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 | 167.15 | ||
Character | \(\chi\) | \(=\) | 210.167 |
Dual form | 210.3.k.a.83.15 |
$q$-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 | ||||
\(3\) | 2.84642 | − | 0.947561i | 0.948808 | − | 0.315854i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 4.64638 | − | 1.84693i | 0.929276 | − | 0.369386i | ||||
\(6\) | −1.89886 | + | 3.79398i | −0.316477 | + | 0.632331i | ||||
\(7\) | −3.13705 | − | 6.25771i | −0.448150 | − | 0.893958i | ||||
\(8\) | 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 | \(-0.969777\pi\) | ||
0.995496 | − | 0.0948073i | \(-0.0302235\pi\) | |||||||
\(12\) | −1.89512 | − | 5.69285i | −0.157927 | − | 0.474404i | ||||
\(13\) | −8.39517 | − | 8.39517i | −0.645782 | − | 0.645782i | 0.306189 | − | 0.951971i | \(-0.400946\pi\) |
−0.951971 | + | 0.306189i | \(0.900946\pi\) | |||||||
\(14\) | 9.39476 | + | 3.12066i | 0.671054 | + | 0.222904i | ||||
\(15\) | 11.4755 | − | 9.65987i | 0.765033 | − | 0.643991i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 4.96522 | + | 4.96522i | 0.292072 | + | 0.292072i | 0.837898 | − | 0.545826i | \(-0.183784\pi\) |
−0.545826 | + | 0.837898i | \(0.683784\pi\) | |||||||
\(18\) | −1.80994 | + | 12.5986i | −0.100552 | + | 0.699921i | ||||
\(19\) | −17.3668 | −0.914041 | −0.457021 | − | 0.889456i | \(-0.651083\pi\) | ||||
−0.457021 | + | 0.889456i | \(0.651083\pi\) | |||||||
\(20\) | −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 | 0.770978 | − | 0.636862i | \(-0.219768\pi\) |
−0.636862 | + | 0.770978i | \(0.719768\pi\) | |||||||
\(24\) | 7.58797 | + | 3.79773i | 0.316165 | + | 0.158239i | ||||
\(25\) | 18.1777 | − | 17.1631i | 0.727109 | − | 0.686523i | ||||
\(26\) | 16.7903 | 0.645782 | ||||||||
\(27\) | 15.3949 | − | 22.1810i | 0.570182 | − | 0.821518i | ||||
\(28\) | −12.5154 | + | 6.27410i | −0.446979 | + | 0.224075i | ||||
\(29\) | 39.1891 | 1.35135 | 0.675674 | − | 0.737201i | \(-0.263853\pi\) | ||||
0.675674 | + | 0.737201i | \(0.263853\pi\) | |||||||
\(30\) | −1.81562 | + | 21.1354i | −0.0605208 | + | 0.704512i | ||||
\(31\) | 42.3954i | 1.36759i | 0.729673 | + | 0.683796i | \(0.239672\pi\) | ||||
−0.729673 | + | 0.683796i | \(0.760328\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | −1.97638 | − | 5.93696i | −0.0598905 | − | 0.179908i | ||||
\(34\) | −9.93045 | −0.292072 | ||||||||
\(35\) | −26.1335 | − | 23.2818i | −0.746671 | − | 0.665194i | ||||
\(36\) | −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 | \(0.439141\pi\) | |||||||
\(42\) | 29.6985 | − | 0.0193943i | 0.707107 | − | 0.000461768i | ||||
\(43\) | 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 | ||||||||
\(45\) | 23.5108 | − | 38.3698i | 0.522462 | − | 0.852662i | ||||
\(46\) | −6.16934 | −0.134116 | ||||||||
\(47\) | 33.4161 | + | 33.4161i | 0.710980 | + | 0.710980i | 0.966740 | − | 0.255760i | \(-0.0823257\pi\) |
−0.255760 | + | 0.966740i | \(0.582326\pi\) | |||||||
\(48\) | −11.3857 | + | 3.79024i | −0.237202 | + | 0.0789634i | ||||
\(49\) | −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 | \(-0.956362\pi\) |
−0.136665 | − | 0.990617i | \(-0.543638\pi\) | |||||||
\(54\) | 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 | ||||
\(57\) | −49.4332 | + | 16.4561i | −0.867250 | + | 0.288703i | ||||
\(58\) | −39.1891 | + | 39.1891i | −0.675674 | + | 0.675674i | ||||
\(59\) | 48.9876i | 0.830298i | 0.909754 | + | 0.415149i | \(0.136270\pi\) | ||||
−0.909754 | + | 0.415149i | \(0.863730\pi\) | |||||||
\(60\) | −19.3197 | − | 22.9510i | −0.321996 | − | 0.382516i | ||||
\(61\) | 82.9406i | 1.35968i | 0.733360 | + | 0.679841i | \(0.237951\pi\) | ||||
−0.733360 | + | 0.679841i | \(0.762049\pi\) | |||||||
\(62\) | −42.3954 | − | 42.3954i | −0.683796 | − | 0.683796i | ||||
\(63\) | −56.3562 | − | 28.1599i | −0.894543 | − | 0.446982i | ||||
\(64\) | 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 | ||||
\(70\) | 49.4153 | − | 2.85168i | 0.705932 | − | 0.0407383i | ||||
\(71\) | 74.9745i | 1.05598i | 0.849251 | + | 0.527990i | \(0.177054\pi\) | ||||
−0.849251 | + | 0.527990i | \(0.822946\pi\) | |||||||
\(72\) | 25.1972 | + | 3.61987i | 0.349960 | + | 0.0502760i | ||||
\(73\) | −75.1938 | − | 75.1938i | −1.03005 | − | 1.03005i | −0.999534 | − | 0.0305180i | \(-0.990284\pi\) |
−0.0305180 | − | 0.999534i | \(-0.509716\pi\) | |||||||
\(74\) | −73.4928 | −0.993146 | ||||||||
\(75\) | 35.4784 | − | 66.0778i | 0.473046 | − | 0.881038i | ||||
\(76\) | 34.7336i | 0.457021i | ||||||||
\(77\) | −13.0521 | + | 6.54314i | −0.169508 | + | 0.0849758i | ||||
\(78\) | 47.7924 | − | 15.9099i | 0.612723 | − | 0.203973i | ||||
\(79\) | − | 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 | ||||||||
\(87\) | 111.549 | − | 37.1340i | 1.28217 | − | 0.426828i | ||||
\(88\) | 4.17152 | − | 4.17152i | 0.0474036 | − | 0.0474036i | ||||
\(89\) | 24.4427i | 0.274637i | 0.990527 | + | 0.137319i | \(0.0438485\pi\) | ||||
−0.990527 | + | 0.137319i | \(0.956152\pi\) | |||||||
\(90\) | 14.8590 | + | 61.8806i | 0.165100 | + | 0.687562i | ||||
\(91\) | −26.1984 | + | 78.8706i | −0.287895 | + | 0.866710i | ||||
\(92\) | 6.16934 | − | 6.16934i | 0.0670580 | − | 0.0670580i | ||||
\(93\) | 40.1722 | + | 120.675i | 0.431959 | + | 1.29758i | ||||
\(94\) | −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 | −0.500933 | − | 0.865486i | \(-0.667010\pi\) |
0.865486 | + | 0.500933i | \(0.167010\pi\) | |||||||
\(98\) | −9.94368 | − | 68.5793i | −0.101466 | − | 0.699789i | ||||
\(99\) | −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 | \(0.520487\pi\) | |||||||
\(102\) | −28.2663 | + | 9.40970i | −0.277120 | + | 0.0922520i | ||||
\(103\) | −45.5816 | − | 45.5816i | −0.442540 | − | 0.442540i | 0.450325 | − | 0.892865i | \(-0.351308\pi\) |
−0.892865 | + | 0.450325i | \(0.851308\pi\) | |||||||
\(104\) | − | 33.5807i | − | 0.322891i | ||||||
\(105\) | −96.4478 | − | 41.5068i | −0.918551 | − | 0.395303i | ||||
\(106\) | 119.492 | 1.12728 | ||||||||
\(107\) | 49.5198 | − | 49.5198i | 0.462802 | − | 0.462802i | −0.436771 | − | 0.899573i | \(-0.643878\pi\) |
0.899573 | + | 0.436771i | \(0.143878\pi\) | |||||||
\(108\) | −44.3620 | − | 30.7898i | −0.410759 | − | 0.285091i | ||||
\(109\) | 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 | ||||
\(112\) | 12.5482 | + | 25.0308i | 0.112038 | + | 0.223490i | ||||
\(113\) | 139.393 | + | 139.393i | 1.23357 | + | 1.23357i | 0.962583 | + | 0.270986i | \(0.0873496\pi\) |
0.270986 | + | 0.962583i | \(0.412650\pi\) | |||||||
\(114\) | 32.9771 | − | 65.8893i | 0.289273 | − | 0.577976i | ||||
\(115\) | 20.0297 | + | 8.63538i | 0.174171 | + | 0.0750903i | ||||
\(116\) | − | 78.3781i | − | 0.675674i | ||||||
\(117\) | −105.767 | − | 15.1947i | −0.903993 | − | 0.129869i | ||||
\(118\) | −48.9876 | − | 48.9876i | −0.415149 | − | 0.415149i | ||||
\(119\) | 15.4948 | − | 46.6471i | 0.130208 | − | 0.391992i | ||||
\(120\) | 42.2707 | + | 3.63125i | 0.352256 | + | 0.0302604i | ||||
\(121\) | 116.650 | 0.964046 | ||||||||
\(122\) | −82.9406 | − | 82.9406i | −0.679841 | − | 0.679841i | ||||
\(123\) | 44.3549 | − | 14.7655i | 0.360609 | − | 0.120045i | ||||
\(124\) | 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 | \(0.498265\pi\) | |||||||
\(132\) | −11.8739 | + | 3.95277i | −0.0899539 | + | 0.0299452i | ||||
\(133\) | 54.4805 | + | 108.676i | 0.409628 | + | 0.817115i | ||||
\(134\) | 109.647 | 0.818258 | ||||||||
\(135\) | 30.5640 | − | 131.495i | 0.226400 | − | 0.974034i | ||||
\(136\) | 19.8609i | 0.146036i | ||||||||
\(137\) | 152.451 | − | 152.451i | 1.11278 | − | 1.11278i | 0.120010 | − | 0.992773i | \(-0.461707\pi\) |
0.992773 | − | 0.120010i | \(-0.0382925\pi\) | |||||||
\(138\) | −17.5605 | + | 5.84582i | −0.127250 | + | 0.0423610i | ||||
\(139\) | −75.0255 | −0.539752 | −0.269876 | − | 0.962895i | \(-0.586983\pi\) | ||||
−0.269876 | + | 0.962895i | \(0.586983\pi\) | |||||||
\(140\) | −46.5636 | + | 52.2669i | −0.332597 | + | 0.373335i | ||||
\(141\) | 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 | ||||||||
\(147\) | −46.2483 | + | 139.535i | −0.314614 | + | 0.949220i | ||||
\(148\) | 73.4928 | − | 73.4928i | 0.496573 | − | 0.496573i | ||||
\(149\) | 183.297 | 1.23018 | 0.615091 | − | 0.788456i | \(-0.289119\pi\) | ||||
0.615091 | + | 0.788456i | \(0.289119\pi\) | |||||||
\(150\) | 30.5994 | + | 101.556i | 0.203996 | + | 0.677042i | ||||
\(151\) | −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 | ||||
\(153\) | 62.5547 | + | 8.98674i | 0.408855 | + | 0.0587369i | ||||
\(154\) | 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 | −0.696311 | − | 0.717740i | \(-0.745177\pi\) |
0.717740 | + | 0.696311i | \(0.245177\pi\) | |||||||
\(158\) | 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 | ||||
\(162\) | 54.9215 | + | 100.527i | 0.339022 | + | 0.620536i | ||||
\(163\) | 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 | ||||||
\(165\) | −20.1482 | − | 23.9351i | −0.122110 | − | 0.145061i | ||||
\(166\) | − | 206.232i | − | 1.24236i | ||||||
\(167\) | −34.3084 | − | 34.3084i | −0.205439 | − | 0.205439i | 0.596886 | − | 0.802326i | \(-0.296404\pi\) |
−0.802326 | + | 0.596886i | \(0.796404\pi\) | |||||||
\(168\) | −0.0387885 | − | 59.3970i | −0.000230884 | − | 0.353553i | ||||
\(169\) | − | 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 | ||||
\(175\) | −164.426 | − | 59.9094i | −0.939576 | − | 0.342340i | ||||
\(176\) | 8.34304i | 0.0474036i | ||||||||
\(177\) | 46.4187 | + | 139.439i | 0.262253 | + | 0.787793i | ||||
\(178\) | −24.4427 | − | 24.4427i | −0.137319 | − | 0.137319i | ||||
\(179\) | −110.880 | −0.619440 | −0.309720 | − | 0.950828i | \(-0.600235\pi\) | ||||
−0.309720 | + | 0.950828i | \(0.600235\pi\) | |||||||
\(180\) | −76.7396 | − | 47.0216i | −0.426331 | − | 0.261231i | ||||
\(181\) | − | 24.2997i | − | 0.134253i | −0.997744 | − | 0.0671264i | \(-0.978617\pi\) | ||
0.997744 | − | 0.0671264i | \(-0.0213831\pi\) | |||||||
\(182\) | −52.6722 | − | 105.069i | −0.289407 | − | 0.577302i | ||||
\(183\) | 78.5913 | + | 236.084i | 0.429460 | + | 1.29008i | ||||
\(184\) | 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 | \(0.140693\pi\) | ||||
−0.903898 | + | 0.427747i | \(0.859307\pi\) | |||||||
\(192\) | 7.58049 | + | 22.7714i | 0.0394817 | + | 0.118601i | ||||
\(193\) | −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 | ||||||||
\(195\) | −177.435 | − | 15.2425i | −0.909923 | − | 0.0781665i | ||||
\(196\) | 78.5230 | + | 58.6356i | 0.400628 | + | 0.299161i | ||||
\(197\) | −19.3286 | + | 19.3286i | −0.0981145 | + | 0.0981145i | −0.754460 | − | 0.656346i | \(-0.772101\pi\) |
0.656346 | + | 0.754460i | \(0.272101\pi\) | |||||||
\(198\) | 26.2776 | + | 3.77509i | 0.132715 | + | 0.0190661i | ||||
\(199\) | −79.6378 | −0.400190 | −0.200095 | − | 0.979776i | \(-0.564125\pi\) | ||||
−0.200095 | + | 0.979776i | \(0.564125\pi\) | |||||||
\(200\) | 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 | ||||
\(203\) | −122.938 | − | 245.234i | −0.605607 | − | 1.20805i | ||||
\(204\) | 18.8566 | − | 37.6760i | 0.0924341 | − | 0.184686i | ||||
\(205\) | 72.4030 | − | 28.7801i | 0.353185 | − | 0.140391i | ||||
\(206\) | 91.1632 | 0.442540 | ||||||||
\(207\) | 38.8624 | + | 5.58305i | 0.187741 | + | 0.0269713i | ||||
\(208\) | 33.5807 | + | 33.5807i | 0.161446 | + | 0.161446i | ||||
\(209\) | 36.2230i | 0.173316i | ||||||||
\(210\) | 137.955 | − | 54.9411i | 0.656927 | − | 0.261624i | ||||
\(211\) | −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 | ||||
\(213\) | 71.0429 | + | 213.409i | 0.333535 | + | 1.00192i | ||||
\(214\) | 99.0397i | 0.462802i | ||||||||
\(215\) | 63.9041 | − | 148.225i | 0.297229 | − | 0.689419i | ||||
\(216\) | 75.1518 | − | 13.5721i | 0.347925 | − | 0.0628340i | ||||
\(217\) | 265.298 | − | 132.996i | 1.22257 | − | 0.612887i | ||||
\(218\) | −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 | ||||||
\(222\) | −209.192 | + | 69.6389i | −0.942305 | + | 0.313689i | ||||
\(223\) | 221.408 | + | 221.408i | 0.992862 | + | 0.992862i | 0.999975 | − | 0.00711229i | \(-0.00226393\pi\) |
−0.00711229 | + | 0.999975i | \(0.502264\pi\) | |||||||
\(224\) | −37.5790 | − | 12.4826i | −0.167764 | − | 0.0557260i | ||||
\(225\) | 38.3738 | − | 221.704i | 0.170550 | − | 0.985349i | ||||
\(226\) | −278.787 | −1.23357 | ||||||||
\(227\) | 70.0030 | + | 70.0030i | 0.308383 | + | 0.308383i | 0.844282 | − | 0.535899i | \(-0.180027\pi\) |
−0.535899 | + | 0.844282i | \(0.680027\pi\) | |||||||
\(228\) | 32.9122 | + | 98.8665i | 0.144352 | + | 0.433625i | ||||
\(229\) | 287.075 | 1.25360 | 0.626802 | − | 0.779178i | \(-0.284363\pi\) | ||||
0.626802 | + | 0.779178i | \(0.284363\pi\) | |||||||
\(230\) | −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 | 0.135245 | − | 0.990812i | \(-0.456818\pi\) |
−0.990812 | + | 0.135245i | \(0.956818\pi\) | |||||||
\(234\) | 120.962 | − | 90.5725i | 0.516931 | − | 0.387062i | ||||
\(235\) | 216.981 | + | 93.5467i | 0.923323 | + | 0.398071i | ||||
\(236\) | 97.9751 | 0.415149 | ||||||||
\(237\) | −3.42134 | − | 10.2775i | −0.0144360 | − | 0.0433651i | ||||
\(238\) | 31.1523 | + | 62.1418i | 0.130892 | + | 0.261100i | ||||
\(239\) | −46.3651 | −0.193996 | −0.0969982 | − | 0.995285i | \(-0.530924\pi\) | ||||
−0.0969982 | + | 0.995285i | \(0.530924\pi\) | |||||||
\(240\) | −45.9020 | + | 38.6395i | −0.191258 | + | 0.160998i | ||||
\(241\) | 65.3496i | 0.271160i | 0.990766 | + | 0.135580i | \(0.0432898\pi\) | ||||
−0.990766 | + | 0.135580i | \(0.956710\pi\) | |||||||
\(242\) | −116.650 | + | 116.650i | −0.482023 | + | 0.482023i | ||||
\(243\) | −8.74241 | − | 242.843i | −0.0359770 | − | 0.999353i | ||||
\(244\) | 165.881 | 0.679841 | ||||||||
\(245\) | −63.7086 | + | 236.572i | −0.260035 | + | 0.965599i | ||||
\(246\) | −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 | \(0.589593\pi\) | |||||||
\(252\) | −56.3198 | + | 112.712i | −0.223491 | + | 0.447271i | ||||
\(253\) | 6.43388 | − | 6.43388i | 0.0254304 | − | 0.0254304i | ||||
\(254\) | 209.105 | 0.823247 | ||||||||
\(255\) | 104.942 | + | 9.01497i | 0.411536 | + | 0.0353528i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 323.691 | + | 323.691i | 1.25950 | + | 1.25950i | 0.951332 | + | 0.308168i | \(0.0997158\pi\) |
0.308168 | + | 0.951332i | \(0.400284\pi\) | |||||||
\(258\) | 43.2606 | + | 129.953i | 0.167677 | + | 0.503693i | ||||
\(259\) | 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 | 0.395523 | − | 0.918456i | \(-0.370563\pi\) |
−0.918456 | + | 0.395523i | \(0.870563\pi\) | |||||||
\(264\) | 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 | ||||
\(267\) | 23.1610 | + | 69.5744i | 0.0867452 | + | 0.260578i | ||||
\(268\) | −109.647 | + | 109.647i | −0.409129 | + | 0.409129i | ||||
\(269\) | − | 391.957i | − | 1.45709i | −0.684998 | − | 0.728545i | \(-0.740197\pi\) | ||
0.684998 | − | 0.728545i | \(-0.259803\pi\) | |||||||
\(270\) | 100.931 | + | 162.059i | 0.373817 | + | 0.600217i | ||||
\(271\) | − | 327.322i | − | 1.20783i | −0.797049 | − | 0.603914i | \(-0.793607\pi\) | ||
0.797049 | − | 0.603914i | \(-0.206393\pi\) | |||||||
\(272\) | −19.8609 | − | 19.8609i | −0.0730180 | − | 0.0730180i | ||||
\(273\) | 0.162818 | + | 249.324i | 0.000596403 | + | 0.913274i | ||||
\(274\) | 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 | ||||
\(280\) | −5.70337 | − | 98.8305i | −0.0203692 | − | 0.352966i | ||||
\(281\) | − | 97.5907i | − | 0.347298i | −0.984808 | − | 0.173649i | \(-0.944444\pi\) | ||
0.984808 | − | 0.173649i | \(-0.0555558\pi\) | |||||||
\(282\) | −190.233 | + | 63.3275i | −0.674584 | + | 0.224566i | ||||
\(283\) | −394.549 | − | 394.549i | −1.39417 | − | 1.39417i | −0.815720 | − | 0.578447i | \(-0.803659\pi\) |
−0.578447 | − | 0.815720i | \(-0.696341\pi\) | |||||||
\(284\) | 149.949 | 0.527990 | ||||||||
\(285\) | −199.292 | + | 167.761i | −0.699272 | + | 0.588635i | ||||
\(286\) | − | 35.0206i | − | 0.122450i | ||||||
\(287\) | −48.8836 | − | 97.5118i | −0.170326 | − | 0.339762i | ||||
\(288\) | 7.23975 | − | 50.3943i | 0.0251380 | − | 0.174980i | ||||
\(289\) | − | 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 | ||||||||
\(297\) | −46.2642 | − | 32.1101i | −0.155772 | − | 0.108115i | ||||
\(298\) | −183.297 | + | 183.297i | −0.615091 | + | 0.615091i | ||||
\(299\) | − | 51.7926i | − | 0.173220i | ||||||
\(300\) | −132.156 | − | 70.9568i | −0.440519 | − | 0.236523i | ||||
\(301\) | −214.458 | − | 71.2364i | −0.712484 | − | 0.236666i | ||||
\(302\) | 203.889 | − | 203.889i | 0.675130 | − | 0.675130i | ||||
\(303\) | −36.9817 | + | 12.3110i | −0.122052 | + | 0.0406304i | ||||
\(304\) | 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 | −0.565180 | − | 0.824967i | \(-0.691193\pi\) |
0.824967 | + | 0.565180i | \(0.191193\pi\) | |||||||
\(308\) | 13.0863 | + | 26.1042i | 0.0424879 | + | 0.0847538i | ||||
\(309\) | −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 | \(0.695839\pi\) | |||||||
\(312\) | −31.8197 | − | 95.5848i | −0.101986 | − | 0.306362i | ||||
\(313\) | 309.220 | + | 309.220i | 0.987922 | + | 0.987922i | 0.999928 | − | 0.0120057i | \(-0.00382162\pi\) |
−0.0120057 | + | 0.999928i | \(0.503822\pi\) | |||||||
\(314\) | 6.72848i | 0.0214283i | ||||||||
\(315\) | −313.862 | − | 26.7557i | −0.996386 | − | 0.0849386i | ||||
\(316\) | −7.22137 | −0.0228524 | ||||||||
\(317\) | −46.3542 | + | 46.3542i | −0.146228 | + | 0.146228i | −0.776431 | − | 0.630203i | \(-0.782972\pi\) |
0.630203 | + | 0.776431i | \(0.282972\pi\) | |||||||
\(318\) | 340.125 | − | 113.226i | 1.06957 | − | 0.356056i | ||||
\(319\) | − | 81.7390i | − | 0.256235i | ||||||
\(320\) | 14.7754 | + | 37.1710i | 0.0461732 | + | 0.116160i | ||||
\(321\) | 94.0314 | − | 187.877i | 0.292933 | − | 0.585288i | ||||
\(322\) | 19.3535 | + | 38.6059i | 0.0601041 | + | 0.119894i | ||||
\(323\) | −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 | ||||||||
\(327\) | 161.487 | + | 485.098i | 0.493844 | + | 1.48348i | ||||
\(328\) | 31.1653 | + | 31.1653i | 0.0950162 | + | 0.0950162i | ||||
\(329\) | 104.280 | − | 313.936i | 0.316961 | − | 0.954213i | ||||
\(330\) | 44.0833 | + | 3.78695i | 0.133586 | + | 0.0114756i | ||||
\(331\) | 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 | ||||
\(333\) | 462.952 | + | 66.5087i | 1.39025 | + | 0.199726i | ||||
\(334\) | 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 | ||||||||
\(342\) | 31.4328 | − | 218.797i | 0.0919087 | − | 0.639757i | ||||
\(343\) | 337.659 | + | 60.2970i | 0.984427 | + | 0.175793i | ||||
\(344\) | 91.3095 | 0.265434 | ||||||||
\(345\) | 65.1956 | + | 5.60060i | 0.188973 | + | 0.0162336i | ||||
\(346\) | − | 423.018i | − | 1.22260i | ||||||
\(347\) | 231.964 | − | 231.964i | 0.668483 | − | 0.668483i | −0.288882 | − | 0.957365i | \(-0.593284\pi\) |
0.957365 | + | 0.288882i | \(0.0932835\pi\) | |||||||
\(348\) | −74.2681 | − | 223.097i | −0.213414 | − | 0.641085i | ||||
\(349\) | −143.315 | −0.410646 | −0.205323 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205323 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(350\) | 224.335 | − | 104.516i | 0.640958 | − | 0.298618i | ||||
\(351\) | −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 | ||||||||
\(357\) | −0.0962968 | − | 147.460i | −0.000269739 | − | 0.413052i | ||||
\(358\) | 110.880 | − | 110.880i | 0.309720 | − | 0.309720i | ||||
\(359\) | 424.811 | 1.18332 | 0.591659 | − | 0.806189i | \(-0.298473\pi\) | ||||
0.591659 | + | 0.806189i | \(0.298473\pi\) | |||||||
\(360\) | 123.761 | − | 29.7180i | 0.343781 | − | 0.0825501i | ||||
\(361\) | −59.3948 | −0.164528 | ||||||||
\(362\) | 24.2997 | + | 24.2997i | 0.0671264 | + | 0.0671264i | ||||
\(363\) | 332.034 | − | 110.533i | 0.914695 | − | 0.304498i | ||||
\(364\) | 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 | \(0.526129\pi\) |
−0.996633 | + | 0.0819951i | \(0.973871\pi\) | |||||||
\(368\) | −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 | ||||
\(372\) | 241.350 | − | 80.3444i | 0.648791 | − | 0.215980i | ||||
\(373\) | 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 | ||||||||
\(375\) | 42.8052 | − | 372.549i | 0.114147 | − | 0.993464i | ||||
\(376\) | 133.664i | 0.355490i | ||||||||
\(377\) | −328.999 | − | 328.999i | −0.872676 | − | 0.872676i | ||||
\(378\) | 213.851 | − | 160.343i | 0.565743 | − | 0.424187i | ||||
\(379\) | − | 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 | ||||
\(385\) | −48.5602 | + | 54.5082i | −0.126130 | + | 0.141580i | ||||
\(386\) | − | 72.7491i | − | 0.188469i | ||||||
\(387\) | 41.3161 | − | 287.592i | 0.106760 | − | 0.743133i | ||||
\(388\) | −70.7233 | − | 70.7233i | −0.182277 | − | 0.182277i | ||||
\(389\) | 365.324 | 0.939136 | 0.469568 | − | 0.882896i | \(-0.344410\pi\) | ||||
0.469568 | + | 0.882896i | \(0.344410\pi\) | |||||||
\(390\) | 192.677 | − | 162.192i | 0.494045 | − | 0.415878i | ||||
\(391\) | 30.6321i | 0.0783431i | ||||||||
\(392\) | −137.159 | + | 19.8874i | −0.349894 | + | 0.0507330i | ||||
\(393\) | 4.06481 | − | 1.35316i | 0.0103430 | − | 0.00344315i | ||||
\(394\) | − | 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 | \(0.642035\pi\) |
−0.902087 | + | 0.431554i | \(0.857965\pi\) | |||||||
\(398\) | 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 | \(-0.925601\pi\) | ||
0.972809 | − | 0.231608i | \(-0.0743986\pi\) | |||||||
\(402\) | 312.101 | − | 103.897i | 0.776369 | − | 0.258450i | ||||
\(403\) | 355.916 | − | 355.916i | 0.883167 | − | 0.883167i | ||||
\(404\) | 25.9847i | 0.0643184i | ||||||||
\(405\) | −37.6012 | − | 403.251i | −0.0928425 | − | 0.995681i | ||||
\(406\) | 368.172 | + | 122.296i | 0.906827 | + | 0.301221i | ||||
\(407\) | 76.6442 | − | 76.6442i | 0.188315 | − | 0.188315i | ||||
\(408\) | 18.8194 | + | 56.5325i | 0.0461260 | + | 0.138560i | ||||
\(409\) | −615.554 | −1.50502 | −0.752511 | − | 0.658579i | \(-0.771158\pi\) | ||||
−0.752511 | + | 0.658579i | \(0.771158\pi\) | |||||||
\(410\) | −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 | ||||
\(413\) | 306.550 | − | 153.676i | 0.742251 | − | 0.372098i | ||||
\(414\) | −44.4455 | + | 33.2794i | −0.107356 | + | 0.0803850i | ||||
\(415\) | −288.668 | + | 669.563i | −0.695586 | + | 1.61341i | ||||
\(416\) | −67.1614 | −0.161446 | ||||||||
\(417\) | −213.554 | + | 71.0913i | −0.512121 | + | 0.170483i | ||||
\(418\) | −36.2230 | − | 36.2230i | −0.0866578 | − | 0.0866578i | ||||
\(419\) | 427.623i | 1.02058i | 0.860002 | + | 0.510290i | \(0.170462\pi\) | ||||
−0.860002 | + | 0.510290i | \(0.829538\pi\) | |||||||
\(420\) | −83.0136 | + | 192.896i | −0.197651 | + | 0.459275i | ||||
\(421\) | −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 | ||||
\(423\) | 420.995 | + | 60.4810i | 0.995260 | + | 0.142981i | ||||
\(424\) | − | 238.984i | − | 0.563641i | ||||||
\(425\) | 175.475 | + | 5.03796i | 0.412882 | + | 0.0118540i | ||||
\(426\) | −284.452 | − | 142.366i | −0.667728 | − | 0.334193i | ||||
\(427\) | 519.018 | − | 260.189i | 1.21550 | − | 0.609342i | ||||
\(428\) | −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 | \(0.325113\pi\) | ||||
−0.522197 | + | 0.852825i | \(0.674887\pi\) | |||||||
\(432\) | −61.5797 | + | 88.7240i | −0.142546 | + | 0.205380i | ||||
\(433\) | 6.15401 | + | 6.15401i | 0.0142125 | + | 0.0142125i | 0.714177 | − | 0.699965i | \(-0.246801\pi\) |
−0.699965 | + | 0.714177i | \(0.746801\pi\) | |||||||
\(434\) | −132.301 | + | 398.294i | −0.304842 | + | 0.917729i | ||||
\(435\) | 449.714 | − | 378.561i | 1.03383 | − | 0.870256i | ||||
\(436\) | 340.847 | 0.781760 | ||||||||
\(437\) | −53.5708 | − | 53.5708i | −0.122588 | − | 0.122588i | ||||
\(438\) | 428.067 | − | 142.501i | 0.977322 | − | 0.325346i | ||||
\(439\) | 701.728 | 1.59847 | 0.799235 | − | 0.601019i | \(-0.205239\pi\) | ||||
0.799235 | + | 0.601019i | \(0.205239\pi\) | |||||||
\(440\) | 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 | 0.479282 | − | 0.877661i | \(-0.340897\pi\) |
−0.877661 | + | 0.479282i | \(0.840897\pi\) | |||||||
\(444\) | 139.553 | − | 278.831i | 0.314308 | − | 0.627997i | ||||
\(445\) | 45.1440 | + | 113.570i | 0.101447 | + | 0.255214i | ||||
\(446\) | −442.817 | −0.992862 | ||||||||
\(447\) | 521.741 | − | 173.685i | 1.16721 | − | 0.388557i | ||||
\(448\) | 50.0617 | − | 25.0964i | 0.111745 | − | 0.0560188i | ||||
\(449\) | −521.716 | −1.16195 | −0.580976 | − | 0.813921i | \(-0.697329\pi\) | ||||
−0.580976 | + | 0.813921i | \(0.697329\pi\) | |||||||
\(450\) | 183.330 | + | 260.077i | 0.407399 | + | 0.577950i | ||||
\(451\) | − | 32.5017i | − | 0.0720659i | ||||||
\(452\) | 278.787 | − | 278.787i | 0.616785 | − | 0.616785i | ||||
\(453\) | −580.355 | + | 193.198i | −1.28114 | + | 0.426485i | ||||
\(454\) | −140.006 | −0.308383 | ||||||||
\(455\) | 23.9404 | + | 414.849i | 0.0526162 | + | 0.911757i | ||||
\(456\) | −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 | \(0.198921\pi\) | |||||||
\(462\) | −0.0404518 | − | 61.9439i | −8.75580e−5 | − | 0.134078i | ||||
\(463\) | −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 | ||||||||
\(465\) | 409.534 | + | 486.508i | 0.880718 | + | 1.04625i | ||||
\(466\) | 398.695 | 0.855568 | ||||||||
\(467\) | −72.4294 | − | 72.4294i | −0.155095 | − | 0.155095i | 0.625294 | − | 0.780389i | \(-0.284979\pi\) |
−0.780389 | + | 0.625294i | \(0.784979\pi\) | |||||||
\(468\) | −30.3894 | + | 211.534i | −0.0649347 | + | 0.451997i | ||||
\(469\) | −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 | ||||
\(477\) | −752.714 | − | 108.136i | −1.57802 | − | 0.226701i | ||||
\(478\) | 46.3651 | − | 46.3651i | 0.0969982 | − | 0.0969982i | ||||
\(479\) | − | 49.3199i | − | 0.102964i | −0.998674 | − | 0.0514822i | \(-0.983605\pi\) | ||
0.998674 | − | 0.0514822i | \(-0.0163945\pi\) | |||||||
\(480\) | 7.26249 | − | 84.5414i | 0.0151302 | − | 0.176128i | ||||
\(481\) | − | 616.985i | − | 1.28271i | ||||||
\(482\) | −65.3496 | − | 65.3496i | −0.135580 | − | 0.135580i | ||||
\(483\) | −0.0598249 | − | 91.6100i | −0.000123861 | − | 0.189669i | ||||
\(484\) | − | 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 | ||||
\(490\) | −172.863 | − | 300.280i | −0.352782 | − | 0.612817i | ||||
\(491\) | − | 655.752i | − | 1.33554i | −0.744366 | − | 0.667771i | \(-0.767248\pi\) | ||
0.744366 | − | 0.667771i | \(-0.232752\pi\) | |||||||
\(492\) | −29.5310 | − | 88.7097i | −0.0600225 | − | 0.180304i | ||||
\(493\) | 194.583 | + | 194.583i | 0.394691 | + | 0.394691i | ||||
\(494\) | −291.594 | −0.590272 | ||||||||
\(495\) | −80.0302 | − | 49.0379i | −0.161677 | − | 0.0990664i | ||||
\(496\) | − | 169.581i | − | 0.341898i | ||||||
\(497\) | 469.169 | − | 235.199i | 0.944002 | − | 0.473237i | ||||
\(498\) | −195.417 | − | 587.023i | −0.392404 | − | 1.17876i | ||||
\(499\) | 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 | ||||||||
\(507\) | −26.5717 | − | 79.8201i | −0.0524098 | − | 0.157436i | ||||
\(508\) | −209.105 | + | 209.105i | −0.411623 | + | 0.411623i | ||||
\(509\) | − | 554.834i | − | 1.09005i | −0.838421 | − | 0.545024i | \(-0.816521\pi\) | ||
0.838421 | − | 0.545024i | \(-0.183479\pi\) | |||||||
\(510\) | −113.957 | + | 95.9268i | −0.223445 | + | 0.188092i | ||||
\(511\) | −234.654 | + | 706.428i | −0.459206 | + | 1.38244i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −267.360 | + | 385.213i | −0.521170 | + | 0.750902i | ||||
\(514\) | −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 | ||||
\(518\) | 230.551 | + | 459.897i | 0.445079 | + | 0.887831i | ||||
\(519\) | −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 | \(0.498858\pi\) | |||||||
\(522\) | −70.9297 | + | 493.727i | −0.135881 | + | 0.945836i | ||||
\(523\) | −638.273 | − | 638.273i | −1.22041 | − | 1.22041i | −0.967487 | − | 0.252921i | \(-0.918609\pi\) |
−0.252921 | − | 0.967487i | \(-0.581391\pi\) | |||||||
\(524\) | − | 2.85608i | − | 0.00545054i | ||||||
\(525\) | −524.793 | − | 14.7241i | −0.999607 | − | 0.0280458i | ||||
\(526\) | 275.063 | 0.522933 | ||||||||
\(527\) | −210.502 | + | 210.502i | −0.399435 | + | 0.399435i | ||||
\(528\) | 7.90554 | + | 23.7478i | 0.0149726 | + | 0.0449770i | ||||
\(529\) | − | 509.970i | − | 0.964026i | ||||||
\(530\) | 555.205 | − | 220.693i | 1.04756 | − | 0.416402i | ||||
\(531\) | 264.255 | + | 352.919i | 0.497655 | + | 0.664631i | ||||
\(532\) | 217.353 | − | 108.961i | 0.408557 | − | 0.204814i | ||||
\(533\) | −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 | ||||||
\(537\) | −315.611 | + | 105.065i | −0.587730 | + | 0.195652i | ||||
\(538\) | 391.957 | + | 391.957i | 0.728545 | + | 0.728545i | ||||
\(539\) | 81.8901 | + | 61.1499i | 0.151930 | + | 0.113451i | ||||
\(540\) | −262.989 | − | 61.1279i | −0.487017 | − | 0.113200i | ||||
\(541\) | −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 | ||||
\(543\) | −23.0255 | − | 69.1674i | −0.0424042 | − | 0.127380i | ||||
\(544\) | 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 | ||||||||
\(552\) | 11.6916 | + | 35.1211i | 0.0211805 | + | 0.0636252i | ||||
\(553\) | −22.5946 | + | 11.3269i | −0.0408582 | + | 0.0204826i | ||||
\(554\) | −76.0232 | −0.137226 | ||||||||
\(555\) | 776.649 | + | 66.7176i | 1.39937 | + | 0.120212i | ||||
\(556\) | 150.051i | 0.269876i | ||||||||
\(557\) | −545.370 | + | 545.370i | −0.979121 | + | 0.979121i | −0.999786 | − | 0.0206659i | \(-0.993421\pi\) |
0.0206659 | + | 0.999786i | \(0.493421\pi\) | |||||||
\(558\) | −534.121 | − | 76.7329i | −0.957207 | − | 0.137514i | ||||
\(559\) | −383.279 | −0.685652 | ||||||||
\(560\) | 104.534 | + | 93.1272i | 0.186668 | + | 0.166298i | ||||
\(561\) | 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 | ||||||||
\(567\) | −557.908 | + | 101.132i | −0.983965 | + | 0.178364i | ||||
\(568\) | −149.949 | + | 149.949i | −0.263995 | + | 0.263995i | ||||
\(569\) | −524.362 | −0.921549 | −0.460775 | − | 0.887517i | \(-0.652428\pi\) | ||||
−0.460775 | + | 0.887517i | \(0.652428\pi\) | |||||||
\(570\) | 31.5315 | − | 367.053i | 0.0553185 | − | 0.643953i | ||||
\(571\) | 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 | ||||
\(573\) | 154.831 | + | 465.104i | 0.270211 | + | 0.811700i | ||||
\(574\) | 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 | −0.903793 | − | 0.427970i | \(-0.859229\pi\) |
0.427970 | + | 0.903793i | \(0.359229\pi\) | |||||||
\(578\) | 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 | ||||
\(582\) | 67.0146 | + | 201.308i | 0.115145 | + | 0.345891i | ||||
\(583\) | −124.616 | + | 124.616i | −0.213749 | + | 0.213749i | ||||
\(584\) | − | 300.775i | − | 0.515026i | ||||||
\(585\) | −519.498 | + | 124.744i | −0.888031 | + | 0.213237i | ||||
\(586\) | − | 124.478i | − | 0.212419i | ||||||
\(587\) | −504.649 | − | 504.649i | −0.859709 | − | 0.859709i | 0.131595 | − | 0.991304i | \(-0.457990\pi\) |
−0.991304 | + | 0.131595i | \(0.957990\pi\) | |||||||
\(588\) | 279.071 | + | 92.4966i | 0.474610 | + | 0.157307i | ||||
\(589\) | − | 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 | ||||
\(595\) | −14.1592 | − | 245.358i | −0.0237971 | − | 0.412366i | ||||
\(596\) | − | 366.594i | − | 0.615091i | ||||||
\(597\) | −226.683 | + | 75.4617i | −0.379703 | + | 0.126401i | ||||
\(598\) | 51.7926 | + | 51.7926i | 0.0866098 | + | 0.0866098i | ||||
\(599\) | 103.401 | 0.172623 | 0.0863115 | − | 0.996268i | \(-0.472492\pi\) | ||||
0.0863115 | + | 0.996268i | \(0.472492\pi\) | |||||||
\(600\) | 203.113 | − | 61.1988i | 0.338521 | − | 0.101998i | ||||
\(601\) | 994.271i | 1.65436i | 0.561936 | + | 0.827180i | \(0.310057\pi\) | ||||
−0.561936 | + | 0.827180i | \(0.689943\pi\) | |||||||
\(602\) | 285.694 | − | 143.221i | 0.474575 | − | 0.237909i | ||||
\(603\) | −690.695 | − | 99.2266i | −1.14543 | − | 0.164555i | ||||
\(604\) | 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 | −0.750602 | − | 0.660755i | \(-0.770236\pi\) |
0.660755 | + | 0.750602i | \(0.270236\pi\) | |||||||
\(608\) | −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 | ||||||
\(612\) | 17.9735 | − | 125.109i | 0.0293684 | − | 0.204427i | ||||
\(613\) | 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 | ||||||||
\(615\) | 178.819 | − | 150.526i | 0.290762 | − | 0.244759i | ||||
\(616\) | −39.1904 | − | 13.0179i | −0.0636208 | − | 0.0211329i | ||||
\(617\) | −37.9474 | + | 37.9474i | −0.0615032 | + | 0.0615032i | −0.737189 | − | 0.675686i | \(-0.763847\pi\) |
0.675686 | + | 0.737189i | \(0.263847\pi\) | |||||||
\(618\) | 259.489 | − | 86.3827i | 0.419885 | − | 0.139778i | ||||
\(619\) | 182.389 | 0.294651 | 0.147326 | − | 0.989088i | \(-0.452933\pi\) | ||||
0.147326 | + | 0.989088i | \(0.452933\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 152.955 | − | 76.6781i | 0.245514 | − | 0.123079i | ||||
\(624\) | 127.405 | + | 63.7651i | 0.204174 | + | 0.102188i | ||||
\(625\) | 35.8585 | − | 623.970i | 0.0573736 | − | 0.998353i | ||||
\(626\) | −618.439 | −0.987922 | ||||||||
\(627\) | 34.3235 | + | 103.106i | 0.0547423 | + | 0.164443i | ||||
\(628\) | −6.72848 | − | 6.72848i | −0.0107141 | − | 0.0107141i | ||||
\(629\) | 364.908i | 0.580140i | ||||||||
\(630\) | 340.617 | − | 287.106i | 0.540662 | − | 0.455724i | ||||
\(631\) | 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 | ||||
\(633\) | −416.904 | + | 138.785i | −0.658617 | + | 0.219250i | ||||
\(634\) | − | 92.7084i | − | 0.146228i | ||||||
\(635\) | −678.891 | − | 292.689i | −1.06912 | − | 0.460928i | ||||
\(636\) | −226.899 | + | 453.351i | −0.356759 | + | 0.712815i | ||||
\(637\) | 575.735 | − | 83.4789i | 0.903823 | − | 0.131050i | ||||
\(638\) | 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 | \(0.0419946\pi\) | ||||
−0.991310 | + | 0.131548i | \(0.958005\pi\) | |||||||
\(642\) | 93.8461 | + | 281.909i | 0.146178 | + | 0.439110i | ||||
\(643\) | 25.2955 | + | 25.2955i | 0.0393398 | + | 0.0393398i | 0.726503 | − | 0.687163i | \(-0.241144\pi\) |
−0.687163 | + | 0.726503i | \(0.741144\pi\) | |||||||
\(644\) | −57.9594 | − | 19.2524i | −0.0899991 | − | 0.0298950i | ||||
\(645\) | 41.4459 | − | 482.465i | 0.0642572 | − | 0.748007i | ||||
\(646\) | 172.460 | 0.266966 | ||||||||
\(647\) | 11.1919 | + | 11.1919i | 0.0172981 | + | 0.0172981i | 0.715703 | − | 0.698405i | \(-0.246106\pi\) |
−0.698405 | + | 0.715703i | \(0.746106\pi\) | |||||||
\(648\) | 201.054 | − | 109.843i | 0.310268 | − | 0.169511i | ||||
\(649\) | 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 | 0.908288 | − | 0.418346i | \(-0.137390\pi\) |
−0.418346 | + | 0.908288i | \(0.637390\pi\) | |||||||
\(654\) | −646.585 | − | 323.611i | −0.988662 | − | 0.494818i | ||||
\(655\) | 6.63522 | − | 2.63749i | 0.0101301 | − | 0.00402670i | ||||
\(656\) | −62.3307 | −0.0950162 | ||||||||
\(657\) | −947.335 | − | 136.096i | −1.44191 | − | 0.207148i | ||||
\(658\) | 209.656 | + | 418.216i | 0.318626 | + | 0.635587i | ||||
\(659\) | 692.273 | 1.05049 | 0.525245 | − | 0.850951i | \(-0.323974\pi\) | ||||
0.525245 | + | 0.850951i | \(0.323974\pi\) | |||||||
\(660\) | −47.8703 | + | 40.2963i | −0.0725307 | + | 0.0610551i | ||||
\(661\) | − | 586.898i | − | 0.887894i | −0.896053 | − | 0.443947i | \(-0.853578\pi\) | ||
0.896053 | − | 0.443947i | \(-0.146422\pi\) | |||||||
\(662\) | −373.528 | + | 373.528i | −0.564242 | + | 0.564242i | ||||
\(663\) | −78.9961 | − | 237.300i | −0.119149 | − | 0.357919i | ||||
\(664\) | −412.464 | −0.621180 | ||||||||
\(665\) | 453.854 | + | 404.330i | 0.682488 | + | 0.608015i | ||||
\(666\) | −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 | ||||||||
\(672\) | −118.794 | + | 0.0775770i | −0.176777 | + | 0.000115442i | ||||
\(673\) | 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 | ||||||||
\(675\) | −100.849 | − | 667.424i | −0.149406 | − | 0.988776i | ||||
\(676\) | −56.0845 | −0.0829653 | ||||||||
\(677\) | −459.724 | − | 459.724i | −0.679061 | − | 0.679061i | 0.280727 | − | 0.959788i | \(-0.409425\pi\) |
−0.959788 | + | 0.280727i | \(0.909425\pi\) | |||||||
\(678\) | −793.545 | + | 264.167i | −1.17042 | + | 0.389627i | ||||
\(679\) | −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 | 0.656619 | − | 0.754222i | \(-0.271986\pi\) |
−0.754222 | + | 0.656619i | \(0.771986\pi\) | |||||||
\(684\) | 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 | ||||
\(687\) | 817.138 | − | 272.021i | 1.18943 | − | 0.395956i | ||||
\(688\) | −91.3095 | + | 91.3095i | −0.132717 | + | 0.132717i | ||||
\(689\) | 1003.16i | 1.45596i | ||||||||
\(690\) | −70.7962 | + | 59.5950i | −0.102603 | + | 0.0863696i | ||||
\(691\) | − | 11.4526i | − | 0.0165739i | −0.999966 | − | 0.00828695i | \(-0.997362\pi\) | ||
0.999966 | − | 0.00828695i | \(-0.00263785\pi\) | |||||||
\(692\) | 423.018 | + | 423.018i | 0.611298 | + | 0.611298i | ||||
\(693\) | −58.7348 | + | 117.546i | −0.0847543 | + | 0.169618i | ||||
\(694\) | 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 | ||||
\(700\) | −119.819 | + | 328.852i | −0.171170 | + | 0.469788i | ||||
\(701\) | − | 635.231i | − | 0.906178i | −0.891465 | − | 0.453089i | \(-0.850322\pi\) | ||
0.891465 | − | 0.453089i | \(-0.149678\pi\) | |||||||
\(702\) | 258.486 | − | 372.426i | 0.368214 | − | 0.530522i | ||||
\(703\) | −638.167 | − | 638.167i | −0.907777 | − | 0.907777i | ||||
\(704\) | 16.6861 | 0.0237018 | ||||||||
\(705\) | 706.261 | + | 60.6710i | 1.00179 | + | 0.0860581i | ||||
\(706\) | 385.875i | 0.546564i | ||||||||
\(707\) | 40.7576 | + | 81.3022i | 0.0576486 | + | 0.114996i | ||||
\(708\) | 278.879 | − | 92.8374i | 0.393896 | − | 0.131126i | ||||
\(709\) | 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 | ||||||||
\(717\) | −131.975 | + | 43.9338i | −0.184065 | + | 0.0612745i | ||||
\(718\) | −424.811 | + | 424.811i | −0.591659 | + | 0.591659i | ||||
\(719\) | − | 457.334i | − | 0.636069i | −0.948079 | − | 0.318034i | \(-0.896977\pi\) | ||
0.948079 | − | 0.318034i | \(-0.103023\pi\) | |||||||
\(720\) | −94.0432 | + | 153.479i | −0.130616 | + | 0.213166i | ||||
\(721\) | −142.245 | + | 428.228i | −0.197288 | + | 0.593936i | ||||
\(722\) | 59.3948 | − | 59.3948i | 0.0822642 | − | 0.0822642i | ||||
\(723\) | 61.9228 | + | 186.013i | 0.0856470 | + | 0.257279i | ||||
\(724\) | −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 | \(-0.336096\pi\) |
0.870333 | − | 0.492464i | \(-0.163904\pi\) | |||||||
\(728\) | −210.138 | + | 105.344i | −0.288651 | + | 0.144704i | ||||
\(729\) | −254.993 | − | 682.949i | −0.349784 | − | 0.936830i | ||||
\(730\) | 698.758 | − | 277.755i | 0.957203 | − | 0.380486i | ||||
\(731\) | 226.686 | 0.310104 | ||||||||
\(732\) | 472.168 | − | 157.183i | 0.645038 | − | 0.214730i | ||||
\(733\) | −443.025 | − | 443.025i | −0.604400 | − | 0.604400i | 0.337077 | − | 0.941477i | \(-0.390562\pi\) |
−0.941477 | + | 0.337077i | \(0.890562\pi\) | |||||||
\(734\) | − | 791.713i | − | 1.07863i | ||||||
\(735\) | 42.8245 | + | 733.751i | 0.0582647 | + | 0.998301i | ||||
\(736\) | 24.6773 | 0.0335290 | ||||||||
\(737\) | −114.348 | + | 114.348i | −0.155154 | + | 0.155154i | ||||
\(738\) | −28.2036 | + | 196.319i | −0.0382163 | + | 0.266015i | ||||
\(739\) | − | 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 | ||||
\(742\) | −374.852 | − | 747.746i | −0.505192 | − | 1.00774i | ||||
\(743\) | 823.562 | + | 823.562i | 1.10843 | + | 1.10843i | 0.993357 | + | 0.115071i | \(0.0367095\pi\) |
0.115071 | + | 0.993357i | \(0.463291\pi\) | |||||||
\(744\) | −161.006 | + | 321.695i | −0.216406 | + | 0.432385i | ||||
\(745\) | 851.668 | − | 338.536i | 1.14318 | − | 0.454411i | ||||
\(746\) | 369.034i | 0.494683i | ||||||||
\(747\) | −186.633 | + | 1299.11i | −0.249844 | + | 1.73911i | ||||
\(748\) | −20.7125 | − | 20.7125i | −0.0276905 | − | 0.0276905i | ||||
\(749\) | −465.227 | − | 154.534i | −0.621131 | − | 0.206321i | ||||
\(750\) | 329.744 | + | 415.354i | 0.439658 | + | 0.553806i | ||||
\(751\) | −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 | ||||
\(753\) | −396.896 | + | 132.125i | −0.527087 | + | 0.175465i | ||||
\(754\) | 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 | \(0.262714\pi\) | |||||||
\(762\) | 595.201 | − | 198.139i | 0.781103 | − | 0.260026i | ||||
\(763\) | 1066.46 | − | 534.628i | 1.39772 | − | 0.700692i | ||||
\(764\) | 326.799 | 0.427747 | ||||||||
\(765\) | 307.251 | − | 73.7783i | 0.401635 | − | 0.0964422i | ||||
\(766\) | 228.424i | 0.298204i | ||||||||
\(767\) | 411.259 | − | 411.259i | 0.536191 | − | 0.536191i | ||||
\(768\) | 45.5428 | − | 15.1610i | 0.0593005 | − | 0.0197409i | ||||
\(769\) | −119.034 | −0.154791 | −0.0773956 | − | 0.997000i | \(-0.524660\pi\) | ||||
−0.0773956 | + | 0.997000i | \(0.524660\pi\) | |||||||
\(770\) | −5.94793 | − | 103.068i | −0.00772458 | − | 0.133855i | ||||
\(771\) | 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 | ||||||||
\(777\) | −0.712669 | − | 1091.31i | −0.000917206 | − | 1.40452i | ||||
\(778\) | −365.324 | + | 365.324i | −0.469568 | + | 0.469568i | ||||
\(779\) | −270.621 | −0.347395 | ||||||||
\(780\) | −30.4849 | + | 354.870i | −0.0390832 | + | 0.454961i | ||||
\(781\) | 156.379 | 0.200229 | ||||||||
\(782\) | −30.6321 | − | 30.6321i | −0.0391715 | − | 0.0391715i | ||||
\(783\) | 603.313 | − | 869.253i | 0.770514 | − | 1.11016i | ||||
\(784\) | 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 | −0.632638 | − | 0.774448i | \(-0.718028\pi\) |
0.774448 | + | 0.632638i | \(0.218028\pi\) | |||||||
\(788\) | 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 | ||||
\(792\) | 7.55019 | − | 52.5552i | 0.00953307 | − | 0.0663576i | ||||
\(793\) | 696.300 | − | 696.300i | 0.878058 | − | 0.878058i | ||||
\(794\) | − | 1058.91i | − | 1.33364i | ||||||
\(795\) | −1262.75 | − | 108.476i | −1.58837 | − | 0.136448i | ||||
\(796\) | 159.276i | 0.200095i | ||||||||
\(797\) | −80.8641 | − | 80.8641i | −0.101461 | − | 0.101461i | 0.654554 | − | 0.756015i | \(-0.272856\pi\) |
−0.756015 | + | 0.654554i | \(0.772856\pi\) | |||||||
\(798\) | −515.767 | + | 0.336816i | −0.646325 | + | 0.000422075i | ||||
\(799\) | 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 | ||||
\(805\) | −8.79650 | − | 152.430i | −0.0109273 | − | 0.189354i | ||||
\(806\) | 711.833i | 0.883167i | ||||||||
\(807\) | −371.403 | − | 1115.68i | −0.460227 | − | 1.38250i | ||||
\(808\) | −25.9847 | − | 25.9847i | −0.0321592 | − | 0.0321592i | ||||
\(809\) | 115.327 | 0.142555 | 0.0712776 | − | 0.997457i | \(-0.477292\pi\) | ||||
0.0712776 | + | 0.997457i | \(0.477292\pi\) | |||||||
\(810\) | 440.852 | + | 365.650i | 0.544262 | + | 0.451419i | ||||
\(811\) | − | 285.468i | − | 0.351996i | −0.984391 | − | 0.175998i | \(-0.943685\pi\) | ||
0.984391 | − | 0.175998i | \(-0.0563152\pi\) | |||||||
\(812\) | −490.468 | + | 245.876i | −0.604024 | + | 0.302803i | ||||
\(813\) | −310.157 | − | 931.696i | −0.381497 | − | 1.14600i | ||||
\(814\) | 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 | \(0.120673\pi\) | ||||
−0.928996 | + | 0.370089i | \(0.879327\pi\) | |||||||
\(822\) | 288.914 | + | 867.881i | 0.351476 | + | 1.05582i | ||||
\(823\) | −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 | ||||||
\(825\) | −137.823 | − | 73.9995i | −0.167058 | − | 0.0896963i | ||||
\(826\) | −152.873 | + | 460.226i | −0.185077 | + | 0.557175i | ||||
\(827\) | −874.440 | + | 874.440i | −1.05736 | + | 1.05736i | −0.0591122 | + | 0.998251i | \(0.518827\pi\) |
−0.998251 | + | 0.0591122i | \(0.981173\pi\) | |||||||
\(828\) | 11.1661 | − | 77.7249i | 0.0134856 | − | 0.0938706i | ||||
\(829\) | 369.045 | 0.445169 | 0.222585 | − | 0.974913i | \(-0.428551\pi\) | ||||
0.222585 | + | 0.974913i | \(0.428551\pi\) | |||||||
\(830\) | −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 | ||||
\(833\) | −340.512 | + | 49.3726i | −0.408777 | + | 0.0592708i | ||||
\(834\) | 142.463 | − | 284.646i | 0.170819 | − | 0.341302i | ||||
\(835\) | −222.775 | − | 96.0447i | −0.266796 | − | 0.115024i | ||||
\(836\) | 72.4459 | 0.0866578 | ||||||||
\(837\) | 940.371 | + | 652.673i | 1.12350 | + | 0.779777i | ||||
\(838\) | −427.623 | − | 427.623i | −0.510290 | − | 0.510290i | ||||
\(839\) | 1424.80i | 1.69821i | 0.528223 | + | 0.849106i | \(0.322858\pi\) | ||||
−0.528223 | + | 0.849106i | \(0.677142\pi\) | |||||||
\(840\) | −109.882 | − | 275.909i | −0.130812 | − | 0.328463i | ||||
\(841\) | 694.784 | 0.826140 | ||||||||
\(842\) | 294.683 | − | 294.683i | 0.349980 | − | 0.349980i | ||||
\(843\) | −92.4731 | − | 277.784i | −0.109695 | − | 0.329519i | ||||
\(844\) | 292.932i | 0.347076i | ||||||||
\(845\) | −51.7920 | − | 130.295i | −0.0612923 | − | 0.154195i | ||||
\(846\) | −481.476 | + | 360.514i | −0.569121 | + | 0.426139i | ||||
\(847\) | −365.936 | − | 729.959i | −0.432037 | − | 0.861817i | ||||
\(848\) | 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 | ||||||||
\(852\) | 426.819 | − | 142.086i | 0.500961 | − | 0.166767i | ||||
\(853\) | −459.198 | − | 459.198i | −0.538332 | − | 0.538332i | 0.384707 | − | 0.923039i | \(-0.374303\pi\) |
−0.923039 | + | 0.384707i | \(0.874303\pi\) | |||||||
\(854\) | −258.829 | + | 779.207i | −0.303079 | + | 0.912420i | ||||
\(855\) | −408.307 | + | 666.360i | −0.477552 | + | 0.779369i | ||||
\(856\) | 198.079 | 0.231401 | ||||||||
\(857\) | −733.866 | − | 733.866i | −0.856319 | − | 0.856319i | 0.134583 | − | 0.990902i | \(-0.457030\pi\) |
−0.990902 | + | 0.134583i | \(0.957030\pi\) | |||||||
\(858\) | −33.1842 | − | 99.6835i | −0.0386762 | − | 0.116181i | ||||
\(859\) | −223.858 | −0.260603 | −0.130301 | − | 0.991474i | \(-0.541595\pi\) | ||||
−0.130301 | + | 0.991474i | \(0.541595\pi\) | |||||||
\(860\) | −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 | 0.934781 | − | 0.355225i | \(-0.115596\pi\) |
−0.355225 | + | 0.934781i | \(0.615596\pi\) | |||||||
\(864\) | −27.1443 | − | 150.304i | −0.0314170 | − | 0.173963i | ||||
\(865\) | −592.110 | + | 1373.39i | −0.684520 | + | 1.58774i | ||||
\(866\) | −12.3080 | −0.0142125 | ||||||||
\(867\) | −227.124 | − | 682.268i | −0.261965 | − | 0.786930i | ||||
\(868\) | −265.993 | − | 530.596i | −0.306443 | − | 0.611285i | ||||
\(869\) | −7.53102 | −0.00866630 | ||||||||
\(870\) | −71.1526 | + | 828.275i | −0.0817846 | + | 0.952041i | ||||
\(871\) | 920.501i | 1.05683i | ||||||||
\(872\) | −340.847 | + | 340.847i | −0.390880 | + | 0.390880i | ||||
\(873\) | 64.0023 | − | 445.506i | 0.0733131 | − | 0.510317i | ||||
\(874\) | 107.142 | 0.122588 | ||||||||
\(875\) | −874.634 | + | 25.3208i | −0.999581 | + | 0.0289380i | ||||
\(876\) | −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 | \(0.888940\pi\) | |||||||
\(882\) | −441.576 | − | 440.424i | −0.500653 | − | 0.499347i | ||||
\(883\) | −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 | ||||||||
\(885\) | 473.213 | + | 562.156i | 0.534704 | + | 0.635205i | ||||
\(886\) | 352.964 | 0.398379 | ||||||||
\(887\) | 1006.62 | + | 1006.62i | 1.13486 | + | 1.13486i | 0.989359 | + | 0.145497i | \(0.0464781\pi\) |
0.145497 | + | 0.989359i | \(0.453522\pi\) | |||||||
\(888\) | 139.278 | + | 418.383i | 0.156844 | + | 0.471152i | ||||
\(889\) | −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 | ||||
\(897\) | −49.0767 | − | 147.424i | −0.0547120 | − | 0.164352i | ||||
\(898\) | 521.716 | − | 521.716i | 0.580976 | − | 0.580976i | ||||
\(899\) | 1661.44i | 1.84809i | ||||||||
\(900\) | −443.407 | − | 76.7477i | −0.492674 | − | 0.0852752i | ||||
\(901\) | − | 593.304i | − | 0.658495i | ||||||
\(902\) | 32.5017 | + | 32.5017i | 0.0360329 | + | 0.0360329i | ||||
\(903\) | −677.938 | + | 0.442720i | −0.750762 | + | 0.000490277i | ||||
\(904\) | 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 | ||||
\(910\) | −438.790 | − | 390.909i | −0.482187 | − | 0.429570i | ||||
\(911\) | − | 297.086i | − | 0.326110i | −0.986617 | − | 0.163055i | \(-0.947865\pi\) | ||
0.986617 | − | 0.163055i | \(-0.0521348\pi\) | |||||||
\(912\) | 197.733 | − | 65.8244i | 0.216812 | − | 0.0721758i | ||||
\(913\) | 215.075 | + | 215.075i | 0.235570 | + | 0.235570i | ||||
\(914\) | −69.6131 | −0.0761631 | ||||||||
\(915\) | 801.195 | + | 951.784i | 0.875623 | + | 1.04020i | ||||
\(916\) | − | 574.151i | − | 0.626802i | ||||||
\(917\) | −4.47984 | − | 8.93627i | −0.00488532 | − | 0.00974511i | ||||
\(918\) | −152.878 | + | 220.267i | −0.166534 | + | 0.239942i | ||||
\(919\) | − | 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 | ||||||
\(927\) | −574.263 | − | 82.4998i | −0.619486 | − | 0.0889965i | ||||
\(928\) | 156.756 | − | 156.756i | 0.168918 | − | 0.168918i | ||||
\(929\) | 81.2126i | 0.0874194i | 0.999044 | + | 0.0437097i | \(0.0139177\pi\) | ||||
−0.999044 | + | 0.0437097i | \(0.986082\pi\) | |||||||
\(930\) | −896.041 | − | 76.9740i | −0.963485 | − | 0.0827677i | ||||
\(931\) | 509.156 | − | 681.846i | 0.546892 | − | 0.732380i | ||||
\(932\) | −398.695 | + | 398.695i | −0.427784 | + | 0.427784i | ||||
\(933\) | −1021.85 | + | 340.168i | −1.09523 | + | 0.364596i | ||||
\(934\) | 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 | −0.452271 | − | 0.891881i | \(-0.649386\pi\) |
0.891881 | + | 0.452271i | \(0.149386\pi\) | |||||||
\(938\) | −343.967 | − | 686.136i | −0.366702 | − | 0.731488i | ||||
\(939\) | 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 | \(0.435333\pi\) | |||||||
\(942\) | 6.37565 | + | 19.1521i | 0.00676821 | + | 0.0203313i | ||||
\(943\) | 48.0674 | + | 48.0674i | 0.0509728 | + | 0.0509728i | ||||
\(944\) | − | 195.950i | − | 0.207574i | ||||||
\(945\) | −918.736 | + | 221.245i | −0.972207 | + | 0.234122i | ||||
\(946\) | 95.2248 | 0.100660 | ||||||||
\(947\) | −54.3340 | + | 54.3340i | −0.0573749 | + | 0.0573749i | −0.735212 | − | 0.677837i | \(-0.762917\pi\) |
0.677837 | + | 0.735212i | \(0.262917\pi\) | |||||||
\(948\) | −20.5551 | + | 6.84268i | −0.0216826 | + | 0.00721802i | ||||
\(949\) | 1262.53i | 1.33038i | ||||||||
\(950\) | 17.6212 | − | 613.756i | 0.0185486 | − | 0.646059i | ||||
\(951\) | −88.0202 | + | 175.867i | −0.0925554 | + | 0.184929i | ||||
\(952\) | 124.284 | − | 62.3046i | 0.130550 | − | 0.0654460i | ||||
\(953\) | 749.903 | + | 749.903i | 0.786887 | + | 0.786887i | 0.980983 | − | 0.194096i | \(-0.0621773\pi\) |
−0.194096 | + | 0.980983i | \(0.562177\pi\) | |||||||
\(954\) | 860.851 | − | 644.578i | 0.902359 | − | 0.675658i | ||||
\(955\) | 301.787 | + | 759.216i | 0.316007 | + | 0.794990i | ||||
\(956\) | 92.7303i | 0.0969982i | ||||||||
\(957\) | −77.4527 | − | 232.664i | −0.0809328 | − | 0.243118i | ||||
\(958\) | 49.3199 | + | 49.3199i | 0.0514822 | + | 0.0514822i | ||||
\(959\) | −1432.24 | − | 475.748i | −1.49347 | − | 0.496087i | ||||
\(960\) | 77.2790 | + | 91.8039i | 0.0804989 | + | 0.0956291i | ||||
\(961\) | −836.367 | −0.870309 | ||||||||
\(962\) | 616.985 | + | 616.985i | 0.641356 | + | 0.641356i | ||||
\(963\) | 89.6278 | − | 623.879i | 0.0930714 | − | 0.647850i | ||||
\(964\) | 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 | \(0.701001\pi\) | |||||||
\(972\) | −485.685 | + | 17.4848i | −0.499676 | + | 0.0179885i | ||||
\(973\) | 235.359 | + | 469.488i | 0.241890 | + | 0.482516i | ||||
\(974\) | −167.717 | −0.172194 | ||||||||
\(975\) | −852.582 | + | 256.887i | −0.874443 | + | 0.263474i | ||||
\(976\) | − | 331.762i | − | 0.339920i | ||||||
\(977\) | −11.8173 | + | 11.8173i | −0.0120955 | + | 0.0120955i | −0.713129 | − | 0.701033i | \(-0.752722\pi\) |
0.701033 | + | 0.713129i | \(0.252722\pi\) | |||||||
\(978\) | 199.457 | + | 599.158i | 0.203943 | + | 0.612636i | ||||
\(979\) | 50.9817 | 0.0520753 | ||||||||
\(980\) | 473.144 | + | 127.417i | 0.482800 | + | 0.130018i | ||||
\(981\) | 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 | ||||||||
\(987\) | −0.648080 | − | 992.407i | −0.000656616 | − | 1.00548i | ||||
\(988\) | 291.594 | − | 291.594i | 0.295136 | − | 0.295136i | ||||
\(989\) | 140.830 | 0.142396 | ||||||||
\(990\) | 129.068 | − | 30.9923i | 0.130372 | − | 0.0313054i | ||||
\(991\) | −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 | ||||
\(993\) | 1063.22 | − | 353.941i | 1.07072 | − | 0.356436i | ||||
\(994\) | −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 | −0.969118 | − | 0.246597i | \(-0.920688\pi\) |
0.246597 | + | 0.969118i | \(0.420688\pi\) | |||||||
\(998\) | −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.a.167.15 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.b.167.7 | yes | 32 | ||
5.3 | odd | 4 | 210.3.k.b.83.10 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.167.2 | yes | 32 | |
15.8 | even | 4 | inner | 210.3.k.a.83.2 | ✓ | 32 | |
21.20 | even | 2 | 210.3.k.b.167.10 | yes | 32 | ||
35.13 | even | 4 | 210.3.k.b.83.7 | yes | 32 | ||
105.83 | odd | 4 | inner | 210.3.k.a.83.15 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.2 | ✓ | 32 | 15.8 | even | 4 | inner | |
210.3.k.a.83.15 | yes | 32 | 105.83 | odd | 4 | inner | |
210.3.k.a.167.2 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.a.167.15 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.k.b.83.7 | yes | 32 | 35.13 | even | 4 | ||
210.3.k.b.83.10 | yes | 32 | 5.3 | odd | 4 | ||
210.3.k.b.167.7 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.167.10 | yes | 32 | 21.20 | even | 2 |