Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 281.3 | ||
Root | \(-0.962473 + 1.44002i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.d.239.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.337674 | + | 1.69882i | −0.194956 | + | 0.980812i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.19168 | − | 2.19168i | 0.980147 | − | 0.980147i | −0.0196593 | − | 0.999807i | \(-0.506258\pi\) |
0.999807 | + | 0.0196593i | \(0.00625814\pi\) | |||||||
\(6\) | −0.962473 | − | 1.44002i | −0.392928 | − | 0.587884i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −2.77195 | − | 1.14729i | −0.923984 | − | 0.382430i | ||||
\(10\) | 3.09950i | 0.980147i | ||||||||
\(11\) | 1.27674 | + | 1.27674i | 0.384952 | + | 0.384952i | 0.872883 | − | 0.487930i | \(-0.162248\pi\) |
−0.487930 | + | 0.872883i | \(0.662248\pi\) | |||||||
\(12\) | 1.69882 | + | 0.337674i | 0.490406 | + | 0.0974780i | ||||
\(13\) | −3.23661 | + | 1.58883i | −0.897674 | + | 0.440661i | ||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | 2.98318 | + | 4.46333i | 0.770255 | + | 1.15243i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.68191 | 0.892995 | 0.446497 | − | 0.894785i | \(-0.352671\pi\) | ||||
0.446497 | + | 0.894785i | \(0.352671\pi\) | |||||||
\(18\) | 2.77132 | − | 1.14881i | 0.653207 | − | 0.270777i | ||||
\(19\) | 5.26937 | + | 5.26937i | 1.20888 | + | 1.20888i | 0.971391 | + | 0.237485i | \(0.0763232\pi\) |
0.237485 | + | 0.971391i | \(0.423677\pi\) | |||||||
\(20\) | −2.19168 | − | 2.19168i | −0.490074 | − | 0.490074i | ||||
\(21\) | −0.962473 | − | 1.44002i | −0.210029 | − | 0.314237i | ||||
\(22\) | −1.80559 | −0.384952 | ||||||||
\(23\) | 8.15820 | 1.70110 | 0.850551 | − | 0.525893i | \(-0.176269\pi\) | ||||
0.850551 | + | 0.525893i | \(0.176269\pi\) | |||||||
\(24\) | −1.44002 | + | 0.962473i | −0.293942 | + | 0.196464i | ||||
\(25\) | − | 4.60689i | − | 0.921378i | ||||||
\(26\) | 1.16516 | − | 3.41210i | 0.228506 | − | 0.669167i | ||||
\(27\) | 2.88505 | − | 4.32163i | 0.555229 | − | 0.831698i | ||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | 9.50505i | 1.76504i | 0.470272 | + | 0.882522i | \(0.344156\pi\) | ||||
−0.470272 | + | 0.882522i | \(0.655844\pi\) | |||||||
\(30\) | −5.26548 | − | 1.04662i | −0.961340 | − | 0.191086i | ||||
\(31\) | −0.125281 | − | 0.125281i | −0.0225011 | − | 0.0225011i | 0.695767 | − | 0.718268i | \(-0.255065\pi\) |
−0.718268 | + | 0.695767i | \(0.755065\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −2.60007 | + | 1.73783i | −0.452614 | + | 0.302517i | ||||
\(34\) | −2.60350 | + | 2.60350i | −0.446497 | + | 0.446497i | ||||
\(35\) | 3.09950i | 0.523911i | ||||||||
\(36\) | −1.14729 | + | 2.77195i | −0.191215 | + | 0.461992i | ||||
\(37\) | −0.328266 | + | 0.328266i | −0.0539666 | + | 0.0539666i | −0.733575 | − | 0.679608i | \(-0.762150\pi\) |
0.679608 | + | 0.733575i | \(0.262150\pi\) | |||||||
\(38\) | −7.45201 | −1.20888 | ||||||||
\(39\) | −1.60620 | − | 6.03491i | −0.257199 | − | 0.966359i | ||||
\(40\) | 3.09950 | 0.490074 | ||||||||
\(41\) | −2.21794 | + | 2.21794i | −0.346383 | + | 0.346383i | −0.858761 | − | 0.512377i | \(-0.828765\pi\) |
0.512377 | + | 0.858761i | \(0.328765\pi\) | |||||||
\(42\) | 1.69882 | + | 0.337674i | 0.262133 | + | 0.0521042i | ||||
\(43\) | 1.43126i | 0.218265i | 0.994027 | + | 0.109133i | \(0.0348073\pi\) | ||||
−0.994027 | + | 0.109133i | \(0.965193\pi\) | |||||||
\(44\) | 1.27674 | − | 1.27674i | 0.192476 | − | 0.192476i | ||||
\(45\) | −8.58971 | + | 3.56073i | −1.28048 | + | 0.530803i | ||||
\(46\) | −5.76872 | + | 5.76872i | −0.850551 | + | 0.850551i | ||||
\(47\) | −0.805736 | − | 0.805736i | −0.117529 | − | 0.117529i | 0.645896 | − | 0.763425i | \(-0.276484\pi\) |
−0.763425 | + | 0.645896i | \(0.776484\pi\) | |||||||
\(48\) | 0.337674 | − | 1.69882i | 0.0487390 | − | 0.245203i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 3.25756 | + | 3.25756i | 0.460689 | + | 0.460689i | ||||
\(51\) | −1.24328 | + | 6.25489i | −0.174095 | + | 0.875860i | ||||
\(52\) | 1.58883 | + | 3.23661i | 0.220330 | + | 0.448837i | ||||
\(53\) | − | 5.59755i | − | 0.768882i | −0.923150 | − | 0.384441i | \(-0.874394\pi\) | ||
0.923150 | − | 0.384441i | \(-0.125606\pi\) | |||||||
\(54\) | 1.01581 | + | 5.09589i | 0.138235 | + | 0.693463i | ||||
\(55\) | 5.59641 | 0.754620 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −10.7310 | + | 7.17236i | −1.42136 | + | 0.950003i | ||||
\(58\) | −6.72109 | − | 6.72109i | −0.882522 | − | 0.882522i | ||||
\(59\) | 1.49217 | + | 1.49217i | 0.194264 | + | 0.194264i | 0.797536 | − | 0.603272i | \(-0.206136\pi\) |
−0.603272 | + | 0.797536i | \(0.706136\pi\) | |||||||
\(60\) | 4.46333 | − | 2.98318i | 0.576213 | − | 0.385127i | ||||
\(61\) | −8.14557 | −1.04293 | −0.521467 | − | 0.853272i | \(-0.674615\pi\) | ||||
−0.521467 | + | 0.853272i | \(0.674615\pi\) | |||||||
\(62\) | 0.177174 | 0.0225011 | ||||||||
\(63\) | 2.77132 | − | 1.14881i | 0.349154 | − | 0.144736i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −3.61141 | + | 10.5758i | −0.447940 | + | 1.31177i | ||||
\(66\) | 0.609699 | − | 3.06736i | 0.0750487 | − | 0.377566i | ||||
\(67\) | −10.6436 | − | 10.6436i | −1.30033 | − | 1.30033i | −0.928170 | − | 0.372157i | \(-0.878618\pi\) |
−0.372157 | − | 0.928170i | \(-0.621382\pi\) | |||||||
\(68\) | − | 3.68191i | − | 0.446497i | ||||||
\(69\) | −2.75481 | + | 13.8593i | −0.331640 | + | 1.66846i | ||||
\(70\) | −2.19168 | − | 2.19168i | −0.261955 | − | 0.261955i | ||||
\(71\) | −0.752235 | + | 0.752235i | −0.0892739 | + | 0.0892739i | −0.750333 | − | 0.661060i | \(-0.770107\pi\) |
0.661060 | + | 0.750333i | \(0.270107\pi\) | |||||||
\(72\) | −1.14881 | − | 2.77132i | −0.135389 | − | 0.326604i | ||||
\(73\) | 3.59354 | − | 3.59354i | 0.420592 | − | 0.420592i | −0.464815 | − | 0.885408i | \(-0.653879\pi\) |
0.885408 | + | 0.464815i | \(0.153879\pi\) | |||||||
\(74\) | − | 0.464238i | − | 0.0539666i | ||||||
\(75\) | 7.82626 | + | 1.55563i | 0.903699 | + | 0.179628i | ||||
\(76\) | 5.26937 | − | 5.26937i | 0.604438 | − | 0.604438i | ||||
\(77\) | −1.80559 | −0.205766 | ||||||||
\(78\) | 5.40308 | + | 3.13157i | 0.611779 | + | 0.354580i | ||||
\(79\) | 4.38864 | 0.493760 | 0.246880 | − | 0.969046i | \(-0.420595\pi\) | ||||
0.246880 | + | 0.969046i | \(0.420595\pi\) | |||||||
\(80\) | −2.19168 | + | 2.19168i | −0.245037 | + | 0.245037i | ||||
\(81\) | 6.36745 | + | 6.36047i | 0.707494 | + | 0.706719i | ||||
\(82\) | − | 3.13663i | − | 0.346383i | ||||||
\(83\) | 9.35133 | − | 9.35133i | 1.02644 | − | 1.02644i | 0.0268014 | − | 0.999641i | \(-0.491468\pi\) |
0.999641 | − | 0.0268014i | \(-0.00853218\pi\) | |||||||
\(84\) | −1.44002 | + | 0.962473i | −0.157119 | + | 0.105014i | ||||
\(85\) | 8.06956 | − | 8.06956i | 0.875266 | − | 0.875266i | ||||
\(86\) | −1.01205 | − | 1.01205i | −0.109133 | − | 0.109133i | ||||
\(87\) | −16.1473 | − | 3.20961i | −1.73118 | − | 0.344106i | ||||
\(88\) | 1.80559i | 0.192476i | ||||||||
\(89\) | 3.19016 | + | 3.19016i | 0.338156 | + | 0.338156i | 0.855673 | − | 0.517517i | \(-0.173144\pi\) |
−0.517517 | + | 0.855673i | \(0.673144\pi\) | |||||||
\(90\) | 3.55603 | − | 8.59166i | 0.374838 | − | 0.905641i | ||||
\(91\) | 1.16516 | − | 3.41210i | 0.122142 | − | 0.357685i | ||||
\(92\) | − | 8.15820i | − | 0.850551i | ||||||
\(93\) | 0.255133 | − | 0.170525i | 0.0264560 | − | 0.0176826i | ||||
\(94\) | 1.13948 | 0.117529 | ||||||||
\(95\) | 23.0975 | 2.36975 | ||||||||
\(96\) | 0.962473 | + | 1.44002i | 0.0982320 | + | 0.146971i | ||||
\(97\) | 1.79334 | + | 1.79334i | 0.182086 | + | 0.182086i | 0.792264 | − | 0.610178i | \(-0.208902\pi\) |
−0.610178 | + | 0.792264i | \(0.708902\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | −2.07427 | − | 5.00386i | −0.208472 | − | 0.502907i | ||||
\(100\) | −4.60689 | −0.460689 | ||||||||
\(101\) | 8.55213 | 0.850969 | 0.425484 | − | 0.904966i | \(-0.360104\pi\) | ||||
0.425484 | + | 0.904966i | \(0.360104\pi\) | |||||||
\(102\) | −3.54374 | − | 5.30201i | −0.350883 | − | 0.524977i | ||||
\(103\) | 6.72083i | 0.662223i | 0.943592 | + | 0.331112i | \(0.107424\pi\) | ||||
−0.943592 | + | 0.331112i | \(0.892576\pi\) | |||||||
\(104\) | −3.41210 | − | 1.16516i | −0.334584 | − | 0.114253i | ||||
\(105\) | −5.26548 | − | 1.04662i | −0.513858 | − | 0.102140i | ||||
\(106\) | 3.95806 | + | 3.95806i | 0.384441 | + | 0.384441i | ||||
\(107\) | 7.64497i | 0.739067i | 0.929217 | + | 0.369534i | \(0.120483\pi\) | ||||
−0.929217 | + | 0.369534i | \(0.879517\pi\) | |||||||
\(108\) | −4.32163 | − | 2.88505i | −0.415849 | − | 0.277614i | ||||
\(109\) | −11.0618 | − | 11.0618i | −1.05953 | − | 1.05953i | −0.998112 | − | 0.0614199i | \(-0.980437\pi\) |
−0.0614199 | − | 0.998112i | \(-0.519563\pi\) | |||||||
\(110\) | −3.95726 | + | 3.95726i | −0.377310 | + | 0.377310i | ||||
\(111\) | −0.446817 | − | 0.668510i | −0.0424100 | − | 0.0634522i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | − | 19.2385i | − | 1.80980i | −0.425619 | − | 0.904902i | \(-0.639944\pi\) | ||
0.425619 | − | 0.904902i | \(-0.360056\pi\) | |||||||
\(114\) | 2.51635 | − | 12.6596i | 0.235678 | − | 1.18568i | ||||
\(115\) | 17.8801 | − | 17.8801i | 1.66733 | − | 1.66733i | ||||
\(116\) | 9.50505 | 0.882522 | ||||||||
\(117\) | 10.7946 | − | 0.690818i | 0.997958 | − | 0.0638661i | ||||
\(118\) | −2.11025 | −0.194264 | ||||||||
\(119\) | −2.60350 | + | 2.60350i | −0.238663 | + | 0.238663i | ||||
\(120\) | −1.04662 | + | 5.26548i | −0.0955428 | + | 0.480670i | ||||
\(121\) | − | 7.73986i | − | 0.703624i | ||||||
\(122\) | 5.75979 | − | 5.75979i | 0.521467 | − | 0.521467i | ||||
\(123\) | −3.01893 | − | 4.51680i | −0.272207 | − | 0.407266i | ||||
\(124\) | −0.125281 | + | 0.125281i | −0.0112505 | + | 0.0112505i | ||||
\(125\) | 0.861568 | + | 0.861568i | 0.0770610 | + | 0.0770610i | ||||
\(126\) | −1.14729 | + | 2.77195i | −0.102209 | + | 0.246945i | ||||
\(127\) | 12.4807i | 1.10749i | 0.832688 | + | 0.553743i | \(0.186801\pi\) | ||||
−0.832688 | + | 0.553743i | \(0.813199\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −2.43145 | − | 0.483299i | −0.214077 | − | 0.0425521i | ||||
\(130\) | −4.92456 | − | 10.0319i | −0.431913 | − | 0.879853i | ||||
\(131\) | 8.33777i | 0.728475i | 0.931306 | + | 0.364237i | \(0.118670\pi\) | ||||
−0.931306 | + | 0.364237i | \(0.881330\pi\) | |||||||
\(132\) | 1.73783 | + | 2.60007i | 0.151258 | + | 0.226307i | ||||
\(133\) | −7.45201 | −0.646172 | ||||||||
\(134\) | 15.0524 | 1.30033 | ||||||||
\(135\) | −3.14851 | − | 15.7947i | −0.270981 | − | 1.35939i | ||||
\(136\) | 2.60350 | + | 2.60350i | 0.223249 | + | 0.223249i | ||||
\(137\) | −14.2203 | − | 14.2203i | −1.21492 | − | 1.21492i | −0.969388 | − | 0.245535i | \(-0.921036\pi\) |
−0.245535 | − | 0.969388i | \(-0.578964\pi\) | |||||||
\(138\) | −7.85205 | − | 11.7479i | −0.668411 | − | 1.00005i | ||||
\(139\) | 5.53897 | 0.469809 | 0.234905 | − | 0.972018i | \(-0.424522\pi\) | ||||
0.234905 | + | 0.972018i | \(0.424522\pi\) | |||||||
\(140\) | 3.09950 | 0.261955 | ||||||||
\(141\) | 1.64087 | − | 1.09672i | 0.138186 | − | 0.0923606i | ||||
\(142\) | − | 1.06382i | − | 0.0892739i | ||||||
\(143\) | −6.16083 | − | 2.10379i | −0.515195 | − | 0.175928i | ||||
\(144\) | 2.77195 | + | 1.14729i | 0.230996 | + | 0.0956076i | ||||
\(145\) | 20.8320 | + | 20.8320i | 1.73000 | + | 1.73000i | ||||
\(146\) | 5.08204i | 0.420592i | ||||||||
\(147\) | 1.69882 | + | 0.337674i | 0.140116 | + | 0.0278509i | ||||
\(148\) | 0.328266 | + | 0.328266i | 0.0269833 | + | 0.0269833i | ||||
\(149\) | −3.72237 | + | 3.72237i | −0.304949 | + | 0.304949i | −0.842946 | − | 0.537998i | \(-0.819181\pi\) |
0.537998 | + | 0.842946i | \(0.319181\pi\) | |||||||
\(150\) | −6.63400 | + | 4.43401i | −0.541663 | + | 0.362035i | ||||
\(151\) | −15.2455 | + | 15.2455i | −1.24066 | + | 1.24066i | −0.280929 | + | 0.959729i | \(0.590642\pi\) |
−0.959729 | + | 0.280929i | \(0.909358\pi\) | |||||||
\(152\) | 7.45201i | 0.604438i | ||||||||
\(153\) | −10.2061 | − | 4.22422i | −0.825113 | − | 0.341508i | ||||
\(154\) | 1.27674 | − | 1.27674i | 0.102883 | − | 0.102883i | ||||
\(155\) | −0.549149 | −0.0441087 | ||||||||
\(156\) | −6.03491 | + | 1.60620i | −0.483179 | + | 0.128599i | ||||
\(157\) | −10.2830 | −0.820676 | −0.410338 | − | 0.911934i | \(-0.634589\pi\) | ||||
−0.410338 | + | 0.911934i | \(0.634589\pi\) | |||||||
\(158\) | −3.10323 | + | 3.10323i | −0.246880 | + | 0.246880i | ||||
\(159\) | 9.50920 | + | 1.89014i | 0.754129 | + | 0.149898i | ||||
\(160\) | − | 3.09950i | − | 0.245037i | ||||||
\(161\) | −5.76872 | + | 5.76872i | −0.454639 | + | 0.454639i | ||||
\(162\) | −9.00000 | + | 0.00493109i | −0.707107 | + | 0.000387423i | ||||
\(163\) | 16.4136 | − | 16.4136i | 1.28561 | − | 1.28561i | 0.348188 | − | 0.937425i | \(-0.386797\pi\) |
0.937425 | − | 0.348188i | \(-0.113203\pi\) | |||||||
\(164\) | 2.21794 | + | 2.21794i | 0.173192 | + | 0.173192i | ||||
\(165\) | −1.88976 | + | 9.50727i | −0.147118 | + | 0.740140i | ||||
\(166\) | 13.2248i | 1.02644i | ||||||||
\(167\) | −10.1688 | − | 10.1688i | −0.786888 | − | 0.786888i | 0.194095 | − | 0.980983i | \(-0.437823\pi\) |
−0.980983 | + | 0.194095i | \(0.937823\pi\) | |||||||
\(168\) | 0.337674 | − | 1.69882i | 0.0260521 | − | 0.131067i | ||||
\(169\) | 7.95127 | − | 10.2848i | 0.611636 | − | 0.791139i | ||||
\(170\) | 11.4121i | 0.875266i | ||||||||
\(171\) | −8.56095 | − | 20.6519i | −0.654672 | − | 1.57929i | ||||
\(172\) | 1.43126 | 0.109133 | ||||||||
\(173\) | −8.72942 | −0.663686 | −0.331843 | − | 0.943335i | \(-0.607670\pi\) | ||||
−0.331843 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(174\) | 13.6874 | − | 9.14836i | 1.03764 | − | 0.693535i | ||||
\(175\) | 3.25756 | + | 3.25756i | 0.246249 | + | 0.246249i | ||||
\(176\) | −1.27674 | − | 1.27674i | −0.0962380 | − | 0.0962380i | ||||
\(177\) | −3.03879 | + | 2.03106i | −0.228410 | + | 0.152664i | ||||
\(178\) | −4.51157 | −0.338156 | ||||||||
\(179\) | −21.4346 | −1.60210 | −0.801048 | − | 0.598600i | \(-0.795724\pi\) | ||||
−0.801048 | + | 0.598600i | \(0.795724\pi\) | |||||||
\(180\) | 3.56073 | + | 8.58971i | 0.265401 | + | 0.640240i | ||||
\(181\) | 7.53227i | 0.559869i | 0.960019 | + | 0.279935i | \(0.0903128\pi\) | ||||
−0.960019 | + | 0.279935i | \(0.909687\pi\) | |||||||
\(182\) | 1.58883 | + | 3.23661i | 0.117772 | + | 0.239913i | ||||
\(183\) | 2.75055 | − | 13.8378i | 0.203326 | − | 1.02292i | ||||
\(184\) | 5.76872 | + | 5.76872i | 0.425275 | + | 0.425275i | ||||
\(185\) | 1.43891i | 0.105790i | ||||||||
\(186\) | −0.0598268 | + | 0.300985i | −0.00438672 | + | 0.0220693i | ||||
\(187\) | 4.70085 | + | 4.70085i | 0.343760 | + | 0.343760i | ||||
\(188\) | −0.805736 | + | 0.805736i | −0.0587644 | + | 0.0587644i | ||||
\(189\) | 1.01581 | + | 5.09589i | 0.0738895 | + | 0.370672i | ||||
\(190\) | −16.3324 | + | 16.3324i | −1.18488 | + | 1.18488i | ||||
\(191\) | − | 1.80118i | − | 0.130329i | −0.997875 | − | 0.0651645i | \(-0.979243\pi\) | ||
0.997875 | − | 0.0651645i | \(-0.0207572\pi\) | |||||||
\(192\) | −1.69882 | − | 0.337674i | −0.122601 | − | 0.0243695i | ||||
\(193\) | 14.4054 | − | 14.4054i | 1.03692 | − | 1.03692i | 0.0376326 | − | 0.999292i | \(-0.488018\pi\) |
0.999292 | − | 0.0376326i | \(-0.0119817\pi\) | |||||||
\(194\) | −2.53616 | −0.182086 | ||||||||
\(195\) | −16.7468 | − | 9.70628i | −1.19927 | − | 0.695081i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 6.93319 | − | 6.93319i | 0.493970 | − | 0.493970i | −0.415585 | − | 0.909554i | \(-0.636423\pi\) |
0.909554 | + | 0.415585i | \(0.136423\pi\) | |||||||
\(198\) | 5.00500 | + | 2.07153i | 0.355690 | + | 0.147217i | ||||
\(199\) | 10.2593i | 0.727262i | 0.931543 | + | 0.363631i | \(0.118463\pi\) | ||||
−0.931543 | + | 0.363631i | \(0.881537\pi\) | |||||||
\(200\) | 3.25756 | − | 3.25756i | 0.230345 | − | 0.230345i | ||||
\(201\) | 21.6756 | − | 14.4875i | 1.52888 | − | 1.02187i | ||||
\(202\) | −6.04727 | + | 6.04727i | −0.425484 | + | 0.425484i | ||||
\(203\) | −6.72109 | − | 6.72109i | −0.471728 | − | 0.471728i | ||||
\(204\) | 6.25489 | + | 1.24328i | 0.437930 | + | 0.0870473i | ||||
\(205\) | 9.72199i | 0.679013i | ||||||||
\(206\) | −4.75235 | − | 4.75235i | −0.331112 | − | 0.331112i | ||||
\(207\) | −22.6141 | − | 9.35983i | −1.57179 | − | 0.650553i | ||||
\(208\) | 3.23661 | − | 1.58883i | 0.224418 | − | 0.110165i | ||||
\(209\) | 13.4552i | 0.930719i | ||||||||
\(210\) | 4.46333 | − | 2.98318i | 0.307999 | − | 0.205859i | ||||
\(211\) | −19.4541 | −1.33928 | −0.669638 | − | 0.742687i | \(-0.733551\pi\) | ||||
−0.669638 | + | 0.742687i | \(0.733551\pi\) | |||||||
\(212\) | −5.59755 | −0.384441 | ||||||||
\(213\) | −1.02390 | − | 1.53192i | −0.0701564 | − | 0.104965i | ||||
\(214\) | −5.40581 | − | 5.40581i | −0.369534 | − | 0.369534i | ||||
\(215\) | 3.13686 | + | 3.13686i | 0.213932 | + | 0.213932i | ||||
\(216\) | 5.09589 | − | 1.01581i | 0.346732 | − | 0.0691173i | ||||
\(217\) | 0.177174 | 0.0120273 | ||||||||
\(218\) | 15.6438 | 1.05953 | ||||||||
\(219\) | 4.89132 | + | 7.31821i | 0.330525 | + | 0.494519i | ||||
\(220\) | − | 5.59641i | − | 0.377310i | ||||||
\(221\) | −11.9169 | + | 5.84991i | −0.801618 | + | 0.393508i | ||||
\(222\) | 0.788656 | + | 0.156761i | 0.0529311 | + | 0.0105211i | ||||
\(223\) | 11.9464 | + | 11.9464i | 0.799992 | + | 0.799992i | 0.983094 | − | 0.183102i | \(-0.0586140\pi\) |
−0.183102 | + | 0.983094i | \(0.558614\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | −5.28544 | + | 12.7701i | −0.352363 | + | 0.851339i | ||||
\(226\) | 13.6037 | + | 13.6037i | 0.904902 | + | 0.904902i | ||||
\(227\) | 18.6457 | − | 18.6457i | 1.23756 | − | 1.23756i | 0.276560 | − | 0.960997i | \(-0.410805\pi\) |
0.960997 | − | 0.276560i | \(-0.0891946\pi\) | |||||||
\(228\) | 7.17236 | + | 10.7310i | 0.475001 | + | 0.710679i | ||||
\(229\) | −1.93830 | + | 1.93830i | −0.128087 | + | 0.128087i | −0.768244 | − | 0.640157i | \(-0.778869\pi\) |
0.640157 | + | 0.768244i | \(0.278869\pi\) | |||||||
\(230\) | 25.2863i | 1.66733i | ||||||||
\(231\) | 0.609699 | − | 3.06736i | 0.0401152 | − | 0.201817i | ||||
\(232\) | −6.72109 | + | 6.72109i | −0.441261 | + | 0.441261i | ||||
\(233\) | −3.76840 | −0.246876 | −0.123438 | − | 0.992352i | \(-0.539392\pi\) | ||||
−0.123438 | + | 0.992352i | \(0.539392\pi\) | |||||||
\(234\) | −7.14443 | + | 8.12140i | −0.467046 | + | 0.530912i | ||||
\(235\) | −3.53183 | −0.230391 | ||||||||
\(236\) | 1.49217 | − | 1.49217i | 0.0971321 | − | 0.0971321i | ||||
\(237\) | −1.48193 | + | 7.45549i | −0.0962615 | + | 0.484286i | ||||
\(238\) | − | 3.68191i | − | 0.238663i | ||||||
\(239\) | −2.94952 | + | 2.94952i | −0.190789 | + | 0.190789i | −0.796037 | − | 0.605248i | \(-0.793074\pi\) |
0.605248 | + | 0.796037i | \(0.293074\pi\) | |||||||
\(240\) | −2.98318 | − | 4.46333i | −0.192564 | − | 0.288107i | ||||
\(241\) | 14.8333 | − | 14.8333i | 0.955499 | − | 0.955499i | −0.0435517 | − | 0.999051i | \(-0.513867\pi\) |
0.999051 | + | 0.0435517i | \(0.0138673\pi\) | |||||||
\(242\) | 5.47291 | + | 5.47291i | 0.351812 | + | 0.351812i | ||||
\(243\) | −12.9554 | + | 8.66936i | −0.831089 | + | 0.556140i | ||||
\(244\) | 8.14557i | 0.521467i | ||||||||
\(245\) | −2.19168 | − | 2.19168i | −0.140021 | − | 0.140021i | ||||
\(246\) | 5.32857 | + | 1.05916i | 0.339737 | + | 0.0675295i | ||||
\(247\) | −25.4270 | − | 8.68278i | −1.61788 | − | 0.552472i | ||||
\(248\) | − | 0.177174i | − | 0.0112505i | ||||||
\(249\) | 12.7285 | + | 19.0439i | 0.806636 | + | 1.20686i | ||||
\(250\) | −1.21844 | −0.0770610 | ||||||||
\(251\) | 26.0328 | 1.64318 | 0.821589 | − | 0.570080i | \(-0.193088\pi\) | ||||
0.821589 | + | 0.570080i | \(0.193088\pi\) | |||||||
\(252\) | −1.14881 | − | 2.77132i | −0.0723682 | − | 0.174577i | ||||
\(253\) | 10.4159 | + | 10.4159i | 0.654843 | + | 0.654843i | ||||
\(254\) | −8.82521 | − | 8.82521i | −0.553743 | − | 0.553743i | ||||
\(255\) | 10.9838 | + | 16.4336i | 0.687833 | + | 1.02911i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.24091 | 0.0774055 | 0.0387028 | − | 0.999251i | \(-0.487677\pi\) | ||||
0.0387028 | + | 0.999251i | \(0.487677\pi\) | |||||||
\(258\) | 2.06104 | − | 1.37755i | 0.128315 | − | 0.0857624i | ||||
\(259\) | − | 0.464238i | − | 0.0288464i | ||||||
\(260\) | 10.5758 | + | 3.61141i | 0.655883 | + | 0.223970i | ||||
\(261\) | 10.9051 | − | 26.3476i | 0.675006 | − | 1.63087i | ||||
\(262\) | −5.89570 | − | 5.89570i | −0.364237 | − | 0.364237i | ||||
\(263\) | − | 11.9752i | − | 0.738425i | −0.929345 | − | 0.369213i | \(-0.879627\pi\) | ||
0.929345 | − | 0.369213i | \(-0.120373\pi\) | |||||||
\(264\) | −3.06736 | − | 0.609699i | −0.188783 | − | 0.0375244i | ||||
\(265\) | −12.2680 | − | 12.2680i | −0.753618 | − | 0.753618i | ||||
\(266\) | 5.26937 | − | 5.26937i | 0.323086 | − | 0.323086i | ||||
\(267\) | −6.49672 | + | 4.34226i | −0.397593 | + | 0.265742i | ||||
\(268\) | −10.6436 | + | 10.6436i | −0.650163 | + | 0.650163i | ||||
\(269\) | − | 7.12840i | − | 0.434626i | −0.976102 | − | 0.217313i | \(-0.930271\pi\) | ||
0.976102 | − | 0.217313i | \(-0.0697293\pi\) | |||||||
\(270\) | 13.3949 | + | 8.94221i | 0.815187 | + | 0.544206i | ||||
\(271\) | 9.80032 | − | 9.80032i | 0.595327 | − | 0.595327i | −0.343738 | − | 0.939065i | \(-0.611693\pi\) |
0.939065 | + | 0.343738i | \(0.111693\pi\) | |||||||
\(272\) | −3.68191 | −0.223249 | ||||||||
\(273\) | 5.40308 | + | 3.13157i | 0.327009 | + | 0.189531i | ||||
\(274\) | 20.1105 | 1.21492 | ||||||||
\(275\) | 5.88181 | − | 5.88181i | 0.354686 | − | 0.354686i | ||||
\(276\) | 13.8593 | + | 2.75481i | 0.834231 | + | 0.165820i | ||||
\(277\) | 1.47925i | 0.0888795i | 0.999012 | + | 0.0444397i | \(0.0141503\pi\) | ||||
−0.999012 | + | 0.0444397i | \(0.985850\pi\) | |||||||
\(278\) | −3.91664 | + | 3.91664i | −0.234905 | + | 0.234905i | ||||
\(279\) | 0.203539 | + | 0.491005i | 0.0121855 | + | 0.0293957i | ||||
\(280\) | −2.19168 | + | 2.19168i | −0.130978 | + | 0.130978i | ||||
\(281\) | −11.3699 | − | 11.3699i | −0.678270 | − | 0.678270i | 0.281339 | − | 0.959609i | \(-0.409222\pi\) |
−0.959609 | + | 0.281339i | \(0.909222\pi\) | |||||||
\(282\) | −0.384773 | + | 1.93577i | −0.0229129 | + | 0.115274i | ||||
\(283\) | 19.9300i | 1.18471i | 0.805676 | + | 0.592357i | \(0.201802\pi\) | ||||
−0.805676 | + | 0.592357i | \(0.798198\pi\) | |||||||
\(284\) | 0.752235 | + | 0.752235i | 0.0446369 | + | 0.0446369i | ||||
\(285\) | −7.79942 | + | 39.2384i | −0.461998 | + | 2.32428i | ||||
\(286\) | 5.84397 | − | 2.86876i | 0.345561 | − | 0.169633i | ||||
\(287\) | − | 3.13663i | − | 0.185150i | ||||||
\(288\) | −2.77132 | + | 1.14881i | −0.163302 | + | 0.0676943i | ||||
\(289\) | −3.44353 | −0.202561 | ||||||||
\(290\) | −29.4609 | −1.73000 | ||||||||
\(291\) | −3.65211 | + | 2.44099i | −0.214090 | + | 0.143093i | ||||
\(292\) | −3.59354 | − | 3.59354i | −0.210296 | − | 0.210296i | ||||
\(293\) | 10.3404 | + | 10.3404i | 0.604092 | + | 0.604092i | 0.941396 | − | 0.337304i | \(-0.109515\pi\) |
−0.337304 | + | 0.941396i | \(0.609515\pi\) | |||||||
\(294\) | −1.44002 | + | 0.962473i | −0.0839834 | + | 0.0561326i | ||||
\(295\) | 6.54072 | 0.380815 | ||||||||
\(296\) | −0.464238 | −0.0269833 | ||||||||
\(297\) | 9.20107 | − | 1.83414i | 0.533900 | − | 0.106427i | ||||
\(298\) | − | 5.26423i | − | 0.304949i | ||||||
\(299\) | −26.4049 | + | 12.9620i | −1.52703 | + | 0.749609i | ||||
\(300\) | 1.55563 | − | 7.82626i | 0.0898141 | − | 0.451849i | ||||
\(301\) | −1.01205 | − | 1.01205i | −0.0583338 | − | 0.0583338i | ||||
\(302\) | − | 21.5603i | − | 1.24066i | ||||||
\(303\) | −2.88783 | + | 14.5285i | −0.165901 | + | 0.834640i | ||||
\(304\) | −5.26937 | − | 5.26937i | −0.302219 | − | 0.302219i | ||||
\(305\) | −17.8525 | + | 17.8525i | −1.02223 | + | 1.02223i | ||||
\(306\) | 10.2038 | − | 4.22981i | 0.583311 | − | 0.241802i | ||||
\(307\) | −6.10278 | + | 6.10278i | −0.348304 | + | 0.348304i | −0.859478 | − | 0.511174i | \(-0.829211\pi\) |
0.511174 | + | 0.859478i | \(0.329211\pi\) | |||||||
\(308\) | 1.80559i | 0.102883i | ||||||||
\(309\) | −11.4175 | − | 2.26945i | −0.649517 | − | 0.129104i | ||||
\(310\) | 0.388307 | − | 0.388307i | 0.0220544 | − | 0.0220544i | ||||
\(311\) | 21.9647 | 1.24550 | 0.622752 | − | 0.782420i | \(-0.286015\pi\) | ||||
0.622752 | + | 0.782420i | \(0.286015\pi\) | |||||||
\(312\) | 3.13157 | − | 5.40308i | 0.177290 | − | 0.305889i | ||||
\(313\) | −4.26972 | −0.241339 | −0.120669 | − | 0.992693i | \(-0.538504\pi\) | ||||
−0.120669 | + | 0.992693i | \(0.538504\pi\) | |||||||
\(314\) | 7.27121 | − | 7.27121i | 0.410338 | − | 0.410338i | ||||
\(315\) | 3.55603 | − | 8.59166i | 0.200359 | − | 0.484085i | ||||
\(316\) | − | 4.38864i | − | 0.246880i | ||||||
\(317\) | −17.6141 | + | 17.6141i | −0.989307 | + | 0.989307i | −0.999943 | − | 0.0106369i | \(-0.996614\pi\) |
0.0106369 | + | 0.999943i | \(0.496614\pi\) | |||||||
\(318\) | −8.06055 | + | 5.38749i | −0.452013 | + | 0.302115i | ||||
\(319\) | −12.1355 | + | 12.1355i | −0.679457 | + | 0.679457i | ||||
\(320\) | 2.19168 | + | 2.19168i | 0.122518 | + | 0.122518i | ||||
\(321\) | −12.9874 | − | 2.58150i | −0.724886 | − | 0.144086i | ||||
\(322\) | − | 8.15820i | − | 0.454639i | ||||||
\(323\) | 19.4014 | + | 19.4014i | 1.07952 | + | 1.07952i | ||||
\(324\) | 6.36047 | − | 6.36745i | 0.353360 | − | 0.353747i | ||||
\(325\) | 7.31954 | + | 14.9107i | 0.406015 | + | 0.827097i | ||||
\(326\) | 23.2123i | 1.28561i | ||||||||
\(327\) | 22.5273 | − | 15.0567i | 1.24576 | − | 0.832639i | ||||
\(328\) | −3.13663 | −0.173192 | ||||||||
\(329\) | 1.13948 | 0.0628217 | ||||||||
\(330\) | −5.38639 | − | 8.05892i | −0.296511 | − | 0.443629i | ||||
\(331\) | −16.3963 | − | 16.3963i | −0.901220 | − | 0.901220i | 0.0943216 | − | 0.995542i | \(-0.469932\pi\) |
−0.995542 | + | 0.0943216i | \(0.969932\pi\) | |||||||
\(332\) | −9.35133 | − | 9.35133i | −0.513221 | − | 0.513221i | ||||
\(333\) | 1.28655 | − | 0.533321i | 0.0705028 | − | 0.0292258i | ||||
\(334\) | 14.3809 | 0.786888 | ||||||||
\(335\) | −46.6548 | −2.54902 | ||||||||
\(336\) | 0.962473 | + | 1.44002i | 0.0525072 | + | 0.0785593i | ||||
\(337\) | 8.77212i | 0.477848i | 0.971038 | + | 0.238924i | \(0.0767947\pi\) | ||||
−0.971038 | + | 0.238924i | \(0.923205\pi\) | |||||||
\(338\) | 1.65006 | + | 12.8949i | 0.0897516 | + | 0.701388i | ||||
\(339\) | 32.6827 | + | 6.49633i | 1.77508 | + | 0.352832i | ||||
\(340\) | −8.06956 | − | 8.06956i | −0.437633 | − | 0.437633i | ||||
\(341\) | − | 0.319902i | − | 0.0173237i | ||||||
\(342\) | 20.6566 | + | 8.54963i | 1.11698 | + | 0.462311i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −1.01205 | + | 1.01205i | −0.0545663 | + | 0.0545663i | ||||
\(345\) | 24.3374 | + | 36.4127i | 1.31028 | + | 1.96039i | ||||
\(346\) | 6.17263 | − | 6.17263i | 0.331843 | − | 0.331843i | ||||
\(347\) | 8.56153i | 0.459607i | 0.973237 | + | 0.229803i | \(0.0738083\pi\) | ||||
−0.973237 | + | 0.229803i | \(0.926192\pi\) | |||||||
\(348\) | −3.20961 | + | 16.1473i | −0.172053 | + | 0.865588i | ||||
\(349\) | −0.0314225 | + | 0.0314225i | −0.00168201 | + | 0.00168201i | −0.707947 | − | 0.706265i | \(-0.750379\pi\) |
0.706265 | + | 0.707947i | \(0.250379\pi\) | |||||||
\(350\) | −4.60689 | −0.246249 | ||||||||
\(351\) | −2.47147 | + | 18.5713i | −0.131917 | + | 0.991261i | ||||
\(352\) | 1.80559 | 0.0962380 | ||||||||
\(353\) | 1.70236 | − | 1.70236i | 0.0906076 | − | 0.0906076i | −0.660350 | − | 0.750958i | \(-0.729592\pi\) |
0.750958 | + | 0.660350i | \(0.229592\pi\) | |||||||
\(354\) | 0.712576 | − | 3.58493i | 0.0378730 | − | 0.190537i | ||||
\(355\) | 3.29731i | 0.175003i | ||||||||
\(356\) | 3.19016 | − | 3.19016i | 0.169078 | − | 0.169078i | ||||
\(357\) | −3.54374 | − | 5.30201i | −0.187555 | − | 0.280612i | ||||
\(358\) | 15.1565 | − | 15.1565i | 0.801048 | − | 0.801048i | ||||
\(359\) | −19.7911 | − | 19.7911i | −1.04453 | − | 1.04453i | −0.998961 | − | 0.0455713i | \(-0.985489\pi\) |
−0.0455713 | − | 0.998961i | \(-0.514511\pi\) | |||||||
\(360\) | −8.59166 | − | 3.55603i | −0.452820 | − | 0.187419i | ||||
\(361\) | 36.5325i | 1.92276i | ||||||||
\(362\) | −5.32612 | − | 5.32612i | −0.279935 | − | 0.279935i | ||||
\(363\) | 13.1486 | + | 2.61355i | 0.690123 | + | 0.137176i | ||||
\(364\) | −3.41210 | − | 1.16516i | −0.178842 | − | 0.0610709i | ||||
\(365\) | − | 15.7518i | − | 0.824485i | ||||||
\(366\) | 7.83989 | + | 11.7298i | 0.409798 | + | 0.613124i | ||||
\(367\) | −18.1422 | −0.947016 | −0.473508 | − | 0.880790i | \(-0.657012\pi\) | ||||
−0.473508 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(368\) | −8.15820 | −0.425275 | ||||||||
\(369\) | 8.69263 | − | 3.60340i | 0.452520 | − | 0.187585i | ||||
\(370\) | −1.01746 | − | 1.01746i | −0.0528952 | − | 0.0528952i | ||||
\(371\) | 3.95806 | + | 3.95806i | 0.205492 | + | 0.205492i | ||||
\(372\) | −0.170525 | − | 0.255133i | −0.00884130 | − | 0.0132280i | ||||
\(373\) | −27.3139 | −1.41426 | −0.707130 | − | 0.707083i | \(-0.750011\pi\) | ||||
−0.707130 | + | 0.707083i | \(0.750011\pi\) | |||||||
\(374\) | −6.64800 | −0.343760 | ||||||||
\(375\) | −1.75457 | + | 1.17272i | −0.0906058 | + | 0.0605588i | ||||
\(376\) | − | 1.13948i | − | 0.0587644i | ||||||
\(377\) | −15.1019 | − | 30.7641i | −0.777786 | − | 1.58443i | ||||
\(378\) | −4.32163 | − | 2.88505i | −0.222281 | − | 0.148391i | ||||
\(379\) | 11.0481 | + | 11.0481i | 0.567502 | + | 0.567502i | 0.931428 | − | 0.363926i | \(-0.118564\pi\) |
−0.363926 | + | 0.931428i | \(0.618564\pi\) | |||||||
\(380\) | − | 23.0975i | − | 1.18488i | ||||||
\(381\) | −21.2025 | − | 4.21441i | −1.08624 | − | 0.215911i | ||||
\(382\) | 1.27363 | + | 1.27363i | 0.0651645 | + | 0.0651645i | ||||
\(383\) | 18.4315 | − | 18.4315i | 0.941808 | − | 0.941808i | −0.0565899 | − | 0.998398i | \(-0.518023\pi\) |
0.998398 | + | 0.0565899i | \(0.0180227\pi\) | |||||||
\(384\) | 1.44002 | − | 0.962473i | 0.0734855 | − | 0.0491160i | ||||
\(385\) | −3.95726 | + | 3.95726i | −0.201681 | + | 0.201681i | ||||
\(386\) | 20.3723i | 1.03692i | ||||||||
\(387\) | 1.64207 | − | 3.96738i | 0.0834712 | − | 0.201673i | ||||
\(388\) | 1.79334 | − | 1.79334i | 0.0910428 | − | 0.0910428i | ||||
\(389\) | 13.3245 | 0.675579 | 0.337790 | − | 0.941222i | \(-0.390321\pi\) | ||||
0.337790 | + | 0.941222i | \(0.390321\pi\) | |||||||
\(390\) | 18.7052 | − | 4.97843i | 0.947174 | − | 0.252093i | ||||
\(391\) | 30.0378 | 1.51907 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | −14.1643 | − | 2.81545i | −0.714497 | − | 0.142020i | ||||
\(394\) | 9.80502i | 0.493970i | ||||||||
\(395\) | 9.61847 | − | 9.61847i | 0.483958 | − | 0.483958i | ||||
\(396\) | −5.00386 | + | 2.07427i | −0.251454 | + | 0.104236i | ||||
\(397\) | −16.7117 | + | 16.7117i | −0.838738 | + | 0.838738i | −0.988693 | − | 0.149955i | \(-0.952087\pi\) |
0.149955 | + | 0.988693i | \(0.452087\pi\) | |||||||
\(398\) | −7.25442 | − | 7.25442i | −0.363631 | − | 0.363631i | ||||
\(399\) | 2.51635 | − | 12.6596i | 0.125975 | − | 0.633773i | ||||
\(400\) | 4.60689i | 0.230345i | ||||||||
\(401\) | −0.352145 | − | 0.352145i | −0.0175853 | − | 0.0175853i | 0.698259 | − | 0.715845i | \(-0.253958\pi\) |
−0.715845 | + | 0.698259i | \(0.753958\pi\) | |||||||
\(402\) | −5.08279 | + | 25.5712i | −0.253506 | + | 1.27538i | ||||
\(403\) | 0.604533 | + | 0.206435i | 0.0301140 | + | 0.0102833i | ||||
\(404\) | − | 8.55213i | − | 0.425484i | ||||||
\(405\) | 27.8955 | − | 0.0152839i | 1.38614 | − | 0.000759463i | ||||
\(406\) | 9.50505 | 0.471728 | ||||||||
\(407\) | −0.838222 | −0.0415491 | ||||||||
\(408\) | −5.30201 | + | 3.54374i | −0.262489 | + | 0.175441i | ||||
\(409\) | −23.1842 | − | 23.1842i | −1.14638 | − | 1.14638i | −0.987258 | − | 0.159126i | \(-0.949132\pi\) |
−0.159126 | − | 0.987258i | \(-0.550868\pi\) | |||||||
\(410\) | −6.87449 | − | 6.87449i | −0.339507 | − | 0.339507i | ||||
\(411\) | 28.9595 | − | 19.3559i | 1.42847 | − | 0.954754i | ||||
\(412\) | 6.72083 | 0.331112 | ||||||||
\(413\) | −2.11025 | −0.103839 | ||||||||
\(414\) | 22.6090 | − | 9.37222i | 1.11117 | − | 0.460619i | ||||
\(415\) | − | 40.9902i | − | 2.01213i | ||||||
\(416\) | −1.16516 | + | 3.41210i | −0.0571266 | + | 0.167292i | ||||
\(417\) | −1.87036 | + | 9.40969i | −0.0915921 | + | 0.460795i | ||||
\(418\) | −9.51430 | − | 9.51430i | −0.465360 | − | 0.465360i | ||||
\(419\) | 9.60922i | 0.469441i | 0.972063 | + | 0.234721i | \(0.0754175\pi\) | ||||
−0.972063 | + | 0.234721i | \(0.924582\pi\) | |||||||
\(420\) | −1.04662 | + | 5.26548i | −0.0510698 | + | 0.256929i | ||||
\(421\) | −10.1653 | − | 10.1653i | −0.495425 | − | 0.495425i | 0.414586 | − | 0.910010i | \(-0.363927\pi\) |
−0.910010 | + | 0.414586i | \(0.863927\pi\) | |||||||
\(422\) | 13.7561 | − | 13.7561i | 0.669638 | − | 0.669638i | ||||
\(423\) | 1.30905 | + | 3.15788i | 0.0636481 | + | 0.153541i | ||||
\(424\) | 3.95806 | − | 3.95806i | 0.192220 | − | 0.192220i | ||||
\(425\) | − | 16.9622i | − | 0.822786i | ||||||
\(426\) | 1.80724 | + | 0.359224i | 0.0875609 | + | 0.0174045i | ||||
\(427\) | 5.75979 | − | 5.75979i | 0.278736 | − | 0.278736i | ||||
\(428\) | 7.64497 | 0.369534 | ||||||||
\(429\) | 5.65431 | − | 9.75573i | 0.272993 | − | 0.471011i | ||||
\(430\) | −4.43619 | −0.213932 | ||||||||
\(431\) | 6.40858 | − | 6.40858i | 0.308690 | − | 0.308690i | −0.535711 | − | 0.844401i | \(-0.679956\pi\) |
0.844401 | + | 0.535711i | \(0.179956\pi\) | |||||||
\(432\) | −2.88505 | + | 4.32163i | −0.138807 | + | 0.207924i | ||||
\(433\) | − | 33.5644i | − | 1.61300i | −0.591232 | − | 0.806502i | \(-0.701358\pi\) | ||
0.591232 | − | 0.806502i | \(-0.298642\pi\) | |||||||
\(434\) | −0.125281 | + | 0.125281i | −0.00601366 | + | 0.00601366i | ||||
\(435\) | −42.4241 | + | 28.3553i | −2.03408 | + | 1.35953i | ||||
\(436\) | −11.0618 | + | 11.0618i | −0.529766 | + | 0.529766i | ||||
\(437\) | 42.9886 | + | 42.9886i | 2.05642 | + | 2.05642i | ||||
\(438\) | −8.63345 | − | 1.71607i | −0.412522 | − | 0.0819970i | ||||
\(439\) | − | 7.08017i | − | 0.337918i | −0.985623 | − | 0.168959i | \(-0.945959\pi\) | ||
0.985623 | − | 0.168959i | \(-0.0540405\pi\) | |||||||
\(440\) | 3.95726 | + | 3.95726i | 0.188655 | + | 0.188655i | ||||
\(441\) | −1.14729 | + | 2.77195i | −0.0546329 | + | 0.131998i | ||||
\(442\) | 4.29001 | − | 12.5630i | 0.204055 | − | 0.597563i | ||||
\(443\) | − | 6.61082i | − | 0.314089i | −0.987591 | − | 0.157045i | \(-0.949803\pi\) | ||
0.987591 | − | 0.157045i | \(-0.0501967\pi\) | |||||||
\(444\) | −0.668510 | + | 0.446817i | −0.0317261 | + | 0.0212050i | ||||
\(445\) | 13.9836 | 0.662886 | ||||||||
\(446\) | −16.8948 | −0.799992 | ||||||||
\(447\) | −5.06668 | − | 7.58057i | −0.239646 | − | 0.358549i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | −15.0860 | − | 15.0860i | −0.711951 | − | 0.711951i | 0.254992 | − | 0.966943i | \(-0.417927\pi\) |
−0.966943 | + | 0.254992i | \(0.917927\pi\) | |||||||
\(450\) | −5.29244 | − | 12.7672i | −0.249488 | − | 0.601851i | ||||
\(451\) | −5.66346 | −0.266682 | ||||||||
\(452\) | −19.2385 | −0.904902 | ||||||||
\(453\) | −20.7512 | − | 31.0472i | −0.974978 | − | 1.45873i | ||||
\(454\) | 26.3690i | 1.23756i | ||||||||
\(455\) | −4.92456 | − | 10.0319i | −0.230867 | − | 0.470301i | ||||
\(456\) | −12.6596 | − | 2.51635i | −0.592840 | − | 0.117839i | ||||
\(457\) | −18.4880 | − | 18.4880i | −0.864831 | − | 0.864831i | 0.127063 | − | 0.991895i | \(-0.459445\pi\) |
−0.991895 | + | 0.127063i | \(0.959445\pi\) | |||||||
\(458\) | − | 2.74117i | − | 0.128087i | ||||||
\(459\) | 10.6225 | − | 15.9119i | 0.495816 | − | 0.742702i | ||||
\(460\) | −17.8801 | − | 17.8801i | −0.833665 | − | 0.833665i | ||||
\(461\) | −11.9307 | + | 11.9307i | −0.555668 | + | 0.555668i | −0.928071 | − | 0.372403i | \(-0.878534\pi\) |
0.372403 | + | 0.928071i | \(0.378534\pi\) | |||||||
\(462\) | 1.73783 | + | 2.60007i | 0.0808511 | + | 0.120966i | ||||
\(463\) | 2.01800 | − | 2.01800i | 0.0937846 | − | 0.0937846i | −0.658658 | − | 0.752443i | \(-0.728876\pi\) |
0.752443 | + | 0.658658i | \(0.228876\pi\) | |||||||
\(464\) | − | 9.50505i | − | 0.441261i | ||||||
\(465\) | 0.185433 | − | 0.932903i | 0.00859926 | − | 0.0432624i | ||||
\(466\) | 2.66466 | − | 2.66466i | 0.123438 | − | 0.123438i | ||||
\(467\) | −11.3847 | −0.526823 | −0.263411 | − | 0.964684i | \(-0.584848\pi\) | ||||
−0.263411 | + | 0.964684i | \(0.584848\pi\) | |||||||
\(468\) | −0.690818 | − | 10.7946i | −0.0319331 | − | 0.498979i | ||||
\(469\) | 15.0524 | 0.695054 | ||||||||
\(470\) | 2.49738 | − | 2.49738i | 0.115195 | − | 0.115195i | ||||
\(471\) | 3.47231 | − | 17.4690i | 0.159996 | − | 0.804929i | ||||
\(472\) | 2.11025i | 0.0971321i | ||||||||
\(473\) | −1.82735 | + | 1.82735i | −0.0840216 | + | 0.0840216i | ||||
\(474\) | −4.22394 | − | 6.31970i | −0.194012 | − | 0.290274i | ||||
\(475\) | 24.2754 | − | 24.2754i | 1.11383 | − | 1.11383i | ||||
\(476\) | 2.60350 | + | 2.60350i | 0.119331 | + | 0.119331i | ||||
\(477\) | −6.42201 | + | 15.5161i | −0.294044 | + | 0.710435i | ||||
\(478\) | − | 4.17126i | − | 0.190789i | ||||||
\(479\) | −21.9770 | − | 21.9770i | −1.00415 | − | 1.00415i | −0.999991 | − | 0.00416246i | \(-0.998675\pi\) |
−0.00416246 | − | 0.999991i | \(-0.501325\pi\) | |||||||
\(480\) | 5.26548 | + | 1.04662i | 0.240335 | + | 0.0477714i | ||||
\(481\) | 0.540911 | − | 1.58403i | 0.0246634 | − | 0.0722254i | ||||
\(482\) | 20.9775i | 0.955499i | ||||||||
\(483\) | −7.85205 | − | 11.7479i | −0.357281 | − | 0.534550i | ||||
\(484\) | −7.73986 | −0.351812 | ||||||||
\(485\) | 7.86082 | 0.356942 | ||||||||
\(486\) | 3.03069 | − | 15.2910i | 0.137475 | − | 0.693614i | ||||
\(487\) | −21.7649 | − | 21.7649i | −0.986263 | − | 0.986263i | 0.0136436 | − | 0.999907i | \(-0.495657\pi\) |
−0.999907 | + | 0.0136436i | \(0.995657\pi\) | |||||||
\(488\) | −5.75979 | − | 5.75979i | −0.260733 | − | 0.260733i | ||||
\(489\) | 22.3413 | + | 33.4261i | 1.01031 | + | 1.51158i | ||||
\(490\) | 3.09950 | 0.140021 | ||||||||
\(491\) | 24.6630 | 1.11303 | 0.556513 | − | 0.830839i | \(-0.312139\pi\) | ||||
0.556513 | + | 0.830839i | \(0.312139\pi\) | |||||||
\(492\) | −4.51680 | + | 3.01893i | −0.203633 | + | 0.136104i | ||||
\(493\) | 34.9968i | 1.57617i | ||||||||
\(494\) | 24.1193 | − | 11.8400i | 1.08518 | − | 0.532705i | ||||
\(495\) | −15.5130 | − | 6.42071i | −0.697257 | − | 0.288589i | ||||
\(496\) | 0.125281 | + | 0.125281i | 0.00562527 | + | 0.00562527i | ||||
\(497\) | − | 1.06382i | − | 0.0477189i | ||||||
\(498\) | −22.4665 | − | 4.46566i | −1.00675 | − | 0.200111i | ||||
\(499\) | 30.6363 | + | 30.6363i | 1.37147 | + | 1.37147i | 0.858268 | + | 0.513202i | \(0.171541\pi\) |
0.513202 | + | 0.858268i | \(0.328459\pi\) | |||||||
\(500\) | 0.861568 | − | 0.861568i | 0.0385305 | − | 0.0385305i | ||||
\(501\) | 20.7087 | − | 13.8412i | 0.925197 | − | 0.618380i | ||||
\(502\) | −18.4080 | + | 18.4080i | −0.821589 | + | 0.821589i | ||||
\(503\) | 34.2723i | 1.52813i | 0.645141 | + | 0.764064i | \(0.276799\pi\) | ||||
−0.645141 | + | 0.764064i | \(0.723201\pi\) | |||||||
\(504\) | 2.77195 | + | 1.14729i | 0.123473 | + | 0.0511044i | ||||
\(505\) | 18.7435 | − | 18.7435i | 0.834075 | − | 0.834075i | ||||
\(506\) | −14.7303 | −0.654843 | ||||||||
\(507\) | 14.7871 | + | 16.9807i | 0.656717 | + | 0.754137i | ||||
\(508\) | 12.4807 | 0.553743 | ||||||||
\(509\) | 3.24519 | − | 3.24519i | 0.143840 | − | 0.143840i | −0.631520 | − | 0.775360i | \(-0.717568\pi\) |
0.775360 | + | 0.631520i | \(0.217568\pi\) | |||||||
\(510\) | −19.3870 | − | 3.85356i | −0.858472 | − | 0.170638i | ||||
\(511\) | 5.08204i | 0.224816i | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 37.9747 | − | 7.56985i | 1.67662 | − | 0.334217i | ||||
\(514\) | −0.877452 | + | 0.877452i | −0.0387028 | + | 0.0387028i | ||||
\(515\) | 14.7299 | + | 14.7299i | 0.649077 | + | 0.649077i | ||||
\(516\) | −0.483299 | + | 2.43145i | −0.0212760 | + | 0.107038i | ||||
\(517\) | − | 2.05743i | − | 0.0904858i | ||||||
\(518\) | 0.328266 | + | 0.328266i | 0.0144232 | + | 0.0144232i | ||||
\(519\) | 2.94770 | − | 14.8297i | 0.129389 | − | 0.650951i | ||||
\(520\) | −10.0319 | + | 4.92456i | −0.439926 | + | 0.215956i | ||||
\(521\) | 44.5505i | 1.95179i | 0.218238 | + | 0.975896i | \(0.429969\pi\) | ||||
−0.218238 | + | 0.975896i | \(0.570031\pi\) | |||||||
\(522\) | 10.9195 | + | 26.3416i | 0.477933 | + | 1.15294i | ||||
\(523\) | 16.3414 | 0.714560 | 0.357280 | − | 0.933997i | \(-0.383704\pi\) | ||||
0.357280 | + | 0.933997i | \(0.383704\pi\) | |||||||
\(524\) | 8.33777 | 0.364237 | ||||||||
\(525\) | −6.63400 | + | 4.43401i | −0.289531 | + | 0.193516i | ||||
\(526\) | 8.46778 | + | 8.46778i | 0.369213 | + | 0.369213i | ||||
\(527\) | −0.461272 | − | 0.461272i | −0.0200933 | − | 0.0200933i | ||||
\(528\) | 2.60007 | − | 1.73783i | 0.113154 | − | 0.0756292i | ||||
\(529\) | 43.5562 | 1.89375 | ||||||||
\(530\) | 17.3496 | 0.753618 | ||||||||
\(531\) | −2.42428 | − | 5.84819i | −0.105205 | − | 0.253790i | ||||
\(532\) | 7.45201i | 0.323086i | ||||||||
\(533\) | 3.65468 | − | 10.7025i | 0.158302 | − | 0.463577i | ||||
\(534\) | 1.52344 | − | 7.66432i | 0.0659256 | − | 0.331668i | ||||
\(535\) | 16.7553 | + | 16.7553i | 0.724395 | + | 0.724395i | ||||
\(536\) | − | 15.0524i | − | 0.650163i | ||||||
\(537\) | 7.23789 | − | 36.4134i | 0.312338 | − | 1.57135i | ||||
\(538\) | 5.04054 | + | 5.04054i | 0.217313 | + | 0.217313i | ||||
\(539\) | 1.27674 | − | 1.27674i | 0.0549932 | − | 0.0549932i | ||||
\(540\) | −15.7947 | + | 3.14851i | −0.679696 | + | 0.135490i | ||||
\(541\) | 14.6761 | − | 14.6761i | 0.630977 | − | 0.630977i | −0.317336 | − | 0.948313i | \(-0.602788\pi\) |
0.948313 | + | 0.317336i | \(0.102788\pi\) | |||||||
\(542\) | 13.8597i | 0.595327i | ||||||||
\(543\) | −12.7959 | − | 2.54345i | −0.549127 | − | 0.109150i | ||||
\(544\) | 2.60350 | − | 2.60350i | 0.111624 | − | 0.111624i | ||||
\(545\) | −48.4879 | −2.07699 | ||||||||
\(546\) | −6.03491 | + | 1.60620i | −0.258270 | + | 0.0687392i | ||||
\(547\) | 3.25656 | 0.139240 | 0.0696202 | − | 0.997574i | \(-0.477821\pi\) | ||||
0.0696202 | + | 0.997574i | \(0.477821\pi\) | |||||||
\(548\) | −14.2203 | + | 14.2203i | −0.607461 | + | 0.607461i | ||||
\(549\) | 22.5791 | + | 9.34534i | 0.963654 | + | 0.398849i | ||||
\(550\) | 8.31814i | 0.354686i | ||||||||
\(551\) | −50.0856 | + | 50.0856i | −2.13372 | + | 2.13372i | ||||
\(552\) | −11.7479 | + | 7.85205i | −0.500025 | + | 0.334205i | ||||
\(553\) | −3.10323 | + | 3.10323i | −0.131963 | + | 0.131963i | ||||
\(554\) | −1.04599 | − | 1.04599i | −0.0444397 | − | 0.0444397i | ||||
\(555\) | −2.44444 | − | 0.485881i | −0.103761 | − | 0.0206245i | ||||
\(556\) | − | 5.53897i | − | 0.234905i | ||||||
\(557\) | 3.70450 | + | 3.70450i | 0.156965 | + | 0.156965i | 0.781220 | − | 0.624255i | \(-0.214598\pi\) |
−0.624255 | + | 0.781220i | \(0.714598\pi\) | |||||||
\(558\) | −0.491117 | − | 0.203270i | −0.0207906 | − | 0.00860509i | ||||
\(559\) | −2.27402 | − | 4.63243i | −0.0961809 | − | 0.195931i | ||||
\(560\) | − | 3.09950i | − | 0.130978i | ||||||
\(561\) | −9.57323 | + | 6.39853i | −0.404182 | + | 0.270146i | ||||
\(562\) | 16.0794 | 0.678270 | ||||||||
\(563\) | 15.3860 | 0.648443 | 0.324221 | − | 0.945981i | \(-0.394898\pi\) | ||||
0.324221 | + | 0.945981i | \(0.394898\pi\) | |||||||
\(564\) | −1.09672 | − | 1.64087i | −0.0461803 | − | 0.0690932i | ||||
\(565\) | −42.1645 | − | 42.1645i | −1.77388 | − | 1.77388i | ||||
\(566\) | −14.0926 | − | 14.0926i | −0.592357 | − | 0.592357i | ||||
\(567\) | −9.00000 | + | 0.00493109i | −0.377964 | + | 0.000207086i | ||||
\(568\) | −1.06382 | −0.0446369 | ||||||||
\(569\) | 33.4793 | 1.40353 | 0.701763 | − | 0.712410i | \(-0.252397\pi\) | ||||
0.701763 | + | 0.712410i | \(0.252397\pi\) | |||||||
\(570\) | −22.2307 | − | 33.2608i | −0.931143 | − | 1.39314i | ||||
\(571\) | 1.76074i | 0.0736845i | 0.999321 | + | 0.0368423i | \(0.0117299\pi\) | ||||
−0.999321 | + | 0.0368423i | \(0.988270\pi\) | |||||||
\(572\) | −2.10379 | + | 6.16083i | −0.0879640 | + | 0.257597i | ||||
\(573\) | 3.05988 | + | 0.608212i | 0.127828 | + | 0.0254084i | ||||
\(574\) | 2.21794 | + | 2.21794i | 0.0925748 | + | 0.0925748i | ||||
\(575\) | − | 37.5839i | − | 1.56736i | ||||||
\(576\) | 1.14729 | − | 2.77195i | 0.0478038 | − | 0.115498i | ||||
\(577\) | −25.8072 | − | 25.8072i | −1.07437 | − | 1.07437i | −0.997003 | − | 0.0773650i | \(-0.975349\pi\) |
−0.0773650 | − | 0.997003i | \(-0.524651\pi\) | |||||||
\(578\) | 2.43494 | − | 2.43494i | 0.101280 | − | 0.101280i | ||||
\(579\) | 19.6078 | + | 29.3365i | 0.814873 | + | 1.21918i | ||||
\(580\) | 20.8320 | − | 20.8320i | 0.865002 | − | 0.865002i | ||||
\(581\) | 13.2248i | 0.548656i | ||||||||
\(582\) | 0.856394 | − | 4.30847i | 0.0354987 | − | 0.178592i | ||||
\(583\) | 7.14662 | − | 7.14662i | 0.295983 | − | 0.295983i | ||||
\(584\) | 5.08204 | 0.210296 | ||||||||
\(585\) | 22.1442 | − | 25.1723i | 0.915548 | − | 1.04074i | ||||
\(586\) | −14.6235 | −0.604092 | ||||||||
\(587\) | −4.03302 | + | 4.03302i | −0.166460 | + | 0.166460i | −0.785422 | − | 0.618961i | \(-0.787554\pi\) |
0.618961 | + | 0.785422i | \(0.287554\pi\) | |||||||
\(588\) | 0.337674 | − | 1.69882i | 0.0139254 | − | 0.0700580i | ||||
\(589\) | − | 1.32030i | − | 0.0544020i | ||||||
\(590\) | −4.62499 | + | 4.62499i | −0.190408 | + | 0.190408i | ||||
\(591\) | 9.43707 | + | 14.1194i | 0.388189 | + | 0.580794i | ||||
\(592\) | 0.328266 | − | 0.328266i | 0.0134917 | − | 0.0134917i | ||||
\(593\) | 1.35646 | + | 1.35646i | 0.0557030 | + | 0.0557030i | 0.734410 | − | 0.678707i | \(-0.237459\pi\) |
−0.678707 | + | 0.734410i | \(0.737459\pi\) | |||||||
\(594\) | −5.20921 | + | 7.80307i | −0.213736 | + | 0.320164i | ||||
\(595\) | 11.4121i | 0.467850i | ||||||||
\(596\) | 3.72237 | + | 3.72237i | 0.152474 | + | 0.152474i | ||||
\(597\) | −17.4287 | − | 3.46429i | −0.713307 | − | 0.141784i | ||||
\(598\) | 9.50560 | − | 27.8366i | 0.388713 | − | 1.13832i | ||||
\(599\) | − | 19.3845i | − | 0.792029i | −0.918244 | − | 0.396014i | \(-0.870393\pi\) | ||
0.918244 | − | 0.396014i | \(-0.129607\pi\) | |||||||
\(600\) | 4.43401 | + | 6.63400i | 0.181018 | + | 0.270832i | ||||
\(601\) | −37.2292 | −1.51861 | −0.759306 | − | 0.650734i | \(-0.774461\pi\) | ||||
−0.759306 | + | 0.650734i | \(0.774461\pi\) | |||||||
\(602\) | 1.43126 | 0.0583338 | ||||||||
\(603\) | 17.2923 | + | 41.7150i | 0.704197 | + | 1.69877i | ||||
\(604\) | 15.2455 | + | 15.2455i | 0.620329 | + | 0.620329i | ||||
\(605\) | −16.9633 | − | 16.9633i | −0.689655 | − | 0.689655i | ||||
\(606\) | −8.23120 | − | 12.3152i | −0.334370 | − | 0.500271i | ||||
\(607\) | −15.3314 | −0.622284 | −0.311142 | − | 0.950363i | \(-0.600711\pi\) | ||||
−0.311142 | + | 0.950363i | \(0.600711\pi\) | |||||||
\(608\) | 7.45201 | 0.302219 | ||||||||
\(609\) | 13.6874 | − | 9.14836i | 0.554642 | − | 0.370710i | ||||
\(610\) | − | 25.2472i | − | 1.02223i | ||||||
\(611\) | 3.88803 | + | 1.32768i | 0.157293 | + | 0.0537121i | ||||
\(612\) | −4.22422 | + | 10.2061i | −0.170754 | + | 0.412557i | ||||
\(613\) | −12.6416 | − | 12.6416i | −0.510591 | − | 0.510591i | 0.404116 | − | 0.914708i | \(-0.367579\pi\) |
−0.914708 | + | 0.404116i | \(0.867579\pi\) | |||||||
\(614\) | − | 8.63063i | − | 0.348304i | ||||||
\(615\) | −16.5159 | − | 3.28286i | −0.665985 | − | 0.132378i | ||||
\(616\) | −1.27674 | − | 1.27674i | −0.0514414 | − | 0.0514414i | ||||
\(617\) | −0.724231 | + | 0.724231i | −0.0291564 | + | 0.0291564i | −0.721535 | − | 0.692378i | \(-0.756563\pi\) |
0.692378 | + | 0.721535i | \(0.256563\pi\) | |||||||
\(618\) | 9.67811 | − | 6.46862i | 0.389311 | − | 0.260206i | ||||
\(619\) | −4.40767 | + | 4.40767i | −0.177159 | + | 0.177159i | −0.790116 | − | 0.612957i | \(-0.789980\pi\) |
0.612957 | + | 0.790116i | \(0.289980\pi\) | |||||||
\(620\) | 0.549149i | 0.0220544i | ||||||||
\(621\) | 23.5368 | − | 35.2567i | 0.944500 | − | 1.41480i | ||||
\(622\) | −15.5314 | + | 15.5314i | −0.622752 | + | 0.622752i | ||||
\(623\) | −4.51157 | −0.180752 | ||||||||
\(624\) | 1.60620 | + | 6.03491i | 0.0642997 | + | 0.241590i | ||||
\(625\) | 26.8110 | 1.07244 | ||||||||
\(626\) | 3.01915 | − | 3.01915i | 0.120669 | − | 0.120669i | ||||
\(627\) | −22.8580 | − | 4.54348i | −0.912860 | − | 0.181449i | ||||
\(628\) | 10.2830i | 0.410338i | ||||||||
\(629\) | −1.20865 | + | 1.20865i | −0.0481919 | + | 0.0481919i | ||||
\(630\) | 3.56073 | + | 8.58971i | 0.141863 | + | 0.342222i | ||||
\(631\) | −9.93188 | + | 9.93188i | −0.395382 | + | 0.395382i | −0.876601 | − | 0.481219i | \(-0.840194\pi\) |
0.481219 | + | 0.876601i | \(0.340194\pi\) | |||||||
\(632\) | 3.10323 | + | 3.10323i | 0.123440 | + | 0.123440i | ||||
\(633\) | 6.56914 | − | 33.0490i | 0.261100 | − | 1.31358i | ||||
\(634\) | − | 24.9101i | − | 0.989307i | ||||||
\(635\) | 27.3537 | + | 27.3537i | 1.08550 | + | 1.08550i | ||||
\(636\) | 1.89014 | − | 9.50920i | 0.0749491 | − | 0.377064i | ||||
\(637\) | 1.58883 | + | 3.23661i | 0.0629516 | + | 0.128239i | ||||
\(638\) | − | 17.1622i | − | 0.679457i | ||||||
\(639\) | 2.94819 | − | 1.22213i | 0.116629 | − | 0.0483466i | ||||
\(640\) | −3.09950 | −0.122518 | ||||||||
\(641\) | 12.1939 | 0.481630 | 0.240815 | − | 0.970571i | \(-0.422585\pi\) | ||||
0.240815 | + | 0.970571i | \(0.422585\pi\) | |||||||
\(642\) | 11.0089 | − | 7.35808i | 0.434486 | − | 0.290400i | ||||
\(643\) | 28.6315 | + | 28.6315i | 1.12912 | + | 1.12912i | 0.990321 | + | 0.138797i | \(0.0443234\pi\) |
0.138797 | + | 0.990321i | \(0.455677\pi\) | |||||||
\(644\) | 5.76872 | + | 5.76872i | 0.227319 | + | 0.227319i | ||||
\(645\) | −6.38818 | + | 4.26971i | −0.251534 | + | 0.168120i | ||||
\(646\) | −27.4377 | −1.07952 | ||||||||
\(647\) | −18.5157 | −0.727925 | −0.363963 | − | 0.931414i | \(-0.618576\pi\) | ||||
−0.363963 | + | 0.931414i | \(0.618576\pi\) | |||||||
\(648\) | 0.00493109 | + | 9.00000i | 0.000193711 | + | 0.353553i | ||||
\(649\) | 3.81024i | 0.149565i | ||||||||
\(650\) | −15.7192 | − | 5.36776i | −0.616556 | − | 0.210541i | ||||
\(651\) | −0.0598268 | + | 0.300985i | −0.00234480 | + | 0.0117965i | ||||
\(652\) | −16.4136 | − | 16.4136i | −0.642806 | − | 0.642806i | ||||
\(653\) | 42.5130i | 1.66366i | 0.555028 | + | 0.831831i | \(0.312707\pi\) | ||||
−0.555028 | + | 0.831831i | \(0.687293\pi\) | |||||||
\(654\) | −5.28250 | + | 26.5759i | −0.206562 | + | 1.03920i | ||||
\(655\) | 18.2737 | + | 18.2737i | 0.714012 | + | 0.714012i | ||||
\(656\) | 2.21794 | − | 2.21794i | 0.0865958 | − | 0.0865958i | ||||
\(657\) | −14.0840 | + | 5.83829i | −0.549468 | + | 0.227774i | ||||
\(658\) | −0.805736 | + | 0.805736i | −0.0314109 | + | 0.0314109i | ||||
\(659\) | − | 26.7078i | − | 1.04039i | −0.854049 | − | 0.520193i | \(-0.825860\pi\) | ||
0.854049 | − | 0.520193i | \(-0.174140\pi\) | |||||||
\(660\) | 9.50727 | + | 1.88976i | 0.370070 | + | 0.0735588i | ||||
\(661\) | −17.9757 | + | 17.9757i | −0.699175 | + | 0.699175i | −0.964233 | − | 0.265057i | \(-0.914609\pi\) |
0.265057 | + | 0.964233i | \(0.414609\pi\) | |||||||
\(662\) | 23.1878 | 0.901220 | ||||||||
\(663\) | −5.91390 | − | 22.2200i | −0.229677 | − | 0.862953i | ||||
\(664\) | 13.2248 | 0.513221 | ||||||||
\(665\) | −16.3324 | + | 16.3324i | −0.633344 | + | 0.633344i | ||||
\(666\) | −0.532616 | + | 1.28685i | −0.0206385 | + | 0.0498643i | ||||
\(667\) | 77.5441i | 3.00252i | ||||||||
\(668\) | −10.1688 | + | 10.1688i | −0.393444 | + | 0.393444i | ||||
\(669\) | −24.3288 | + | 16.2608i | −0.940604 | + | 0.628678i | ||||
\(670\) | 32.9899 | − | 32.9899i | 1.27451 | − | 1.27451i | ||||
\(671\) | −10.3998 | − | 10.3998i | −0.401480 | − | 0.401480i | ||||
\(672\) | −1.69882 | − | 0.337674i | −0.0655333 | − | 0.0130260i | ||||
\(673\) | 17.8573i | 0.688350i | 0.938906 | + | 0.344175i | \(0.111841\pi\) | ||||
−0.938906 | + | 0.344175i | \(0.888159\pi\) | |||||||
\(674\) | −6.20283 | − | 6.20283i | −0.238924 | − | 0.238924i | ||||
\(675\) | −19.9093 | − | 13.2911i | −0.766308 | − | 0.511575i | ||||
\(676\) | −10.2848 | − | 7.95127i | −0.395570 | − | 0.305818i | ||||
\(677\) | − | 7.00399i | − | 0.269185i | −0.990901 | − | 0.134593i | \(-0.957027\pi\) | ||
0.990901 | − | 0.134593i | \(-0.0429726\pi\) | |||||||
\(678\) | −27.7037 | + | 18.5165i | −1.06396 | + | 0.711123i | ||||
\(679\) | −2.53616 | −0.0973289 | ||||||||
\(680\) | 11.4121 | 0.437633 | ||||||||
\(681\) | 25.3794 | + | 37.9717i | 0.972542 | + | 1.45508i | ||||
\(682\) | 0.226205 | + | 0.226205i | 0.00866183 | + | 0.00866183i | ||||
\(683\) | −2.50202 | − | 2.50202i | −0.0957372 | − | 0.0957372i | 0.657616 | − | 0.753353i | \(-0.271565\pi\) |
−0.753353 | + | 0.657616i | \(0.771565\pi\) | |||||||
\(684\) | −20.6519 | + | 8.56095i | −0.789647 | + | 0.327336i | ||||
\(685\) | −62.3326 | −2.38161 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −2.63830 | − | 3.94733i | −0.100658 | − | 0.150600i | ||||
\(688\) | − | 1.43126i | − | 0.0545663i | ||||||
\(689\) | 8.89352 | + | 18.1171i | 0.338816 | + | 0.690205i | ||||
\(690\) | −42.9568 | − | 8.53853i | −1.63534 | − | 0.325056i | ||||
\(691\) | −16.1198 | − | 16.1198i | −0.613227 | − | 0.613227i | 0.330558 | − | 0.943786i | \(-0.392763\pi\) |
−0.943786 | + | 0.330558i | \(0.892763\pi\) | |||||||
\(692\) | 8.72942i | 0.331843i | ||||||||
\(693\) | 5.00500 | + | 2.07153i | 0.190124 | + | 0.0786910i | ||||
\(694\) | −6.05391 | − | 6.05391i | −0.229803 | − | 0.229803i | ||||
\(695\) | 12.1396 | − | 12.1396i | 0.460482 | − | 0.460482i | ||||
\(696\) | −9.14836 | − | 13.6874i | −0.346768 | − | 0.518820i | ||||
\(697\) | −8.16624 | + | 8.16624i | −0.309318 | + | 0.309318i | ||||
\(698\) | − | 0.0444381i | − | 0.00168201i | ||||||
\(699\) | 1.27249 | − | 6.40182i | 0.0481300 | − | 0.242139i | ||||
\(700\) | 3.25756 | − | 3.25756i | 0.123124 | − | 0.123124i | ||||
\(701\) | 44.4648 | 1.67941 | 0.839706 | − | 0.543041i | \(-0.182727\pi\) | ||||
0.839706 | + | 0.543041i | \(0.182727\pi\) | |||||||
\(702\) | −11.3843 | − | 14.8795i | −0.429672 | − | 0.561589i | ||||
\(703\) | −3.45951 | −0.130478 | ||||||||
\(704\) | −1.27674 | + | 1.27674i | −0.0481190 | + | 0.0481190i | ||||
\(705\) | 1.19260 | − | 5.99992i | 0.0449161 | − | 0.225970i | ||||
\(706\) | 2.40751i | 0.0906076i | ||||||||
\(707\) | −6.04727 | + | 6.04727i | −0.227431 | + | 0.227431i | ||||
\(708\) | 2.03106 | + | 3.03879i | 0.0763319 | + | 0.114205i | ||||
\(709\) | 17.0295 | − | 17.0295i | 0.639557 | − | 0.639557i | −0.310890 | − | 0.950446i | \(-0.600627\pi\) |
0.950446 | + | 0.310890i | \(0.100627\pi\) | |||||||
\(710\) | −2.33155 | − | 2.33155i | −0.0875016 | − | 0.0875016i | ||||
\(711\) | −12.1651 | − | 5.03504i | −0.456227 | − | 0.188829i | ||||
\(712\) | 4.51157i | 0.169078i | ||||||||
\(713\) | −1.02206 | − | 1.02206i | −0.0382766 | − | 0.0382766i | ||||
\(714\) | 6.25489 | + | 1.24328i | 0.234083 | + | 0.0465287i | ||||
\(715\) | −18.1134 | + | 8.89172i | −0.677402 | + | 0.332531i | ||||
\(716\) | 21.4346i | 0.801048i | ||||||||
\(717\) | −4.01472 | − | 6.00667i | −0.149933 | − | 0.224323i | ||||
\(718\) | 27.9888 | 1.04453 | ||||||||
\(719\) | 6.18328 | 0.230598 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(720\) | 8.58971 | − | 3.56073i | 0.320120 | − | 0.132701i | ||||
\(721\) | −4.75235 | − | 4.75235i | −0.176987 | − | 0.176987i | ||||
\(722\) | −25.8324 | − | 25.8324i | −0.961382 | − | 0.961382i | ||||
\(723\) | 20.1903 | + | 30.2079i | 0.750885 | + | 1.12345i | ||||
\(724\) | 7.53227 | 0.279935 | ||||||||
\(725\) | 43.7887 | 1.62627 | ||||||||
\(726\) | −11.1455 | + | 7.44941i | −0.413649 | + | 0.276473i | ||||
\(727\) | − | 38.6481i | − | 1.43338i | −0.697392 | − | 0.716690i | \(-0.745656\pi\) | ||
0.697392 | − | 0.716690i | \(-0.254344\pi\) | |||||||
\(728\) | 3.23661 | − | 1.58883i | 0.119957 | − | 0.0588858i | ||||
\(729\) | −10.3529 | − | 24.9362i | −0.383443 | − | 0.923565i | ||||
\(730\) | 11.1382 | + | 11.1382i | 0.412243 | + | 0.412243i | ||||
\(731\) | 5.26977i | 0.194909i | ||||||||
\(732\) | −13.8378 | − | 2.75055i | −0.511461 | − | 0.101663i | ||||
\(733\) | −11.6899 | − | 11.6899i | −0.431776 | − | 0.431776i | 0.457456 | − | 0.889232i | \(-0.348761\pi\) |
−0.889232 | + | 0.457456i | \(0.848761\pi\) | |||||||
\(734\) | 12.8285 | − | 12.8285i | 0.473508 | − | 0.473508i | ||||
\(735\) | 4.46333 | − | 2.98318i | 0.164632 | − | 0.110036i | ||||
\(736\) | 5.76872 | − | 5.76872i | 0.212638 | − | 0.212638i | ||||
\(737\) | − | 27.1783i | − | 1.00113i | ||||||
\(738\) | −3.59863 | + | 8.69460i | −0.132467 | + | 0.320053i | ||||
\(739\) | −3.88750 | + | 3.88750i | −0.143004 | + | 0.143004i | −0.774984 | − | 0.631980i | \(-0.782242\pi\) |
0.631980 | + | 0.774984i | \(0.282242\pi\) | |||||||
\(740\) | 1.43891 | 0.0528952 | ||||||||
\(741\) | 23.3365 | − | 40.2638i | 0.857287 | − | 1.47913i | ||||
\(742\) | −5.59755 | −0.205492 | ||||||||
\(743\) | −1.32188 | + | 1.32188i | −0.0484952 | + | 0.0484952i | −0.730939 | − | 0.682443i | \(-0.760917\pi\) |
0.682443 | + | 0.730939i | \(0.260917\pi\) | |||||||
\(744\) | 0.300985 | + | 0.0598268i | 0.0110347 | + | 0.00219336i | ||||
\(745\) | 16.3165i | 0.597789i | ||||||||
\(746\) | 19.3138 | − | 19.3138i | 0.707130 | − | 0.707130i | ||||
\(747\) | −36.6502 | + | 15.1928i | −1.34096 | + | 0.555874i | ||||
\(748\) | 4.70085 | − | 4.70085i | 0.171880 | − | 0.171880i | ||||
\(749\) | −5.40581 | − | 5.40581i | −0.197524 | − | 0.197524i | ||||
\(750\) | 0.411436 | − | 2.06991i | 0.0150235 | − | 0.0755823i | ||||
\(751\) | 14.9686i | 0.546210i | 0.961984 | + | 0.273105i | \(0.0880507\pi\) | ||||
−0.961984 | + | 0.273105i | \(0.911949\pi\) | |||||||
\(752\) | 0.805736 | + | 0.805736i | 0.0293822 | + | 0.0293822i | ||||
\(753\) | −8.79060 | + | 44.2250i | −0.320347 | + | 1.61165i | ||||
\(754\) | 32.4322 | + | 11.0749i | 1.18111 | + | 0.403324i | ||||
\(755\) | 66.8262i | 2.43205i | ||||||||
\(756\) | 5.09589 | − | 1.01581i | 0.185336 | − | 0.0369448i | ||||
\(757\) | 16.6501 | 0.605159 | 0.302579 | − | 0.953124i | \(-0.402152\pi\) | ||||
0.302579 | + | 0.953124i | \(0.402152\pi\) | |||||||
\(758\) | −15.6243 | −0.567502 | ||||||||
\(759\) | −21.2119 | + | 14.1775i | −0.769943 | + | 0.514612i | ||||
\(760\) | 16.3324 | + | 16.3324i | 0.592439 | + | 0.592439i | ||||
\(761\) | −0.381043 | − | 0.381043i | −0.0138128 | − | 0.0138128i | 0.700167 | − | 0.713979i | \(-0.253109\pi\) |
−0.713979 | + | 0.700167i | \(0.753109\pi\) | |||||||
\(762\) | 17.9725 | − | 12.0124i | 0.651073 | − | 0.435162i | ||||
\(763\) | 15.6438 | 0.566344 | ||||||||
\(764\) | −1.80118 | −0.0651645 | ||||||||
\(765\) | −31.6266 | + | 13.1103i | −1.14346 | + | 0.474004i | ||||
\(766\) | 26.0661i | 0.941808i | ||||||||
\(767\) | −7.20038 | − | 2.45878i | −0.259991 | − | 0.0887813i | ||||
\(768\) | −0.337674 | + | 1.69882i | −0.0121847 | + | 0.0613007i | ||||
\(769\) | 29.7844 | + | 29.7844i | 1.07405 | + | 1.07405i | 0.997029 | + | 0.0770249i | \(0.0245421\pi\) |
0.0770249 | + | 0.997029i | \(0.475458\pi\) | |||||||
\(770\) | − | 5.59641i | − | 0.201681i | ||||||
\(771\) | −0.419021 | + | 2.10807i | −0.0150907 | + | 0.0759203i | ||||
\(772\) | −14.4054 | − | 14.4054i | −0.518462 | − | 0.518462i | ||||
\(773\) | 22.5034 | − | 22.5034i | 0.809390 | − | 0.809390i | −0.175151 | − | 0.984541i | \(-0.556042\pi\) |
0.984541 | + | 0.175151i | \(0.0560415\pi\) | |||||||
\(774\) | 1.64424 | + | 3.96648i | 0.0591011 | + | 0.142572i | ||||
\(775\) | −0.577154 | + | 0.577154i | −0.0207320 | + | 0.0207320i | ||||
\(776\) | 2.53616i | 0.0910428i | ||||||||
\(777\) | 0.788656 | + | 0.156761i | 0.0282929 | + | 0.00562377i | ||||
\(778\) | −9.42185 | + | 9.42185i | −0.337790 | + | 0.337790i | ||||
\(779\) | −23.3742 | −0.837469 | ||||||||
\(780\) | −9.70628 | + | 16.7468i | −0.347541 | + | 0.599633i | ||||
\(781\) | −1.92082 | −0.0687323 | ||||||||
\(782\) | −21.2399 | + | 21.2399i | −0.759537 | + | 0.759537i | ||||
\(783\) | 41.0773 | + | 27.4226i | 1.46798 | + | 0.980003i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | −22.5371 | + | 22.5371i | −0.804383 | + | 0.804383i | ||||
\(786\) | 12.0065 | − | 8.02488i | 0.428259 | − | 0.286238i | ||||
\(787\) | −21.9665 | + | 21.9665i | −0.783021 | + | 0.783021i | −0.980340 | − | 0.197318i | \(-0.936777\pi\) |
0.197318 | + | 0.980340i | \(0.436777\pi\) | |||||||
\(788\) | −6.93319 | − | 6.93319i | −0.246985 | − | 0.246985i | ||||
\(789\) | 20.3437 | + | 4.04373i | 0.724256 | + | 0.143960i | ||||
\(790\) | 13.6026i | 0.483958i | ||||||||
\(791\) | 13.6037 | + | 13.6037i | 0.483691 | + | 0.483691i | ||||
\(792\) | 2.07153 | − | 5.00500i | 0.0736087 | − | 0.177845i | ||||
\(793\) | 26.3640 | − | 12.9419i | 0.936214 | − | 0.459580i | ||||
\(794\) | − | 23.6340i | − | 0.838738i | ||||||
\(795\) | 24.9837 | − | 16.6985i | 0.886080 | − | 0.592235i | ||||
\(796\) | 10.2593 | 0.363631 | ||||||||
\(797\) | 38.7028 | 1.37092 | 0.685461 | − | 0.728109i | \(-0.259601\pi\) | ||||
0.685461 | + | 0.728109i | \(0.259601\pi\) | |||||||
\(798\) | 7.17236 | + | 10.7310i | 0.253899 | + | 0.379874i | ||||
\(799\) | −2.96665 | − | 2.96665i | −0.104952 | − | 0.104952i | ||||
\(800\) | −3.25756 | − | 3.25756i | −0.115172 | − | 0.115172i | ||||
\(801\) | −5.18293 | − | 12.5030i | −0.183130 | − | 0.441772i | ||||
\(802\) | 0.498008 | 0.0175853 | ||||||||
\(803\) | 9.17605 | 0.323816 | ||||||||
\(804\) | −14.4875 | − | 21.6756i | −0.510935 | − | 0.764441i | ||||
\(805\) | 25.2863i | 0.891226i | ||||||||
\(806\) | −0.573441 | + | 0.281498i | −0.0201986 | + | 0.00991534i | ||||
\(807\) | 12.1098 | + | 2.40707i | 0.426287 | + | 0.0847330i | ||||
\(808\) | 6.04727 | + | 6.04727i | 0.212742 | + | 0.212742i | ||||
\(809\) | − | 29.2625i | − | 1.02881i | −0.857546 | − | 0.514407i | \(-0.828012\pi\) | ||
0.857546 | − | 0.514407i | \(-0.171988\pi\) | |||||||
\(810\) | −19.7143 | + | 19.7359i | −0.692689 | + | 0.693449i | ||||
\(811\) | 6.61904 | + | 6.61904i | 0.232426 | + | 0.232426i | 0.813705 | − | 0.581279i | \(-0.197447\pi\) |
−0.581279 | + | 0.813705i | \(0.697447\pi\) | |||||||
\(812\) | −6.72109 | + | 6.72109i | −0.235864 | + | 0.235864i | ||||
\(813\) | 13.3396 | + | 19.9583i | 0.467841 | + | 0.699967i | ||||
\(814\) | 0.592712 | − | 0.592712i | 0.0207746 | − | 0.0207746i | ||||
\(815\) | − | 71.9466i | − | 2.52018i | ||||||
\(816\) | 1.24328 | − | 6.25489i | 0.0435237 | − | 0.218965i | ||||
\(817\) | −7.54184 | + | 7.54184i | −0.263855 | + | 0.263855i | ||||
\(818\) | 32.7874 | 1.14638 | ||||||||
\(819\) | −7.14443 | + | 8.12140i | −0.249647 | + | 0.283785i | ||||
\(820\) | 9.72199 | 0.339507 | ||||||||
\(821\) | −5.05583 | + | 5.05583i | −0.176450 | + | 0.176450i | −0.789806 | − | 0.613357i | \(-0.789819\pi\) |
0.613357 | + | 0.789806i | \(0.289819\pi\) | |||||||
\(822\) | −6.79080 | + | 34.1641i | −0.236856 | + | 1.19161i | ||||
\(823\) | 18.8908i | 0.658493i | 0.944244 | + | 0.329246i | \(0.106795\pi\) | ||||
−0.944244 | + | 0.329246i | \(0.893205\pi\) | |||||||
\(824\) | −4.75235 | + | 4.75235i | −0.165556 | + | 0.165556i | ||||
\(825\) | 8.00598 | + | 11.9782i | 0.278733 | + | 0.417029i | ||||
\(826\) | 1.49217 | − | 1.49217i | 0.0519193 | − | 0.0519193i | ||||
\(827\) | 11.3749 | + | 11.3749i | 0.395543 | + | 0.395543i | 0.876658 | − | 0.481115i | \(-0.159768\pi\) |
−0.481115 | + | 0.876658i | \(0.659768\pi\) | |||||||
\(828\) | −9.35983 | + | 22.6141i | −0.325276 | + | 0.785896i | ||||
\(829\) | − | 13.7831i | − | 0.478708i | −0.970932 | − | 0.239354i | \(-0.923064\pi\) | ||
0.970932 | − | 0.239354i | \(-0.0769357\pi\) | |||||||
\(830\) | 28.9844 | + | 28.9844i | 1.00606 | + | 1.00606i | ||||
\(831\) | −2.51297 | − | 0.499503i | −0.0871740 | − | 0.0173276i | ||||
\(832\) | −1.58883 | − | 3.23661i | −0.0550826 | − | 0.112209i | ||||
\(833\) | − | 3.68191i | − | 0.127571i | ||||||
\(834\) | −5.33111 | − | 7.97621i | −0.184601 | − | 0.276193i | ||||
\(835\) | −44.5736 | −1.54253 | ||||||||
\(836\) | 13.4552 | 0.465360 | ||||||||
\(837\) | −0.902857 | + | 0.179975i | −0.0312073 | + | 0.00622085i | ||||
\(838\) | −6.79475 | − | 6.79475i | −0.234721 | − | 0.234721i | ||||
\(839\) | −2.49384 | − | 2.49384i | −0.0860970 | − | 0.0860970i | 0.662747 | − | 0.748844i | \(-0.269391\pi\) |
−0.748844 | + | 0.662747i | \(0.769391\pi\) | |||||||
\(840\) | −2.98318 | − | 4.46333i | −0.102930 | − | 0.153999i | ||||
\(841\) | −61.3460 | −2.11538 | ||||||||
\(842\) | 14.3759 | 0.495425 | ||||||||
\(843\) | 23.1546 | − | 15.4760i | 0.797488 | − | 0.533023i | ||||
\(844\) | 19.4541i | 0.669638i | ||||||||
\(845\) | −5.11437 | − | 39.9676i | −0.175940 | − | 1.37493i | ||||
\(846\) | −3.15859 | − | 1.30732i | −0.108595 | − | 0.0449465i | ||||
\(847\) | 5.47291 | + | 5.47291i | 0.188051 | + | 0.188051i | ||||
\(848\) | 5.59755i | 0.192220i | ||||||||
\(849\) | −33.8573 | − | 6.72982i | −1.16198 | − | 0.230967i | ||||
\(850\) | 11.9941 | + | 11.9941i | 0.411393 | + | 0.411393i | ||||
\(851\) | −2.67806 | + | 2.67806i | −0.0918027 | + | 0.0918027i | ||||
\(852\) | −1.53192 | + | 1.02390i | −0.0524827 | + | 0.0350782i | ||||
\(853\) | 25.6064 | − | 25.6064i | 0.876745 | − | 0.876745i | −0.116451 | − | 0.993196i | \(-0.537152\pi\) |
0.993196 | + | 0.116451i | \(0.0371519\pi\) | |||||||
\(854\) | 8.14557i | 0.278736i | ||||||||
\(855\) | −64.0252 | − | 26.4996i | −2.18962 | − | 0.906266i | ||||
\(856\) | −5.40581 | + | 5.40581i | −0.184767 | + | 0.184767i | ||||
\(857\) | 42.3721 | 1.44740 | 0.723701 | − | 0.690113i | \(-0.242439\pi\) | ||||
0.723701 | + | 0.690113i | \(0.242439\pi\) | |||||||
\(858\) | 2.90014 | + | 10.8965i | 0.0990092 | + | 0.372002i | ||||
\(859\) | −6.25574 | −0.213443 | −0.106722 | − | 0.994289i | \(-0.534035\pi\) | ||||
−0.106722 | + | 0.994289i | \(0.534035\pi\) | |||||||
\(860\) | 3.13686 | − | 3.13686i | 0.106966 | − | 0.106966i | ||||
\(861\) | 5.32857 | + | 1.05916i | 0.181597 | + | 0.0360960i | ||||
\(862\) | 9.06310i | 0.308690i | ||||||||
\(863\) | 20.0524 | − | 20.0524i | 0.682591 | − | 0.682591i | −0.277992 | − | 0.960583i | \(-0.589669\pi\) |
0.960583 | + | 0.277992i | \(0.0896689\pi\) | |||||||
\(864\) | −1.01581 | − | 5.09589i | −0.0345587 | − | 0.173366i | ||||
\(865\) | −19.1321 | + | 19.1321i | −0.650510 | + | 0.650510i | ||||
\(866\) | 23.7336 | + | 23.7336i | 0.806502 | + | 0.806502i | ||||
\(867\) | 1.16279 | − | 5.84993i | 0.0394904 | − | 0.198674i | ||||
\(868\) | − | 0.177174i | − | 0.00601366i | ||||||
\(869\) | 5.60315 | + | 5.60315i | 0.190074 | + | 0.190074i | ||||
\(870\) | 9.94817 | − | 50.0486i | 0.337274 | − | 1.69681i | ||||
\(871\) | 51.3601 | + | 17.5384i | 1.74027 | + | 0.594266i | ||||
\(872\) | − | 15.6438i | − | 0.529766i | ||||||
\(873\) | −2.91356 | − | 7.02852i | −0.0986092 | − | 0.237879i | ||||
\(874\) | −60.7950 | −2.05642 | ||||||||
\(875\) | −1.21844 | −0.0411908 | ||||||||
\(876\) | 7.31821 | − | 4.89132i | 0.247260 | − | 0.165263i | ||||
\(877\) | 2.73719 | + | 2.73719i | 0.0924283 | + | 0.0924283i | 0.751809 | − | 0.659381i | \(-0.229181\pi\) |
−0.659381 | + | 0.751809i | \(0.729181\pi\) | |||||||
\(878\) | 5.00643 | + | 5.00643i | 0.168959 | + | 0.168959i | ||||
\(879\) | −21.0581 | + | 14.0747i | −0.710272 | + | 0.474729i | ||||
\(880\) | −5.59641 | −0.188655 | ||||||||
\(881\) | 1.97857 | 0.0666596 | 0.0333298 | − | 0.999444i | \(-0.489389\pi\) | ||||
0.0333298 | + | 0.999444i | \(0.489389\pi\) | |||||||
\(882\) | −1.14881 | − | 2.77132i | −0.0386824 | − | 0.0933153i | ||||
\(883\) | − | 13.2612i | − | 0.446275i | −0.974787 | − | 0.223137i | \(-0.928370\pi\) | ||
0.974787 | − | 0.223137i | \(-0.0716298\pi\) | |||||||
\(884\) | 5.84991 | + | 11.9169i | 0.196754 | + | 0.400809i | ||||
\(885\) | −2.20863 | + | 11.1115i | −0.0742422 | + | 0.373508i | ||||
\(886\) | 4.67455 | + | 4.67455i | 0.157045 | + | 0.157045i | ||||
\(887\) | 19.8583i | 0.666778i | 0.942789 | + | 0.333389i | \(0.108192\pi\) | ||||
−0.942789 | + | 0.333389i | \(0.891808\pi\) | |||||||
\(888\) | 0.156761 | − | 0.788656i | 0.00526056 | − | 0.0264655i | ||||
\(889\) | −8.82521 | − | 8.82521i | −0.295988 | − | 0.295988i | ||||
\(890\) | −9.88789 | + | 9.88789i | −0.331443 | + | 0.331443i | ||||
\(891\) | 0.00890350 | + | 16.2503i | 0.000298279 | + | 0.544404i | ||||
\(892\) | 11.9464 | − | 11.9464i | 0.399996 | − | 0.399996i | ||||
\(893\) | − | 8.49144i | − | 0.284155i | ||||||
\(894\) | 8.94296 | + | 1.77759i | 0.299097 | + | 0.0594515i | ||||
\(895\) | −46.9777 | + | 46.9777i | −1.57029 | + | 1.57029i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −13.1037 | − | 49.2340i | −0.437521 | − | 1.64387i | ||||
\(898\) | 21.3348 | 0.711951 | ||||||||
\(899\) | 1.19080 | − | 1.19080i | 0.0397154 | − | 0.0397154i | ||||
\(900\) | 12.7701 | + | 5.28544i | 0.425669 | + | 0.176181i | ||||
\(901\) | − | 20.6097i | − | 0.686607i | ||||||
\(902\) | 4.00467 | − | 4.00467i | 0.133341 | − | 0.133341i | ||||
\(903\) | 2.06104 | − | 1.37755i | 0.0685870 | − | 0.0458420i | ||||
\(904\) | 13.6037 | − | 13.6037i | 0.452451 | − | 0.452451i | ||||
\(905\) | 16.5083 | + | 16.5083i | 0.548755 | + | 0.548755i | ||||
\(906\) | 36.6270 | + | 7.28035i | 1.21685 | + | 0.241874i | ||||
\(907\) | 45.3220i | 1.50489i | 0.658654 | + | 0.752446i | \(0.271126\pi\) | ||||
−0.658654 | + | 0.752446i | \(0.728874\pi\) | |||||||
\(908\) | −18.6457 | − | 18.6457i | −0.618778 | − | 0.618778i | ||||
\(909\) | −23.7061 | − | 9.81178i | −0.786282 | − | 0.325436i | ||||
\(910\) | 10.5758 | + | 3.61141i | 0.350584 | + | 0.119717i | ||||
\(911\) | 6.89031i | 0.228286i | 0.993464 | + | 0.114143i | \(0.0364122\pi\) | ||||
−0.993464 | + | 0.114143i | \(0.963588\pi\) | |||||||
\(912\) | 10.7310 | − | 7.17236i | 0.355340 | − | 0.237501i | ||||
\(913\) | 23.8785 | 0.790262 | ||||||||
\(914\) | 26.1460 | 0.864831 | ||||||||
\(915\) | −24.2997 | − | 36.3564i | −0.803325 | − | 1.20190i | ||||
\(916\) | 1.93830 | + | 1.93830i | 0.0640433 | + | 0.0640433i | ||||
\(917\) | −5.89570 | − | 5.89570i | −0.194693 | − | 0.194693i | ||||
\(918\) | 3.74013 | + | 18.7626i | 0.123443 | + | 0.619259i | ||||
\(919\) | 25.9569 | 0.856239 | 0.428119 | − | 0.903722i | \(-0.359176\pi\) | ||||
0.428119 | + | 0.903722i | \(0.359176\pi\) | |||||||
\(920\) | 25.2863 | 0.833665 | ||||||||
\(921\) | −8.30675 | − | 12.4282i | −0.273717 | − | 0.409525i | ||||
\(922\) | − | 16.8726i | − | 0.555668i | ||||||
\(923\) | 1.23952 | − | 3.62986i | 0.0407993 | − | 0.119478i | ||||
\(924\) | −3.06736 | − | 0.609699i | −0.100909 | − | 0.0200576i | ||||
\(925\) | 1.51229 | + | 1.51229i | 0.0497237 | + | 0.0497237i | ||||
\(926\) | 2.85389i | 0.0937846i | ||||||||
\(927\) | 7.71075 | − | 18.6298i | 0.253254 | − | 0.611884i | ||||
\(928\) | 6.72109 | + | 6.72109i | 0.220630 | + | 0.220630i | ||||
\(929\) | 0.188091 | − | 0.188091i | 0.00617106 | − | 0.00617106i | −0.704015 | − | 0.710186i | \(-0.748611\pi\) |
0.710186 | + | 0.704015i | \(0.248611\pi\) | |||||||
\(930\) | 0.528541 | + | 0.790783i | 0.0173316 | + | 0.0259308i | ||||
\(931\) | 5.26937 | − | 5.26937i | 0.172697 | − | 0.172697i | ||||
\(932\) | 3.76840i | 0.123438i | ||||||||
\(933\) | −7.41690 | + | 37.3140i | −0.242818 | + | 1.22160i | ||||
\(934\) | 8.05022 | − | 8.05022i | 0.263411 | − | 0.263411i | ||||
\(935\) | 20.6055 | 0.673871 | ||||||||
\(936\) | 8.12140 | + | 7.14443i | 0.265456 | + | 0.233523i | ||||
\(937\) | −31.1002 | −1.01600 | −0.508000 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508000 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(938\) | −10.6436 | + | 10.6436i | −0.347527 | + | 0.347527i | ||||
\(939\) | 1.44177 | − | 7.25347i | 0.0470504 | − | 0.236708i | ||||
\(940\) | 3.53183i | 0.115195i | ||||||||
\(941\) | −8.58050 | + | 8.58050i | −0.279716 | + | 0.279716i | −0.832996 | − | 0.553279i | \(-0.813376\pi\) |
0.553279 | + | 0.832996i | \(0.313376\pi\) | |||||||
\(942\) | 9.89715 | + | 14.8077i | 0.322466 | + | 0.482462i | ||||
\(943\) | −18.0944 | + | 18.0944i | −0.589233 | + | 0.589233i | ||||
\(944\) | −1.49217 | − | 1.49217i | −0.0485661 | − | 0.0485661i | ||||
\(945\) | 13.3949 | + | 8.94221i | 0.435736 | + | 0.290890i | ||||
\(946\) | − | 2.58426i | − | 0.0840216i | ||||||
\(947\) | −14.0525 | − | 14.0525i | −0.456644 | − | 0.456644i | 0.440908 | − | 0.897552i | \(-0.354656\pi\) |
−0.897552 | + | 0.440908i | \(0.854656\pi\) | |||||||
\(948\) | 7.45549 | + | 1.48193i | 0.242143 | + | 0.0481307i | ||||
\(949\) | −5.92138 | + | 17.3404i | −0.192216 | + | 0.562893i | ||||
\(950\) | 34.3306i | 1.11383i | ||||||||
\(951\) | −23.9753 | − | 35.8709i | −0.777453 | − | 1.16319i | ||||
\(952\) | −3.68191 | −0.119331 | ||||||||
\(953\) | 55.9530 | 1.81250 | 0.906248 | − | 0.422747i | \(-0.138934\pi\) | ||||
0.906248 | + | 0.422747i | \(0.138934\pi\) | |||||||
\(954\) | −6.43051 | − | 15.5126i | −0.208196 | − | 0.502239i | ||||
\(955\) | −3.94761 | − | 3.94761i | −0.127742 | − | 0.127742i | ||||
\(956\) | 2.94952 | + | 2.94952i | 0.0953944 | + | 0.0953944i | ||||
\(957\) | −16.5181 | − | 24.7138i | −0.533956 | − | 0.798884i | ||||
\(958\) | 31.0801 | 1.00415 | ||||||||
\(959\) | 20.1105 | 0.649404 | ||||||||
\(960\) | −4.46333 | + | 2.98318i | −0.144053 | + | 0.0962818i | ||||
\(961\) | − | 30.9686i | − | 0.998987i | ||||||
\(962\) | 0.737594 | + | 1.50256i | 0.0237810 | + | 0.0484444i | ||||
\(963\) | 8.77100 | − | 21.1915i | 0.282642 | − | 0.682886i | ||||
\(964\) | −14.8333 | − | 14.8333i | −0.477750 | − | 0.477750i | ||||
\(965\) | − | 63.1440i | − | 2.03268i | ||||||
\(966\) | 13.8593 | + | 2.75481i | 0.445915 | + | 0.0886345i | ||||
\(967\) | 2.62952 | + | 2.62952i | 0.0845598 | + | 0.0845598i | 0.748122 | − | 0.663562i | \(-0.230956\pi\) |
−0.663562 | + | 0.748122i | \(0.730956\pi\) | |||||||
\(968\) | 5.47291 | − | 5.47291i | 0.175906 | − | 0.175906i | ||||
\(969\) | −39.5107 | + | 26.4080i | −1.26927 | + | 0.848347i | ||||
\(970\) | −5.55844 | + | 5.55844i | −0.178471 | + | 0.178471i | ||||
\(971\) | 17.7506i | 0.569645i | 0.958580 | + | 0.284823i | \(0.0919347\pi\) | ||||
−0.958580 | + | 0.284823i | \(0.908065\pi\) | |||||||
\(972\) | 8.66936 | + | 12.9554i | 0.278070 | + | 0.415544i | ||||
\(973\) | −3.91664 | + | 3.91664i | −0.125562 | + | 0.125562i | ||||
\(974\) | 30.7803 | 0.986263 | ||||||||
\(975\) | −27.8022 | + | 7.39961i | −0.890382 | + | 0.236977i | ||||
\(976\) | 8.14557 | 0.260733 | ||||||||
\(977\) | −8.56492 | + | 8.56492i | −0.274016 | + | 0.274016i | −0.830715 | − | 0.556699i | \(-0.812068\pi\) |
0.556699 | + | 0.830715i | \(0.312068\pi\) | |||||||
\(978\) | −39.4335 | − | 7.83820i | −1.26094 | − | 0.250638i | ||||
\(979\) | 8.14602i | 0.260348i | ||||||||
\(980\) | −2.19168 | + | 2.19168i | −0.0700105 | + | 0.0700105i | ||||
\(981\) | 17.9717 | + | 43.3540i | 0.573794 | + | 1.38419i | ||||
\(982\) | −17.4394 | + | 17.4394i | −0.556513 | + | 0.556513i | ||||
\(983\) | −4.10551 | − | 4.10551i | −0.130945 | − | 0.130945i | 0.638596 | − | 0.769542i | \(-0.279515\pi\) |
−0.769542 | + | 0.638596i | \(0.779515\pi\) | |||||||
\(984\) | 1.05916 | − | 5.32857i | 0.0337647 | − | 0.169868i | ||||
\(985\) | − | 30.3906i | − | 0.968326i | ||||||
\(986\) | −24.7464 | − | 24.7464i | −0.788087 | − | 0.788087i | ||||
\(987\) | −0.384773 | + | 1.93577i | −0.0122475 | + | 0.0616163i | ||||
\(988\) | −8.68278 | + | 25.4270i | −0.276236 | + | 0.808941i | ||||
\(989\) | 11.6765i | 0.371291i | ||||||||
\(990\) | 15.5095 | − | 6.42921i | 0.492923 | − | 0.204334i | ||||
\(991\) | 60.0976 | 1.90906 | 0.954532 | − | 0.298108i | \(-0.0963555\pi\) | ||||
0.954532 | + | 0.298108i | \(0.0963555\pi\) | |||||||
\(992\) | −0.177174 | −0.00562527 | ||||||||
\(993\) | 33.3908 | − | 22.3177i | 1.05963 | − | 0.708229i | ||||
\(994\) | 0.752235 | + | 0.752235i | 0.0238594 | + | 0.0238594i | ||||
\(995\) | 22.4851 | + | 22.4851i | 0.712824 | + | 0.712824i | ||||
\(996\) | 19.0439 | − | 12.7285i | 0.603429 | − | 0.403318i | ||||
\(997\) | 55.3278 | 1.75225 | 0.876124 | − | 0.482086i | \(-0.160121\pi\) | ||||
0.876124 | + | 0.482086i | \(0.160121\pi\) | |||||||
\(998\) | −43.3263 | −1.37147 | ||||||||
\(999\) | 0.471579 | + | 2.36571i | 0.0149201 | + | 0.0748477i |
(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 | 546.2.p.d.281.3 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.c.281.8 | yes | 20 | ||
13.5 | odd | 4 | 546.2.p.c.239.8 | ✓ | 20 | ||
39.5 | even | 4 | inner | 546.2.p.d.239.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.8 | ✓ | 20 | 13.5 | odd | 4 | ||
546.2.p.c.281.8 | yes | 20 | 3.2 | odd | 2 | ||
546.2.p.d.239.3 | yes | 20 | 39.5 | even | 4 | inner | |
546.2.p.d.281.3 | yes | 20 | 1.1 | even | 1 | trivial |