Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(36,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.726638658394\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 43.5 | ||
Root | \(1.40744 - 0.138282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.43 |
Dual form | 91.2.q.a.36.5 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0.837044 | − | 0.547136i | \(-0.184282\pi\) |
−0.0553113 | + | 0.998469i | \(0.517615\pi\) | |||||||
\(3\) | 0.583963 | − | 1.01145i | 0.337151 | − | 0.583963i | −0.646745 | − | 0.762707i | \(-0.723870\pi\) |
0.983896 | + | 0.178744i | \(0.0572034\pi\) | |||||||
\(4\) | −0.185192 | − | 0.320762i | −0.0925960 | − | 0.160381i | ||||
\(5\) | 1.81487i | 0.811636i | 0.913954 | + | 0.405818i | \(0.133013\pi\) | ||||
−0.913954 | + | 0.405818i | \(0.866987\pi\) | |||||||
\(6\) | 1.29118 | − | 0.745466i | 0.527124 | − | 0.304335i | ||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | ||||
\(8\) | − | 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 | 0.0912671 | − | 0.995826i | \(-0.470908\pi\) |
−0.816777 | + | 0.576953i | \(0.804242\pi\) | |||||||
\(12\) | −0.432581 | −0.124875 | ||||||||
\(13\) | −3.58305 | + | 0.402155i | −0.993760 | + | 0.111538i | ||||
\(14\) | −1.27656 | −0.341176 | ||||||||
\(15\) | 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 | \(0.725355\pi\) | |||||||
\(18\) | 2.08840i | 0.492240i | ||||||||
\(19\) | −5.08351 | + | 2.93497i | −1.16624 | + | 0.673327i | −0.952791 | − | 0.303628i | \(-0.901802\pi\) |
−0.213446 | + | 0.976955i | \(0.568469\pi\) | |||||||
\(20\) | 0.582143 | − | 0.336100i | 0.130171 | − | 0.0751543i | ||||
\(21\) | 1.16793i | 0.254862i | ||||||||
\(22\) | −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 | \(-0.0936763\pi\) | |||||||
\(24\) | −3.06060 | − | 1.76704i | −0.624743 | − | 0.360696i | ||||
\(25\) | 1.70623 | 0.341247 | ||||||||
\(26\) | −4.21789 | − | 1.84240i | −0.827195 | − | 0.361325i | ||||
\(27\) | 5.41444 | 1.04201 | ||||||||
\(28\) | 0.320762 | + | 0.185192i | 0.0606183 | + | 0.0349980i | ||||
\(29\) | 1.75806 | − | 3.04505i | 0.326463 | − | 0.565451i | −0.655344 | − | 0.755330i | \(-0.727476\pi\) |
0.981807 | + | 0.189879i | \(0.0608097\pi\) | |||||||
\(30\) | 1.35293 | + | 2.34334i | 0.247009 | + | 0.427833i | ||||
\(31\) | − | 2.06697i | − | 0.371238i | −0.982622 | − | 0.185619i | \(-0.940571\pi\) | ||
0.982622 | − | 0.185619i | \(-0.0594290\pi\) | |||||||
\(32\) | −1.78956 | + | 1.03320i | −0.316352 | + | 0.182646i | ||||
\(33\) | −2.81031 | + | 1.62254i | −0.489213 | + | 0.282447i | ||||
\(34\) | 3.50284i | 0.600732i | ||||||||
\(35\) | −0.907437 | − | 1.57173i | −0.153385 | − | 0.265670i | ||||
\(36\) | 0.302965 | − | 0.524751i | 0.0504942 | − | 0.0874585i | ||||
\(37\) | 1.50950 | + | 0.871512i | 0.248161 | + | 0.143276i | 0.618922 | − | 0.785453i | \(-0.287570\pi\) |
−0.370761 | + | 0.928728i | \(0.620903\pi\) | |||||||
\(38\) | −7.49334 | −1.21558 | ||||||||
\(39\) | −1.68561 | + | 3.85893i | −0.269913 | + | 0.617924i | ||||
\(40\) | 5.49171 | 0.868316 | ||||||||
\(41\) | 5.51406 | + | 3.18355i | 0.861152 | + | 0.497186i | 0.864398 | − | 0.502808i | \(-0.167700\pi\) |
−0.00324599 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(42\) | −0.745466 | + | 1.29118i | −0.115028 | + | 0.199234i | ||||
\(43\) | 4.55195 | + | 7.88422i | 0.694167 | + | 1.20233i | 0.970461 | + | 0.241259i | \(0.0775603\pi\) |
−0.276294 | + | 0.961073i | \(0.589106\pi\) | |||||||
\(44\) | 1.02911i | 0.155144i | ||||||||
\(45\) | −2.57127 | + | 1.48452i | −0.383302 | + | 0.221299i | ||||
\(46\) | 7.73776 | − | 4.46740i | 1.14087 | − | 0.658681i | ||||
\(47\) | − | 6.65932i | − | 0.971361i | −0.874136 | − | 0.485681i | \(-0.838572\pi\) | ||
0.874136 | − | 0.485681i | \(-0.161428\pi\) | |||||||
\(48\) | −1.82316 | − | 3.15780i | −0.263150 | − | 0.455790i | ||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 1.88631 | + | 1.08906i | 0.266764 | + | 0.154016i | ||||
\(51\) | 3.20474 | 0.448753 | ||||||||
\(52\) | 0.792549 | + | 1.07483i | 0.109907 | + | 0.149052i | ||||
\(53\) | −10.4879 | −1.44063 | −0.720313 | − | 0.693649i | \(-0.756002\pi\) | ||||
−0.720313 | + | 0.693649i | \(0.756002\pi\) | |||||||
\(54\) | 5.98587 | + | 3.45594i | 0.814573 | + | 0.470294i | ||||
\(55\) | 2.52131 | − | 4.36703i | 0.339973 | − | 0.588850i | ||||
\(56\) | 1.51297 | + | 2.62055i | 0.202180 | + | 0.350185i | ||||
\(57\) | 6.85564i | 0.908052i | ||||||||
\(58\) | 3.88720 | − | 2.24427i | 0.510414 | − | 0.294688i | ||||
\(59\) | 2.66212 | − | 1.53698i | 0.346579 | − | 0.200097i | −0.316598 | − | 0.948560i | \(-0.602541\pi\) |
0.663177 | + | 0.748462i | \(0.269207\pi\) | |||||||
\(60\) | − | 0.785080i | − | 0.101353i | ||||||
\(61\) | −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 | ||||
\(63\) | −1.41677 | − | 0.817975i | −0.178497 | − | 0.103055i | ||||
\(64\) | −8.88199 | −1.11025 | ||||||||
\(65\) | −0.729860 | − | 6.50279i | −0.0905280 | − | 0.806572i | ||||
\(66\) | −4.14254 | −0.509912 | ||||||||
\(67\) | 4.34568 | + | 2.50898i | 0.530910 | + | 0.306521i | 0.741387 | − | 0.671078i | \(-0.234168\pi\) |
−0.210477 | + | 0.977599i | \(0.567502\pi\) | |||||||
\(68\) | 0.508159 | − | 0.880158i | 0.0616234 | − | 0.106735i | ||||
\(69\) | −4.08721 | − | 7.07925i | −0.492042 | − | 0.852242i | ||||
\(70\) | − | 2.31680i | − | 0.276911i | ||||||
\(71\) | 2.35453 | − | 1.35939i | 0.279431 | − | 0.161330i | −0.353735 | − | 0.935346i | \(-0.615088\pi\) |
0.633166 | + | 0.774016i | \(0.281755\pi\) | |||||||
\(72\) | 4.28709 | − | 2.47515i | 0.505238 | − | 0.291699i | ||||
\(73\) | 7.67213i | 0.897955i | 0.893543 | + | 0.448978i | \(0.148212\pi\) | ||||
−0.893543 | + | 0.448978i | \(0.851788\pi\) | |||||||
\(74\) | 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 | ||||
\(77\) | 2.77849 | 0.316639 | ||||||||
\(78\) | −4.32659 | + | 3.19030i | −0.489890 | + | 0.361230i | ||||
\(79\) | −15.7399 | −1.77087 | −0.885436 | − | 0.464761i | \(-0.846140\pi\) | ||||
−0.885436 | + | 0.464761i | \(0.846140\pi\) | |||||||
\(80\) | 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 | \(-0.855816\pi\) | ||
0.899153 | − | 0.437635i | \(-0.144184\pi\) | |||||||
\(84\) | 0.374626 | − | 0.216290i | 0.0408751 | − | 0.0235992i | ||||
\(85\) | −4.31275 | + | 2.48997i | −0.467784 | + | 0.270075i | ||||
\(86\) | 11.6217i | 1.25320i | ||||||||
\(87\) | −2.05328 | − | 3.55639i | −0.220135 | − | 0.381285i | ||||
\(88\) | −4.20379 | + | 7.28117i | −0.448125 | + | 0.776176i | ||||
\(89\) | −13.9118 | − | 8.03198i | −1.47465 | − | 0.851388i | −0.475055 | − | 0.879956i | \(-0.657572\pi\) |
−0.999592 | + | 0.0285683i | \(0.990905\pi\) | |||||||
\(90\) | −3.79017 | −0.399519 | ||||||||
\(91\) | 2.90194 | − | 2.13980i | 0.304206 | − | 0.224312i | ||||
\(92\) | −2.59235 | −0.270271 | ||||||||
\(93\) | −2.09064 | − | 1.20703i | −0.216789 | − | 0.125163i | ||||
\(94\) | 4.25052 | − | 7.36212i | 0.438408 | − | 0.759345i | ||||
\(95\) | −5.32659 | − | 9.22592i | −0.546497 | − | 0.946560i | ||||
\(96\) | 2.41340i | 0.246317i | ||||||||
\(97\) | −12.3209 | + | 7.11347i | −1.25100 | + | 0.722263i | −0.971307 | − | 0.237827i | \(-0.923565\pi\) |
−0.279689 | + | 0.960091i | \(0.590231\pi\) | |||||||
\(98\) | 1.10554 | − | 0.638282i | 0.111676 | − | 0.0644762i | ||||
\(99\) | − | 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 | ||||
\(103\) | 12.9196 | 1.27301 | 0.636503 | − | 0.771275i | \(-0.280380\pi\) | ||||
0.636503 | + | 0.771275i | \(0.280380\pi\) | |||||||
\(104\) | 1.21690 | + | 10.8421i | 0.119327 | + | 1.06316i | ||||
\(105\) | −2.11964 | −0.206855 | ||||||||
\(106\) | −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 | ||||
\(109\) | 1.98589i | 0.190214i | 0.995467 | + | 0.0951071i | \(0.0303194\pi\) | ||||
−0.995467 | + | 0.0951071i | \(0.969681\pi\) | |||||||
\(110\) | 5.57479 | − | 3.21861i | 0.531536 | − | 0.306882i | ||||
\(111\) | 1.76299 | − | 1.01786i | 0.167335 | − | 0.0966110i | ||||
\(112\) | 3.12205i | 0.295006i | ||||||||
\(113\) | 5.28711 | + | 9.15754i | 0.497369 | + | 0.861469i | 0.999995 | − | 0.00303506i | \(-0.000966090\pi\) |
−0.502626 | + | 0.864504i | \(0.667633\pi\) | |||||||
\(114\) | −4.37583 | + | 7.57916i | −0.409834 | + | 0.709854i | ||||
\(115\) | 11.0007 | + | 6.35123i | 1.02582 | + | 0.592256i | ||||
\(116\) | −1.30231 | −0.120917 | ||||||||
\(117\) | −3.50061 | − | 4.74743i | −0.323632 | − | 0.438900i | ||||
\(118\) | 3.92410 | 0.361243 | ||||||||
\(119\) | −2.37634 | − | 1.37198i | −0.217839 | − | 0.125769i | ||||
\(120\) | 3.20695 | − | 5.55461i | 0.292753 | − | 0.507064i | ||||
\(121\) | −1.63999 | − | 2.84054i | −0.149090 | − | 0.258231i | ||||
\(122\) | − | 1.38097i | − | 0.125027i | ||||||
\(123\) | 6.44001 | − | 3.71814i | 0.580676 | − | 0.335254i | ||||
\(124\) | −0.663004 | + | 0.382786i | −0.0595395 | + | 0.0343752i | ||||
\(125\) | 12.1710i | 1.08860i | ||||||||
\(126\) | −1.04420 | − | 1.80860i | −0.0930246 | − | 0.161123i | ||||
\(127\) | 5.63478 | − | 9.75972i | 0.500006 | − | 0.866035i | −0.499994 | − | 0.866029i | \(-0.666665\pi\) |
1.00000 | 6.53271e-6i | \(-2.07943e-6\pi\) | ||||||||
\(128\) | −6.24025 | − | 3.60281i | −0.551566 | − | 0.318447i | ||||
\(129\) | 10.6327 | 0.936156 | ||||||||
\(130\) | 3.34373 | − | 7.65493i | 0.293264 | − | 0.671382i | ||||
\(131\) | 3.06481 | 0.267774 | 0.133887 | − | 0.990997i | \(-0.457254\pi\) | ||||
0.133887 | + | 0.990997i | \(0.457254\pi\) | |||||||
\(132\) | 1.04090 | + | 0.600962i | 0.0905984 | + | 0.0523070i | ||||
\(133\) | 2.93497 | − | 5.08351i | 0.254494 | − | 0.440796i | ||||
\(134\) | 3.20288 | + | 5.54754i | 0.276686 | + | 0.479235i | ||||
\(135\) | 9.82653i | 0.845733i | ||||||||
\(136\) | 7.19067 | − | 4.15154i | 0.616595 | − | 0.355991i | ||||
\(137\) | 18.9512 | − | 10.9415i | 1.61911 | − | 0.934796i | 0.631965 | − | 0.774997i | \(-0.282249\pi\) |
0.987150 | − | 0.159799i | \(-0.0510845\pi\) | |||||||
\(138\) | − | 10.4352i | − | 0.888300i | ||||||
\(139\) | −5.53535 | − | 9.58750i | −0.469502 | − | 0.813201i | 0.529890 | − | 0.848066i | \(-0.322233\pi\) |
−0.999392 | + | 0.0348652i | \(0.988900\pi\) | |||||||
\(140\) | −0.336100 | + | 0.582143i | −0.0284056 | + | 0.0492000i | ||||
\(141\) | −6.73559 | − | 3.88879i | −0.567239 | − | 0.327495i | ||||
\(142\) | 3.47069 | 0.291254 | ||||||||
\(143\) | 9.18040 | + | 4.01006i | 0.767703 | + | 0.335338i | ||||
\(144\) | 5.10752 | 0.425626 | ||||||||
\(145\) | 5.52637 | + | 3.19065i | 0.458940 | + | 0.264969i | ||||
\(146\) | −4.89699 | + | 8.48183i | −0.405277 | + | 0.701961i | ||||
\(147\) | −0.583963 | − | 1.01145i | −0.0481644 | − | 0.0834232i | ||||
\(148\) | − | 0.645588i | − | 0.0530670i | ||||||
\(149\) | −1.99824 | + | 1.15369i | −0.163702 | + | 0.0945136i | −0.579613 | − | 0.814892i | \(-0.696796\pi\) |
0.415911 | + | 0.909406i | \(0.363463\pi\) | |||||||
\(150\) | 2.20306 | − | 1.27194i | 0.179879 | − | 0.103853i | ||||
\(151\) | 20.6158i | 1.67769i | 0.544371 | + | 0.838845i | \(0.316768\pi\) | ||||
−0.544371 | + | 0.838845i | \(0.683232\pi\) | |||||||
\(152\) | 8.88105 | + | 15.3824i | 0.720348 | + | 1.24768i | ||||
\(153\) | −2.24449 | + | 3.88757i | −0.181456 | + | 0.314292i | ||||
\(154\) | 3.07173 | + | 1.77346i | 0.247527 | + | 0.142910i | ||||
\(155\) | 3.75128 | 0.301310 | ||||||||
\(156\) | 1.54996 | − | 0.173964i | 0.124096 | − | 0.0139283i | ||||
\(157\) | 2.89649 | 0.231165 | 0.115582 | − | 0.993298i | \(-0.463127\pi\) | ||||
0.115582 | + | 0.993298i | \(0.463127\pi\) | |||||||
\(158\) | −17.4010 | − | 10.0465i | −1.38435 | − | 0.799254i | ||||
\(159\) | −6.12455 | + | 10.6080i | −0.485709 | + | 0.841272i | ||||
\(160\) | −1.87513 | − | 3.24782i | −0.148242 | − | 0.256763i | ||||
\(161\) | 6.99909i | 0.551606i | ||||||||
\(162\) | 1.56523 | − | 0.903688i | 0.122976 | − | 0.0710004i | ||||
\(163\) | −20.2944 | + | 11.7170i | −1.58958 | + | 0.917743i | −0.596201 | + | 0.802835i | \(0.703324\pi\) |
−0.993376 | + | 0.114907i | \(0.963343\pi\) | |||||||
\(164\) | − | 2.35827i | − | 0.184150i | ||||||
\(165\) | −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 | 0.732606 | − | 0.680653i | \(-0.238304\pi\) |
−0.223160 | + | 0.974782i | \(0.571637\pi\) | |||||||
\(168\) | 3.53408 | 0.272660 | ||||||||
\(169\) | 12.6765 | − | 2.88188i | 0.975119 | − | 0.221683i | ||||
\(170\) | −6.35721 | −0.487576 | ||||||||
\(171\) | −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 | ||||||
\(175\) | −1.47764 | + | 0.853117i | −0.111699 | + | 0.0644896i | ||||
\(176\) | −7.51241 | + | 4.33729i | −0.566269 | + | 0.326936i | ||||
\(177\) | − | 3.59015i | − | 0.269852i | ||||||
\(178\) | −10.2533 | − | 17.7593i | −0.768520 | − | 1.33112i | ||||
\(179\) | −6.14571 | + | 10.6447i | −0.459352 | + | 0.795621i | −0.998927 | − | 0.0463168i | \(-0.985252\pi\) |
0.539575 | + | 0.841938i | \(0.318585\pi\) | |||||||
\(180\) | 0.952357 | + | 0.549843i | 0.0709845 | + | 0.0409829i | ||||
\(181\) | −21.8525 | −1.62428 | −0.812140 | − | 0.583463i | \(-0.801697\pi\) | ||||
−0.812140 | + | 0.583463i | \(0.801697\pi\) | |||||||
\(182\) | 4.57400 | − | 0.513376i | 0.339047 | − | 0.0380540i | ||||
\(183\) | −1.26344 | −0.0933964 | ||||||||
\(184\) | −18.3415 | − | 10.5894i | −1.35215 | − | 0.780664i | ||||
\(185\) | −1.58168 | + | 2.73956i | −0.116288 | + | 0.201416i | ||||
\(186\) | −1.54085 | − | 2.66883i | −0.112981 | − | 0.195688i | ||||
\(187\) | − | 7.62407i | − | 0.557527i | ||||||
\(188\) | −2.13606 | + | 1.23325i | −0.155788 | + | 0.0899442i | ||||
\(189\) | −4.68905 | + | 2.70722i | −0.341078 | + | 0.196921i | ||||
\(190\) | − | 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 | 0.846861 | − | 0.531814i | \(-0.178489\pi\) |
−0.0371334 | + | 0.999310i | \(0.511823\pi\) | |||||||
\(194\) | −18.1616 | −1.30393 | ||||||||
\(195\) | −7.00347 | − | 3.05917i | −0.501529 | − | 0.219071i | ||||
\(196\) | −0.370384 | −0.0264560 | ||||||||
\(197\) | 16.4772 | + | 9.51312i | 1.17395 | + | 0.677781i | 0.954608 | − | 0.297866i | \(-0.0962749\pi\) |
0.219344 | + | 0.975648i | \(0.429608\pi\) | |||||||
\(198\) | 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 | \(-0.417975\pi\) | |||||||
\(200\) | − | 5.16298i | − | 0.365078i | ||||||
\(201\) | 5.07543 | − | 2.93030i | 0.357993 | − | 0.206688i | ||||
\(202\) | −0.0808396 | + | 0.0466728i | −0.00568785 | + | 0.00328388i | ||||
\(203\) | 3.51612i | 0.246783i | ||||||||
\(204\) | −0.593492 | − | 1.02796i | −0.0415528 | − | 0.0719715i | ||||
\(205\) | −5.77773 | + | 10.0073i | −0.403534 | + | 0.698942i | ||||
\(206\) | 14.2831 | + | 8.24634i | 0.995150 | + | 0.574550i | ||||
\(207\) | 11.4502 | 0.795842 | ||||||||
\(208\) | −4.50590 | + | 10.3155i | −0.312428 | + | 0.715254i | ||||
\(209\) | 16.3096 | 1.12816 | ||||||||
\(210\) | −2.34334 | − | 1.35293i | −0.161706 | − | 0.0933608i | ||||
\(211\) | −5.00015 | + | 8.66052i | −0.344225 | + | 0.596215i | −0.985213 | − | 0.171336i | \(-0.945192\pi\) |
0.640988 | + | 0.767551i | \(0.278525\pi\) | |||||||
\(212\) | 1.94228 | + | 3.36413i | 0.133396 | + | 0.231049i | ||||
\(213\) | − | 3.17532i | − | 0.217570i | ||||||
\(214\) | −4.43160 | + | 2.55858i | −0.302938 | + | 0.174901i | ||||
\(215\) | −14.3089 | + | 8.26122i | −0.975856 | + | 0.563411i | ||||
\(216\) | − | 16.3838i | − | 1.11478i | ||||||
\(217\) | 1.03348 | + | 1.79004i | 0.0701574 | + | 0.121516i | ||||
\(218\) | −1.26756 | + | 2.19548i | −0.0858501 | + | 0.148697i | ||||
\(219\) | 7.76000 | + | 4.48024i | 0.524372 | + | 0.302747i | ||||
\(220\) | −1.86770 | −0.125921 | ||||||||
\(221\) | −5.87153 | − | 7.96280i | −0.394962 | − | 0.535636i | ||||
\(222\) | 2.59873 | 0.174415 | ||||||||
\(223\) | 7.25954 | + | 4.19130i | 0.486135 | + | 0.280670i | 0.722970 | − | 0.690880i | \(-0.242777\pi\) |
−0.236835 | + | 0.971550i | \(0.576110\pi\) | |||||||
\(224\) | 1.03320 | − | 1.78956i | 0.0690336 | − | 0.119570i | ||||
\(225\) | 1.39566 | + | 2.41735i | 0.0930439 | + | 0.161157i | ||||
\(226\) | 13.4987i | 0.897918i | ||||||||
\(227\) | −0.796500 | + | 0.459860i | −0.0528656 | + | 0.0305220i | −0.526200 | − | 0.850361i | \(-0.676384\pi\) |
0.473334 | + | 0.880883i | \(0.343050\pi\) | |||||||
\(228\) | 2.19903 | − | 1.26961i | 0.145634 | − | 0.0840820i | ||||
\(229\) | − | 24.6208i | − | 1.62699i | −0.581574 | − | 0.813494i | \(-0.697563\pi\) | ||
0.581574 | − | 0.813494i | \(-0.302437\pi\) | |||||||
\(230\) | 8.10776 | + | 14.0430i | 0.534610 | + | 0.925971i | ||||
\(231\) | 1.62254 | − | 2.81031i | 0.106755 | − | 0.184905i | ||||
\(232\) | −9.21415 | − | 5.31979i | −0.604939 | − | 0.349261i | ||||
\(233\) | 17.2769 | 1.13185 | 0.565925 | − | 0.824457i | \(-0.308519\pi\) | ||||
0.565925 | + | 0.824457i | \(0.308519\pi\) | |||||||
\(234\) | −0.839858 | − | 7.48283i | −0.0549032 | − | 0.489168i | ||||
\(235\) | 12.0858 | 0.788392 | ||||||||
\(236\) | −0.986008 | − | 0.569272i | −0.0641837 | − | 0.0370565i | ||||
\(237\) | −9.19149 | + | 15.9201i | −0.597051 | + | 1.03412i | ||||
\(238\) | −1.75142 | − | 3.03355i | −0.113528 | − | 0.196636i | ||||
\(239\) | − | 14.4828i | − | 0.936816i | −0.883512 | − | 0.468408i | \(-0.844828\pi\) | ||
0.883512 | − | 0.468408i | \(-0.155172\pi\) | |||||||
\(240\) | 5.73101 | − | 3.30880i | 0.369935 | − | 0.213582i | ||||
\(241\) | −7.30441 | + | 4.21720i | −0.470518 | + | 0.271654i | −0.716457 | − | 0.697632i | \(-0.754237\pi\) |
0.245938 | + | 0.969285i | \(0.420904\pi\) | |||||||
\(242\) | − | 4.18710i | − | 0.269157i | ||||||
\(243\) | 7.29488 | + | 12.6351i | 0.467967 | + | 0.810543i | ||||
\(244\) | −0.200338 | + | 0.346995i | −0.0128253 | + | 0.0222141i | ||||
\(245\) | 1.57173 | + | 0.907437i | 0.100414 | + | 0.0579740i | ||||
\(246\) | 9.49290 | 0.605245 | ||||||||
\(247\) | 17.0342 | − | 12.5605i | 1.08386 | − | 0.799205i | ||||
\(248\) | −6.25453 | −0.397163 | ||||||||
\(249\) | −8.06541 | − | 4.65657i | −0.511124 | − | 0.295098i | ||||
\(250\) | −7.76851 | + | 13.4555i | −0.491324 | + | 0.850998i | ||||
\(251\) | −7.33631 | − | 12.7069i | −0.463064 | − | 0.802050i | 0.536048 | − | 0.844188i | \(-0.319917\pi\) |
−0.999112 | + | 0.0421373i | \(0.986583\pi\) | |||||||
\(252\) | 0.605930i | 0.0381700i | ||||||||
\(253\) | −16.8415 | + | 9.72346i | −1.05882 | + | 0.611309i | ||||
\(254\) | 12.4589 | − | 7.19315i | 0.781742 | − | 0.451339i | ||||
\(255\) | 5.81620i | 0.364224i | ||||||||
\(256\) | 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 | ||||
\(259\) | −1.74302 | −0.108306 | ||||||||
\(260\) | −1.95068 | + | 1.43838i | −0.120976 | + | 0.0892043i | ||||
\(261\) | 5.75219 | 0.356052 | ||||||||
\(262\) | 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 | ||||||
\(266\) | 6.48942 | − | 3.74667i | 0.397892 | − | 0.229723i | ||||
\(267\) | −16.2479 | + | 9.38075i | −0.994357 | + | 0.574092i | ||||
\(268\) | − | 1.85857i | − | 0.113530i | ||||||
\(269\) | 11.1625 | + | 19.3340i | 0.680589 | + | 1.17881i | 0.974801 | + | 0.223074i | \(0.0716093\pi\) |
−0.294213 | + | 0.955740i | \(0.595057\pi\) | |||||||
\(270\) | −6.27210 | + | 10.8636i | −0.381708 | + | 0.661137i | ||||
\(271\) | −8.14054 | − | 4.69994i | −0.494502 | − | 0.285501i | 0.231938 | − | 0.972731i | \(-0.425493\pi\) |
−0.726440 | + | 0.687230i | \(0.758827\pi\) | |||||||
\(272\) | 8.56677 | 0.519437 | ||||||||
\(273\) | −0.469686 | − | 4.18474i | −0.0284267 | − | 0.253272i | ||||
\(274\) | 27.9351 | 1.68762 | ||||||||
\(275\) | −4.10562 | − | 2.37038i | −0.247578 | − | 0.142939i | ||||
\(276\) | −1.51384 | + | 2.62204i | −0.0911223 | + | 0.157828i | ||||
\(277\) | −7.17133 | − | 12.4211i | −0.430883 | − | 0.746312i | 0.566066 | − | 0.824360i | \(-0.308465\pi\) |
−0.996950 | + | 0.0780478i | \(0.975131\pi\) | |||||||
\(278\) | − | 14.1324i | − | 0.847608i | ||||||
\(279\) | 2.92842 | − | 1.69073i | 0.175320 | − | 0.101221i | ||||
\(280\) | −4.75596 | + | 2.74586i | −0.284223 | + | 0.164096i | ||||
\(281\) | − | 0.0988416i | − | 0.00589640i | −0.999996 | − | 0.00294820i | \(-0.999062\pi\) | ||
0.999996 | − | 0.00294820i | \(-0.000938442\pi\) | |||||||
\(282\) | −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 | ||||
\(285\) | −12.4421 | −0.737007 | ||||||||
\(286\) | 7.58972 | + | 10.2930i | 0.448789 | + | 0.608635i | ||||
\(287\) | −6.36709 | −0.375837 | ||||||||
\(288\) | −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 | ||||
\(291\) | 16.6160i | 0.974047i | ||||||||
\(292\) | 2.46093 | − | 1.42082i | 0.144015 | − | 0.0831471i | ||||
\(293\) | 21.5586 | − | 12.4469i | 1.25947 | − | 0.727153i | 0.286496 | − | 0.958082i | \(-0.407510\pi\) |
0.972971 | + | 0.230928i | \(0.0741762\pi\) | |||||||
\(294\) | − | 1.49093i | − | 0.0869529i | ||||||
\(295\) | 2.78942 | + | 4.83142i | 0.162406 | + | 0.281296i | ||||
\(296\) | 2.63715 | − | 4.56767i | 0.153281 | − | 0.265491i | ||||
\(297\) | −13.0285 | − | 7.52200i | −0.755989 | − | 0.436471i | ||||
\(298\) | −2.94551 | −0.170629 | ||||||||
\(299\) | −10.1014 | + | 23.1256i | −0.584182 | + | 1.33739i | ||||
\(300\) | −0.738085 | −0.0426133 | ||||||||
\(301\) | −7.88422 | − | 4.55195i | −0.454439 | − | 0.262370i | ||||
\(302\) | −13.1587 | + | 22.7915i | −0.757197 | + | 1.31150i | ||||
\(303\) | 0.0427008 | + | 0.0739599i | 0.00245310 | + | 0.00424889i | ||||
\(304\) | 18.3262i | 1.05108i | ||||||||
\(305\) | 1.70027 | − | 0.981651i | 0.0973571 | − | 0.0562091i | ||||
\(306\) | −4.96274 | + | 2.86524i | −0.283701 | + | 0.163795i | ||||
\(307\) | − | 9.89767i | − | 0.564890i | −0.959284 | − | 0.282445i | \(-0.908855\pi\) | ||
0.959284 | − | 0.282445i | \(-0.0911455\pi\) | |||||||
\(308\) | −0.514555 | − | 0.891235i | −0.0293195 | − | 0.0507828i | ||||
\(309\) | 7.54456 | − | 13.0676i | 0.429195 | − | 0.743387i | ||||
\(310\) | 4.14718 | + | 2.39437i | 0.235544 | + | 0.135991i | ||||
\(311\) | −7.23790 | −0.410423 | −0.205212 | − | 0.978718i | \(-0.565788\pi\) | ||||
−0.205212 | + | 0.978718i | \(0.565788\pi\) | |||||||
\(312\) | 11.6769 | + | 5.10056i | 0.661076 | + | 0.288763i | ||||
\(313\) | 32.6606 | 1.84609 | 0.923043 | − | 0.384696i | \(-0.125694\pi\) | ||||
0.923043 | + | 0.384696i | \(0.125694\pi\) | |||||||
\(314\) | 3.20217 | + | 1.84877i | 0.180709 | + | 0.104332i | ||||
\(315\) | 1.48452 | − | 2.57127i | 0.0836433 | − | 0.144874i | ||||
\(316\) | 2.91490 | + | 5.04875i | 0.163976 | + | 0.284014i | ||||
\(317\) | − | 17.1744i | − | 0.964608i | −0.876004 | − | 0.482304i | \(-0.839800\pi\) | ||
0.876004 | − | 0.482304i | \(-0.160200\pi\) | |||||||
\(318\) | −13.5418 | + | 7.81838i | −0.759388 | + | 0.438433i | ||||
\(319\) | −8.46064 | + | 4.88475i | −0.473705 | + | 0.273494i | ||||
\(320\) | − | 16.1197i | − | 0.901118i | ||||||
\(321\) | 2.34084 | + | 4.05446i | 0.130653 | + | 0.226298i | ||||
\(322\) | −4.46740 | + | 7.73776i | −0.248958 | + | 0.431208i | ||||
\(323\) | −13.9489 | − | 8.05342i | −0.776140 | − | 0.448105i | ||||
\(324\) | −0.524395 | −0.0291330 | ||||||||
\(325\) | −6.11353 | + | 0.686170i | −0.339118 | + | 0.0380619i | ||||
\(326\) | −29.9149 | −1.65683 | ||||||||
\(327\) | 2.00864 | + | 1.15969i | 0.111078 | + | 0.0641309i | ||||
\(328\) | 9.63324 | − | 16.6853i | 0.531907 | − | 0.921289i | ||||
\(329\) | 3.32966 | + | 5.76714i | 0.183570 | + | 0.317953i | ||||
\(330\) | − | 7.51819i | − | 0.413863i | ||||||
\(331\) | 17.2633 | − | 9.96698i | 0.948877 | − | 0.547835i | 0.0561454 | − | 0.998423i | \(-0.482119\pi\) |
0.892732 | + | 0.450588i | \(0.148786\pi\) | |||||||
\(332\) | −2.55778 | + | 1.47674i | −0.140377 | + | 0.0810465i | ||||
\(333\) | 2.85150i | 0.156261i | ||||||||
\(334\) | 4.85219 | + | 8.40424i | 0.265500 | + | 0.459860i | ||||
\(335\) | −4.55348 | + | 7.88687i | −0.248783 | + | 0.430905i | ||||
\(336\) | 3.15780 | + | 1.82316i | 0.172272 | + | 0.0994615i | ||||
\(337\) | 1.27189 | 0.0692842 | 0.0346421 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346421 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(338\) | 15.8538 | + | 4.90518i | 0.862335 | + | 0.266807i | ||||
\(339\) | 12.3499 | 0.670754 | ||||||||
\(340\) | 1.59738 | + | 0.922245i | 0.0866298 | + | 0.0500158i | ||||
\(341\) | −2.87152 | + | 4.97363i | −0.155502 | + | 0.269337i | ||||
\(342\) | −6.12937 | − | 10.6164i | −0.331438 | − | 0.574068i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 23.8572 | − | 13.7740i | 1.28630 | − | 0.742643i | ||||
\(345\) | 12.8479 | − | 7.41777i | 0.691710 | − | 0.399359i | ||||
\(346\) | 6.88989i | 0.370403i | ||||||||
\(347\) | −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 | 0.0416774 | − | 0.999131i | \(-0.486730\pi\) |
−0.844434 | + | 0.535659i | \(0.820063\pi\) | |||||||
\(350\) | −2.17812 | −0.116425 | ||||||||
\(351\) | −19.4002 | + | 2.17744i | −1.03551 | + | 0.116223i | ||||
\(352\) | 5.74148 | 0.306022 | ||||||||
\(353\) | −21.9533 | − | 12.6747i | −1.16846 | − | 0.674608i | −0.215140 | − | 0.976583i | \(-0.569021\pi\) |
−0.953316 | + | 0.301975i | \(0.902354\pi\) | |||||||
\(354\) | 2.29153 | − | 3.96904i | 0.121793 | − | 0.210952i | ||||
\(355\) | 2.46711 | + | 4.27317i | 0.130941 | + | 0.226796i | ||||
\(356\) | 5.94983i | 0.315341i | ||||||||
\(357\) | −2.77539 | + | 1.60237i | −0.146889 | + | 0.0848064i | ||||
\(358\) | −13.5886 | + | 7.84539i | −0.718181 | + | 0.414642i | ||||
\(359\) | 5.27044i | 0.278163i | 0.990281 | + | 0.139082i | \(0.0444151\pi\) | ||||
−0.990281 | + | 0.139082i | \(0.955585\pi\) | |||||||
\(360\) | 4.49208 | + | 7.78052i | 0.236754 | + | 0.410069i | ||||
\(361\) | 7.72804 | − | 13.3854i | 0.406739 | − | 0.704493i | ||||
\(362\) | −24.1587 | − | 13.9480i | −1.26975 | − | 0.733092i | ||||
\(363\) | −3.83077 | −0.201063 | ||||||||
\(364\) | −1.22378 | − | 0.534557i | −0.0641437 | − | 0.0280184i | ||||
\(365\) | −13.9240 | −0.728813 | ||||||||
\(366\) | −1.39678 | − | 0.806433i | −0.0730110 | − | 0.0421529i | ||||
\(367\) | −12.6588 | + | 21.9257i | −0.660783 | + | 1.14451i | 0.319627 | + | 0.947544i | \(0.396443\pi\) |
−0.980410 | + | 0.196967i | \(0.936891\pi\) | |||||||
\(368\) | −10.9257 | − | 18.9240i | −0.569544 | − | 0.986479i | ||||
\(369\) | 10.4162i | 0.542248i | ||||||||
\(370\) | −3.49722 | + | 2.01912i | −0.181812 | + | 0.104969i | ||||
\(371\) | 9.08280 | − | 5.24396i | 0.471556 | − | 0.272253i | ||||
\(372\) | 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 | ||||
\(376\) | −20.1507 | −1.03920 | ||||||||
\(377\) | −5.07464 | + | 11.6176i | −0.261357 | + | 0.598336i | ||||
\(378\) | −6.91188 | −0.355509 | ||||||||
\(379\) | 10.6717 | + | 6.16130i | 0.548168 | + | 0.316485i | 0.748383 | − | 0.663267i | \(-0.230831\pi\) |
−0.200215 | + | 0.979752i | \(0.564164\pi\) | |||||||
\(380\) | −1.97288 | + | 3.41714i | −0.101207 | + | 0.175295i | ||||
\(381\) | −6.58100 | − | 11.3986i | −0.337155 | − | 0.583969i | ||||
\(382\) | − | 3.51970i | − | 0.180083i | ||||||
\(383\) | −6.28662 | + | 3.62958i | −0.321232 | + | 0.185463i | −0.651941 | − | 0.758269i | \(-0.726045\pi\) |
0.330710 | + | 0.943732i | \(0.392712\pi\) | |||||||
\(384\) | −7.28815 | + | 4.20782i | −0.371922 | + | 0.214729i | ||||
\(385\) | 5.04261i | 0.256995i | ||||||||
\(386\) | 8.29086 | + | 14.3602i | 0.421994 | + | 0.730915i | ||||
\(387\) | −7.44677 | + | 12.8982i | −0.378541 | + | 0.655652i | ||||
\(388\) | 4.56346 | + | 2.63472i | 0.231675 | + | 0.133757i | ||||
\(389\) | 7.14811 | 0.362424 | 0.181212 | − | 0.983444i | \(-0.441998\pi\) | ||||
0.181212 | + | 0.983444i | \(0.441998\pi\) | |||||||
\(390\) | −5.78999 | − | 7.85221i | −0.293187 | − | 0.397612i | ||||
\(391\) | 19.2052 | 0.971250 | ||||||||
\(392\) | −2.62055 | − | 1.51297i | −0.132358 | − | 0.0764167i | ||||
\(393\) | 1.78974 | − | 3.09991i | 0.0902802 | − | 0.156370i | ||||
\(394\) | 12.1441 | + | 21.0342i | 0.611811 | + | 1.05969i | ||||
\(395\) | − | 28.5659i | − | 1.43730i | ||||||
\(396\) | −1.45802 | + | 0.841786i | −0.0732681 | + | 0.0423014i | ||||
\(397\) | −19.4520 | + | 11.2306i | −0.976266 | + | 0.563647i | −0.901141 | − | 0.433527i | \(-0.857269\pi\) |
−0.0751252 | + | 0.997174i | \(0.523936\pi\) | |||||||
\(398\) | − | 25.5718i | − | 1.28180i | ||||||
\(399\) | −3.42782 | − | 5.93716i | −0.171606 | − | 0.297230i | ||||
\(400\) | 2.66347 | − | 4.61327i | 0.133174 | − | 0.230663i | ||||
\(401\) | −2.64547 | − | 1.52736i | −0.132108 | − | 0.0762729i | 0.432489 | − | 0.901639i | \(-0.357635\pi\) |
−0.564598 | + | 0.825366i | \(0.690969\pi\) | |||||||
\(402\) | 7.48144 | 0.373140 | ||||||||
\(403\) | 0.831240 | + | 7.40605i | 0.0414070 | + | 0.368921i | ||||
\(404\) | 0.0270834 | 0.00134745 | ||||||||
\(405\) | 2.22527 | + | 1.28476i | 0.110575 | + | 0.0638403i | ||||
\(406\) | −2.24427 | + | 3.88720i | −0.111381 | + | 0.192918i | ||||
\(407\) | −2.42149 | − | 4.19414i | −0.120029 | − | 0.207896i | ||||
\(408\) | − | 9.69737i | − | 0.480091i | ||||||
\(409\) | 4.85482 | − | 2.80293i | 0.240055 | − | 0.138596i | −0.375147 | − | 0.926965i | \(-0.622408\pi\) |
0.615202 | + | 0.788369i | \(0.289074\pi\) | |||||||
\(410\) | −12.7750 | + | 7.37564i | −0.630912 | + | 0.364257i | ||||
\(411\) | − | 25.5577i | − | 1.26067i | ||||||
\(412\) | −2.39261 | − | 4.14412i | −0.117875 | − | 0.204166i | ||||
\(413\) | −1.53698 | + | 2.66212i | −0.0756297 | + | 0.130995i | ||||
\(414\) | 12.6586 | + | 7.30844i | 0.622136 | + | 0.359190i | ||||
\(415\) | 14.4719 | 0.710400 | ||||||||
\(416\) | 5.99657 | − | 4.42169i | 0.294006 | − | 0.216791i | ||||
\(417\) | −12.9297 | −0.633172 | ||||||||
\(418\) | 18.0308 | + | 10.4101i | 0.881916 | + | 0.509175i | ||||
\(419\) | −3.06969 | + | 5.31687i | −0.149964 | + | 0.259746i | −0.931214 | − | 0.364473i | \(-0.881249\pi\) |
0.781250 | + | 0.624219i | \(0.214583\pi\) | |||||||
\(420\) | 0.392540 | + | 0.679899i | 0.0191540 | + | 0.0331757i | ||||
\(421\) | 1.92589i | 0.0938622i | 0.998898 | + | 0.0469311i | \(0.0149441\pi\) | ||||
−0.998898 | + | 0.0469311i | \(0.985056\pi\) | |||||||
\(422\) | −11.0557 | + | 6.38302i | −0.538184 | + | 0.310720i | ||||
\(423\) | 9.43475 | − | 5.44716i | 0.458733 | − | 0.264850i | ||||
\(424\) | 31.7359i | 1.54123i | ||||||||
\(425\) | 2.34092 | + | 4.05459i | 0.113551 | + | 0.196677i | ||||
\(426\) | 2.02675 | − | 3.51044i | 0.0981965 | − | 0.170081i | ||||
\(427\) | 0.936853 | + | 0.540892i | 0.0453375 | + | 0.0261756i | ||||
\(428\) | 1.48470 | 0.0717658 | ||||||||
\(429\) | 9.41700 | − | 6.94381i | 0.454657 | − | 0.335250i | ||||
\(430\) | −21.0920 | −1.01714 | ||||||||
\(431\) | 9.30923 | + | 5.37469i | 0.448410 | + | 0.258890i | 0.707158 | − | 0.707055i | \(-0.249977\pi\) |
−0.258749 | + | 0.965945i | \(0.583310\pi\) | |||||||
\(432\) | 8.45207 | − | 14.6394i | 0.406651 | − | 0.704340i | ||||
\(433\) | 20.1328 | + | 34.8710i | 0.967520 | + | 1.67579i | 0.702685 | + | 0.711501i | \(0.251984\pi\) |
0.264835 | + | 0.964294i | \(0.414682\pi\) | |||||||
\(434\) | 2.63861i | 0.126658i | ||||||||
\(435\) | 6.45439 | − | 3.72644i | 0.309464 | − | 0.178669i | ||||
\(436\) | 0.637000 | − | 0.367772i | 0.0305068 | − | 0.0176131i | ||||
\(437\) | 41.0842i | 1.96532i | ||||||||
\(438\) | 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 | ||||
\(441\) | 1.63595 | 0.0779024 | ||||||||
\(442\) | −1.40868 | − | 12.5509i | −0.0670042 | − | 0.596984i | ||||
\(443\) | −27.8963 | −1.32539 | −0.662697 | − | 0.748887i | \(-0.730588\pi\) | ||||
−0.662697 | + | 0.748887i | \(0.730588\pi\) | |||||||
\(444\) | −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 | ||||||||
\(448\) | 7.69203 | − | 4.44099i | 0.363414 | − | 0.209817i | ||||
\(449\) | 19.1056 | − | 11.0306i | 0.901648 | − | 0.520567i | 0.0239134 | − | 0.999714i | \(-0.492387\pi\) |
0.877734 | + | 0.479147i | \(0.159054\pi\) | |||||||
\(450\) | 3.56329i | 0.167975i | ||||||||
\(451\) | −8.84546 | − | 15.3208i | −0.416516 | − | 0.721427i | ||||
\(452\) | 1.95826 | − | 3.39181i | 0.0921088 | − | 0.159537i | ||||
\(453\) | 20.8519 | + | 12.0389i | 0.979708 | + | 0.565635i | ||||
\(454\) | −1.17408 | −0.0551023 | ||||||||
\(455\) | 3.88347 | + | 5.26665i | 0.182060 | + | 0.246904i | ||||
\(456\) | 20.7448 | 0.971464 | ||||||||
\(457\) | 4.77724 | + | 2.75814i | 0.223470 | + | 0.129020i | 0.607556 | − | 0.794277i | \(-0.292150\pi\) |
−0.384086 | + | 0.923297i | \(0.625483\pi\) | |||||||
\(458\) | 15.7150 | − | 27.2192i | 0.734314 | − | 1.27187i | ||||
\(459\) | 7.42851 | + | 12.8665i | 0.346733 | + | 0.600559i | ||||
\(460\) | − | 4.70479i | − | 0.219362i | ||||||
\(461\) | 25.0092 | − | 14.4391i | 1.16479 | − | 0.672494i | 0.212346 | − | 0.977195i | \(-0.431890\pi\) |
0.952448 | + | 0.304700i | \(0.0985562\pi\) | |||||||
\(462\) | 3.58755 | − | 2.07127i | 0.166908 | − | 0.0963643i | ||||
\(463\) | − | 14.2284i | − | 0.661251i | −0.943762 | − | 0.330625i | \(-0.892740\pi\) | ||
0.943762 | − | 0.330625i | \(-0.107260\pi\) | |||||||
\(464\) | −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 | ||||
\(467\) | 4.54326 | 0.210237 | 0.105118 | − | 0.994460i | \(-0.466478\pi\) | ||||
0.105118 | + | 0.994460i | \(0.466478\pi\) | |||||||
\(468\) | −0.874509 | + | 2.00205i | −0.0404242 | + | 0.0925448i | ||||
\(469\) | −5.01796 | −0.231708 | ||||||||
\(470\) | 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 | ||||
\(473\) | − | 25.2951i | − | 1.16307i | ||||||
\(474\) | −20.3231 | + | 11.7335i | −0.933469 | + | 0.538939i | ||||
\(475\) | −8.67366 | + | 5.00774i | −0.397975 | + | 0.229771i | ||||
\(476\) | 1.01632i | 0.0465829i | ||||||||
\(477\) | −8.57886 | − | 14.8590i | −0.392799 | − | 0.680348i | ||||
\(478\) | 9.24413 | − | 16.0113i | 0.422817 | − | 0.732340i | ||||
\(479\) | −1.44239 | − | 0.832764i | −0.0659044 | − | 0.0380499i | 0.466686 | − | 0.884423i | \(-0.345448\pi\) |
−0.532590 | + | 0.846373i | \(0.678781\pi\) | |||||||
\(480\) | −4.38002 | −0.199920 | ||||||||
\(481\) | −5.75911 | − | 2.51562i | −0.262593 | − | 0.114702i | ||||
\(482\) | −10.7671 | −0.490426 | ||||||||
\(483\) | 7.07925 | + | 4.08721i | 0.322117 | + | 0.185974i | ||||
\(484\) | −0.607426 | + | 1.05209i | −0.0276103 | + | 0.0478224i | ||||
\(485\) | −12.9100 | − | 22.3608i | −0.586215 | − | 1.01535i | ||||
\(486\) | 18.6248i | 0.844837i | ||||||||
\(487\) | −1.28598 | + | 0.742463i | −0.0582735 | + | 0.0336442i | −0.528854 | − | 0.848713i | \(-0.677378\pi\) |
0.470580 | + | 0.882357i | \(0.344045\pi\) | |||||||
\(488\) | −2.83487 | + | 1.63671i | −0.128328 | + | 0.0740904i | ||||
\(489\) | 27.3691i | 1.23767i | ||||||||
\(490\) | 1.15840 | + | 2.00641i | 0.0523312 | + | 0.0906403i | ||||
\(491\) | 7.99791 | − | 13.8528i | 0.360941 | − | 0.625167i | −0.627175 | − | 0.778878i | \(-0.715789\pi\) |
0.988116 | + | 0.153711i | \(0.0491224\pi\) | |||||||
\(492\) | −2.38528 | − | 1.37714i | −0.107537 | − | 0.0620863i | ||||
\(493\) | 9.64808 | 0.434528 | ||||||||
\(494\) | 26.8490 | − | 3.01348i | 1.20800 | − | 0.135583i | ||||
\(495\) | 8.24947 | 0.370786 | ||||||||
\(496\) | −5.58860 | − | 3.22658i | −0.250936 | − | 0.144878i | ||||
\(497\) | −1.35939 | + | 2.35453i | −0.0609768 | + | 0.105615i | ||||
\(498\) | −5.94440 | − | 10.2960i | −0.266375 | − | 0.461375i | ||||
\(499\) | 17.7199i | 0.793253i | 0.917980 | + | 0.396627i | \(0.129819\pi\) | ||||
−0.917980 | + | 0.396627i | \(0.870181\pi\) | |||||||
\(500\) | 3.90398 | − | 2.25397i | 0.174591 | − | 0.100800i | ||||
\(501\) | 7.68902 | − | 4.43926i | 0.343520 | − | 0.198331i | ||||
\(502\) | − | 18.7305i | − | 0.835985i | ||||||
\(503\) | 0.598451 | + | 1.03655i | 0.0266836 | + | 0.0462174i | 0.879059 | − | 0.476713i | \(-0.158172\pi\) |
−0.852375 | + | 0.522931i | \(0.824839\pi\) | |||||||
\(504\) | −2.47515 | + | 4.28709i | −0.110252 | + | 0.190962i | ||||
\(505\) | −0.114929 | − | 0.0663540i | −0.00511425 | − | 0.00295272i | ||||
\(506\) | −24.8253 | −1.10362 | ||||||||
\(507\) | 4.48774 | − | 14.5046i | 0.199307 | − | 0.644174i | ||||
\(508\) | −4.17406 | −0.185194 | ||||||||
\(509\) | 5.44396 | + | 3.14307i | 0.241299 | + | 0.139314i | 0.615774 | − | 0.787923i | \(-0.288844\pi\) |
−0.374474 | + | 0.927237i | \(0.622177\pi\) | |||||||
\(510\) | −3.71237 | + | 6.43002i | −0.164387 | + | 0.284726i | ||||
\(511\) | −3.83607 | − | 6.64426i | −0.169698 | − | 0.293925i | ||||
\(512\) | 25.3457i | 1.12013i | ||||||||
\(513\) | −27.5244 | + | 15.8912i | −1.21523 | + | 0.701614i | ||||
\(514\) | 32.4238 | − | 18.7199i | 1.43015 | − | 0.825699i | ||||
\(515\) | 23.4474i | 1.03322i | ||||||||
\(516\) | −1.96909 | − | 3.41056i | −0.0866843 | − | 0.150142i | ||||
\(517\) | −9.25143 | + | 16.0240i | −0.406878 | + | 0.704733i | ||||
\(518\) | −1.92698 | − | 1.11254i | −0.0846665 | − | 0.0488822i | ||||
\(519\) | 6.30354 | 0.276695 | ||||||||
\(520\) | −19.6771 | + | 2.20852i | −0.862898 | + | 0.0968499i | ||||
\(521\) | −10.8473 | −0.475230 | −0.237615 | − | 0.971359i | \(-0.576366\pi\) | ||||
−0.237615 | + | 0.971359i | \(0.576366\pi\) | |||||||
\(522\) | 6.35926 | + | 3.67152i | 0.278337 | + | 0.160698i | ||||
\(523\) | −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 | ||||
\(525\) | 1.99275i | 0.0869709i | ||||||||
\(526\) | −22.0167 | + | 12.7113i | −0.959974 | + | 0.554241i | ||||
\(527\) | 4.91181 | − | 2.83583i | 0.213962 | − | 0.123531i | ||||
\(528\) | 10.1313i | 0.440907i | ||||||||
\(529\) | −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 | ||||
\(532\) | −2.17413 | −0.0942605 | ||||||||
\(533\) | −21.0375 | − | 9.18931i | −0.911233 | − | 0.398033i | ||||
\(534\) | −23.9502 | −1.03643 | ||||||||
\(535\) | −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 | ||||||||
\(539\) | −2.40625 | + | 1.38925i | −0.103644 | + | 0.0598391i | ||||
\(540\) | 3.15198 | − | 1.81980i | 0.135640 | − | 0.0783115i | ||||
\(541\) | 20.1571i | 0.866621i | 0.901245 | + | 0.433310i | \(0.142655\pi\) | ||||
−0.901245 | + | 0.433310i | \(0.857345\pi\) | |||||||
\(542\) | −5.99978 | − | 10.3919i | −0.257712 | − | 0.446371i | ||||
\(543\) | −12.7610 | + | 22.1027i | −0.547628 | + | 0.948519i | ||||
\(544\) | −4.91047 | − | 2.83506i | −0.210535 | − | 0.121552i | ||||
\(545\) | −3.60415 | −0.154385 | ||||||||
\(546\) | 2.15179 | − | 4.92618i | 0.0920880 | − | 0.210821i | ||||
\(547\) | −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 | ||||
\(549\) | 0.884873 | − | 1.53264i | 0.0377654 | − | 0.0654117i | ||||
\(550\) | −3.02594 | − | 5.24109i | −0.129027 | − | 0.223481i | ||||
\(551\) | 20.6394i | 0.879266i | ||||||||
\(552\) | −21.4214 | + | 12.3677i | −0.911757 | + | 0.526403i | ||||
\(553\) | 13.6311 | − | 7.86993i | 0.579654 | − | 0.334663i | ||||
\(554\) | − | 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 | −0.00157977 | − | 0.999999i | \(-0.500503\pi\) |
−0.866814 | + | 0.498631i | \(0.833836\pi\) | |||||||
\(558\) | 4.31664 | 0.182738 | ||||||||
\(559\) | −19.4806 | − | 26.4190i | −0.823940 | − | 1.11740i | ||||
\(560\) | −5.66612 | −0.239437 | ||||||||
\(561\) | −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 | \(0.625688\pi\) | |||||||
\(564\) | 2.88069i | 0.121299i | ||||||||
\(565\) | −16.6198 | + | 9.59543i | −0.699199 | + | 0.403683i | ||||
\(566\) | −0.686177 | + | 0.396164i | −0.0288422 | + | 0.0166520i | ||||
\(567\) | 1.41581i | 0.0594585i | ||||||||
\(568\) | −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 | \(0.969704\pi\) | |||||||
\(570\) | −13.7552 | − | 7.94158i | −0.576143 | − | 0.332636i | ||||
\(571\) | −12.9655 | −0.542588 | −0.271294 | − | 0.962497i | \(-0.587452\pi\) | ||||
−0.271294 | + | 0.962497i | \(0.587452\pi\) | |||||||
\(572\) | −0.413861 | − | 3.68736i | −0.0173044 | − | 0.154176i | ||||
\(573\) | −3.22016 | −0.134524 | ||||||||
\(574\) | −7.03905 | − | 4.06400i | −0.293804 | − | 0.169628i | ||||
\(575\) | 5.97105 | − | 10.3422i | 0.249010 | − | 0.431298i | ||||
\(576\) | −7.26525 | − | 12.5838i | −0.302719 | − | 0.524324i | ||||
\(577\) | 9.46047i | 0.393844i | 0.980419 | + | 0.196922i | \(0.0630947\pi\) | ||||
−0.980419 | + | 0.196922i | \(0.936905\pi\) | |||||||
\(578\) | 10.4702 | − | 6.04497i | 0.435503 | − | 0.251438i | ||||
\(579\) | 13.1381 | − | 7.58529i | 0.546001 | − | 0.315234i | ||||
\(580\) | − | 2.36354i | − | 0.0981405i | ||||||
\(581\) | 3.98704 | + | 6.90576i | 0.165410 | + | 0.286499i | ||||
\(582\) | −10.6057 | + | 18.3696i | −0.439620 | + | 0.761444i | ||||
\(583\) | 25.2365 | + | 14.5703i | 1.04519 | + | 0.603440i | ||||
\(584\) | 23.2155 | 0.960663 | ||||||||
\(585\) | 8.61598 | − | 6.35317i | 0.356227 | − | 0.262671i | ||||
\(586\) | 31.7784 | 1.31275 | ||||||||
\(587\) | −18.6673 | − | 10.7776i | −0.770481 | − | 0.444837i | 0.0625654 | − | 0.998041i | \(-0.480072\pi\) |
−0.833046 | + | 0.553204i | \(0.813405\pi\) | |||||||
\(588\) | −0.216290 | + | 0.374626i | −0.00891967 | + | 0.0154493i | ||||
\(589\) | 6.06647 | + | 10.5074i | 0.249965 | + | 0.432951i | ||||
\(590\) | 7.12175i | 0.293198i | ||||||||
\(591\) | 19.2441 | − | 11.1106i | 0.791598 | − | 0.457029i | ||||
\(592\) | 4.71274 | − | 2.72090i | 0.193692 | − | 0.111828i | ||||
\(593\) | 3.97234i | 0.163124i | 0.996668 | + | 0.0815622i | \(0.0259909\pi\) | ||||
−0.996668 | + | 0.0815622i | \(0.974009\pi\) | |||||||
\(594\) | −9.60231 | − | 16.6317i | −0.393988 | − | 0.682407i | ||||
\(595\) | 2.48997 | − | 4.31275i | 0.102079 | − | 0.176806i | ||||
\(596\) | 0.740117 | + | 0.427307i | 0.0303164 | + | 0.0175032i | ||||
\(597\) | −23.3956 | −0.957517 | ||||||||
\(598\) | −25.9282 | + | 19.1187i | −1.06028 | + | 0.781821i | ||||
\(599\) | −19.5049 | −0.796950 | −0.398475 | − | 0.917179i | \(-0.630460\pi\) | ||||
−0.398475 | + | 0.917179i | \(0.630460\pi\) | |||||||
\(600\) | −5.22211 | − | 3.01498i | −0.213192 | − | 0.123086i | ||||
\(601\) | 13.4368 | − | 23.2733i | 0.548100 | − | 0.949336i | −0.450305 | − | 0.892875i | \(-0.648685\pi\) |
0.998405 | − | 0.0564616i | \(-0.0179818\pi\) | |||||||
\(602\) | −5.81086 | − | 10.0647i | −0.236833 | − | 0.410207i | ||||
\(603\) | 8.20914i | 0.334302i | ||||||||
\(604\) | 6.61276 | − | 3.81788i | 0.269070 | − | 0.155347i | ||||
\(605\) | 5.15523 | − | 2.97637i | 0.209590 | − | 0.121007i | ||||
\(606\) | 0.109021i | 0.00442866i | ||||||||
\(607\) | −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 | ||||
\(609\) | 3.55639 | + | 2.05328i | 0.144112 | + | 0.0832031i | ||||
\(610\) | 2.50628 | 0.101476 | ||||||||
\(611\) | 2.67808 | + | 23.8607i | 0.108343 | + | 0.965300i | ||||
\(612\) | 1.66265 | 0.0672086 | ||||||||
\(613\) | −18.4970 | − | 10.6793i | −0.747088 | − | 0.431332i | 0.0775527 | − | 0.996988i | \(-0.475289\pi\) |
−0.824641 | + | 0.565657i | \(0.808623\pi\) | |||||||
\(614\) | 6.31751 | − | 10.9422i | 0.254954 | − | 0.441593i | ||||
\(615\) | 6.74796 | + | 11.6878i | 0.272104 | + | 0.471298i | ||||
\(616\) | − | 8.40757i | − | 0.338751i | ||||||
\(617\) | −28.5425 | + | 16.4790i | −1.14908 | + | 0.663420i | −0.948662 | − | 0.316291i | \(-0.897562\pi\) |
−0.200415 | + | 0.979711i | \(0.564229\pi\) | |||||||
\(618\) | 16.6816 | − | 9.63111i | 0.671031 | − | 0.387420i | ||||
\(619\) | − | 48.9117i | − | 1.96593i | −0.183795 | − | 0.982965i | \(-0.558838\pi\) | ||
0.183795 | − | 0.982965i | \(-0.441162\pi\) | |||||||
\(620\) | −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 | ||||
\(623\) | 16.0640 | 0.643589 | ||||||||
\(624\) | 7.80240 | + | 10.5814i | 0.312346 | + | 0.423595i | ||||
\(625\) | −13.5576 | −0.542304 | ||||||||
\(626\) | 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 | ||||||||
\(630\) | 3.28239 | − | 1.89509i | 0.130773 | − | 0.0755021i | ||||
\(631\) | 4.65076 | − | 2.68512i | 0.185144 | − | 0.106893i | −0.404563 | − | 0.914510i | \(-0.632576\pi\) |
0.589707 | + | 0.807617i | \(0.299243\pi\) | |||||||
\(632\) | 47.6280i | 1.89454i | ||||||||
\(633\) | 5.83981 | + | 10.1148i | 0.232111 | + | 0.402029i | ||||
\(634\) | 10.9621 | − | 18.9869i | 0.435360 | − | 0.754066i | ||||
\(635\) | 17.7127 | + | 10.2264i | 0.702905 | + | 0.405823i | ||||
\(636\) | 4.53687 | 0.179899 | ||||||||
\(637\) | −1.44325 | + | 3.30409i | −0.0571837 | + | 0.130913i | ||||
\(638\) | −12.4714 | −0.493747 | ||||||||
\(639\) | 3.85189 | + | 2.22389i | 0.152378 | + | 0.0879757i | ||||
\(640\) | 6.53865 | − | 11.3253i | 0.258463 | − | 0.447671i | ||||
\(641\) | 19.8510 | + | 34.3829i | 0.784066 | + | 1.35804i | 0.929555 | + | 0.368683i | \(0.120191\pi\) |
−0.145489 | + | 0.989360i | \(0.546475\pi\) | |||||||
\(642\) | 5.97647i | 0.235872i | ||||||||
\(643\) | 27.8388 | − | 16.0727i | 1.09785 | − | 0.633847i | 0.162198 | − | 0.986758i | \(-0.448142\pi\) |
0.935657 | + | 0.352911i | \(0.114808\pi\) | |||||||
\(644\) | 2.24504 | − | 1.29618i | 0.0884671 | − | 0.0510765i | ||||
\(645\) | 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 | ||||
\(649\) | −8.54096 | −0.335262 | ||||||||
\(650\) | −7.19670 | − | 3.14357i | −0.282278 | − | 0.123301i | ||||
\(651\) | 2.41406 | 0.0946145 | ||||||||
\(652\) | 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 | ||||
\(655\) | 5.56225i | 0.217335i | ||||||||
\(656\) | 17.2152 | − | 9.93918i | 0.672139 | − | 0.388060i | ||||
\(657\) | −10.8697 | + | 6.27562i | −0.424067 | + | 0.244835i | ||||
\(658\) | 8.50105i | 0.331405i | ||||||||
\(659\) | 3.60729 | + | 6.24801i | 0.140520 | + | 0.243388i | 0.927693 | − | 0.373345i | \(-0.121789\pi\) |
−0.787173 | + | 0.616733i | \(0.788456\pi\) | |||||||
\(660\) | −1.09067 | + | 1.88909i | −0.0424542 | + | 0.0735329i | ||||
\(661\) | 14.5068 | + | 8.37548i | 0.564248 | + | 0.325769i | 0.754849 | − | 0.655899i | \(-0.227710\pi\) |
−0.190601 | + | 0.981668i | \(0.561044\pi\) | |||||||
\(662\) | 25.4470 | 0.989025 | ||||||||
\(663\) | −11.4828 | + | 1.28880i | −0.445953 | + | 0.0500529i | ||||
\(664\) | −24.1291 | −0.936393 | ||||||||
\(665\) | 9.22592 | + | 5.32659i | 0.357766 | + | 0.206556i | ||||
\(666\) | −1.82006 | + | 3.15244i | −0.0705259 | + | 0.122155i | ||||
\(667\) | −12.3048 | − | 21.3126i | −0.476444 | − | 0.825226i | ||||
\(668\) | − | 2.81564i | − | 0.108941i | ||||||
\(669\) | 8.47860 | − | 4.89512i | 0.327802 | − | 0.189256i | ||||
\(670\) | −10.0681 | + | 5.81281i | −0.388964 | + | 0.224569i | ||||
\(671\) | 3.00573i | 0.116035i | ||||||||
\(672\) | −1.20670 | − | 2.09007i | −0.0465495 | − | 0.0806261i | ||||
\(673\) | −18.6684 | + | 32.3346i | −0.719614 | + | 1.24641i | 0.241539 | + | 0.970391i | \(0.422348\pi\) |
−0.961153 | + | 0.276016i | \(0.910986\pi\) | |||||||
\(674\) | 1.40612 | + | 0.811824i | 0.0541618 | + | 0.0312703i | ||||
\(675\) | 9.23831 | 0.355583 | ||||||||
\(676\) | −3.27199 | − | 3.53245i | −0.125846 | − | 0.135864i | ||||
\(677\) | 28.1341 | 1.08128 | 0.540641 | − | 0.841253i | \(-0.318182\pi\) | ||||
0.540641 | + | 0.841253i | \(0.318182\pi\) | |||||||
\(678\) | 13.6533 | + | 7.88271i | 0.524350 | + | 0.302734i | ||||
\(679\) | 7.11347 | − | 12.3209i | 0.272990 | − | 0.472832i | ||||
\(680\) | 7.53452 | + | 13.0502i | 0.288935 | + | 0.500451i | ||||
\(681\) | 1.07416i | 0.0411620i | ||||||||
\(682\) | −6.34915 | + | 3.66568i | −0.243122 | + | 0.140366i | ||||
\(683\) | −1.79295 | + | 1.03516i | −0.0686053 | + | 0.0396093i | −0.533910 | − | 0.845541i | \(-0.679278\pi\) |
0.465305 | + | 0.885150i | \(0.345945\pi\) | |||||||
\(684\) | 3.55677i | 0.135996i | ||||||||
\(685\) | 19.8574 | + | 34.3941i | 0.758714 | + | 1.31413i | ||||
\(686\) | −0.638282 | + | 1.10554i | −0.0243697 | + | 0.0422096i | ||||
\(687\) | −24.9028 | − | 14.3776i | −0.950100 | − | 0.548540i | ||||
\(688\) | 28.4228 | 1.08361 | ||||||||
\(689\) | 37.5788 | − | 4.21776i | 1.43164 | − | 0.160684i | ||||
\(690\) | 18.9385 | 0.720977 | ||||||||
\(691\) | 31.0542 | + | 17.9291i | 1.18136 | + | 0.682057i | 0.956328 | − | 0.292295i | \(-0.0944190\pi\) |
0.225029 | + | 0.974352i | \(0.427752\pi\) | |||||||
\(692\) | 0.999521 | − | 1.73122i | 0.0379961 | − | 0.0658112i | ||||
\(693\) | 2.27274 | + | 3.93650i | 0.0863342 | + | 0.149535i | ||||
\(694\) | − | 33.0417i | − | 1.25425i | ||||||
\(695\) | 17.4001 | − | 10.0460i | 0.660023 | − | 0.381065i | ||||
\(696\) | −10.7614 | + | 6.21312i | −0.407911 | + | 0.235508i | ||||
\(697\) | 17.4710i | 0.661763i | ||||||||
\(698\) | −11.0530 | − | 19.1443i | −0.418361 | − | 0.724622i | ||||
\(699\) | 10.0891 | − | 17.4748i | 0.381604 | − | 0.660958i | ||||
\(700\) | 0.547295 | + | 0.315981i | 0.0206858 | + | 0.0119430i | ||||
\(701\) | −44.8940 | −1.69562 | −0.847812 | − | 0.530297i | \(-0.822081\pi\) | ||||
−0.847812 | + | 0.530297i | \(0.822081\pi\) | |||||||
\(702\) | −22.8375 | − | 9.97558i | −0.861946 | − | 0.376504i | ||||
\(703\) | −10.2314 | −0.385885 | ||||||||
\(704\) | 21.3722 | + | 12.3393i | 0.805497 | + | 0.465054i | ||||
\(705\) | 7.05767 | − | 12.2242i | 0.265807 | − | 0.460391i | ||||
\(706\) | −16.1801 | − | 28.0248i | −0.608947 | − | 1.05473i | ||||
\(707\) | − | 0.0731225i | − | 0.00275005i | ||||||
\(708\) | −1.15158 | + | 0.664867i | −0.0432792 | + | 0.0249872i | ||||
\(709\) | −14.0864 | + | 8.13279i | −0.529026 | + | 0.305433i | −0.740620 | − | 0.671924i | \(-0.765468\pi\) |
0.211594 | + | 0.977358i | \(0.432135\pi\) | |||||||
\(710\) | 6.29886i | 0.236392i | ||||||||
\(711\) | −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 | ||||
\(714\) | −4.09105 | −0.153104 | ||||||||
\(715\) | −7.27775 | + | 16.6613i | −0.272173 | + | 0.623096i | ||||
\(716\) | 4.55255 | 0.170137 | ||||||||
\(717\) | −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 | ||||||||
\(721\) | −11.1887 | + | 6.45980i | −0.416689 | + | 0.240575i | ||||
\(722\) | 17.0873 | − | 9.86534i | 0.635922 | − | 0.367150i | ||||
\(723\) | 9.85076i | 0.366354i | ||||||||
\(724\) | 4.04690 | + | 7.00944i | 0.150402 | + | 0.260504i | ||||
\(725\) | 2.99966 | − | 5.19556i | 0.111405 | − | 0.192958i | ||||
\(726\) | −4.23506 | − | 2.44511i | −0.157178 | − | 0.0907466i | ||||
\(727\) | 34.5299 | 1.28064 | 0.640322 | − | 0.768106i | \(-0.278801\pi\) | ||||
0.640322 | + | 0.768106i | \(0.278801\pi\) | |||||||
\(728\) | −6.47493 | − | 8.78111i | −0.239977 | − | 0.325450i | ||||
\(729\) | 21.2872 | 0.788415 | ||||||||
\(730\) | −15.3934 | − | 8.88741i | −0.569737 | − | 0.328938i | ||||
\(731\) | −12.4904 | + | 21.6340i | −0.461973 | + | 0.800161i | ||||
\(732\) | 0.233980 | + | 0.405265i | 0.00864814 | + | 0.0149790i | ||||
\(733\) | − | 33.1360i | − | 1.22391i | −0.790894 | − | 0.611953i | \(-0.790384\pi\) | ||
0.790894 | − | 0.611953i | \(-0.209616\pi\) | |||||||
\(734\) | −27.9895 | + | 16.1598i | −1.03311 | + | 0.596468i | ||||
\(735\) | 1.83566 | − | 1.05982i | 0.0677093 | − | 0.0390920i | ||||
\(736\) | 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 | 0.434670 | − | 0.900590i | \(-0.356865\pi\) |
−0.562598 | + | 0.826730i | \(0.690198\pi\) | |||||||
\(740\) | 1.17166 | 0.0430711 | ||||||||
\(741\) | −2.75703 | − | 24.5641i | −0.101282 | − | 0.902386i | ||||
\(742\) | 13.3885 | 0.491507 | ||||||||
\(743\) | 10.8361 | + | 6.25622i | 0.397538 | + | 0.229519i | 0.685421 | − | 0.728147i | \(-0.259618\pi\) |
−0.287883 | + | 0.957666i | \(0.592952\pi\) | |||||||
\(744\) | −3.65241 | + | 6.32616i | −0.133904 | + | 0.231928i | ||||
\(745\) | −2.09379 | − | 3.62656i | −0.0767107 | − | 0.132867i | ||||
\(746\) | 8.66508i | 0.317251i | ||||||||
\(747\) | 11.2975 | − | 6.52260i | 0.413353 | − | 0.238650i | ||||
\(748\) | −2.44551 | + | 1.41192i | −0.0894168 | + | 0.0516248i | ||||
\(749\) | − | 4.00855i | − | 0.146469i | ||||||
\(750\) | 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 | \(-0.0733065\pi\) | |||||||
\(752\) | −18.0053 | − | 10.3954i | −0.656585 | − | 0.379080i | ||||
\(753\) | −17.1365 | −0.624490 | ||||||||
\(754\) | −13.0255 | + | 9.60461i | −0.474360 | + | 0.349779i | ||||
\(755\) | −37.4150 | −1.36167 | ||||||||
\(756\) | 1.73675 | + | 1.00271i | 0.0631649 | + | 0.0364683i | ||||
\(757\) | 17.5223 | − | 30.3496i | 0.636860 | − | 1.10307i | −0.349258 | − | 0.937027i | \(-0.613566\pi\) |
0.986118 | − | 0.166047i | \(-0.0531004\pi\) | |||||||
\(758\) | 7.86530 | + | 13.6231i | 0.285680 | + | 0.494813i | ||||
\(759\) | 22.7126i | 0.824414i | ||||||||
\(760\) | −27.9172 | + | 16.1180i | −1.01266 | + | 0.584661i | ||||
\(761\) | −3.72586 | + | 2.15113i | −0.135062 | + | 0.0779782i | −0.566009 | − | 0.824399i | \(-0.691513\pi\) |
0.430946 | + | 0.902378i | \(0.358180\pi\) | |||||||
\(762\) | − | 16.8021i | − | 0.608677i | ||||||
\(763\) | −0.992947 | − | 1.71984i | −0.0359471 | − | 0.0622622i | ||||
\(764\) | −0.510605 | + | 0.884394i | −0.0184730 | + | 0.0319962i | ||||
\(765\) | −7.05545 | − | 4.07347i | −0.255090 | − | 0.147277i | ||||
\(766\) | −9.26679 | −0.334823 | ||||||||
\(767\) | −8.92043 | + | 6.57766i | −0.322098 | + | 0.237506i | ||||
\(768\) | 10.0039 | 0.360985 | ||||||||
\(769\) | 10.6146 | + | 6.12834i | 0.382772 | + | 0.220994i | 0.679024 | − | 0.734116i | \(-0.262403\pi\) |
−0.296251 | + | 0.955110i | \(0.595737\pi\) | |||||||
\(770\) | −3.21861 | + | 5.57479i | −0.115991 | + | 0.200902i | ||||
\(771\) | −17.1268 | − | 29.6645i | −0.616806 | − | 1.06834i | ||||
\(772\) | − | 4.81105i | − | 0.173153i | ||||||
\(773\) | −3.29372 | + | 1.90163i | −0.118467 | + | 0.0683970i | −0.558063 | − | 0.829799i | \(-0.688455\pi\) |
0.439596 | + | 0.898196i | \(0.355122\pi\) | |||||||
\(774\) | −16.4654 | + | 9.50628i | −0.591835 | + | 0.341696i | ||||
\(775\) | − | 3.52673i | − | 0.126684i | ||||||
\(776\) | 21.5250 | + | 37.2824i | 0.772702 | + | 1.33836i | ||||
\(777\) | −1.01786 | + | 1.76299i | −0.0365155 | + | 0.0632468i | ||||
\(778\) | 7.90250 | + | 4.56251i | 0.283318 | + | 0.163574i | ||||
\(779\) | −37.3744 | −1.33908 | ||||||||
\(780\) | 0.315723 | + | 2.81298i | 0.0113047 | + | 0.100721i | ||||
\(781\) | −7.55409 | −0.270307 | ||||||||
\(782\) | 21.2321 | + | 12.2583i | 0.759258 | + | 0.438358i | ||||
\(783\) | 9.51891 | − | 16.4872i | 0.340178 | − | 0.589206i | ||||
\(784\) | −1.56102 | − | 2.70377i | −0.0557508 | − | 0.0965633i | ||||
\(785\) | 5.25675i | 0.187622i | ||||||||
\(786\) | 3.95724 | − | 2.28471i | 0.141150 | − | 0.0814930i | ||||
\(787\) | 15.0114 | − | 8.66684i | 0.535099 | − | 0.308940i | −0.207991 | − | 0.978131i | \(-0.566693\pi\) |
0.743090 | + | 0.669191i | \(0.233359\pi\) | |||||||
\(788\) | − | 7.04701i | − | 0.251039i | ||||||
\(789\) | 11.6296 | + | 20.1430i | 0.414024 | + | 0.717110i | ||||
\(790\) | 18.2331 | − | 31.5806i | 0.648704 | − | 1.12359i | ||||
\(791\) | −9.15754 | − | 5.28711i | −0.325605 | − | 0.187988i | ||||
\(792\) | −13.7544 | −0.488740 | ||||||||
\(793\) | 2.31480 | + | 3.13927i | 0.0822011 | + | 0.111479i | ||||
\(794\) | −28.6731 | −1.01757 | ||||||||
\(795\) | −19.2522 | − | 11.1153i | −0.682807 | − | 0.394219i | ||||
\(796\) | −3.70972 | + | 6.42542i | −0.131488 | + | 0.227743i | ||||
\(797\) | 25.1707 | + | 43.5969i | 0.891592 | + | 1.54428i | 0.837967 | + | 0.545721i | \(0.183744\pi\) |
0.0536245 | + | 0.998561i | \(0.482923\pi\) | |||||||
\(798\) | − | 8.75166i | − | 0.309806i | ||||||
\(799\) | 15.8248 | − | 9.13645i | 0.559841 | − | 0.323224i | ||||
\(800\) | −3.05340 | + | 1.76288i | −0.107954 | + | 0.0623273i | ||||
\(801\) | − | 26.2798i | − | 0.928552i | ||||||
\(802\) | −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 | ||||
\(805\) | −12.7025 | −0.447703 | ||||||||
\(806\) | −3.80818 | + | 8.71822i | −0.134137 | + | 0.307086i | ||||
\(807\) | 26.0739 | 0.917845 | ||||||||
\(808\) | 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 | \(0.224982\pi\) | ||||
−0.760443 | + | 0.649404i | \(0.775018\pi\) | |||||||
\(812\) | 1.12784 | − | 0.651157i | 0.0395793 | − | 0.0228511i | ||||
\(813\) | −9.50754 | + | 5.48918i | −0.333444 | + | 0.192514i | ||||
\(814\) | − | 6.18237i | − | 0.216692i | ||||||
\(815\) | −21.2648 | − | 36.8317i | −0.744873 | − | 1.29016i | ||||
\(816\) | 5.00267 | − | 8.66488i | 0.175129 | − | 0.303332i | ||||
\(817\) | −46.2798 | − | 26.7197i | −1.61913 | − | 0.934803i | ||||
\(818\) | 7.15624 | 0.250212 | ||||||||
\(819\) | 5.40533 | + | 2.36109i | 0.188878 | + | 0.0825031i | ||||
\(820\) | 4.27996 | 0.149463 | ||||||||
\(821\) | 26.1021 | + | 15.0700i | 0.910968 | + | 0.525948i | 0.880743 | − | 0.473595i | \(-0.157044\pi\) |
0.0302256 | + | 0.999543i | \(0.490377\pi\) | |||||||
\(822\) | 16.3130 | − | 28.2550i | 0.568982 | − | 0.985507i | ||||
\(823\) | 20.8251 | + | 36.0702i | 0.725918 | + | 1.25733i | 0.958595 | + | 0.284773i | \(0.0919181\pi\) |
−0.232677 | + | 0.972554i | \(0.574749\pi\) | |||||||
\(824\) | − | 39.0940i | − | 1.36190i | ||||||
\(825\) | −4.79506 | + | 2.76843i | −0.166942 | + | 0.0963842i | ||||
\(826\) | −3.39837 | + | 1.96205i | −0.118244 | + | 0.0682685i | ||||
\(827\) | − | 37.6524i | − | 1.30930i | −0.755932 | − | 0.654651i | \(-0.772816\pi\) | ||
0.755932 | − | 0.654651i | \(-0.227184\pi\) | |||||||
\(828\) | −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 | ||||
\(831\) | −16.7512 | −0.581091 | ||||||||
\(832\) | 31.8246 | − | 3.57193i | 1.10332 | − | 0.123834i | ||||
\(833\) | 2.74396 | 0.0950725 | ||||||||
\(834\) | −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 | ||||
\(837\) | − | 11.1915i | − | 0.386834i | ||||||
\(838\) | −6.78732 | + | 3.91866i | −0.234464 | + | 0.135368i | ||||
\(839\) | −9.51957 | + | 5.49613i | −0.328652 | + | 0.189747i | −0.655242 | − | 0.755419i | \(-0.727434\pi\) |
0.326590 | + | 0.945166i | \(0.394100\pi\) | |||||||
\(840\) | 6.41391i | 0.221301i | ||||||||
\(841\) | 8.31846 | + | 14.4080i | 0.286843 | + | 0.496827i | ||||
\(842\) | −1.22926 | + | 2.12914i | −0.0423632 | + | 0.0733752i | ||||
\(843\) | −0.0999736 | − | 0.0577198i | −0.00344328 | − | 0.00198798i | ||||
\(844\) | 3.70396 | 0.127495 | ||||||||
\(845\) | 5.23025 | + | 23.0063i | 0.179926 | + | 0.791442i | ||||
\(846\) | 13.9073 | 0.478143 | ||||||||
\(847\) | 2.84054 | + | 1.63999i | 0.0976022 | + | 0.0563507i | ||||
\(848\) | −16.3719 | + | 28.3569i | −0.562213 | + | 0.973781i | ||||
\(849\) | 0.362450 | + | 0.627781i | 0.0124392 | + | 0.0215454i | ||||
\(850\) | 5.97667i | 0.204998i | ||||||||
\(851\) | 10.5651 | − | 6.09979i | 0.362169 | − | 0.209098i | ||||
\(852\) | −1.01852 | + | 0.588045i | −0.0348940 | + | 0.0201461i | ||||
\(853\) | − | 35.2031i | − | 1.20533i | −0.797994 | − | 0.602666i | \(-0.794105\pi\) | ||
0.797994 | − | 0.602666i | \(-0.205895\pi\) | |||||||
\(854\) | 0.690483 | + | 1.19595i | 0.0236279 | + | 0.0409246i | ||||
\(855\) | 8.71404 | − | 15.0932i | 0.298014 | − | 0.516175i | ||||
\(856\) | 10.5046 | + | 6.06483i | 0.359040 | + | 0.207292i | ||||
\(857\) | −30.3681 | −1.03736 | −0.518678 | − | 0.854970i | \(-0.673576\pi\) | ||||
−0.518678 | + | 0.854970i | \(0.673576\pi\) | |||||||
\(858\) | 14.8429 | − | 1.66594i | 0.506730 | − | 0.0568743i | ||||
\(859\) | −35.8306 | −1.22252 | −0.611262 | − | 0.791429i | \(-0.709338\pi\) | ||||
−0.611262 | + | 0.791429i | \(0.709338\pi\) | |||||||
\(860\) | 5.29977 | + | 3.05983i | 0.180721 | + | 0.104339i | ||||
\(861\) | −3.71814 | + | 6.44001i | −0.126714 | + | 0.219475i | ||||
\(862\) | 6.86113 | + | 11.8838i | 0.233691 | + | 0.404765i | ||||
\(863\) | − | 32.3403i | − | 1.10088i | −0.834876 | − | 0.550438i | \(-0.814461\pi\) | ||
0.834876 | − | 0.550438i | \(-0.185539\pi\) | |||||||
\(864\) | −9.68945 | + | 5.59421i | −0.329642 | + | 0.190319i | ||||
\(865\) | −8.48294 | + | 4.89763i | −0.288429 | + | 0.166524i | ||||
\(866\) | 51.4016i | 1.74670i | ||||||||
\(867\) | −5.53053 | − | 9.57916i | −0.187827 | − | 0.325325i | ||||
\(868\) | 0.382786 | − | 0.663004i | 0.0129926 | − | 0.0225038i | ||||
\(869\) | 37.8740 | + | 21.8665i | 1.28479 | + | 0.741772i | ||||
\(870\) | 9.51409 | 0.322558 | ||||||||
\(871\) | −16.5798 | − | 7.24218i | −0.561786 | − | 0.245392i | ||||
\(872\) | 6.00921 | 0.203498 | ||||||||
\(873\) | −20.1564 | − | 11.6373i | −0.682190 | − | 0.393862i | ||||
\(874\) | −26.2233 | + | 45.4201i | −0.887016 | + | 1.53636i | ||||
\(875\) | −6.08548 | − | 10.5404i | −0.205727 | − | 0.356329i | ||||
\(876\) | − | 3.31882i | − | 0.112133i | ||||||
\(877\) | 3.82446 | − | 2.20805i | 0.129143 | − | 0.0745607i | −0.434037 | − | 0.900895i | \(-0.642911\pi\) |
0.563180 | + | 0.826334i | \(0.309578\pi\) | |||||||
\(878\) | −24.2674 | + | 14.0108i | −0.818984 | + | 0.472841i | ||||
\(879\) | − | 29.0740i | − | 0.980642i | ||||||
\(880\) | −7.87164 | − | 13.6341i | −0.265353 | − | 0.459605i | ||||
\(881\) | 9.97753 | − | 17.2816i | 0.336152 | − | 0.582232i | −0.647554 | − | 0.762020i | \(-0.724208\pi\) |
0.983705 | + | 0.179788i | \(0.0575412\pi\) | |||||||
\(882\) | 1.80860 | + | 1.04420i | 0.0608989 | + | 0.0351600i | ||||
\(883\) | −12.9725 | −0.436559 | −0.218280 | − | 0.975886i | \(-0.570045\pi\) | ||||
−0.218280 | + | 0.975886i | \(0.570045\pi\) | |||||||
\(884\) | −1.46680 | + | 3.35801i | −0.0493339 | + | 0.112942i | ||||
\(885\) | 6.51567 | 0.219022 | ||||||||
\(886\) | −30.8404 | − | 17.8057i | −1.03610 | − | 0.598195i | ||||
\(887\) | −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 | ||||
\(889\) | 11.2696i | 0.377969i | ||||||||
\(890\) | 32.2309 | − | 18.6085i | 1.08038 | − | 0.623758i | ||||
\(891\) | −3.40679 | + | 1.96691i | −0.114132 | + | 0.0658941i | ||||
\(892\) | − | 3.10478i | − | 0.103956i | ||||||
\(893\) | 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 | ||||
\(896\) | 7.20562 | 0.240723 | ||||||||
\(897\) | 17.4916 | + | 23.7216i | 0.584029 | + | 0.792043i | ||||
\(898\) | 28.1626 | 0.939797 | ||||||||
\(899\) | −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 | ||||||
\(903\) | −9.20818 | + | 5.31634i | −0.306429 | + | 0.176917i | ||||
\(904\) | 27.7102 | − | 15.9985i | 0.921629 | − | 0.532103i | ||||
\(905\) | − | 39.6594i | − | 1.31832i | ||||||
\(906\) | 15.3684 | + | 26.6188i | 0.510580 | + | 0.884350i | ||||
\(907\) | −1.29570 | + | 2.24421i | −0.0430229 | + | 0.0745178i | −0.886735 | − | 0.462278i | \(-0.847032\pi\) |
0.843712 | + | 0.536796i | \(0.180365\pi\) | |||||||
\(908\) | 0.295011 | + | 0.170325i | 0.00979029 | + | 0.00565242i | ||||
\(909\) | −0.119625 | −0.00396770 | ||||||||
\(910\) | 0.931713 | + | 8.30123i | 0.0308860 | + | 0.275183i | ||||
\(911\) | 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 | ||||
\(913\) | −11.0780 | + | 19.1876i | −0.366627 | + | 0.635017i | ||||
\(914\) | 3.52094 | + | 6.09845i | 0.116462 | + | 0.201719i | ||||
\(915\) | − | 2.29299i | − | 0.0758039i | ||||||
\(916\) | −7.89741 | + | 4.55957i | −0.260938 | + | 0.150653i | ||||
\(917\) | −2.65421 | + | 1.53241i | −0.0876496 | + | 0.0506045i | ||||
\(918\) | 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 | ||||
\(922\) | 36.8648 | 1.21408 | ||||||||
\(923\) | −7.88971 | + | 5.81764i | −0.259693 | + | 0.191490i | ||||
\(924\) | −1.20192 | −0.0395404 | ||||||||
\(925\) | 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 | ||||
\(928\) | 7.26571i | 0.238509i | ||||||||
\(929\) | −23.0067 | + | 13.2830i | −0.754827 | + | 0.435800i | −0.827435 | − | 0.561561i | \(-0.810201\pi\) |
0.0726084 | + | 0.997361i | \(0.476868\pi\) | |||||||
\(930\) | 4.84359 | − | 2.79645i | 0.158828 | − | 0.0916992i | ||||
\(931\) | 5.86993i | 0.192379i | ||||||||
\(932\) | −3.19955 | − | 5.54179i | −0.104805 | − | 0.181527i | ||||
\(933\) | −4.22666 | + | 7.32079i | −0.138375 | + | 0.239672i | ||||
\(934\) | 5.02274 | + | 2.89988i | 0.164349 | + | 0.0948869i | ||||
\(935\) | 13.8367 | 0.452509 | ||||||||
\(936\) | −14.3655 | + | 10.5927i | −0.469550 | + | 0.346232i | ||||
\(937\) | 3.02509 | 0.0988255 | 0.0494128 | − | 0.998778i | \(-0.484265\pi\) | ||||
0.0494128 | + | 0.998778i | \(0.484265\pi\) | |||||||
\(938\) | −5.54754 | − | 3.20288i | −0.181134 | − | 0.104578i | ||||
\(939\) | 19.0726 | − | 33.0347i | 0.622410 | − | 1.07805i | ||||
\(940\) | −2.23820 | − | 3.87667i | −0.0730020 | − | 0.126443i | ||||
\(941\) | 6.48465i | 0.211394i | 0.994398 | + | 0.105697i | \(0.0337073\pi\) | ||||
−0.994398 | + | 0.105697i | \(0.966293\pi\) | |||||||
\(942\) | 3.73990 | − | 2.15923i | 0.121852 | − | 0.0703515i | ||||
\(943\) | 38.5934 | − | 22.2819i | 1.25678 | − | 0.725599i | ||||
\(944\) | − | 9.59704i | − | 0.312357i | ||||||
\(945\) | −4.91326 | − | 8.51002i | −0.159829 | − | 0.276831i | ||||
\(946\) | 16.1454 | − | 27.9647i | 0.524934 | − | 0.909212i | ||||
\(947\) | 18.3193 | + | 10.5767i | 0.595298 | + | 0.343695i | 0.767190 | − | 0.641420i | \(-0.221655\pi\) |
−0.171892 | + | 0.985116i | \(0.554988\pi\) | |||||||
\(948\) | 6.80876 | 0.221138 | ||||||||
\(949\) | −3.08538 | − | 27.4897i | −0.100156 | − | 0.892352i | ||||
\(950\) | −12.7854 | −0.414813 | ||||||||
\(951\) | −17.3711 | − | 10.0292i | −0.563295 | − | 0.325219i | ||||
\(952\) | −4.15154 | + | 7.19067i | −0.134552 | + | 0.233051i | ||||
\(953\) | −18.1393 | − | 31.4182i | −0.587590 | − | 1.01774i | −0.994547 | − | 0.104289i | \(-0.966743\pi\) |
0.406957 | − | 0.913447i | \(-0.366590\pi\) | |||||||
\(954\) | − | 21.9029i | − | 0.709133i | ||||||
\(955\) | 4.33351 | − | 2.50195i | 0.140229 | − | 0.0809613i | ||||
\(956\) | −4.64554 | + | 2.68211i | −0.150248 | + | 0.0867455i | ||||
\(957\) | 11.4101i | 0.368835i | ||||||||
\(958\) | −1.06308 | − | 1.84130i | −0.0343464 | − | 0.0594898i | ||||
\(959\) | −10.9415 | + | 18.9512i | −0.353320 | + | 0.611968i | ||||
\(960\) | −16.3043 | − | 9.41329i | −0.526219 | − | 0.303813i | ||||
\(961\) | 26.7277 | 0.862182 | ||||||||
\(962\) | −4.76123 | − | 6.45705i | −0.153508 | − | 0.208184i | ||||
\(963\) | −6.55779 | −0.211322 | ||||||||
\(964\) | 2.70544 | + | 1.56199i | 0.0871363 | + | 0.0503082i | ||||
\(965\) | −11.7870 | + | 20.4157i | −0.379437 | + | 0.657204i | ||||
\(966\) | 5.21758 | + | 9.03712i | 0.167873 | + | 0.290765i | ||||
\(967\) | 16.2828i | 0.523621i | 0.965119 | + | 0.261810i | \(0.0843195\pi\) | ||||
−0.965119 | + | 0.261810i | \(0.915681\pi\) | |||||||
\(968\) | −8.59534 | + | 4.96252i | −0.276265 | + | 0.159501i | ||||
\(969\) | −16.2913 | + | 9.40580i | −0.523353 | + | 0.302158i | ||||
\(970\) | − | 32.9610i | − | 1.05831i | ||||||
\(971\) | 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 | ||||
\(973\) | 9.58750 | + | 5.53535i | 0.307361 | + | 0.177455i | ||||
\(974\) | −1.89560 | −0.0607390 | ||||||||
\(975\) | −2.87604 | + | 6.58424i | −0.0921071 | + | 0.210865i | ||||
\(976\) | −3.37738 | −0.108107 | ||||||||
\(977\) | 9.45681 | + | 5.45989i | 0.302550 | + | 0.174677i | 0.643588 | − | 0.765372i | \(-0.277445\pi\) |
−0.341038 | + | 0.940050i | \(0.610778\pi\) | |||||||
\(978\) | −17.4692 | + | 30.2575i | −0.558603 | + | 0.967528i | ||||
\(979\) | 22.3168 | + | 38.6538i | 0.713248 | + | 1.23538i | ||||
\(980\) | − | 0.672200i | − | 0.0214727i | ||||||
\(981\) | −2.81357 | + | 1.62441i | −0.0898302 | + | 0.0518635i | ||||
\(982\) | 17.6840 | − | 10.2098i | 0.564318 | − | 0.325809i | ||||
\(983\) | − | 19.6715i | − | 0.627423i | −0.949518 | − | 0.313711i | \(-0.898428\pi\) | ||
0.949518 | − | 0.313711i | \(-0.101572\pi\) | |||||||
\(984\) | −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 | ||||
\(987\) | 7.77759 | 0.247563 | ||||||||
\(988\) | −7.18352 | − | 3.13781i | −0.228538 | − | 0.0998271i | ||||
\(989\) | 63.7191 | 2.02615 | ||||||||
\(990\) | 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 | ||||||
\(994\) | −3.00570 | + | 1.73534i | −0.0953352 | + | 0.0550418i | ||||
\(995\) | 31.4844 | − | 18.1775i | 0.998123 | − | 0.576267i | ||||
\(996\) | 3.44944i | 0.109300i | ||||||||
\(997\) | 23.4768 | + | 40.6631i | 0.743519 | + | 1.28781i | 0.950884 | + | 0.309549i | \(0.100178\pi\) |
−0.207365 | + | 0.978264i | \(0.566489\pi\) | |||||||
\(998\) | −11.3103 | + | 19.5900i | −0.358022 | + | 0.620112i | ||||
\(999\) | 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 | 91.2.q.a.43.5 | yes | 12 | |
3.2 | odd | 2 | 819.2.ct.a.316.2 | 12 | |||
4.3 | odd | 2 | 1456.2.cc.c.225.2 | 12 | |||
7.2 | even | 3 | 637.2.k.h.459.2 | 12 | |||
7.3 | odd | 6 | 637.2.u.i.30.2 | 12 | |||
7.4 | even | 3 | 637.2.u.h.30.2 | 12 | |||
7.5 | odd | 6 | 637.2.k.g.459.2 | 12 | |||
7.6 | odd | 2 | 637.2.q.h.589.5 | 12 | |||
13.4 | even | 6 | 1183.2.c.i.337.9 | 12 | |||
13.6 | odd | 12 | 1183.2.a.m.1.3 | 6 | |||
13.7 | odd | 12 | 1183.2.a.p.1.4 | 6 | |||
13.9 | even | 3 | 1183.2.c.i.337.4 | 12 | |||
13.10 | even | 6 | inner | 91.2.q.a.36.5 | ✓ | 12 | |
39.23 | odd | 6 | 819.2.ct.a.127.2 | 12 | |||
52.23 | odd | 6 | 1456.2.cc.c.673.2 | 12 | |||
91.6 | even | 12 | 8281.2.a.by.1.3 | 6 | |||
91.10 | odd | 6 | 637.2.k.g.569.5 | 12 | |||
91.20 | even | 12 | 8281.2.a.ch.1.4 | 6 | |||
91.23 | even | 6 | 637.2.u.h.361.2 | 12 | |||
91.62 | odd | 6 | 637.2.q.h.491.5 | 12 | |||
91.75 | odd | 6 | 637.2.u.i.361.2 | 12 | |||
91.88 | even | 6 | 637.2.k.h.569.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.5 | ✓ | 12 | 13.10 | even | 6 | inner | |
91.2.q.a.43.5 | yes | 12 | 1.1 | even | 1 | trivial | |
637.2.k.g.459.2 | 12 | 7.5 | odd | 6 | |||
637.2.k.g.569.5 | 12 | 91.10 | odd | 6 | |||
637.2.k.h.459.2 | 12 | 7.2 | even | 3 | |||
637.2.k.h.569.5 | 12 | 91.88 | even | 6 | |||
637.2.q.h.491.5 | 12 | 91.62 | odd | 6 | |||
637.2.q.h.589.5 | 12 | 7.6 | odd | 2 | |||
637.2.u.h.30.2 | 12 | 7.4 | even | 3 | |||
637.2.u.h.361.2 | 12 | 91.23 | even | 6 | |||
637.2.u.i.30.2 | 12 | 7.3 | odd | 6 | |||
637.2.u.i.361.2 | 12 | 91.75 | odd | 6 | |||
819.2.ct.a.127.2 | 12 | 39.23 | odd | 6 | |||
819.2.ct.a.316.2 | 12 | 3.2 | odd | 2 | |||
1183.2.a.m.1.3 | 6 | 13.6 | odd | 12 | |||
1183.2.a.p.1.4 | 6 | 13.7 | odd | 12 | |||
1183.2.c.i.337.4 | 12 | 13.9 | even | 3 | |||
1183.2.c.i.337.9 | 12 | 13.4 | even | 6 | |||
1456.2.cc.c.225.2 | 12 | 4.3 | odd | 2 | |||
1456.2.cc.c.673.2 | 12 | 52.23 | odd | 6 | |||
8281.2.a.by.1.3 | 6 | 91.6 | even | 12 | |||
8281.2.a.ch.1.4 | 6 | 91.20 | even | 12 |