Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(1.40744 - 0.138282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.361 |
Dual form | 637.2.u.h.30.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10554 | − | 0.638282i | −0.781733 | − | 0.451334i | 0.0553113 | − | 0.998469i | \(-0.482385\pi\) |
−0.837044 | + | 0.547136i | \(0.815718\pi\) | |||||||
\(3\) | −1.16793 | −0.674302 | −0.337151 | − | 0.941451i | \(-0.609463\pi\) | ||||
−0.337151 | + | 0.941451i | \(0.609463\pi\) | |||||||
\(4\) | −0.185192 | − | 0.320762i | −0.0925960 | − | 0.160381i | ||||
\(5\) | −1.57173 | + | 0.907437i | −0.702897 | + | 0.405818i | −0.808426 | − | 0.588598i | \(-0.799680\pi\) |
0.105528 | + | 0.994416i | \(0.466347\pi\) | |||||||
\(6\) | 1.29118 | + | 0.745466i | 0.527124 | + | 0.304335i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.02595i | 1.06983i | ||||||||
\(9\) | −1.63595 | −0.545317 | ||||||||
\(10\) | 2.31680 | 0.732637 | ||||||||
\(11\) | − | 2.77849i | − | 0.837747i | −0.908045 | − | 0.418874i | \(-0.862425\pi\) | ||
0.908045 | − | 0.418874i | \(-0.137575\pi\) | |||||||
\(12\) | 0.216290 | + | 0.374626i | 0.0624377 | + | 0.108145i | ||||
\(13\) | −3.58305 | − | 0.402155i | −0.993760 | − | 0.111538i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.83566 | − | 1.05982i | 0.473965 | − | 0.273644i | ||||
\(16\) | 1.56102 | − | 2.70377i | 0.390256 | − | 0.675943i | ||||
\(17\) | 1.37198 | + | 2.37634i | 0.332754 | + | 0.576347i | 0.983051 | − | 0.183334i | \(-0.0586888\pi\) |
−0.650297 | + | 0.759680i | \(0.725355\pi\) | |||||||
\(18\) | 1.80860 | + | 1.04420i | 0.426292 | + | 0.246120i | ||||
\(19\) | 5.86993i | 1.34665i | 0.739345 | + | 0.673327i | \(0.235135\pi\) | ||||
−0.739345 | + | 0.673327i | \(0.764865\pi\) | |||||||
\(20\) | 0.582143 | + | 0.336100i | 0.130171 | + | 0.0751543i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.77346 | + | 3.07173i | −0.378103 | + | 0.654894i | ||||
\(23\) | 3.49955 | − | 6.06139i | 0.729706 | − | 1.26389i | −0.227302 | − | 0.973824i | \(-0.572990\pi\) |
0.957007 | − | 0.290063i | \(-0.0936763\pi\) | |||||||
\(24\) | − | 3.53408i | − | 0.721391i | ||||||
\(25\) | −0.853117 | + | 1.47764i | −0.170623 | + | 0.295528i | ||||
\(26\) | 3.70451 | + | 2.73160i | 0.726514 | + | 0.535710i | ||||
\(27\) | 5.41444 | 1.04201 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75806 | + | 3.04505i | 0.326463 | + | 0.565451i | 0.981807 | − | 0.189879i | \(-0.0608097\pi\) |
−0.655344 | + | 0.755330i | \(0.727476\pi\) | |||||||
\(30\) | −2.70585 | −0.494019 | ||||||||
\(31\) | −1.79004 | − | 1.03348i | −0.321501 | − | 0.185619i | 0.330560 | − | 0.943785i | \(-0.392762\pi\) |
−0.652062 | + | 0.758166i | \(0.726096\pi\) | |||||||
\(32\) | 1.78956 | − | 1.03320i | 0.316352 | − | 0.182646i | ||||
\(33\) | 3.24507i | 0.564894i | ||||||||
\(34\) | − | 3.50284i | − | 0.600732i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.302965 | + | 0.524751i | 0.0504942 | + | 0.0874585i | ||||
\(37\) | −1.50950 | − | 0.871512i | −0.248161 | − | 0.143276i | 0.370761 | − | 0.928728i | \(-0.379097\pi\) |
−0.618922 | + | 0.785453i | \(0.712430\pi\) | |||||||
\(38\) | 3.74667 | − | 6.48942i | 0.607790 | − | 1.05272i | ||||
\(39\) | 4.18474 | + | 0.469686i | 0.670094 | + | 0.0752100i | ||||
\(40\) | −2.74586 | − | 4.75596i | −0.434158 | − | 0.751984i | ||||
\(41\) | 5.51406 | − | 3.18355i | 0.861152 | − | 0.497186i | −0.00324599 | − | 0.999995i | \(-0.501033\pi\) |
0.864398 | + | 0.502808i | \(0.167700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.55195 | − | 7.88422i | 0.694167 | − | 1.20233i | −0.276294 | − | 0.961073i | \(-0.589106\pi\) |
0.970461 | − | 0.241259i | \(-0.0775603\pi\) | |||||||
\(44\) | −0.891235 | + | 0.514555i | −0.134359 | + | 0.0775721i | ||||
\(45\) | 2.57127 | − | 1.48452i | 0.383302 | − | 0.221299i | ||||
\(46\) | −7.73776 | + | 4.46740i | −1.14087 | + | 0.658681i | ||||
\(47\) | 5.76714 | − | 3.32966i | 0.841224 | − | 0.485681i | −0.0164563 | − | 0.999865i | \(-0.505238\pi\) |
0.857680 | + | 0.514184i | \(0.171905\pi\) | |||||||
\(48\) | −1.82316 | + | 3.15780i | −0.263150 | + | 0.455790i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.88631 | − | 1.08906i | 0.266764 | − | 0.154016i | ||||
\(51\) | −1.60237 | − | 2.77539i | −0.224377 | − | 0.388632i | ||||
\(52\) | 0.534557 | + | 1.22378i | 0.0741297 | + | 0.169708i | ||||
\(53\) | 5.24396 | − | 9.08280i | 0.720313 | − | 1.24762i | −0.240561 | − | 0.970634i | \(-0.577331\pi\) |
0.960874 | − | 0.276985i | \(-0.0893352\pi\) | |||||||
\(54\) | −5.98587 | − | 3.45594i | −0.814573 | − | 0.470294i | ||||
\(55\) | 2.52131 | + | 4.36703i | 0.339973 | + | 0.588850i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.85564i | − | 0.908052i | ||||||
\(58\) | − | 4.48855i | − | 0.589375i | ||||||
\(59\) | −2.66212 | + | 1.53698i | −0.346579 | + | 0.200097i | −0.663177 | − | 0.748462i | \(-0.730793\pi\) |
0.316598 | + | 0.948560i | \(0.397459\pi\) | |||||||
\(60\) | −0.679899 | − | 0.392540i | −0.0877746 | − | 0.0506767i | ||||
\(61\) | 1.08178 | 0.138508 | 0.0692541 | − | 0.997599i | \(-0.477938\pi\) | ||||
0.0692541 | + | 0.997599i | \(0.477938\pi\) | |||||||
\(62\) | 1.31931 | + | 2.28511i | 0.167552 | + | 0.290209i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.88199 | −1.11025 | ||||||||
\(65\) | 5.99651 | − | 2.61932i | 0.743775 | − | 0.324886i | ||||
\(66\) | 2.07127 | − | 3.58755i | 0.254956 | − | 0.441596i | ||||
\(67\) | 5.01796i | 0.613042i | 0.951864 | + | 0.306521i | \(0.0991649\pi\) | ||||
−0.951864 | + | 0.306521i | \(0.900835\pi\) | |||||||
\(68\) | 0.508159 | − | 0.880158i | 0.0616234 | − | 0.106735i | ||||
\(69\) | −4.08721 | + | 7.07925i | −0.492042 | + | 0.852242i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.35453 | + | 1.35939i | 0.279431 | + | 0.161330i | 0.633166 | − | 0.774016i | \(-0.281755\pi\) |
−0.353735 | + | 0.935346i | \(0.615088\pi\) | |||||||
\(72\) | − | 4.95030i | − | 0.583399i | ||||||
\(73\) | 6.64426 | + | 3.83607i | 0.777652 | + | 0.448978i | 0.835598 | − | 0.549342i | \(-0.185122\pi\) |
−0.0579454 | + | 0.998320i | \(0.518455\pi\) | |||||||
\(74\) | 1.11254 | + | 1.92698i | 0.129330 | + | 0.224006i | ||||
\(75\) | 0.996377 | − | 1.72578i | 0.115052 | − | 0.199275i | ||||
\(76\) | 1.88285 | − | 1.08706i | 0.215978 | − | 0.124695i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.32659 | − | 3.19030i | −0.489890 | − | 0.361230i | ||||
\(79\) | 7.86993 | + | 13.6311i | 0.885436 | + | 1.53362i | 0.845213 | + | 0.534430i | \(0.179474\pi\) |
0.0402236 | + | 0.999191i | \(0.487193\pi\) | |||||||
\(80\) | 5.66612i | 0.633492i | ||||||||
\(81\) | −1.41581 | −0.157313 | ||||||||
\(82\) | −8.12800 | −0.897587 | ||||||||
\(83\) | 7.97408i | 0.875269i | 0.899153 | + | 0.437635i | \(0.144184\pi\) | ||||
−0.899153 | + | 0.437635i | \(0.855816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.31275 | − | 2.48997i | −0.467784 | − | 0.270075i | ||||
\(86\) | −10.0647 | + | 5.81086i | −1.08531 | + | 0.626601i | ||||
\(87\) | −2.05328 | − | 3.55639i | −0.220135 | − | 0.381285i | ||||
\(88\) | 8.40757 | 0.896250 | ||||||||
\(89\) | 13.9118 | + | 8.03198i | 1.47465 | + | 0.851388i | 0.999592 | − | 0.0285683i | \(-0.00909482\pi\) |
0.475055 | + | 0.879956i | \(0.342428\pi\) | |||||||
\(90\) | −3.79017 | −0.399519 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.59235 | −0.270271 | ||||||||
\(93\) | 2.09064 | + | 1.20703i | 0.216789 | + | 0.125163i | ||||
\(94\) | −8.50105 | −0.876816 | ||||||||
\(95\) | −5.32659 | − | 9.22592i | −0.546497 | − | 0.946560i | ||||
\(96\) | −2.09007 | + | 1.20670i | −0.213317 | + | 0.123158i | ||||
\(97\) | −12.3209 | − | 7.11347i | −1.25100 | − | 0.722263i | −0.279689 | − | 0.960091i | \(-0.590231\pi\) |
−0.971307 | + | 0.237827i | \(0.923565\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.54548i | 0.456838i | ||||||||
\(100\) | 0.631962 | 0.0631962 | ||||||||
\(101\) | 0.0731225 | 0.00727596 | 0.00363798 | − | 0.999993i | \(-0.498842\pi\) | ||||
0.00363798 | + | 0.999993i | \(0.498842\pi\) | |||||||
\(102\) | 4.09105i | 0.405075i | ||||||||
\(103\) | −6.45980 | − | 11.1887i | −0.636503 | − | 1.10245i | −0.986195 | − | 0.165590i | \(-0.947047\pi\) |
0.349692 | − | 0.936865i | \(-0.386286\pi\) | |||||||
\(104\) | 1.21690 | − | 10.8421i | 0.119327 | − | 1.06316i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.5948 | + | 6.69425i | −1.12618 | + | 0.650203i | ||||
\(107\) | −2.00427 | + | 3.47150i | −0.193761 | + | 0.335603i | −0.946493 | − | 0.322723i | \(-0.895402\pi\) |
0.752733 | + | 0.658326i | \(0.228735\pi\) | |||||||
\(108\) | −1.00271 | − | 1.73675i | −0.0964860 | − | 0.167119i | ||||
\(109\) | 1.71984 | + | 0.992947i | 0.164730 | + | 0.0951071i | 0.580099 | − | 0.814546i | \(-0.303014\pi\) |
−0.415368 | + | 0.909653i | \(0.636347\pi\) | |||||||
\(110\) | − | 6.43722i | − | 0.613765i | ||||||
\(111\) | 1.76299 | + | 1.01786i | 0.167335 | + | 0.0966110i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.28711 | − | 9.15754i | 0.497369 | − | 0.861469i | −0.502626 | − | 0.864504i | \(-0.667633\pi\) |
0.999995 | + | 0.00303506i | \(0.000966090\pi\) | |||||||
\(114\) | −4.37583 | + | 7.57916i | −0.409834 | + | 0.709854i | ||||
\(115\) | 12.7025i | 1.18451i | ||||||||
\(116\) | 0.651157 | − | 1.12784i | 0.0604584 | − | 0.104717i | ||||
\(117\) | 5.86170 | + | 0.657905i | 0.541914 | + | 0.0608233i | ||||
\(118\) | 3.92410 | 0.361243 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.20695 | + | 5.55461i | 0.292753 | + | 0.507064i | ||||
\(121\) | 3.27998 | 0.298180 | ||||||||
\(122\) | −1.19595 | − | 0.690483i | −0.108276 | − | 0.0625134i | ||||
\(123\) | −6.44001 | + | 3.71814i | −0.580676 | + | 0.335254i | ||||
\(124\) | 0.765571i | 0.0687503i | ||||||||
\(125\) | − | 12.1710i | − | 1.08860i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.63478 | + | 9.75972i | 0.500006 | + | 0.866035i | 1.00000 | 6.53271e-6i | \(2.07943e-6\pi\) | |
−0.499994 | + | 0.866029i | \(0.666665\pi\) | |||||||
\(128\) | 6.24025 | + | 3.60281i | 0.551566 | + | 0.318447i | ||||
\(129\) | −5.31634 | + | 9.20818i | −0.468078 | + | 0.810735i | ||||
\(130\) | −8.30123 | − | 0.931713i | −0.728066 | − | 0.0817166i | ||||
\(131\) | −1.53241 | − | 2.65421i | −0.133887 | − | 0.231899i | 0.791285 | − | 0.611448i | \(-0.209413\pi\) |
−0.925172 | + | 0.379549i | \(0.876079\pi\) | |||||||
\(132\) | 1.04090 | − | 0.600962i | 0.0905984 | − | 0.0523070i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.20288 | − | 5.54754i | 0.276686 | − | 0.479235i | ||||
\(135\) | −8.51002 | + | 4.91326i | −0.732426 | + | 0.422867i | ||||
\(136\) | −7.19067 | + | 4.15154i | −0.616595 | + | 0.355991i | ||||
\(137\) | −18.9512 | + | 10.9415i | −1.61911 | + | 0.934796i | −0.631965 | + | 0.774997i | \(0.717751\pi\) |
−0.987150 | + | 0.159799i | \(0.948915\pi\) | |||||||
\(138\) | 9.03712 | − | 5.21758i | 0.769291 | − | 0.444150i | ||||
\(139\) | −5.53535 | + | 9.58750i | −0.469502 | + | 0.813201i | −0.999392 | − | 0.0348652i | \(-0.988900\pi\) |
0.529890 | + | 0.848066i | \(0.322233\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.73559 | + | 3.88879i | −0.567239 | + | 0.327495i | ||||
\(142\) | −1.73534 | − | 3.00570i | −0.145627 | − | 0.252233i | ||||
\(143\) | −1.11738 | + | 9.95549i | −0.0934403 | + | 0.832520i | ||||
\(144\) | −2.55376 | + | 4.42324i | −0.212813 | + | 0.368603i | ||||
\(145\) | −5.52637 | − | 3.19065i | −0.458940 | − | 0.264969i | ||||
\(146\) | −4.89699 | − | 8.48183i | −0.405277 | − | 0.701961i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.645588i | 0.0530670i | ||||||||
\(149\) | 2.30737i | 0.189027i | 0.995524 | + | 0.0945136i | \(0.0301296\pi\) | ||||
−0.995524 | + | 0.0945136i | \(0.969870\pi\) | |||||||
\(150\) | −2.20306 | + | 1.27194i | −0.179879 | + | 0.103853i | ||||
\(151\) | 17.8538 | + | 10.3079i | 1.45292 | + | 0.838845i | 0.998646 | − | 0.0520168i | \(-0.0165649\pi\) |
0.454275 | + | 0.890861i | \(0.349898\pi\) | |||||||
\(152\) | −17.7621 | −1.44070 | ||||||||
\(153\) | −2.24449 | − | 3.88757i | −0.181456 | − | 0.314292i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.75128 | 0.301310 | ||||||||
\(156\) | −0.624323 | − | 1.42929i | −0.0499858 | − | 0.114435i | ||||
\(157\) | −1.44824 | + | 2.50843i | −0.115582 | + | 0.200194i | −0.918012 | − | 0.396552i | \(-0.870207\pi\) |
0.802430 | + | 0.596746i | \(0.203540\pi\) | |||||||
\(158\) | − | 20.0929i | − | 1.59851i | ||||||
\(159\) | −6.12455 | + | 10.6080i | −0.485709 | + | 0.841272i | ||||
\(160\) | −1.87513 | + | 3.24782i | −0.148242 | + | 0.256763i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.56523 | + | 0.903688i | 0.122976 | + | 0.0710004i | ||||
\(163\) | 23.4339i | 1.83549i | 0.397175 | + | 0.917743i | \(0.369990\pi\) | ||||
−0.397175 | + | 0.917743i | \(0.630010\pi\) | |||||||
\(164\) | −2.04232 | − | 1.17913i | −0.159478 | − | 0.0920750i | ||||
\(165\) | −2.94470 | − | 5.10037i | −0.229244 | − | 0.397063i | ||||
\(166\) | 5.08971 | − | 8.81564i | 0.395038 | − | 0.684226i | ||||
\(167\) | 6.58349 | − | 3.80098i | 0.509446 | − | 0.294129i | −0.223160 | − | 0.974782i | \(-0.571637\pi\) |
0.732606 | + | 0.680653i | \(0.238304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6765 | + | 2.88188i | 0.975119 | + | 0.221683i | ||||
\(170\) | 3.17861 | + | 5.50551i | 0.243788 | + | 0.422253i | ||||
\(171\) | − | 9.60292i | − | 0.734353i | ||||||
\(172\) | −3.37194 | −0.257108 | ||||||||
\(173\) | −5.39721 | −0.410343 | −0.205171 | − | 0.978726i | \(-0.565775\pi\) | ||||
−0.205171 | + | 0.978726i | \(0.565775\pi\) | |||||||
\(174\) | 5.24229i | 0.397417i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.51241 | − | 4.33729i | −0.566269 | − | 0.326936i | ||||
\(177\) | 3.10916 | − | 1.79508i | 0.233699 | − | 0.134926i | ||||
\(178\) | −10.2533 | − | 17.7593i | −0.768520 | − | 1.33112i | ||||
\(179\) | 12.2914 | 0.918704 | 0.459352 | − | 0.888254i | \(-0.348082\pi\) | ||||
0.459352 | + | 0.888254i | \(0.348082\pi\) | |||||||
\(180\) | −0.952357 | − | 0.549843i | −0.0709845 | − | 0.0409829i | ||||
\(181\) | −21.8525 | −1.62428 | −0.812140 | − | 0.583463i | \(-0.801697\pi\) | ||||
−0.812140 | + | 0.583463i | \(0.801697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.26344 | −0.0933964 | ||||||||
\(184\) | 18.3415 | + | 10.5894i | 1.35215 | + | 0.780664i | ||||
\(185\) | 3.16337 | 0.232575 | ||||||||
\(186\) | −1.54085 | − | 2.66883i | −0.112981 | − | 0.195688i | ||||
\(187\) | 6.60264 | − | 3.81204i | 0.482833 | − | 0.278764i | ||||
\(188\) | −2.13606 | − | 1.23325i | −0.155788 | − | 0.0899442i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.5995i | 0.986609i | ||||||||
\(191\) | 2.75716 | 0.199501 | 0.0997507 | − | 0.995012i | \(-0.468195\pi\) | ||||
0.0997507 | + | 0.995012i | \(0.468195\pi\) | |||||||
\(192\) | 10.3735 | 0.748643 | ||||||||
\(193\) | 12.9893i | 0.934993i | 0.883995 | + | 0.467497i | \(0.154844\pi\) | ||||
−0.883995 | + | 0.467497i | \(0.845156\pi\) | |||||||
\(194\) | 9.08080 | + | 15.7284i | 0.651963 | + | 1.12923i | ||||
\(195\) | −7.00347 | + | 3.05917i | −0.501529 | + | 0.219071i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.4772 | − | 9.51312i | 1.17395 | − | 0.677781i | 0.219344 | − | 0.975648i | \(-0.429608\pi\) |
0.954608 | + | 0.297866i | \(0.0962749\pi\) | |||||||
\(198\) | 2.90130 | − | 5.02519i | 0.206186 | − | 0.357125i | ||||
\(199\) | −10.0159 | − | 17.3480i | −0.710006 | − | 1.22977i | −0.964854 | − | 0.262786i | \(-0.915359\pi\) |
0.254848 | − | 0.966981i | \(-0.417975\pi\) | |||||||
\(200\) | −4.47127 | − | 2.58149i | −0.316166 | − | 0.182539i | ||||
\(201\) | − | 5.86061i | − | 0.413375i | ||||||
\(202\) | −0.0808396 | − | 0.0466728i | −0.00568785 | − | 0.00328388i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.593492 | + | 1.02796i | −0.0415528 | + | 0.0719715i | ||||
\(205\) | −5.77773 | + | 10.0073i | −0.403534 | + | 0.698942i | ||||
\(206\) | 16.4927i | 1.14910i | ||||||||
\(207\) | −5.72509 | + | 9.91614i | −0.397921 | + | 0.689219i | ||||
\(208\) | −6.68057 | + | 9.05999i | −0.463214 | + | 0.628197i | ||||
\(209\) | 16.3096 | 1.12816 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00015 | − | 8.66052i | −0.344225 | − | 0.596215i | 0.640988 | − | 0.767551i | \(-0.278525\pi\) |
−0.985213 | + | 0.171336i | \(0.945192\pi\) | |||||||
\(212\) | −3.88456 | −0.266793 | ||||||||
\(213\) | −2.74991 | − | 1.58766i | −0.188421 | − | 0.108785i | ||||
\(214\) | 4.43160 | − | 2.55858i | 0.302938 | − | 0.174901i | ||||
\(215\) | 16.5224i | 1.12682i | ||||||||
\(216\) | 16.3838i | 1.11478i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.26756 | − | 2.19548i | −0.0858501 | − | 0.148697i | ||||
\(219\) | −7.76000 | − | 4.48024i | −0.524372 | − | 0.302747i | ||||
\(220\) | 0.933852 | − | 1.61748i | 0.0629603 | − | 0.109050i | ||||
\(221\) | −3.96022 | − | 9.06629i | −0.266393 | − | 0.609865i | ||||
\(222\) | −1.29936 | − | 2.25056i | −0.0872076 | − | 0.151048i | ||||
\(223\) | 7.25954 | − | 4.19130i | 0.486135 | − | 0.280670i | −0.236835 | − | 0.971550i | \(-0.576110\pi\) |
0.722970 | + | 0.690880i | \(0.242777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.39566 | − | 2.41735i | 0.0930439 | − | 0.161157i | ||||
\(226\) | −11.6902 | + | 6.74933i | −0.777620 | + | 0.448959i | ||||
\(227\) | 0.796500 | − | 0.459860i | 0.0528656 | − | 0.0305220i | −0.473334 | − | 0.880883i | \(-0.656950\pi\) |
0.526200 | + | 0.850361i | \(0.323616\pi\) | |||||||
\(228\) | −2.19903 | + | 1.26961i | −0.145634 | + | 0.0840820i | ||||
\(229\) | 21.3222 | − | 12.3104i | 1.40901 | − | 0.813494i | 0.413719 | − | 0.910404i | \(-0.364229\pi\) |
0.995293 | + | 0.0969108i | \(0.0308962\pi\) | |||||||
\(230\) | 8.10776 | − | 14.0430i | 0.534610 | − | 0.925971i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.21415 | + | 5.31979i | −0.604939 | + | 0.349261i | ||||
\(233\) | −8.63847 | − | 14.9623i | −0.565925 | − | 0.980211i | −0.996963 | − | 0.0778773i | \(-0.975186\pi\) |
0.431038 | − | 0.902334i | \(-0.358148\pi\) | |||||||
\(234\) | −6.06040 | − | 4.46876i | −0.396180 | − | 0.292132i | ||||
\(235\) | −6.04291 | + | 10.4666i | −0.394196 | + | 0.682767i | ||||
\(236\) | 0.986008 | + | 0.569272i | 0.0641837 | + | 0.0370565i | ||||
\(237\) | −9.19149 | − | 15.9201i | −0.597051 | − | 1.03412i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.4828i | 0.936816i | 0.883512 | + | 0.468408i | \(0.155172\pi\) | ||||
−0.883512 | + | 0.468408i | \(0.844828\pi\) | |||||||
\(240\) | − | 6.61760i | − | 0.427165i | ||||||
\(241\) | 7.30441 | − | 4.21720i | 0.470518 | − | 0.271654i | −0.245938 | − | 0.969285i | \(-0.579096\pi\) |
0.716457 | + | 0.697632i | \(0.245763\pi\) | |||||||
\(242\) | −3.62614 | − | 2.09355i | −0.233097 | − | 0.134579i | ||||
\(243\) | −14.5898 | −0.935934 | ||||||||
\(244\) | −0.200338 | − | 0.346995i | −0.0128253 | − | 0.0222141i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.49290 | 0.605245 | ||||||||
\(247\) | 2.36062 | − | 21.0323i | 0.150203 | − | 1.33825i | ||||
\(248\) | 3.12726 | − | 5.41658i | 0.198581 | − | 0.343953i | ||||
\(249\) | − | 9.31313i | − | 0.590196i | ||||||
\(250\) | −7.76851 | + | 13.4555i | −0.491324 | + | 0.850998i | ||||
\(251\) | −7.33631 | + | 12.7069i | −0.463064 | + | 0.802050i | −0.999112 | − | 0.0421373i | \(-0.986583\pi\) |
0.536048 | + | 0.844188i | \(0.319917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8415 | − | 9.72346i | −1.05882 | − | 0.611309i | ||||
\(254\) | − | 14.3863i | − | 0.902677i | ||||||
\(255\) | 5.03697 | + | 2.90810i | 0.315427 | + | 0.182112i | ||||
\(256\) | 4.28277 | + | 7.41797i | 0.267673 | + | 0.463623i | ||||
\(257\) | 14.6643 | − | 25.3993i | 0.914733 | − | 1.58436i | 0.107441 | − | 0.994211i | \(-0.465734\pi\) |
0.807292 | − | 0.590152i | \(-0.200932\pi\) | |||||||
\(258\) | 11.7548 | − | 6.78665i | 0.731824 | − | 0.422519i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.95068 | − | 1.43838i | −0.120976 | − | 0.0892043i | ||||
\(261\) | −2.87610 | − | 4.98155i | −0.178026 | − | 0.308350i | ||||
\(262\) | 3.91243i | 0.241711i | ||||||||
\(263\) | 19.9149 | 1.22801 | 0.614004 | − | 0.789303i | \(-0.289558\pi\) | ||||
0.614004 | + | 0.789303i | \(0.289558\pi\) | |||||||
\(264\) | −9.81942 | −0.604343 | ||||||||
\(265\) | 19.0342i | 1.16926i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.2479 | − | 9.38075i | −0.994357 | − | 0.574092i | ||||
\(268\) | 1.60957 | − | 0.929287i | 0.0983203 | − | 0.0567652i | ||||
\(269\) | 11.1625 | + | 19.3340i | 0.680589 | + | 1.17881i | 0.974801 | + | 0.223074i | \(0.0716093\pi\) |
−0.294213 | + | 0.955740i | \(0.595057\pi\) | |||||||
\(270\) | 12.5442 | 0.763415 | ||||||||
\(271\) | 8.14054 | + | 4.69994i | 0.494502 | + | 0.285501i | 0.726440 | − | 0.687230i | \(-0.241173\pi\) |
−0.231938 | + | 0.972731i | \(0.574507\pi\) | |||||||
\(272\) | 8.56677 | 0.519437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.9351 | 1.68762 | ||||||||
\(275\) | 4.10562 | + | 2.37038i | 0.247578 | + | 0.142939i | ||||
\(276\) | 3.02767 | 0.182245 | ||||||||
\(277\) | −7.17133 | − | 12.4211i | −0.430883 | − | 0.746312i | 0.566066 | − | 0.824360i | \(-0.308465\pi\) |
−0.996950 | + | 0.0780478i | \(0.975131\pi\) | |||||||
\(278\) | 12.2391 | − | 7.06622i | 0.734050 | − | 0.423804i | ||||
\(279\) | 2.92842 | + | 1.69073i | 0.175320 | + | 0.101221i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0988416i | 0.00589640i | 0.999996 | + | 0.00294820i | \(0.000938442\pi\) | ||||
−0.999996 | + | 0.00294820i | \(0.999062\pi\) | |||||||
\(282\) | 9.92859 | 0.591239 | ||||||||
\(283\) | 0.620673 | 0.0368952 | 0.0184476 | − | 0.999830i | \(-0.494128\pi\) | ||||
0.0184476 | + | 0.999830i | \(0.494128\pi\) | |||||||
\(284\) | − | 1.00699i | − | 0.0597539i | ||||||
\(285\) | 6.22106 | + | 10.7752i | 0.368504 | + | 0.638267i | ||||
\(286\) | 7.58972 | − | 10.2930i | 0.448789 | − | 0.608635i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.92763 | + | 1.69027i | −0.172512 | + | 0.0995998i | ||||
\(289\) | 4.73534 | − | 8.20186i | 0.278550 | − | 0.482462i | ||||
\(290\) | 4.07307 | + | 7.05477i | 0.239179 | + | 0.414270i | ||||
\(291\) | 14.3899 | + | 8.30800i | 0.843549 | + | 0.487023i | ||||
\(292\) | − | 2.84164i | − | 0.166294i | ||||||
\(293\) | 21.5586 | + | 12.4469i | 1.25947 | + | 0.727153i | 0.972971 | − | 0.230928i | \(-0.0741762\pi\) |
0.286496 | + | 0.958082i | \(0.407510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.78942 | − | 4.83142i | 0.162406 | − | 0.281296i | ||||
\(296\) | 2.63715 | − | 4.56767i | 0.153281 | − | 0.265491i | ||||
\(297\) | − | 15.0440i | − | 0.872941i | ||||||
\(298\) | 1.47275 | − | 2.55088i | 0.0853143 | − | 0.147769i | ||||
\(299\) | −14.9767 | + | 20.3109i | −0.866124 | + | 1.17461i | ||||
\(300\) | −0.738085 | −0.0426133 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.1587 | − | 22.7915i | −0.757197 | − | 1.31150i | ||||
\(303\) | −0.0854016 | −0.00490619 | ||||||||
\(304\) | 15.8710 | + | 9.16310i | 0.910262 | + | 0.525540i | ||||
\(305\) | −1.70027 | + | 0.981651i | −0.0973571 | + | 0.0562091i | ||||
\(306\) | 5.73047i | 0.327589i | ||||||||
\(307\) | 9.89767i | 0.564890i | 0.959284 | + | 0.282445i | \(0.0911455\pi\) | ||||
−0.959284 | + | 0.282445i | \(0.908855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.54456 | + | 13.0676i | 0.429195 | + | 0.743387i | ||||
\(310\) | −4.14718 | − | 2.39437i | −0.235544 | − | 0.135991i | ||||
\(311\) | 3.61895 | − | 6.26820i | 0.205212 | − | 0.355437i | −0.744988 | − | 0.667077i | \(-0.767545\pi\) |
0.950200 | + | 0.311640i | \(0.100878\pi\) | |||||||
\(312\) | −1.42125 | + | 12.6628i | −0.0804622 | + | 0.716890i | ||||
\(313\) | −16.3303 | − | 28.2849i | −0.923043 | − | 1.59876i | −0.794678 | − | 0.607031i | \(-0.792360\pi\) |
−0.128365 | − | 0.991727i | \(-0.540973\pi\) | |||||||
\(314\) | 3.20217 | − | 1.84877i | 0.180709 | − | 0.104332i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.91490 | − | 5.04875i | 0.163976 | − | 0.284014i | ||||
\(317\) | 14.8734 | − | 8.58718i | 0.835375 | − | 0.482304i | −0.0203143 | − | 0.999794i | \(-0.506467\pi\) |
0.855690 | + | 0.517489i | \(0.173133\pi\) | |||||||
\(318\) | 13.5418 | − | 7.81838i | 0.759388 | − | 0.438433i | ||||
\(319\) | 8.46064 | − | 4.88475i | 0.473705 | − | 0.273494i | ||||
\(320\) | 13.9601 | − | 8.05984i | 0.780391 | − | 0.450559i | ||||
\(321\) | 2.34084 | − | 4.05446i | 0.130653 | − | 0.226298i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.9489 | + | 8.05342i | −0.776140 | + | 0.448105i | ||||
\(324\) | 0.262197 | + | 0.454139i | 0.0145665 | + | 0.0252299i | ||||
\(325\) | 3.65101 | − | 4.95139i | 0.202521 | − | 0.274654i | ||||
\(326\) | 14.9574 | − | 25.9071i | 0.828416 | − | 1.43486i | ||||
\(327\) | −2.00864 | − | 1.15969i | −0.111078 | − | 0.0641309i | ||||
\(328\) | 9.63324 | + | 16.6853i | 0.531907 | + | 0.921289i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.51819i | 0.413863i | ||||||||
\(331\) | − | 19.9340i | − | 1.09567i | −0.836587 | − | 0.547835i | \(-0.815452\pi\) | ||
0.836587 | − | 0.547835i | \(-0.184548\pi\) | |||||||
\(332\) | 2.55778 | − | 1.47674i | 0.140377 | − | 0.0810465i | ||||
\(333\) | 2.46947 | + | 1.42575i | 0.135326 | + | 0.0781306i | ||||
\(334\) | −9.70438 | −0.531000 | ||||||||
\(335\) | −4.55348 | − | 7.88687i | −0.248783 | − | 0.430905i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.27189 | 0.0692842 | 0.0346421 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346421 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(338\) | −12.1749 | − | 11.2772i | −0.662229 | − | 0.613401i | ||||
\(339\) | −6.17495 | + | 10.6953i | −0.335377 | + | 0.580890i | ||||
\(340\) | 1.84449i | 0.100032i | ||||||||
\(341\) | −2.87152 | + | 4.97363i | −0.155502 | + | 0.269337i | ||||
\(342\) | −6.12937 | + | 10.6164i | −0.331438 | + | 0.574068i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 23.8572 | + | 13.7740i | 1.28630 | + | 0.742643i | ||||
\(345\) | − | 14.8355i | − | 0.798718i | ||||||
\(346\) | 5.96682 | + | 3.44494i | 0.320778 | + | 0.185201i | ||||
\(347\) | −12.9417 | − | 22.4156i | −0.694744 | − | 1.20333i | −0.970267 | − | 0.242038i | \(-0.922184\pi\) |
0.275522 | − | 0.961295i | \(-0.411149\pi\) | |||||||
\(348\) | −0.760503 | + | 1.31723i | −0.0407672 | + | 0.0706109i | ||||
\(349\) | −14.9967 | + | 8.65837i | −0.802757 | + | 0.463472i | −0.844434 | − | 0.535659i | \(-0.820063\pi\) |
0.0416774 | + | 0.999131i | \(0.486730\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.4002 | − | 2.17744i | −1.03551 | − | 0.116223i | ||||
\(352\) | −2.87074 | − | 4.97227i | −0.153011 | − | 0.265023i | ||||
\(353\) | − | 25.3495i | − | 1.34922i | −0.738176 | − | 0.674608i | \(-0.764313\pi\) | ||
0.738176 | − | 0.674608i | \(-0.235687\pi\) | |||||||
\(354\) | −4.58306 | −0.243587 | ||||||||
\(355\) | −4.93423 | −0.261882 | ||||||||
\(356\) | − | 5.94983i | − | 0.315341i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.5886 | − | 7.84539i | −0.718181 | − | 0.414642i | ||||
\(359\) | −4.56434 | + | 2.63522i | −0.240897 | + | 0.139082i | −0.615589 | − | 0.788068i | \(-0.711082\pi\) |
0.374692 | + | 0.927149i | \(0.377748\pi\) | |||||||
\(360\) | 4.49208 | + | 7.78052i | 0.236754 | + | 0.410069i | ||||
\(361\) | −15.4561 | −0.813478 | ||||||||
\(362\) | 24.1587 | + | 13.9480i | 1.26975 | + | 0.733092i | ||||
\(363\) | −3.83077 | −0.201063 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.9240 | −0.728813 | ||||||||
\(366\) | 1.39678 | + | 0.806433i | 0.0730110 | + | 0.0421529i | ||||
\(367\) | 25.3176 | 1.32157 | 0.660783 | − | 0.750577i | \(-0.270224\pi\) | ||||
0.660783 | + | 0.750577i | \(0.270224\pi\) | |||||||
\(368\) | −10.9257 | − | 18.9240i | −0.569544 | − | 0.986479i | ||||
\(369\) | −9.02073 | + | 5.20812i | −0.469601 | + | 0.271124i | ||||
\(370\) | −3.49722 | − | 2.01912i | −0.181812 | − | 0.104969i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 0.894130i | − | 0.0463585i | ||||||
\(373\) | −6.78782 | −0.351460 | −0.175730 | − | 0.984438i | \(-0.556229\pi\) | ||||
−0.175730 | + | 0.984438i | \(0.556229\pi\) | |||||||
\(374\) | −9.73261 | −0.503262 | ||||||||
\(375\) | 14.2148i | 0.734048i | ||||||||
\(376\) | 10.0754 | + | 17.4511i | 0.519598 | + | 0.899970i | ||||
\(377\) | −5.07464 | − | 11.6176i | −0.261357 | − | 0.598336i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.6717 | − | 6.16130i | 0.548168 | − | 0.316485i | −0.200215 | − | 0.979752i | \(-0.564164\pi\) |
0.748383 | + | 0.663267i | \(0.230831\pi\) | |||||||
\(380\) | −1.97288 | + | 3.41714i | −0.101207 | + | 0.175295i | ||||
\(381\) | −6.58100 | − | 11.3986i | −0.337155 | − | 0.583969i | ||||
\(382\) | −3.04815 | − | 1.75985i | −0.155957 | − | 0.0900417i | ||||
\(383\) | 7.25917i | 0.370926i | 0.982651 | + | 0.185463i | \(0.0593785\pi\) | ||||
−0.982651 | + | 0.185463i | \(0.940621\pi\) | |||||||
\(384\) | −7.28815 | − | 4.20782i | −0.371922 | − | 0.214729i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.29086 | − | 14.3602i | 0.421994 | − | 0.730915i | ||||
\(387\) | −7.44677 | + | 12.8982i | −0.378541 | + | 0.655652i | ||||
\(388\) | 5.26943i | 0.267515i | ||||||||
\(389\) | −3.57406 | + | 6.19045i | −0.181212 | + | 0.313868i | −0.942293 | − | 0.334788i | \(-0.891335\pi\) |
0.761082 | + | 0.648656i | \(0.224669\pi\) | |||||||
\(390\) | 9.69521 | + | 1.08817i | 0.490936 | + | 0.0551017i | ||||
\(391\) | 19.2052 | 0.971250 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.78974 | + | 3.09991i | 0.0902802 | + | 0.156370i | ||||
\(394\) | −24.2882 | −1.22362 | ||||||||
\(395\) | −24.7388 | − | 14.2829i | −1.24474 | − | 0.718652i | ||||
\(396\) | 1.45802 | − | 0.841786i | 0.0732681 | − | 0.0423014i | ||||
\(397\) | 22.4612i | 1.12729i | 0.826016 | + | 0.563647i | \(0.190602\pi\) | ||||
−0.826016 | + | 0.563647i | \(0.809398\pi\) | |||||||
\(398\) | 25.5718i | 1.28180i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.66347 | + | 4.61327i | 0.133174 | + | 0.230663i | ||||
\(401\) | 2.64547 | + | 1.52736i | 0.132108 | + | 0.0762729i | 0.564598 | − | 0.825366i | \(-0.309031\pi\) |
−0.432489 | + | 0.901639i | \(0.642365\pi\) | |||||||
\(402\) | −3.74072 | + | 6.47912i | −0.186570 | + | 0.323149i | ||||
\(403\) | 5.99820 | + | 4.42290i | 0.298792 | + | 0.220320i | ||||
\(404\) | −0.0135417 | − | 0.0234549i | −0.000673725 | − | 0.00116693i | ||||
\(405\) | 2.22527 | − | 1.28476i | 0.110575 | − | 0.0638403i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.42149 | + | 4.19414i | −0.120029 | + | 0.207896i | ||||
\(408\) | 8.39817 | − | 4.84869i | 0.415771 | − | 0.240046i | ||||
\(409\) | −4.85482 | + | 2.80293i | −0.240055 | + | 0.138596i | −0.615202 | − | 0.788369i | \(-0.710926\pi\) |
0.375147 | + | 0.926965i | \(0.377592\pi\) | |||||||
\(410\) | 12.7750 | − | 7.37564i | 0.630912 | − | 0.364257i | ||||
\(411\) | 22.1336 | − | 12.7789i | 1.09177 | − | 0.630335i | ||||
\(412\) | −2.39261 | + | 4.14412i | −0.117875 | + | 0.204166i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.6586 | − | 7.30844i | 0.622136 | − | 0.359190i | ||||
\(415\) | −7.23597 | − | 12.5331i | −0.355200 | − | 0.615224i | ||||
\(416\) | −6.82758 | + | 2.98233i | −0.334750 | + | 0.146221i | ||||
\(417\) | 6.46487 | − | 11.1975i | 0.316586 | − | 0.548343i | ||||
\(418\) | −18.0308 | − | 10.4101i | −0.881916 | − | 0.509175i | ||||
\(419\) | −3.06969 | − | 5.31687i | −0.149964 | − | 0.259746i | 0.781250 | − | 0.624219i | \(-0.214583\pi\) |
−0.931214 | + | 0.364473i | \(0.881249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.92589i | − | 0.0938622i | −0.998898 | − | 0.0469311i | \(-0.985056\pi\) | ||
0.998898 | − | 0.0469311i | \(-0.0149441\pi\) | |||||||
\(422\) | 12.7660i | 0.621441i | ||||||||
\(423\) | −9.43475 | + | 5.44716i | −0.458733 | + | 0.264850i | ||||
\(424\) | 27.4841 | + | 15.8679i | 1.33475 | + | 0.770615i | ||||
\(425\) | −4.68184 | −0.227102 | ||||||||
\(426\) | 2.02675 | + | 3.51044i | 0.0981965 | + | 0.170081i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.48470 | 0.0717658 | ||||||||
\(429\) | 1.30502 | − | 11.6273i | 0.0630070 | − | 0.561370i | ||||
\(430\) | 10.5460 | − | 18.2662i | 0.508572 | − | 0.880873i | ||||
\(431\) | 10.7494i | 0.517779i | 0.965907 | + | 0.258890i | \(0.0833566\pi\) | ||||
−0.965907 | + | 0.258890i | \(0.916643\pi\) | |||||||
\(432\) | 8.45207 | − | 14.6394i | 0.406651 | − | 0.704340i | ||||
\(433\) | 20.1328 | − | 34.8710i | 0.967520 | − | 1.67579i | 0.264835 | − | 0.964294i | \(-0.414682\pi\) |
0.702685 | − | 0.711501i | \(-0.251984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.45439 | + | 3.72644i | 0.309464 | + | 0.178669i | ||||
\(436\) | − | 0.735544i | − | 0.0352262i | ||||||
\(437\) | 35.5799 | + | 20.5421i | 1.70202 | + | 0.982662i | ||||
\(438\) | 5.71931 | + | 9.90614i | 0.273279 | + | 0.473334i | ||||
\(439\) | −10.9754 | + | 19.0099i | −0.523826 | + | 0.907294i | 0.475789 | + | 0.879560i | \(0.342163\pi\) |
−0.999615 | + | 0.0277345i | \(0.991171\pi\) | |||||||
\(440\) | −13.2144 | + | 7.62934i | −0.629972 | + | 0.363715i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.40868 | + | 12.5509i | −0.0670042 | + | 0.596984i | ||||
\(443\) | 13.9482 | + | 24.1589i | 0.662697 | + | 1.14783i | 0.979904 | + | 0.199469i | \(0.0639217\pi\) |
−0.317207 | + | 0.948356i | \(0.602745\pi\) | |||||||
\(444\) | − | 0.753999i | − | 0.0357832i | ||||||
\(445\) | −29.1540 | −1.38203 | ||||||||
\(446\) | −10.7009 | −0.506703 | ||||||||
\(447\) | − | 2.69484i | − | 0.127461i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.1056 | + | 11.0306i | 0.901648 | + | 0.520567i | 0.877734 | − | 0.479147i | \(-0.159054\pi\) |
0.0239134 | + | 0.999714i | \(0.492387\pi\) | |||||||
\(450\) | −3.08590 | + | 1.78165i | −0.145471 | + | 0.0839876i | ||||
\(451\) | −8.84546 | − | 15.3208i | −0.416516 | − | 0.721427i | ||||
\(452\) | −3.91652 | −0.184218 | ||||||||
\(453\) | −20.8519 | − | 12.0389i | −0.979708 | − | 0.565635i | ||||
\(454\) | −1.17408 | −0.0551023 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.7448 | 0.971464 | ||||||||
\(457\) | −4.77724 | − | 2.75814i | −0.223470 | − | 0.129020i | 0.384086 | − | 0.923297i | \(-0.374517\pi\) |
−0.607556 | + | 0.794277i | \(0.707850\pi\) | |||||||
\(458\) | −31.4300 | −1.46863 | ||||||||
\(459\) | 7.42851 | + | 12.8665i | 0.346733 | + | 0.600559i | ||||
\(460\) | 4.07447 | − | 2.35240i | 0.189973 | − | 0.109681i | ||||
\(461\) | 25.0092 | + | 14.4391i | 1.16479 | + | 0.672494i | 0.952448 | − | 0.304700i | \(-0.0985562\pi\) |
0.212346 | + | 0.977195i | \(0.431890\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.2284i | 0.661251i | 0.943762 | + | 0.330625i | \(0.107260\pi\) | ||||
−0.943762 | + | 0.330625i | \(0.892740\pi\) | |||||||
\(464\) | 10.9775 | 0.509617 | ||||||||
\(465\) | −4.38121 | −0.203174 | ||||||||
\(466\) | 22.0551i | 1.02168i | ||||||||
\(467\) | −2.27163 | − | 3.93457i | −0.105118 | − | 0.182070i | 0.808668 | − | 0.588265i | \(-0.200189\pi\) |
−0.913787 | + | 0.406195i | \(0.866855\pi\) | |||||||
\(468\) | −0.874509 | − | 2.00205i | −0.0404242 | − | 0.0925448i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.3613 | − | 7.71416i | 0.616312 | − | 0.355828i | ||||
\(471\) | 1.69144 | − | 2.92966i | 0.0779374 | − | 0.134992i | ||||
\(472\) | −4.65081 | − | 8.05545i | −0.214071 | − | 0.370782i | ||||
\(473\) | −21.9062 | − | 12.6476i | −1.00725 | − | 0.581536i | ||||
\(474\) | 23.4671i | 1.07788i | ||||||||
\(475\) | −8.67366 | − | 5.00774i | −0.397975 | − | 0.229771i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.57886 | + | 14.8590i | −0.392799 | + | 0.680348i | ||||
\(478\) | 9.24413 | − | 16.0113i | 0.422817 | − | 0.732340i | ||||
\(479\) | − | 1.66553i | − | 0.0760999i | −0.999276 | − | 0.0380499i | \(-0.987885\pi\) | ||
0.999276 | − | 0.0380499i | \(-0.0121146\pi\) | |||||||
\(480\) | 2.19001 | − | 3.79321i | 0.0999598 | − | 0.173135i | ||||
\(481\) | 5.05815 | + | 3.72973i | 0.230632 | + | 0.170061i | ||||
\(482\) | −10.7671 | −0.490426 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.607426 | − | 1.05209i | −0.0276103 | − | 0.0478224i | ||||
\(485\) | 25.8201 | 1.17243 | ||||||||
\(486\) | 16.1295 | + | 9.31239i | 0.731650 | + | 0.422418i | ||||
\(487\) | 1.28598 | − | 0.742463i | 0.0582735 | − | 0.0336442i | −0.470580 | − | 0.882357i | \(-0.655955\pi\) |
0.528854 | + | 0.848713i | \(0.322622\pi\) | |||||||
\(488\) | 3.27342i | 0.148181i | ||||||||
\(489\) | − | 27.3691i | − | 1.23767i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.99791 | + | 13.8528i | 0.360941 | + | 0.625167i | 0.988116 | − | 0.153711i | \(-0.0491224\pi\) |
−0.627175 | + | 0.778878i | \(0.715789\pi\) | |||||||
\(492\) | 2.38528 | + | 1.37714i | 0.107537 | + | 0.0620863i | ||||
\(493\) | −4.82404 | + | 8.35548i | −0.217264 | + | 0.376312i | ||||
\(494\) | −16.0343 | + | 21.7452i | −0.721416 | + | 0.978363i | ||||
\(495\) | −4.12473 | − | 7.14425i | −0.185393 | − | 0.321110i | ||||
\(496\) | −5.58860 | + | 3.22658i | −0.250936 | + | 0.144878i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.94440 | + | 10.2960i | −0.266375 | + | 0.461375i | ||||
\(499\) | −15.3459 | + | 8.85997i | −0.686977 | + | 0.396627i | −0.802479 | − | 0.596681i | \(-0.796486\pi\) |
0.115501 | + | 0.993307i | \(0.463153\pi\) | |||||||
\(500\) | −3.90398 | + | 2.25397i | −0.174591 | + | 0.100800i | ||||
\(501\) | −7.68902 | + | 4.43926i | −0.343520 | + | 0.198331i | ||||
\(502\) | 16.2211 | − | 9.36527i | 0.723984 | − | 0.417993i | ||||
\(503\) | 0.598451 | − | 1.03655i | 0.0266836 | − | 0.0462174i | −0.852375 | − | 0.522931i | \(-0.824839\pi\) |
0.879059 | + | 0.476713i | \(0.158172\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.114929 | + | 0.0663540i | −0.00511425 | + | 0.00295272i | ||||
\(506\) | 12.4126 | + | 21.4993i | 0.551809 | + | 0.955760i | ||||
\(507\) | −14.8053 | − | 3.36582i | −0.657524 | − | 0.149481i | ||||
\(508\) | 2.08703 | − | 3.61485i | 0.0925971 | − | 0.160383i | ||||
\(509\) | −5.44396 | − | 3.14307i | −0.241299 | − | 0.139314i | 0.374474 | − | 0.927237i | \(-0.377823\pi\) |
−0.615774 | + | 0.787923i | \(0.711156\pi\) | |||||||
\(510\) | −3.71237 | − | 6.43002i | −0.164387 | − | 0.284726i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 25.3457i | − | 1.12013i | ||||||
\(513\) | 31.7824i | 1.40323i | ||||||||
\(514\) | −32.4238 | + | 18.7199i | −1.43015 | + | 0.825699i | ||||
\(515\) | 20.3061 | + | 11.7237i | 0.894792 | + | 0.516608i | ||||
\(516\) | 3.93818 | 0.173369 | ||||||||
\(517\) | −9.25143 | − | 16.0240i | −0.406878 | − | 0.704733i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.30354 | 0.276695 | ||||||||
\(520\) | 7.92592 | + | 18.1451i | 0.347574 | + | 0.795716i | ||||
\(521\) | 5.42367 | − | 9.39407i | 0.237615 | − | 0.411562i | −0.722414 | − | 0.691460i | \(-0.756968\pi\) |
0.960029 | + | 0.279899i | \(0.0903010\pi\) | |||||||
\(522\) | 7.34304i | 0.321396i | ||||||||
\(523\) | −0.673629 | + | 1.16676i | −0.0294557 | + | 0.0510188i | −0.880377 | − | 0.474274i | \(-0.842711\pi\) |
0.850922 | + | 0.525292i | \(0.176044\pi\) | |||||||
\(524\) | −0.567579 | + | 0.983076i | −0.0247948 | + | 0.0429459i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.0167 | − | 12.7113i | −0.959974 | − | 0.554241i | ||||
\(527\) | − | 5.67167i | − | 0.247062i | ||||||
\(528\) | 8.77394 | + | 5.06563i | 0.381837 | + | 0.220453i | ||||
\(529\) | −12.9936 | − | 22.5057i | −0.564941 | − | 0.978507i | ||||
\(530\) | 12.1492 | − | 21.0431i | 0.527728 | − | 0.914052i | ||||
\(531\) | 4.35510 | − | 2.51442i | 0.188995 | − | 0.109117i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.0375 | + | 9.18931i | −0.911233 | + | 0.398033i | ||||
\(534\) | 11.9751 | + | 20.7415i | 0.518214 | + | 0.897574i | ||||
\(535\) | − | 7.27501i | − | 0.314526i | ||||||
\(536\) | −15.1841 | −0.655853 | ||||||||
\(537\) | −14.3555 | −0.619484 | ||||||||
\(538\) | − | 28.4993i | − | 1.22869i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.15198 | + | 1.81980i | 0.135640 | + | 0.0783115i | ||||
\(541\) | −17.4565 | + | 10.0785i | −0.750516 | + | 0.433310i | −0.825880 | − | 0.563846i | \(-0.809321\pi\) |
0.0753646 | + | 0.997156i | \(0.475988\pi\) | |||||||
\(542\) | −5.99978 | − | 10.3919i | −0.257712 | − | 0.446371i | ||||
\(543\) | 25.5220 | 1.09526 | ||||||||
\(544\) | 4.91047 | + | 2.83506i | 0.210535 | + | 0.121552i | ||||
\(545\) | −3.60415 | −0.154385 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.42286 | −0.146351 | −0.0731755 | − | 0.997319i | \(-0.523313\pi\) | ||||
−0.0731755 | + | 0.997319i | \(0.523313\pi\) | |||||||
\(548\) | 7.01924 | + | 4.05256i | 0.299847 | + | 0.173117i | ||||
\(549\) | −1.76975 | −0.0755309 | ||||||||
\(550\) | −3.02594 | − | 5.24109i | −0.129027 | − | 0.223481i | ||||
\(551\) | −17.8742 | + | 10.3197i | −0.761467 | + | 0.439633i | ||||
\(552\) | −21.4214 | − | 12.3677i | −0.911757 | − | 0.526403i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.3093i | 0.777889i | ||||||||
\(555\) | −3.69458 | −0.156826 | ||||||||
\(556\) | 4.10041 | 0.173896 | ||||||||
\(557\) | − | 23.6654i | − | 1.00273i | −0.865234 | − | 0.501367i | \(-0.832830\pi\) | ||
0.865234 | − | 0.501367i | \(-0.167170\pi\) | |||||||
\(558\) | −2.15832 | − | 3.73832i | −0.0913690 | − | 0.158256i | ||||
\(559\) | −19.4806 | + | 26.4190i | −0.823940 | + | 1.11740i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.71139 | + | 4.45217i | −0.325575 | + | 0.187971i | ||||
\(562\) | 0.0630888 | − | 0.109273i | 0.00266124 | − | 0.00460941i | ||||
\(563\) | 14.4037 | + | 24.9480i | 0.607045 | + | 1.05143i | 0.991725 | + | 0.128382i | \(0.0409784\pi\) |
−0.384680 | + | 0.923050i | \(0.625688\pi\) | |||||||
\(564\) | 2.49475 | + | 1.44035i | 0.105048 | + | 0.0606496i | ||||
\(565\) | 19.1909i | 0.807366i | ||||||||
\(566\) | −0.686177 | − | 0.396164i | −0.0288422 | − | 0.0166520i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.11343 | + | 7.12467i | −0.172596 | + | 0.298945i | ||||
\(569\) | −13.8361 | + | 23.9648i | −0.580040 | + | 1.00466i | 0.415434 | + | 0.909623i | \(0.363630\pi\) |
−0.995474 | + | 0.0950353i | \(0.969704\pi\) | |||||||
\(570\) | − | 15.8832i | − | 0.665272i | ||||||
\(571\) | 6.48273 | − | 11.2284i | 0.271294 | − | 0.469895i | −0.697899 | − | 0.716196i | \(-0.745882\pi\) |
0.969193 | + | 0.246301i | \(0.0792151\pi\) | |||||||
\(572\) | 3.40027 | − | 1.48526i | 0.142173 | − | 0.0621020i | ||||
\(573\) | −3.22016 | −0.134524 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.97105 | + | 10.3422i | 0.249010 | + | 0.431298i | ||||
\(576\) | 14.5305 | 0.605437 | ||||||||
\(577\) | 8.19301 | + | 4.73023i | 0.341079 | + | 0.196922i | 0.660749 | − | 0.750607i | \(-0.270239\pi\) |
−0.319670 | + | 0.947529i | \(0.603572\pi\) | |||||||
\(578\) | −10.4702 | + | 6.04497i | −0.435503 | + | 0.251438i | ||||
\(579\) | − | 15.1706i | − | 0.630468i | ||||||
\(580\) | 2.36354i | 0.0981405i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.6057 | − | 18.3696i | −0.439620 | − | 0.761444i | ||||
\(583\) | −25.2365 | − | 14.5703i | −1.04519 | − | 0.603440i | ||||
\(584\) | −11.6077 | + | 20.1052i | −0.480332 | + | 0.831959i | ||||
\(585\) | −9.80999 | + | 4.28507i | −0.405593 | + | 0.177166i | ||||
\(586\) | −15.8892 | − | 27.5209i | −0.656377 | − | 1.13688i | ||||
\(587\) | −18.6673 | + | 10.7776i | −0.770481 | + | 0.444837i | −0.833046 | − | 0.553204i | \(-0.813405\pi\) |
0.0625654 | + | 0.998041i | \(0.480072\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.06647 | − | 10.5074i | 0.249965 | − | 0.432951i | ||||
\(590\) | −6.16761 | + | 3.56087i | −0.253917 | + | 0.146599i | ||||
\(591\) | −19.2441 | + | 11.1106i | −0.791598 | + | 0.457029i | ||||
\(592\) | −4.71274 | + | 2.72090i | −0.193692 | + | 0.111828i | ||||
\(593\) | −3.44015 | + | 1.98617i | −0.141270 | + | 0.0815622i | −0.568969 | − | 0.822359i | \(-0.692658\pi\) |
0.427699 | + | 0.903921i | \(0.359324\pi\) | |||||||
\(594\) | −9.60231 | + | 16.6317i | −0.393988 | + | 0.682407i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.740117 | − | 0.427307i | 0.0303164 | − | 0.0175032i | ||||
\(597\) | 11.6978 | + | 20.2612i | 0.478759 | + | 0.829234i | ||||
\(598\) | 29.5214 | − | 12.8951i | 1.20722 | − | 0.527322i | ||||
\(599\) | 9.75246 | − | 16.8918i | 0.398475 | − | 0.690179i | −0.595063 | − | 0.803679i | \(-0.702873\pi\) |
0.993538 | + | 0.113500i | \(0.0362063\pi\) | |||||||
\(600\) | 5.22211 | + | 3.01498i | 0.213192 | + | 0.123086i | ||||
\(601\) | 13.4368 | + | 23.2733i | 0.548100 | + | 0.949336i | 0.998405 | + | 0.0564616i | \(0.0179818\pi\) |
−0.450305 | + | 0.892875i | \(0.648685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 8.20914i | − | 0.334302i | ||||||
\(604\) | − | 7.63576i | − | 0.310695i | ||||||
\(605\) | −5.15523 | + | 2.97637i | −0.209590 | + | 0.121007i | ||||
\(606\) | 0.0944146 | + | 0.0545103i | 0.00383533 | + | 0.00221433i | ||||
\(607\) | 25.0203 | 1.01554 | 0.507772 | − | 0.861491i | \(-0.330469\pi\) | ||||
0.507772 | + | 0.861491i | \(0.330469\pi\) | |||||||
\(608\) | 6.06482 | + | 10.5046i | 0.245961 | + | 0.426016i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.50628 | 0.101476 | ||||||||
\(611\) | −22.0030 | + | 9.61106i | −0.890146 | + | 0.388822i | ||||
\(612\) | −0.831324 | + | 1.43990i | −0.0336043 | + | 0.0582043i | ||||
\(613\) | − | 21.3585i | − | 0.862663i | −0.902194 | − | 0.431332i | \(-0.858044\pi\) | ||
0.902194 | − | 0.431332i | \(-0.141956\pi\) | |||||||
\(614\) | 6.31751 | − | 10.9422i | 0.254954 | − | 0.441593i | ||||
\(615\) | 6.74796 | − | 11.6878i | 0.272104 | − | 0.471298i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5425 | − | 16.4790i | −1.14908 | − | 0.663420i | −0.200415 | − | 0.979711i | \(-0.564229\pi\) |
−0.948662 | + | 0.316291i | \(0.897562\pi\) | |||||||
\(618\) | − | 19.2622i | − | 0.774840i | ||||||
\(619\) | −42.3588 | − | 24.4559i | −1.70254 | − | 0.982965i | −0.943170 | − | 0.332311i | \(-0.892172\pi\) |
−0.759375 | − | 0.650654i | \(-0.774495\pi\) | |||||||
\(620\) | −0.694707 | − | 1.20327i | −0.0279001 | − | 0.0483244i | ||||
\(621\) | 18.9481 | − | 32.8191i | 0.760361 | − | 1.31698i | ||||
\(622\) | −8.00176 | + | 4.61982i | −0.320841 | + | 0.185238i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.80240 | − | 10.5814i | 0.312346 | − | 0.423595i | ||||
\(625\) | 6.77880 | + | 11.7412i | 0.271152 | + | 0.469649i | ||||
\(626\) | 41.6934i | 1.66640i | ||||||||
\(627\) | −19.0483 | −0.760718 | ||||||||
\(628\) | 1.07281 | 0.0428099 | ||||||||
\(629\) | − | 4.78278i | − | 0.190702i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.65076 | + | 2.68512i | 0.185144 | + | 0.106893i | 0.589707 | − | 0.807617i | \(-0.299243\pi\) |
−0.404563 | + | 0.914510i | \(0.632576\pi\) | |||||||
\(632\) | −41.2470 | + | 23.8140i | −1.64072 | + | 0.947270i | ||||
\(633\) | 5.83981 | + | 10.1148i | 0.232111 | + | 0.402029i | ||||
\(634\) | −21.9242 | −0.870720 | ||||||||
\(635\) | −17.7127 | − | 10.2264i | −0.702905 | − | 0.405823i | ||||
\(636\) | 4.53687 | 0.179899 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12.4714 | −0.493747 | ||||||||
\(639\) | −3.85189 | − | 2.22389i | −0.152378 | − | 0.0879757i | ||||
\(640\) | −13.0773 | −0.516926 | ||||||||
\(641\) | 19.8510 | + | 34.3829i | 0.784066 | + | 1.35804i | 0.929555 | + | 0.368683i | \(0.120191\pi\) |
−0.145489 | + | 0.989360i | \(0.546475\pi\) | |||||||
\(642\) | −5.17578 | + | 2.98824i | −0.204272 | + | 0.117936i | ||||
\(643\) | 27.8388 | + | 16.0727i | 1.09785 | + | 0.633847i | 0.935657 | − | 0.352911i | \(-0.114808\pi\) |
0.162198 | + | 0.986758i | \(0.448142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 19.2970i | − | 0.759818i | ||||||
\(646\) | 20.5614 | 0.808978 | ||||||||
\(647\) | 19.8500 | 0.780385 | 0.390193 | − | 0.920733i | \(-0.372408\pi\) | ||||
0.390193 | + | 0.920733i | \(0.372408\pi\) | |||||||
\(648\) | − | 4.28417i | − | 0.168298i | ||||||
\(649\) | 4.27048 | + | 7.39669i | 0.167631 | + | 0.290346i | ||||
\(650\) | −7.19670 | + | 3.14357i | −0.282278 | + | 0.123301i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.51671 | − | 4.33977i | 0.294377 | − | 0.169959i | ||||
\(653\) | 9.50024 | − | 16.4549i | 0.371773 | − | 0.643930i | −0.618065 | − | 0.786127i | \(-0.712083\pi\) |
0.989838 | + | 0.142197i | \(0.0454165\pi\) | |||||||
\(654\) | 1.48042 | + | 2.56416i | 0.0578889 | + | 0.100266i | ||||
\(655\) | 4.81705 | + | 2.78112i | 0.188218 | + | 0.108667i | ||||
\(656\) | − | 19.8784i | − | 0.776120i | ||||||
\(657\) | −10.8697 | − | 6.27562i | −0.424067 | − | 0.244835i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.60729 | − | 6.24801i | 0.140520 | − | 0.243388i | −0.787173 | − | 0.616733i | \(-0.788456\pi\) |
0.927693 | + | 0.373345i | \(0.121789\pi\) | |||||||
\(660\) | −1.09067 | + | 1.88909i | −0.0424542 | + | 0.0735329i | ||||
\(661\) | 16.7510i | 0.651537i | 0.945450 | + | 0.325769i | \(0.105623\pi\) | ||||
−0.945450 | + | 0.325769i | \(0.894377\pi\) | |||||||
\(662\) | −12.7235 | + | 22.0377i | −0.494512 | + | 0.856520i | ||||
\(663\) | 4.62524 | + | 10.5888i | 0.179629 | + | 0.411233i | ||||
\(664\) | −24.1291 | −0.936393 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.82006 | − | 3.15244i | −0.0705259 | − | 0.122155i | ||||
\(667\) | 24.6096 | 0.952889 | ||||||||
\(668\) | −2.43842 | − | 1.40782i | −0.0943453 | − | 0.0544703i | ||||
\(669\) | −8.47860 | + | 4.89512i | −0.327802 | + | 0.189256i | ||||
\(670\) | 11.6256i | 0.449137i | ||||||||
\(671\) | − | 3.00573i | − | 0.116035i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6684 | − | 32.3346i | −0.719614 | − | 1.24641i | −0.961153 | − | 0.276016i | \(-0.910986\pi\) |
0.241539 | − | 0.970391i | \(-0.422348\pi\) | |||||||
\(674\) | −1.40612 | − | 0.811824i | −0.0541618 | − | 0.0312703i | ||||
\(675\) | −4.61916 | + | 8.00061i | −0.177791 | + | 0.307944i | ||||
\(676\) | −1.42320 | − | 4.59986i | −0.0547383 | − | 0.176918i | ||||
\(677\) | −14.0671 | − | 24.3649i | −0.540641 | − | 0.936418i | −0.998867 | − | 0.0475826i | \(-0.984848\pi\) |
0.458226 | − | 0.888836i | \(-0.348485\pi\) | |||||||
\(678\) | 13.6533 | − | 7.88271i | 0.524350 | − | 0.302734i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.53452 | − | 13.0502i | 0.288935 | − | 0.500451i | ||||
\(681\) | −0.930253 | + | 0.537082i | −0.0356474 | + | 0.0205810i | ||||
\(682\) | 6.34915 | − | 3.66568i | 0.243122 | − | 0.140366i | ||||
\(683\) | 1.79295 | − | 1.03516i | 0.0686053 | − | 0.0396093i | −0.465305 | − | 0.885150i | \(-0.654055\pi\) |
0.533910 | + | 0.845541i | \(0.320722\pi\) | |||||||
\(684\) | −3.08025 | + | 1.77838i | −0.117776 | + | 0.0679982i | ||||
\(685\) | 19.8574 | − | 34.3941i | 0.758714 | − | 1.31413i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.9028 | + | 14.3776i | −0.950100 | + | 0.548540i | ||||
\(688\) | −14.2114 | − | 24.6149i | −0.541805 | − | 0.938434i | ||||
\(689\) | −22.4421 | + | 30.4353i | −0.854975 | + | 1.15949i | ||||
\(690\) | −9.46925 | + | 16.4012i | −0.360488 | + | 0.624384i | ||||
\(691\) | −31.0542 | − | 17.9291i | −1.18136 | − | 0.682057i | −0.225029 | − | 0.974352i | \(-0.572248\pi\) |
−0.956328 | + | 0.292295i | \(0.905581\pi\) | |||||||
\(692\) | 0.999521 | + | 1.73122i | 0.0379961 | + | 0.0658112i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.0417i | 1.25425i | ||||||||
\(695\) | − | 20.0919i | − | 0.762129i | ||||||
\(696\) | 10.7614 | − | 6.21312i | 0.407911 | − | 0.235508i | ||||
\(697\) | 15.1304 | + | 8.73552i | 0.573103 | + | 0.330881i | ||||
\(698\) | 22.1059 | 0.836722 | ||||||||
\(699\) | 10.0891 | + | 17.4748i | 0.381604 | + | 0.660958i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.8940 | −1.69562 | −0.847812 | − | 0.530297i | \(-0.822081\pi\) | ||||
−0.847812 | + | 0.530297i | \(0.822081\pi\) | |||||||
\(702\) | 20.0579 | + | 14.7901i | 0.757035 | + | 0.558215i | ||||
\(703\) | 5.11571 | − | 8.86067i | 0.192943 | − | 0.334187i | ||||
\(704\) | 24.6785i | 0.930107i | ||||||||
\(705\) | 7.05767 | − | 12.2242i | 0.265807 | − | 0.460391i | ||||
\(706\) | −16.1801 | + | 28.0248i | −0.608947 | + | 1.05473i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.15158 | − | 0.664867i | −0.0432792 | − | 0.0249872i | ||||
\(709\) | 16.2656i | 0.610866i | 0.952213 | + | 0.305433i | \(0.0988013\pi\) | ||||
−0.952213 | + | 0.305433i | \(0.901199\pi\) | |||||||
\(710\) | 5.45497 | + | 3.14943i | 0.204721 | + | 0.118196i | ||||
\(711\) | −12.8748 | − | 22.2998i | −0.482843 | − | 0.836309i | ||||
\(712\) | −24.3043 | + | 42.0963i | −0.910843 | + | 1.57763i | ||||
\(713\) | −12.5287 | + | 7.23344i | −0.469203 | + | 0.270894i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.27775 | − | 16.6613i | −0.272173 | − | 0.623096i | ||||
\(716\) | −2.27627 | − | 3.94262i | −0.0850683 | − | 0.147343i | ||||
\(717\) | − | 16.9149i | − | 0.631697i | ||||||
\(718\) | 6.72806 | 0.251089 | ||||||||
\(719\) | 10.0149 | 0.373492 | 0.186746 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186746 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(720\) | − | 9.26949i | − | 0.345454i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.0873 | + | 9.86534i | 0.635922 | + | 0.367150i | ||||
\(723\) | −8.53100 | + | 4.92538i | −0.317271 | + | 0.183177i | ||||
\(724\) | 4.04690 | + | 7.00944i | 0.150402 | + | 0.260504i | ||||
\(725\) | −5.99932 | −0.222809 | ||||||||
\(726\) | 4.23506 | + | 2.44511i | 0.157178 | + | 0.0907466i | ||||
\(727\) | 34.5299 | 1.28064 | 0.640322 | − | 0.768106i | \(-0.278801\pi\) | ||||
0.640322 | + | 0.768106i | \(0.278801\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.2872 | 0.788415 | ||||||||
\(730\) | 15.3934 | + | 8.88741i | 0.569737 | + | 0.328938i | ||||
\(731\) | 24.9808 | 0.923947 | ||||||||
\(732\) | 0.233980 | + | 0.405265i | 0.00864814 | + | 0.0149790i | ||||
\(733\) | 28.6966 | − | 16.5680i | 1.05993 | − | 0.611953i | 0.134520 | − | 0.990911i | \(-0.457051\pi\) |
0.925414 | + | 0.378958i | \(0.123717\pi\) | |||||||
\(734\) | −27.9895 | − | 16.1598i | −1.03311 | − | 0.596468i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 14.4629i | − | 0.533111i | ||||||
\(737\) | 13.9424 | 0.513574 | ||||||||
\(738\) | 13.2970 | 0.489470 | ||||||||
\(739\) | − | 4.01567i | − | 0.147719i | −0.997269 | − | 0.0738594i | \(-0.976468\pi\) | ||
0.997269 | − | 0.0738594i | \(-0.0235316\pi\) | |||||||
\(740\) | −0.585830 | − | 1.01469i | −0.0215356 | − | 0.0373007i | ||||
\(741\) | −2.75703 | + | 24.5641i | −0.101282 | + | 0.902386i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8361 | − | 6.25622i | 0.397538 | − | 0.229519i | −0.287883 | − | 0.957666i | \(-0.592952\pi\) |
0.685421 | + | 0.728147i | \(0.259618\pi\) | |||||||
\(744\) | −3.65241 | + | 6.32616i | −0.133904 | + | 0.231928i | ||||
\(745\) | −2.09379 | − | 3.62656i | −0.0767107 | − | 0.132867i | ||||
\(746\) | 7.50418 | + | 4.33254i | 0.274748 | + | 0.158626i | ||||
\(747\) | − | 13.0452i | − | 0.477299i | ||||||
\(748\) | −2.44551 | − | 1.41192i | −0.0894168 | − | 0.0516248i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.07304 | − | 15.7150i | 0.331300 | − | 0.573829i | ||||
\(751\) | 18.7579 | − | 32.4896i | 0.684486 | − | 1.18556i | −0.289112 | − | 0.957295i | \(-0.593360\pi\) |
0.973598 | − | 0.228269i | \(-0.0733065\pi\) | |||||||
\(752\) | − | 20.7907i | − | 0.758159i | ||||||
\(753\) | 8.56826 | − | 14.8407i | 0.312245 | − | 0.540824i | ||||
\(754\) | −1.80509 | + | 16.0827i | −0.0657375 | + | 0.585698i | ||||
\(755\) | −37.4150 | −1.36167 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.5223 | + | 30.3496i | 0.636860 | + | 1.10307i | 0.986118 | + | 0.166047i | \(0.0531004\pi\) |
−0.349258 | + | 0.937027i | \(0.613566\pi\) | |||||||
\(758\) | −15.7306 | −0.571361 | ||||||||
\(759\) | 19.6697 | + | 11.3563i | 0.713963 | + | 0.412207i | ||||
\(760\) | 27.9172 | − | 16.1180i | 1.01266 | − | 0.584661i | ||||
\(761\) | 4.30225i | 0.155956i | 0.996955 | + | 0.0779782i | \(0.0248465\pi\) | ||||
−0.996955 | + | 0.0779782i | \(0.975154\pi\) | |||||||
\(762\) | 16.8021i | 0.608677i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.510605 | − | 0.884394i | −0.0184730 | − | 0.0319962i | ||||
\(765\) | 7.05545 | + | 4.07347i | 0.255090 | + | 0.147277i | ||||
\(766\) | 4.63340 | − | 8.02528i | 0.167411 | − | 0.289965i | ||||
\(767\) | 10.1566 | − | 4.43649i | 0.366735 | − | 0.160192i | ||||
\(768\) | −5.00195 | − | 8.66363i | −0.180492 | − | 0.312622i | ||||
\(769\) | 10.6146 | − | 6.12834i | 0.382772 | − | 0.220994i | −0.296251 | − | 0.955110i | \(-0.595737\pi\) |
0.679024 | + | 0.734116i | \(0.262403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.1268 | + | 29.6645i | −0.616806 | + | 1.06834i | ||||
\(772\) | 4.16649 | − | 2.40552i | 0.149955 | − | 0.0865767i | ||||
\(773\) | 3.29372 | − | 1.90163i | 0.118467 | − | 0.0683970i | −0.439596 | − | 0.898196i | \(-0.644878\pi\) |
0.558063 | + | 0.829799i | \(0.311545\pi\) | |||||||
\(774\) | 16.4654 | − | 9.50628i | 0.591835 | − | 0.341696i | ||||
\(775\) | 3.05424 | − | 1.76336i | 0.109711 | − | 0.0633419i | ||||
\(776\) | 21.5250 | − | 37.2824i | 0.772702 | − | 1.33836i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.90250 | − | 4.56251i | 0.283318 | − | 0.163574i | ||||
\(779\) | 18.6872 | + | 32.3672i | 0.669538 | + | 1.15967i | ||||
\(780\) | 2.27825 | + | 1.67992i | 0.0815745 | + | 0.0601506i | ||||
\(781\) | 3.77705 | − | 6.54204i | 0.135153 | − | 0.234092i | ||||
\(782\) | −21.2321 | − | 12.2583i | −0.759258 | − | 0.438358i | ||||
\(783\) | 9.51891 | + | 16.4872i | 0.340178 | + | 0.589206i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.25675i | − | 0.187622i | ||||||
\(786\) | − | 4.56943i | − | 0.162986i | ||||||
\(787\) | −15.0114 | + | 8.66684i | −0.535099 | + | 0.308940i | −0.743090 | − | 0.669191i | \(-0.766641\pi\) |
0.207991 | + | 0.978131i | \(0.433307\pi\) | |||||||
\(788\) | −6.10289 | − | 3.52351i | −0.217407 | − | 0.125520i | ||||
\(789\) | −23.2592 | −0.828048 | ||||||||
\(790\) | 18.2331 | + | 31.5806i | 0.648704 | + | 1.12359i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.7544 | −0.488740 | ||||||||
\(793\) | −3.87609 | − | 0.435044i | −0.137644 | − | 0.0154489i | ||||
\(794\) | 14.3366 | − | 24.8317i | 0.508786 | − | 0.881243i | ||||
\(795\) | − | 22.2306i | − | 0.788437i | ||||||
\(796\) | −3.70972 | + | 6.42542i | −0.131488 | + | 0.227743i | ||||
\(797\) | 25.1707 | − | 43.5969i | 0.891592 | − | 1.54428i | 0.0536245 | − | 0.998561i | \(-0.482923\pi\) |
0.837967 | − | 0.545721i | \(-0.183744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.8248 | + | 9.13645i | 0.559841 | + | 0.323224i | ||||
\(800\) | 3.52576i | 0.124655i | ||||||||
\(801\) | −22.7590 | − | 13.1399i | −0.804150 | − | 0.464276i | ||||
\(802\) | −1.94978 | − | 3.37711i | −0.0688490 | − | 0.119250i | ||||
\(803\) | 10.6585 | − | 18.4610i | 0.376130 | − | 0.651476i | ||||
\(804\) | −1.87986 | + | 1.08534i | −0.0662975 | + | 0.0382769i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.80818 | − | 8.71822i | −0.134137 | − | 0.307086i | ||||
\(807\) | −13.0369 | − | 22.5807i | −0.458922 | − | 0.794877i | ||||
\(808\) | 0.221265i | 0.00778407i | ||||||||
\(809\) | 16.0739 | 0.565128 | 0.282564 | − | 0.959249i | \(-0.408815\pi\) | ||||
0.282564 | + | 0.959249i | \(0.408815\pi\) | |||||||
\(810\) | −3.28016 | −0.115253 | ||||||||
\(811\) | − | 36.9875i | − | 1.29881i | −0.760443 | − | 0.649404i | \(-0.775018\pi\) | ||
0.760443 | − | 0.649404i | \(-0.224982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.50754 | − | 5.48918i | −0.333444 | − | 0.192514i | ||||
\(814\) | 5.35409 | − | 3.09119i | 0.187661 | − | 0.108346i | ||||
\(815\) | −21.2648 | − | 36.8317i | −0.744873 | − | 1.29016i | ||||
\(816\) | −10.0053 | −0.350257 | ||||||||
\(817\) | 46.2798 | + | 26.7197i | 1.61913 | + | 0.934803i | ||||
\(818\) | 7.15624 | 0.250212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.27996 | 0.149463 | ||||||||
\(821\) | −26.1021 | − | 15.0700i | −0.910968 | − | 0.525948i | −0.0302256 | − | 0.999543i | \(-0.509623\pi\) |
−0.880743 | + | 0.473595i | \(0.842956\pi\) | |||||||
\(822\) | −32.6261 | −1.13796 | ||||||||
\(823\) | 20.8251 | + | 36.0702i | 0.725918 | + | 1.25733i | 0.958595 | + | 0.284773i | \(0.0919181\pi\) |
−0.232677 | + | 0.972554i | \(0.574749\pi\) | |||||||
\(824\) | 33.8564 | − | 19.5470i | 1.17944 | − | 0.680952i | ||||
\(825\) | −4.79506 | − | 2.76843i | −0.166942 | − | 0.0963842i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.6524i | 1.30930i | 0.755932 | + | 0.654651i | \(0.227184\pi\) | ||||
−0.755932 | + | 0.654651i | \(0.772816\pi\) | |||||||
\(828\) | 4.24096 | 0.147384 | ||||||||
\(829\) | 7.47474 | 0.259609 | 0.129804 | − | 0.991540i | \(-0.458565\pi\) | ||||
0.129804 | + | 0.991540i | \(0.458565\pi\) | |||||||
\(830\) | 18.4744i | 0.641255i | ||||||||
\(831\) | 8.37558 | + | 14.5069i | 0.290546 | + | 0.503240i | ||||
\(832\) | 31.8246 | + | 3.57193i | 1.10332 | + | 0.123834i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.2943 | + | 8.25282i | −0.494971 | + | 0.285772i | ||||
\(835\) | −6.89829 | + | 11.9482i | −0.238725 | + | 0.413484i | ||||
\(836\) | −3.02040 | − | 5.23149i | −0.104463 | − | 0.180935i | ||||
\(837\) | −9.69209 | − | 5.59573i | −0.335008 | − | 0.193417i | ||||
\(838\) | 7.83732i | 0.270736i | ||||||||
\(839\) | −9.51957 | − | 5.49613i | −0.328652 | − | 0.189747i | 0.326590 | − | 0.945166i | \(-0.394100\pi\) |
−0.655242 | + | 0.755419i | \(0.727434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.31846 | − | 14.4080i | 0.286843 | − | 0.496827i | ||||
\(842\) | −1.22926 | + | 2.12914i | −0.0423632 | + | 0.0733752i | ||||
\(843\) | − | 0.115440i | − | 0.00397595i | ||||||
\(844\) | −1.85198 | + | 3.20772i | −0.0637477 | + | 0.110414i | ||||
\(845\) | −22.5392 | + | 6.97363i | −0.775372 | + | 0.239900i | ||||
\(846\) | 13.9073 | 0.478143 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.3719 | − | 28.3569i | −0.562213 | − | 0.973781i | ||||
\(849\) | −0.724899 | −0.0248785 | ||||||||
\(850\) | 5.17594 | + | 2.98833i | 0.177533 | + | 0.102499i | ||||
\(851\) | −10.5651 | + | 6.09979i | −0.362169 | + | 0.209098i | ||||
\(852\) | 1.17609i | 0.0402922i | ||||||||
\(853\) | 35.2031i | 1.20533i | 0.797994 | + | 0.602666i | \(0.205895\pi\) | ||||
−0.797994 | + | 0.602666i | \(0.794105\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.71404 | + | 15.0932i | 0.298014 | + | 0.516175i | ||||
\(856\) | −10.5046 | − | 6.06483i | −0.359040 | − | 0.207292i | ||||
\(857\) | 15.1841 | − | 26.2996i | 0.518678 | − | 0.898377i | −0.481086 | − | 0.876673i | \(-0.659758\pi\) |
0.999764 | − | 0.0217035i | \(-0.00690898\pi\) | |||||||
\(858\) | −8.86422 | + | 12.0214i | −0.302620 | + | 0.410404i | ||||
\(859\) | 17.9153 | + | 31.0302i | 0.611262 | + | 1.05874i | 0.991028 | + | 0.133654i | \(0.0426710\pi\) |
−0.379767 | + | 0.925082i | \(0.623996\pi\) | |||||||
\(860\) | 5.29977 | − | 3.05983i | 0.180721 | − | 0.104339i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.86113 | − | 11.8838i | 0.233691 | − | 0.404765i | ||||
\(863\) | 28.0075 | − | 16.1702i | 0.953387 | − | 0.550438i | 0.0592557 | − | 0.998243i | \(-0.481127\pi\) |
0.894131 | + | 0.447805i | \(0.147794\pi\) | |||||||
\(864\) | 9.68945 | − | 5.59421i | 0.329642 | − | 0.190319i | ||||
\(865\) | 8.48294 | − | 4.89763i | 0.288429 | − | 0.166524i | ||||
\(866\) | −44.5151 | + | 25.7008i | −1.51268 | + | 0.873349i | ||||
\(867\) | −5.53053 | + | 9.57916i | −0.187827 | + | 0.325325i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.8740 | − | 21.8665i | 1.28479 | − | 0.741772i | ||||
\(870\) | −4.75705 | − | 8.23944i | −0.161279 | − | 0.279343i | ||||
\(871\) | 2.01800 | − | 17.9796i | 0.0683772 | − | 0.609216i | ||||
\(872\) | −3.00461 | + | 5.20413i | −0.101749 | + | 0.176234i | ||||
\(873\) | 20.1564 | + | 11.6373i | 0.682190 | + | 0.393862i | ||||
\(874\) | −26.2233 | − | 45.4201i | −0.887016 | − | 1.53636i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.31882i | 0.112133i | ||||||||
\(877\) | − | 4.41611i | − | 0.149121i | −0.997216 | − | 0.0745607i | \(-0.976245\pi\) | ||
0.997216 | − | 0.0745607i | \(-0.0237555\pi\) | |||||||
\(878\) | 24.2674 | − | 14.0108i | 0.818984 | − | 0.472841i | ||||
\(879\) | −25.1788 | − | 14.5370i | −0.849261 | − | 0.490321i | ||||
\(880\) | 15.7433 | 0.530706 | ||||||||
\(881\) | 9.97753 | + | 17.2816i | 0.336152 | + | 0.582232i | 0.983705 | − | 0.179788i | \(-0.0575412\pi\) |
−0.647554 | + | 0.762020i | \(0.724208\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.9725 | −0.436559 | −0.218280 | − | 0.975886i | \(-0.570045\pi\) | ||||
−0.218280 | + | 0.975886i | \(0.570045\pi\) | |||||||
\(884\) | −2.17472 | + | 2.94929i | −0.0731438 | + | 0.0991955i | ||||
\(885\) | −3.25783 | + | 5.64273i | −0.109511 | + | 0.189678i | ||||
\(886\) | − | 35.6114i | − | 1.19639i | ||||||
\(887\) | −27.0862 | + | 46.9147i | −0.909467 | + | 1.57524i | −0.0946605 | + | 0.995510i | \(0.530177\pi\) |
−0.814806 | + | 0.579733i | \(0.803157\pi\) | |||||||
\(888\) | −3.07999 | + | 5.33470i | −0.103358 | + | 0.179021i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32.2309 | + | 18.6085i | 1.08038 | + | 0.623758i | ||||
\(891\) | 3.93383i | 0.131788i | ||||||||
\(892\) | −2.68882 | − | 1.55239i | −0.0900283 | − | 0.0519779i | ||||
\(893\) | 19.5449 | + | 33.8527i | 0.654044 | + | 1.13284i | ||||
\(894\) | −1.72007 | + | 2.97924i | −0.0575276 | + | 0.0996408i | ||||
\(895\) | −19.3187 | + | 11.1537i | −0.645755 | + | 0.372827i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.4916 | − | 23.7216i | 0.584029 | − | 0.792043i | ||||
\(898\) | −14.0813 | − | 24.3895i | −0.469898 | − | 0.813888i | ||||
\(899\) | − | 7.26769i | − | 0.242391i | ||||||
\(900\) | −1.03386 | −0.0344620 | ||||||||
\(901\) | 28.7784 | 0.958748 | ||||||||
\(902\) | 22.5836i | 0.751951i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.7102 | + | 15.9985i | 0.921629 | + | 0.532103i | ||||
\(905\) | 34.3461 | − | 19.8297i | 1.14170 | − | 0.659162i | ||||
\(906\) | 15.3684 | + | 26.6188i | 0.510580 | + | 0.884350i | ||||
\(907\) | 2.59139 | 0.0860457 | 0.0430229 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430229 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(908\) | −0.295011 | − | 0.170325i | −0.00979029 | − | 0.00565242i | ||||
\(909\) | −0.119625 | −0.00396770 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.59896 | 0.119239 | 0.0596195 | − | 0.998221i | \(-0.481011\pi\) | ||||
0.0596195 | + | 0.998221i | \(0.481011\pi\) | |||||||
\(912\) | −18.5361 | − | 10.7018i | −0.613791 | − | 0.354373i | ||||
\(913\) | 22.1559 | 0.733254 | ||||||||
\(914\) | 3.52094 | + | 6.09845i | 0.116462 | + | 0.201719i | ||||
\(915\) | 1.98579 | − | 1.14649i | 0.0656481 | − | 0.0379019i | ||||
\(916\) | −7.89741 | − | 4.55957i | −0.260938 | − | 0.150653i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 18.9659i | − | 0.625969i | ||||||
\(919\) | −27.9249 | −0.921156 | −0.460578 | − | 0.887619i | \(-0.652358\pi\) | ||||
−0.460578 | + | 0.887619i | \(0.652358\pi\) | |||||||
\(920\) | −38.4370 | −1.26723 | ||||||||
\(921\) | − | 11.5597i | − | 0.380906i | ||||||
\(922\) | −18.4324 | − | 31.9258i | −0.607039 | − | 1.05142i | ||||
\(923\) | −7.88971 | − | 5.81764i | −0.259693 | − | 0.191490i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.57557 | − | 1.48700i | 0.0846841 | − | 0.0488924i | ||||
\(926\) | 9.08174 | − | 15.7300i | 0.298445 | − | 0.516921i | ||||
\(927\) | 10.5679 | + | 18.3042i | 0.347096 | + | 0.601187i | ||||
\(928\) | 6.29229 | + | 3.63285i | 0.206554 | + | 0.119254i | ||||
\(929\) | 26.5659i | 0.871599i | 0.900044 | + | 0.435800i | \(0.143534\pi\) | ||||
−0.900044 | + | 0.435800i | \(0.856466\pi\) | |||||||
\(930\) | 4.84359 | + | 2.79645i | 0.158828 | + | 0.0916992i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.19955 | + | 5.54179i | −0.104805 | + | 0.181527i | ||||
\(933\) | −4.22666 | + | 7.32079i | −0.138375 | + | 0.239672i | ||||
\(934\) | 5.79976i | 0.189774i | ||||||||
\(935\) | −6.91836 | + | 11.9830i | −0.226255 | + | 0.391885i | ||||
\(936\) | −1.99079 | + | 17.7372i | −0.0650709 | + | 0.579758i | ||||
\(937\) | 3.02509 | 0.0988255 | 0.0494128 | − | 0.998778i | \(-0.484265\pi\) | ||||
0.0494128 | + | 0.998778i | \(0.484265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0726 | + | 33.0347i | 0.622410 | + | 1.07805i | ||||
\(940\) | 4.47640 | 0.146004 | ||||||||
\(941\) | 5.61587 | + | 3.24232i | 0.183072 | + | 0.105697i | 0.588735 | − | 0.808326i | \(-0.299626\pi\) |
−0.405663 | + | 0.914023i | \(0.632959\pi\) | |||||||
\(942\) | −3.73990 | + | 2.15923i | −0.121852 | + | 0.0703515i | ||||
\(943\) | − | 44.5639i | − | 1.45120i | ||||||
\(944\) | 9.59704i | 0.312357i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.1454 | + | 27.9647i | 0.524934 | + | 0.909212i | ||||
\(947\) | −18.3193 | − | 10.5767i | −0.595298 | − | 0.343695i | 0.171892 | − | 0.985116i | \(-0.445012\pi\) |
−0.767190 | + | 0.641420i | \(0.778345\pi\) | |||||||
\(948\) | −3.40438 | + | 5.89656i | −0.110569 | + | 0.191511i | ||||
\(949\) | −22.2641 | − | 16.4169i | −0.722722 | − | 0.532914i | ||||
\(950\) | 6.39270 | + | 11.0725i | 0.207407 | + | 0.359239i | ||||
\(951\) | −17.3711 | + | 10.0292i | −0.563295 | + | 0.325219i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.1393 | + | 31.4182i | −0.587590 | + | 1.01774i | 0.406957 | + | 0.913447i | \(0.366590\pi\) |
−0.994547 | + | 0.104289i | \(0.966743\pi\) | |||||||
\(954\) | 18.9685 | − | 10.9515i | 0.614128 | − | 0.354567i | ||||
\(955\) | −4.33351 | + | 2.50195i | −0.140229 | + | 0.0809613i | ||||
\(956\) | 4.64554 | − | 2.68211i | 0.150248 | − | 0.0867455i | ||||
\(957\) | −9.88140 | + | 5.70503i | −0.319420 | + | 0.184417i | ||||
\(958\) | −1.06308 | + | 1.84130i | −0.0343464 | + | 0.0594898i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16.3043 | + | 9.41329i | −0.526219 | + | 0.303813i | ||||
\(961\) | −13.3638 | − | 23.1468i | −0.431091 | − | 0.746672i | ||||
\(962\) | −3.21135 | − | 7.35187i | −0.103538 | − | 0.237034i | ||||
\(963\) | 3.27889 | − | 5.67921i | 0.105661 | − | 0.183010i | ||||
\(964\) | −2.70544 | − | 1.56199i | −0.0871363 | − | 0.0503082i | ||||
\(965\) | −11.7870 | − | 20.4157i | −0.379437 | − | 0.657204i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.2828i | − | 0.523621i | −0.965119 | − | 0.261810i | \(-0.915681\pi\) | ||
0.965119 | − | 0.261810i | \(-0.0843195\pi\) | |||||||
\(968\) | 9.92504i | 0.319003i | ||||||||
\(969\) | 16.2913 | − | 9.40580i | 0.523353 | − | 0.302158i | ||||
\(970\) | −28.5451 | − | 16.4805i | −0.916527 | − | 0.529157i | ||||
\(971\) | −24.5210 | −0.786915 | −0.393458 | − | 0.919343i | \(-0.628721\pi\) | ||||
−0.393458 | + | 0.919343i | \(0.628721\pi\) | |||||||
\(972\) | 2.70191 | + | 4.67984i | 0.0866638 | + | 0.150106i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.89560 | −0.0607390 | ||||||||
\(975\) | −4.26410 | + | 5.78285i | −0.136561 | + | 0.185199i | ||||
\(976\) | 1.68869 | − | 2.92490i | 0.0540537 | − | 0.0936237i | ||||
\(977\) | 10.9198i | 0.349355i | 0.984626 | + | 0.174677i | \(0.0558883\pi\) | ||||
−0.984626 | + | 0.174677i | \(0.944112\pi\) | |||||||
\(978\) | −17.4692 | + | 30.2575i | −0.558603 | + | 0.967528i | ||||
\(979\) | 22.3168 | − | 38.6538i | 0.713248 | − | 1.23538i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.81357 | − | 1.62441i | −0.0898302 | − | 0.0518635i | ||||
\(982\) | − | 20.4197i | − | 0.651618i | ||||||
\(983\) | −17.0360 | − | 9.83574i | −0.543364 | − | 0.313711i | 0.203077 | − | 0.979163i | \(-0.434906\pi\) |
−0.746441 | + | 0.665451i | \(0.768239\pi\) | |||||||
\(984\) | −11.2509 | − | 19.4871i | −0.358666 | − | 0.621227i | ||||
\(985\) | −17.2651 | + | 29.9040i | −0.550112 | + | 0.952822i | ||||
\(986\) | 10.6663 | − | 6.15820i | 0.339685 | − | 0.196117i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.18352 | + | 3.13781i | −0.228538 | + | 0.0998271i | ||||
\(989\) | −31.8596 | − | 55.1824i | −1.01307 | − | 1.75470i | ||||
\(990\) | 10.5310i | 0.334696i | ||||||||
\(991\) | −1.73800 | −0.0552094 | −0.0276047 | − | 0.999619i | \(-0.508788\pi\) | ||||
−0.0276047 | + | 0.999619i | \(0.508788\pi\) | |||||||
\(992\) | −4.27118 | −0.135610 | ||||||||
\(993\) | 23.2814i | 0.738812i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.4844 | + | 18.1775i | 0.998123 | + | 0.576267i | ||||
\(996\) | −2.98730 | + | 1.72472i | −0.0946562 | + | 0.0546498i | ||||
\(997\) | 23.4768 | + | 40.6631i | 0.743519 | + | 1.28781i | 0.950884 | + | 0.309549i | \(0.100178\pi\) |
−0.207365 | + | 0.978264i | \(0.566489\pi\) | |||||||
\(998\) | 22.6206 | 0.716044 | ||||||||
\(999\) | −8.17312 | − | 4.71875i | −0.258586 | − | 0.149295i |
(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 | 637.2.u.h.361.2 | 12 | ||
7.2 | even | 3 | 637.2.k.h.569.5 | 12 | |||
7.3 | odd | 6 | 637.2.q.h.491.5 | 12 | |||
7.4 | even | 3 | 91.2.q.a.36.5 | ✓ | 12 | ||
7.5 | odd | 6 | 637.2.k.g.569.5 | 12 | |||
7.6 | odd | 2 | 637.2.u.i.361.2 | 12 | |||
13.4 | even | 6 | 637.2.k.h.459.2 | 12 | |||
21.11 | odd | 6 | 819.2.ct.a.127.2 | 12 | |||
28.11 | odd | 6 | 1456.2.cc.c.673.2 | 12 | |||
91.4 | even | 6 | 91.2.q.a.43.5 | yes | 12 | ||
91.11 | odd | 12 | 1183.2.a.m.1.3 | 6 | |||
91.17 | odd | 6 | 637.2.q.h.589.5 | 12 | |||
91.24 | even | 12 | 8281.2.a.by.1.3 | 6 | |||
91.30 | even | 6 | inner | 637.2.u.h.30.2 | 12 | ||
91.67 | odd | 12 | 1183.2.a.p.1.4 | 6 | |||
91.69 | odd | 6 | 637.2.k.g.459.2 | 12 | |||
91.80 | even | 12 | 8281.2.a.ch.1.4 | 6 | |||
91.81 | even | 3 | 1183.2.c.i.337.9 | 12 | |||
91.82 | odd | 6 | 637.2.u.i.30.2 | 12 | |||
91.88 | even | 6 | 1183.2.c.i.337.4 | 12 | |||
273.95 | odd | 6 | 819.2.ct.a.316.2 | 12 | |||
364.95 | odd | 6 | 1456.2.cc.c.225.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.5 | ✓ | 12 | 7.4 | even | 3 | ||
91.2.q.a.43.5 | yes | 12 | 91.4 | even | 6 | ||
637.2.k.g.459.2 | 12 | 91.69 | odd | 6 | |||
637.2.k.g.569.5 | 12 | 7.5 | odd | 6 | |||
637.2.k.h.459.2 | 12 | 13.4 | even | 6 | |||
637.2.k.h.569.5 | 12 | 7.2 | even | 3 | |||
637.2.q.h.491.5 | 12 | 7.3 | odd | 6 | |||
637.2.q.h.589.5 | 12 | 91.17 | odd | 6 | |||
637.2.u.h.30.2 | 12 | 91.30 | even | 6 | inner | ||
637.2.u.h.361.2 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.i.30.2 | 12 | 91.82 | odd | 6 | |||
637.2.u.i.361.2 | 12 | 7.6 | odd | 2 | |||
819.2.ct.a.127.2 | 12 | 21.11 | odd | 6 | |||
819.2.ct.a.316.2 | 12 | 273.95 | odd | 6 | |||
1183.2.a.m.1.3 | 6 | 91.11 | odd | 12 | |||
1183.2.a.p.1.4 | 6 | 91.67 | odd | 12 | |||
1183.2.c.i.337.4 | 12 | 91.88 | even | 6 | |||
1183.2.c.i.337.9 | 12 | 91.81 | even | 3 | |||
1456.2.cc.c.225.2 | 12 | 364.95 | odd | 6 | |||
1456.2.cc.c.673.2 | 12 | 28.11 | odd | 6 | |||
8281.2.a.by.1.3 | 6 | 91.24 | even | 12 | |||
8281.2.a.ch.1.4 | 6 | 91.80 | even | 12 |