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 | 281.8 | ||
Root | \(-0.962473 + 1.44002i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.c.239.8 |
$q$-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 | −0.999807 | − | 0.0196593i | \(-0.993742\pi\) |
0.0196593 | + | 0.999807i | \(0.493742\pi\) | |||||||
\(6\) | −1.44002 | − | 0.962473i | −0.587884 | − | 0.392928i | ||||
\(7\) | −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 | 0.487930 | − | 0.872883i | \(-0.337752\pi\) |
−0.872883 | + | 0.487930i | \(0.837752\pi\) | |||||||
\(12\) | −1.69882 | + | 0.337674i | −0.490406 | + | 0.0974780i | ||||
\(13\) | −3.23661 | + | 1.58883i | −0.897674 | + | 0.440661i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 4.46333 | + | 2.98318i | 1.15243 | + | 0.770255i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.68191 | −0.892995 | −0.446497 | − | 0.894785i | \(-0.647329\pi\) | ||||
−0.446497 | + | 0.894785i | \(0.647329\pi\) | |||||||
\(18\) | −1.14881 | + | 2.77132i | −0.270777 | + | 0.653207i | ||||
\(19\) | 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 | ||||
\(21\) | 1.44002 | + | 0.962473i | 0.314237 | + | 0.210029i | ||||
\(22\) | −1.80559 | −0.384952 | ||||||||
\(23\) | −8.15820 | −1.70110 | −0.850551 | − | 0.525893i | \(-0.823731\pi\) | ||||
−0.850551 | + | 0.525893i | \(0.823731\pi\) | |||||||
\(24\) | −0.962473 | + | 1.44002i | −0.196464 | + | 0.293942i | ||||
\(25\) | − | 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 | \(-0.655844\pi\) | ||
0.470272 | − | 0.882522i | \(-0.344156\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | −1.73783 | + | 2.60007i | −0.302517 | + | 0.452614i | ||||
\(34\) | −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 | ||||||||
\(39\) | 3.79204 | + | 4.96190i | 0.607212 | + | 0.794540i | ||||
\(40\) | 3.09950 | 0.490074 | ||||||||
\(41\) | 2.21794 | − | 2.21794i | 0.346383 | − | 0.346383i | −0.512377 | − | 0.858761i | \(-0.671235\pi\) |
0.858761 | + | 0.512377i | \(0.171235\pi\) | |||||||
\(42\) | 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 | ||||
\(45\) | 3.56073 | − | 8.58971i | 0.530803 | − | 1.28048i | ||||
\(46\) | −5.76872 | + | 5.76872i | −0.850551 | + | 0.850551i | ||||
\(47\) | 0.805736 | + | 0.805736i | 0.117529 | + | 0.117529i | 0.763425 | − | 0.645896i | \(-0.223516\pi\) |
−0.645896 | + | 0.763425i | \(0.723516\pi\) | |||||||
\(48\) | 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 | \(0.125606\pi\) | ||||
−0.923150 | + | 0.384441i | \(0.874394\pi\) | |||||||
\(54\) | 5.09589 | + | 1.01581i | 0.693463 | + | 0.138235i | ||||
\(55\) | 5.59641 | 0.754620 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 7.17236 | − | 10.7310i | 0.950003 | − | 1.42136i | ||||
\(58\) | −6.72109 | − | 6.72109i | −0.882522 | − | 0.882522i | ||||
\(59\) | −1.49217 | − | 1.49217i | −0.194264 | − | 0.194264i | 0.603272 | − | 0.797536i | \(-0.293864\pi\) |
−0.797536 | + | 0.603272i | \(0.793864\pi\) | |||||||
\(60\) | 2.98318 | − | 4.46333i | 0.385127 | − | 0.576213i | ||||
\(61\) | −8.14557 | −1.04293 | −0.521467 | − | 0.853272i | \(-0.674615\pi\) | ||||
−0.521467 | + | 0.853272i | \(0.674615\pi\) | |||||||
\(62\) | −0.177174 | −0.0225011 | ||||||||
\(63\) | 1.14881 | − | 2.77132i | 0.144736 | − | 0.349154i | ||||
\(64\) | 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 | −0.661060 | − | 0.750333i | \(-0.729893\pi\) |
0.750333 | + | 0.661060i | \(0.229893\pi\) | |||||||
\(72\) | 2.77132 | + | 1.14881i | 0.326604 | + | 0.135389i | ||||
\(73\) | 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 | ||||||||
\(78\) | 6.18997 | + | 0.827215i | 0.700876 | + | 0.0936637i | ||||
\(79\) | 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 | \(0.508532\pi\) |
−0.999641 | + | 0.0268014i | \(0.991468\pi\) | |||||||
\(84\) | 0.962473 | − | 1.44002i | 0.105014 | − | 0.157119i | ||||
\(85\) | 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 | 0.517517 | − | 0.855673i | \(-0.326856\pi\) |
−0.855673 | + | 0.517517i | \(0.826856\pi\) | |||||||
\(90\) | −3.55603 | − | 8.59166i | −0.374838 | − | 0.905641i | ||||
\(91\) | 1.16516 | − | 3.41210i | 0.122142 | − | 0.357685i | ||||
\(92\) | 8.15820i | 0.850551i | ||||||||
\(93\) | −0.170525 | + | 0.255133i | −0.0176826 | + | 0.0264560i | ||||
\(94\) | 1.13948 | 0.117529 | ||||||||
\(95\) | −23.0975 | −2.36975 | ||||||||
\(96\) | 1.44002 | + | 0.962473i | 0.146971 | + | 0.0982320i | ||||
\(97\) | 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 | ||||
\(99\) | 5.00386 | + | 2.07427i | 0.502907 | + | 0.208472i | ||||
\(100\) | −4.60689 | −0.460689 | ||||||||
\(101\) | −8.55213 | −0.850969 | −0.425484 | − | 0.904966i | \(-0.639896\pi\) | ||||
−0.425484 | + | 0.904966i | \(0.639896\pi\) | |||||||
\(102\) | 5.30201 | + | 3.54374i | 0.524977 | + | 0.350883i | ||||
\(103\) | 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 | \(-0.879517\pi\) | ||
0.929217 | − | 0.369534i | \(-0.120483\pi\) | |||||||
\(108\) | 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 | ||||
\(111\) | 0.668510 | + | 0.446817i | 0.0634522 | + | 0.0424100i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | 19.2385i | 1.80980i | 0.425619 | + | 0.904902i | \(0.360056\pi\) | ||||
−0.425619 | + | 0.904902i | \(0.639944\pi\) | |||||||
\(114\) | −2.51635 | − | 12.6596i | −0.235678 | − | 1.18568i | ||||
\(115\) | 17.8801 | − | 17.8801i | 1.66733 | − | 1.66733i | ||||
\(116\) | −9.50505 | −0.882522 | ||||||||
\(117\) | 7.14888 | − | 8.11748i | 0.660914 | − | 0.750461i | ||||
\(118\) | −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 | ||||
\(123\) | −4.51680 | − | 3.01893i | −0.407266 | − | 0.272207i | ||||
\(124\) | −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 | \(-0.881330\pi\) | ||
0.931306 | − | 0.364237i | \(-0.118670\pi\) | |||||||
\(132\) | 2.60007 | + | 1.73783i | 0.226307 | + | 0.151258i | ||||
\(133\) | −7.45201 | −0.646172 | ||||||||
\(134\) | −15.0524 | −1.30033 | ||||||||
\(135\) | −15.7947 | − | 3.14851i | −1.35939 | − | 0.270981i | ||||
\(136\) | 2.60350 | + | 2.60350i | 0.223249 | + | 0.223249i | ||||
\(137\) | 14.2203 | + | 14.2203i | 1.21492 | + | 1.21492i | 0.969388 | + | 0.245535i | \(0.0789636\pi\) |
0.245535 | + | 0.969388i | \(0.421036\pi\) | |||||||
\(138\) | 11.7479 | + | 7.85205i | 1.00005 | + | 0.668411i | ||||
\(139\) | 5.53897 | 0.469809 | 0.234905 | − | 0.972018i | \(-0.424522\pi\) | ||||
0.234905 | + | 0.972018i | \(0.424522\pi\) | |||||||
\(140\) | −3.09950 | −0.261955 | ||||||||
\(141\) | 1.09672 | − | 1.64087i | 0.0923606 | − | 0.138186i | ||||
\(142\) | − | 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 | −0.537998 | − | 0.842946i | \(-0.680819\pi\) |
0.842946 | + | 0.537998i | \(0.180819\pi\) | |||||||
\(150\) | −4.43401 | + | 6.63400i | −0.362035 | + | 0.541663i | ||||
\(151\) | −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 | ||||||||
\(156\) | 4.96190 | − | 3.79204i | 0.397270 | − | 0.303606i | ||||
\(157\) | −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 | ||||
\(162\) | 0.00493109 | − | 9.00000i | 0.000387423 | − | 0.707107i | ||||
\(163\) | 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 | 0.980983 | − | 0.194095i | \(-0.0621770\pi\) |
−0.194095 | + | 0.980983i | \(0.562177\pi\) | |||||||
\(168\) | −0.337674 | − | 1.69882i | −0.0260521 | − | 0.131067i | ||||
\(169\) | 7.95127 | − | 10.2848i | 0.611636 | − | 0.791139i | ||||
\(170\) | − | 11.4121i | − | 0.875266i | ||||||
\(171\) | −20.6519 | − | 8.56095i | −1.57929 | − | 0.654672i | ||||
\(172\) | 1.43126 | 0.109133 | ||||||||
\(173\) | 8.72942 | 0.663686 | 0.331843 | − | 0.943335i | \(-0.392330\pi\) | ||||
0.331843 | + | 0.943335i | \(0.392330\pi\) | |||||||
\(174\) | −9.14836 | + | 13.6874i | −0.693535 | + | 1.03764i | ||||
\(175\) | 3.25756 | + | 3.25756i | 0.246249 | + | 0.246249i | ||||
\(176\) | 1.27674 | + | 1.27674i | 0.0962380 | + | 0.0962380i | ||||
\(177\) | −2.03106 | + | 3.03879i | −0.152664 | + | 0.228410i | ||||
\(178\) | −4.51157 | −0.338156 | ||||||||
\(179\) | 21.4346 | 1.60210 | 0.801048 | − | 0.598600i | \(-0.204276\pi\) | ||||
0.801048 | + | 0.598600i | \(0.204276\pi\) | |||||||
\(180\) | −8.58971 | − | 3.56073i | −0.640240 | − | 0.265401i | ||||
\(181\) | 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 | ||||
\(189\) | −5.09589 | − | 1.01581i | −0.370672 | − | 0.0738895i | ||||
\(190\) | −16.3324 | + | 16.3324i | −1.18488 | + | 1.18488i | ||||
\(191\) | 1.80118i | 0.130329i | 0.997875 | + | 0.0651645i | \(0.0207572\pi\) | ||||
−0.997875 | + | 0.0651645i | \(0.979243\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −19.1858 | − | 2.56395i | −1.37392 | − | 0.183608i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −6.93319 | + | 6.93319i | −0.493970 | + | 0.493970i | −0.909554 | − | 0.415585i | \(-0.863577\pi\) |
0.415585 | + | 0.909554i | \(0.363577\pi\) | |||||||
\(198\) | 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 | ||||
\(201\) | −14.4875 | + | 21.6756i | −1.02187 | + | 1.52888i | ||||
\(202\) | −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 | ||||||
\(210\) | −2.98318 | + | 4.46333i | −0.205859 | + | 0.307999i | ||||
\(211\) | −19.4541 | −1.33928 | −0.669638 | − | 0.742687i | \(-0.733551\pi\) | ||||
−0.669638 | + | 0.742687i | \(0.733551\pi\) | |||||||
\(212\) | 5.59755 | 0.384441 | ||||||||
\(213\) | −1.53192 | − | 1.02390i | −0.104965 | − | 0.0701564i | ||||
\(214\) | −5.40581 | − | 5.40581i | −0.369534 | − | 0.369534i | ||||
\(215\) | −3.13686 | − | 3.13686i | −0.213932 | − | 0.213932i | ||||
\(216\) | 1.01581 | − | 5.09589i | 0.0691173 | − | 0.346732i | ||||
\(217\) | 0.177174 | 0.0120273 | ||||||||
\(218\) | −15.6438 | −1.05953 | ||||||||
\(219\) | −7.31821 | − | 4.89132i | −0.494519 | − | 0.330525i | ||||
\(220\) | − | 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 | \(0.589195\pi\) |
−0.960997 | + | 0.276560i | \(0.910805\pi\) | |||||||
\(228\) | −10.7310 | − | 7.17236i | −0.710679 | − | 0.475001i | ||||
\(229\) | −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 | \(-0.460608\pi\) | ||||
0.123438 | + | 0.992352i | \(0.460608\pi\) | |||||||
\(234\) | −0.684903 | − | 10.7949i | −0.0447735 | − | 0.705688i | ||||
\(235\) | −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 | −0.605248 | − | 0.796037i | \(-0.706926\pi\) |
0.796037 | + | 0.605248i | \(0.206926\pi\) | |||||||
\(240\) | −4.46333 | − | 2.98318i | −0.288107 | − | 0.192564i | ||||
\(241\) | 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 | ||||||||
\(249\) | 19.0439 | + | 12.7285i | 1.20686 | + | 0.806636i | ||||
\(250\) | −1.21844 | −0.0770610 | ||||||||
\(251\) | −26.0328 | −1.64318 | −0.821589 | − | 0.570080i | \(-0.806912\pi\) | ||||
−0.821589 | + | 0.570080i | \(0.806912\pi\) | |||||||
\(252\) | −2.77132 | − | 1.14881i | −0.174577 | − | 0.0723682i | ||||
\(253\) | 10.4159 | + | 10.4159i | 0.654843 | + | 0.654843i | ||||
\(254\) | 8.82521 | + | 8.82521i | 0.553743 | + | 0.553743i | ||||
\(255\) | −16.4336 | − | 10.9838i | −1.02911 | − | 0.687833i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.24091 | −0.0774055 | −0.0387028 | − | 0.999251i | \(-0.512323\pi\) | ||||
−0.0387028 | + | 0.999251i | \(0.512323\pi\) | |||||||
\(258\) | 1.37755 | − | 2.06104i | 0.0857624 | − | 0.128315i | ||||
\(259\) | − | 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 | \(0.120373\pi\) | ||||
−0.929345 | + | 0.369213i | \(0.879627\pi\) | |||||||
\(264\) | 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 | ||||
\(267\) | −4.34226 | + | 6.49672i | −0.265742 | + | 0.397593i | ||||
\(268\) | −10.6436 | + | 10.6436i | −0.650163 | + | 0.650163i | ||||
\(269\) | 7.12840i | 0.434626i | 0.976102 | + | 0.217313i | \(0.0697293\pi\) | ||||
−0.976102 | + | 0.217313i | \(0.930271\pi\) | |||||||
\(270\) | −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 | ||||||||
\(273\) | −6.18997 | − | 0.827215i | −0.374634 | − | 0.0500653i | ||||
\(274\) | 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 | ||||
\(279\) | 0.491005 | + | 0.203539i | 0.0293957 | + | 0.0121855i | ||||
\(280\) | −2.19168 | + | 2.19168i | −0.130978 | + | 0.130978i | ||||
\(281\) | 11.3699 | + | 11.3699i | 0.678270 | + | 0.678270i | 0.959609 | − | 0.281339i | \(-0.0907784\pi\) |
−0.281339 | + | 0.959609i | \(0.590778\pi\) | |||||||
\(282\) | −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 | ||||||||
\(288\) | 1.14881 | − | 2.77132i | 0.0676943 | − | 0.163302i | ||||
\(289\) | −3.44353 | −0.202561 | ||||||||
\(290\) | 29.4609 | 1.73000 | ||||||||
\(291\) | 2.44099 | − | 3.65211i | 0.143093 | − | 0.214090i | ||||
\(292\) | −3.59354 | − | 3.59354i | −0.210296 | − | 0.210296i | ||||
\(293\) | −10.3404 | − | 10.3404i | −0.604092 | − | 0.604092i | 0.337304 | − | 0.941396i | \(-0.390485\pi\) |
−0.941396 | + | 0.337304i | \(0.890485\pi\) | |||||||
\(294\) | −0.962473 | + | 1.44002i | −0.0561326 | + | 0.0839834i | ||||
\(295\) | 6.54072 | 0.380815 | ||||||||
\(296\) | 0.464238 | 0.0269833 | ||||||||
\(297\) | 1.83414 | − | 9.20107i | 0.106427 | − | 0.533900i | ||||
\(298\) | − | 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 | ||||
\(306\) | 4.22981 | − | 10.2038i | 0.241802 | − | 0.583311i | ||||
\(307\) | −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 | \(-0.713985\pi\) | ||||
−0.622752 | + | 0.782420i | \(0.713985\pi\) | |||||||
\(312\) | 0.827215 | − | 6.18997i | 0.0468318 | − | 0.350438i | ||||
\(313\) | −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 | −0.0106369 | − | 0.999943i | \(-0.503386\pi\) |
0.999943 | + | 0.0106369i | \(0.00338588\pi\) | |||||||
\(318\) | 5.38749 | − | 8.06055i | 0.302115 | − | 0.452013i | ||||
\(319\) | −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 | ||||||
\(327\) | −15.0567 | + | 22.5273i | −0.832639 | + | 1.24576i | ||||
\(328\) | −3.13663 | −0.173192 | ||||||||
\(329\) | −1.13948 | −0.0628217 | ||||||||
\(330\) | −8.05892 | − | 5.38639i | −0.443629 | − | 0.296511i | ||||
\(331\) | −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 | ||||
\(333\) | 0.533321 | − | 1.28655i | 0.0292258 | − | 0.0705028i | ||||
\(334\) | 14.3809 | 0.786888 | ||||||||
\(335\) | 46.6548 | 2.54902 | ||||||||
\(336\) | −1.44002 | − | 0.962473i | −0.0785593 | − | 0.0525072i | ||||
\(337\) | 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 | ||||
\(345\) | −36.4127 | − | 24.3374i | −1.96039 | − | 1.31028i | ||||
\(346\) | 6.17263 | − | 6.17263i | 0.331843 | − | 0.331843i | ||||
\(347\) | − | 8.56153i | − | 0.459607i | −0.973237 | − | 0.229803i | \(-0.926192\pi\) | ||
0.973237 | − | 0.229803i | \(-0.0738083\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | −16.2041 | − | 9.40358i | −0.864911 | − | 0.501926i | ||||
\(352\) | 1.80559 | 0.0962380 | ||||||||
\(353\) | −1.70236 | + | 1.70236i | −0.0906076 | + | 0.0906076i | −0.750958 | − | 0.660350i | \(-0.770408\pi\) |
0.660350 | + | 0.750958i | \(0.270408\pi\) | |||||||
\(354\) | 0.712576 | + | 3.58493i | 0.0378730 | + | 0.190537i | ||||
\(355\) | 3.29731i | 0.175003i | ||||||||
\(356\) | −3.19016 | + | 3.19016i | −0.169078 | + | 0.169078i | ||||
\(357\) | −5.30201 | − | 3.54374i | −0.280612 | − | 0.187555i | ||||
\(358\) | 15.1565 | − | 15.1565i | 0.801048 | − | 0.801048i | ||||
\(359\) | 19.7911 | + | 19.7911i | 1.04453 | + | 1.04453i | 0.998961 | + | 0.0455713i | \(0.0145108\pi\) |
0.0455713 | + | 0.998961i | \(0.485489\pi\) | |||||||
\(360\) | −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 | ||||||||
\(366\) | 11.7298 | + | 7.83989i | 0.613124 | + | 0.409798i | ||||
\(367\) | −18.1422 | −0.947016 | −0.473508 | − | 0.880790i | \(-0.657012\pi\) | ||||
−0.473508 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(368\) | 8.15820 | 0.425275 | ||||||||
\(369\) | −3.60340 | + | 8.69263i | −0.187585 | + | 0.452520i | ||||
\(370\) | −1.01746 | − | 1.01746i | −0.0528952 | − | 0.0528952i | ||||
\(371\) | −3.95806 | − | 3.95806i | −0.205492 | − | 0.205492i | ||||
\(372\) | 0.255133 | + | 0.170525i | 0.0132280 | + | 0.00884130i | ||||
\(373\) | −27.3139 | −1.41426 | −0.707130 | − | 0.707083i | \(-0.750011\pi\) | ||||
−0.707130 | + | 0.707083i | \(0.750011\pi\) | |||||||
\(374\) | 6.64800 | 0.343760 | ||||||||
\(375\) | −1.17272 | + | 1.75457i | −0.0605588 | + | 0.0906058i | ||||
\(376\) | − | 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 | −0.998398 | − | 0.0565899i | \(-0.981977\pi\) |
0.0565899 | + | 0.998398i | \(0.481977\pi\) | |||||||
\(384\) | 0.962473 | − | 1.44002i | 0.0491160 | − | 0.0734855i | ||||
\(385\) | −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 | \(-0.609679\pi\) | ||||
−0.337790 | + | 0.941222i | \(0.609679\pi\) | |||||||
\(390\) | −15.3794 | + | 11.7534i | −0.778766 | + | 0.595158i | ||||
\(391\) | 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 | ||||
\(396\) | 2.07427 | − | 5.00386i | 0.104236 | − | 0.251454i | ||||
\(397\) | −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 | 0.715845 | − | 0.698259i | \(-0.246042\pi\) |
−0.698259 | + | 0.715845i | \(0.746042\pi\) | |||||||
\(402\) | 5.08279 | + | 25.5712i | 0.253506 | + | 1.27538i | ||||
\(403\) | 0.604533 | + | 0.206435i | 0.0301140 | + | 0.0102833i | ||||
\(404\) | 8.55213i | 0.425484i | ||||||||
\(405\) | −0.0152839 | + | 27.8955i | −0.000759463 | + | 1.38614i | ||||
\(406\) | 9.50505 | 0.471728 | ||||||||
\(407\) | 0.838222 | 0.0415491 | ||||||||
\(408\) | 3.54374 | − | 5.30201i | 0.175441 | − | 0.262489i | ||||
\(409\) | −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 | ||||
\(411\) | 19.3559 | − | 28.9595i | 0.954754 | − | 1.42847i | ||||
\(412\) | 6.72083 | 0.331112 | ||||||||
\(413\) | 2.11025 | 0.103839 | ||||||||
\(414\) | 9.37222 | − | 22.6090i | 0.460619 | − | 1.11117i | ||||
\(415\) | − | 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 | \(-0.924582\pi\) | ||
0.972063 | − | 0.234721i | \(-0.0754175\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | −3.15788 | − | 1.30905i | −0.153541 | − | 0.0636481i | ||||
\(424\) | 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 | ||||||||
\(429\) | 1.49361 | − | 11.1765i | 0.0721120 | − | 0.539607i | ||||
\(430\) | −4.43619 | −0.213932 | ||||||||
\(431\) | −6.40858 | + | 6.40858i | −0.308690 | + | 0.308690i | −0.844401 | − | 0.535711i | \(-0.820044\pi\) |
0.535711 | + | 0.844401i | \(0.320044\pi\) | |||||||
\(432\) | −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 | ||||
\(435\) | 28.3553 | − | 42.4241i | 1.35953 | − | 2.03408i | ||||
\(436\) | −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 | \(0.0501967\pi\) | ||||
−0.987591 | + | 0.157045i | \(0.949803\pi\) | |||||||
\(444\) | 0.446817 | − | 0.668510i | 0.0212050 | − | 0.0317261i | ||||
\(445\) | 13.9836 | 0.662886 | ||||||||
\(446\) | 16.8948 | 0.799992 | ||||||||
\(447\) | −7.58057 | − | 5.06668i | −0.358549 | − | 0.239646i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | 15.0860 | + | 15.0860i | 0.711951 | + | 0.711951i | 0.966943 | − | 0.254992i | \(-0.0820728\pi\) |
−0.254992 | + | 0.966943i | \(0.582073\pi\) | |||||||
\(450\) | 12.7672 | + | 5.29244i | 0.601851 | + | 0.249488i | ||||
\(451\) | −5.66346 | −0.266682 | ||||||||
\(452\) | 19.2385 | 0.904902 | ||||||||
\(453\) | 31.0472 | + | 20.7512i | 1.45873 | + | 0.974978i | ||||
\(454\) | 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 | −0.372403 | − | 0.928071i | \(-0.621466\pi\) |
0.928071 | + | 0.372403i | \(0.121466\pi\) | |||||||
\(462\) | −2.60007 | − | 1.73783i | −0.120966 | − | 0.0808511i | ||||
\(463\) | 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 | \(-0.415152\pi\) | ||||
0.263411 | + | 0.964684i | \(0.415152\pi\) | |||||||
\(468\) | −8.11748 | − | 7.14888i | −0.375231 | − | 0.330457i | ||||
\(469\) | 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 | ||||
\(474\) | −6.31970 | − | 4.22394i | −0.290274 | − | 0.194012i | ||||
\(475\) | 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 | \(0.00132496\pi\) |
0.00416246 | + | 0.999991i | \(0.498675\pi\) | |||||||
\(480\) | −5.26548 | + | 1.04662i | −0.240335 | + | 0.0477714i | ||||
\(481\) | 0.540911 | − | 1.58403i | 0.0246634 | − | 0.0722254i | ||||
\(482\) | − | 20.9775i | − | 0.955499i | ||||||
\(483\) | −11.7479 | − | 7.85205i | −0.534550 | − | 0.357281i | ||||
\(484\) | −7.73986 | −0.351812 | ||||||||
\(485\) | −7.86082 | −0.356942 | ||||||||
\(486\) | −15.2910 | + | 3.03069i | −0.693614 | + | 0.137475i | ||||
\(487\) | −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 | ||||
\(489\) | −33.4261 | − | 22.3413i | −1.51158 | − | 1.01031i | ||||
\(490\) | 3.09950 | 0.140021 | ||||||||
\(491\) | −24.6630 | −1.11303 | −0.556513 | − | 0.830839i | \(-0.687861\pi\) | ||||
−0.556513 | + | 0.830839i | \(0.687861\pi\) | |||||||
\(492\) | −3.01893 | + | 4.51680i | −0.136104 | + | 0.203633i | ||||
\(493\) | 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 | ||||
\(501\) | 13.8412 | − | 20.7087i | 0.618380 | − | 0.925197i | ||||
\(502\) | −18.4080 | + | 18.4080i | −0.821589 | + | 0.821589i | ||||
\(503\) | − | 34.2723i | − | 1.52813i | −0.645141 | − | 0.764064i | \(-0.723201\pi\) | ||
0.645141 | − | 0.764064i | \(-0.276799\pi\) | |||||||
\(504\) | −2.77195 | + | 1.14729i | −0.123473 | + | 0.0511044i | ||||
\(505\) | 18.7435 | − | 18.7435i | 0.834075 | − | 0.834075i | ||||
\(506\) | 14.7303 | 0.654843 | ||||||||
\(507\) | −20.1569 | − | 10.0348i | −0.895201 | − | 0.445663i | ||||
\(508\) | 12.4807 | 0.553743 | ||||||||
\(509\) | −3.24519 | + | 3.24519i | −0.143840 | + | 0.143840i | −0.775360 | − | 0.631520i | \(-0.782432\pi\) |
0.631520 | + | 0.775360i | \(0.282432\pi\) | |||||||
\(510\) | −19.3870 | + | 3.85356i | −0.858472 | + | 0.170638i | ||||
\(511\) | 5.08204i | 0.224816i | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −7.56985 | + | 37.9747i | −0.334217 | + | 1.67662i | ||||
\(514\) | −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 | \(-0.570031\pi\) | ||
0.218238 | − | 0.975896i | \(-0.429969\pi\) | |||||||
\(522\) | 26.3416 | + | 10.9195i | 1.15294 | + | 0.477933i | ||||
\(523\) | 16.3414 | 0.714560 | 0.357280 | − | 0.933997i | \(-0.383704\pi\) | ||||
0.357280 | + | 0.933997i | \(0.383704\pi\) | |||||||
\(524\) | −8.33777 | −0.364237 | ||||||||
\(525\) | 4.43401 | − | 6.63400i | 0.193516 | − | 0.289531i | ||||
\(526\) | 8.46778 | + | 8.46778i | 0.369213 | + | 0.369213i | ||||
\(527\) | 0.461272 | + | 0.461272i | 0.0200933 | + | 0.0200933i | ||||
\(528\) | 1.73783 | − | 2.60007i | 0.0756292 | − | 0.113154i | ||||
\(529\) | 43.5562 | 1.89375 | ||||||||
\(530\) | −17.3496 | −0.753618 | ||||||||
\(531\) | 5.84819 | + | 2.42428i | 0.253790 | + | 0.105205i | ||||
\(532\) | 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 | ||||
\(540\) | −3.14851 | + | 15.7947i | −0.135490 | + | 0.679696i | ||||
\(541\) | 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 | ||||||||
\(546\) | −4.96190 | + | 3.79204i | −0.212350 | + | 0.162284i | ||||
\(547\) | 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 | ||||
\(552\) | 7.85205 | − | 11.7479i | 0.334205 | − | 0.500025i | ||||
\(553\) | −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 | 0.624255 | − | 0.781220i | \(-0.285402\pi\) |
−0.781220 | + | 0.624255i | \(0.785402\pi\) | |||||||
\(558\) | 0.491117 | − | 0.203270i | 0.0207906 | − | 0.00860509i | ||||
\(559\) | −2.27402 | − | 4.63243i | −0.0961809 | − | 0.195931i | ||||
\(560\) | 3.09950i | 0.130978i | ||||||||
\(561\) | 6.39853 | − | 9.57323i | 0.270146 | − | 0.404182i | ||||
\(562\) | 16.0794 | 0.678270 | ||||||||
\(563\) | −15.3860 | −0.648443 | −0.324221 | − | 0.945981i | \(-0.605102\pi\) | ||||
−0.324221 | + | 0.945981i | \(0.605102\pi\) | |||||||
\(564\) | −1.64087 | − | 1.09672i | −0.0690932 | − | 0.0461803i | ||||
\(565\) | −42.1645 | − | 42.1645i | −1.77388 | − | 1.77388i | ||||
\(566\) | 14.0926 | + | 14.0926i | 0.592357 | + | 0.592357i | ||||
\(567\) | −0.00493109 | + | 9.00000i | −0.000207086 | + | 0.377964i | ||||
\(568\) | −1.06382 | −0.0446369 | ||||||||
\(569\) | −33.4793 | −1.40353 | −0.701763 | − | 0.712410i | \(-0.747603\pi\) | ||||
−0.701763 | + | 0.712410i | \(0.747603\pi\) | |||||||
\(570\) | 33.2608 | + | 22.2307i | 1.39314 | + | 0.931143i | ||||
\(571\) | 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 | ||||
\(579\) | −29.3365 | − | 19.6078i | −1.21918 | − | 0.814873i | ||||
\(580\) | 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 | ||||||||
\(585\) | 2.12286 | + | 33.4589i | 0.0877693 | + | 1.38336i | ||||
\(586\) | −14.6235 | −0.604092 | ||||||||
\(587\) | 4.03302 | − | 4.03302i | 0.166460 | − | 0.166460i | −0.618961 | − | 0.785422i | \(-0.712446\pi\) |
0.785422 | + | 0.618961i | \(0.212446\pi\) | |||||||
\(588\) | 0.337674 | + | 1.69882i | 0.0139254 | + | 0.0700580i | ||||
\(589\) | − | 1.32030i | − | 0.0544020i | ||||||
\(590\) | 4.62499 | − | 4.62499i | 0.190408 | − | 0.190408i | ||||
\(591\) | 14.1194 | + | 9.43707i | 0.580794 | + | 0.388189i | ||||
\(592\) | 0.328266 | − | 0.328266i | 0.0134917 | − | 0.0134917i | ||||
\(593\) | −1.35646 | − | 1.35646i | −0.0557030 | − | 0.0557030i | 0.678707 | − | 0.734410i | \(-0.262541\pi\) |
−0.734410 | + | 0.678707i | \(0.762541\pi\) | |||||||
\(594\) | −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 | \(0.129607\pi\) | ||||
−0.918244 | + | 0.396014i | \(0.870393\pi\) | |||||||
\(600\) | 6.63400 | + | 4.43401i | 0.270832 | + | 0.181018i | ||||
\(601\) | −37.2292 | −1.51861 | −0.759306 | − | 0.650734i | \(-0.774461\pi\) | ||||
−0.759306 | + | 0.650734i | \(0.774461\pi\) | |||||||
\(602\) | −1.43126 | −0.0583338 | ||||||||
\(603\) | 41.7150 | + | 17.2923i | 1.69877 | + | 0.704197i | ||||
\(604\) | 15.2455 | + | 15.2455i | 0.620329 | + | 0.620329i | ||||
\(605\) | 16.9633 | + | 16.9633i | 0.689655 | + | 0.689655i | ||||
\(606\) | 12.3152 | + | 8.23120i | 0.500271 | + | 0.334370i | ||||
\(607\) | −15.3314 | −0.622284 | −0.311142 | − | 0.950363i | \(-0.600711\pi\) | ||||
−0.311142 | + | 0.950363i | \(0.600711\pi\) | |||||||
\(608\) | −7.45201 | −0.302219 | ||||||||
\(609\) | 9.14836 | − | 13.6874i | 0.370710 | − | 0.554642i | ||||
\(610\) | − | 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 | −0.692378 | − | 0.721535i | \(-0.743437\pi\) |
0.721535 | + | 0.692378i | \(0.243437\pi\) | |||||||
\(618\) | 6.46862 | − | 9.67811i | 0.260206 | − | 0.389311i | ||||
\(619\) | −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 | ||||||||
\(624\) | −3.79204 | − | 4.96190i | −0.151803 | − | 0.198635i | ||||
\(625\) | 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 | ||||
\(630\) | 8.58971 | + | 3.56073i | 0.342222 | + | 0.141863i | ||||
\(631\) | −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 | ||||||||
\(639\) | −1.22213 | + | 2.94819i | −0.0483466 | + | 0.116629i | ||||
\(640\) | −3.09950 | −0.122518 | ||||||||
\(641\) | −12.1939 | −0.481630 | −0.240815 | − | 0.970571i | \(-0.577415\pi\) | ||||
−0.240815 | + | 0.970571i | \(0.577415\pi\) | |||||||
\(642\) | −7.35808 | + | 11.0089i | −0.290400 | + | 0.434486i | ||||
\(643\) | 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 | ||||
\(645\) | −4.26971 | + | 6.38818i | −0.168120 | + | 0.251534i | ||||
\(646\) | −27.4377 | −1.07952 | ||||||||
\(647\) | 18.5157 | 0.727925 | 0.363963 | − | 0.931414i | \(-0.381424\pi\) | ||||
0.363963 | + | 0.931414i | \(0.381424\pi\) | |||||||
\(648\) | −9.00000 | − | 0.00493109i | −0.353553 | − | 0.000193711i | ||||
\(649\) | 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 | \(-0.687293\pi\) | ||
0.555028 | − | 0.831831i | \(-0.312707\pi\) | |||||||
\(654\) | 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 | ||||
\(657\) | −5.83829 | + | 14.0840i | −0.227774 | + | 0.549468i | ||||
\(658\) | −0.805736 | + | 0.805736i | −0.0314109 | + | 0.0314109i | ||||
\(659\) | 26.7078i | 1.04039i | 0.854049 | + | 0.520193i | \(0.174140\pi\) | ||||
−0.854049 | + | 0.520193i | \(0.825860\pi\) | |||||||
\(660\) | −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 | ||||||||
\(663\) | −13.9620 | − | 18.2693i | −0.542237 | − | 0.709520i | ||||
\(664\) | 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 | ||||
\(669\) | 16.2608 | − | 24.3288i | 0.628678 | − | 0.940604i | ||||
\(670\) | 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 | \(0.0429726\pi\) | ||||
−0.990901 | + | 0.134593i | \(0.957027\pi\) | |||||||
\(678\) | 18.5165 | − | 27.7037i | 0.711123 | − | 1.06396i | ||||
\(679\) | −2.53616 | −0.0973289 | ||||||||
\(680\) | −11.4121 | −0.437633 | ||||||||
\(681\) | 37.9717 | + | 25.3794i | 1.45508 | + | 0.972542i | ||||
\(682\) | 0.226205 | + | 0.226205i | 0.00866183 | + | 0.00866183i | ||||
\(683\) | 2.50202 | + | 2.50202i | 0.0957372 | + | 0.0957372i | 0.753353 | − | 0.657616i | \(-0.228435\pi\) |
−0.657616 | + | 0.753353i | \(0.728435\pi\) | |||||||
\(684\) | −8.56095 | + | 20.6519i | −0.327336 | + | 0.789647i | ||||
\(685\) | −62.3326 | −2.38161 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 3.94733 | + | 2.63830i | 0.150600 | + | 0.100658i | ||||
\(688\) | − | 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 | ||||
\(696\) | 13.6874 | + | 9.14836i | 0.518820 | + | 0.346768i | ||||
\(697\) | −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 | \(-0.817273\pi\) | ||||
−0.839706 | + | 0.543041i | \(0.817273\pi\) | |||||||
\(702\) | −18.1074 | + | 4.80869i | −0.683418 | + | 0.181492i | ||||
\(703\) | −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 | ||||
\(708\) | 3.03879 | + | 2.03106i | 0.114205 | + | 0.0763319i | ||||
\(709\) | 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 | ||||||
\(717\) | −6.00667 | − | 4.01472i | −0.224323 | − | 0.149933i | ||||
\(718\) | 27.9888 | 1.04453 | ||||||||
\(719\) | −6.18328 | −0.230598 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(720\) | −3.56073 | + | 8.58971i | −0.132701 | + | 0.320120i | ||||
\(721\) | −4.75235 | − | 4.75235i | −0.176987 | − | 0.176987i | ||||
\(722\) | 25.8324 | + | 25.8324i | 0.961382 | + | 0.961382i | ||||
\(723\) | −30.2079 | − | 20.1903i | −1.12345 | − | 0.750885i | ||||
\(724\) | 7.53227 | 0.279935 | ||||||||
\(725\) | −43.7887 | −1.62627 | ||||||||
\(726\) | −7.44941 | + | 11.1455i | −0.276473 | + | 0.413649i | ||||
\(727\) | − | 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 | ||||
\(735\) | 2.98318 | − | 4.46333i | 0.110036 | − | 0.164632i | ||||
\(736\) | 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 | ||||||||
\(741\) | −6.16442 | + | 46.1277i | −0.226456 | + | 1.69454i | ||||
\(742\) | −5.59755 | −0.205492 | ||||||||
\(743\) | 1.32188 | − | 1.32188i | 0.0484952 | − | 0.0484952i | −0.682443 | − | 0.730939i | \(-0.739083\pi\) |
0.730939 | + | 0.682443i | \(0.239083\pi\) | |||||||
\(744\) | 0.300985 | − | 0.0598268i | 0.0110347 | − | 0.00219336i | ||||
\(745\) | 16.3165i | 0.597789i | ||||||||
\(746\) | −19.3138 | + | 19.3138i | −0.707130 | + | 0.707130i | ||||
\(747\) | 15.1928 | − | 36.6502i | 0.555874 | − | 1.34096i | ||||
\(748\) | 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 | ||||||
\(756\) | −1.01581 | + | 5.09589i | −0.0369448 | + | 0.185336i | ||||
\(757\) | 16.6501 | 0.605159 | 0.302579 | − | 0.953124i | \(-0.402152\pi\) | ||||
0.302579 | + | 0.953124i | \(0.402152\pi\) | |||||||
\(758\) | 15.6243 | 0.567502 | ||||||||
\(759\) | 14.1775 | − | 21.2119i | 0.514612 | − | 0.769943i | ||||
\(760\) | 16.3324 | + | 16.3324i | 0.592439 | + | 0.592439i | ||||
\(761\) | 0.381043 | + | 0.381043i | 0.0138128 | + | 0.0138128i | 0.713979 | − | 0.700167i | \(-0.246891\pi\) |
−0.700167 | + | 0.713979i | \(0.746891\pi\) | |||||||
\(762\) | 12.0124 | − | 17.9725i | 0.435162 | − | 0.651073i | ||||
\(763\) | 15.6438 | 0.566344 | ||||||||
\(764\) | 1.80118 | 0.0651645 | ||||||||
\(765\) | −13.1103 | + | 31.6266i | −0.474004 | + | 1.14346i | ||||
\(766\) | 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 | −0.984541 | − | 0.175151i | \(-0.943958\pi\) |
0.175151 | + | 0.984541i | \(0.443958\pi\) | |||||||
\(774\) | −3.96648 | − | 1.64424i | −0.142572 | − | 0.0591011i | ||||
\(775\) | −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 | ||||||||
\(780\) | −2.56395 | + | 19.1858i | −0.0918042 | + | 0.686962i | ||||
\(781\) | −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 | ||||
\(786\) | −8.02488 | + | 12.0065i | −0.286238 | + | 0.428259i | ||||
\(787\) | −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 | ||||||||
\(795\) | −16.6985 | + | 24.9837i | −0.592235 | + | 0.886080i | ||||
\(796\) | 10.2593 | 0.363631 | ||||||||
\(797\) | −38.7028 | −1.37092 | −0.685461 | − | 0.728109i | \(-0.740399\pi\) | ||||
−0.685461 | + | 0.728109i | \(0.740399\pi\) | |||||||
\(798\) | 10.7310 | + | 7.17236i | 0.379874 | + | 0.253899i | ||||
\(799\) | −2.96665 | − | 2.96665i | −0.104952 | − | 0.104952i | ||||
\(800\) | 3.25756 | + | 3.25756i | 0.115172 | + | 0.115172i | ||||
\(801\) | 12.5030 | + | 5.18293i | 0.441772 | + | 0.183130i | ||||
\(802\) | 0.498008 | 0.0175853 | ||||||||
\(803\) | −9.17605 | −0.323816 | ||||||||
\(804\) | 21.6756 | + | 14.4875i | 0.764441 | + | 0.510935i | ||||
\(805\) | 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 | \(0.171988\pi\) | ||||
−0.857546 | + | 0.514407i | \(0.828012\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | −19.9583 | − | 13.3396i | −0.699967 | − | 0.467841i | ||||
\(814\) | 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 | ||||||||
\(819\) | 0.684903 | + | 10.7949i | 0.0239325 | + | 0.377206i | ||||
\(820\) | 9.72199 | 0.339507 | ||||||||
\(821\) | 5.05583 | − | 5.05583i | 0.176450 | − | 0.176450i | −0.613357 | − | 0.789806i | \(-0.710181\pi\) |
0.789806 | + | 0.613357i | \(0.210181\pi\) | |||||||
\(822\) | −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 | ||||
\(825\) | 11.9782 | + | 8.00598i | 0.417029 | + | 0.278733i | ||||
\(826\) | 1.49217 | − | 1.49217i | 0.0519193 | − | 0.0519193i | ||||
\(827\) | −11.3749 | − | 11.3749i | −0.395543 | − | 0.395543i | 0.481115 | − | 0.876658i | \(-0.340232\pi\) |
−0.876658 | + | 0.481115i | \(0.840232\pi\) | |||||||
\(828\) | −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 | ||||||||
\(834\) | −7.97621 | − | 5.33111i | −0.276193 | − | 0.184601i | ||||
\(835\) | −44.5736 | −1.54253 | ||||||||
\(836\) | −13.4552 | −0.465360 | ||||||||
\(837\) | 0.179975 | − | 0.902857i | 0.00622085 | − | 0.0312073i | ||||
\(838\) | −6.79475 | − | 6.79475i | −0.234721 | − | 0.234721i | ||||
\(839\) | 2.49384 | + | 2.49384i | 0.0860970 | + | 0.0860970i | 0.748844 | − | 0.662747i | \(-0.230609\pi\) |
−0.662747 | + | 0.748844i | \(0.730609\pi\) | |||||||
\(840\) | 4.46333 | + | 2.98318i | 0.153999 | + | 0.102930i | ||||
\(841\) | −61.3460 | −2.11538 | ||||||||
\(842\) | −14.3759 | −0.495425 | ||||||||
\(843\) | 15.4760 | − | 23.1546i | 0.533023 | − | 0.797488i | ||||
\(844\) | 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 | ||||
\(852\) | −1.02390 | + | 1.53192i | −0.0350782 | + | 0.0524827i | ||||
\(853\) | 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 | \(-0.757561\pi\) | ||||
−0.723701 | + | 0.690113i | \(0.757561\pi\) | |||||||
\(858\) | −6.84685 | − | 8.95913i | −0.233748 | − | 0.305860i | ||||
\(859\) | −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 | −0.960583 | − | 0.277992i | \(-0.910331\pi\) |
0.277992 | + | 0.960583i | \(0.410331\pi\) | |||||||
\(864\) | −5.09589 | − | 1.01581i | −0.173366 | − | 0.0345587i | ||||
\(865\) | −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 | ||||||||
\(873\) | −7.02852 | − | 2.91356i | −0.237879 | − | 0.0986092i | ||||
\(874\) | −60.7950 | −2.05642 | ||||||||
\(875\) | 1.21844 | 0.0411908 | ||||||||
\(876\) | −4.89132 | + | 7.31821i | −0.165263 | + | 0.247260i | ||||
\(877\) | 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 | ||||
\(879\) | −14.0747 | + | 21.0581i | −0.474729 | + | 0.710272i | ||||
\(880\) | −5.59641 | −0.188655 | ||||||||
\(881\) | −1.97857 | −0.0666596 | −0.0333298 | − | 0.999444i | \(-0.510611\pi\) | ||||
−0.0333298 | + | 0.999444i | \(0.510611\pi\) | |||||||
\(882\) | 2.77132 | + | 1.14881i | 0.0933153 | + | 0.0386824i | ||||
\(883\) | − | 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 | \(-0.891808\pi\) | ||
0.942789 | − | 0.333389i | \(-0.108192\pi\) | |||||||
\(888\) | −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 | ||||
\(891\) | −16.2503 | − | 0.00890350i | −0.544404 | − | 0.000298279i | ||||
\(892\) | 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 | ||||||||
\(897\) | −30.9362 | − | 40.4802i | −1.03293 | − | 1.35159i | ||||
\(898\) | 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 | ||||
\(903\) | −1.37755 | + | 2.06104i | −0.0458420 | + | 0.0685870i | ||||
\(904\) | 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 | \(-0.963588\pi\) | ||
0.993464 | − | 0.114143i | \(-0.0364122\pi\) | |||||||
\(912\) | −7.17236 | + | 10.7310i | −0.237501 | + | 0.355340i | ||||
\(913\) | 23.8785 | 0.790262 | ||||||||
\(914\) | −26.1460 | −0.864831 | ||||||||
\(915\) | −36.3564 | − | 24.2997i | −1.20190 | − | 0.803325i | ||||
\(916\) | 1.93830 | + | 1.93830i | 0.0640433 | + | 0.0640433i | ||||
\(917\) | 5.89570 | + | 5.89570i | 0.194693 | + | 0.194693i | ||||
\(918\) | −18.7626 | − | 3.74013i | −0.619259 | − | 0.123443i | ||||
\(919\) | 25.9569 | 0.856239 | 0.428119 | − | 0.903722i | \(-0.359176\pi\) | ||||
0.428119 | + | 0.903722i | \(0.359176\pi\) | |||||||
\(920\) | −25.2863 | −0.833665 | ||||||||
\(921\) | 12.4282 | + | 8.30675i | 0.409525 | + | 0.273717i | ||||
\(922\) | − | 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 | −0.710186 | − | 0.704015i | \(-0.751389\pi\) |
0.704015 | + | 0.710186i | \(0.251389\pi\) | |||||||
\(930\) | −0.790783 | − | 0.528541i | −0.0259308 | − | 0.0173316i | ||||
\(931\) | 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 | ||||||||
\(936\) | −10.7949 | + | 0.684903i | −0.352844 | + | 0.0223868i | ||||
\(937\) | −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 | −0.553279 | − | 0.832996i | \(-0.686624\pi\) |
0.832996 | + | 0.553279i | \(0.186624\pi\) | |||||||
\(942\) | 14.8077 | + | 9.89715i | 0.482462 | + | 0.322466i | ||||
\(943\) | −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 | 0.897552 | − | 0.440908i | \(-0.145344\pi\) |
−0.440908 | + | 0.897552i | \(0.645344\pi\) | |||||||
\(948\) | −7.45549 | + | 1.48193i | −0.242143 | + | 0.0481307i | ||||
\(949\) | −5.92138 | + | 17.3404i | −0.192216 | + | 0.562893i | ||||
\(950\) | − | 34.3306i | − | 1.11383i | ||||||
\(951\) | −35.8709 | − | 23.9753i | −1.16319 | − | 0.777453i | ||||
\(952\) | −3.68191 | −0.119331 | ||||||||
\(953\) | −55.9530 | −1.81250 | −0.906248 | − | 0.422747i | \(-0.861066\pi\) | ||||
−0.906248 | + | 0.422747i | \(0.861066\pi\) | |||||||
\(954\) | −15.5126 | − | 6.43051i | −0.502239 | − | 0.208196i | ||||
\(955\) | −3.94761 | − | 3.94761i | −0.127742 | − | 0.127742i | ||||
\(956\) | −2.94952 | − | 2.94952i | −0.0953944 | − | 0.0953944i | ||||
\(957\) | 24.7138 | + | 16.5181i | 0.798884 | + | 0.533956i | ||||
\(958\) | 31.0801 | 1.00415 | ||||||||
\(959\) | −20.1105 | −0.649404 | ||||||||
\(960\) | −2.98318 | + | 4.46333i | −0.0962818 | + | 0.144053i | ||||
\(961\) | − | 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 | ||||
\(969\) | −26.4080 | + | 39.5107i | −0.848347 | + | 1.26927i | ||||
\(970\) | −5.55844 | + | 5.55844i | −0.178471 | + | 0.178471i | ||||
\(971\) | − | 17.7506i | − | 0.569645i | −0.958580 | − | 0.284823i | \(-0.908065\pi\) | ||
0.958580 | − | 0.284823i | \(-0.0919347\pi\) | |||||||
\(972\) | −8.66936 | + | 12.9554i | −0.278070 | + | 0.415544i | ||||
\(973\) | −3.91664 | + | 3.91664i | −0.125562 | + | 0.125562i | ||||
\(974\) | −30.7803 | −0.986263 | ||||||||
\(975\) | 22.8589 | − | 17.4695i | 0.732071 | − | 0.559472i | ||||
\(976\) | 8.14557 | 0.260733 | ||||||||
\(977\) | 8.56492 | − | 8.56492i | 0.274016 | − | 0.274016i | −0.556699 | − | 0.830715i | \(-0.687932\pi\) |
0.830715 | + | 0.556699i | \(0.187932\pi\) | |||||||
\(978\) | −39.4335 | + | 7.83820i | −1.26094 | + | 0.250638i | ||||
\(979\) | 8.14602i | 0.260348i | ||||||||
\(980\) | 2.19168 | − | 2.19168i | 0.0700105 | − | 0.0700105i | ||||
\(981\) | 43.3540 | + | 17.9717i | 1.38419 | + | 0.573794i | ||||
\(982\) | −17.4394 | + | 17.4394i | −0.556513 | + | 0.556513i | ||||
\(983\) | 4.10551 | + | 4.10551i | 0.130945 | + | 0.130945i | 0.769542 | − | 0.638596i | \(-0.220485\pi\) |
−0.638596 | + | 0.769542i | \(0.720485\pi\) | |||||||
\(984\) | 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 | ||||||
\(990\) | −6.42921 | + | 15.5095i | −0.204334 | + | 0.492923i | ||||
\(991\) | 60.0976 | 1.90906 | 0.954532 | − | 0.298108i | \(-0.0963555\pi\) | ||||
0.954532 | + | 0.298108i | \(0.0963555\pi\) | |||||||
\(992\) | 0.177174 | 0.00562527 | ||||||||
\(993\) | −22.3177 | + | 33.3908i | −0.708229 | + | 1.05963i | ||||
\(994\) | 0.752235 | + | 0.752235i | 0.0238594 | + | 0.0238594i | ||||
\(995\) | −22.4851 | − | 22.4851i | −0.712824 | − | 0.712824i | ||||
\(996\) | 12.7285 | − | 19.0439i | 0.403318 | − | 0.603429i | ||||
\(997\) | 55.3278 | 1.75225 | 0.876124 | − | 0.482086i | \(-0.160121\pi\) | ||||
0.876124 | + | 0.482086i | \(0.160121\pi\) | |||||||
\(998\) | 43.3263 | 1.37147 | ||||||||
\(999\) | −2.36571 | − | 0.471579i | −0.0748477 | − | 0.0149201i |
(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.c.281.8 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.d.281.3 | yes | 20 | ||
13.5 | odd | 4 | 546.2.p.d.239.3 | yes | 20 | ||
39.5 | even | 4 | inner | 546.2.p.c.239.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.8 | ✓ | 20 | 39.5 | even | 4 | inner | |
546.2.p.c.281.8 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.p.d.239.3 | yes | 20 | 13.5 | odd | 4 | ||
546.2.p.d.281.3 | yes | 20 | 3.2 | odd | 2 |