Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
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([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (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: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 569.5 | ||
Root | \(1.40744 + 0.138282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.569 |
Dual form | 637.2.k.h.459.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.27656i | 0.902667i | 0.892355 | + | 0.451334i | \(0.149052\pi\) | ||||
−0.892355 | + | 0.451334i | \(0.850948\pi\) | |||||||
\(3\) | 0.583963 | − | 1.01145i | 0.337151 | − | 0.583963i | −0.646745 | − | 0.762707i | \(-0.723870\pi\) |
0.983896 | + | 0.178744i | \(0.0572034\pi\) | |||||||
\(4\) | 0.370384 | 0.185192 | ||||||||
\(5\) | 1.57173 | + | 0.907437i | 0.702897 | + | 0.405818i | 0.808426 | − | 0.588598i | \(-0.200320\pi\) |
−0.105528 | + | 0.994416i | \(0.533653\pi\) | |||||||
\(6\) | 1.29118 | + | 0.745466i | 0.527124 | + | 0.304335i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.02595i | 1.06983i | ||||||||
\(9\) | 0.817975 | + | 1.41677i | 0.272658 | + | 0.472258i | ||||
\(10\) | −1.15840 | + | 2.00641i | −0.366319 | + | 0.634482i | ||||
\(11\) | 2.40625 | + | 1.38925i | 0.725510 | + | 0.418874i | 0.816777 | − | 0.576953i | \(-0.195758\pi\) |
−0.0912671 | + | 0.995826i | \(0.529092\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | −3.12205 | −0.780512 | ||||||||
\(17\) | −2.74396 | −0.665508 | −0.332754 | − | 0.943014i | \(-0.607978\pi\) | ||||
−0.332754 | + | 0.943014i | \(0.607978\pi\) | |||||||
\(18\) | −1.80860 | + | 1.04420i | −0.426292 | + | 0.246120i | ||||
\(19\) | 5.08351 | − | 2.93497i | 1.16624 | − | 0.673327i | 0.213446 | − | 0.976955i | \(-0.431531\pi\) |
0.952791 | + | 0.303628i | \(0.0981979\pi\) | |||||||
\(20\) | 0.582143 | + | 0.336100i | 0.130171 | + | 0.0751543i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.77346 | + | 3.07173i | −0.378103 | + | 0.654894i | ||||
\(23\) | −6.99909 | −1.45941 | −0.729706 | − | 0.683761i | \(-0.760343\pi\) | ||||
−0.729706 | + | 0.683761i | \(0.760343\pi\) | |||||||
\(24\) | 3.06060 | + | 1.76704i | 0.624743 | + | 0.360696i | ||||
\(25\) | −0.853117 | − | 1.47764i | −0.170623 | − | 0.295528i | ||||
\(26\) | 0.513376 | − | 4.57400i | 0.100681 | − | 0.897035i | ||||
\(27\) | 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 | \(0.727476\pi\) | |||||||
\(30\) | 1.35293 | + | 2.34334i | 0.247009 | + | 0.427833i | ||||
\(31\) | 1.79004 | − | 1.03348i | 0.321501 | − | 0.185619i | −0.330560 | − | 0.943785i | \(-0.607238\pi\) |
0.652062 | + | 0.758166i | \(0.273904\pi\) | |||||||
\(32\) | 2.06640i | 0.365292i | ||||||||
\(33\) | 2.81031 | − | 1.62254i | 0.489213 | − | 0.282447i | ||||
\(34\) | − | 3.50284i | − | 0.600732i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.302965 | + | 0.524751i | 0.0504942 | + | 0.0874585i | ||||
\(37\) | 1.74302i | 0.286551i | 0.989683 | + | 0.143276i | \(0.0457635\pi\) | ||||
−0.989683 | + | 0.143276i | \(0.954236\pi\) | |||||||
\(38\) | 3.74667 | + | 6.48942i | 0.607790 | + | 1.05272i | ||||
\(39\) | −2.49913 | + | 3.38925i | −0.400181 | + | 0.542714i | ||||
\(40\) | −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 | ||||
\(45\) | 2.96904i | 0.442599i | ||||||||
\(46\) | − | 8.93479i | − | 1.31736i | ||||||
\(47\) | −5.76714 | − | 3.32966i | −0.841224 | − | 0.485681i | 0.0164563 | − | 0.999865i | \(-0.494762\pi\) |
−0.857680 | + | 0.514184i | \(0.828095\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | −1.32711 | − | 0.148952i | −0.184037 | − | 0.0206559i | ||||
\(53\) | 5.24396 | + | 9.08280i | 0.720313 | + | 1.24762i | 0.960874 | + | 0.276985i | \(0.0893352\pi\) |
−0.240561 | + | 0.970634i | \(0.577331\pi\) | |||||||
\(54\) | 6.91188i | 0.940588i | ||||||||
\(55\) | 2.52131 | + | 4.36703i | 0.339973 | + | 0.588850i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.85564i | − | 0.908052i | ||||||
\(58\) | −3.88720 | + | 2.24427i | −0.510414 | + | 0.294688i | ||||
\(59\) | − | 3.07396i | − | 0.400195i | −0.979776 | − | 0.200097i | \(-0.935874\pi\) | ||
0.979776 | − | 0.200097i | \(-0.0641259\pi\) | |||||||
\(60\) | 0.679899 | − | 0.392540i | 0.0877746 | − | 0.0506767i | ||||
\(61\) | −0.540892 | − | 0.936853i | −0.0692541 | − | 0.119952i | 0.829319 | − | 0.558775i | \(-0.188729\pi\) |
−0.898573 | + | 0.438824i | \(0.855395\pi\) | |||||||
\(62\) | 1.31931 | + | 2.28511i | 0.167552 | + | 0.290209i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.88199 | −1.11025 | ||||||||
\(65\) | −5.26665 | − | 3.88347i | −0.653248 | − | 0.481685i | ||||
\(66\) | 2.07127 | + | 3.58755i | 0.254956 | + | 0.441596i | ||||
\(67\) | −4.34568 | − | 2.50898i | −0.530910 | − | 0.306521i | 0.210477 | − | 0.977599i | \(-0.432498\pi\) |
−0.741387 | + | 0.671078i | \(0.765832\pi\) | |||||||
\(68\) | −1.01632 | −0.123247 | ||||||||
\(69\) | −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 | \(0.615088\pi\) | |||||||
\(72\) | −4.28709 | + | 2.47515i | −0.505238 | + | 0.291699i | ||||
\(73\) | −6.64426 | + | 3.83607i | −0.777652 | + | 0.448978i | −0.835598 | − | 0.549342i | \(-0.814878\pi\) |
0.0579454 | + | 0.998320i | \(0.481545\pi\) | |||||||
\(74\) | −2.22508 | −0.258660 | ||||||||
\(75\) | −1.99275 | −0.230103 | ||||||||
\(76\) | 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 | 0.0402236 | − | 0.999191i | \(-0.487193\pi\) |
0.845213 | − | 0.534430i | \(-0.179474\pi\) | |||||||
\(80\) | −4.90700 | − | 2.83306i | −0.548620 | − | 0.316746i | ||||
\(81\) | 0.707906 | − | 1.22613i | 0.0786563 | − | 0.136237i | ||||
\(82\) | 4.06400 | + | 7.03905i | 0.448794 | + | 0.777333i | ||||
\(83\) | 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 | ||||
\(87\) | 4.10656 | 0.440270 | ||||||||
\(88\) | −4.20379 | + | 7.28117i | −0.448125 | + | 0.776176i | ||||
\(89\) | − | 16.0640i | − | 1.70278i | −0.524537 | − | 0.851388i | \(-0.675761\pi\) | ||
0.524537 | − | 0.851388i | \(-0.324239\pi\) | |||||||
\(90\) | −3.79017 | −0.399519 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.59235 | −0.270271 | ||||||||
\(93\) | − | 2.41406i | − | 0.250326i | ||||||
\(94\) | 4.25052 | − | 7.36212i | 0.438408 | − | 0.759345i | ||||
\(95\) | 10.6532 | 1.09299 | ||||||||
\(96\) | 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 | ||||||||
\(100\) | −0.315981 | − | 0.547295i | −0.0315981 | − | 0.0547295i | ||||
\(101\) | −0.0365612 | + | 0.0633259i | −0.00363798 | + | 0.00630117i | −0.867839 | − | 0.496846i | \(-0.834491\pi\) |
0.864201 | + | 0.503147i | \(0.167825\pi\) | |||||||
\(102\) | −3.54296 | − | 2.04553i | −0.350805 | − | 0.202537i | ||||
\(103\) | −6.45980 | + | 11.1887i | −0.636503 | + | 1.10245i | 0.349692 | + | 0.936865i | \(0.386286\pi\) |
−0.986195 | + | 0.165590i | \(0.947047\pi\) | |||||||
\(104\) | 1.21690 | − | 10.8421i | 0.119327 | − | 1.06316i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.5948 | + | 6.69425i | −1.12618 | + | 0.650203i | ||||
\(107\) | 4.00855 | 0.387521 | 0.193761 | − | 0.981049i | \(-0.437932\pi\) | ||||
0.193761 | + | 0.981049i | \(0.437932\pi\) | |||||||
\(108\) | 2.00542 | 0.192972 | ||||||||
\(109\) | −1.71984 | + | 0.992947i | −0.164730 | + | 0.0951071i | −0.580099 | − | 0.814546i | \(-0.696986\pi\) |
0.415368 | + | 0.909653i | \(0.363653\pi\) | |||||||
\(110\) | −5.57479 | + | 3.21861i | −0.531536 | + | 0.306882i | ||||
\(111\) | 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 | \(0.000966090\pi\) | |||||||
\(114\) | 8.75166 | 0.819668 | ||||||||
\(115\) | −11.0007 | − | 6.35123i | −1.02582 | − | 0.592256i | ||||
\(116\) | 0.651157 | + | 1.12784i | 0.0604584 | + | 0.104717i | ||||
\(117\) | −2.36109 | − | 5.40533i | −0.218283 | − | 0.499723i | ||||
\(118\) | 3.92410 | 0.361243 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.20695 | + | 5.55461i | 0.292753 | + | 0.507064i | ||||
\(121\) | −1.63999 | − | 2.84054i | −0.149090 | − | 0.258231i | ||||
\(122\) | 1.19595 | − | 0.690483i | 0.108276 | − | 0.0625134i | ||||
\(123\) | − | 7.43629i | − | 0.670507i | ||||||
\(124\) | 0.663004 | − | 0.382786i | 0.0595395 | − | 0.0343752i | ||||
\(125\) | − | 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 | \(0.666665\pi\) | |||||||
\(128\) | − | 7.20562i | − | 0.636893i | ||||||
\(129\) | −5.31634 | − | 9.20818i | −0.468078 | − | 0.810735i | ||||
\(130\) | 4.95750 | − | 6.72322i | 0.434801 | − | 0.589665i | ||||
\(131\) | −1.53241 | + | 2.65421i | −0.133887 | + | 0.231899i | −0.925172 | − | 0.379549i | \(-0.876079\pi\) |
0.791285 | + | 0.611448i | \(0.209413\pi\) | |||||||
\(132\) | 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 | ||||
\(136\) | − | 8.30308i | − | 0.711983i | ||||||
\(137\) | − | 21.8830i | − | 1.86959i | −0.355185 | − | 0.934796i | \(-0.615582\pi\) | ||
0.355185 | − | 0.934796i | \(-0.384418\pi\) | |||||||
\(138\) | −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 | ||||
\(143\) | −8.06301 | − | 5.94543i | −0.674263 | − | 0.497182i | ||||
\(144\) | −2.55376 | − | 4.42324i | −0.212813 | − | 0.368603i | ||||
\(145\) | 6.38131i | 0.529939i | ||||||||
\(146\) | −4.89699 | − | 8.48183i | −0.405277 | − | 0.701961i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.645588i | 0.0530670i | ||||||||
\(149\) | 1.99824 | − | 1.15369i | 0.163702 | − | 0.0945136i | −0.415911 | − | 0.909406i | \(-0.636537\pi\) |
0.579613 | + | 0.814892i | \(0.303204\pi\) | |||||||
\(150\) | − | 2.54388i | − | 0.207707i | ||||||
\(151\) | −17.8538 | + | 10.3079i | −1.45292 | + | 0.838845i | −0.998646 | − | 0.0520168i | \(-0.983435\pi\) |
−0.454275 | + | 0.890861i | \(0.650102\pi\) | |||||||
\(152\) | 8.88105 | + | 15.3824i | 0.720348 | + | 1.24768i | ||||
\(153\) | −2.24449 | − | 3.88757i | −0.181456 | − | 0.314292i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.75128 | 0.301310 | ||||||||
\(156\) | −0.925638 | + | 1.25532i | −0.0741103 | + | 0.100506i | ||||
\(157\) | −1.44824 | − | 2.50843i | −0.115582 | − | 0.200194i | 0.802430 | − | 0.596746i | \(-0.203540\pi\) |
−0.918012 | + | 0.396552i | \(0.870207\pi\) | |||||||
\(158\) | 17.4010 | + | 10.0465i | 1.38435 | + | 0.799254i | ||||
\(159\) | 12.2491 | 0.971417 | ||||||||
\(160\) | −1.87513 | + | 3.24782i | −0.148242 | + | 0.256763i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.56523 | + | 0.903688i | 0.122976 | + | 0.0710004i | ||||
\(163\) | 20.2944 | − | 11.7170i | 1.58958 | − | 0.917743i | 0.596201 | − | 0.802835i | \(-0.296676\pi\) |
0.993376 | − | 0.114907i | \(-0.0366571\pi\) | |||||||
\(164\) | 2.04232 | − | 1.17913i | 0.159478 | − | 0.0920750i | ||||
\(165\) | 5.88939 | 0.458489 | ||||||||
\(166\) | −10.1794 | −0.790077 | ||||||||
\(167\) | 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 | ||||
\(171\) | 8.31637 | + | 4.80146i | 0.635969 | + | 0.367177i | ||||
\(172\) | 1.68597 | − | 2.92019i | 0.128554 | − | 0.222662i | ||||
\(173\) | 2.69861 | + | 4.67412i | 0.205171 | + | 0.355367i | 0.950187 | − | 0.311679i | \(-0.100892\pi\) |
−0.745016 | + | 0.667047i | \(0.767558\pi\) | |||||||
\(174\) | 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 | ||||
\(178\) | 20.5067 | 1.53704 | ||||||||
\(179\) | −6.14571 | + | 10.6447i | −0.459352 | + | 0.795621i | −0.998927 | − | 0.0463168i | \(-0.985252\pi\) |
0.539575 | + | 0.841938i | \(0.318585\pi\) | |||||||
\(180\) | 1.09969i | 0.0819658i | ||||||||
\(181\) | −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 | ||||||||
\(184\) | − | 21.1789i | − | 1.56133i | ||||||
\(185\) | −1.58168 | + | 2.73956i | −0.116288 | + | 0.201416i | ||||
\(186\) | 3.08170 | 0.225961 | ||||||||
\(187\) | −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 | ||||||||
\(191\) | −1.37858 | − | 2.38777i | −0.0997507 | − | 0.172773i | 0.811831 | − | 0.583893i | \(-0.198471\pi\) |
−0.911581 | + | 0.411120i | \(0.865138\pi\) | |||||||
\(192\) | −5.18675 | + | 8.98371i | −0.374321 | + | 0.648344i | ||||
\(193\) | −11.2491 | − | 6.49467i | −0.809728 | − | 0.467497i | 0.0371334 | − | 0.999310i | \(-0.488177\pi\) |
−0.846861 | + | 0.531814i | \(0.821511\pi\) | |||||||
\(194\) | 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 | \(0.0962749\pi\) | |||||||
\(198\) | −5.80259 | −0.412372 | ||||||||
\(199\) | 20.0317 | 1.42001 | 0.710006 | − | 0.704195i | \(-0.248692\pi\) | ||||
0.710006 | + | 0.704195i | \(0.248692\pi\) | |||||||
\(200\) | 4.47127 | − | 2.58149i | 0.316166 | − | 0.182539i | ||||
\(201\) | −5.07543 | + | 2.93030i | −0.357993 | + | 0.206688i | ||||
\(202\) | −0.0808396 | − | 0.0466728i | −0.00568785 | − | 0.00328388i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.593492 | + | 1.02796i | −0.0415528 | + | 0.0719715i | ||||
\(205\) | 11.5555 | 0.807069 | ||||||||
\(206\) | −14.2831 | − | 8.24634i | −0.995150 | − | 0.574550i | ||||
\(207\) | −5.72509 | − | 9.91614i | −0.397921 | − | 0.689219i | ||||
\(208\) | 11.1865 | + | 1.25555i | 0.775642 | + | 0.0870564i | ||||
\(209\) | 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 | \(0.945192\pi\) | |||||||
\(212\) | 1.94228 | + | 3.36413i | 0.133396 | + | 0.231049i | ||||
\(213\) | 2.74991 | − | 1.58766i | 0.188421 | − | 0.108785i | ||||
\(214\) | 5.11717i | 0.349802i | ||||||||
\(215\) | 14.3089 | − | 8.26122i | 0.975856 | − | 0.563411i | ||||
\(216\) | 16.3838i | 1.11478i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.26756 | − | 2.19548i | −0.0858501 | − | 0.148697i | ||||
\(219\) | 8.96048i | 0.605493i | ||||||||
\(220\) | 0.933852 | + | 1.61748i | 0.0629603 | + | 0.109050i | ||||
\(221\) | 9.83175 | + | 1.10350i | 0.661355 | + | 0.0742292i | ||||
\(222\) | −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 | ||||
\(227\) | 0.919719i | 0.0610439i | 0.999534 | + | 0.0305220i | \(0.00971695\pi\) | ||||
−0.999534 | + | 0.0305220i | \(0.990283\pi\) | |||||||
\(228\) | − | 2.53922i | − | 0.168164i | ||||||
\(229\) | −21.3222 | − | 12.3104i | −1.40901 | − | 0.813494i | −0.413719 | − | 0.910404i | \(-0.635771\pi\) |
−0.995293 | + | 0.0969108i | \(0.969104\pi\) | |||||||
\(230\) | 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 | 0.431038 | + | 0.902334i | \(0.358148\pi\) |
−0.996963 | + | 0.0778773i | \(0.975186\pi\) | |||||||
\(234\) | 6.90025 | − | 3.01408i | 0.451084 | − | 0.197036i | ||||
\(235\) | −6.04291 | − | 10.4666i | −0.394196 | − | 0.682767i | ||||
\(236\) | − | 1.13854i | − | 0.0741129i | ||||||
\(237\) | −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 | \(0.844828\pi\) | |||||||
\(240\) | −5.73101 | + | 3.30880i | −0.369935 | + | 0.213582i | ||||
\(241\) | 8.43441i | 0.543308i | 0.962395 | + | 0.271654i | \(0.0875706\pi\) | ||||
−0.962395 | + | 0.271654i | \(0.912429\pi\) | |||||||
\(242\) | 3.62614 | − | 2.09355i | 0.233097 | − | 0.134579i | ||||
\(243\) | 7.29488 | + | 12.6351i | 0.467967 | + | 0.810543i | ||||
\(244\) | −0.200338 | − | 0.346995i | −0.0128253 | − | 0.0222141i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.49290 | 0.605245 | ||||||||
\(247\) | −19.3948 | + | 8.47178i | −1.23406 | + | 0.539046i | ||||
\(248\) | 3.12726 | + | 5.41658i | 0.198581 | + | 0.343953i | ||||
\(249\) | 8.06541 | + | 4.65657i | 0.511124 | + | 0.295098i | ||||
\(250\) | 15.5370 | 0.982647 | ||||||||
\(251\) | −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 | ||||
\(254\) | −12.4589 | + | 7.19315i | −0.781742 | + | 0.451339i | ||||
\(255\) | −5.03697 | + | 2.90810i | −0.315427 | + | 0.182112i | ||||
\(256\) | −8.56553 | −0.535346 | ||||||||
\(257\) | −29.3286 | −1.82947 | −0.914733 | − | 0.404059i | \(-0.867599\pi\) | ||||
−0.914733 | + | 0.404059i | \(0.867599\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | −3.38826 | − | 1.95622i | −0.209328 | − | 0.120855i | ||||
\(263\) | −9.95747 | + | 17.2468i | −0.614004 | + | 1.06349i | 0.376555 | + | 0.926394i | \(0.377109\pi\) |
−0.990558 | + | 0.137091i | \(0.956225\pi\) | |||||||
\(264\) | 4.90971 | + | 8.50386i | 0.302172 | + | 0.523377i | ||||
\(265\) | 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 | ||||
\(269\) | −22.3250 | −1.36118 | −0.680589 | − | 0.732666i | \(-0.738276\pi\) | ||||
−0.680589 | + | 0.732666i | \(0.738276\pi\) | |||||||
\(270\) | −6.27210 | + | 10.8636i | −0.381708 | + | 0.661137i | ||||
\(271\) | − | 9.39988i | − | 0.571002i | −0.958378 | − | 0.285501i | \(-0.907840\pi\) | ||
0.958378 | − | 0.285501i | \(-0.0921600\pi\) | |||||||
\(272\) | 8.56677 | 0.519437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.9351 | 1.68762 | ||||||||
\(275\) | − | 4.74076i | − | 0.285879i | ||||||
\(276\) | −1.51384 | + | 2.62204i | −0.0911223 | + | 0.157828i | ||||
\(277\) | 14.3427 | 0.861767 | 0.430883 | − | 0.902408i | \(-0.358202\pi\) | ||||
0.430883 | + | 0.902408i | \(0.358202\pi\) | |||||||
\(278\) | −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 | \(0.999062\pi\) | |||||||
\(282\) | −4.96429 | − | 8.59841i | −0.295619 | − | 0.512028i | ||||
\(283\) | −0.310336 | + | 0.537518i | −0.0184476 | + | 0.0319521i | −0.875102 | − | 0.483939i | \(-0.839206\pi\) |
0.856654 | + | 0.515891i | \(0.172539\pi\) | |||||||
\(284\) | 0.872079 | + | 0.503495i | 0.0517484 | + | 0.0298769i | ||||
\(285\) | 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 | ||||
\(289\) | −9.47069 | −0.557099 | ||||||||
\(290\) | −8.14615 | −0.478358 | ||||||||
\(291\) | −14.3899 | + | 8.30800i | −0.843549 | + | 0.487023i | ||||
\(292\) | −2.46093 | + | 1.42082i | −0.144015 | + | 0.0831471i | ||||
\(293\) | 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 | ||||
\(296\) | −5.27430 | −0.306562 | ||||||||
\(297\) | 13.0285 | + | 7.52200i | 0.755989 | + | 0.436471i | ||||
\(298\) | 1.47275 | + | 2.55088i | 0.0853143 | + | 0.147769i | ||||
\(299\) | 25.0781 | + | 2.81472i | 1.45031 | + | 0.162779i | ||||
\(300\) | −0.738085 | −0.0426133 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.1587 | − | 22.7915i | −0.757197 | − | 1.31150i | ||||
\(303\) | 0.0427008 | + | 0.0739599i | 0.00245310 | + | 0.00424889i | ||||
\(304\) | −15.8710 | + | 9.16310i | −0.910262 | + | 0.525540i | ||||
\(305\) | − | 1.96330i | − | 0.112418i | ||||||
\(306\) | 4.96274 | − | 2.86524i | 0.283701 | − | 0.163795i | ||||
\(307\) | 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 | ||||
\(310\) | 4.78875i | 0.271983i | ||||||||
\(311\) | 3.61895 | + | 6.26820i | 0.205212 | + | 0.355437i | 0.950200 | − | 0.311640i | \(-0.100878\pi\) |
−0.744988 | + | 0.667077i | \(0.767545\pi\) | |||||||
\(312\) | −10.2557 | − | 7.56223i | −0.580614 | − | 0.428127i | ||||
\(313\) | −16.3303 | + | 28.2849i | −0.923043 | + | 1.59876i | −0.128365 | + | 0.991727i | \(0.540973\pi\) |
−0.794678 | + | 0.607031i | \(0.792360\pi\) | |||||||
\(314\) | 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 | \(-0.493533\pi\) |
−0.855690 | + | 0.517489i | \(0.826867\pi\) | |||||||
\(318\) | 15.6368i | 0.876866i | ||||||||
\(319\) | 9.76951i | 0.546987i | ||||||||
\(320\) | −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 | ||||
\(325\) | 2.46252 | + | 5.63756i | 0.136596 | + | 0.312715i | ||||
\(326\) | 14.9574 | + | 25.9071i | 0.828416 | + | 1.43486i | ||||
\(327\) | 2.31938i | 0.128262i | ||||||||
\(328\) | 9.63324 | + | 16.6853i | 0.531907 | + | 0.921289i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.51819i | 0.413863i | ||||||||
\(331\) | −17.2633 | + | 9.96698i | −0.948877 | + | 0.547835i | −0.892732 | − | 0.450588i | \(-0.851214\pi\) |
−0.0561454 | + | 0.998423i | \(0.517881\pi\) | |||||||
\(332\) | 2.95347i | 0.162093i | ||||||||
\(333\) | −2.46947 | + | 1.42575i | −0.135326 | + | 0.0781306i | ||||
\(334\) | 4.85219 | + | 8.40424i | 0.265500 | + | 0.459860i | ||||
\(335\) | −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 | \(0.488971\pi\) | |||||||
\(338\) | −3.67891 | + | 16.1824i | −0.200106 | + | 0.880208i | ||||
\(339\) | −6.17495 | − | 10.6953i | −0.335377 | − | 0.580890i | ||||
\(340\) | −1.59738 | − | 0.922245i | −0.0866298 | − | 0.0500158i | ||||
\(341\) | 5.74305 | 0.311004 | ||||||||
\(342\) | −6.12937 | + | 10.6164i | −0.331438 | + | 0.574068i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 23.8572 | + | 13.7740i | 1.28630 | + | 0.742643i | ||||
\(345\) | −12.8479 | + | 7.41777i | −0.691710 | + | 0.399359i | ||||
\(346\) | −5.96682 | + | 3.44494i | −0.320778 | + | 0.185201i | ||||
\(347\) | 25.8833 | 1.38949 | 0.694744 | − | 0.719257i | \(-0.255518\pi\) | ||||
0.694744 | + | 0.719257i | \(0.255518\pi\) | |||||||
\(348\) | 1.52101 | 0.0815344 | ||||||||
\(349\) | −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 | ||||
\(353\) | 21.9533 | + | 12.6747i | 1.16846 | + | 0.674608i | 0.953316 | − | 0.301975i | \(-0.0976459\pi\) |
0.215140 | + | 0.976583i | \(0.430979\pi\) | |||||||
\(354\) | 2.29153 | − | 3.96904i | 0.121793 | − | 0.210952i | ||||
\(355\) | 2.46711 | + | 4.27317i | 0.130941 | + | 0.226796i | ||||
\(356\) | − | 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 | \(-0.288918\pi\) |
−0.374692 | + | 0.927149i | \(0.622252\pi\) | |||||||
\(360\) | −8.98417 | −0.473507 | ||||||||
\(361\) | 7.72804 | − | 13.3854i | 0.406739 | − | 0.704493i | ||||
\(362\) | − | 27.8961i | − | 1.46618i | ||||||
\(363\) | −3.83077 | −0.201063 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.9240 | −0.728813 | ||||||||
\(366\) | − | 1.61287i | − | 0.0843058i | ||||||
\(367\) | −12.6588 | + | 21.9257i | −0.660783 | + | 1.14451i | 0.319627 | + | 0.947544i | \(0.396443\pi\) |
−0.980410 | + | 0.196967i | \(0.936891\pi\) | |||||||
\(368\) | 21.8515 | 1.13909 | ||||||||
\(369\) | 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 | ||||||
\(373\) | 3.39391 | + | 5.87842i | 0.175730 | + | 0.304373i | 0.940414 | − | 0.340033i | \(-0.110438\pi\) |
−0.764684 | + | 0.644406i | \(0.777105\pi\) | |||||||
\(374\) | 4.86631 | − | 8.42869i | 0.251631 | − | 0.435837i | ||||
\(375\) | −12.3104 | − | 7.10739i | −0.635704 | − | 0.367024i | ||||
\(376\) | 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 | \(0.230831\pi\) | |||||||
\(380\) | 3.94577 | 0.202414 | ||||||||
\(381\) | 13.1620 | 0.674310 | ||||||||
\(382\) | 3.04815 | − | 1.75985i | 0.155957 | − | 0.0900417i | ||||
\(383\) | 6.28662 | − | 3.62958i | 0.321232 | − | 0.185463i | −0.330710 | − | 0.943732i | \(-0.607288\pi\) |
0.651941 | + | 0.758269i | \(0.273955\pi\) | |||||||
\(384\) | −7.28815 | − | 4.20782i | −0.371922 | − | 0.214729i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.29086 | − | 14.3602i | 0.421994 | − | 0.730915i | ||||
\(387\) | 14.8935 | 0.757082 | ||||||||
\(388\) | −4.56346 | − | 2.63472i | −0.231675 | − | 0.133757i | ||||
\(389\) | −3.57406 | − | 6.19045i | −0.181212 | − | 0.313868i | 0.761082 | − | 0.648656i | \(-0.224669\pi\) |
−0.942293 | + | 0.334788i | \(0.891335\pi\) | |||||||
\(390\) | −3.90522 | − | 8.94038i | −0.197749 | − | 0.452714i | ||||
\(391\) | 19.2052 | 0.971250 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.78974 | + | 3.09991i | 0.0902802 | + | 0.156370i | ||||
\(394\) | 12.1441 | + | 21.0342i | 0.611811 | + | 1.05969i | ||||
\(395\) | 24.7388 | − | 14.2829i | 1.24474 | − | 0.718652i | ||||
\(396\) | 1.68357i | 0.0846027i | ||||||||
\(397\) | 19.4520 | − | 11.2306i | 0.976266 | − | 0.563647i | 0.0751252 | − | 0.997174i | \(-0.476064\pi\) |
0.901141 | + | 0.433527i | \(0.142731\pi\) | |||||||
\(398\) | 25.5718i | 1.28180i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.66347 | + | 4.61327i | 0.133174 | + | 0.230663i | ||||
\(401\) | − | 3.05473i | − | 0.152546i | −0.997087 | − | 0.0762729i | \(-0.975698\pi\) | ||
0.997087 | − | 0.0762729i | \(-0.0243020\pi\) | |||||||
\(402\) | −3.74072 | − | 6.47912i | −0.186570 | − | 0.323149i | ||||
\(403\) | −6.82944 | + | 2.98315i | −0.340199 | + | 0.148601i | ||||
\(404\) | −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 | ||||
\(409\) | − | 5.60586i | − | 0.277192i | −0.990349 | − | 0.138596i | \(-0.955741\pi\) | ||
0.990349 | − | 0.138596i | \(-0.0442590\pi\) | |||||||
\(410\) | 14.7513i | 0.728514i | ||||||||
\(411\) | −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 | ||||
\(416\) | 0.831013 | − | 7.40403i | 0.0407437 | − | 0.363012i | ||||
\(417\) | 6.46487 | + | 11.1975i | 0.316586 | + | 0.548343i | ||||
\(418\) | 20.8202i | 1.01835i | ||||||||
\(419\) | −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 | \(-0.0149441\pi\) | |||||||
\(422\) | 11.0557 | − | 6.38302i | 0.538184 | − | 0.310720i | ||||
\(423\) | − | 10.8943i | − | 0.529700i | ||||||
\(424\) | −27.4841 | + | 15.8679i | −1.33475 | + | 0.770615i | ||||
\(425\) | 2.34092 | + | 4.05459i | 0.113551 | + | 0.196677i | ||||
\(426\) | 2.02675 | + | 3.51044i | 0.0981965 | + | 0.170081i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.48470 | 0.0717658 | ||||||||
\(429\) | −10.7220 | + | 4.68345i | −0.517664 | + | 0.226119i | ||||
\(430\) | 10.5460 | + | 18.2662i | 0.508572 | + | 0.880873i | ||||
\(431\) | −9.30923 | − | 5.37469i | −0.448410 | − | 0.258890i | 0.258749 | − | 0.965945i | \(-0.416690\pi\) |
−0.707158 | + | 0.707055i | \(0.750023\pi\) | |||||||
\(432\) | −16.9041 | −0.813301 | ||||||||
\(433\) | 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 | ||||
\(436\) | −0.637000 | + | 0.367772i | −0.0305068 | + | 0.0176131i | ||||
\(437\) | −35.5799 | + | 20.5421i | −1.70202 | + | 0.982662i | ||||
\(438\) | −11.4386 | −0.546559 | ||||||||
\(439\) | 21.9508 | 1.04765 | 0.523826 | − | 0.851825i | \(-0.324504\pi\) | ||||
0.523826 | + | 0.851825i | \(0.324504\pi\) | |||||||
\(440\) | −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 | −0.317207 | − | 0.948356i | \(-0.602745\pi\) |
0.979904 | − | 0.199469i | \(-0.0639217\pi\) | |||||||
\(444\) | 0.652982 | + | 0.376999i | 0.0309892 | + | 0.0178916i | ||||
\(445\) | 14.5770 | − | 25.2481i | 0.691017 | − | 1.19688i | ||||
\(446\) | 5.35046 | + | 9.26727i | 0.253352 | + | 0.438818i | ||||
\(447\) | − | 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 | ||||
\(451\) | 17.6909 | 0.833033 | ||||||||
\(452\) | 1.95826 | − | 3.39181i | 0.0921088 | − | 0.159537i | ||||
\(453\) | 24.0777i | 1.13127i | ||||||||
\(454\) | −1.17408 | −0.0551023 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.7448 | 0.971464 | ||||||||
\(457\) | 5.51628i | 0.258041i | 0.991642 | + | 0.129020i | \(0.0411833\pi\) | ||||
−0.991642 | + | 0.129020i | \(0.958817\pi\) | |||||||
\(458\) | 15.7150 | − | 27.2192i | 0.734314 | − | 1.27187i | ||||
\(459\) | −14.8570 | −0.693466 | ||||||||
\(460\) | −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 | \(0.892740\pi\) | |||||||
\(464\) | −5.48874 | − | 9.50678i | −0.254808 | − | 0.441341i | ||||
\(465\) | 2.19061 | − | 3.79424i | 0.101587 | − | 0.175954i | ||||
\(466\) | −19.1003 | − | 11.0276i | −0.884804 | − | 0.510842i | ||||
\(467\) | −2.27163 | + | 3.93457i | −0.105118 | + | 0.182070i | −0.913787 | − | 0.406195i | \(-0.866855\pi\) |
0.808668 | + | 0.588265i | \(0.200189\pi\) | |||||||
\(468\) | −0.874509 | − | 2.00205i | −0.0404242 | − | 0.0925448i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.3613 | − | 7.71416i | 0.616312 | − | 0.355828i | ||||
\(471\) | −3.38288 | −0.155875 | ||||||||
\(472\) | 9.30163 | 0.428142 | ||||||||
\(473\) | 21.9062 | − | 12.6476i | 1.00725 | − | 0.581536i | ||||
\(474\) | 20.3231 | − | 11.7335i | 0.933469 | − | 0.538939i | ||||
\(475\) | −8.67366 | − | 5.00774i | −0.397975 | − | 0.229771i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.57886 | + | 14.8590i | −0.392799 | + | 0.680348i | ||||
\(478\) | −18.4883 | −0.845633 | ||||||||
\(479\) | 1.44239 | + | 0.832764i | 0.0659044 | + | 0.0380499i | 0.532590 | − | 0.846373i | \(-0.321219\pi\) |
−0.466686 | + | 0.884423i | \(0.654552\pi\) | |||||||
\(480\) | 2.19001 | + | 3.79321i | 0.0999598 | + | 0.173135i | ||||
\(481\) | 0.700965 | − | 6.24535i | 0.0319612 | − | 0.284763i | ||||
\(482\) | −10.7671 | −0.490426 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.607426 | − | 1.05209i | −0.0276103 | − | 0.0478224i | ||||
\(485\) | −12.9100 | − | 22.3608i | −0.586215 | − | 1.01535i | ||||
\(486\) | −16.1295 | + | 9.31239i | −0.731650 | + | 0.422418i | ||||
\(487\) | 1.48493i | 0.0672884i | 0.999434 | + | 0.0336442i | \(0.0107113\pi\) | ||||
−0.999434 | + | 0.0336442i | \(0.989289\pi\) | |||||||
\(488\) | 2.83487 | − | 1.63671i | 0.128328 | − | 0.0740904i | ||||
\(489\) | − | 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 | \(0.715789\pi\) | |||||||
\(492\) | − | 2.75428i | − | 0.124173i | ||||||
\(493\) | −4.82404 | − | 8.35548i | −0.217264 | − | 0.376312i | ||||
\(494\) | −10.8148 | − | 24.7587i | −0.486580 | − | 1.11395i | ||||
\(495\) | −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 | \(-0.203514\pi\) |
−0.115501 | + | 0.993307i | \(0.536847\pi\) | |||||||
\(500\) | − | 4.50793i | − | 0.201601i | ||||||
\(501\) | − | 8.87852i | − | 0.396663i | ||||||
\(502\) | −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 | ||||
\(507\) | 10.3175 | − | 11.1388i | 0.458217 | − | 0.494692i | ||||
\(508\) | 2.08703 | + | 3.61485i | 0.0925971 | + | 0.160383i | ||||
\(509\) | 6.28614i | 0.278628i | 0.990248 | + | 0.139314i | \(0.0444898\pi\) | ||||
−0.990248 | + | 0.139314i | \(0.955510\pi\) | |||||||
\(510\) | −3.71237 | − | 6.43002i | −0.164387 | − | 0.284726i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 25.3457i | − | 1.12013i | ||||||
\(513\) | 27.5244 | − | 15.8912i | 1.21523 | − | 0.701614i | ||||
\(514\) | − | 37.4398i | − | 1.65140i | ||||||
\(515\) | −20.3061 | + | 11.7237i | −0.894792 | + | 0.516608i | ||||
\(516\) | −1.96909 | − | 3.41056i | −0.0866843 | − | 0.150142i | ||||
\(517\) | −9.25143 | − | 16.0240i | −0.406878 | − | 0.704733i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.30354 | 0.276695 | ||||||||
\(520\) | 11.7512 | − | 15.9366i | 0.515323 | − | 0.698866i | ||||
\(521\) | 5.42367 | + | 9.39407i | 0.237615 | + | 0.411562i | 0.960029 | − | 0.279899i | \(-0.0903010\pi\) |
−0.722414 | + | 0.691460i | \(0.756968\pi\) | |||||||
\(522\) | −6.35926 | − | 3.67152i | −0.278337 | − | 0.160698i | ||||
\(523\) | 1.34726 | 0.0589114 | 0.0294557 | − | 0.999566i | \(-0.490623\pi\) | ||||
0.0294557 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(524\) | −0.567579 | + | 0.983076i | −0.0247948 | + | 0.0429459i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.0167 | − | 12.7113i | −0.959974 | − | 0.554241i | ||||
\(527\) | −4.91181 | + | 2.83583i | −0.213962 | + | 0.123531i | ||||
\(528\) | −8.77394 | + | 5.06563i | −0.381837 | + | 0.220453i | ||||
\(529\) | 25.9873 | 1.12988 | ||||||||
\(530\) | −24.2984 | −1.05546 | ||||||||
\(531\) | 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 | ||||
\(535\) | 6.30034 | + | 3.63750i | 0.272388 | + | 0.157263i | ||||
\(536\) | 7.59205 | − | 13.1498i | 0.327926 | − | 0.567985i | ||||
\(537\) | 7.17773 | + | 12.4322i | 0.309742 | + | 0.536489i | ||||
\(538\) | − | 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 | \(-0.190679\pi\) |
−0.0753646 | + | 0.997156i | \(0.524012\pi\) | |||||||
\(542\) | 11.9996 | 0.515425 | ||||||||
\(543\) | −12.7610 | + | 22.1027i | −0.547628 | + | 0.948519i | ||||
\(544\) | − | 5.67012i | − | 0.243104i | ||||||
\(545\) | −3.60415 | −0.154385 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.42286 | −0.146351 | −0.0731755 | − | 0.997319i | \(-0.523313\pi\) | ||||
−0.0731755 | + | 0.997319i | \(0.523313\pi\) | |||||||
\(548\) | − | 8.10512i | − | 0.346234i | ||||||
\(549\) | 0.884873 | − | 1.53264i | 0.0377654 | − | 0.0654117i | ||||
\(550\) | 6.05188 | 0.258053 | ||||||||
\(551\) | 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 | ||||||||
\(555\) | 1.84729 | + | 3.19960i | 0.0784130 | + | 0.135815i | ||||
\(556\) | −2.05020 | + | 3.55106i | −0.0869480 | + | 0.150598i | ||||
\(557\) | 20.4948 | + | 11.8327i | 0.868394 | + | 0.501367i | 0.866814 | − | 0.498631i | \(-0.166164\pi\) |
0.00157977 | + | 0.999999i | \(0.499497\pi\) | |||||||
\(558\) | −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 | ||||
\(562\) | −0.126178 | −0.00532248 | ||||||||
\(563\) | −28.8075 | −1.21409 | −0.607045 | − | 0.794668i | \(-0.707645\pi\) | ||||
−0.607045 | + | 0.794668i | \(0.707645\pi\) | |||||||
\(564\) | −2.49475 | + | 1.44035i | −0.105048 | + | 0.0606496i | ||||
\(565\) | 16.6198 | − | 9.59543i | 0.699199 | − | 0.403683i | ||||
\(566\) | −0.686177 | − | 0.396164i | −0.0288422 | − | 0.0166520i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.11343 | + | 7.12467i | −0.172596 | + | 0.298945i | ||||
\(569\) | 27.6722 | 1.16008 | 0.580040 | − | 0.814588i | \(-0.303037\pi\) | ||||
0.580040 | + | 0.814588i | \(0.303037\pi\) | |||||||
\(570\) | 13.7552 | + | 7.94158i | 0.576143 | + | 0.332636i | ||||
\(571\) | 6.48273 | + | 11.2284i | 0.271294 | + | 0.469895i | 0.969193 | − | 0.246301i | \(-0.0792151\pi\) |
−0.697899 | + | 0.716196i | \(0.745882\pi\) | |||||||
\(572\) | −2.98641 | − | 2.20209i | −0.124868 | − | 0.0920741i | ||||
\(573\) | −3.22016 | −0.134524 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.97105 | + | 10.3422i | 0.249010 | + | 0.431298i | ||||
\(576\) | −7.26525 | − | 12.5838i | −0.302719 | − | 0.524324i | ||||
\(577\) | −8.19301 | + | 4.73023i | −0.341079 | + | 0.196922i | −0.660749 | − | 0.750607i | \(-0.729761\pi\) |
0.319670 | + | 0.947529i | \(0.396428\pi\) | |||||||
\(578\) | − | 12.0899i | − | 0.502875i | ||||||
\(579\) | −13.1381 | + | 7.58529i | −0.546001 | + | 0.315234i | ||||
\(580\) | 2.36354i | 0.0981405i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.6057 | − | 18.3696i | −0.439620 | − | 0.761444i | ||||
\(583\) | 29.1406i | 1.20688i | ||||||||
\(584\) | −11.6077 | − | 20.1052i | −0.480332 | − | 0.831959i | ||||
\(585\) | 1.19401 | − | 10.6382i | 0.0493664 | − | 0.439837i | ||||
\(586\) | −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 | ||||
\(591\) | − | 22.2212i | − | 0.914059i | ||||||
\(592\) | − | 5.44180i | − | 0.223657i | ||||||
\(593\) | 3.44015 | + | 1.98617i | 0.141270 | + | 0.0815622i | 0.568969 | − | 0.822359i | \(-0.307342\pi\) |
−0.427699 | + | 0.903921i | \(0.640676\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | −3.59317 | + | 32.0138i | −0.146936 | + | 1.30914i | ||||
\(599\) | 9.75246 | + | 16.8918i | 0.398475 | + | 0.690179i | 0.993538 | − | 0.113500i | \(-0.0362063\pi\) |
−0.595063 | + | 0.803679i | \(0.702873\pi\) | |||||||
\(600\) | − | 6.02997i | − | 0.246172i | ||||||
\(601\) | 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 | ||||||
\(604\) | −6.61276 | + | 3.81788i | −0.269070 | + | 0.155347i | ||||
\(605\) | − | 5.95274i | − | 0.242013i | ||||||
\(606\) | −0.0944146 | + | 0.0545103i | −0.00383533 | + | 0.00221433i | ||||
\(607\) | −12.5102 | − | 21.6682i | −0.507772 | − | 0.879487i | −0.999960 | − | 0.00899773i | \(-0.997136\pi\) |
0.492187 | − | 0.870489i | \(-0.336197\pi\) | |||||||
\(608\) | 6.06482 | + | 10.5046i | 0.245961 | + | 0.426016i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.50628 | 0.101476 | ||||||||
\(611\) | 19.3249 | + | 14.2496i | 0.781803 | + | 0.576478i | ||||
\(612\) | −0.831324 | − | 1.43990i | −0.0336043 | − | 0.0582043i | ||||
\(613\) | 18.4970 | + | 10.6793i | 0.747088 | + | 0.431332i | 0.824641 | − | 0.565657i | \(-0.191377\pi\) |
−0.0775527 | + | 0.996988i | \(0.524711\pi\) | |||||||
\(614\) | −12.6350 | −0.509908 | ||||||||
\(615\) | 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 | \(0.897562\pi\) | |||||||
\(618\) | −16.6816 | + | 9.63111i | −0.671031 | + | 0.387420i | ||||
\(619\) | 42.3588 | − | 24.4559i | 1.70254 | − | 0.982965i | 0.759375 | − | 0.650654i | \(-0.225505\pi\) |
0.943170 | − | 0.332311i | \(-0.107828\pi\) | |||||||
\(620\) | 1.38941 | 0.0558002 | ||||||||
\(621\) | −37.8962 | −1.52072 | ||||||||
\(622\) | −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 | ||||
\(626\) | −36.1075 | − | 20.8467i | −1.44315 | − | 0.833201i | ||||
\(627\) | 9.52417 | − | 16.4964i | 0.380359 | − | 0.658801i | ||||
\(628\) | −0.536406 | − | 0.929083i | −0.0214049 | − | 0.0370744i | ||||
\(629\) | − | 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 | ||||
\(633\) | −11.6796 | −0.464223 | ||||||||
\(634\) | 10.9621 | − | 18.9869i | 0.435360 | − | 0.754066i | ||||
\(635\) | 20.4528i | 0.811645i | ||||||||
\(636\) | 4.53687 | 0.179899 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12.4714 | −0.493747 | ||||||||
\(639\) | 4.44778i | 0.175951i | ||||||||
\(640\) | 6.53865 | − | 11.3253i | 0.258463 | − | 0.447671i | ||||
\(641\) | −39.7020 | −1.56813 | −0.784066 | − | 0.620677i | \(-0.786858\pi\) | ||||
−0.784066 | + | 0.620677i | \(0.786858\pi\) | |||||||
\(642\) | 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 | ||||||
\(646\) | −10.2807 | − | 17.8067i | −0.404489 | − | 0.700596i | ||||
\(647\) | −9.92502 | + | 17.1906i | −0.390193 | + | 0.675833i | −0.992475 | − | 0.122450i | \(-0.960925\pi\) |
0.602282 | + | 0.798283i | \(0.294258\pi\) | |||||||
\(648\) | 3.71020 | + | 2.14209i | 0.145751 | + | 0.0841491i | ||||
\(649\) | 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 | ||||
\(653\) | −19.0005 | −0.743547 | −0.371773 | − | 0.928324i | \(-0.621250\pi\) | ||||
−0.371773 | + | 0.928324i | \(0.621250\pi\) | |||||||
\(654\) | −2.96083 | −0.115778 | ||||||||
\(655\) | −4.81705 | + | 2.78112i | −0.188218 | + | 0.108667i | ||||
\(656\) | −17.2152 | + | 9.93918i | −0.672139 | + | 0.388060i | ||||
\(657\) | −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 | \(0.121789\pi\) | |||||||
\(660\) | 2.18134 | 0.0849085 | ||||||||
\(661\) | −14.5068 | − | 8.37548i | −0.564248 | − | 0.325769i | 0.190601 | − | 0.981668i | \(-0.438956\pi\) |
−0.754849 | + | 0.655899i | \(0.772290\pi\) | |||||||
\(662\) | −12.7235 | − | 22.0377i | −0.494512 | − | 0.856520i | ||||
\(663\) | 6.85751 | − | 9.29995i | 0.266324 | − | 0.361180i | ||||
\(664\) | −24.1291 | −0.936393 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.82006 | − | 3.15244i | −0.0705259 | − | 0.122155i | ||||
\(667\) | −12.3048 | − | 21.3126i | −0.476444 | − | 0.825226i | ||||
\(668\) | 2.43842 | − | 1.40782i | 0.0943453 | − | 0.0544703i | ||||
\(669\) | − | 9.79025i | − | 0.378513i | ||||||
\(670\) | 10.0681 | − | 5.81281i | 0.388964 | − | 0.224569i | ||||
\(671\) | − | 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 | \(-0.422348\pi\) | |||||||
\(674\) | 1.62365i | 0.0625406i | ||||||||
\(675\) | −4.61916 | − | 8.00061i | −0.177791 | − | 0.307944i | ||||
\(676\) | 4.69519 | + | 1.06740i | 0.180584 | + | 0.0410540i | ||||
\(677\) | −14.0671 | + | 24.3649i | −0.540641 | + | 0.936418i | 0.458226 | + | 0.888836i | \(0.348485\pi\) |
−0.998867 | + | 0.0475826i | \(0.984848\pi\) | |||||||
\(678\) | 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 | ||||
\(682\) | 7.33137i | 0.280733i | ||||||||
\(683\) | 2.07032i | 0.0792186i | 0.999215 | + | 0.0396093i | \(0.0126113\pi\) | ||||
−0.999215 | + | 0.0396093i | \(0.987389\pi\) | |||||||
\(684\) | 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 | ||||
\(689\) | −15.1367 | − | 34.6531i | −0.576662 | − | 1.32018i | ||||
\(690\) | −9.46925 | − | 16.4012i | −0.360488 | − | 0.624384i | ||||
\(691\) | 35.8583i | 1.36411i | 0.731299 | + | 0.682057i | \(0.238914\pi\) | ||||
−0.731299 | + | 0.682057i | \(0.761086\pi\) | |||||||
\(692\) | 0.999521 | + | 1.73122i | 0.0379961 | + | 0.0658112i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.0417i | 1.25425i | ||||||||
\(695\) | −17.4001 | + | 10.0460i | −0.660023 | + | 0.381065i | ||||
\(696\) | 12.4262i | 0.471015i | ||||||||
\(697\) | −15.1304 | + | 8.73552i | −0.573103 | + | 0.330881i | ||||
\(698\) | −11.0530 | − | 19.1443i | −0.418361 | − | 0.724622i | ||||
\(699\) | 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 | \(0.822081\pi\) | |||||||
\(702\) | 2.77965 | − | 24.7657i | 0.104911 | − | 0.934719i | ||||
\(703\) | 5.11571 | + | 8.86067i | 0.192943 | + | 0.334187i | ||||
\(704\) | −21.3722 | − | 12.3393i | −0.805497 | − | 0.465054i | ||||
\(705\) | −14.1153 | −0.531614 | ||||||||
\(706\) | −16.1801 | + | 28.0248i | −0.608947 | + | 1.05473i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.15158 | − | 0.664867i | −0.0432792 | − | 0.0249872i | ||||
\(709\) | 14.0864 | − | 8.13279i | 0.529026 | − | 0.305433i | −0.211594 | − | 0.977358i | \(-0.567865\pi\) |
0.740620 | + | 0.671924i | \(0.234532\pi\) | |||||||
\(710\) | −5.45497 | + | 3.14943i | −0.204721 | + | 0.118196i | ||||
\(711\) | 25.7496 | 0.965687 | ||||||||
\(712\) | 48.6087 | 1.82169 | ||||||||
\(713\) | −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 | ||||
\(717\) | 14.6487 | + | 8.45743i | 0.547066 | + | 0.315849i | ||||
\(718\) | −3.36403 | + | 5.82667i | −0.125544 | + | 0.217449i | ||||
\(719\) | −5.00744 | − | 8.67314i | −0.186746 | − | 0.323454i | 0.757417 | − | 0.652931i | \(-0.226461\pi\) |
−0.944164 | + | 0.329477i | \(0.893127\pi\) | |||||||
\(720\) | − | 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 | ||||
\(724\) | −8.09380 | −0.300804 | ||||||||
\(725\) | 2.99966 | − | 5.19556i | 0.111405 | − | 0.192958i | ||||
\(726\) | − | 4.89022i | − | 0.181493i | ||||||
\(727\) | 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 | ||||||||
\(730\) | − | 17.7748i | − | 0.657875i | ||||||
\(731\) | −12.4904 | + | 21.6340i | −0.461973 | + | 0.800161i | ||||
\(732\) | −0.467959 | −0.0172963 | ||||||||
\(733\) | −28.6966 | − | 16.5680i | −1.05993 | − | 0.611953i | −0.134520 | − | 0.990911i | \(-0.542949\pi\) |
−0.925414 | + | 0.378958i | \(0.876283\pi\) | |||||||
\(734\) | −27.9895 | − | 16.1598i | −1.03311 | − | 0.596468i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 14.4629i | − | 0.533111i | ||||||
\(737\) | −6.97119 | − | 12.0745i | −0.256787 | − | 0.444768i | ||||
\(738\) | −6.64850 | + | 11.5155i | −0.244735 | + | 0.423893i | ||||
\(739\) | 3.47767 | + | 2.00784i | 0.127928 | + | 0.0738594i | 0.562598 | − | 0.826730i | \(-0.309802\pi\) |
−0.434670 | + | 0.900590i | \(0.643135\pi\) | |||||||
\(740\) | −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 | \(0.259618\pi\) | |||||||
\(744\) | 7.30482 | 0.267808 | ||||||||
\(745\) | 4.18759 | 0.153421 | ||||||||
\(746\) | −7.50418 | + | 4.33254i | −0.274748 | + | 0.158626i | ||||
\(747\) | −11.2975 | + | 6.52260i | −0.413353 | + | 0.238650i | ||||
\(748\) | −2.44551 | − | 1.41192i | −0.0894168 | − | 0.0516248i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.07304 | − | 15.7150i | 0.331300 | − | 0.573829i | ||||
\(751\) | −37.5158 | −1.36897 | −0.684486 | − | 0.729026i | \(-0.739973\pi\) | ||||
−0.684486 | + | 0.729026i | \(0.739973\pi\) | |||||||
\(752\) | 18.0053 | + | 10.3954i | 0.656585 | + | 0.379080i | ||||
\(753\) | 8.56826 | + | 14.8407i | 0.312245 | + | 0.540824i | ||||
\(754\) | 14.8306 | − | 6.47810i | 0.540098 | − | 0.235919i | ||||
\(755\) | −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 | \(0.613566\pi\) | |||||||
\(758\) | 7.86530 | + | 13.6231i | 0.285680 | + | 0.494813i | ||||
\(759\) | −19.6697 | + | 11.3563i | −0.713963 | + | 0.412207i | ||||
\(760\) | 32.2360i | 1.16932i | ||||||||
\(761\) | 3.72586 | − | 2.15113i | 0.135062 | − | 0.0779782i | −0.430946 | − | 0.902378i | \(-0.641820\pi\) |
0.566009 | + | 0.824399i | \(0.308487\pi\) | |||||||
\(762\) | 16.8021i | 0.608677i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.510605 | − | 0.884394i | −0.0184730 | − | 0.0319962i | ||||
\(765\) | − | 8.14693i | − | 0.294553i | ||||||
\(766\) | 4.63340 | + | 8.02528i | 0.167411 | + | 0.289965i | ||||
\(767\) | −1.23621 | + | 11.0141i | −0.0446368 | + | 0.397698i | ||||
\(768\) | −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 | ||||
\(773\) | 3.80327i | 0.136794i | 0.997658 | + | 0.0683970i | \(0.0217884\pi\) | ||||
−0.997658 | + | 0.0683970i | \(0.978212\pi\) | |||||||
\(774\) | 19.0126i | 0.683393i | ||||||||
\(775\) | −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 | ||||
\(780\) | −2.59398 | + | 1.13307i | −0.0928792 | + | 0.0405703i | ||||
\(781\) | 3.77705 | + | 6.54204i | 0.135153 | + | 0.234092i | ||||
\(782\) | 24.5167i | 0.876715i | ||||||||
\(783\) | 9.51891 | + | 16.4872i | 0.340178 | + | 0.589206i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.25675i | − | 0.187622i | ||||||
\(786\) | −3.95724 | + | 2.28471i | −0.141150 | + | 0.0814930i | ||||
\(787\) | − | 17.3337i | − | 0.617879i | −0.951082 | − | 0.308940i | \(-0.900026\pi\) | ||
0.951082 | − | 0.308940i | \(-0.0999741\pi\) | |||||||
\(788\) | 6.10289 | − | 3.52351i | 0.217407 | − | 0.125520i | ||||
\(789\) | 11.6296 | + | 20.1430i | 0.414024 | + | 0.717110i | ||||
\(790\) | 18.2331 | + | 31.5806i | 0.648704 | + | 1.12359i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.7544 | −0.488740 | ||||||||
\(793\) | 1.56129 | + | 3.57431i | 0.0554429 | + | 0.126928i | ||||
\(794\) | 14.3366 | + | 24.8317i | 0.508786 | + | 0.881243i | ||||
\(795\) | 19.2522 | + | 11.1153i | 0.682807 | + | 0.394219i | ||||
\(796\) | 7.41944 | 0.262975 | ||||||||
\(797\) | 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 | ||||
\(800\) | 3.05340 | − | 1.76288i | 0.107954 | − | 0.0623273i | ||||
\(801\) | 22.7590 | − | 13.1399i | 0.804150 | − | 0.464276i | ||||
\(802\) | 3.89955 | 0.137698 | ||||||||
\(803\) | −21.3170 | −0.752260 | ||||||||
\(804\) | −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 | ||||
\(808\) | −0.191621 | − | 0.110632i | −0.00674120 | − | 0.00389203i | ||||
\(809\) | −8.03694 | + | 13.9204i | −0.282564 | + | 0.489415i | −0.972015 | − | 0.234917i | \(-0.924518\pi\) |
0.689452 | + | 0.724332i | \(0.257852\pi\) | |||||||
\(810\) | 1.64008 | + | 2.84070i | 0.0576265 | + | 0.0998120i | ||||
\(811\) | − | 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 | ||||
\(815\) | 42.5296 | 1.48975 | ||||||||
\(816\) | 5.00267 | − | 8.66488i | 0.175129 | − | 0.303332i | ||||
\(817\) | − | 53.4393i | − | 1.86961i | ||||||
\(818\) | 7.15624 | 0.250212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.27996 | 0.149463 | ||||||||
\(821\) | 30.1401i | 1.05190i | 0.850517 | + | 0.525948i | \(0.176289\pi\) | ||||
−0.850517 | + | 0.525948i | \(0.823711\pi\) | |||||||
\(822\) | 16.3130 | − | 28.2550i | 0.568982 | − | 0.985507i | ||||
\(823\) | −41.6502 | −1.45184 | −0.725918 | − | 0.687781i | \(-0.758585\pi\) | ||||
−0.725918 | + | 0.687781i | \(0.758585\pi\) | |||||||
\(824\) | −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 | \(0.772816\pi\) | |||||||
\(828\) | −2.12048 | − | 3.67278i | −0.0736918 | − | 0.127638i | ||||
\(829\) | −3.73737 | + | 6.47332i | −0.129804 | + | 0.224828i | −0.923601 | − | 0.383356i | \(-0.874768\pi\) |
0.793796 | + | 0.608184i | \(0.208102\pi\) | |||||||
\(830\) | −15.9993 | − | 9.23718i | −0.555343 | − | 0.320627i | ||||
\(831\) | 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 | ||||
\(835\) | 13.7966 | 0.477451 | ||||||||
\(836\) | 6.04080 | 0.208926 | ||||||||
\(837\) | 9.69209 | − | 5.59573i | 0.335008 | − | 0.193417i | ||||
\(838\) | 6.78732 | − | 3.91866i | 0.234464 | − | 0.135368i | ||||
\(839\) | −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 | ||||
\(842\) | 2.45852 | 0.0847263 | ||||||||
\(843\) | 0.0999736 | + | 0.0577198i | 0.00344328 | + | 0.00198798i | ||||
\(844\) | −1.85198 | − | 3.20772i | −0.0637477 | − | 0.110414i | ||||
\(845\) | 17.3089 | + | 16.0327i | 0.595445 | + | 0.551541i | ||||
\(846\) | 13.9073 | 0.478143 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.3719 | − | 28.3569i | −0.562213 | − | 0.973781i | ||||
\(849\) | 0.362450 | + | 0.627781i | 0.0124392 | + | 0.0215454i | ||||
\(850\) | −5.17594 | + | 2.98833i | −0.177533 | + | 0.102499i | ||||
\(851\) | − | 12.1996i | − | 0.418196i | ||||||
\(852\) | 1.01852 | − | 0.588045i | 0.0348940 | − | 0.0201461i | ||||
\(853\) | 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 | ||||
\(856\) | 12.1297i | 0.414583i | ||||||||
\(857\) | 15.1841 | + | 26.2996i | 0.518678 | + | 0.898377i | 0.999764 | + | 0.0217035i | \(0.00690898\pi\) |
−0.481086 | + | 0.876673i | \(0.659758\pi\) | |||||||
\(858\) | −5.97873 | − | 13.6873i | −0.204110 | − | 0.467278i | ||||
\(859\) | 17.9153 | − | 31.0302i | 0.611262 | − | 1.05874i | −0.379767 | − | 0.925082i | \(-0.623996\pi\) |
0.991028 | − | 0.133654i | \(-0.0426710\pi\) | |||||||
\(860\) | 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 | \(-0.518873\pi\) |
−0.894131 | + | 0.447805i | \(0.852206\pi\) | |||||||
\(864\) | 11.1884i | 0.380638i | ||||||||
\(865\) | 9.79526i | 0.333049i | ||||||||
\(866\) | 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 | ||||
\(871\) | 14.5618 | + | 10.7375i | 0.493408 | + | 0.363825i | ||||
\(872\) | −3.00461 | − | 5.20413i | −0.101749 | − | 0.176234i | ||||
\(873\) | − | 23.2746i | − | 0.787725i | ||||||
\(874\) | −26.2233 | − | 45.4201i | −0.887016 | − | 1.53636i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.31882i | 0.112133i | ||||||||
\(877\) | −3.82446 | + | 2.20805i | −0.129143 | + | 0.0745607i | −0.563180 | − | 0.826334i | \(-0.690422\pi\) |
0.434037 | + | 0.900895i | \(0.357089\pi\) | |||||||
\(878\) | 28.0216i | 0.945682i | ||||||||
\(879\) | 25.1788 | − | 14.5370i | 0.849261 | − | 0.490321i | ||||
\(880\) | −7.87164 | − | 13.6341i | −0.265353 | − | 0.459605i | ||||
\(881\) | 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 | \(0.570045\pi\) | |||||||
\(884\) | 3.64153 | + | 0.408717i | 0.122478 | + | 0.0137467i | ||||
\(885\) | −3.25783 | − | 5.64273i | −0.109511 | − | 0.189678i | ||||
\(886\) | 30.8404 | + | 17.8057i | 1.03610 | + | 0.598195i | ||||
\(887\) | 54.1725 | 1.81893 | 0.909467 | − | 0.415776i | \(-0.136490\pi\) | ||||
0.909467 | + | 0.415776i | \(0.136490\pi\) | |||||||
\(888\) | −3.07999 | + | 5.33470i | −0.103358 | + | 0.179021i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32.2309 | + | 18.6085i | 1.08038 | + | 0.623758i | ||||
\(891\) | 3.40679 | − | 1.96691i | 0.114132 | − | 0.0658941i | ||||
\(892\) | 2.68882 | − | 1.55239i | 0.0900283 | − | 0.0519779i | ||||
\(893\) | −39.0897 | −1.30809 | ||||||||
\(894\) | 3.44013 | 0.115055 | ||||||||
\(895\) | −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 | ||||
\(899\) | 6.29401 | + | 3.63385i | 0.209917 | + | 0.121196i | ||||
\(900\) | 0.516930 | − | 0.895348i | 0.0172310 | − | 0.0298449i | ||||
\(901\) | −14.3892 | − | 24.9228i | −0.479374 | − | 0.830300i | ||||
\(902\) | 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 | ||||
\(906\) | −30.7367 | −1.02116 | ||||||||
\(907\) | −1.29570 | + | 2.24421i | −0.0430229 | + | 0.0745178i | −0.886735 | − | 0.462278i | \(-0.847032\pi\) |
0.843712 | + | 0.536796i | \(0.180365\pi\) | |||||||
\(908\) | 0.340649i | 0.0113048i | ||||||||
\(909\) | −0.119625 | −0.00396770 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.59896 | 0.119239 | 0.0596195 | − | 0.998221i | \(-0.481011\pi\) | ||||
0.0596195 | + | 0.998221i | \(0.481011\pi\) | |||||||
\(912\) | 21.4036i | 0.708745i | ||||||||
\(913\) | −11.0780 | + | 19.1876i | −0.366627 | + | 0.635017i | ||||
\(914\) | −7.04189 | −0.232925 | ||||||||
\(915\) | −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 | ||||||
\(919\) | 13.9624 | + | 24.1836i | 0.460578 | + | 0.797745i | 0.998990 | − | 0.0449372i | \(-0.0143088\pi\) |
−0.538412 | + | 0.842682i | \(0.680975\pi\) | |||||||
\(920\) | 19.2185 | − | 33.2874i | 0.633615 | − | 1.09745i | ||||
\(921\) | 10.0110 | + | 5.77987i | 0.329875 | + | 0.190453i | ||||
\(922\) | −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 | ||||
\(926\) | −18.1635 | −0.596889 | ||||||||
\(927\) | −21.1358 | −0.694191 | ||||||||
\(928\) | −6.29229 | + | 3.63285i | −0.206554 | + | 0.119254i | ||||
\(929\) | 23.0067 | − | 13.2830i | 0.754827 | − | 0.435800i | −0.0726084 | − | 0.997361i | \(-0.523132\pi\) |
0.827435 | + | 0.561561i | \(0.189799\pi\) | |||||||
\(930\) | 4.84359 | + | 2.79645i | 0.158828 | + | 0.0916992i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.19955 | + | 5.54179i | −0.104805 | + | 0.181527i | ||||
\(933\) | 8.45332 | 0.276749 | ||||||||
\(934\) | −5.02274 | − | 2.89988i | −0.164349 | − | 0.0948869i | ||||
\(935\) | −6.91836 | − | 11.9830i | −0.226255 | − | 0.391885i | ||||
\(936\) | 16.3563 | − | 7.14452i | 0.534621 | − | 0.233526i | ||||
\(937\) | 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 | ||||
\(940\) | −2.23820 | − | 3.87667i | −0.0730020 | − | 0.126443i | ||||
\(941\) | −5.61587 | + | 3.24232i | −0.183072 | + | 0.105697i | −0.588735 | − | 0.808326i | \(-0.700374\pi\) |
0.405663 | + | 0.914023i | \(0.367041\pi\) | |||||||
\(942\) | − | 4.31846i | − | 0.140703i | ||||||
\(943\) | −38.5934 | + | 22.2819i | −1.25678 | + | 0.725599i | ||||
\(944\) | 9.59704i | 0.312357i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.1454 | + | 27.9647i | 0.524934 | + | 0.909212i | ||||
\(947\) | 21.1533i | 0.687391i | 0.939081 | + | 0.343695i | \(0.111679\pi\) | ||||
−0.939081 | + | 0.343695i | \(0.888321\pi\) | |||||||
\(948\) | −3.40438 | − | 5.89656i | −0.110569 | − | 0.191511i | ||||
\(949\) | 25.3494 | − | 11.0728i | 0.822878 | − | 0.359439i | ||||
\(950\) | 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 | ||||
\(955\) | − | 5.00390i | − | 0.161923i | ||||||
\(956\) | 5.36421i | 0.173491i | ||||||||
\(957\) | 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 | ||||
\(962\) | 7.97258 | + | 0.894826i | 0.257046 | + | 0.0288504i | ||||
\(963\) | 3.27889 | + | 5.67921i | 0.105661 | + | 0.183010i | ||||
\(964\) | 3.12397i | 0.100616i | ||||||||
\(965\) | −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 | \(-0.0843195\pi\) | |||||||
\(968\) | 8.59534 | − | 4.96252i | 0.276265 | − | 0.159501i | ||||
\(969\) | 18.8116i | 0.604315i | ||||||||
\(970\) | 28.5451 | − | 16.4805i | 0.916527 | − | 0.529157i | ||||
\(971\) | 12.2605 | + | 21.2358i | 0.393458 | + | 0.681489i | 0.992903 | − | 0.118927i | \(-0.0379455\pi\) |
−0.599445 | + | 0.800416i | \(0.704612\pi\) | |||||||
\(972\) | 2.70191 | + | 4.67984i | 0.0866638 | + | 0.150106i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.89560 | −0.0607390 | ||||||||
\(975\) | 7.14014 | + | 0.801395i | 0.228668 | + | 0.0256652i | ||||
\(976\) | 1.68869 | + | 2.92490i | 0.0540537 | + | 0.0936237i | ||||
\(977\) | −9.45681 | − | 5.45989i | −0.302550 | − | 0.174677i | 0.341038 | − | 0.940050i | \(-0.389222\pi\) |
−0.643588 | + | 0.765372i | \(0.722555\pi\) | |||||||
\(978\) | 34.9384 | 1.11721 | ||||||||
\(979\) | 22.3168 | − | 38.6538i | 0.713248 | − | 1.23538i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.81357 | − | 1.62441i | −0.0898302 | − | 0.0518635i | ||||
\(982\) | −17.6840 | + | 10.2098i | −0.564318 | + | 0.325809i | ||||
\(983\) | 17.0360 | − | 9.83574i | 0.543364 | − | 0.313711i | −0.203077 | − | 0.979163i | \(-0.565094\pi\) |
0.746441 | + | 0.665451i | \(0.231761\pi\) | |||||||
\(984\) | 22.5018 | 0.717331 | ||||||||
\(985\) | 34.5302 | 1.10022 | ||||||||
\(986\) | 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 | ||||
\(990\) | −9.12009 | − | 5.26549i | −0.289855 | − | 0.167348i | ||||
\(991\) | 0.869000 | − | 1.50515i | 0.0276047 | − | 0.0478127i | −0.851893 | − | 0.523716i | \(-0.824545\pi\) |
0.879498 | + | 0.475903i | \(0.157879\pi\) | |||||||
\(992\) | 2.13559 | + | 3.69895i | 0.0678050 | + | 0.117442i | ||||
\(993\) | 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 | ||||
\(997\) | −46.9537 | −1.48704 | −0.743519 | − | 0.668715i | \(-0.766845\pi\) | ||||
−0.743519 | + | 0.668715i | \(0.766845\pi\) | |||||||
\(998\) | −11.3103 | + | 19.5900i | −0.358022 | + | 0.620112i | ||||
\(999\) | 9.43750i | 0.298589i |
(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.k.h.569.5 | 12 | ||
7.2 | even | 3 | 91.2.q.a.36.5 | ✓ | 12 | ||
7.3 | odd | 6 | 637.2.u.i.361.2 | 12 | |||
7.4 | even | 3 | 637.2.u.h.361.2 | 12 | |||
7.5 | odd | 6 | 637.2.q.h.491.5 | 12 | |||
7.6 | odd | 2 | 637.2.k.g.569.5 | 12 | |||
13.4 | even | 6 | 637.2.u.h.30.2 | 12 | |||
21.2 | odd | 6 | 819.2.ct.a.127.2 | 12 | |||
28.23 | odd | 6 | 1456.2.cc.c.673.2 | 12 | |||
91.2 | odd | 12 | 1183.2.a.p.1.4 | 6 | |||
91.4 | even | 6 | inner | 637.2.k.h.459.2 | 12 | ||
91.16 | even | 3 | 1183.2.c.i.337.9 | 12 | |||
91.17 | odd | 6 | 637.2.k.g.459.2 | 12 | |||
91.23 | even | 6 | 1183.2.c.i.337.4 | 12 | |||
91.30 | even | 6 | 91.2.q.a.43.5 | yes | 12 | ||
91.37 | odd | 12 | 1183.2.a.m.1.3 | 6 | |||
91.54 | even | 12 | 8281.2.a.ch.1.4 | 6 | |||
91.69 | odd | 6 | 637.2.u.i.30.2 | 12 | |||
91.82 | odd | 6 | 637.2.q.h.589.5 | 12 | |||
91.89 | even | 12 | 8281.2.a.by.1.3 | 6 | |||
273.212 | odd | 6 | 819.2.ct.a.316.2 | 12 | |||
364.303 | 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 | 7.2 | even | 3 | ||
91.2.q.a.43.5 | yes | 12 | 91.30 | even | 6 | ||
637.2.k.g.459.2 | 12 | 91.17 | odd | 6 | |||
637.2.k.g.569.5 | 12 | 7.6 | odd | 2 | |||
637.2.k.h.459.2 | 12 | 91.4 | even | 6 | inner | ||
637.2.k.h.569.5 | 12 | 1.1 | even | 1 | trivial | ||
637.2.q.h.491.5 | 12 | 7.5 | odd | 6 | |||
637.2.q.h.589.5 | 12 | 91.82 | odd | 6 | |||
637.2.u.h.30.2 | 12 | 13.4 | even | 6 | |||
637.2.u.h.361.2 | 12 | 7.4 | even | 3 | |||
637.2.u.i.30.2 | 12 | 91.69 | odd | 6 | |||
637.2.u.i.361.2 | 12 | 7.3 | odd | 6 | |||
819.2.ct.a.127.2 | 12 | 21.2 | odd | 6 | |||
819.2.ct.a.316.2 | 12 | 273.212 | odd | 6 | |||
1183.2.a.m.1.3 | 6 | 91.37 | odd | 12 | |||
1183.2.a.p.1.4 | 6 | 91.2 | odd | 12 | |||
1183.2.c.i.337.4 | 12 | 91.23 | even | 6 | |||
1183.2.c.i.337.9 | 12 | 91.16 | even | 3 | |||
1456.2.cc.c.225.2 | 12 | 364.303 | odd | 6 | |||
1456.2.cc.c.673.2 | 12 | 28.23 | odd | 6 | |||
8281.2.a.by.1.3 | 6 | 91.89 | even | 12 | |||
8281.2.a.ch.1.4 | 6 | 91.54 | even | 12 |