Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(83,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 167.10 | ||
Character | \(\chi\) | \(=\) | 210.167 |
Dual form | 210.3.k.b.83.10 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.947561 | − | 2.84642i | 0.315854 | − | 0.948808i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 4.64638 | − | 1.84693i | 0.929276 | − | 0.369386i | ||||
\(6\) | −1.89886 | − | 3.79398i | −0.316477 | − | 0.632331i | ||||
\(7\) | −6.25771 | − | 3.13705i | −0.893958 | − | 0.448150i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | −7.20426 | − | 5.39432i | −0.800473 | − | 0.599369i | ||||
\(10\) | 2.79945 | − | 6.49331i | 0.279945 | − | 0.649331i | ||||
\(11\) | 2.08576i | 0.189615i | 0.995496 | + | 0.0948073i | \(0.0302235\pi\) | ||||
−0.995496 | + | 0.0948073i | \(0.969777\pi\) | |||||||
\(12\) | −5.69285 | − | 1.89512i | −0.474404 | − | 0.157927i | ||||
\(13\) | 8.39517 | + | 8.39517i | 0.645782 | + | 0.645782i | 0.951971 | − | 0.306189i | \(-0.0990538\pi\) |
−0.306189 | + | 0.951971i | \(0.599054\pi\) | |||||||
\(14\) | −9.39476 | + | 3.12066i | −0.671054 | + | 0.222904i | ||||
\(15\) | −0.854411 | − | 14.9756i | −0.0569607 | − | 0.998376i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 4.96522 | + | 4.96522i | 0.292072 | + | 0.292072i | 0.837898 | − | 0.545826i | \(-0.183784\pi\) |
−0.545826 | + | 0.837898i | \(0.683784\pi\) | |||||||
\(18\) | −12.5986 | + | 1.80994i | −0.699921 | + | 0.100552i | ||||
\(19\) | 17.3668 | 0.914041 | 0.457021 | − | 0.889456i | \(-0.348917\pi\) | ||||
0.457021 | + | 0.889456i | \(0.348917\pi\) | |||||||
\(20\) | −3.69386 | − | 9.29276i | −0.184693 | − | 0.464638i | ||||
\(21\) | −14.8589 | + | 14.8395i | −0.707568 | + | 0.706645i | ||||
\(22\) | 2.08576 | + | 2.08576i | 0.0948073 | + | 0.0948073i | ||||
\(23\) | −3.08467 | − | 3.08467i | −0.134116 | − | 0.134116i | 0.636862 | − | 0.770978i | \(-0.280232\pi\) |
−0.770978 | + | 0.636862i | \(0.780232\pi\) | |||||||
\(24\) | −7.58797 | + | 3.79773i | −0.316165 | + | 0.158239i | ||||
\(25\) | 18.1777 | − | 17.1631i | 0.727109 | − | 0.686523i | ||||
\(26\) | 16.7903 | 0.645782 | ||||||||
\(27\) | −22.1810 | + | 15.3949i | −0.821518 | + | 0.570182i | ||||
\(28\) | −6.27410 | + | 12.5154i | −0.224075 | + | 0.446979i | ||||
\(29\) | −39.1891 | −1.35135 | −0.675674 | − | 0.737201i | \(-0.736147\pi\) | ||||
−0.675674 | + | 0.737201i | \(0.736147\pi\) | |||||||
\(30\) | −15.8301 | − | 14.1212i | −0.527669 | − | 0.470708i | ||||
\(31\) | − | 42.3954i | − | 1.36759i | −0.729673 | − | 0.683796i | \(-0.760328\pi\) | ||
0.729673 | − | 0.683796i | \(-0.239672\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 5.93696 | + | 1.97638i | 0.179908 | + | 0.0598905i | ||||
\(34\) | 9.93045 | 0.292072 | ||||||||
\(35\) | −34.8696 | − | 3.01840i | −0.996274 | − | 0.0862399i | ||||
\(36\) | −10.7886 | + | 14.4085i | −0.299684 | + | 0.400236i | ||||
\(37\) | 36.7464 | + | 36.7464i | 0.993146 | + | 0.993146i | 0.999977 | − | 0.00683066i | \(-0.00217428\pi\) |
−0.00683066 | + | 0.999977i | \(0.502174\pi\) | |||||||
\(38\) | 17.3668 | − | 17.3668i | 0.457021 | − | 0.457021i | ||||
\(39\) | 31.8511 | − | 15.9413i | 0.816696 | − | 0.408751i | ||||
\(40\) | −12.9866 | − | 5.59891i | −0.324665 | − | 0.139973i | ||||
\(41\) | 15.5827 | 0.380065 | 0.190032 | − | 0.981778i | \(-0.439141\pi\) | ||||
0.190032 | + | 0.981778i | \(0.439141\pi\) | |||||||
\(42\) | −0.0193943 | + | 29.6985i | −0.000461768 | + | 0.707107i | ||||
\(43\) | 22.8274 | − | 22.8274i | 0.530869 | − | 0.530869i | −0.389962 | − | 0.920831i | \(-0.627512\pi\) |
0.920831 | + | 0.389962i | \(0.127512\pi\) | |||||||
\(44\) | 4.17152 | 0.0948073 | ||||||||
\(45\) | −43.4366 | − | 11.7583i | −0.965259 | − | 0.261296i | ||||
\(46\) | −6.16934 | −0.134116 | ||||||||
\(47\) | 33.4161 | + | 33.4161i | 0.710980 | + | 0.710980i | 0.966740 | − | 0.255760i | \(-0.0823257\pi\) |
−0.255760 | + | 0.966740i | \(0.582326\pi\) | |||||||
\(48\) | −3.79024 | + | 11.3857i | −0.0789634 | + | 0.237202i | ||||
\(49\) | 29.3178 | + | 39.2615i | 0.598323 | + | 0.801255i | ||||
\(50\) | 1.01465 | − | 35.3408i | 0.0202930 | − | 0.706816i | ||||
\(51\) | 18.8380 | − | 9.42828i | 0.369372 | − | 0.184868i | ||||
\(52\) | 16.7903 | − | 16.7903i | 0.322891 | − | 0.322891i | ||||
\(53\) | 59.7460 | + | 59.7460i | 1.12728 | + | 1.12728i | 0.990617 | + | 0.136665i | \(0.0436385\pi\) |
0.136665 | + | 0.990617i | \(0.456362\pi\) | |||||||
\(54\) | −6.78607 | + | 37.5759i | −0.125668 | + | 0.695850i | ||||
\(55\) | 3.85225 | + | 9.69124i | 0.0700409 | + | 0.176204i | ||||
\(56\) | 6.24131 | + | 18.7895i | 0.111452 | + | 0.335527i | ||||
\(57\) | 16.4561 | − | 49.4332i | 0.288703 | − | 0.867250i | ||||
\(58\) | −39.1891 | + | 39.1891i | −0.675674 | + | 0.675674i | ||||
\(59\) | 48.9876i | 0.830298i | 0.909754 | + | 0.415149i | \(0.136270\pi\) | ||||
−0.909754 | + | 0.415149i | \(0.863730\pi\) | |||||||
\(60\) | −29.9513 | + | 1.70882i | −0.499188 | + | 0.0284804i | ||||
\(61\) | − | 82.9406i | − | 1.35968i | −0.733360 | − | 0.679841i | \(-0.762049\pi\) | ||
0.733360 | − | 0.679841i | \(-0.237951\pi\) | |||||||
\(62\) | −42.3954 | − | 42.3954i | −0.683796 | − | 0.683796i | ||||
\(63\) | 28.1599 | + | 56.3562i | 0.446982 | + | 0.894543i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 54.5124 | + | 23.5019i | 0.838653 | + | 0.361567i | ||||
\(66\) | 7.91334 | − | 3.96057i | 0.119899 | − | 0.0600087i | ||||
\(67\) | −54.8233 | − | 54.8233i | −0.818258 | − | 0.818258i | 0.167598 | − | 0.985855i | \(-0.446399\pi\) |
−0.985855 | + | 0.167598i | \(0.946399\pi\) | |||||||
\(68\) | 9.93045 | − | 9.93045i | 0.146036 | − | 0.146036i | ||||
\(69\) | −11.7032 | + | 5.85736i | −0.169611 | + | 0.0848893i | ||||
\(70\) | −37.8880 | + | 31.8512i | −0.541257 | + | 0.455017i | ||||
\(71\) | − | 74.9745i | − | 1.05598i | −0.849251 | − | 0.527990i | \(-0.822946\pi\) | ||
0.849251 | − | 0.527990i | \(-0.177054\pi\) | |||||||
\(72\) | 3.61987 | + | 25.1972i | 0.0502760 | + | 0.349960i | ||||
\(73\) | 75.1938 | + | 75.1938i | 1.03005 | + | 1.03005i | 0.999534 | + | 0.0305180i | \(0.00971569\pi\) |
0.0305180 | + | 0.999534i | \(0.490284\pi\) | |||||||
\(74\) | 73.4928 | 0.993146 | ||||||||
\(75\) | −31.6289 | − | 68.0045i | −0.421718 | − | 0.906727i | ||||
\(76\) | − | 34.7336i | − | 0.457021i | ||||||
\(77\) | 6.54314 | − | 13.0521i | 0.0849758 | − | 0.169508i | ||||
\(78\) | 15.9099 | − | 47.7924i | 0.203973 | − | 0.612723i | ||||
\(79\) | − | 3.61068i | − | 0.0457048i | −0.999739 | − | 0.0228524i | \(-0.992725\pi\) | ||
0.999739 | − | 0.0228524i | \(-0.00727479\pi\) | |||||||
\(80\) | −18.5855 | + | 7.38771i | −0.232319 | + | 0.0923464i | ||||
\(81\) | 22.8026 | + | 77.7241i | 0.281514 | + | 0.959557i | ||||
\(82\) | 15.5827 | − | 15.5827i | 0.190032 | − | 0.190032i | ||||
\(83\) | −103.116 | + | 103.116i | −1.24236 | + | 1.24236i | −0.283341 | + | 0.959019i | \(0.591443\pi\) |
−0.959019 | + | 0.283341i | \(0.908557\pi\) | |||||||
\(84\) | 29.6791 | + | 29.7179i | 0.353322 | + | 0.353784i | ||||
\(85\) | 32.2407 | + | 13.8999i | 0.379303 | + | 0.163528i | ||||
\(86\) | − | 45.6547i | − | 0.530869i | ||||||
\(87\) | −37.1340 | + | 111.549i | −0.426828 | + | 1.28217i | ||||
\(88\) | 4.17152 | − | 4.17152i | 0.0474036 | − | 0.0474036i | ||||
\(89\) | 24.4427i | 0.274637i | 0.990527 | + | 0.137319i | \(0.0438485\pi\) | ||||
−0.990527 | + | 0.137319i | \(0.956152\pi\) | |||||||
\(90\) | −55.1950 | + | 31.6783i | −0.613277 | + | 0.351981i | ||||
\(91\) | −26.1984 | − | 78.8706i | −0.287895 | − | 0.866710i | ||||
\(92\) | −6.16934 | + | 6.16934i | −0.0670580 | + | 0.0670580i | ||||
\(93\) | −120.675 | − | 40.1722i | −1.29758 | − | 0.431959i | ||||
\(94\) | 66.8321 | 0.710980 | ||||||||
\(95\) | 80.6927 | − | 32.0752i | 0.849397 | − | 0.337634i | ||||
\(96\) | 7.59545 | + | 15.1759i | 0.0791193 | + | 0.158083i | ||||
\(97\) | −35.3616 | + | 35.3616i | −0.364553 | + | 0.364553i | −0.865486 | − | 0.500933i | \(-0.832990\pi\) |
0.500933 | + | 0.865486i | \(0.332990\pi\) | |||||||
\(98\) | 68.5793 | + | 9.94368i | 0.699789 | + | 0.101466i | ||||
\(99\) | 11.2513 | − | 15.0264i | 0.113649 | − | 0.151781i | ||||
\(100\) | −34.3261 | − | 36.3554i | −0.343261 | − | 0.363554i | ||||
\(101\) | −12.9923 | −0.128637 | −0.0643184 | − | 0.997929i | \(-0.520487\pi\) | ||||
−0.0643184 | + | 0.997929i | \(0.520487\pi\) | |||||||
\(102\) | 9.40970 | − | 28.2663i | 0.0922520 | − | 0.277120i | ||||
\(103\) | 45.5816 | + | 45.5816i | 0.442540 | + | 0.442540i | 0.892865 | − | 0.450325i | \(-0.148692\pi\) |
−0.450325 | + | 0.892865i | \(0.648692\pi\) | |||||||
\(104\) | − | 33.5807i | − | 0.322891i | ||||||
\(105\) | −41.6327 | + | 96.3936i | −0.396502 | + | 0.918034i | ||||
\(106\) | 119.492 | 1.12728 | ||||||||
\(107\) | −49.5198 | + | 49.5198i | −0.462802 | + | 0.462802i | −0.899573 | − | 0.436771i | \(-0.856122\pi\) |
0.436771 | + | 0.899573i | \(0.356122\pi\) | |||||||
\(108\) | 30.7898 | + | 44.3620i | 0.285091 | + | 0.410759i | ||||
\(109\) | 170.424i | 1.56352i | 0.623579 | + | 0.781760i | \(0.285678\pi\) | ||||
−0.623579 | + | 0.781760i | \(0.714322\pi\) | |||||||
\(110\) | 13.5435 | + | 5.83899i | 0.123123 | + | 0.0530817i | ||||
\(111\) | 139.415 | − | 69.7764i | 1.25599 | − | 0.628616i | ||||
\(112\) | 25.0308 | + | 12.5482i | 0.223490 | + | 0.112038i | ||||
\(113\) | −139.393 | − | 139.393i | −1.23357 | − | 1.23357i | −0.962583 | − | 0.270986i | \(-0.912650\pi\) |
−0.270986 | − | 0.962583i | \(-0.587350\pi\) | |||||||
\(114\) | −32.9771 | − | 65.8893i | −0.289273 | − | 0.577976i | ||||
\(115\) | −20.0297 | − | 8.63538i | −0.174171 | − | 0.0750903i | ||||
\(116\) | 78.3781i | 0.675674i | ||||||||
\(117\) | −15.1947 | − | 105.767i | −0.129869 | − | 0.903993i | ||||
\(118\) | 48.9876 | + | 48.9876i | 0.415149 | + | 0.415149i | ||||
\(119\) | −15.4948 | − | 46.6471i | −0.130208 | − | 0.391992i | ||||
\(120\) | −28.2425 | + | 31.6601i | −0.235354 | + | 0.263834i | ||||
\(121\) | 116.650 | 0.964046 | ||||||||
\(122\) | −82.9406 | − | 82.9406i | −0.679841 | − | 0.679841i | ||||
\(123\) | 14.7655 | − | 44.3549i | 0.120045 | − | 0.360609i | ||||
\(124\) | −84.7907 | −0.683796 | ||||||||
\(125\) | 52.7616 | − | 113.319i | 0.422093 | − | 0.906553i | ||||
\(126\) | 84.5161 | + | 28.1963i | 0.670763 | + | 0.223780i | ||||
\(127\) | −104.552 | − | 104.552i | −0.823247 | − | 0.823247i | 0.163325 | − | 0.986572i | \(-0.447778\pi\) |
−0.986572 | + | 0.163325i | \(0.947778\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −43.3460 | − | 86.6067i | −0.336016 | − | 0.671370i | ||||
\(130\) | 78.0143 | − | 31.0106i | 0.600110 | − | 0.238543i | ||||
\(131\) | 1.42804 | 0.0109011 | 0.00545054 | − | 0.999985i | \(-0.498265\pi\) | ||||
0.00545054 | + | 0.999985i | \(0.498265\pi\) | |||||||
\(132\) | 3.95277 | − | 11.8739i | 0.0299452 | − | 0.0899539i | ||||
\(133\) | −108.676 | − | 54.4805i | −0.817115 | − | 0.409628i | ||||
\(134\) | −109.647 | −0.818258 | ||||||||
\(135\) | −74.6280 | + | 112.497i | −0.552800 | + | 0.833314i | ||||
\(136\) | − | 19.8609i | − | 0.146036i | ||||||
\(137\) | −152.451 | + | 152.451i | −1.11278 | + | 1.11278i | −0.120010 | + | 0.992773i | \(0.538293\pi\) |
−0.992773 | + | 0.120010i | \(0.961707\pi\) | |||||||
\(138\) | −5.84582 | + | 17.5605i | −0.0423610 | + | 0.127250i | ||||
\(139\) | 75.0255 | 0.539752 | 0.269876 | − | 0.962895i | \(-0.413017\pi\) | ||||
0.269876 | + | 0.962895i | \(0.413017\pi\) | |||||||
\(140\) | −6.03679 | + | 69.7392i | −0.0431200 | + | 0.498137i | ||||
\(141\) | 126.780 | − | 63.4525i | 0.899149 | − | 0.450018i | ||||
\(142\) | −74.9745 | − | 74.9745i | −0.527990 | − | 0.527990i | ||||
\(143\) | −17.5103 | + | 17.5103i | −0.122450 | + | 0.122450i | ||||
\(144\) | 28.8170 | + | 21.5773i | 0.200118 | + | 0.149842i | ||||
\(145\) | −182.087 | + | 72.3794i | −1.25577 | + | 0.499168i | ||||
\(146\) | 150.388 | 1.03005 | ||||||||
\(147\) | 139.535 | − | 46.2483i | 0.949220 | − | 0.314614i | ||||
\(148\) | 73.4928 | − | 73.4928i | 0.496573 | − | 0.496573i | ||||
\(149\) | −183.297 | −1.23018 | −0.615091 | − | 0.788456i | \(-0.710881\pi\) | ||||
−0.615091 | + | 0.788456i | \(0.710881\pi\) | |||||||
\(150\) | −99.6334 | − | 36.3757i | −0.664223 | − | 0.242504i | ||||
\(151\) | −203.889 | −1.35026 | −0.675130 | − | 0.737699i | \(-0.735913\pi\) | ||||
−0.675130 | + | 0.737699i | \(0.735913\pi\) | |||||||
\(152\) | −34.7336 | − | 34.7336i | −0.228510 | − | 0.228510i | ||||
\(153\) | −8.98674 | − | 62.5547i | −0.0587369 | − | 0.408855i | ||||
\(154\) | −6.50894 | − | 19.5952i | −0.0422659 | − | 0.127242i | ||||
\(155\) | −78.3012 | − | 196.985i | −0.505169 | − | 1.27087i | ||||
\(156\) | −31.8826 | − | 63.7023i | −0.204375 | − | 0.408348i | ||||
\(157\) | −3.36424 | + | 3.36424i | −0.0214283 | + | 0.0214283i | −0.717740 | − | 0.696311i | \(-0.754823\pi\) |
0.696311 | + | 0.717740i | \(0.254823\pi\) | |||||||
\(158\) | −3.61068 | − | 3.61068i | −0.0228524 | − | 0.0228524i | ||||
\(159\) | 226.675 | − | 113.449i | 1.42563 | − | 0.713518i | ||||
\(160\) | −11.1978 | + | 25.9732i | −0.0699863 | + | 0.162333i | ||||
\(161\) | 9.62619 | + | 28.9797i | 0.0597900 | + | 0.179998i | ||||
\(162\) | 100.527 | + | 54.9215i | 0.620536 | + | 0.339022i | ||||
\(163\) | 105.247 | − | 105.247i | 0.645690 | − | 0.645690i | −0.306259 | − | 0.951948i | \(-0.599077\pi\) |
0.951948 | + | 0.306259i | \(0.0990772\pi\) | |||||||
\(164\) | − | 31.1653i | − | 0.190032i | ||||||
\(165\) | 31.2356 | − | 1.78210i | 0.189307 | − | 0.0108006i | ||||
\(166\) | 206.232i | 1.24236i | ||||||||
\(167\) | −34.3084 | − | 34.3084i | −0.205439 | − | 0.205439i | 0.596886 | − | 0.802326i | \(-0.296404\pi\) |
−0.802326 | + | 0.596886i | \(0.796404\pi\) | |||||||
\(168\) | 59.3970 | + | 0.0387885i | 0.353553 | + | 0.000230884i | ||||
\(169\) | − | 28.0423i | − | 0.165931i | ||||||
\(170\) | 46.1406 | − | 18.3408i | 0.271416 | − | 0.107887i | ||||
\(171\) | −125.115 | − | 93.6820i | −0.731665 | − | 0.547848i | ||||
\(172\) | −45.6547 | − | 45.6547i | −0.265434 | − | 0.265434i | ||||
\(173\) | −211.509 | + | 211.509i | −1.22260 | + | 1.22260i | −0.255891 | + | 0.966706i | \(0.582369\pi\) |
−0.966706 | + | 0.255891i | \(0.917631\pi\) | |||||||
\(174\) | 74.4147 | + | 148.683i | 0.427671 | + | 0.854499i | ||||
\(175\) | −167.592 | + | 50.3770i | −0.957670 | + | 0.287869i | ||||
\(176\) | − | 8.34304i | − | 0.0474036i | ||||||
\(177\) | 139.439 | + | 46.4187i | 0.787793 | + | 0.262253i | ||||
\(178\) | 24.4427 | + | 24.4427i | 0.137319 | + | 0.137319i | ||||
\(179\) | 110.880 | 0.619440 | 0.309720 | − | 0.950828i | \(-0.399765\pi\) | ||||
0.309720 | + | 0.950828i | \(0.399765\pi\) | |||||||
\(180\) | −23.5166 | + | 86.8733i | −0.130648 | + | 0.482629i | ||||
\(181\) | 24.2997i | 0.134253i | 0.997744 | + | 0.0671264i | \(0.0213831\pi\) | ||||
−0.997744 | + | 0.0671264i | \(0.978617\pi\) | |||||||
\(182\) | −105.069 | − | 52.6722i | −0.577302 | − | 0.289407i | ||||
\(183\) | −236.084 | − | 78.5913i | −1.29008 | − | 0.429460i | ||||
\(184\) | 12.3387i | 0.0670580i | ||||||||
\(185\) | 238.606 | + | 102.870i | 1.28976 | + | 0.556053i | ||||
\(186\) | −160.847 | + | 80.5030i | −0.864771 | + | 0.432812i | ||||
\(187\) | −10.3563 | + | 10.3563i | −0.0553811 | + | 0.0553811i | ||||
\(188\) | 66.8321 | − | 66.8321i | 0.355490 | − | 0.355490i | ||||
\(189\) | 187.097 | − | 26.7540i | 0.989930 | − | 0.141556i | ||||
\(190\) | 48.6175 | − | 112.768i | 0.255882 | − | 0.593515i | ||||
\(191\) | − | 163.399i | − | 0.855494i | −0.903898 | − | 0.427747i | \(-0.859307\pi\) | ||
0.903898 | − | 0.427747i | \(-0.140693\pi\) | |||||||
\(192\) | 22.7714 | + | 7.58049i | 0.118601 | + | 0.0394817i | ||||
\(193\) | −36.3745 | + | 36.3745i | −0.188469 | + | 0.188469i | −0.795034 | − | 0.606565i | \(-0.792547\pi\) |
0.606565 | + | 0.795034i | \(0.292547\pi\) | |||||||
\(194\) | 70.7233i | 0.364553i | ||||||||
\(195\) | 118.550 | − | 132.896i | 0.607950 | − | 0.681518i | ||||
\(196\) | 78.5230 | − | 58.6356i | 0.400628 | − | 0.299161i | ||||
\(197\) | 19.3286 | − | 19.3286i | 0.0981145 | − | 0.0981145i | −0.656346 | − | 0.754460i | \(-0.727899\pi\) |
0.754460 | + | 0.656346i | \(0.227899\pi\) | |||||||
\(198\) | −3.77509 | − | 26.2776i | −0.0190661 | − | 0.132715i | ||||
\(199\) | 79.6378 | 0.400190 | 0.200095 | − | 0.979776i | \(-0.435875\pi\) | ||||
0.200095 | + | 0.979776i | \(0.435875\pi\) | |||||||
\(200\) | −70.6816 | − | 2.02930i | −0.353408 | − | 0.0101465i | ||||
\(201\) | −207.999 | + | 104.102i | −1.03482 | + | 0.517920i | ||||
\(202\) | −12.9923 | + | 12.9923i | −0.0643184 | + | 0.0643184i | ||||
\(203\) | 245.234 | + | 122.938i | 1.20805 | + | 0.605607i | ||||
\(204\) | −18.8566 | − | 37.6760i | −0.0924341 | − | 0.184686i | ||||
\(205\) | 72.4030 | − | 28.7801i | 0.353185 | − | 0.140391i | ||||
\(206\) | 91.1632 | 0.442540 | ||||||||
\(207\) | 5.58305 | + | 38.8624i | 0.0269713 | + | 0.187741i | ||||
\(208\) | −33.5807 | − | 33.5807i | −0.161446 | − | 0.161446i | ||||
\(209\) | 36.2230i | 0.173316i | ||||||||
\(210\) | 54.7608 | + | 138.026i | 0.260766 | + | 0.657268i | ||||
\(211\) | −146.466 | −0.694152 | −0.347076 | − | 0.937837i | \(-0.612825\pi\) | ||||
−0.347076 | + | 0.937837i | \(0.612825\pi\) | |||||||
\(212\) | 119.492 | − | 119.492i | 0.563641 | − | 0.563641i | ||||
\(213\) | −213.409 | − | 71.0429i | −1.00192 | − | 0.333535i | ||||
\(214\) | 99.0397i | 0.462802i | ||||||||
\(215\) | 63.9041 | − | 148.225i | 0.297229 | − | 0.689419i | ||||
\(216\) | 75.1518 | + | 13.5721i | 0.347925 | + | 0.0628340i | ||||
\(217\) | −132.996 | + | 265.298i | −0.612887 | + | 1.22257i | ||||
\(218\) | 170.424 | + | 170.424i | 0.781760 | + | 0.781760i | ||||
\(219\) | 285.284 | − | 142.783i | 1.30267 | − | 0.651976i | ||||
\(220\) | 19.3825 | − | 7.70450i | 0.0881022 | − | 0.0350204i | ||||
\(221\) | 83.3678i | 0.377230i | ||||||||
\(222\) | 69.6389 | − | 209.192i | 0.313689 | − | 0.942305i | ||||
\(223\) | −221.408 | − | 221.408i | −0.992862 | − | 0.992862i | 0.00711229 | − | 0.999975i | \(-0.497736\pi\) |
−0.999975 | + | 0.00711229i | \(0.997736\pi\) | |||||||
\(224\) | 37.5790 | − | 12.4826i | 0.167764 | − | 0.0557260i | ||||
\(225\) | −223.540 | + | 25.5907i | −0.993511 | + | 0.113737i | ||||
\(226\) | −278.787 | −1.23357 | ||||||||
\(227\) | 70.0030 | + | 70.0030i | 0.308383 | + | 0.308383i | 0.844282 | − | 0.535899i | \(-0.180027\pi\) |
−0.535899 | + | 0.844282i | \(0.680027\pi\) | |||||||
\(228\) | −98.8665 | − | 32.9122i | −0.433625 | − | 0.144352i | ||||
\(229\) | −287.075 | −1.25360 | −0.626802 | − | 0.779178i | \(-0.715637\pi\) | ||||
−0.626802 | + | 0.779178i | \(0.715637\pi\) | |||||||
\(230\) | −28.6651 | + | 11.3943i | −0.124631 | + | 0.0495405i | ||||
\(231\) | −30.9517 | − | 30.9922i | −0.133990 | − | 0.134165i | ||||
\(232\) | 78.3781 | + | 78.3781i | 0.337837 | + | 0.337837i | ||||
\(233\) | 199.347 | + | 199.347i | 0.855568 | + | 0.855568i | 0.990812 | − | 0.135245i | \(-0.0431820\pi\) |
−0.135245 | + | 0.990812i | \(0.543182\pi\) | |||||||
\(234\) | −120.962 | − | 90.5725i | −0.516931 | − | 0.387062i | ||||
\(235\) | 216.981 | + | 93.5467i | 0.923323 | + | 0.398071i | ||||
\(236\) | 97.9751 | 0.415149 | ||||||||
\(237\) | −10.2775 | − | 3.42134i | −0.0433651 | − | 0.0144360i | ||||
\(238\) | −62.1418 | − | 31.1523i | −0.261100 | − | 0.130892i | ||||
\(239\) | 46.3651 | 0.193996 | 0.0969982 | − | 0.995285i | \(-0.469076\pi\) | ||||
0.0969982 | + | 0.995285i | \(0.469076\pi\) | |||||||
\(240\) | 3.41764 | + | 59.9026i | 0.0142402 | + | 0.249594i | ||||
\(241\) | − | 65.3496i | − | 0.271160i | −0.990766 | − | 0.135580i | \(-0.956710\pi\) | ||
0.990766 | − | 0.135580i | \(-0.0432898\pi\) | |||||||
\(242\) | 116.650 | − | 116.650i | 0.482023 | − | 0.482023i | ||||
\(243\) | 242.843 | + | 8.74241i | 0.999353 | + | 0.0359770i | ||||
\(244\) | −165.881 | −0.679841 | ||||||||
\(245\) | 208.735 | + | 128.276i | 0.851979 | + | 0.523575i | ||||
\(246\) | −29.5893 | − | 59.1204i | −0.120282 | − | 0.240327i | ||||
\(247\) | 145.797 | + | 145.797i | 0.590272 | + | 0.590272i | ||||
\(248\) | −84.7907 | + | 84.7907i | −0.341898 | + | 0.341898i | ||||
\(249\) | 195.803 | + | 391.220i | 0.786357 | + | 1.57116i | ||||
\(250\) | −60.5574 | − | 166.081i | −0.242230 | − | 0.664323i | ||||
\(251\) | −139.437 | −0.555525 | −0.277763 | − | 0.960650i | \(-0.589593\pi\) | ||||
−0.277763 | + | 0.960650i | \(0.589593\pi\) | |||||||
\(252\) | 112.712 | − | 56.3198i | 0.447271 | − | 0.223491i | ||||
\(253\) | 6.43388 | − | 6.43388i | 0.0254304 | − | 0.0254304i | ||||
\(254\) | −209.105 | −0.823247 | ||||||||
\(255\) | 70.1151 | − | 78.5998i | 0.274961 | − | 0.308234i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 323.691 | + | 323.691i | 1.25950 | + | 1.25950i | 0.951332 | + | 0.308168i | \(0.0997158\pi\) |
0.308168 | + | 0.951332i | \(0.400284\pi\) | |||||||
\(258\) | −129.953 | − | 43.2606i | −0.503693 | − | 0.167677i | ||||
\(259\) | −114.673 | − | 345.224i | −0.442753 | − | 1.33291i | ||||
\(260\) | 47.0038 | − | 109.025i | 0.180784 | − | 0.419326i | ||||
\(261\) | 282.328 | + | 211.398i | 1.08172 | + | 0.809956i | ||||
\(262\) | 1.42804 | − | 1.42804i | 0.00545054 | − | 0.00545054i | ||||
\(263\) | 137.531 | + | 137.531i | 0.522933 | + | 0.522933i | 0.918456 | − | 0.395523i | \(-0.129437\pi\) |
−0.395523 | + | 0.918456i | \(0.629437\pi\) | |||||||
\(264\) | −7.92115 | − | 15.8267i | −0.0300043 | − | 0.0599496i | ||||
\(265\) | 387.949 | + | 167.256i | 1.46396 | + | 0.631155i | ||||
\(266\) | −163.157 | + | 54.1958i | −0.613371 | + | 0.203744i | ||||
\(267\) | 69.5744 | + | 23.1610i | 0.260578 | + | 0.0867452i | ||||
\(268\) | −109.647 | + | 109.647i | −0.409129 | + | 0.409129i | ||||
\(269\) | − | 391.957i | − | 1.45709i | −0.684998 | − | 0.728545i | \(-0.740197\pi\) | ||
0.684998 | − | 0.728545i | \(-0.259803\pi\) | |||||||
\(270\) | 37.8693 | + | 187.125i | 0.140257 | + | 0.693057i | ||||
\(271\) | 327.322i | 1.20783i | 0.797049 | + | 0.603914i | \(0.206393\pi\) | ||||
−0.797049 | + | 0.603914i | \(0.793607\pi\) | |||||||
\(272\) | −19.8609 | − | 19.8609i | −0.0730180 | − | 0.0730180i | ||||
\(273\) | −249.324 | − | 0.162818i | −0.913274 | − | 0.000596403i | ||||
\(274\) | 304.902i | 1.11278i | ||||||||
\(275\) | 35.7980 | + | 37.9144i | 0.130175 | + | 0.137870i | ||||
\(276\) | 11.7147 | + | 23.4064i | 0.0424447 | + | 0.0848057i | ||||
\(277\) | 38.0116 | + | 38.0116i | 0.137226 | + | 0.137226i | 0.772383 | − | 0.635157i | \(-0.219065\pi\) |
−0.635157 | + | 0.772383i | \(0.719065\pi\) | |||||||
\(278\) | 75.0255 | − | 75.0255i | 0.269876 | − | 0.269876i | ||||
\(279\) | −228.694 | + | 305.427i | −0.819692 | + | 1.09472i | ||||
\(280\) | 63.7024 | + | 75.7760i | 0.227509 | + | 0.270629i | ||||
\(281\) | 97.5907i | 0.347298i | 0.984808 | + | 0.173649i | \(0.0555558\pi\) | ||||
−0.984808 | + | 0.173649i | \(0.944444\pi\) | |||||||
\(282\) | 63.3275 | − | 190.233i | 0.224566 | − | 0.674584i | ||||
\(283\) | 394.549 | + | 394.549i | 1.39417 | + | 1.39417i | 0.815720 | + | 0.578447i | \(0.196341\pi\) |
0.578447 | + | 0.815720i | \(0.303659\pi\) | |||||||
\(284\) | −149.949 | −0.527990 | ||||||||
\(285\) | −14.8384 | − | 260.079i | −0.0520645 | − | 0.912557i | ||||
\(286\) | 35.0206i | 0.122450i | ||||||||
\(287\) | −97.5118 | − | 48.8836i | −0.339762 | − | 0.170326i | ||||
\(288\) | 50.3943 | − | 7.23975i | 0.174980 | − | 0.0251380i | ||||
\(289\) | − | 239.693i | − | 0.829388i | ||||||
\(290\) | −109.708 | + | 254.467i | −0.378303 | + | 0.877472i | ||||
\(291\) | 67.1469 | + | 134.162i | 0.230745 | + | 0.461036i | ||||
\(292\) | 150.388 | − | 150.388i | 0.515026 | − | 0.515026i | ||||
\(293\) | −62.2388 | + | 62.2388i | −0.212419 | + | 0.212419i | −0.805294 | − | 0.592875i | \(-0.797993\pi\) |
0.592875 | + | 0.805294i | \(0.297993\pi\) | |||||||
\(294\) | 93.2870 | − | 185.784i | 0.317303 | − | 0.631917i | ||||
\(295\) | 90.4765 | + | 227.615i | 0.306700 | + | 0.771576i | ||||
\(296\) | − | 146.986i | − | 0.496573i | ||||||
\(297\) | −32.1101 | − | 46.2642i | −0.108115 | − | 0.155772i | ||||
\(298\) | −183.297 | + | 183.297i | −0.615091 | + | 0.615091i | ||||
\(299\) | − | 51.7926i | − | 0.173220i | ||||||
\(300\) | −136.009 | + | 63.2577i | −0.453363 | + | 0.210859i | ||||
\(301\) | −214.458 | + | 71.2364i | −0.712484 | + | 0.236666i | ||||
\(302\) | −203.889 | + | 203.889i | −0.675130 | + | 0.675130i | ||||
\(303\) | −12.3110 | + | 36.9817i | −0.0406304 | + | 0.122052i | ||||
\(304\) | −69.4671 | −0.228510 | ||||||||
\(305\) | −153.185 | − | 385.374i | −0.502247 | − | 1.26352i | ||||
\(306\) | −71.5415 | − | 53.5680i | −0.233796 | − | 0.175059i | ||||
\(307\) | −79.7547 | + | 79.7547i | −0.259787 | + | 0.259787i | −0.824967 | − | 0.565180i | \(-0.808807\pi\) |
0.565180 | + | 0.824967i | \(0.308807\pi\) | |||||||
\(308\) | −26.1042 | − | 13.0863i | −0.0847538 | − | 0.0424879i | ||||
\(309\) | 172.936 | − | 86.5532i | 0.559663 | − | 0.280107i | ||||
\(310\) | −275.286 | − | 118.684i | −0.888020 | − | 0.382851i | ||||
\(311\) | −358.994 | −1.15432 | −0.577160 | − | 0.816631i | \(-0.695839\pi\) | ||||
−0.577160 | + | 0.816631i | \(0.695839\pi\) | |||||||
\(312\) | −95.5848 | − | 31.8197i | −0.306362 | − | 0.101986i | ||||
\(313\) | −309.220 | − | 309.220i | −0.987922 | − | 0.987922i | 0.0120057 | − | 0.999928i | \(-0.496178\pi\) |
−0.999928 | + | 0.0120057i | \(0.996178\pi\) | |||||||
\(314\) | 6.72848i | 0.0214283i | ||||||||
\(315\) | 234.927 | + | 209.843i | 0.745801 | + | 0.666169i | ||||
\(316\) | −7.22137 | −0.0228524 | ||||||||
\(317\) | 46.3542 | − | 46.3542i | 0.146228 | − | 0.146228i | −0.630203 | − | 0.776431i | \(-0.717028\pi\) |
0.776431 | + | 0.630203i | \(0.217028\pi\) | |||||||
\(318\) | 113.226 | − | 340.125i | 0.356056 | − | 1.06957i | ||||
\(319\) | − | 81.7390i | − | 0.256235i | ||||||
\(320\) | 14.7754 | + | 37.1710i | 0.0461732 | + | 0.116160i | ||||
\(321\) | 94.0314 | + | 187.877i | 0.292933 | + | 0.585288i | ||||
\(322\) | 38.6059 | + | 19.3535i | 0.119894 | + | 0.0601041i | ||||
\(323\) | 86.2300 | + | 86.2300i | 0.266966 | + | 0.266966i | ||||
\(324\) | 155.448 | − | 45.6053i | 0.479779 | − | 0.140757i | ||||
\(325\) | 296.692 | + | 8.51815i | 0.912898 | + | 0.0262097i | ||||
\(326\) | − | 210.495i | − | 0.645690i | ||||||
\(327\) | 485.098 | + | 161.487i | 1.48348 | + | 0.493844i | ||||
\(328\) | −31.1653 | − | 31.1653i | −0.0950162 | − | 0.0950162i | ||||
\(329\) | −104.280 | − | 313.936i | −0.316961 | − | 0.954213i | ||||
\(330\) | 29.4535 | − | 33.0177i | 0.0892531 | − | 0.100054i | ||||
\(331\) | 373.528 | 1.12848 | 0.564242 | − | 0.825609i | \(-0.309168\pi\) | ||||
0.564242 | + | 0.825609i | \(0.309168\pi\) | |||||||
\(332\) | 206.232 | + | 206.232i | 0.621180 | + | 0.621180i | ||||
\(333\) | −66.5087 | − | 462.952i | −0.199726 | − | 1.39025i | ||||
\(334\) | −68.6168 | −0.205439 | ||||||||
\(335\) | −355.984 | − | 153.475i | −1.06264 | − | 0.458135i | ||||
\(336\) | 59.4357 | − | 59.3582i | 0.176892 | − | 0.176661i | ||||
\(337\) | −163.577 | − | 163.577i | −0.485392 | − | 0.485392i | 0.421457 | − | 0.906848i | \(-0.361519\pi\) |
−0.906848 | + | 0.421457i | \(0.861519\pi\) | |||||||
\(338\) | −28.0423 | − | 28.0423i | −0.0829653 | − | 0.0829653i | ||||
\(339\) | −528.856 | + | 264.689i | −1.56005 | + | 0.780793i | ||||
\(340\) | 27.7998 | − | 64.4815i | 0.0817642 | − | 0.189651i | ||||
\(341\) | 88.4266 | 0.259315 | ||||||||
\(342\) | −218.797 | + | 31.4328i | −0.639757 | + | 0.0919087i | ||||
\(343\) | −60.2970 | − | 337.659i | −0.175793 | − | 0.984427i | ||||
\(344\) | −91.3095 | −0.265434 | ||||||||
\(345\) | −43.5593 | + | 48.8305i | −0.126259 | + | 0.141538i | ||||
\(346\) | 423.018i | 1.22260i | ||||||||
\(347\) | −231.964 | + | 231.964i | −0.668483 | + | 0.668483i | −0.957365 | − | 0.288882i | \(-0.906716\pi\) |
0.288882 | + | 0.957365i | \(0.406716\pi\) | |||||||
\(348\) | 223.097 | + | 74.2681i | 0.641085 | + | 0.213414i | ||||
\(349\) | 143.315 | 0.410646 | 0.205323 | − | 0.978694i | \(-0.434175\pi\) | ||||
0.205323 | + | 0.978694i | \(0.434175\pi\) | |||||||
\(350\) | −117.215 | + | 217.969i | −0.334901 | + | 0.622769i | ||||
\(351\) | −315.456 | − | 56.9702i | −0.898735 | − | 0.162308i | ||||
\(352\) | −8.34304 | − | 8.34304i | −0.0237018 | − | 0.0237018i | ||||
\(353\) | 192.937 | − | 192.937i | 0.546564 | − | 0.546564i | −0.378881 | − | 0.925445i | \(-0.623691\pi\) |
0.925445 | + | 0.378881i | \(0.123691\pi\) | |||||||
\(354\) | 185.858 | − | 93.0206i | 0.525023 | − | 0.262770i | ||||
\(355\) | −138.473 | − | 348.360i | −0.390064 | − | 0.981296i | ||||
\(356\) | 48.8855 | 0.137319 | ||||||||
\(357\) | −147.460 | − | 0.0962968i | −0.413052 | − | 0.000269739i | ||||
\(358\) | 110.880 | − | 110.880i | 0.309720 | − | 0.309720i | ||||
\(359\) | −424.811 | −1.18332 | −0.591659 | − | 0.806189i | \(-0.701527\pi\) | ||||
−0.591659 | + | 0.806189i | \(0.701527\pi\) | |||||||
\(360\) | 63.3566 | + | 110.390i | 0.175991 | + | 0.306639i | ||||
\(361\) | −59.3948 | −0.164528 | ||||||||
\(362\) | 24.2997 | + | 24.2997i | 0.0671264 | + | 0.0671264i | ||||
\(363\) | 110.533 | − | 332.034i | 0.304498 | − | 0.914695i | ||||
\(364\) | −157.741 | + | 52.3969i | −0.433355 | + | 0.143948i | ||||
\(365\) | 488.257 | + | 210.502i | 1.33769 | + | 0.576717i | ||||
\(366\) | −314.675 | + | 157.493i | −0.859769 | + | 0.430308i | ||||
\(367\) | 395.856 | − | 395.856i | 1.07863 | − | 1.07863i | 0.0819951 | − | 0.996633i | \(-0.473871\pi\) |
0.996633 | − | 0.0819951i | \(-0.0261292\pi\) | |||||||
\(368\) | 12.3387 | + | 12.3387i | 0.0335290 | + | 0.0335290i | ||||
\(369\) | −112.262 | − | 84.0579i | −0.304232 | − | 0.227799i | ||||
\(370\) | 341.476 | − | 135.736i | 0.922907 | − | 0.366854i | ||||
\(371\) | −186.447 | − | 561.299i | −0.502552 | − | 1.51294i | ||||
\(372\) | −80.3444 | + | 241.350i | −0.215980 | + | 0.648791i | ||||
\(373\) | 184.517 | − | 184.517i | 0.494683 | − | 0.494683i | −0.415095 | − | 0.909778i | \(-0.636252\pi\) |
0.909778 | + | 0.415095i | \(0.136252\pi\) | |||||||
\(374\) | 20.7125i | 0.0553811i | ||||||||
\(375\) | −272.559 | − | 257.559i | −0.726825 | − | 0.686823i | ||||
\(376\) | − | 133.664i | − | 0.355490i | ||||||
\(377\) | −328.999 | − | 328.999i | −0.872676 | − | 0.872676i | ||||
\(378\) | 160.343 | − | 213.851i | 0.424187 | − | 0.565743i | ||||
\(379\) | − | 127.438i | − | 0.336249i | −0.985766 | − | 0.168124i | \(-0.946229\pi\) | ||
0.985766 | − | 0.168124i | \(-0.0537710\pi\) | |||||||
\(380\) | −64.1504 | − | 161.385i | −0.168817 | − | 0.424698i | ||||
\(381\) | −396.670 | + | 198.531i | −1.04113 | + | 0.521078i | ||||
\(382\) | −163.399 | − | 163.399i | −0.427747 | − | 0.427747i | ||||
\(383\) | 114.212 | − | 114.212i | 0.298204 | − | 0.298204i | −0.542106 | − | 0.840310i | \(-0.682373\pi\) |
0.840310 | + | 0.542106i | \(0.182373\pi\) | |||||||
\(384\) | 30.3519 | − | 15.1909i | 0.0790413 | − | 0.0395596i | ||||
\(385\) | 6.29565 | − | 72.7296i | 0.0163523 | − | 0.188908i | ||||
\(386\) | 72.7491i | 0.188469i | ||||||||
\(387\) | −287.592 | + | 41.3161i | −0.743133 | + | 0.106760i | ||||
\(388\) | 70.7233 | + | 70.7233i | 0.182277 | + | 0.182277i | ||||
\(389\) | −365.324 | −0.939136 | −0.469568 | − | 0.882896i | \(-0.655590\pi\) | ||||
−0.469568 | + | 0.882896i | \(0.655590\pi\) | |||||||
\(390\) | −14.3459 | − | 251.446i | −0.0367842 | − | 0.644734i | ||||
\(391\) | − | 30.6321i | − | 0.0783431i | ||||||
\(392\) | 19.8874 | − | 137.159i | 0.0507330 | − | 0.349894i | ||||
\(393\) | 1.35316 | − | 4.06481i | 0.00344315 | − | 0.0103430i | ||||
\(394\) | − | 38.6571i | − | 0.0981145i | ||||||
\(395\) | −6.66867 | − | 16.7766i | −0.0168827 | − | 0.0424724i | ||||
\(396\) | −30.0527 | − | 22.5025i | −0.0758907 | − | 0.0568245i | ||||
\(397\) | 529.456 | − | 529.456i | 1.33364 | − | 1.33364i | 0.431554 | − | 0.902087i | \(-0.357965\pi\) |
0.902087 | − | 0.431554i | \(-0.142035\pi\) | |||||||
\(398\) | 79.6378 | − | 79.6378i | 0.200095 | − | 0.200095i | ||||
\(399\) | −258.052 | + | 257.715i | −0.646747 | + | 0.645903i | ||||
\(400\) | −72.7109 | + | 68.6523i | −0.181777 | + | 0.171631i | ||||
\(401\) | 185.749i | 0.463216i | 0.972809 | + | 0.231608i | \(0.0743986\pi\) | ||||
−0.972809 | + | 0.231608i | \(0.925601\pi\) | |||||||
\(402\) | −103.897 | + | 312.101i | −0.258450 | + | 0.776369i | ||||
\(403\) | 355.916 | − | 355.916i | 0.883167 | − | 0.883167i | ||||
\(404\) | 25.9847i | 0.0643184i | ||||||||
\(405\) | 249.501 | + | 319.021i | 0.616051 | + | 0.787706i | ||||
\(406\) | 368.172 | − | 122.296i | 0.906827 | − | 0.301221i | ||||
\(407\) | −76.6442 | + | 76.6442i | −0.188315 | + | 0.188315i | ||||
\(408\) | −56.5325 | − | 18.8194i | −0.138560 | − | 0.0461260i | ||||
\(409\) | 615.554 | 1.50502 | 0.752511 | − | 0.658579i | \(-0.228842\pi\) | ||||
0.752511 | + | 0.658579i | \(0.228842\pi\) | |||||||
\(410\) | 43.6229 | − | 101.183i | 0.106397 | − | 0.246788i | ||||
\(411\) | 289.484 | + | 578.397i | 0.704340 | + | 1.40729i | ||||
\(412\) | 91.1632 | − | 91.1632i | 0.221270 | − | 0.221270i | ||||
\(413\) | 153.676 | − | 306.550i | 0.372098 | − | 0.742251i | ||||
\(414\) | 44.4455 | + | 33.2794i | 0.107356 | + | 0.0803850i | ||||
\(415\) | −288.668 | + | 669.563i | −0.695586 | + | 1.61341i | ||||
\(416\) | −67.1614 | −0.161446 | ||||||||
\(417\) | 71.0913 | − | 213.554i | 0.170483 | − | 0.512121i | ||||
\(418\) | 36.2230 | + | 36.2230i | 0.0866578 | + | 0.0866578i | ||||
\(419\) | 427.623i | 1.02058i | 0.860002 | + | 0.510290i | \(0.170462\pi\) | ||||
−0.860002 | + | 0.510290i | \(0.829538\pi\) | |||||||
\(420\) | 192.787 | + | 83.2654i | 0.459017 | + | 0.198251i | ||||
\(421\) | −294.683 | −0.699959 | −0.349980 | − | 0.936757i | \(-0.613811\pi\) | ||||
−0.349980 | + | 0.936757i | \(0.613811\pi\) | |||||||
\(422\) | −146.466 | + | 146.466i | −0.347076 | + | 0.347076i | ||||
\(423\) | −60.4810 | − | 420.995i | −0.142981 | − | 0.995260i | ||||
\(424\) | − | 238.984i | − | 0.563641i | ||||||
\(425\) | 175.475 | + | 5.03796i | 0.412882 | + | 0.0118540i | ||||
\(426\) | −284.452 | + | 142.366i | −0.667728 | + | 0.334193i | ||||
\(427\) | −260.189 | + | 519.018i | −0.609342 | + | 1.21550i | ||||
\(428\) | 99.0397 | + | 99.0397i | 0.231401 | + | 0.231401i | ||||
\(429\) | 33.2497 | + | 66.4339i | 0.0775051 | + | 0.154857i | ||||
\(430\) | −84.3210 | − | 212.129i | −0.196095 | − | 0.493324i | ||||
\(431\) | − | 735.135i | − | 1.70565i | −0.522197 | − | 0.852825i | \(-0.674887\pi\) | ||
0.522197 | − | 0.852825i | \(-0.325113\pi\) | |||||||
\(432\) | 88.7240 | − | 61.5797i | 0.205380 | − | 0.142546i | ||||
\(433\) | −6.15401 | − | 6.15401i | −0.0142125 | − | 0.0142125i | 0.699965 | − | 0.714177i | \(-0.253199\pi\) |
−0.714177 | + | 0.699965i | \(0.753199\pi\) | |||||||
\(434\) | 132.301 | + | 398.294i | 0.304842 | + | 0.917729i | ||||
\(435\) | 33.4836 | + | 586.882i | 0.0769738 | + | 1.34915i | ||||
\(436\) | 340.847 | 0.781760 | ||||||||
\(437\) | −53.5708 | − | 53.5708i | −0.122588 | − | 0.122588i | ||||
\(438\) | 142.501 | − | 428.067i | 0.325346 | − | 0.977322i | ||||
\(439\) | −701.728 | −1.59847 | −0.799235 | − | 0.601019i | \(-0.794761\pi\) | ||||
−0.799235 | + | 0.601019i | \(0.794761\pi\) | |||||||
\(440\) | 11.6780 | − | 27.0870i | 0.0265409 | − | 0.0615613i | ||||
\(441\) | 0.575980 | − | 441.000i | 0.00130608 | − | 0.999999i | ||||
\(442\) | 83.3678 | + | 83.3678i | 0.188615 | + | 0.188615i | ||||
\(443\) | 176.482 | + | 176.482i | 0.398379 | + | 0.398379i | 0.877661 | − | 0.479282i | \(-0.159103\pi\) |
−0.479282 | + | 0.877661i | \(0.659103\pi\) | |||||||
\(444\) | −139.553 | − | 278.831i | −0.314308 | − | 0.627997i | ||||
\(445\) | 45.1440 | + | 113.570i | 0.101447 | + | 0.255214i | ||||
\(446\) | −442.817 | −0.992862 | ||||||||
\(447\) | −173.685 | + | 521.741i | −0.388557 | + | 1.16721i | ||||
\(448\) | 25.0964 | − | 50.0617i | 0.0560188 | − | 0.111745i | ||||
\(449\) | 521.716 | 1.16195 | 0.580976 | − | 0.813921i | \(-0.302671\pi\) | ||||
0.580976 | + | 0.813921i | \(0.302671\pi\) | |||||||
\(450\) | −197.949 | + | 249.131i | −0.439887 | + | 0.553624i | ||||
\(451\) | 32.5017i | 0.0720659i | ||||||||
\(452\) | −278.787 | + | 278.787i | −0.616785 | + | 0.616785i | ||||
\(453\) | −193.198 | + | 580.355i | −0.426485 | + | 1.28114i | ||||
\(454\) | 140.006 | 0.308383 | ||||||||
\(455\) | −267.396 | − | 318.076i | −0.587684 | − | 0.699069i | ||||
\(456\) | −131.779 | + | 65.9543i | −0.288988 | + | 0.144637i | ||||
\(457\) | 34.8065 | + | 34.8065i | 0.0761631 | + | 0.0761631i | 0.744162 | − | 0.667999i | \(-0.232849\pi\) |
−0.667999 | + | 0.744162i | \(0.732849\pi\) | |||||||
\(458\) | −287.075 | + | 287.075i | −0.626802 | + | 0.626802i | ||||
\(459\) | −186.573 | − | 33.6944i | −0.406477 | − | 0.0734082i | ||||
\(460\) | −17.2708 | + | 40.0594i | −0.0375451 | + | 0.0870857i | ||||
\(461\) | 747.746 | 1.62201 | 0.811005 | − | 0.585040i | \(-0.198921\pi\) | ||||
0.811005 | + | 0.585040i | \(0.198921\pi\) | |||||||
\(462\) | −61.9439 | − | 0.0404518i | −0.134078 | − | 8.75580e-5i | ||||
\(463\) | −629.053 | + | 629.053i | −1.35865 | + | 1.35865i | −0.483055 | + | 0.875590i | \(0.660473\pi\) |
−0.875590 | + | 0.483055i | \(0.839527\pi\) | |||||||
\(464\) | 156.756 | 0.337837 | ||||||||
\(465\) | −634.898 | + | 36.2231i | −1.36537 | + | 0.0778991i | ||||
\(466\) | 398.695 | 0.855568 | ||||||||
\(467\) | −72.4294 | − | 72.4294i | −0.155095 | − | 0.155095i | 0.625294 | − | 0.780389i | \(-0.284979\pi\) |
−0.780389 | + | 0.625294i | \(0.784979\pi\) | |||||||
\(468\) | −211.534 | + | 30.3894i | −0.451997 | + | 0.0649347i | ||||
\(469\) | 171.085 | + | 515.051i | 0.364786 | + | 1.09819i | ||||
\(470\) | 310.528 | − | 123.434i | 0.660697 | − | 0.262626i | ||||
\(471\) | 6.38823 | + | 12.7639i | 0.0135631 | + | 0.0270995i | ||||
\(472\) | 97.9751 | − | 97.9751i | 0.207574 | − | 0.207574i | ||||
\(473\) | 47.6124 | + | 47.6124i | 0.100660 | + | 0.100660i | ||||
\(474\) | −13.6989 | + | 6.85619i | −0.0289006 | + | 0.0144645i | ||||
\(475\) | 315.688 | − | 298.067i | 0.664607 | − | 0.627510i | ||||
\(476\) | −93.2942 | + | 30.9895i | −0.195996 | + | 0.0651040i | ||||
\(477\) | −108.136 | − | 752.714i | −0.226701 | − | 1.57802i | ||||
\(478\) | 46.3651 | − | 46.3651i | 0.0969982 | − | 0.0969982i | ||||
\(479\) | − | 49.3199i | − | 0.102964i | −0.998674 | − | 0.0514822i | \(-0.983605\pi\) | ||
0.998674 | − | 0.0514822i | \(-0.0163945\pi\) | |||||||
\(480\) | 63.3202 | + | 56.4849i | 0.131917 | + | 0.117677i | ||||
\(481\) | 616.985i | 1.28271i | ||||||||
\(482\) | −65.3496 | − | 65.3496i | −0.135580 | − | 0.135580i | ||||
\(483\) | 91.6100 | + | 0.0598249i | 0.189669 | + | 0.000123861i | ||||
\(484\) | − | 233.299i | − | 0.482023i | ||||||
\(485\) | −98.9933 | + | 229.614i | −0.204110 | + | 0.473431i | ||||
\(486\) | 251.585 | − | 234.100i | 0.517665 | − | 0.481688i | ||||
\(487\) | 83.8584 | + | 83.8584i | 0.172194 | + | 0.172194i | 0.787943 | − | 0.615749i | \(-0.211146\pi\) |
−0.615749 | + | 0.787943i | \(0.711146\pi\) | |||||||
\(488\) | −165.881 | + | 165.881i | −0.339920 | + | 0.339920i | ||||
\(489\) | −199.850 | − | 399.307i | −0.408692 | − | 0.816579i | ||||
\(490\) | 337.011 | − | 80.4590i | 0.687777 | − | 0.164202i | ||||
\(491\) | 655.752i | 1.33554i | 0.744366 | + | 0.667771i | \(0.232752\pi\) | ||||
−0.744366 | + | 0.667771i | \(0.767248\pi\) | |||||||
\(492\) | −88.7097 | − | 29.5310i | −0.180304 | − | 0.0600225i | ||||
\(493\) | −194.583 | − | 194.583i | −0.394691 | − | 0.394691i | ||||
\(494\) | 291.594 | 0.590272 | ||||||||
\(495\) | 24.5250 | − | 90.5984i | 0.0495455 | − | 0.183027i | ||||
\(496\) | 169.581i | 0.341898i | ||||||||
\(497\) | −235.199 | + | 469.169i | −0.473237 | + | 0.944002i | ||||
\(498\) | 587.023 | + | 195.417i | 1.17876 | + | 0.392404i | ||||
\(499\) | 433.348i | 0.868433i | 0.900809 | + | 0.434216i | \(0.142975\pi\) | ||||
−0.900809 | + | 0.434216i | \(0.857025\pi\) | |||||||
\(500\) | −226.638 | − | 105.523i | −0.453276 | − | 0.211047i | ||||
\(501\) | −130.165 | + | 65.1469i | −0.259811 | + | 0.130034i | ||||
\(502\) | −139.437 | + | 139.437i | −0.277763 | + | 0.277763i | ||||
\(503\) | −147.463 | + | 147.463i | −0.293167 | + | 0.293167i | −0.838330 | − | 0.545163i | \(-0.816468\pi\) |
0.545163 | + | 0.838330i | \(0.316468\pi\) | |||||||
\(504\) | 56.3926 | − | 169.032i | 0.111890 | − | 0.335381i | ||||
\(505\) | −60.3673 | + | 23.9959i | −0.119539 | + | 0.0475166i | ||||
\(506\) | − | 12.8678i | − | 0.0254304i | ||||||
\(507\) | −79.8201 | − | 26.5717i | −0.157436 | − | 0.0524098i | ||||
\(508\) | −209.105 | + | 209.105i | −0.411623 | + | 0.411623i | ||||
\(509\) | − | 554.834i | − | 1.09005i | −0.838421 | − | 0.545024i | \(-0.816521\pi\) | ||
0.838421 | − | 0.545024i | \(-0.183479\pi\) | |||||||
\(510\) | −8.48468 | − | 148.715i | −0.0166366 | − | 0.291598i | ||||
\(511\) | −234.654 | − | 706.428i | −0.459206 | − | 1.38244i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −385.213 | + | 267.360i | −0.750902 | + | 0.521170i | ||||
\(514\) | 647.383 | 1.25950 | ||||||||
\(515\) | 295.975 | + | 127.604i | 0.574709 | + | 0.247774i | ||||
\(516\) | −173.213 | + | 86.6921i | −0.335685 | + | 0.168008i | ||||
\(517\) | −69.6979 | + | 69.6979i | −0.134812 | + | 0.134812i | ||||
\(518\) | −459.897 | − | 230.551i | −0.887831 | − | 0.445079i | ||||
\(519\) | 401.627 | + | 802.463i | 0.773848 | + | 1.54617i | ||||
\(520\) | −62.0211 | − | 156.029i | −0.119271 | − | 0.300055i | ||||
\(521\) | 3.73694 | 0.00717263 | 0.00358632 | − | 0.999994i | \(-0.498858\pi\) | ||||
0.00358632 | + | 0.999994i | \(0.498858\pi\) | |||||||
\(522\) | 493.727 | − | 70.9297i | 0.945836 | − | 0.135881i | ||||
\(523\) | 638.273 | + | 638.273i | 1.22041 | + | 1.22041i | 0.967487 | + | 0.252921i | \(0.0813912\pi\) |
0.252921 | + | 0.967487i | \(0.418609\pi\) | |||||||
\(524\) | − | 2.85608i | − | 0.00545054i | ||||||
\(525\) | −15.4095 | + | 524.774i | −0.0293514 | + | 0.999569i | ||||
\(526\) | 275.063 | 0.522933 | ||||||||
\(527\) | 210.502 | − | 210.502i | 0.399435 | − | 0.399435i | ||||
\(528\) | −23.7478 | − | 7.90554i | −0.0449770 | − | 0.0149726i | ||||
\(529\) | − | 509.970i | − | 0.964026i | ||||||
\(530\) | 555.205 | − | 220.693i | 1.04756 | − | 0.416402i | ||||
\(531\) | 264.255 | − | 352.919i | 0.497655 | − | 0.664631i | ||||
\(532\) | −108.961 | + | 217.353i | −0.204814 | + | 0.408557i | ||||
\(533\) | 130.819 | + | 130.819i | 0.245439 | + | 0.245439i | ||||
\(534\) | 92.7354 | − | 46.4134i | 0.173662 | − | 0.0869165i | ||||
\(535\) | −138.628 | + | 321.548i | −0.259119 | + | 0.601024i | ||||
\(536\) | 219.293i | 0.409129i | ||||||||
\(537\) | 105.065 | − | 315.611i | 0.195652 | − | 0.587730i | ||||
\(538\) | −391.957 | − | 391.957i | −0.728545 | − | 0.728545i | ||||
\(539\) | −81.8901 | + | 61.1499i | −0.151930 | + | 0.113451i | ||||
\(540\) | 224.995 | + | 149.256i | 0.416657 | + | 0.276400i | ||||
\(541\) | −967.493 | −1.78834 | −0.894171 | − | 0.447725i | \(-0.852234\pi\) | ||||
−0.894171 | + | 0.447725i | \(0.852234\pi\) | |||||||
\(542\) | 327.322 | + | 327.322i | 0.603914 | + | 0.603914i | ||||
\(543\) | 69.1674 | + | 23.0255i | 0.127380 | + | 0.0424042i | ||||
\(544\) | −39.7218 | −0.0730180 | ||||||||
\(545\) | 314.760 | + | 791.854i | 0.577542 | + | 1.45294i | ||||
\(546\) | −249.487 | + | 249.161i | −0.456935 | + | 0.456339i | ||||
\(547\) | 400.474 | + | 400.474i | 0.732129 | + | 0.732129i | 0.971041 | − | 0.238913i | \(-0.0767909\pi\) |
−0.238913 | + | 0.971041i | \(0.576791\pi\) | |||||||
\(548\) | 304.902 | + | 304.902i | 0.556391 | + | 0.556391i | ||||
\(549\) | −447.408 | + | 597.525i | −0.814951 | + | 1.08839i | ||||
\(550\) | 73.7124 | + | 2.11631i | 0.134023 | + | 0.00384784i | ||||
\(551\) | −680.588 | −1.23519 | ||||||||
\(552\) | 35.1211 | + | 11.6916i | 0.0636252 | + | 0.0211805i | ||||
\(553\) | −11.3269 | + | 22.5946i | −0.0204826 | + | 0.0408582i | ||||
\(554\) | 76.0232 | 0.137226 | ||||||||
\(555\) | 518.905 | − | 581.698i | 0.934963 | − | 1.04810i | ||||
\(556\) | − | 150.051i | − | 0.269876i | ||||||
\(557\) | 545.370 | − | 545.370i | 0.979121 | − | 0.979121i | −0.0206659 | − | 0.999786i | \(-0.506579\pi\) |
0.999786 | + | 0.0206659i | \(0.00657863\pi\) | |||||||
\(558\) | 76.7329 | + | 534.121i | 0.137514 | + | 0.957207i | ||||
\(559\) | 383.279 | 0.685652 | ||||||||
\(560\) | 139.478 | + | 12.0736i | 0.249069 | + | 0.0215600i | ||||
\(561\) | 19.6651 | + | 39.2915i | 0.0350537 | + | 0.0700383i | ||||
\(562\) | 97.5907 | + | 97.5907i | 0.173649 | + | 0.173649i | ||||
\(563\) | 575.914 | − | 575.914i | 1.02294 | − | 1.02294i | 0.0232074 | − | 0.999731i | \(-0.492612\pi\) |
0.999731 | − | 0.0232074i | \(-0.00738780\pi\) | |||||||
\(564\) | −126.905 | − | 253.560i | −0.225009 | − | 0.449575i | ||||
\(565\) | −905.124 | − | 390.225i | −1.60199 | − | 0.690664i | ||||
\(566\) | 789.098 | 1.39417 | ||||||||
\(567\) | 101.132 | − | 557.908i | 0.178364 | − | 0.983965i | ||||
\(568\) | −149.949 | + | 149.949i | −0.263995 | + | 0.263995i | ||||
\(569\) | 524.362 | 0.921549 | 0.460775 | − | 0.887517i | \(-0.347572\pi\) | ||||
0.460775 | + | 0.887517i | \(0.347572\pi\) | |||||||
\(570\) | −274.917 | − | 245.240i | −0.482311 | − | 0.430246i | ||||
\(571\) | 607.181 | 1.06337 | 0.531683 | − | 0.846944i | \(-0.321560\pi\) | ||||
0.531683 | + | 0.846944i | \(0.321560\pi\) | |||||||
\(572\) | 35.0206 | + | 35.0206i | 0.0612249 | + | 0.0612249i | ||||
\(573\) | −465.104 | − | 154.831i | −0.811700 | − | 0.270211i | ||||
\(574\) | −146.395 | + | 48.6281i | −0.255044 | + | 0.0847180i | ||||
\(575\) | −109.015 | − | 3.12986i | −0.189591 | − | 0.00544323i | ||||
\(576\) | 43.1546 | − | 57.6341i | 0.0749211 | − | 0.100059i | ||||
\(577\) | 274.550 | − | 274.550i | 0.475823 | − | 0.475823i | −0.427970 | − | 0.903793i | \(-0.640771\pi\) |
0.903793 | + | 0.427970i | \(0.140771\pi\) | |||||||
\(578\) | −239.693 | − | 239.693i | −0.414694 | − | 0.414694i | ||||
\(579\) | 69.0702 | + | 138.004i | 0.119292 | + | 0.238350i | ||||
\(580\) | 144.759 | + | 364.175i | 0.249584 | + | 0.627887i | ||||
\(581\) | 968.749 | − | 321.789i | 1.66738 | − | 0.553854i | ||||
\(582\) | 201.308 | + | 67.0146i | 0.345891 | + | 0.115145i | ||||
\(583\) | −124.616 | + | 124.616i | −0.213749 | + | 0.213749i | ||||
\(584\) | − | 300.775i | − | 0.515026i | ||||||
\(585\) | −265.945 | − | 463.371i | −0.454607 | − | 0.792087i | ||||
\(586\) | 124.478i | 0.212419i | ||||||||
\(587\) | −504.649 | − | 504.649i | −0.859709 | − | 0.859709i | 0.131595 | − | 0.991304i | \(-0.457990\pi\) |
−0.991304 | + | 0.131595i | \(0.957990\pi\) | |||||||
\(588\) | −92.4966 | − | 279.071i | −0.157307 | − | 0.474610i | ||||
\(589\) | − | 736.271i | − | 1.25004i | ||||||
\(590\) | 318.091 | + | 137.138i | 0.539138 | + | 0.232438i | ||||
\(591\) | −36.7023 | − | 73.3322i | −0.0621020 | − | 0.124082i | ||||
\(592\) | −146.986 | − | 146.986i | −0.248287 | − | 0.248287i | ||||
\(593\) | −615.151 | + | 615.151i | −1.03735 | + | 1.03735i | −0.0380802 | + | 0.999275i | \(0.512124\pi\) |
−0.999275 | + | 0.0380802i | \(0.987876\pi\) | |||||||
\(594\) | −78.3743 | − | 14.1541i | −0.131943 | − | 0.0238285i | ||||
\(595\) | −158.148 | − | 188.122i | −0.265796 | − | 0.316172i | ||||
\(596\) | 366.594i | 0.615091i | ||||||||
\(597\) | 75.4617 | − | 226.683i | 0.126401 | − | 0.379703i | ||||
\(598\) | −51.7926 | − | 51.7926i | −0.0866098 | − | 0.0866098i | ||||
\(599\) | −103.401 | −0.172623 | −0.0863115 | − | 0.996268i | \(-0.527508\pi\) | ||||
−0.0863115 | + | 0.996268i | \(0.527508\pi\) | |||||||
\(600\) | −72.7513 | + | 199.267i | −0.121252 | + | 0.332111i | ||||
\(601\) | − | 994.271i | − | 1.65436i | −0.561936 | − | 0.827180i | \(-0.689943\pi\) | ||
0.561936 | − | 0.827180i | \(-0.310057\pi\) | |||||||
\(602\) | −143.221 | + | 285.694i | −0.237909 | + | 0.474575i | ||||
\(603\) | 99.2266 | + | 690.695i | 0.164555 | + | 1.14543i | ||||
\(604\) | 407.779i | 0.675130i | ||||||||
\(605\) | 541.999 | − | 215.443i | 0.895865 | − | 0.356105i | ||||
\(606\) | 24.6706 | + | 49.2927i | 0.0407106 | + | 0.0813411i | ||||
\(607\) | 54.5368 | − | 54.5368i | 0.0898464 | − | 0.0898464i | −0.660755 | − | 0.750602i | \(-0.729764\pi\) |
0.750602 | + | 0.660755i | \(0.229764\pi\) | |||||||
\(608\) | −69.4671 | + | 69.4671i | −0.114255 | + | 0.114255i | ||||
\(609\) | 582.308 | − | 581.548i | 0.956171 | − | 0.954923i | ||||
\(610\) | −538.559 | − | 232.188i | −0.882883 | − | 0.380636i | ||||
\(611\) | 561.067i | 0.918277i | ||||||||
\(612\) | −125.109 | + | 17.9735i | −0.204427 | + | 0.0293684i | ||||
\(613\) | 23.2311 | − | 23.2311i | 0.0378975 | − | 0.0378975i | −0.687904 | − | 0.725802i | \(-0.741469\pi\) |
0.725802 | + | 0.687904i | \(0.241469\pi\) | |||||||
\(614\) | 159.509i | 0.259787i | ||||||||
\(615\) | −13.3140 | − | 233.360i | −0.0216488 | − | 0.379448i | ||||
\(616\) | −39.1904 | + | 13.0179i | −0.0636208 | + | 0.0211329i | ||||
\(617\) | 37.9474 | − | 37.9474i | 0.0615032 | − | 0.0615032i | −0.675686 | − | 0.737189i | \(-0.736153\pi\) |
0.737189 | + | 0.675686i | \(0.236153\pi\) | |||||||
\(618\) | 86.3827 | − | 259.489i | 0.139778 | − | 0.419885i | ||||
\(619\) | −182.389 | −0.294651 | −0.147326 | − | 0.989088i | \(-0.547067\pi\) | ||||
−0.147326 | + | 0.989088i | \(0.547067\pi\) | |||||||
\(620\) | −393.970 | + | 156.602i | −0.635436 | + | 0.252585i | ||||
\(621\) | 115.909 | + | 20.9328i | 0.186649 | + | 0.0337082i | ||||
\(622\) | −358.994 | + | 358.994i | −0.577160 | + | 0.577160i | ||||
\(623\) | 76.6781 | − | 152.955i | 0.123079 | − | 0.245514i | ||||
\(624\) | −127.405 | + | 63.7651i | −0.204174 | + | 0.102188i | ||||
\(625\) | 35.8585 | − | 623.970i | 0.0573736 | − | 0.998353i | ||||
\(626\) | −618.439 | −0.987922 | ||||||||
\(627\) | 103.106 | + | 34.3235i | 0.164443 | + | 0.0547423i | ||||
\(628\) | 6.72848 | + | 6.72848i | 0.0107141 | + | 0.0107141i | ||||
\(629\) | 364.908i | 0.580140i | ||||||||
\(630\) | 444.770 | − | 25.0843i | 0.705985 | − | 0.0398163i | ||||
\(631\) | 165.153 | 0.261732 | 0.130866 | − | 0.991400i | \(-0.458224\pi\) | ||||
0.130866 | + | 0.991400i | \(0.458224\pi\) | |||||||
\(632\) | −7.22137 | + | 7.22137i | −0.0114262 | + | 0.0114262i | ||||
\(633\) | −138.785 | + | 416.904i | −0.219250 | + | 0.658617i | ||||
\(634\) | − | 92.7084i | − | 0.146228i | ||||||
\(635\) | −678.891 | − | 292.689i | −1.06912 | − | 0.460928i | ||||
\(636\) | −226.899 | − | 453.351i | −0.356759 | − | 0.712815i | ||||
\(637\) | −83.4789 | + | 575.735i | −0.131050 | + | 0.903823i | ||||
\(638\) | −81.7390 | − | 81.7390i | −0.128118 | − | 0.128118i | ||||
\(639\) | −404.437 | + | 540.136i | −0.632921 | + | 0.845283i | ||||
\(640\) | 51.9465 | + | 22.3956i | 0.0811664 | + | 0.0349932i | ||||
\(641\) | − | 168.644i | − | 0.263095i | −0.991310 | − | 0.131548i | \(-0.958005\pi\) | ||
0.991310 | − | 0.131548i | \(-0.0419946\pi\) | |||||||
\(642\) | 281.909 | + | 93.8461i | 0.439110 | + | 0.146178i | ||||
\(643\) | −25.2955 | − | 25.2955i | −0.0393398 | − | 0.0393398i | 0.687163 | − | 0.726503i | \(-0.258856\pi\) |
−0.726503 | + | 0.687163i | \(0.758856\pi\) | |||||||
\(644\) | 57.9594 | − | 19.2524i | 0.0899991 | − | 0.0298950i | ||||
\(645\) | −361.359 | − | 322.351i | −0.560246 | − | 0.499768i | ||||
\(646\) | 172.460 | 0.266966 | ||||||||
\(647\) | 11.1919 | + | 11.1919i | 0.0172981 | + | 0.0172981i | 0.715703 | − | 0.698405i | \(-0.246106\pi\) |
−0.698405 | + | 0.715703i | \(0.746106\pi\) | |||||||
\(648\) | 109.843 | − | 201.054i | 0.169511 | − | 0.310268i | ||||
\(649\) | −102.176 | −0.157437 | ||||||||
\(650\) | 305.210 | − | 288.174i | 0.469554 | − | 0.443344i | ||||
\(651\) | 629.128 | + | 629.950i | 0.966402 | + | 0.967665i | ||||
\(652\) | −210.495 | − | 210.495i | −0.322845 | − | 0.322845i | ||||
\(653\) | −319.932 | − | 319.932i | −0.489941 | − | 0.489941i | 0.418346 | − | 0.908288i | \(-0.362610\pi\) |
−0.908288 | + | 0.418346i | \(0.862610\pi\) | |||||||
\(654\) | 646.585 | − | 323.611i | 0.988662 | − | 0.494818i | ||||
\(655\) | 6.63522 | − | 2.63749i | 0.0101301 | − | 0.00402670i | ||||
\(656\) | −62.3307 | −0.0950162 | ||||||||
\(657\) | −136.096 | − | 947.335i | −0.207148 | − | 1.44191i | ||||
\(658\) | −418.216 | − | 209.656i | −0.635587 | − | 0.318626i | ||||
\(659\) | −692.273 | −1.05049 | −0.525245 | − | 0.850951i | \(-0.676026\pi\) | ||||
−0.525245 | + | 0.850951i | \(0.676026\pi\) | |||||||
\(660\) | −3.56419 | − | 62.4712i | −0.00540029 | − | 0.0946534i | ||||
\(661\) | 586.898i | 0.887894i | 0.896053 | + | 0.443947i | \(0.146422\pi\) | ||||
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(662\) | 373.528 | − | 373.528i | 0.564242 | − | 0.564242i | ||||
\(663\) | 237.300 | + | 78.9961i | 0.357919 | + | 0.119149i | ||||
\(664\) | 412.464 | 0.621180 | ||||||||
\(665\) | −605.573 | − | 52.4199i | −0.910636 | − | 0.0788268i | ||||
\(666\) | −529.461 | − | 396.444i | −0.794987 | − | 0.595261i | ||||
\(667\) | 120.885 | + | 120.885i | 0.181237 | + | 0.181237i | ||||
\(668\) | −68.6168 | + | 68.6168i | −0.102720 | + | 0.102720i | ||||
\(669\) | −840.020 | + | 420.424i | −1.25563 | + | 0.628437i | ||||
\(670\) | −509.460 | + | 202.509i | −0.760387 | + | 0.302253i | ||||
\(671\) | 172.994 | 0.257815 | ||||||||
\(672\) | 0.0775770 | − | 118.794i | 0.000115442 | − | 0.176777i | ||||
\(673\) | 419.099 | − | 419.099i | 0.622732 | − | 0.622732i | −0.323497 | − | 0.946229i | \(-0.604859\pi\) |
0.946229 | + | 0.323497i | \(0.104859\pi\) | |||||||
\(674\) | −327.154 | −0.485392 | ||||||||
\(675\) | −138.976 | + | 660.538i | −0.205890 | + | 0.978575i | ||||
\(676\) | −56.0845 | −0.0829653 | ||||||||
\(677\) | −459.724 | − | 459.724i | −0.679061 | − | 0.679061i | 0.280727 | − | 0.959788i | \(-0.409425\pi\) |
−0.959788 | + | 0.280727i | \(0.909425\pi\) | |||||||
\(678\) | −264.167 | + | 793.545i | −0.389627 | + | 1.17042i | ||||
\(679\) | 332.214 | − | 110.352i | 0.489270 | − | 0.162521i | ||||
\(680\) | −36.6816 | − | 92.2813i | −0.0539436 | − | 0.135708i | ||||
\(681\) | 265.590 | − | 132.926i | 0.390000 | − | 0.195192i | ||||
\(682\) | 88.4266 | − | 88.4266i | 0.129658 | − | 0.129658i | ||||
\(683\) | 66.6626 | + | 66.6626i | 0.0976027 | + | 0.0976027i | 0.754222 | − | 0.656619i | \(-0.228014\pi\) |
−0.656619 | + | 0.754222i | \(0.728014\pi\) | |||||||
\(684\) | −187.364 | + | 250.230i | −0.273924 | + | 0.365833i | ||||
\(685\) | −426.780 | + | 989.913i | −0.623036 | + | 1.44513i | ||||
\(686\) | −397.956 | − | 277.361i | −0.580110 | − | 0.404317i | ||||
\(687\) | −272.021 | + | 817.138i | −0.395956 | + | 1.18943i | ||||
\(688\) | −91.3095 | + | 91.3095i | −0.132717 | + | 0.132717i | ||||
\(689\) | 1003.16i | 1.45596i | ||||||||
\(690\) | 5.27115 | + | 92.3898i | 0.00763935 | + | 0.133898i | ||||
\(691\) | 11.4526i | 0.0165739i | 0.999966 | + | 0.00828695i | \(0.00263785\pi\) | ||||
−0.999966 | + | 0.00828695i | \(0.997362\pi\) | |||||||
\(692\) | 423.018 | + | 423.018i | 0.611298 | + | 0.611298i | ||||
\(693\) | −117.546 | + | 58.7348i | −0.169618 | + | 0.0847543i | ||||
\(694\) | 463.927i | 0.668483i | ||||||||
\(695\) | 348.597 | − | 138.567i | 0.501579 | − | 0.199377i | ||||
\(696\) | 297.365 | − | 148.829i | 0.427249 | − | 0.213835i | ||||
\(697\) | 77.3714 | + | 77.3714i | 0.111006 | + | 0.111006i | ||||
\(698\) | 143.315 | − | 143.315i | 0.205323 | − | 0.205323i | ||||
\(699\) | 756.321 | − | 378.533i | 1.08200 | − | 0.541535i | ||||
\(700\) | 100.754 | + | 335.184i | 0.143934 | + | 0.478835i | ||||
\(701\) | 635.231i | 0.906178i | 0.891465 | + | 0.453089i | \(0.149678\pi\) | ||||
−0.891465 | + | 0.453089i | \(0.850322\pi\) | |||||||
\(702\) | −372.426 | + | 258.486i | −0.530522 | + | 0.368214i | ||||
\(703\) | 638.167 | + | 638.167i | 0.907777 | + | 0.907777i | ||||
\(704\) | −16.6861 | −0.0237018 | ||||||||
\(705\) | 471.876 | − | 528.978i | 0.669328 | − | 0.750324i | ||||
\(706\) | − | 385.875i | − | 0.546564i | ||||||
\(707\) | 81.3022 | + | 40.7576i | 0.114996 | + | 0.0576486i | ||||
\(708\) | 92.8374 | − | 278.879i | 0.131126 | − | 0.393896i | ||||
\(709\) | 68.9098i | 0.0971930i | 0.998818 | + | 0.0485965i | \(0.0154748\pi\) | ||||
−0.998818 | + | 0.0485965i | \(0.984525\pi\) | |||||||
\(710\) | −486.833 | − | 209.888i | −0.685680 | − | 0.295616i | ||||
\(711\) | −19.4772 | + | 26.0123i | −0.0273941 | + | 0.0365855i | ||||
\(712\) | 48.8855 | − | 48.8855i | 0.0686594 | − | 0.0686594i | ||||
\(713\) | −130.776 | + | 130.776i | −0.183416 | + | 0.183416i | ||||
\(714\) | −147.556 | + | 147.363i | −0.206661 | + | 0.206391i | ||||
\(715\) | −49.0193 | + | 113.700i | −0.0685584 | + | 0.159021i | ||||
\(716\) | − | 221.760i | − | 0.309720i | ||||||
\(717\) | 43.9338 | − | 131.975i | 0.0612745 | − | 0.184065i | ||||
\(718\) | −424.811 | + | 424.811i | −0.591659 | + | 0.591659i | ||||
\(719\) | − | 457.334i | − | 0.636069i | −0.948079 | − | 0.318034i | \(-0.896977\pi\) | ||
0.948079 | − | 0.318034i | \(-0.103023\pi\) | |||||||
\(720\) | 173.747 | + | 47.0333i | 0.241315 | + | 0.0653240i | ||||
\(721\) | −142.245 | − | 428.228i | −0.197288 | − | 0.593936i | ||||
\(722\) | −59.3948 | + | 59.3948i | −0.0822642 | + | 0.0822642i | ||||
\(723\) | −186.013 | − | 61.9228i | −0.257279 | − | 0.0856470i | ||||
\(724\) | 48.5995 | 0.0671264 | ||||||||
\(725\) | −712.368 | + | 672.605i | −0.982576 | + | 0.927730i | ||||
\(726\) | −221.502 | − | 442.567i | −0.305099 | − | 0.609596i | ||||
\(727\) | −990.753 | + | 990.753i | −1.36280 | + | 1.36280i | −0.492464 | + | 0.870333i | \(0.663904\pi\) |
−0.870333 | + | 0.492464i | \(0.836096\pi\) | |||||||
\(728\) | −105.344 | + | 210.138i | −0.144704 | + | 0.288651i | ||||
\(729\) | 254.993 | − | 682.949i | 0.349784 | − | 0.936830i | ||||
\(730\) | 698.758 | − | 277.755i | 0.957203 | − | 0.380486i | ||||
\(731\) | 226.686 | 0.310104 | ||||||||
\(732\) | −157.183 | + | 472.168i | −0.214730 | + | 0.645038i | ||||
\(733\) | 443.025 | + | 443.025i | 0.604400 | + | 0.604400i | 0.941477 | − | 0.337077i | \(-0.109438\pi\) |
−0.337077 | + | 0.941477i | \(0.609438\pi\) | |||||||
\(734\) | − | 791.713i | − | 1.07863i | ||||||
\(735\) | 562.917 | − | 472.599i | 0.765873 | − | 0.642992i | ||||
\(736\) | 24.6773 | 0.0335290 | ||||||||
\(737\) | 114.348 | − | 114.348i | 0.155154 | − | 0.155154i | ||||
\(738\) | −196.319 | + | 28.2036i | −0.266015 | + | 0.0382163i | ||||
\(739\) | − | 1424.55i | − | 1.92768i | −0.266488 | − | 0.963838i | \(-0.585863\pi\) | ||
0.266488 | − | 0.963838i | \(-0.414137\pi\) | |||||||
\(740\) | 205.740 | − | 477.212i | 0.278027 | − | 0.644880i | ||||
\(741\) | 553.152 | − | 276.849i | 0.746494 | − | 0.373615i | ||||
\(742\) | −747.746 | − | 374.852i | −1.00774 | − | 0.505192i | ||||
\(743\) | −823.562 | − | 823.562i | −1.10843 | − | 1.10843i | −0.993357 | − | 0.115071i | \(-0.963291\pi\) |
−0.115071 | − | 0.993357i | \(-0.536709\pi\) | |||||||
\(744\) | 161.006 | + | 321.695i | 0.216406 | + | 0.432385i | ||||
\(745\) | −851.668 | + | 338.536i | −1.14318 | + | 0.454411i | ||||
\(746\) | − | 369.034i | − | 0.494683i | ||||||
\(747\) | 1299.11 | − | 186.633i | 1.73911 | − | 0.249844i | ||||
\(748\) | 20.7125 | + | 20.7125i | 0.0276905 | + | 0.0276905i | ||||
\(749\) | 465.227 | − | 154.534i | 0.621131 | − | 0.206321i | ||||
\(750\) | −530.118 | + | 15.0005i | −0.706824 | + | 0.0200007i | ||||
\(751\) | −436.270 | −0.580919 | −0.290459 | − | 0.956887i | \(-0.593808\pi\) | ||||
−0.290459 | + | 0.956887i | \(0.593808\pi\) | |||||||
\(752\) | −133.664 | − | 133.664i | −0.177745 | − | 0.177745i | ||||
\(753\) | −132.125 | + | 396.896i | −0.175465 | + | 0.527087i | ||||
\(754\) | −657.998 | −0.872676 | ||||||||
\(755\) | −947.348 | + | 376.569i | −1.25476 | + | 0.498767i | ||||
\(756\) | −53.5080 | − | 374.194i | −0.0707778 | − | 0.494965i | ||||
\(757\) | 39.6428 | + | 39.6428i | 0.0523684 | + | 0.0523684i | 0.732806 | − | 0.680438i | \(-0.238210\pi\) |
−0.680438 | + | 0.732806i | \(0.738210\pi\) | |||||||
\(758\) | −127.438 | − | 127.438i | −0.168124 | − | 0.168124i | ||||
\(759\) | −12.2171 | − | 24.4100i | −0.0160962 | − | 0.0321608i | ||||
\(760\) | −225.536 | − | 97.2350i | −0.296758 | − | 0.127941i | ||||
\(761\) | 1032.38 | 1.35661 | 0.678307 | − | 0.734778i | \(-0.262714\pi\) | ||||
0.678307 | + | 0.734778i | \(0.262714\pi\) | |||||||
\(762\) | −198.139 | + | 595.201i | −0.260026 | + | 0.781103i | ||||
\(763\) | 534.628 | − | 1066.46i | 0.700692 | − | 1.39772i | ||||
\(764\) | −326.799 | −0.427747 | ||||||||
\(765\) | −157.290 | − | 274.055i | −0.205608 | − | 0.358242i | ||||
\(766\) | − | 228.424i | − | 0.298204i | ||||||
\(767\) | −411.259 | + | 411.259i | −0.536191 | + | 0.536191i | ||||
\(768\) | 15.1610 | − | 45.5428i | 0.0197409 | − | 0.0593005i | ||||
\(769\) | 119.034 | 0.154791 | 0.0773956 | − | 0.997000i | \(-0.475340\pi\) | ||||
0.0773956 | + | 0.997000i | \(0.475340\pi\) | |||||||
\(770\) | −66.4340 | − | 79.0253i | −0.0862779 | − | 0.102630i | ||||
\(771\) | 1228.08 | − | 614.646i | 1.59284 | − | 0.797206i | ||||
\(772\) | 72.7491 | + | 72.7491i | 0.0942345 | + | 0.0942345i | ||||
\(773\) | −386.934 | + | 386.934i | −0.500562 | + | 0.500562i | −0.911612 | − | 0.411051i | \(-0.865162\pi\) |
0.411051 | + | 0.911612i | \(0.365162\pi\) | |||||||
\(774\) | −246.276 | + | 328.908i | −0.318186 | + | 0.424946i | ||||
\(775\) | −727.634 | − | 770.651i | −0.938883 | − | 0.994388i | ||||
\(776\) | 141.447 | 0.182277 | ||||||||
\(777\) | −1091.31 | − | 0.712669i | −1.40452 | − | 0.000917206i | ||||
\(778\) | −365.324 | + | 365.324i | −0.469568 | + | 0.469568i | ||||
\(779\) | 270.621 | 0.347395 | ||||||||
\(780\) | −265.792 | − | 237.100i | −0.340759 | − | 0.303975i | ||||
\(781\) | 156.379 | 0.200229 | ||||||||
\(782\) | −30.6321 | − | 30.6321i | −0.0391715 | − | 0.0391715i | ||||
\(783\) | 869.253 | − | 603.313i | 1.11016 | − | 0.770514i | ||||
\(784\) | −117.271 | − | 157.046i | −0.149581 | − | 0.200314i | ||||
\(785\) | −9.41804 | + | 21.8451i | −0.0119975 | + | 0.0278281i | ||||
\(786\) | −2.71165 | − | 5.41797i | −0.00344994 | − | 0.00689309i | ||||
\(787\) | −111.605 | + | 111.605i | −0.141810 | + | 0.141810i | −0.774448 | − | 0.632638i | \(-0.781972\pi\) |
0.632638 | + | 0.774448i | \(0.281972\pi\) | |||||||
\(788\) | −38.6571 | − | 38.6571i | −0.0490572 | − | 0.0490572i | ||||
\(789\) | 521.792 | − | 261.153i | 0.661333 | − | 0.330993i | ||||
\(790\) | −23.4453 | − | 10.1079i | −0.0296776 | − | 0.0127949i | ||||
\(791\) | 434.999 | + | 1309.57i | 0.549935 | + | 1.65558i | ||||
\(792\) | −52.5552 | + | 7.55019i | −0.0663576 | + | 0.00953307i | ||||
\(793\) | 696.300 | − | 696.300i | 0.878058 | − | 0.878058i | ||||
\(794\) | − | 1058.91i | − | 1.33364i | ||||||
\(795\) | 843.687 | − | 945.782i | 1.06124 | − | 1.18966i | ||||
\(796\) | − | 159.276i | − | 0.200095i | ||||||
\(797\) | −80.8641 | − | 80.8641i | −0.101461 | − | 0.101461i | 0.654554 | − | 0.756015i | \(-0.272856\pi\) |
−0.756015 | + | 0.654554i | \(0.772856\pi\) | |||||||
\(798\) | −0.336816 | + | 515.767i | −0.000422075 | + | 0.646325i | ||||
\(799\) | 331.837i | 0.415315i | ||||||||
\(800\) | −4.05860 | + | 141.363i | −0.00507324 | + | 0.176704i | ||||
\(801\) | 131.852 | − | 176.092i | 0.164609 | − | 0.219840i | ||||
\(802\) | 185.749 | + | 185.749i | 0.231608 | + | 0.231608i | ||||
\(803\) | −156.836 | + | 156.836i | −0.195313 | + | 0.195313i | ||||
\(804\) | 208.204 | + | 415.997i | 0.258960 | + | 0.517410i | ||||
\(805\) | 98.2504 | + | 116.872i | 0.122050 | + | 0.145183i | ||||
\(806\) | − | 711.833i | − | 0.883167i | ||||||
\(807\) | −1115.68 | − | 371.403i | −1.38250 | − | 0.460227i | ||||
\(808\) | 25.9847 | + | 25.9847i | 0.0321592 | + | 0.0321592i | ||||
\(809\) | −115.327 | −0.142555 | −0.0712776 | − | 0.997457i | \(-0.522708\pi\) | ||||
−0.0712776 | + | 0.997457i | \(0.522708\pi\) | |||||||
\(810\) | 568.522 | + | 69.5205i | 0.701879 | + | 0.0858278i | ||||
\(811\) | 285.468i | 0.351996i | 0.984391 | + | 0.175998i | \(0.0563152\pi\) | ||||
−0.984391 | + | 0.175998i | \(0.943685\pi\) | |||||||
\(812\) | 245.876 | − | 490.468i | 0.302803 | − | 0.604024i | ||||
\(813\) | 931.696 | + | 310.157i | 1.14600 | + | 0.381497i | ||||
\(814\) | 153.288i | 0.188315i | ||||||||
\(815\) | 294.635 | − | 683.404i | 0.361516 | − | 0.838533i | ||||
\(816\) | −75.3519 | + | 37.7131i | −0.0923430 | + | 0.0462170i | ||||
\(817\) | 396.438 | − | 396.438i | 0.485236 | − | 0.485236i | ||||
\(818\) | 615.554 | − | 615.554i | 0.752511 | − | 0.752511i | ||||
\(819\) | −236.713 | + | 709.527i | −0.289027 | + | 0.866333i | ||||
\(820\) | −57.5601 | − | 144.806i | −0.0701953 | − | 0.176593i | ||||
\(821\) | − | 607.687i | − | 0.740179i | −0.928996 | − | 0.370089i | \(-0.879327\pi\) | ||
0.928996 | − | 0.370089i | \(-0.120673\pi\) | |||||||
\(822\) | 867.881 | + | 288.914i | 1.05582 | + | 0.351476i | ||||
\(823\) | −1073.10 | + | 1073.10i | −1.30388 | + | 1.30388i | −0.378132 | + | 0.925752i | \(0.623433\pi\) |
−0.925752 | + | 0.378132i | \(0.876567\pi\) | |||||||
\(824\) | − | 182.326i | − | 0.221270i | ||||||
\(825\) | 141.841 | − | 65.9702i | 0.171929 | − | 0.0799639i | ||||
\(826\) | −152.873 | − | 460.226i | −0.185077 | − | 0.557175i | ||||
\(827\) | 874.440 | − | 874.440i | 1.05736 | − | 1.05736i | 0.0591122 | − | 0.998251i | \(-0.481173\pi\) |
0.998251 | − | 0.0591122i | \(-0.0188270\pi\) | |||||||
\(828\) | 77.7249 | − | 11.1661i | 0.0938706 | − | 0.0134856i | ||||
\(829\) | −369.045 | −0.445169 | −0.222585 | − | 0.974913i | \(-0.571449\pi\) | ||||
−0.222585 | + | 0.974913i | \(0.571449\pi\) | |||||||
\(830\) | 380.895 | + | 958.231i | 0.458910 | + | 1.15450i | ||||
\(831\) | 144.215 | − | 72.1788i | 0.173544 | − | 0.0868578i | ||||
\(832\) | −67.1614 | + | 67.1614i | −0.0807228 | + | 0.0807228i | ||||
\(833\) | −49.3726 | + | 340.512i | −0.0592708 | + | 0.408777i | ||||
\(834\) | −142.463 | − | 284.646i | −0.170819 | − | 0.341302i | ||||
\(835\) | −222.775 | − | 96.0447i | −0.266796 | − | 0.115024i | ||||
\(836\) | 72.4459 | 0.0866578 | ||||||||
\(837\) | 652.673 | + | 940.371i | 0.779777 | + | 1.12350i | ||||
\(838\) | 427.623 | + | 427.623i | 0.510290 | + | 0.510290i | ||||
\(839\) | 1424.80i | 1.69821i | 0.528223 | + | 0.849106i | \(0.322858\pi\) | ||||
−0.528223 | + | 0.849106i | \(0.677142\pi\) | |||||||
\(840\) | 276.053 | − | 109.522i | 0.328634 | − | 0.130383i | ||||
\(841\) | 694.784 | 0.826140 | ||||||||
\(842\) | −294.683 | + | 294.683i | −0.349980 | + | 0.349980i | ||||
\(843\) | 277.784 | + | 92.4731i | 0.329519 | + | 0.109695i | ||||
\(844\) | 292.932i | 0.347076i | ||||||||
\(845\) | −51.7920 | − | 130.295i | −0.0612923 | − | 0.154195i | ||||
\(846\) | −481.476 | − | 360.514i | −0.569121 | − | 0.426139i | ||||
\(847\) | −729.959 | − | 365.936i | −0.861817 | − | 0.432037i | ||||
\(848\) | −238.984 | − | 238.984i | −0.281821 | − | 0.281821i | ||||
\(849\) | 1496.91 | − | 749.195i | 1.76315 | − | 0.882444i | ||||
\(850\) | 180.513 | − | 170.437i | 0.212368 | − | 0.200514i | ||||
\(851\) | − | 226.701i | − | 0.266394i | ||||||
\(852\) | −142.086 | + | 426.819i | −0.166767 | + | 0.500961i | ||||
\(853\) | 459.198 | + | 459.198i | 0.538332 | + | 0.538332i | 0.923039 | − | 0.384707i | \(-0.125697\pi\) |
−0.384707 | + | 0.923039i | \(0.625697\pi\) | |||||||
\(854\) | 258.829 | + | 779.207i | 0.303079 | + | 0.912420i | ||||
\(855\) | −754.355 | − | 204.204i | −0.882286 | − | 0.238835i | ||||
\(856\) | 198.079 | 0.231401 | ||||||||
\(857\) | −733.866 | − | 733.866i | −0.856319 | − | 0.856319i | 0.134583 | − | 0.990902i | \(-0.457030\pi\) |
−0.990902 | + | 0.134583i | \(0.957030\pi\) | |||||||
\(858\) | 99.6835 | + | 33.1842i | 0.116181 | + | 0.0386762i | ||||
\(859\) | 223.858 | 0.260603 | 0.130301 | − | 0.991474i | \(-0.458405\pi\) | ||||
0.130301 | + | 0.991474i | \(0.458405\pi\) | |||||||
\(860\) | −296.450 | − | 127.808i | −0.344710 | − | 0.148614i | ||||
\(861\) | −231.542 | + | 231.240i | −0.268922 | + | 0.268571i | ||||
\(862\) | −735.135 | − | 735.135i | −0.852825 | − | 0.852825i | ||||
\(863\) | −500.157 | − | 500.157i | −0.579556 | − | 0.579556i | 0.355225 | − | 0.934781i | \(-0.384404\pi\) |
−0.934781 | + | 0.355225i | \(0.884404\pi\) | |||||||
\(864\) | 27.1443 | − | 150.304i | 0.0314170 | − | 0.173963i | ||||
\(865\) | −592.110 | + | 1373.39i | −0.684520 | + | 1.58774i | ||||
\(866\) | −12.3080 | −0.0142125 | ||||||||
\(867\) | −682.268 | − | 227.124i | −0.786930 | − | 0.261965i | ||||
\(868\) | 530.596 | + | 265.993i | 0.611285 | + | 0.306443i | ||||
\(869\) | 7.53102 | 0.00866630 | ||||||||
\(870\) | 620.365 | + | 553.398i | 0.713064 | + | 0.636090i | ||||
\(871\) | − | 920.501i | − | 1.05683i | ||||||
\(872\) | 340.847 | − | 340.847i | 0.390880 | − | 0.390880i | ||||
\(873\) | 445.506 | − | 64.0023i | 0.510317 | − | 0.0733131i | ||||
\(874\) | −107.142 | −0.122588 | ||||||||
\(875\) | −685.655 | + | 543.602i | −0.783605 | + | 0.621259i | ||||
\(876\) | −285.565 | − | 570.568i | −0.325988 | − | 0.651334i | ||||
\(877\) | −845.141 | − | 845.141i | −0.963673 | − | 0.963673i | 0.0356898 | − | 0.999363i | \(-0.488637\pi\) |
−0.999363 | + | 0.0356898i | \(0.988637\pi\) | |||||||
\(878\) | −701.728 | + | 701.728i | −0.799235 | + | 0.799235i | ||||
\(879\) | 118.183 | + | 236.133i | 0.134452 | + | 0.268638i | ||||
\(880\) | −15.4090 | − | 38.7649i | −0.0175102 | − | 0.0440511i | ||||
\(881\) | −1655.83 | −1.87949 | −0.939747 | − | 0.341870i | \(-0.888940\pi\) | ||||
−0.939747 | + | 0.341870i | \(0.888940\pi\) | |||||||
\(882\) | −440.424 | − | 441.576i | −0.499347 | − | 0.500653i | ||||
\(883\) | −128.174 | + | 128.174i | −0.145158 | + | 0.145158i | −0.775951 | − | 0.630793i | \(-0.782730\pi\) |
0.630793 | + | 0.775951i | \(0.282730\pi\) | |||||||
\(884\) | 166.736 | 0.188615 | ||||||||
\(885\) | 733.620 | − | 41.8555i | 0.828949 | − | 0.0472944i | ||||
\(886\) | 352.964 | 0.398379 | ||||||||
\(887\) | 1006.62 | + | 1006.62i | 1.13486 | + | 1.13486i | 0.989359 | + | 0.145497i | \(0.0464781\pi\) |
0.145497 | + | 0.989359i | \(0.453522\pi\) | |||||||
\(888\) | −418.383 | − | 139.278i | −0.471152 | − | 0.156844i | ||||
\(889\) | 326.272 | + | 982.244i | 0.367010 | + | 1.10489i | ||||
\(890\) | 158.714 | + | 68.4263i | 0.178331 | + | 0.0768835i | ||||
\(891\) | −162.114 | + | 47.5608i | −0.181946 | + | 0.0533791i | ||||
\(892\) | −442.817 | + | 442.817i | −0.496431 | + | 0.496431i | ||||
\(893\) | 580.330 | + | 580.330i | 0.649865 | + | 0.649865i | ||||
\(894\) | 348.056 | + | 695.426i | 0.389324 | + | 0.777881i | ||||
\(895\) | 515.190 | − | 204.787i | 0.575631 | − | 0.228812i | ||||
\(896\) | −24.9653 | − | 75.1581i | −0.0278630 | − | 0.0838818i | ||||
\(897\) | −147.424 | − | 49.0767i | −0.164352 | − | 0.0547120i | ||||
\(898\) | 521.716 | − | 521.716i | 0.580976 | − | 0.580976i | ||||
\(899\) | 1661.44i | 1.84809i | ||||||||
\(900\) | 51.1814 | + | 447.080i | 0.0568683 | + | 0.496755i | ||||
\(901\) | 593.304i | 0.658495i | ||||||||
\(902\) | 32.5017 | + | 32.5017i | 0.0360329 | + | 0.0360329i | ||||
\(903\) | −0.442720 | + | 677.938i | −0.000490277 | + | 0.750762i | ||||
\(904\) | 557.573i | 0.616785i | ||||||||
\(905\) | 44.8799 | + | 112.906i | 0.0495910 | + | 0.124758i | ||||
\(906\) | 387.158 | + | 773.553i | 0.427327 | + | 0.853811i | ||||
\(907\) | 9.93474 | + | 9.93474i | 0.0109534 | + | 0.0109534i | 0.712562 | − | 0.701609i | \(-0.247535\pi\) |
−0.701609 | + | 0.712562i | \(0.747535\pi\) | |||||||
\(908\) | 140.006 | − | 140.006i | 0.154192 | − | 0.154192i | ||||
\(909\) | 93.6001 | + | 70.0848i | 0.102970 | + | 0.0771010i | ||||
\(910\) | −585.472 | − | 50.6799i | −0.643376 | − | 0.0556922i | ||||
\(911\) | 297.086i | 0.326110i | 0.986617 | + | 0.163055i | \(0.0521348\pi\) | ||||
−0.986617 | + | 0.163055i | \(0.947865\pi\) | |||||||
\(912\) | −65.8244 | + | 197.733i | −0.0721758 | + | 0.216812i | ||||
\(913\) | −215.075 | − | 215.075i | −0.235570 | − | 0.235570i | ||||
\(914\) | 69.6131 | 0.0761631 | ||||||||
\(915\) | −1242.09 | + | 70.8654i | −1.35747 | + | 0.0774485i | ||||
\(916\) | 574.151i | 0.626802i | ||||||||
\(917\) | −8.93627 | − | 4.47984i | −0.00974511 | − | 0.00488532i | ||||
\(918\) | −220.267 | + | 152.878i | −0.239942 | + | 0.166534i | ||||
\(919\) | − | 67.9916i | − | 0.0739843i | −0.999316 | − | 0.0369922i | \(-0.988222\pi\) | ||
0.999316 | − | 0.0369922i | \(-0.0117777\pi\) | |||||||
\(920\) | 22.7886 | + | 57.3302i | 0.0247703 | + | 0.0623154i | ||||
\(921\) | 151.443 | + | 302.588i | 0.164433 | + | 0.328543i | ||||
\(922\) | 747.746 | − | 747.746i | 0.811005 | − | 0.811005i | ||||
\(923\) | 629.424 | − | 629.424i | 0.681933 | − | 0.681933i | ||||
\(924\) | −61.9844 | + | 61.9035i | −0.0670826 | + | 0.0669951i | ||||
\(925\) | 1298.65 | + | 37.2847i | 1.40394 | + | 0.0403078i | ||||
\(926\) | 1258.11i | 1.35865i | ||||||||
\(927\) | −82.4998 | − | 574.263i | −0.0889965 | − | 0.619486i | ||||
\(928\) | 156.756 | − | 156.756i | 0.168918 | − | 0.168918i | ||||
\(929\) | 81.2126i | 0.0874194i | 0.999044 | + | 0.0437097i | \(0.0139177\pi\) | ||||
−0.999044 | + | 0.0437097i | \(0.986082\pi\) | |||||||
\(930\) | −598.675 | + | 671.121i | −0.643737 | + | 0.721636i | ||||
\(931\) | 509.156 | + | 681.846i | 0.546892 | + | 0.732380i | ||||
\(932\) | 398.695 | − | 398.695i | 0.427784 | − | 0.427784i | ||||
\(933\) | −340.168 | + | 1021.85i | −0.364596 | + | 1.09523i | ||||
\(934\) | −144.859 | −0.155095 | ||||||||
\(935\) | −28.9919 | + | 67.2464i | −0.0310074 | + | 0.0719213i | ||||
\(936\) | −181.145 | + | 241.924i | −0.193531 | + | 0.258466i | ||||
\(937\) | −411.914 | + | 411.914i | −0.439609 | + | 0.439609i | −0.891881 | − | 0.452271i | \(-0.850614\pi\) |
0.452271 | + | 0.891881i | \(0.350614\pi\) | |||||||
\(938\) | 686.136 | + | 343.967i | 0.731488 | + | 0.366702i | ||||
\(939\) | −1173.17 | + | 587.166i | −1.24939 | + | 0.625310i | ||||
\(940\) | 187.093 | − | 433.962i | 0.199036 | − | 0.461661i | ||||
\(941\) | 379.719 | 0.403528 | 0.201764 | − | 0.979434i | \(-0.435333\pi\) | ||||
0.201764 | + | 0.979434i | \(0.435333\pi\) | |||||||
\(942\) | 19.1521 | + | 6.37565i | 0.0203313 | + | 0.00676821i | ||||
\(943\) | −48.0674 | − | 48.0674i | −0.0509728 | − | 0.0509728i | ||||
\(944\) | − | 195.950i | − | 0.207574i | ||||||
\(945\) | 819.910 | − | 469.864i | 0.867630 | − | 0.497210i | ||||
\(946\) | 95.2248 | 0.100660 | ||||||||
\(947\) | 54.3340 | − | 54.3340i | 0.0573749 | − | 0.0573749i | −0.677837 | − | 0.735212i | \(-0.737083\pi\) |
0.735212 | + | 0.677837i | \(0.237083\pi\) | |||||||
\(948\) | −6.84268 | + | 20.5551i | −0.00721802 | + | 0.0216826i | ||||
\(949\) | 1262.53i | 1.33038i | ||||||||
\(950\) | 17.6212 | − | 613.756i | 0.0185486 | − | 0.646059i | ||||
\(951\) | −88.0202 | − | 175.867i | −0.0925554 | − | 0.184929i | ||||
\(952\) | −62.3046 | + | 124.284i | −0.0654460 | + | 0.130550i | ||||
\(953\) | −749.903 | − | 749.903i | −0.786887 | − | 0.786887i | 0.194096 | − | 0.980983i | \(-0.437823\pi\) |
−0.980983 | + | 0.194096i | \(0.937823\pi\) | |||||||
\(954\) | −860.851 | − | 644.578i | −0.902359 | − | 0.675658i | ||||
\(955\) | −301.787 | − | 759.216i | −0.316007 | − | 0.794990i | ||||
\(956\) | − | 92.7303i | − | 0.0969982i | ||||||
\(957\) | −232.664 | − | 77.4527i | −0.243118 | − | 0.0809328i | ||||
\(958\) | −49.3199 | − | 49.3199i | −0.0514822 | − | 0.0514822i | ||||
\(959\) | 1432.24 | − | 475.748i | 1.49347 | − | 0.496087i | ||||
\(960\) | 119.805 | − | 6.83529i | 0.124797 | − | 0.00712009i | ||||
\(961\) | −836.367 | −0.870309 | ||||||||
\(962\) | 616.985 | + | 616.985i | 0.641356 | + | 0.641356i | ||||
\(963\) | 623.879 | − | 89.6278i | 0.647850 | − | 0.0930714i | ||||
\(964\) | −130.699 | −0.135580 | ||||||||
\(965\) | −101.829 | + | 236.191i | −0.105522 | + | 0.244758i | ||||
\(966\) | 91.6698 | − | 91.5501i | 0.0948963 | − | 0.0947724i | ||||
\(967\) | 401.607 | + | 401.607i | 0.415313 | + | 0.415313i | 0.883584 | − | 0.468272i | \(-0.155123\pi\) |
−0.468272 | + | 0.883584i | \(0.655123\pi\) | |||||||
\(968\) | −233.299 | − | 233.299i | −0.241012 | − | 0.241012i | ||||
\(969\) | 327.155 | − | 163.739i | 0.337621 | − | 0.168977i | ||||
\(970\) | 130.621 | + | 328.607i | 0.134661 | + | 0.338770i | ||||
\(971\) | −1146.42 | −1.18065 | −0.590327 | − | 0.807164i | \(-0.701001\pi\) | ||||
−0.590327 | + | 0.807164i | \(0.701001\pi\) | |||||||
\(972\) | 17.4848 | − | 485.685i | 0.0179885 | − | 0.499676i | ||||
\(973\) | −469.488 | − | 235.359i | −0.482516 | − | 0.241890i | ||||
\(974\) | 167.717 | 0.172194 | ||||||||
\(975\) | 305.380 | − | 836.439i | 0.313210 | − | 0.857886i | ||||
\(976\) | 331.762i | 0.339920i | ||||||||
\(977\) | 11.8173 | − | 11.8173i | 0.0120955 | − | 0.0120955i | −0.701033 | − | 0.713129i | \(-0.747278\pi\) |
0.713129 | + | 0.701033i | \(0.247278\pi\) | |||||||
\(978\) | −599.158 | − | 199.457i | −0.612636 | − | 0.203943i | ||||
\(979\) | −50.9817 | −0.0520753 | ||||||||
\(980\) | 256.552 | − | 417.470i | 0.261788 | − | 0.425990i | ||||
\(981\) | 919.320 | − | 1227.78i | 0.937126 | − | 1.25156i | ||||
\(982\) | 655.752 | + | 655.752i | 0.667771 | + | 0.667771i | ||||
\(983\) | 884.682 | − | 884.682i | 0.899982 | − | 0.899982i | −0.0954519 | − | 0.995434i | \(-0.530430\pi\) |
0.995434 | + | 0.0954519i | \(0.0304296\pi\) | |||||||
\(984\) | −118.241 | + | 59.1787i | −0.120163 | + | 0.0601409i | ||||
\(985\) | 54.1094 | − | 125.506i | 0.0549334 | − | 0.127418i | ||||
\(986\) | −389.165 | −0.394691 | ||||||||
\(987\) | −992.407 | − | 0.648080i | −1.00548 | − | 0.000656616i | ||||
\(988\) | 291.594 | − | 291.594i | 0.295136 | − | 0.295136i | ||||
\(989\) | −140.830 | −0.142396 | ||||||||
\(990\) | −66.0734 | − | 115.123i | −0.0667408 | − | 0.116286i | ||||
\(991\) | −227.430 | −0.229496 | −0.114748 | − | 0.993395i | \(-0.536606\pi\) | ||||
−0.114748 | + | 0.993395i | \(0.536606\pi\) | |||||||
\(992\) | 169.581 | + | 169.581i | 0.170949 | + | 0.170949i | ||||
\(993\) | 353.941 | − | 1063.22i | 0.356436 | − | 1.07072i | ||||
\(994\) | 233.970 | + | 704.368i | 0.235382 | + | 0.708619i | ||||
\(995\) | 370.028 | − | 147.085i | 0.371887 | − | 0.147824i | ||||
\(996\) | 782.440 | − | 391.606i | 0.785582 | − | 0.393179i | ||||
\(997\) | 720.354 | − | 720.354i | 0.722521 | − | 0.722521i | −0.246597 | − | 0.969118i | \(-0.579312\pi\) |
0.969118 | + | 0.246597i | \(0.0793123\pi\) | |||||||
\(998\) | 433.348 | + | 433.348i | 0.434216 | + | 0.434216i | ||||
\(999\) | −1380.78 | − | 249.364i | −1.38216 | − | 0.249613i |
(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 | 210.3.k.b.167.10 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.a.167.2 | yes | 32 | ||
5.3 | odd | 4 | 210.3.k.a.83.15 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.b.167.7 | yes | 32 | |
15.8 | even | 4 | inner | 210.3.k.b.83.7 | yes | 32 | |
21.20 | even | 2 | 210.3.k.a.167.15 | yes | 32 | ||
35.13 | even | 4 | 210.3.k.a.83.2 | ✓ | 32 | ||
105.83 | odd | 4 | inner | 210.3.k.b.83.10 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.2 | ✓ | 32 | 35.13 | even | 4 | ||
210.3.k.a.83.15 | yes | 32 | 5.3 | odd | 4 | ||
210.3.k.a.167.2 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.a.167.15 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.b.83.7 | yes | 32 | 15.8 | even | 4 | inner | |
210.3.k.b.83.10 | yes | 32 | 105.83 | odd | 4 | inner | |
210.3.k.b.167.7 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.b.167.10 | yes | 32 | 1.1 | even | 1 | trivial |