\(211\) | −4.91417 | −0.338305 | −0.169153 | − | 0.985590i | \(-0.554103\pi\) | ||||
−0.169153 | + | 0.985590i | \(0.554103\pi\) | |||||||
\(212\) | 9.67459 | + | 9.67459i | 0.664454 | + | 0.664454i | ||||
\(213\) | 1.18886 | + | 3.78951i | 0.0814595 | + | 0.259653i | ||||
\(214\) | 8.73982i | 0.597442i | ||||||||
\(215\) | −10.4214 | − | 21.5801i | −0.710731 | − | 1.47175i | ||||
\(216\) | −0.656086 | − | 5.15457i | −0.0446410 | − | 0.350724i | ||||
\(217\) | 12.4796 | − | 12.4796i | 0.847167 | − | 0.847167i | ||||
\(218\) | 9.73222 | − | 9.73222i | 0.659149 | − | 0.659149i | ||||
\(219\) | −15.9672 | − | 8.34109i | −1.07896 | − | 0.563639i | ||||
\(220\) | −11.8685 | − | 4.13847i | −0.800174 | − | 0.279016i | ||||
\(221\) | − | 0.0994763i | − | 0.00669150i | ||||||
\(222\) | 13.7574 | − | 4.31602i | 0.923334 | − | 0.289673i | ||||
\(223\) | −6.07075 | − | 6.07075i | −0.406527 | − | 0.406527i | 0.473998 | − | 0.880526i | \(-0.342810\pi\) |
−0.880526 | + | 0.473998i | \(0.842810\pi\) | |||||||
\(224\) | −3.45230 | −0.230666 | ||||||||
\(225\) | 14.9702 | + | 0.944697i | 0.998015 | + | 0.0629798i | ||||
\(226\) | −19.2097 | −1.27781 | ||||||||
\(227\) | 12.5348 | + | 12.5348i | 0.831965 | + | 0.831965i | 0.987785 | − | 0.155820i | \(-0.0498021\pi\) |
−0.155820 | + | 0.987785i | \(0.549802\pi\) | |||||||
\(228\) | 1.65263 | − | 0.518471i | 0.109448 | − | 0.0343366i | ||||
\(229\) | − | 4.03489i | − | 0.266633i | −0.991073 | − | 0.133317i | \(-0.957437\pi\) | ||
0.991073 | − | 0.133317i | \(-0.0425627\pi\) | |||||||
\(230\) | −2.51326 | − | 0.876358i | −0.165719 | − | 0.0577853i | ||||
\(231\) | −29.7920 | − | 15.5630i | −1.96017 | − | 1.02397i | ||||
\(232\) | 4.64204 | − | 4.64204i | 0.304765 | − | 0.304765i | ||||
\(233\) | 13.7826 | − | 13.7826i | 0.902931 | − | 0.902931i | −0.0927575 | − | 0.995689i | \(-0.529568\pi\) |
0.995689 | + | 0.0927575i | \(0.0295681\pi\) | |||||||
\(234\) | −2.26320 | − | 3.25198i | −0.147950 | − | 0.212588i | ||||
\(235\) | −3.63254 | − | 7.52210i | −0.236961 | − | 0.490688i | ||||
\(236\) | 11.0697i | 0.720579i | ||||||||
\(237\) | −1.77216 | − | 5.64879i | −0.115114 | − | 0.366928i | ||||
\(238\) | −0.183874 | − | 0.183874i | −0.0119188 | − | 0.0119188i | ||||
\(239\) | 0.604284 | 0.0390879 | 0.0195439 | − | 0.999809i | \(-0.493779\pi\) | ||||
0.0195439 | + | 0.999809i | \(0.493779\pi\) | |||||||
\(240\) | −3.87106 | − | 0.122020i | −0.249876 | − | 0.00787639i | ||||
\(241\) | −1.64307 | −0.105839 | −0.0529196 | − | 0.998599i | \(-0.516853\pi\) | ||||
−0.0529196 | + | 0.998599i | \(0.516853\pi\) | |||||||
\(242\) | 14.5647 | + | 14.5647i | 0.936255 | + | 0.936255i | ||||
\(243\) | 0.791496 | − | 15.5684i | 0.0507745 | − | 0.998710i | ||||
\(244\) | 9.82484i | 0.628971i | ||||||||
\(245\) | 3.62103 | − | 10.3845i | 0.231339 | − | 0.663444i | ||||
\(246\) | −4.61867 | + | 8.84143i | −0.294475 | + | 0.563709i | ||||
\(247\) | 0.933851 | − | 0.933851i | 0.0594195 | − | 0.0594195i | ||||
\(248\) | −3.61486 | + | 3.61486i | −0.229544 | + | 0.229544i | ||||
\(249\) | −5.49477 | + | 10.5185i | −0.348217 | + | 0.666585i | ||||
\(250\) | 2.45225 | − | 10.9081i | 0.155094 | − | 0.689888i | ||||
\(251\) | − | 0.800477i | − | 0.0505256i | −0.999681 | − | 0.0252628i | \(-0.991958\pi\) | ||
0.999681 | − | 0.0252628i | \(-0.00804226\pi\) | |||||||
\(252\) | −10.1943 | − | 1.82767i | −0.642183 | − | 0.115132i | ||||
\(253\) | 4.73131 | + | 4.73131i | 0.297455 | + | 0.297455i | ||||
\(254\) | 6.84738 | 0.429643 | ||||||||
\(255\) | −0.199679 | − | 0.212677i | −0.0125044 | − | 0.0133183i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.187825 | − | 0.187825i | −0.0117162 | − | 0.0117162i | 0.701224 | − | 0.712941i | \(-0.252637\pi\) |
−0.712941 | + | 0.701224i | \(0.752637\pi\) | |||||||
\(258\) | 5.55661 | + | 17.7118i | 0.345940 | + | 1.10269i | ||||
\(259\) | − | 28.7387i | − | 1.78574i | ||||||
\(260\) | −2.65925 | + | 1.28420i | −0.164920 | + | 0.0796425i | ||||
\(261\) | 16.1651 | − | 11.2500i | 1.00059 | − | 0.696360i | ||||
\(262\) | 0.0940236 | − | 0.0940236i | 0.00580880 | − | 0.00580880i | ||||
\(263\) | −0.0979650 | + | 0.0979650i | −0.00604078 | + | 0.00604078i | −0.710121 | − | 0.704080i | \(-0.751360\pi\) |
0.704080 | + | 0.710121i | \(0.251360\pi\) | |||||||
\(264\) | 8.62963 | + | 4.50803i | 0.531117 | + | 0.277450i | ||||
\(265\) | 27.5495 | − | 13.3041i | 1.69235 | − | 0.817266i | ||||
\(266\) | − | 3.45230i | − | 0.211674i | ||||||
\(267\) | −7.75759 | + | 2.43375i | −0.474757 | + | 0.148943i | ||||
\(268\) | 6.27631 | + | 6.27631i | 0.383387 | + | 0.383387i | ||||
\(269\) | 15.3546 | 0.936185 | 0.468093 | − | 0.883679i | \(-0.344941\pi\) | ||||
0.468093 | + | 0.883679i | \(0.344941\pi\) | |||||||
\(270\) | −11.3663 | − | 2.40969i | −0.691733 | − | 0.146649i | ||||
\(271\) | 8.91573 | 0.541592 | 0.270796 | − | 0.962637i | \(-0.412713\pi\) | ||||
0.270796 | + | 0.962637i | \(0.412713\pi\) | |||||||
\(272\) | 0.0532613 | + | 0.0532613i | 0.00322944 | + | 0.00322944i | ||||
\(273\) | −7.53488 | + | 2.36388i | −0.456032 | + | 0.143068i | ||||
\(274\) | 16.7509i | 1.01196i | ||||||||
\(275\) | −17.4759 | + | 22.0122i | −1.05383 | + | 1.32738i | ||||
\(276\) | 1.82740 | + | 0.954615i | 0.109997 | + | 0.0574611i | ||||
\(277\) | −5.23704 | + | 5.23704i | −0.314663 | + | 0.314663i | −0.846713 | − | 0.532050i | \(-0.821422\pi\) |
0.532050 | + | 0.846713i | \(0.321422\pi\) | |||||||
\(278\) | 8.09478 | − | 8.09478i | 0.485493 | − | 0.485493i | ||||
\(279\) | −12.5881 | + | 8.76065i | −0.753631 | + | 0.524486i | ||||
\(280\) | −2.54168 | + | 7.28914i | −0.151894 | + | 0.435610i | ||||
\(281\) | − | 1.07688i | − | 0.0642410i | −0.999484 | − | 0.0321205i | \(-0.989774\pi\) | ||
0.999484 | − | 0.0321205i | \(-0.0102260\pi\) | |||||||
\(282\) | 1.93685 | + | 6.17374i | 0.115338 | + | 0.367641i | ||||
\(283\) | −13.3657 | − | 13.3657i | −0.794508 | − | 0.794508i | 0.187715 | − | 0.982223i | \(-0.439892\pi\) |
−0.982223 | + | 0.187715i | \(0.939892\pi\) | |||||||
\(284\) | −2.29302 | −0.136066 | ||||||||
\(285\) | 0.122020 | − | 3.87106i | 0.00722787 | − | 0.229302i | ||||
\(286\) | 7.42369 | 0.438972 | ||||||||
\(287\) | 14.0589 | + | 14.0589i | 0.829868 | + | 0.829868i | ||||
\(288\) | 2.95292 | + | 0.529408i | 0.174002 | + | 0.0311956i | ||||
\(289\) | − | 16.9943i | − | 0.999666i | ||||||
\(290\) | −6.38356 | − | 13.2188i | −0.374855 | − | 0.776233i | ||||
\(291\) | −4.74321 | + | 9.07984i | −0.278052 | + | 0.532270i | ||||
\(292\) | 7.35442 | − | 7.35442i | 0.430385 | − | 0.430385i | ||||
\(293\) | 0.952778 | − | 0.952778i | 0.0556619 | − | 0.0556619i | −0.678728 | − | 0.734390i | \(-0.737468\pi\) |
0.734390 | + | 0.678728i | \(0.237468\pi\) | |||||||
\(294\) | −3.94437 | + | 7.55064i | −0.230041 | + | 0.440362i | ||||
\(295\) | 23.3726 | + | 8.14987i | 1.36080 | + | 0.474503i | ||||
\(296\) | 8.32453i | 0.483853i | ||||||||
\(297\) | 23.0960 | + | 17.8804i | 1.34017 | + | 1.03753i | ||||
\(298\) | 15.3972 | + | 15.3972i | 0.891934 | + | 0.891934i | ||||
\(299\) | 1.57203 | 0.0909130 | ||||||||
\(300\) | −3.10762 | + | 8.08348i | −0.179418 | + | 0.466700i | ||||
\(301\) | 36.9993 | 2.13261 | ||||||||
\(302\) | 9.18387 | + | 9.18387i | 0.528472 | + | 0.528472i | ||||
\(303\) | −0.438253 | − | 1.39694i | −0.0251770 | − | 0.0802519i | ||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | 20.7441 | + | 7.23333i | 1.18780 | + | 0.414179i | ||||
\(306\) | 0.129079 | + | 0.185473i | 0.00737898 | + | 0.0106028i | ||||
\(307\) | 12.7740 | − | 12.7740i | 0.729052 | − | 0.729052i | −0.241379 | − | 0.970431i | \(-0.577600\pi\) |
0.970431 | + | 0.241379i | \(0.0775997\pi\) | |||||||
\(308\) | 13.7221 | − | 13.7221i | 0.781888 | − | 0.781888i | ||||
\(309\) | 3.73491 | + | 1.95108i | 0.212472 | + | 0.110993i | ||||
\(310\) | 4.97101 | + | 10.2937i | 0.282334 | + | 0.584645i | ||||
\(311\) | − | 6.21244i | − | 0.352275i | −0.984366 | − | 0.176138i | \(-0.943640\pi\) | ||
0.984366 | − | 0.176138i | \(-0.0563604\pi\) | |||||||
\(312\) | 2.18257 | − | 0.684726i | 0.123564 | − | 0.0387650i | ||||
\(313\) | −1.38773 | − | 1.38773i | −0.0784393 | − | 0.0784393i | 0.666799 | − | 0.745238i | \(-0.267664\pi\) |
−0.745238 | + | 0.666799i | \(0.767664\pi\) | |||||||
\(314\) | −14.5328 | −0.820131 | ||||||||
\(315\) | −11.3643 | + | 20.1787i | −0.640306 | + | 1.13694i | ||||
\(316\) | 3.41806 | 0.192281 | ||||||||
\(317\) | 6.17490 | + | 6.17490i | 0.346817 | + | 0.346817i | 0.858922 | − | 0.512106i | \(-0.171134\pi\) |
−0.512106 | + | 0.858922i | \(0.671134\pi\) | |||||||
\(318\) | −22.6112 | + | 7.09368i | −1.26797 | + | 0.397794i | ||||
\(319\) | 36.9021i | 2.06612i | ||||||||
\(320\) | 0.736229 | − | 2.11139i | 0.0411564 | − | 0.118030i | ||||
\(321\) | −13.4174 | − | 7.00910i | −0.748885 | − | 0.391210i | ||||
\(322\) | 2.90577 | − | 2.90577i | 0.161932 | − | 0.161932i | ||||
\(323\) | −0.0532613 | + | 0.0532613i | −0.00296354 | + | 0.00296354i | ||||
\(324\) | 8.43946 | + | 3.12659i | 0.468859 | + | 0.173700i | ||||
\(325\) | 0.753621 | + | 6.56018i | 0.0418034 | + | 0.363893i | ||||
\(326\) | − | 7.03502i | − | 0.389634i | ||||||
\(327\) | 7.13594 | + | 22.7459i | 0.394618 | + | 1.25785i | ||||
\(328\) | −4.07232 | − | 4.07232i | −0.224856 | − | 0.224856i | ||||
\(329\) | 12.8967 | 0.711021 | ||||||||
\(330\) | 15.8716 | − | 14.9016i | 0.873702 | − | 0.820305i | ||||
\(331\) | 9.52357 | 0.523463 | 0.261731 | − | 0.965141i | \(-0.415707\pi\) | ||||
0.261731 | + | 0.965141i | \(0.415707\pi\) | |||||||
\(332\) | −4.84479 | − | 4.84479i | −0.265892 | − | 0.265892i | ||||
\(333\) | −4.40707 | + | 24.5817i | −0.241506 | + | 1.34707i | ||||
\(334\) | 15.9970i | 0.875319i | ||||||||
\(335\) | 17.8725 | − | 8.63094i | 0.976481 | − | 0.471559i | ||||
\(336\) | 2.76865 | − | 5.29997i | 0.151042 | − | 0.289137i | ||||
\(337\) | −16.6674 | + | 16.6674i | −0.907932 | + | 0.907932i | −0.996105 | − | 0.0881729i | \(-0.971897\pi\) |
0.0881729 | + | 0.996105i | \(0.471897\pi\) | |||||||
\(338\) | −7.95908 | + | 7.95908i | −0.432917 | + | 0.432917i | ||||
\(339\) | 15.4056 | − | 29.4907i | 0.836718 | − | 1.60171i | ||||
\(340\) | 0.151668 | − | 0.0732429i | 0.00822535 | − | 0.00397215i | ||||
\(341\) | − | 28.7365i | − | 1.55617i | ||||||
\(342\) | −0.529408 | + | 2.95292i | −0.0286271 | + | 0.159676i | ||||
\(343\) | −5.08162 | − | 5.08162i | −0.274382 | − | 0.274382i | ||||
\(344\) | −10.7173 | −0.577839 | ||||||||
\(345\) | 3.36095 | − | 3.15554i | 0.180947 | − | 0.169889i | ||||
\(346\) | 23.4227 | 1.25921 | ||||||||
\(347\) | −7.59916 | − | 7.59916i | −0.407944 | − | 0.407944i | 0.473077 | − | 0.881021i | \(-0.343143\pi\) |
−0.881021 | + | 0.473077i | \(0.843143\pi\) | |||||||
\(348\) | 3.40368 | + | 10.8493i | 0.182456 | + | 0.581581i | ||||
\(349\) | − | 9.65125i | − | 0.516619i | −0.966062 | − | 0.258310i | \(-0.916835\pi\) | ||
0.966062 | − | 0.258310i | \(-0.0831655\pi\) | |||||||
\(350\) | 13.5190 | + | 10.7330i | 0.722619 | + | 0.573700i | ||||
\(351\) | 6.80746 | − | 0.866471i | 0.363355 | − | 0.0462488i | ||||
\(352\) | −3.97477 | + | 3.97477i | −0.211856 | + | 0.211856i | ||||
\(353\) | 1.80197 | − | 1.80197i | 0.0959090 | − | 0.0959090i | −0.657524 | − | 0.753433i | \(-0.728396\pi\) |
0.753433 | + | 0.657524i | \(0.228396\pi\) | |||||||
\(354\) | −16.9943 | − | 8.87763i | −0.903236 | − | 0.471841i | ||||
\(355\) | −1.68819 | + | 4.84145i | −0.0895996 | + | 0.256958i | ||||
\(356\) | − | 4.69409i | − | 0.248786i | ||||||
\(357\) | 0.429745 | − | 0.134821i | 0.0227445 | − | 0.00713551i | ||||
\(358\) | −9.52759 | − | 9.52759i | −0.503549 | − | 0.503549i | ||||
\(359\) | 16.7534 | 0.884209 | 0.442104 | − | 0.896964i | \(-0.354232\pi\) | ||||
0.442104 | + | 0.896964i | \(0.354232\pi\) | |||||||
\(360\) | 3.29181 | − | 5.84500i | 0.173494 | − | 0.308058i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −7.42232 | − | 7.42232i | −0.390108 | − | 0.390108i | ||||
\(363\) | −34.0403 | + | 10.6793i | −1.78665 | + | 0.560516i | ||||
\(364\) | − | 4.55933i | − | 0.238974i | ||||||
\(365\) | −10.1135 | − | 20.9426i | −0.529366 | − | 1.09619i | ||||
\(366\) | −15.0831 | − | 7.87925i | −0.788406 | − | 0.411855i | ||||
\(367\) | 7.97950 | − | 7.97950i | 0.416526 | − | 0.416526i | −0.467478 | − | 0.884005i | \(-0.654837\pi\) |
0.884005 | + | 0.467478i | \(0.154837\pi\) | |||||||
\(368\) | −0.841693 | + | 0.841693i | −0.0438763 | + | 0.0438763i | ||||
\(369\) | −9.86932 | − | 14.1812i | −0.513776 | − | 0.738241i | ||||
\(370\) | 17.5763 | + | 6.12876i | 0.913750 | + | 0.318619i | ||||
\(371\) | 47.2341i | 2.45227i | ||||||||
\(372\) | −2.65052 | − | 8.44855i | −0.137423 | − | 0.438037i | ||||
\(373\) | 13.0474 | + | 13.0474i | 0.675570 | + | 0.675570i | 0.958995 | − | 0.283424i | \(-0.0914704\pi\) |
−0.283424 | + | 0.958995i | \(0.591470\pi\) | |||||||
\(374\) | −0.423403 | −0.0218937 | ||||||||
\(375\) | 14.7795 | + | 12.5127i | 0.763208 | + | 0.646152i | ||||
\(376\) | −3.73570 | −0.192654 | ||||||||
\(377\) | 6.13059 | + | 6.13059i | 0.315741 | + | 0.315741i | ||||
\(378\) | 10.9814 | − | 14.1846i | 0.564824 | − | 0.729578i | ||||
\(379\) | − | 29.4531i | − | 1.51290i | −0.654050 | − | 0.756451i | \(-0.726931\pi\) | ||
0.654050 | − | 0.756451i | \(-0.273069\pi\) | |||||||
\(380\) | 2.11139 | + | 0.736229i | 0.108312 | + | 0.0377677i | ||||
\(381\) | −5.49141 | + | 10.5121i | −0.281334 | + | 0.538551i | ||||
\(382\) | 11.4880 | − | 11.4880i | 0.587775 | − | 0.587775i | ||||
\(383\) | −8.01839 | + | 8.01839i | −0.409721 | + | 0.409721i | −0.881641 | − | 0.471921i | \(-0.843561\pi\) |
0.471921 | + | 0.881641i | \(0.343561\pi\) | |||||||
\(384\) | −0.801972 | + | 1.53520i | −0.0409255 | + | 0.0783429i | ||||
\(385\) | −18.8701 | − | 39.0753i | −0.961708 | − | 1.99146i | ||||
\(386\) | 3.16174i | 0.160928i | ||||||||
\(387\) | −31.6473 | − | 5.67383i | −1.60873 | − | 0.288417i | ||||
\(388\) | −4.18214 | − | 4.18214i | −0.212316 | − | 0.212316i | ||||
\(389\) | 23.1601 | 1.17426 | 0.587131 | − | 0.809492i | \(-0.300257\pi\) | ||||
0.587131 | + | 0.809492i | \(0.300257\pi\) | |||||||
\(390\) | 0.161148 | − | 5.11238i | 0.00816006 | − | 0.258875i | ||||
\(391\) | −0.0896594 | −0.00453427 | ||||||||
\(392\) | −3.47779 | − | 3.47779i | −0.175655 | − | 0.175655i | ||||
\(393\) | 0.0689408 | + | 0.219749i | 0.00347760 | + | 0.0110849i | ||||
\(394\) | − | 7.79862i | − | 0.392889i | ||||||
\(395\) | 2.51647 | − | 7.21685i | 0.126617 | − | 0.363119i | ||||
\(396\) | −13.8415 | + | 9.63290i | −0.695559 | + | 0.484072i | ||||
\(397\) | −16.3811 | + | 16.3811i | −0.822143 | + | 0.822143i | −0.986415 | − | 0.164272i | \(-0.947472\pi\) |
0.164272 | + | 0.986415i | \(0.447472\pi\) | |||||||
\(398\) | 15.7905 | − | 15.7905i | 0.791508 | − | 0.791508i | ||||
\(399\) | 5.29997 | + | 2.76865i | 0.265330 | + | 0.138606i | ||||
\(400\) | −3.91593 | − | 3.10893i | −0.195797 | − | 0.155447i | ||||
\(401\) | − | 33.9549i | − | 1.69563i | −0.530295 | − | 0.847813i | \(-0.677919\pi\) | ||
0.530295 | − | 0.847813i | \(-0.322081\pi\) | |||||||
\(402\) | −14.6688 | + | 4.60197i | −0.731614 | + | 0.229525i | ||||
\(403\) | −4.77402 | − | 4.77402i | −0.237811 | − | 0.237811i | ||||
\(404\) | 0.845280 | 0.0420543 | ||||||||
\(405\) | 12.8148 | − | 15.5171i | 0.636774 | − | 0.771050i | ||||
\(406\) | 22.6638 | 1.12478 | ||||||||
\(407\) | −33.0881 | − | 33.0881i | −1.64012 | − | 1.64012i | ||||
\(408\) | −0.124481 | + | 0.0390527i | −0.00616272 | + | 0.00193340i | ||||
\(409\) | − | 33.7198i | − | 1.66734i | −0.552266 | − | 0.833668i | \(-0.686237\pi\) | ||
0.552266 | − | 0.833668i | \(-0.313763\pi\) | |||||||
\(410\) | −11.5964 | + | 5.60010i | −0.572706 | + | 0.276569i | ||||
\(411\) | −25.7160 | − | 13.4338i | −1.26848 | − | 0.662639i | ||||
\(412\) | −1.72028 | + | 1.72028i | −0.0847523 | + | 0.0847523i | ||||
\(413\) | −27.0228 | + | 27.0228i | −1.32971 | + | 1.32971i | ||||
\(414\) | −2.93105 | + | 2.03985i | −0.144053 | + | 0.100253i | ||||
\(415\) | −13.7961 | + | 6.66237i | −0.677225 | + | 0.327043i | ||||
\(416\) | 1.32067i | 0.0647509i | ||||||||
\(417\) | 5.93532 | + | 18.9189i | 0.290654 | + | 0.926463i | ||||
\(418\) | −3.97477 | − | 3.97477i | −0.194412 | − | 0.194412i | ||||
\(419\) | 1.26502 | 0.0618005 | 0.0309003 | − | 0.999522i | \(-0.490163\pi\) | ||||
0.0309003 | + | 0.999522i | \(0.490163\pi\) | |||||||
\(420\) | −9.15194 | − | 9.74768i | −0.446569 | − | 0.475638i | ||||
\(421\) | −4.67210 | −0.227704 | −0.113852 | − | 0.993498i | \(-0.536319\pi\) | ||||
−0.113852 | + | 0.993498i | \(0.536319\pi\) | |||||||
\(422\) | 3.47484 | + | 3.47484i | 0.169153 | + | 0.169153i | ||||
\(423\) | −11.0312 | − | 1.97771i | −0.536356 | − | 0.0961595i | ||||
\(424\) | − | 13.6819i | − | 0.664454i | ||||||
\(425\) | −0.0429820 | − | 0.374154i | −0.00208494 | − | 0.0181491i | ||||
\(426\) | 1.83894 | − | 3.52024i | 0.0890967 | − | 0.170556i | ||||
\(427\) | −23.9838 | + | 23.9838i | −1.16066 | + | 1.16066i | ||||
\(428\) | 6.17999 | − | 6.17999i | 0.298721 | − | 0.298721i | ||||
\(429\) | −5.95360 | + | 11.3969i | −0.287442 | + | 0.550245i | ||||
\(430\) | −7.89039 | + | 22.6284i | −0.380509 | + | 1.09124i | ||||
\(431\) | 13.2679i | 0.639093i | 0.947571 | + | 0.319546i | \(0.103531\pi\) | ||||
−0.947571 | + | 0.319546i | \(0.896469\pi\) | |||||||
\(432\) | −3.18091 | + | 4.10875i | −0.153041 | + | 0.197682i | ||||
\(433\) | 27.9513 | + | 27.9513i | 1.34326 | + | 1.34326i | 0.892797 | + | 0.450459i | \(0.148740\pi\) |
0.450459 | + | 0.892797i | \(0.351260\pi\) | |||||||
\(434\) | −17.6488 | −0.847167 | ||||||||
\(435\) | 25.4129 | + | 0.801045i | 1.21845 | + | 0.0384072i | ||||
\(436\) | −13.7634 | −0.659149 | ||||||||
\(437\) | −0.841693 | − | 0.841693i | −0.0402636 | − | 0.0402636i | ||||
\(438\) | 5.39247 | + | 17.1886i | 0.257662 | + | 0.821301i | ||||
\(439\) | 6.40984i | 0.305925i | 0.988232 | + | 0.152962i | \(0.0488813\pi\) | ||||
−0.988232 | + | 0.152962i | \(0.951119\pi\) | |||||||
\(440\) | 5.46595 | + | 11.3186i | 0.260579 | + | 0.539595i | ||||
\(441\) | −8.42847 | − | 12.1108i | −0.401356 | − | 0.576705i | ||||
\(442\) | −0.0703404 | + | 0.0703404i | −0.00334575 | + | 0.00334575i | ||||
\(443\) | −19.7293 | + | 19.7293i | −0.937366 | + | 0.937366i | −0.998151 | − | 0.0607845i | \(-0.980640\pi\) |
0.0607845 | + | 0.998151i | \(0.480640\pi\) | |||||||
\(444\) | −12.7798 | − | 6.67604i | −0.606503 | − | 0.316831i | ||||
\(445\) | −9.91105 | − | 3.45592i | −0.469829 | − | 0.163826i | ||||
\(446\) | 8.58534i | 0.406527i | ||||||||
\(447\) | −35.9859 | + | 11.2896i | −1.70207 | + | 0.533982i | ||||
\(448\) | 2.44114 | + | 2.44114i | 0.115333 | + | 0.115333i | ||||
\(449\) | −18.2109 | −0.859426 | −0.429713 | − | 0.902966i | \(-0.641385\pi\) | ||||
−0.429713 | + | 0.902966i | \(0.641385\pi\) | |||||||
\(450\) | −9.91754 | − | 11.2535i | −0.467517 | − | 0.530497i | ||||
\(451\) | 32.3731 | 1.52439 | ||||||||
\(452\) | 13.5833 | + | 13.5833i | 0.638904 | + | 0.638904i | ||||
\(453\) | −21.4643 | + | 6.73387i | −1.00848 | + | 0.316385i | ||||
\(454\) | − | 17.7269i | − | 0.831965i | ||||||
\(455\) | −9.62652 | − | 3.35671i | −0.451298 | − | 0.157365i | ||||
\(456\) | −1.53520 | − | 0.801972i | −0.0718923 | − | 0.0375558i | ||||
\(457\) | −6.89858 | + | 6.89858i | −0.322702 | + | 0.322702i | −0.849803 | − | 0.527101i | \(-0.823279\pi\) |
0.527101 | + | 0.849803i | \(0.323279\pi\) | |||||||
\(458\) | −2.85310 | + | 2.85310i | −0.133317 | + | 0.133317i | ||||
\(459\) | −0.388257 | + | 0.0494183i | −0.0181223 | + | 0.00230665i | ||||
\(460\) | 1.15746 | + | 2.39682i | 0.0539670 | + | 0.111752i | ||||
\(461\) | 14.4915i | 0.674935i | 0.941337 | + | 0.337467i | \(0.109570\pi\) | ||||
−0.941337 | + | 0.337467i | \(0.890430\pi\) | |||||||
\(462\) | 10.0614 | + | 32.0709i | 0.468100 | + | 1.49207i | ||||
\(463\) | −19.3659 | − | 19.3659i | −0.900009 | − | 0.900009i | 0.0954276 | − | 0.995436i | \(-0.469578\pi\) |
−0.995436 | + | 0.0954276i | \(0.969578\pi\) | |||||||
\(464\) | −6.56484 | −0.304765 | ||||||||
\(465\) | −19.7896 | − | 0.623791i | −0.917719 | − | 0.0289276i | ||||
\(466\) | −19.4916 | −0.902931 | ||||||||
\(467\) | 1.06586 | + | 1.06586i | 0.0493219 | + | 0.0493219i | 0.731338 | − | 0.682016i | \(-0.238896\pi\) |
−0.682016 | + | 0.731338i | \(0.738896\pi\) | |||||||
\(468\) | −0.699170 | + | 3.89982i | −0.0323192 | + | 0.180269i | ||||
\(469\) | 30.6427i | 1.41495i | ||||||||
\(470\) | −2.75033 | + | 7.88752i | −0.126863 | + | 0.363824i | ||||
\(471\) | 11.6549 | − | 22.3107i | 0.537028 | − | 1.02802i | ||||
\(472\) | 7.82749 | − | 7.82749i | 0.360290 | − | 0.360290i | ||||
\(473\) | 42.5989 | − | 42.5989i | 1.95870 | − | 1.95870i | ||||
\(474\) | −2.74119 | + | 5.24740i | −0.125907 | + | 0.241021i | ||||
\(475\) | 3.10893 | − | 3.91593i | 0.142648 | − | 0.179675i | ||||
\(476\) | 0.260037i | 0.0119188i | ||||||||
\(477\) | 7.24332 | − | 40.4016i | 0.331649 | − | 1.84986i | ||||
\(478\) | −0.427293 | − | 0.427293i | −0.0195439 | − | 0.0195439i | ||||
\(479\) | 10.1543 | 0.463962 | 0.231981 | − | 0.972720i | \(-0.425479\pi\) | ||||
0.231981 | + | 0.972720i | \(0.425479\pi\) | |||||||
\(480\) | 2.65097 | + | 2.82353i | 0.121000 | + | 0.128876i | ||||
\(481\) | −10.9939 | −0.501279 | ||||||||
\(482\) | 1.16182 | + | 1.16182i | 0.0529196 | + | 0.0529196i | ||||
\(483\) | 2.13059 | + | 6.79129i | 0.0969454 | + | 0.309015i | ||||
\(484\) | − | 20.5976i | − | 0.936255i | ||||||
\(485\) | −11.9091 | + | 5.75111i | −0.540766 | + | 0.261144i | ||||
\(486\) | −11.5682 | + | 10.4488i | −0.524742 | + | 0.473968i | ||||
\(487\) | −20.9045 | + | 20.9045i | −0.947275 | + | 0.947275i | −0.998678 | − | 0.0514027i | \(-0.983631\pi\) |
0.0514027 | + | 0.998678i | \(0.483631\pi\) | |||||||
\(488\) | 6.94721 | − | 6.94721i | 0.314485 | − | 0.314485i | ||||
\(489\) | 10.8002 | + | 5.64189i | 0.488400 | + | 0.255135i | ||||
\(490\) | −9.90343 | + | 4.78253i | −0.447391 | + | 0.216053i | ||||
\(491\) | − | 1.07122i | − | 0.0483436i | −0.999708 | − | 0.0241718i | \(-0.992305\pi\) | ||
0.999708 | − | 0.0241718i | \(-0.00769487\pi\) | |||||||
\(492\) | 9.51772 | − | 2.98594i | 0.429092 | − | 0.134617i | ||||
\(493\) | −0.349652 | − | 0.349652i | −0.0157475 | − | 0.0157475i | ||||
\(494\) | −1.32067 | −0.0594195 | ||||||||
\(495\) | 10.1483 | + | 36.3167i | 0.456134 | + | 1.63232i | ||||
\(496\) | 5.11218 | 0.229544 | ||||||||
\(497\) | −5.59758 | − | 5.59758i | −0.251086 | − | 0.251086i | ||||
\(498\) | 11.3231 | − | 3.55234i | 0.507401 | − | 0.159184i | ||||
\(499\) | 2.97605i | 0.133226i | 0.997779 | + | 0.0666132i | \(0.0212193\pi\) | ||||
−0.997779 | + | 0.0666132i | \(0.978781\pi\) | |||||||
\(500\) | −9.44719 | + | 5.97918i | −0.422491 | + | 0.267397i | ||||
\(501\) | −24.5587 | − | 12.8292i | −1.09720 | − | 0.573166i | ||||
\(502\) | −0.566023 | + | 0.566023i | −0.0252628 | + | 0.0252628i | ||||
\(503\) | 22.6375 | − | 22.6375i | 1.00936 | − | 1.00936i | 0.00940114 | − | 0.999956i | \(-0.497007\pi\) |
0.999956 | − | 0.00940114i | \(-0.00299252\pi\) | |||||||
\(504\) | 5.91613 | + | 8.50085i | 0.263526 | + | 0.378658i | ||||
\(505\) | 0.622320 | − | 1.78472i | 0.0276929 | − | 0.0794188i | ||||
\(506\) | − | 6.69108i | − | 0.297455i | ||||||
\(507\) | −5.83582 | − | 18.6018i | −0.259178 | − | 0.826133i | ||||
\(508\) | −4.84183 | − | 4.84183i | −0.214822 | − | 0.214822i | ||||
\(509\) | −13.7670 | −0.610210 | −0.305105 | − | 0.952319i | \(-0.598692\pi\) | ||||
−0.305105 | + | 0.952319i | \(0.598692\pi\) | |||||||
\(510\) | −0.00919093 | + | 0.291579i | −0.000406981 | + | 0.0129114i | ||||
\(511\) | 35.9064 | 1.58840 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −4.10875 | − | 3.18091i | −0.181406 | − | 0.140440i | ||||
\(514\) | 0.265624i | 0.0117162i | ||||||||
\(515\) | 2.36567 | + | 4.89871i | 0.104244 | + | 0.215863i | ||||
\(516\) | 8.59499 | − | 16.4532i | 0.378373 | − | 0.724313i | ||||
\(517\) | 14.8486 | − | 14.8486i | 0.653039 | − | 0.653039i | ||||
\(518\) | −20.3213 | + | 20.3213i | −0.892869 | + | 0.892869i | ||||
\(519\) | −18.7844 | + | 35.9586i | −0.824543 | + | 1.57841i | ||||
\(520\) | 2.78844 | + | 0.972312i | 0.122281 | + | 0.0426387i | ||||
\(521\) | 1.77371i | 0.0777075i | 0.999245 | + | 0.0388537i | \(0.0123706\pi\) | ||||
−0.999245 | + | 0.0388537i | \(0.987629\pi\) | |||||||
\(522\) | −19.3854 | − | 3.47548i | −0.848478 | − | 0.152117i | ||||
\(523\) | 15.4539 | + | 15.4539i | 0.675753 | + | 0.675753i | 0.959036 | − | 0.283283i | \(-0.0914237\pi\) |
−0.283283 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(524\) | −0.132969 | −0.00580880 | ||||||||
\(525\) | −27.3191 | + | 12.1468i | −1.19230 | + | 0.530129i | ||||
\(526\) | 0.138543 | 0.00604078 | ||||||||
\(527\) | 0.272282 | + | 0.272282i | 0.0118608 | + | 0.0118608i | ||||
\(528\) | −2.91441 | − | 9.28973i | −0.126834 | − | 0.404284i | ||||
\(529\) | 21.5831i | 0.938396i | ||||||||
\(530\) | −28.8879 | − | 10.0730i | −1.25481 | − | 0.437545i | ||||
\(531\) | 27.2579 | − | 18.9700i | 1.18289 | − | 0.823228i | ||||
\(532\) | −2.44114 | + | 2.44114i | −0.105837 | + | 0.105837i | ||||
\(533\) | 5.37818 | − | 5.37818i | 0.232955 | − | 0.232955i | ||||
\(534\) | 7.20637 | + | 3.76453i | 0.311850 | + | 0.162907i | ||||
\(535\) | −8.49848 | − | 17.5983i | −0.367421 | − | 0.760839i | ||||
\(536\) | − | 8.87605i | − | 0.383387i | ||||||
\(537\) | 22.2676 | − | 6.98590i | 0.960919 | − | 0.301464i | ||||
\(538\) | −10.8573 | − | 10.8573i | −0.468093 | − | 0.468093i | ||||
\(539\) | 27.6469 | 1.19084 | ||||||||
\(540\) | 6.33330 | + | 9.74111i | 0.272542 | + | 0.419191i | ||||
\(541\) | 11.0282 | 0.474141 | 0.237070 | − | 0.971492i | \(-0.423813\pi\) | ||||
0.237070 | + | 0.971492i | \(0.423813\pi\) | |||||||
\(542\) | −6.30438 | − | 6.30438i | −0.270796 | − | 0.270796i | ||||
\(543\) | 17.3472 | − | 5.44225i | 0.744441 | − | 0.233549i | ||||
\(544\) | − | 0.0753229i | − | 0.00322944i | ||||||
\(545\) | −10.1330 | + | 29.0600i | −0.434052 | + | 1.24479i | ||||
\(546\) | 6.99948 | + | 3.65645i | 0.299550 | + | 0.156482i | ||||
\(547\) | −8.33939 | + | 8.33939i | −0.356567 | + | 0.356567i | −0.862546 | − | 0.505979i | \(-0.831131\pi\) |
0.505979 | + | 0.862546i | \(0.331131\pi\) | |||||||
\(548\) | 11.8447 | − | 11.8447i | 0.505980 | − | 0.505980i | ||||
\(549\) | 24.1925 | − | 16.8366i | 1.03251 | − | 0.718570i | ||||
\(550\) | 27.9222 | − | 3.20765i | 1.19061 | − | 0.136775i | ||||
\(551\) | − | 6.56484i | − | 0.279672i | ||||||
\(552\) | −0.617153 | − | 1.96718i | −0.0262678 | − | 0.0837288i | ||||
\(553\) | 8.34396 | + | 8.34396i | 0.354821 | + | 0.354821i | ||||
\(554\) | 7.40629 | 0.314663 | ||||||||
\(555\) | −23.5046 | + | 22.0681i | −0.997714 | + | 0.936738i | ||||
\(556\) | −11.4478 | −0.485493 | ||||||||
\(557\) | −8.91400 | − | 8.91400i | −0.377698 | − | 0.377698i | 0.492573 | − | 0.870271i | \(-0.336057\pi\) |
−0.870271 | + | 0.492573i | \(0.836057\pi\) | |||||||
\(558\) | 15.0959 | + | 2.70643i | 0.639058 | + | 0.114572i | ||||
\(559\) | − | 14.1540i | − | 0.598650i | ||||||
\(560\) | 6.95144 | − | 3.35696i | 0.293752 | − | 0.141858i | ||||
\(561\) | 0.339558 | − | 0.650009i | 0.0143361 | − | 0.0274434i | ||||
\(562\) | −0.761466 | + | 0.761466i | −0.0321205 | + | 0.0321205i | ||||
\(563\) | 17.4579 | − | 17.4579i | 0.735761 | − | 0.735761i | −0.235993 | − | 0.971755i | \(-0.575834\pi\) |
0.971755 | + | 0.235993i | \(0.0758344\pi\) | |||||||
\(564\) | 2.99593 | − | 5.73505i | 0.126151 | − | 0.241489i | ||||
\(565\) | 38.6800 | − | 18.6792i | 1.62728 | − | 0.785840i | ||||
\(566\) | 18.9019i | 0.794508i | ||||||||
\(567\) | 12.9694 | + | 28.2344i | 0.544665 | + | 1.18573i | ||||
\(568\) | 1.62141 | + | 1.62141i | 0.0680328 | + | 0.0680328i | ||||
\(569\) | −6.84928 | −0.287137 | −0.143568 | − | 0.989640i | \(-0.545858\pi\) | ||||
−0.143568 | + | 0.989640i | \(0.545858\pi\) | |||||||
\(570\) | −2.82353 | + | 2.65097i | −0.118265 | + | 0.111037i | ||||
\(571\) | −30.2902 | −1.26761 | −0.633803 | − | 0.773495i | \(-0.718507\pi\) | ||||
−0.633803 | + | 0.773495i | \(0.718507\pi\) | |||||||
\(572\) | −5.24934 | − | 5.24934i | −0.219486 | − | 0.219486i | ||||
\(573\) | 8.42329 | + | 26.8493i | 0.351888 | + | 1.12165i | ||||
\(574\) | − | 19.8822i | − | 0.829868i | ||||||
\(575\) | 5.91278 | − | 0.679249i | 0.246580 | − | 0.0283266i | ||||
\(576\) | −1.71368 | − | 2.46238i | −0.0714034 | − | 0.102599i | ||||
\(577\) | −31.9328 | + | 31.9328i | −1.32938 | + | 1.32938i | −0.423471 | + | 0.905910i | \(0.639189\pi\) |
−0.905910 | + | 0.423471i | \(0.860811\pi\) | |||||||
\(578\) | −12.0168 | + | 12.0168i | −0.499833 | + | 0.499833i | ||||
\(579\) | −4.85391 | − | 2.53563i | −0.201722 | − | 0.105377i | ||||
\(580\) | −4.83322 | + | 13.8609i | −0.200689 | + | 0.575544i | ||||
\(581\) | − | 23.6536i | − | 0.981318i | ||||||
\(582\) | 9.77437 | − | 3.06646i | 0.405161 | − | 0.127109i | ||||
\(583\) | 54.3826 | + | 54.3826i | 2.25230 | + | 2.25230i | ||||
\(584\) | −10.4007 | −0.430385 | ||||||||
\(585\) | 7.71929 | + | 4.34738i | 0.319153 | + | 0.179742i | ||||
\(586\) | −1.34743 | −0.0556619 | ||||||||
\(587\) | −27.2033 | − | 27.2033i | −1.12280 | − | 1.12280i | −0.991319 | − | 0.131481i | \(-0.958027\pi\) |
−0.131481 | − | 0.991319i | \(-0.541973\pi\) | |||||||
\(588\) | 8.12820 | − | 2.55002i | 0.335201 | − | 0.105161i | ||||
\(589\) | 5.11218i | 0.210644i | ||||||||
\(590\) | −10.7641 | − | 22.2897i | −0.443150 | − | 0.917653i | ||||
\(591\) | 11.9724 | + | 6.25427i | 0.492480 | + | 0.257266i | ||||
\(592\) | 5.88633 | − | 5.88633i | 0.241927 | − | 0.241927i | ||||
\(593\) | −1.77591 | + | 1.77591i | −0.0729280 | + | 0.0729280i | −0.742630 | − | 0.669702i | \(-0.766422\pi\) |
0.669702 | + | 0.742630i | \(0.266422\pi\) | |||||||
\(594\) | −3.68798 | − | 28.9747i | −0.151320 | − | 1.18885i | ||||
\(595\) | 0.549039 | + | 0.191447i | 0.0225084 | + | 0.00784855i | ||||
\(596\) | − | 21.7749i | − | 0.891934i | ||||||
\(597\) | 11.5781 | + | 36.9052i | 0.473858 | + | 1.51043i | ||||
\(598\) | −1.11159 | − | 1.11159i | −0.0454565 | − | 0.0454565i | ||||
\(599\) | 4.67096 | 0.190850 | 0.0954252 | − | 0.995437i | \(-0.469579\pi\) | ||||
0.0954252 | + | 0.995437i | \(0.469579\pi\) | |||||||
\(600\) | 7.91330 | − | 3.51847i | 0.323059 | − | 0.143641i | ||||
\(601\) | −46.7693 | −1.90776 | −0.953880 | − | 0.300187i | \(-0.902951\pi\) | ||||
−0.953880 | + | 0.300187i | \(0.902951\pi\) | |||||||
\(602\) | −26.1625 | − | 26.1625i | −1.06630 | − | 1.06630i | ||||
\(603\) | 4.69905 | − | 26.2102i | 0.191360 | − | 1.06736i | ||||
\(604\) | − | 12.9880i | − | 0.528472i | ||||||
\(605\) | −43.4896 | − | 15.1646i | −1.76810 | − | 0.616527i | ||||
\(606\) | −0.677891 | + | 1.29767i | −0.0275374 | + | 0.0527144i | ||||
\(607\) | −10.3777 | + | 10.3777i | −0.421219 | + | 0.421219i | −0.885623 | − | 0.464404i | \(-0.846268\pi\) |
0.464404 | + | 0.885623i | \(0.346268\pi\) | |||||||
\(608\) | 0.707107 | − | 0.707107i | 0.0286770 | − | 0.0286770i | ||||
\(609\) | −18.1757 | + | 34.7934i | −0.736517 | + | 1.40990i | ||||
\(610\) | −9.55353 | − | 19.7830i | −0.386811 | − | 0.800990i | ||||
\(611\) | − | 4.93361i | − | 0.199593i | ||||||
\(612\) | 0.0398765 | − | 0.222422i | 0.00161191 | − | 0.00899089i | ||||
\(613\) | −0.440870 | − | 0.440870i | −0.0178066 | − | 0.0178066i | 0.698147 | − | 0.715954i | \(-0.254008\pi\) |
−0.715954 | + | 0.698147i | \(0.754008\pi\) | |||||||
\(614\) | −18.0652 | −0.729052 | ||||||||
\(615\) | 0.702732 | − | 22.2940i | 0.0283369 | − | 0.898979i | ||||
\(616\) | −19.4060 | −0.781888 | ||||||||
\(617\) | 32.7653 | + | 32.7653i | 1.31908 | + | 1.31908i | 0.914504 | + | 0.404577i | \(0.132581\pi\) |
0.404577 | + | 0.914504i | \(0.367419\pi\) | |||||||
\(618\) | −1.26136 | − | 4.02060i | −0.0507394 | − | 0.161732i | ||||
\(619\) | − | 48.9217i | − | 1.96633i | −0.182725 | − | 0.983164i | \(-0.558492\pi\) | ||
0.182725 | − | 0.983164i | \(-0.441508\pi\) | |||||||
\(620\) | 3.76373 | − | 10.7938i | 0.151155 | − | 0.433490i | ||||
\(621\) | −0.780962 | − | 6.13565i | −0.0313389 | − | 0.246215i | ||||
\(622\) | −4.39286 | + | 4.39286i | −0.176138 | + | 0.176138i | ||||
\(623\) | 11.4589 | − | 11.4589i | 0.459092 | − | 0.459092i | ||||
\(624\) | −2.02749 | − | 1.05914i | −0.0811644 | − | 0.0423994i | ||||
\(625\) | 5.66909 | + | 24.3487i | 0.226763 | + | 0.973950i | ||||
\(626\) | 1.96255i | 0.0784393i | ||||||||
\(627\) | 9.28973 | − | 2.91441i | 0.370996 | − | 0.116391i | ||||
\(628\) | 10.2762 | + | 10.2762i | 0.410066 | + | 0.410066i | ||||
\(629\) | 0.627027 | 0.0250012 | ||||||||
\(630\) | 22.3042 | − | 6.23269i | 0.888622 | − | 0.248316i | ||||
\(631\) | −2.96028 | −0.117847 | −0.0589235 | − | 0.998263i | \(-0.518767\pi\) | ||||
−0.0589235 | + | 0.998263i | \(0.518767\pi\) | |||||||
\(632\) | −2.41693 | − | 2.41693i | −0.0961404 | − | 0.0961404i | ||||
\(633\) | −8.12130 | + | 2.54785i | −0.322793 | + | 0.101268i | ||||
\(634\) | − | 8.73263i | − | 0.346817i | ||||||
\(635\) | −13.7877 | + | 6.65830i | −0.547148 | + | 0.264226i | ||||
\(636\) | 21.0045 | + | 10.9725i | 0.832883 | + | 0.435089i | ||||
\(637\) | 4.59300 | − | 4.59300i | 0.181981 | − | 0.181981i | ||||
\(638\) | 26.0937 | − | 26.0937i | 1.03306 | − | 1.03306i | ||||
\(639\) | 3.92950 | + | 5.64627i | 0.155449 | + | 0.223363i | ||||
\(640\) | −2.01357 | + | 0.972386i | −0.0795934 | + | 0.0384369i | ||||
\(641\) | 33.7063i | 1.33132i | 0.746256 | + | 0.665659i | \(0.231849\pi\) | ||||
−0.746256 | + | 0.665659i | \(0.768151\pi\) | |||||||
\(642\) | 4.53134 | + | 14.4437i | 0.178838 | + | 0.570047i | ||||
\(643\) | 27.8461 | + | 27.8461i | 1.09814 | + | 1.09814i | 0.994628 | + | 0.103516i | \(0.0330093\pi\) |
0.103516 | + | 0.994628i | \(0.466991\pi\) | |||||||
\(644\) | −4.10938 | −0.161932 | ||||||||
\(645\) | −28.4113 | − | 30.2607i | −1.11869 | − | 1.19151i | ||||
\(646\) | 0.0753229 | 0.00296354 | ||||||||
\(647\) | 18.8461 | + | 18.8461i | 0.740918 | + | 0.740918i | 0.972755 | − | 0.231837i | \(-0.0744736\pi\) |
−0.231837 | + | 0.972755i | \(0.574474\pi\) | |||||||
\(648\) | −3.75676 | − | 8.17843i | −0.147579 | − | 0.321279i | ||||
\(649\) | 62.2250i | 2.44254i | ||||||||
\(650\) | 4.10586 | − | 5.17164i | 0.161045 | − | 0.202848i | ||||
\(651\) | 14.1538 | − | 27.0944i | 0.554732 | − | 1.06191i | ||||
\(652\) | −4.97451 | + | 4.97451i | −0.194817 | + | 0.194817i | ||||
\(653\) | 27.2344 | − | 27.2344i | 1.06577 | − | 1.06577i | 0.0680864 | − | 0.997679i | \(-0.478311\pi\) |
0.997679 | − | 0.0680864i | \(-0.0216894\pi\) | |||||||
\(654\) | 11.0379 | − | 21.1296i | 0.431616 | − | 0.826234i | ||||
\(655\) | −0.0978959 | + | 0.280750i | −0.00382511 | + | 0.0109698i | ||||
\(656\) | 5.75913i | 0.224856i | ||||||||
\(657\) | −30.7125 | − | 5.50622i | −1.19821 | − | 0.214818i | ||||
\(658\) | −9.11938 | − | 9.11938i | −0.355510 | − | 0.355510i | ||||
\(659\) | −25.2158 | −0.982269 | −0.491135 | − | 0.871084i | \(-0.663418\pi\) | ||||
−0.491135 | + | 0.871084i | \(0.663418\pi\) | |||||||
\(660\) | −21.7599 | − | 0.685899i | −0.847003 | − | 0.0266986i | ||||
\(661\) | 4.05017 | 0.157533 | 0.0787666 | − | 0.996893i | \(-0.474902\pi\) | ||||
0.0787666 | + | 0.996893i | \(0.474902\pi\) | |||||||
\(662\) | −6.73418 | − | 6.73418i | −0.261731 | − | 0.261731i | ||||
\(663\) | −0.0515756 | − | 0.164398i | −0.00200303 | − | 0.00638468i | ||||
\(664\) | 6.85157i | 0.265892i | ||||||||
\(665\) | 3.35696 | + | 6.95144i | 0.130177 | + | 0.269565i | ||||
\(666\) | 20.4981 | − | 14.2656i | 0.794286 | − | 0.552780i | ||||
\(667\) | 5.52558 | − | 5.52558i | 0.213951 | − | 0.213951i | ||||
\(668\) | 11.3116 | − | 11.3116i | 0.437660 | − | 0.437660i | ||||
\(669\) | −13.1802 | − | 6.88520i | −0.509576 | − | 0.266197i | ||||
\(670\) | −18.7408 | − | 6.53480i | −0.724020 | − | 0.252461i | ||||
\(671\) | 55.2271i | 2.13202i | ||||||||
\(672\) | −5.70537 | + | 1.78991i | −0.220089 | + | 0.0690474i | ||||
\(673\) | 14.9688 | + | 14.9688i | 0.577004 | + | 0.577004i | 0.934077 | − | 0.357073i | \(-0.116225\pi\) |
−0.357073 | + | 0.934077i | \(0.616225\pi\) | |||||||
\(674\) | 23.5713 | 0.907932 | ||||||||
\(675\) | 25.2300 | − | 6.20039i | 0.971105 | − | 0.238653i | ||||
\(676\) | 11.2558 | 0.432917 | ||||||||
\(677\) | 4.56460 | + | 4.56460i | 0.175432 | + | 0.175432i | 0.789361 | − | 0.613929i | \(-0.210412\pi\) |
−0.613929 | + | 0.789361i | \(0.710412\pi\) | |||||||
\(678\) | −31.7465 | + | 9.95964i | −1.21922 | + | 0.382498i | ||||
\(679\) | − | 20.4184i | − | 0.783585i | ||||||
\(680\) | −0.159036 | − | 0.0554549i | −0.00609875 | − | 0.00212660i | ||||
\(681\) | 27.2144 | + | 14.2165i | 1.04286 | + | 0.544777i | ||||
\(682\) | −20.3198 | + | 20.3198i | −0.778083 | + | 0.778083i | ||||
\(683\) | −23.6277 | + | 23.6277i | −0.904089 | + | 0.904089i | −0.995787 | − | 0.0916982i | \(-0.970770\pi\) |
0.0916982 | + | 0.995787i | \(0.470770\pi\) | |||||||
\(684\) | 2.46238 | − | 1.71368i | 0.0941513 | − | 0.0655242i | ||||
\(685\) | −16.2884 | − | 33.7291i | −0.622346 | − | 1.28872i | ||||
\(686\) | 7.18650i | 0.274382i | ||||||||
\(687\) | −2.09197 | − | 6.66819i | −0.0798138 | − | 0.254407i | ||||
\(688\) | 7.57828 | + | 7.57828i | 0.288919 | + | 0.288919i | ||||
\(689\) | 18.0693 | 0.688384 | ||||||||
\(690\) | −4.60785 | − | 0.145245i | −0.175418 | − | 0.00552939i | ||||
\(691\) | 33.5858 | 1.27766 | 0.638831 | − | 0.769347i | \(-0.279418\pi\) | ||||
0.638831 | + | 0.769347i | \(0.279418\pi\) | |||||||
\(692\) | −16.5624 | − | 16.5624i | −0.629607 | − | 0.629607i | ||||
\(693\) | −57.3042 | − | 10.2737i | −2.17681 | − | 0.390264i | ||||
\(694\) | 10.7468i | 0.407944i | ||||||||
\(695\) | −8.42816 | + | 24.1707i | −0.319698 | + | 0.916846i | ||||
\(696\) | 5.26482 | − | 10.0783i | 0.199562 | − | 0.382019i | ||||
\(697\) | −0.306739 | + | 0.306739i | −0.0116186 | + | 0.0116186i | ||||
\(698\) | −6.82446 | + | 6.82446i | −0.258310 | + | 0.258310i | ||||
\(699\) | 15.6317 | − | 29.9235i | 0.591246 | − | 1.13181i | ||||
\(700\) | −1.97001 | − | 17.1487i | −0.0744593 | − | 0.648160i | ||||
\(701\) | − | 41.1049i | − | 1.55251i | −0.630419 | − | 0.776255i | \(-0.717117\pi\) | ||
0.630419 | − | 0.776255i | \(-0.282883\pi\) | |||||||
\(702\) | −5.42629 | − | 4.20091i | −0.204802 | − | 0.158553i | ||||
\(703\) | 5.88633 | + | 5.88633i | 0.222007 | + | 0.222007i | ||||
\(704\) | 5.62118 | 0.211856 | ||||||||
\(705\) | −9.90324 | − | 10.5479i | −0.372978 | − | 0.397256i | ||||
\(706\) | −2.54837 | −0.0959090 | ||||||||
\(707\) | 2.06345 | + | 2.06345i | 0.0776040 | + | 0.0776040i | ||||
\(708\) | 5.73934 | + | 18.2942i | 0.215698 | + | 0.687538i | ||||
\(709\) | − | 12.7911i | − | 0.480378i | −0.970726 | − | 0.240189i | \(-0.922791\pi\) | ||
0.970726 | − | 0.240189i | \(-0.0772095\pi\) | |||||||
\(710\) | 4.61715 | − | 2.22970i | 0.173279 | − | 0.0836791i | ||||
\(711\) | −5.85746 | − | 8.41654i | −0.219672 | − | 0.315645i | ||||
\(712\) | −3.31922 | + | 3.31922i | −0.124393 | + | 0.124393i | ||||
\(713\) | −4.30289 | + | 4.30289i | −0.161144 | + | 0.161144i | ||||
\(714\) | −0.399209 | − | 0.208542i | −0.0149400 | − | 0.00780450i | ||||
\(715\) | −14.9481 | + | 7.21869i | −0.559028 | + | 0.269964i | ||||
\(716\) | 13.4740i | 0.503549i | ||||||||
\(717\) | 0.998658 | − | 0.313304i | 0.0372956 | − | 0.0117005i | ||||
\(718\) | −11.8464 | − | 11.8464i | −0.442104 | − | 0.442104i | ||||
\(719\) | −20.7582 | −0.774149 | −0.387075 | − | 0.922048i | \(-0.626514\pi\) | ||||
−0.387075 | + | 0.922048i | \(0.626514\pi\) | |||||||
\(720\) | −6.46070 | + | 1.80538i | −0.240776 | + | 0.0672824i | ||||
\(721\) | −8.39891 | −0.312792 | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.0263158 | + | 0.0263158i | ||||
\(723\) | −2.71538 | + | 0.851882i | −0.100986 | + | 0.0316818i | ||||
\(724\) | 10.4967i | 0.390108i | ||||||||
\(725\) | 25.7075 | + | 20.4096i | 0.954752 | + | 0.757995i | ||||
\(726\) | 31.6215 | + | 16.5187i | 1.17358 | + | 0.613067i | ||||
\(727\) | −7.71093 | + | 7.71093i | −0.285983 | + | 0.285983i | −0.835489 | − | 0.549507i | \(-0.814816\pi\) |
0.549507 | + | 0.835489i | \(0.314816\pi\) | |||||||
\(728\) | −3.22393 | + | 3.22393i | −0.119487 | + | 0.119487i | ||||
\(729\) | −6.76368 | − | 26.1391i | −0.250507 | − | 0.968115i | ||||
\(730\) | −7.65731 | + | 21.9600i | −0.283410 | + | 0.812775i | ||||
\(731\) | 0.807259i | 0.0298575i | ||||||||
\(732\) | 5.09389 | + | 16.2368i | 0.188276 | + | 0.600131i | ||||
\(733\) | 21.6850 | + | 21.6850i | 0.800954 | + | 0.800954i | 0.983245 | − | 0.182291i | \(-0.0583512\pi\) |
−0.182291 | + | 0.983245i | \(0.558351\pi\) | |||||||
\(734\) | −11.2847 | −0.416526 | ||||||||
\(735\) | 0.600138 | − | 19.0392i | 0.0221364 | − | 0.702272i | ||||
\(736\) | 1.19033 | 0.0438763 | ||||||||
\(737\) | 35.2803 | + | 35.2803i | 1.29956 | + | 1.29956i | ||||
\(738\) | −3.04893 | + | 17.0063i | −0.112233 | + | 0.626009i | ||||
\(739\) | − | 9.14938i | − | 0.336565i | −0.985739 | − | 0.168283i | \(-0.946178\pi\) | ||
0.985739 | − | 0.168283i | \(-0.0538221\pi\) | |||||||
\(740\) | −8.09465 | − | 16.7620i | −0.297565 | − | 0.616184i | ||||
\(741\) | 1.05914 | − | 2.02749i | 0.0389084 | − | 0.0744816i | ||||
\(742\) | 33.3995 | − | 33.3995i | 1.22614 | − | 1.22614i | ||||
\(743\) | 28.3515 | − | 28.3515i | 1.04012 | − | 1.04012i | 0.0409557 | − | 0.999161i | \(-0.486960\pi\) |
0.999161 | − | 0.0409557i | \(-0.0130403\pi\) | |||||||
\(744\) | −4.09983 | + | 7.84822i | −0.150307 | + | 0.287730i | ||||
\(745\) | −45.9753 | − | 16.0313i | −1.68440 | − | 0.587341i | ||||
\(746\) | − | 18.4519i | − | 0.675570i | ||||||
\(747\) | −3.62727 | + | 20.2321i | −0.132715 | + | 0.740255i | ||||
\(748\) | 0.299391 | + | 0.299391i | 0.0109468 | + | 0.0109468i | ||||
\(749\) | 30.1725 | 1.10248 | ||||||||
\(750\) | −1.60286 | − | 19.2985i | −0.0585280 | − | 0.704680i | ||||
\(751\) | 19.6549 | 0.717219 | 0.358609 | − | 0.933488i | \(-0.383251\pi\) | ||||
0.358609 | + | 0.933488i | \(0.383251\pi\) | |||||||
\(752\) | 2.64154 | + | 2.64154i | 0.0963271 | + | 0.0963271i | ||||
\(753\) | −0.415024 | − | 1.32289i | −0.0151243 | − | 0.0482089i | ||||
\(754\) | − | 8.66996i | − | 0.315741i | ||||||
\(755\) | −27.4226 | − | 9.56210i | −0.998012 | − | 0.348001i | ||||
\(756\) | −17.7951 | + | 2.26500i | −0.647201 | + | 0.0823774i | ||||
\(757\) | −7.94564 | + | 7.94564i | −0.288789 | + | 0.288789i | −0.836601 | − | 0.547812i | \(-0.815461\pi\) |
0.547812 | + | 0.836601i | \(0.315461\pi\) | |||||||
\(758\) | −20.8265 | + | 20.8265i | −0.756451 | + | 0.756451i | ||||
\(759\) | 10.2721 | + | 5.36606i | 0.372855 | + | 0.194776i | ||||
\(760\) | −0.972386 | − | 2.01357i | −0.0352721 | − | 0.0730399i | ||||
\(761\) | − | 8.05394i | − | 0.291955i | −0.989288 | − | 0.145977i | \(-0.953367\pi\) | ||
0.989288 | − | 0.145977i | \(-0.0466327\pi\) | |||||||
\(762\) | 11.3162 | − | 3.55017i | 0.409943 | − | 0.128609i | ||||
\(763\) | −33.5985 | − | 33.5985i | −1.21635 | − | 1.21635i | ||||
\(764\) | −16.2464 | −0.587775 | ||||||||
\(765\) | −0.440262 | − | 0.247949i | −0.0159177 | − | 0.00896460i | ||||
\(766\) | 11.3397 | 0.409721 | ||||||||
\(767\) | 10.3375 | + | 10.3375i | 0.373265 | + | 0.373265i | ||||
\(768\) | 1.65263 | − | 0.518471i | 0.0596342 | − | 0.0187087i | ||||
\(769\) | − | 29.3869i | − | 1.05972i | −0.848086 | − | 0.529859i | \(-0.822245\pi\) | ||
0.848086 | − | 0.529859i | \(-0.177755\pi\) | |||||||
\(770\) | −14.2872 | + | 40.9735i | −0.514876 | + | 1.47658i | ||||
\(771\) | −0.407787 | − | 0.213023i | −0.0146861 | − | 0.00767185i | ||||
\(772\) | 2.23569 | − | 2.23569i | 0.0804642 | − | 0.0804642i | ||||
\(773\) | −7.89291 | + | 7.89291i | −0.283888 | + | 0.283888i | −0.834658 | − | 0.550769i | \(-0.814334\pi\) |
0.550769 | + | 0.834658i | \(0.314334\pi\) | |||||||
\(774\) | 18.3661 | + | 26.3901i | 0.660154 | + | 0.948571i | ||||
\(775\) | −20.0190 | − | 15.8934i | −0.719102 | − | 0.570909i | ||||
\(776\) | 5.91443i | 0.212316i | ||||||||
\(777\) | −14.9002 | − | 47.4945i | −0.534541 | − | 1.70386i | ||||
\(778\) | −16.3766 | − | 16.3766i | −0.587131 | − | 0.587131i | ||||
\(779\) | −5.75913 | −0.206342 | ||||||||
\(780\) | −3.72894 | + | 3.50105i | −0.133518 | + | 0.125358i | ||||
\(781\) | −12.8895 | −0.461221 | ||||||||
\(782\) | 0.0633988 | + | 0.0633988i | 0.00226713 | + | 0.00226713i | ||||
\(783\) | 20.8821 | − | 26.9733i | 0.746267 | − | 0.963947i | ||||
\(784\) | 4.91834i | 0.175655i | ||||||||
\(785\) | 29.2627 | − | 14.1315i | 1.04443 | − | 0.504373i | ||||
\(786\) | 0.106638 | − | 0.204135i | 0.00380364 | − | 0.00728125i | ||||
\(787\) | 11.1698 | − | 11.1698i | 0.398160 | − | 0.398160i | −0.479424 | − | 0.877583i | \(-0.659154\pi\) |
0.877583 | + | 0.479424i | \(0.159154\pi\) | |||||||
\(788\) | −5.51445 | + | 5.51445i | −0.196444 | + | 0.196444i | ||||
\(789\) | −0.111108 | + | 0.212692i | −0.00395555 | + | 0.00757203i | ||||
\(790\) | −6.88250 | + | 3.32367i | −0.244868 | + | 0.118251i | ||||
\(791\) | 66.3174i | 2.35798i | ||||||||
\(792\) | 16.5989 | + | 2.97589i | 0.589815 | + | 0.105744i | ||||
\(793\) | 9.17494 | + | 9.17494i | 0.325812 | + | 0.325812i | ||||
\(794\) | 23.1663 | 0.822143 | ||||||||
\(795\) | 38.6314 | − | 36.2704i | 1.37012 | − | 1.28638i | ||||
\(796\) | −22.3312 | −0.791508 | ||||||||
\(797\) | −5.95116 | − | 5.95116i | −0.210801 | − | 0.210801i | 0.593807 | − | 0.804608i | \(-0.297624\pi\) |
−0.804608 | + | 0.593807i | \(0.797624\pi\) | |||||||
\(798\) | −1.78991 | − | 5.70537i | −0.0633623 | − | 0.201968i | ||||
\(799\) | 0.281384i | 0.00995465i | ||||||||
\(800\) | 0.570637 | + | 4.96733i | 0.0201751 | + | 0.175622i | ||||
\(801\) | −11.5586 | + | 8.04417i | −0.408403 | + | 0.284227i | ||||
\(802\) | −24.0097 | + | 24.0097i | −0.847813 | + | 0.847813i | ||||
\(803\) | 41.3405 | − | 41.3405i | 1.45887 | − | 1.45887i | ||||
\(804\) | 13.6265 | + | 7.11834i | 0.480570 | + | 0.251045i | ||||
\(805\) | −3.02545 | + | 8.67651i | −0.106633 | + | 0.305807i | ||||
\(806\) | 6.75148i | 0.237811i | ||||||||
\(807\) | 25.3754 | − | 7.96090i | 0.893258 | − | 0.280237i | ||||
\(808\) | −0.597703 | − | 0.597703i | −0.0210271 | − | 0.0210271i | ||||
\(809\) | −43.0115 | −1.51220 | −0.756101 | − | 0.654455i | \(-0.772898\pi\) | ||||
−0.756101 | + | 0.654455i | \(0.772898\pi\) | |||||||
\(810\) | −20.0337 | + | 1.91079i | −0.703912 | + | 0.0671382i | ||||
\(811\) | −4.06527 | −0.142751 | −0.0713755 | − | 0.997450i | \(-0.522739\pi\) | ||||
−0.0713755 | + | 0.997450i | \(0.522739\pi\) | |||||||
\(812\) | −16.0257 | − | 16.0257i | −0.562392 | − | 0.562392i | ||||
\(813\) | 14.7344 | − | 4.62255i | 0.516759 | − | 0.162120i | ||||
\(814\) | 46.7936i | 1.64012i | ||||||||
\(815\) | 6.84075 | + | 14.1655i | 0.239621 | + | 0.496196i | ||||
\(816\) | 0.115636 | + | 0.0604069i | 0.00404806 | + | 0.00211466i | ||||
\(817\) | −7.57828 | + | 7.57828i | −0.265131 | + | 0.265131i | ||||
\(818\) | −23.8435 | + | 23.8435i | −0.833668 | + | 0.833668i | ||||
\(819\) | −11.2268 | + | 7.81323i | −0.392295 | + | 0.273016i | ||||
\(820\) | 12.1598 | + | 4.24004i | 0.424638 | + | 0.148069i | ||||
\(821\) | 50.9029i | 1.77652i | 0.459336 | + | 0.888262i | \(0.348087\pi\) | ||||
−0.459336 | + | 0.888262i | \(0.651913\pi\) | |||||||
\(822\) | 8.68486 | + | 27.6831i | 0.302919 | + | 0.965558i | ||||
\(823\) | 1.05777 | + | 1.05777i | 0.0368716 | + | 0.0368716i | 0.725302 | − | 0.688431i | \(-0.241700\pi\) |
−0.688431 | + | 0.725302i | \(0.741700\pi\) | |||||||
\(824\) | 2.43285 | 0.0847523 | ||||||||
\(825\) | −17.4685 | + | 45.4387i | −0.608174 | + | 1.58197i | ||||
\(826\) | 38.2160 | 1.32971 | ||||||||
\(827\) | 18.7028 | + | 18.7028i | 0.650360 | + | 0.650360i | 0.953080 | − | 0.302720i | \(-0.0978945\pi\) |
−0.302720 | + | 0.953080i | \(0.597895\pi\) | |||||||
\(828\) | 3.51496 | + | 0.630172i | 0.122153 | + | 0.0219000i | ||||
\(829\) | 16.8360i | 0.584737i | 0.956306 | + | 0.292369i | \(0.0944434\pi\) | ||||
−0.956306 | + | 0.292369i | \(0.905557\pi\) | |||||||
\(830\) | 14.4663 | + | 5.04432i | 0.502134 | + | 0.175091i | ||||
\(831\) | −5.93964 | + | 11.3701i | −0.206044 | + | 0.394426i | ||||
\(832\) | 0.933851 | − | 0.933851i | 0.0323755 | − | 0.0323755i | ||||
\(833\) | −0.261957 | + | 0.261957i | −0.00907629 | + | 0.00907629i | ||||
\(834\) | 9.18078 | − | 17.5746i | 0.317904 | − | 0.608558i | ||||
\(835\) | −15.5553 | − | 32.2112i | −0.538313 | − | 1.11471i | ||||
\(836\) | 5.62118i | 0.194412i | ||||||||
\(837\) | −16.2614 | + | 21.0047i | −0.562075 | + | 0.726028i | ||||
\(838\) | −0.894508 | − | 0.894508i | −0.0309003 | − | 0.0309003i | ||||
\(839\) | 7.29360 | 0.251803 | 0.125901 | − | 0.992043i | \(-0.459818\pi\) | ||||
0.125901 | + | 0.992043i | \(0.459818\pi\) | |||||||
\(840\) | −0.421251 | + | 13.3640i | −0.0145345 | + | 0.461103i | ||||
\(841\) | 14.0971 | 0.486108 | ||||||||
\(842\) | 3.30367 | + | 3.30367i | 0.113852 | + | 0.113852i | ||||
\(843\) | −0.558328 | − | 1.77968i | −0.0192298 | − | 0.0612953i | ||||
\(844\) | − | 4.91417i | − | 0.169153i | ||||||
\(845\) | 8.28687 | − | 23.7655i | 0.285077 | − | 0.817557i | ||||
\(846\) | 6.40180 | + | 9.19870i | 0.220098 | + | 0.316258i | ||||
\(847\) | 50.2817 | − | 50.2817i | 1.72770 | − | 1.72770i | ||||
\(848\) | −9.67459 | + | 9.67459i | −0.332227 | + | 0.332227i | ||||
\(849\) | −29.0183 | − | 15.1588i | −0.995905 | − | 0.520250i | ||||
\(850\) | −0.234174 | + | 0.294960i | −0.00803209 | + | 0.0101170i | ||||
\(851\) | 9.90897i | 0.339675i | ||||||||
\(852\) | −3.78951 | + | 1.18886i | −0.129826 | + | 0.0407297i | ||||
\(853\) | −18.3610 | − | 18.3610i | −0.628669 | − | 0.628669i | 0.319064 | − | 0.947733i | \(-0.396631\pi\) |
−0.947733 | + | 0.319064i | \(0.896631\pi\) | |||||||
\(854\) | 33.9182 | 1.16066 | ||||||||
\(855\) | −1.80538 | − | 6.46070i | −0.0617426 | − | 0.220951i | ||||
\(856\) | −8.73982 | −0.298721 | ||||||||
\(857\) | 34.2645 | + | 34.2645i | 1.17045 | + | 1.17045i | 0.982102 | + | 0.188352i | \(0.0603146\pi\) |
0.188352 | + | 0.982102i | \(0.439685\pi\) | |||||||
\(858\) | 12.2686 | − | 3.84897i | 0.418844 | − | 0.131402i | ||||
\(859\) | − | 15.3525i | − | 0.523820i | −0.965092 | − | 0.261910i | \(-0.915648\pi\) | ||
0.965092 | − | 0.261910i | \(-0.0843524\pi\) | |||||||
\(860\) | 21.5801 | − | 10.4214i | 0.735874 | − | 0.355365i | ||||
\(861\) | 30.5232 | + | 15.9450i | 1.04023 | + | 0.543404i | ||||
\(862\) | 9.38183 | − | 9.38183i | 0.319546 | − | 0.319546i | ||||
\(863\) | 6.56803 | − | 6.56803i | 0.223578 | − | 0.223578i | −0.586425 | − | 0.810003i | \(-0.699465\pi\) |
0.810003 | + | 0.586425i | \(0.199465\pi\) | |||||||
\(864\) | 5.15457 | − | 0.656086i | 0.175362 | − | 0.0223205i | ||||
\(865\) | −47.1634 | + | 22.7759i | −1.60360 | + | 0.774405i | ||||
\(866\) | − | 39.5292i | − | 1.34326i | ||||||
\(867\) | −8.81106 | − | 28.0853i | −0.299239 | − | 0.953828i | ||||
\(868\) | 12.4796 | + | 12.4796i | 0.423584 | + | 0.423584i | ||||
\(869\) | 19.2135 | 0.651773 | ||||||||
\(870\) | −17.4032 | − | 18.5361i | −0.590024 | − | 0.628431i | ||||
\(871\) | 11.7223 | 0.397195 | ||||||||
\(872\) | 9.73222 | + | 9.73222i | 0.329575 | + | 0.329575i | ||||
\(873\) | −3.13115 | + | 17.4648i | −0.105973 | + | 0.591095i | ||||
\(874\) | 1.19033i | 0.0402636i | ||||||||
\(875\) | −37.6580 | − | 8.46590i | −1.27307 | − | 0.286200i | ||||
\(876\) | 8.34109 | − | 15.9672i | 0.281819 | − | 0.539482i | ||||
\(877\) | −13.7736 | + | 13.7736i | −0.465103 | + | 0.465103i | −0.900324 | − | 0.435221i | \(-0.856670\pi\) |
0.435221 | + | 0.900324i | \(0.356670\pi\) | |||||||
\(878\) | 4.53244 | − | 4.53244i | 0.152962 | − | 0.152962i | ||||
\(879\) | 1.08060 | − | 2.06858i | 0.0364478 | − | 0.0697714i | ||||
\(880\) | 4.13847 | − | 11.8685i | 0.139508 | − | 0.400087i | ||||
\(881\) | 13.2041i | 0.444859i | 0.974949 | + | 0.222429i | \(0.0713986\pi\) | ||||
−0.974949 | + | 0.222429i | \(0.928601\pi\) | |||||||
\(882\) | −2.60381 | + | 14.5235i | −0.0876748 | + | 0.489031i | ||||
\(883\) | −34.9199 | − | 34.9199i | −1.17515 | − | 1.17515i | −0.980966 | − | 0.194181i | \(-0.937795\pi\) |
−0.194181 | − | 0.980966i | \(-0.562205\pi\) | |||||||
\(884\) | 0.0994763 | 0.00334575 | ||||||||
\(885\) | 42.8517 | + | 1.35074i | 1.44044 | + | 0.0454045i | ||||
\(886\) | 27.9014 | 0.937366 | ||||||||
\(887\) | 5.21923 | + | 5.21923i | 0.175245 | + | 0.175245i | 0.789279 | − | 0.614035i | \(-0.210454\pi\) |
−0.614035 | + | 0.789279i | \(0.710454\pi\) | |||||||
\(888\) | 4.31602 | + | 13.7574i | 0.144836 | + | 0.461667i | ||||
\(889\) | − | 23.6392i | − | 0.792833i | ||||||
\(890\) | 4.56446 | + | 9.45188i | 0.153001 | + | 0.316828i | ||||
\(891\) | 47.4397 | + | 17.5751i | 1.58929 | + | 0.588789i | ||||
\(892\) | 6.07075 | − | 6.07075i | 0.203264 | − | 0.203264i | ||||
\(893\) | −2.64154 | + | 2.64154i | −0.0883958 | + | 0.0883958i | ||||
\(894\) | 33.4288 | + | 17.4629i | 1.11803 | + | 0.584045i | ||||
\(895\) | 28.4490 | + | 9.91998i | 0.950944 | + | 0.331588i | ||||
\(896\) | − | 3.45230i | − | 0.115333i | ||||||
\(897\) | 2.59799 | − | 0.815053i | 0.0867443 | − | 0.0272138i | ||||
\(898\) | 12.8771 | + | 12.8771i | 0.429713 | + | 0.429713i | ||||
\(899\) | −33.5606 | −1.11931 | ||||||||
\(900\) | −0.944697 | + | 14.9702i | −0.0314899 | + | 0.499007i | ||||
\(901\) | −1.03056 | −0.0343330 | ||||||||
\(902\) | −22.8912 | − | 22.8912i | −0.762195 | − | 0.762195i | ||||
\(903\) | 61.1462 | − | 19.1831i | 2.03482 | − | 0.638372i | ||||
\(904\) | − | 19.2097i | − | 0.638904i | ||||||
\(905\) | 22.1627 | + | 7.72800i | 0.736714 | + | 0.256888i | ||||
\(906\) | 19.9391 | + | 10.4160i | 0.662433 | + | 0.346048i | ||||
\(907\) | −19.6088 | + | 19.6088i | −0.651100 | + | 0.651100i | −0.953258 | − | 0.302158i | \(-0.902293\pi\) |
0.302158 | + | 0.953258i | \(0.402293\pi\) | |||||||
\(908\) | −12.5348 | + | 12.5348i | −0.415983 | + | 0.415983i | ||||
\(909\) | −1.44854 | − | 2.08140i | −0.0480451 | − | 0.0690356i | ||||
\(910\) | 4.43342 | + | 9.18053i | 0.146967 | + | 0.304331i | ||||
\(911\) | − | 49.5704i | − | 1.64234i | −0.570683 | − | 0.821170i | \(-0.693322\pi\) | ||
0.570683 | − | 0.821170i | \(-0.306678\pi\) | |||||||
\(912\) | 0.518471 | + | 1.65263i | 0.0171683 | + | 0.0547241i | ||||
\(913\) | −27.2334 | − | 27.2334i | −0.901295 | − | 0.901295i | ||||
\(914\) | 9.75606 | 0.322702 | ||||||||
\(915\) | 38.0325 | + | 1.19883i | 1.25732 | + | 0.0396321i | ||||
\(916\) | 4.03489 | 0.133317 | ||||||||
\(917\) | −0.324597 | − | 0.324597i | −0.0107191 | − | 0.0107191i | ||||
\(918\) | 0.309483 | + | 0.239595i | 0.0102145 | + | 0.00790781i | ||||
\(919\) | 46.5841i | 1.53667i | 0.640049 | + | 0.768334i | \(0.278914\pi\) | ||||
−0.640049 | + | 0.768334i | \(0.721086\pi\) | |||||||
\(920\) | 0.876358 | − | 2.51326i | 0.0288927 | − | 0.0828597i | ||||
\(921\) | 14.4878 | − | 27.7337i | 0.477389 | − | 0.913856i | ||||
\(922\) | 10.2470 | − | 10.2470i | 0.337467 | − | 0.337467i | ||||
\(923\) | −2.14134 | + | 2.14134i | −0.0704830 | + | 0.0704830i | ||||
\(924\) | 15.5630 | − | 29.7920i | 0.511986 | − | 0.980086i | ||||
\(925\) | −41.3507 | + | 4.75028i | −1.35960 | + | 0.156188i | ||||
\(926\) | 27.3875i | 0.900009i | ||||||||
\(927\) | 7.18400 | + | 1.28797i | 0.235954 | + | 0.0423024i | ||||
\(928\) | 4.64204 | + | 4.64204i | 0.152383 | + | 0.152383i | ||||
\(929\) | −58.9237 | −1.93322 | −0.966611 | − | 0.256247i | \(-0.917514\pi\) | ||||
−0.966611 | + | 0.256247i | \(0.917514\pi\) | |||||||
\(930\) | 13.5522 | + | 14.4344i | 0.444396 | + | 0.473323i | ||||
\(931\) | −4.91834 | −0.161192 | ||||||||
\(932\) | 13.7826 | + | 13.7826i | 0.451466 | + | 0.451466i | ||||
\(933\) | −3.22097 | − | 10.2669i | −0.105450 | − | 0.336122i | ||||
\(934\) | − | 1.50735i | − | 0.0493219i | ||||||
\(935\) | 0.852552 | − | 0.411711i | 0.0278814 | − | 0.0134644i | ||||
\(936\) | 3.25198 | − | 2.26320i | 0.106294 | − | 0.0739750i | ||||
\(937\) | −8.63180 | + | 8.63180i | −0.281989 | + | 0.281989i | −0.833902 | − | 0.551913i | \(-0.813898\pi\) |
0.551913 | + | 0.833902i | \(0.313898\pi\) | |||||||
\(938\) | 21.6677 | − | 21.6677i | 0.707475 | − | 0.707475i | ||||
\(939\) | −3.01291 | − | 1.57391i | −0.0983226 | − | 0.0513627i | ||||
\(940\) | 7.52210 | − | 3.63254i | 0.245344 | − | 0.118481i | ||||
\(941\) | − | 45.8679i | − | 1.49525i | −0.664120 | − | 0.747626i | \(-0.731194\pi\) | ||
0.664120 | − | 0.747626i | \(-0.268806\pi\) | |||||||
\(942\) | −24.0173 | + | 7.53481i | −0.782526 | + | 0.245497i | ||||
\(943\) | −4.84742 | − | 4.84742i | −0.157854 | − | 0.157854i | ||||
\(944\) | −11.0697 | −0.360290 | ||||||||
\(945\) | −8.31895 | + | 39.2399i | −0.270615 | + | 1.27647i | ||||
\(946\) | −60.2439 | −1.95870 | ||||||||
\(947\) | 14.0103 | + | 14.0103i | 0.455272 | + | 0.455272i | 0.897100 | − | 0.441828i | \(-0.145670\pi\) |
−0.441828 | + | 0.897100i | \(0.645670\pi\) | |||||||
\(948\) | 5.64879 | − | 1.77216i | 0.183464 | − | 0.0575572i | ||||
\(949\) | − | 13.7359i | − | 0.445885i | ||||||
\(950\) | −4.96733 | + | 0.570637i | −0.161161 | + | 0.0185139i | ||||
\(951\) | 13.4063 | + | 7.00332i | 0.434730 | + | 0.227098i | ||||
\(952\) | 0.183874 | − | 0.183874i | 0.00595939 | − | 0.00595939i | ||||
\(953\) | −8.61696 | + | 8.61696i | −0.279131 | + | 0.279131i | −0.832762 | − | 0.553631i | \(-0.813242\pi\) |
0.553631 | + | 0.832762i | \(0.313242\pi\) | |||||||
\(954\) | −33.6901 | + | 23.4465i | −1.09076 | + | 0.759108i | ||||
\(955\) | −11.9611 | + | 34.3025i | −0.387052 | + | 1.11000i | ||||
\(956\) | 0.604284i | 0.0195439i | ||||||||
\(957\) | 19.1327 | + | 60.9856i | 0.618471 | + | 1.97138i | ||||
\(958\) | −7.18017 | − | 7.18017i | −0.231981 | − | 0.231981i | ||||
\(959\) | 57.8291 | 1.86740 | ||||||||
\(960\) | 0.122020 | − | 3.87106i | 0.00393819 | − | 0.124938i | ||||
\(961\) | −4.86561 | −0.156955 | ||||||||
\(962\) | 7.77387 | + | 7.77387i | 0.250640 | + | 0.250640i | ||||
\(963\) | −25.8080 | − | 4.62693i | −0.831651 | − | 0.149101i | ||||
\(964\) | − | 1.64307i | − | 0.0529196i | ||||||
\(965\) | −3.07443 | − | 6.36639i | −0.0989695 | − | 0.204941i | ||||
\(966\) | 3.29561 | − | 6.30873i | 0.106035 | − | 0.202980i | ||||
\(967\) | 19.4154 | − | 19.4154i | 0.624358 | − | 0.624358i | −0.322285 | − | 0.946643i | \(-0.604451\pi\) |
0.946643 | + | 0.322285i | \(0.104451\pi\) | |||||||
\(968\) | −14.5647 | + | 14.5647i | −0.468128 | + | 0.468128i | ||||
\(969\) | −0.0604069 | + | 0.115636i | −0.00194055 | + | 0.00371476i | ||||
\(970\) | 12.4877 | + | 4.35438i | 0.400955 | + | 0.139811i | ||||
\(971\) | 23.5075i | 0.754391i | 0.926134 | + | 0.377196i | \(0.123112\pi\) | ||||
−0.926134 | + | 0.377196i | \(0.876888\pi\) | |||||||
\(972\) | 15.5684 | + | 0.791496i | 0.499355 | + | 0.0253873i | ||||
\(973\) | −27.9456 | − | 27.9456i | −0.895894 | − | 0.895894i | ||||
\(974\) | 29.5635 | 0.947275 | ||||||||
\(975\) | 4.64672 | + | 10.4508i | 0.148814 | + | 0.334694i | ||||
\(976\) | −9.82484 | −0.314485 | ||||||||
\(977\) | −1.74859 | − | 1.74859i | −0.0559423 | − | 0.0559423i | 0.678582 | − | 0.734524i | \(-0.262595\pi\) |
−0.734524 | + | 0.678582i | \(0.762595\pi\) | |||||||
\(978\) | −3.64745 | − | 11.6263i | −0.116633 | − | 0.371768i | ||||
\(979\) | − | 26.3863i | − | 0.843310i | ||||||
\(980\) | 10.3845 | + | 3.62103i | 0.331722 | + | 0.115669i | ||||
\(981\) | 23.5861 | + | 33.8908i | 0.753048 | + | 1.08205i | ||||
\(982\) | −0.757468 | + | 0.757468i | −0.0241718 | + | 0.0241718i | ||||
\(983\) | −17.3240 | + | 17.3240i | −0.552548 | + | 0.552548i | −0.927176 | − | 0.374627i | \(-0.877771\pi\) |
0.374627 | + | 0.927176i | \(0.377771\pi\) | |||||||
\(984\) | −8.84143 | − | 4.61867i | −0.281854 | − | 0.147238i | ||||
\(985\) | 7.58326 | + | 15.7031i | 0.241623 | + | 0.500341i | ||||
\(986\) | 0.494483i | 0.0157475i | ||||||||
\(987\) | 21.3136 | − | 6.68658i | 0.678418 | − | 0.212836i | ||||
\(988\) | 0.933851 | + | 0.933851i | 0.0297098 | + | 0.0297098i | ||||
\(989\) | −12.7572 | −0.405655 | ||||||||
\(990\) | 18.5038 | − | 32.8558i | 0.588091 | − | 1.04422i | ||||
\(991\) | −13.0550 | −0.414705 | −0.207352 | − | 0.978266i | \(-0.566485\pi\) | ||||
−0.207352 | + | 0.978266i | \(0.566485\pi\) | |||||||
\(992\) | −3.61486 | − | 3.61486i | −0.114772 | − | 0.114772i | ||||
\(993\) | 15.7389 | − | 4.93769i | 0.499460 | − | 0.156693i | ||||
\(994\) | 7.91617i | 0.251086i | ||||||||
\(995\) | −16.4409 | + | 47.1498i | −0.521210 | + | 1.49475i | ||||
\(996\) | −10.5185 | − | 5.49477i | −0.333292 | − | 0.174108i | ||||
\(997\) | −41.9934 | + | 41.9934i | −1.32994 | + | 1.32994i | −0.424530 | + | 0.905414i | \(0.639561\pi\) |
−0.905414 | + | 0.424530i | \(0.860439\pi\) | |||||||
\(998\) | 2.10439 | − | 2.10439i | 0.0666132 | − | 0.0666132i | ||||
\(999\) | 5.46161 | + | 42.9093i | 0.172798 | + | 1.35759i |
(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 | 570.2.k.a.533.9 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.a.533.13 | yes | 36 | |
5.2 | odd | 4 | inner | 570.2.k.a.77.13 | yes | 36 | |
15.2 | even | 4 | inner | 570.2.k.a.77.9 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.a.77.9 | ✓ | 36 | 15.2 | even | 4 | inner | |
570.2.k.a.77.13 | yes | 36 | 5.2 | odd | 4 | inner | |
570.2.k.a.533.9 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.a.533.13 | yes | 36 | 3.2 | odd | 2 | inner |