Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,2,Mod(163,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.y (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.91640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 187.5 | ||
Root | \(0.237728 + 1.39409i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.187 |
Dual form | 240.2.y.e.163.5 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.429059 | + | 1.34756i | 0.303390 | + | 0.952866i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.63182 | + | 1.15636i | −0.815909 | + | 0.578181i | ||||
\(5\) | 2.23531 | − | 0.0583995i | 0.999659 | − | 0.0261170i | ||||
\(6\) | 0.429059 | + | 1.34756i | 0.175162 | + | 0.550138i | ||||
\(7\) | 0.747384 | + | 0.747384i | 0.282485 | + | 0.282485i | 0.834099 | − | 0.551615i | \(-0.185988\pi\) |
−0.551615 | + | 0.834099i | \(0.685988\pi\) | |||||||
\(8\) | −2.25841 | − | 1.70282i | −0.798468 | − | 0.602038i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.03777 | + | 2.98714i | 0.328173 | + | 0.944618i | ||||
\(11\) | −0.920311 | + | 0.920311i | −0.277484 | + | 0.277484i | −0.832104 | − | 0.554620i | \(-0.812864\pi\) |
0.554620 | + | 0.832104i | \(0.312864\pi\) | |||||||
\(12\) | −1.63182 | + | 1.15636i | −0.471065 | + | 0.333813i | ||||
\(13\) | − | 0.996441i | − | 0.276363i | −0.990407 | − | 0.138182i | \(-0.955874\pi\) | ||
0.990407 | − | 0.138182i | \(-0.0441257\pi\) | |||||||
\(14\) | −0.686471 | + | 1.32781i | −0.183467 | + | 0.354873i | ||||
\(15\) | 2.23531 | − | 0.0583995i | 0.577153 | − | 0.0150787i | ||||
\(16\) | 1.32566 | − | 3.77394i | 0.331414 | − | 0.943485i | ||||
\(17\) | −0.982332 | − | 0.982332i | −0.238251 | − | 0.238251i | 0.577875 | − | 0.816125i | \(-0.303882\pi\) |
−0.816125 | + | 0.577875i | \(0.803882\pi\) | |||||||
\(18\) | 0.429059 | + | 1.34756i | 0.101130 | + | 0.317622i | ||||
\(19\) | −1.03458 | + | 1.03458i | −0.237349 | + | 0.237349i | −0.815751 | − | 0.578403i | \(-0.803676\pi\) |
0.578403 | + | 0.815751i | \(0.303676\pi\) | |||||||
\(20\) | −3.58008 | + | 2.68012i | −0.800530 | + | 0.599293i | ||||
\(21\) | 0.747384 | + | 0.747384i | 0.163093 | + | 0.163093i | ||||
\(22\) | −1.63504 | − | 0.845304i | −0.348591 | − | 0.180219i | ||||
\(23\) | −4.77394 | + | 4.77394i | −0.995436 | + | 0.995436i | −0.999990 | − | 0.00455400i | \(-0.998550\pi\) |
0.00455400 | + | 0.999990i | \(0.498550\pi\) | |||||||
\(24\) | −2.25841 | − | 1.70282i | −0.460996 | − | 0.347587i | ||||
\(25\) | 4.99318 | − | 0.261081i | 0.998636 | − | 0.0522163i | ||||
\(26\) | 1.34276 | − | 0.427532i | 0.263337 | − | 0.0838458i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.08384 | − | 0.355348i | −0.393809 | − | 0.0671545i | ||||
\(29\) | −2.95516 | − | 2.95516i | −0.548760 | − | 0.548760i | 0.377322 | − | 0.926082i | \(-0.376845\pi\) |
−0.926082 | + | 0.377322i | \(0.876845\pi\) | |||||||
\(30\) | 1.03777 | + | 2.98714i | 0.189471 | + | 0.545375i | ||||
\(31\) | − | 10.4545i | − | 1.87768i | −0.344351 | − | 0.938841i | \(-0.611901\pi\) | ||
0.344351 | − | 0.938841i | \(-0.388099\pi\) | |||||||
\(32\) | 5.65438 | + | 0.167155i | 0.999563 | + | 0.0295491i | ||||
\(33\) | −0.920311 | + | 0.920311i | −0.160206 | + | 0.160206i | ||||
\(34\) | 0.902270 | − | 1.74523i | 0.154738 | − | 0.299304i | ||||
\(35\) | 1.71428 | + | 1.62698i | 0.289766 | + | 0.275011i | ||||
\(36\) | −1.63182 | + | 1.15636i | −0.271970 | + | 0.192727i | ||||
\(37\) | − | 8.22694i | − | 1.35250i | −0.736672 | − | 0.676251i | \(-0.763604\pi\) | ||
0.736672 | − | 0.676251i | \(-0.236396\pi\) | |||||||
\(38\) | −1.83805 | − | 0.950259i | −0.298171 | − | 0.154152i | ||||
\(39\) | − | 0.996441i | − | 0.159558i | ||||||
\(40\) | −5.14767 | − | 3.67443i | −0.813919 | − | 0.580979i | ||||
\(41\) | 5.70040i | 0.890253i | 0.895468 | + | 0.445127i | \(0.146841\pi\) | ||||
−0.895468 | + | 0.445127i | \(0.853159\pi\) | |||||||
\(42\) | −0.686471 | + | 1.32781i | −0.105925 | + | 0.204886i | ||||
\(43\) | 5.22869i | 0.797368i | 0.917088 | + | 0.398684i | \(0.130533\pi\) | ||||
−0.917088 | + | 0.398684i | \(0.869467\pi\) | |||||||
\(44\) | 0.437567 | − | 2.56599i | 0.0659658 | − | 0.386838i | ||||
\(45\) | 2.23531 | − | 0.0583995i | 0.333220 | − | 0.00870568i | ||||
\(46\) | −8.48146 | − | 4.38486i | −1.25052 | − | 0.646512i | ||||
\(47\) | 0.0548243 | − | 0.0548243i | 0.00799695 | − | 0.00799695i | −0.703097 | − | 0.711094i | \(-0.748200\pi\) |
0.711094 | + | 0.703097i | \(0.248200\pi\) | |||||||
\(48\) | 1.32566 | − | 3.77394i | 0.191342 | − | 0.544722i | ||||
\(49\) | − | 5.88283i | − | 0.840405i | ||||||
\(50\) | 2.49419 | + | 6.61657i | 0.352731 | + | 0.935725i | ||||
\(51\) | −0.982332 | − | 0.982332i | −0.137554 | − | 0.137554i | ||||
\(52\) | 1.15225 | + | 1.62601i | 0.159788 | + | 0.225487i | ||||
\(53\) | 5.13957 | 0.705974 | 0.352987 | − | 0.935628i | \(-0.385166\pi\) | ||||
0.352987 | + | 0.935628i | \(0.385166\pi\) | |||||||
\(54\) | 0.429059 | + | 1.34756i | 0.0583875 | + | 0.183379i | ||||
\(55\) | −2.00343 | + | 2.11092i | −0.270142 | + | 0.284637i | ||||
\(56\) | −0.415238 | − | 2.96056i | −0.0554885 | − | 0.395621i | ||||
\(57\) | −1.03458 | + | 1.03458i | −0.137033 | + | 0.137033i | ||||
\(58\) | 2.71431 | − | 5.25018i | 0.356406 | − | 0.689383i | ||||
\(59\) | −2.30403 | − | 2.30403i | −0.299959 | − | 0.299959i | 0.541039 | − | 0.840998i | \(-0.318031\pi\) |
−0.840998 | + | 0.541039i | \(0.818031\pi\) | |||||||
\(60\) | −3.58008 | + | 2.68012i | −0.462186 | + | 0.346002i | ||||
\(61\) | 10.8244 | − | 10.8244i | 1.38592 | − | 1.38592i | 0.552234 | − | 0.833689i | \(-0.313776\pi\) |
0.833689 | − | 0.552234i | \(-0.186224\pi\) | |||||||
\(62\) | 14.0880 | − | 4.48559i | 1.78918 | − | 0.569670i | ||||
\(63\) | 0.747384 | + | 0.747384i | 0.0941615 | + | 0.0941615i | ||||
\(64\) | 2.20081 | + | 7.69132i | 0.275101 | + | 0.961415i | ||||
\(65\) | −0.0581916 | − | 2.22735i | −0.00721778 | − | 0.276269i | ||||
\(66\) | −1.63504 | − | 0.845304i | −0.201259 | − | 0.104050i | ||||
\(67\) | 8.99029i | 1.09834i | 0.835711 | + | 0.549169i | \(0.185056\pi\) | ||||
−0.835711 | + | 0.549169i | \(0.814944\pi\) | |||||||
\(68\) | 2.73892 | + | 0.467056i | 0.332143 | + | 0.0566388i | ||||
\(69\) | −4.77394 | + | 4.77394i | −0.574715 | + | 0.574715i | ||||
\(70\) | −1.45693 | + | 3.00816i | −0.174136 | + | 0.359544i | ||||
\(71\) | −14.1421 | −1.67836 | −0.839180 | − | 0.543853i | \(-0.816965\pi\) | ||||
−0.839180 | + | 0.543853i | \(0.816965\pi\) | |||||||
\(72\) | −2.25841 | − | 1.70282i | −0.266156 | − | 0.200679i | ||||
\(73\) | 6.35840 | + | 6.35840i | 0.744195 | + | 0.744195i | 0.973382 | − | 0.229188i | \(-0.0736070\pi\) |
−0.229188 | + | 0.973382i | \(0.573607\pi\) | |||||||
\(74\) | 11.0863 | − | 3.52984i | 1.28875 | − | 0.410336i | ||||
\(75\) | 4.99318 | − | 0.261081i | 0.576563 | − | 0.0301471i | ||||
\(76\) | 0.491897 | − | 2.88459i | 0.0564245 | − | 0.330886i | ||||
\(77\) | −1.37565 | −0.156770 | ||||||||
\(78\) | 1.34276 | − | 0.427532i | 0.152038 | − | 0.0484084i | ||||
\(79\) | −8.76588 | −0.986238 | −0.493119 | − | 0.869962i | \(-0.664143\pi\) | ||||
−0.493119 | + | 0.869962i | \(0.664143\pi\) | |||||||
\(80\) | 2.74285 | − | 8.51333i | 0.306660 | − | 0.951819i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.68161 | + | 2.44581i | −0.848292 | + | 0.270094i | ||||
\(83\) | 12.3589 | 1.35657 | 0.678284 | − | 0.734800i | \(-0.262724\pi\) | ||||
0.678284 | + | 0.734800i | \(0.262724\pi\) | |||||||
\(84\) | −2.08384 | − | 0.355348i | −0.227366 | − | 0.0387717i | ||||
\(85\) | −2.25318 | − | 2.13845i | −0.244392 | − | 0.231947i | ||||
\(86\) | −7.04595 | + | 2.24341i | −0.759785 | + | 0.241914i | ||||
\(87\) | −2.95516 | − | 2.95516i | −0.316827 | − | 0.316827i | ||||
\(88\) | 3.64556 | − | 0.511314i | 0.388618 | − | 0.0545062i | ||||
\(89\) | −18.0456 | −1.91283 | −0.956414 | − | 0.292014i | \(-0.905675\pi\) | ||||
−0.956414 | + | 0.292014i | \(0.905675\pi\) | |||||||
\(90\) | 1.03777 | + | 2.98714i | 0.109391 | + | 0.314873i | ||||
\(91\) | 0.744724 | − | 0.744724i | 0.0780683 | − | 0.0780683i | ||||
\(92\) | 2.26980 | − | 13.3106i | 0.236643 | − | 1.38773i | ||||
\(93\) | − | 10.4545i | − | 1.08408i | ||||||
\(94\) | 0.0974017 | + | 0.0503560i | 0.0100462 | + | 0.00519383i | ||||
\(95\) | −2.25218 | + | 2.37302i | −0.231069 | + | 0.243467i | ||||
\(96\) | 5.65438 | + | 0.167155i | 0.577098 | + | 0.0170602i | ||||
\(97\) | 1.29787 | + | 1.29787i | 0.131779 | + | 0.131779i | 0.769920 | − | 0.638141i | \(-0.220296\pi\) |
−0.638141 | + | 0.769920i | \(0.720296\pi\) | |||||||
\(98\) | 7.92745 | − | 2.52408i | 0.800794 | − | 0.254971i | ||||
\(99\) | −0.920311 | + | 0.920311i | −0.0924947 | + | 0.0924947i | ||||
\(100\) | −7.84605 | + | 6.19996i | −0.784605 | + | 0.619996i | ||||
\(101\) | 4.25125 | + | 4.25125i | 0.423015 | + | 0.423015i | 0.886241 | − | 0.463225i | \(-0.153308\pi\) |
−0.463225 | + | 0.886241i | \(0.653308\pi\) | |||||||
\(102\) | 0.902270 | − | 1.74523i | 0.0893381 | − | 0.172803i | ||||
\(103\) | −5.92346 | + | 5.92346i | −0.583656 | + | 0.583656i | −0.935906 | − | 0.352250i | \(-0.885417\pi\) |
0.352250 | + | 0.935906i | \(0.385417\pi\) | |||||||
\(104\) | −1.69676 | + | 2.25037i | −0.166381 | + | 0.220667i | ||||
\(105\) | 1.71428 | + | 1.62698i | 0.167296 | + | 0.158777i | ||||
\(106\) | 2.20518 | + | 6.92586i | 0.214186 | + | 0.672699i | ||||
\(107\) | −0.0554707 | −0.00536256 | −0.00268128 | − | 0.999996i | \(-0.500853\pi\) | ||||
−0.00268128 | + | 0.999996i | \(0.500853\pi\) | |||||||
\(108\) | −1.63182 | + | 1.15636i | −0.157022 | + | 0.111271i | ||||
\(109\) | −0.947769 | − | 0.947769i | −0.0907798 | − | 0.0907798i | 0.660259 | − | 0.751038i | \(-0.270447\pi\) |
−0.751038 | + | 0.660259i | \(0.770447\pi\) | |||||||
\(110\) | −3.70418 | − | 1.79403i | −0.353179 | − | 0.171054i | ||||
\(111\) | − | 8.22694i | − | 0.780867i | ||||||
\(112\) | 3.81136 | − | 1.82981i | 0.360139 | − | 0.172901i | ||||
\(113\) | −10.8801 | + | 10.8801i | −1.02351 | + | 1.02351i | −0.0237977 | + | 0.999717i | \(0.507576\pi\) |
−0.999717 | + | 0.0237977i | \(0.992424\pi\) | |||||||
\(114\) | −1.83805 | − | 0.950259i | −0.172149 | − | 0.0889999i | ||||
\(115\) | −10.3924 | + | 10.9500i | −0.969098 | + | 1.02109i | ||||
\(116\) | 8.23952 | + | 1.40505i | 0.765020 | + | 0.130456i | ||||
\(117\) | − | 0.996441i | − | 0.0921210i | ||||||
\(118\) | 2.11624 | − | 4.09337i | 0.194816 | − | 0.376825i | ||||
\(119\) | − | 1.46836i | − | 0.134604i | ||||||
\(120\) | −5.14767 | − | 3.67443i | −0.469916 | − | 0.335428i | ||||
\(121\) | 9.30606i | 0.846005i | ||||||||
\(122\) | 19.2308 | + | 9.94219i | 1.74107 | + | 0.900124i | ||||
\(123\) | 5.70040i | 0.513988i | ||||||||
\(124\) | 12.0892 | + | 17.0598i | 1.08564 | + | 1.53202i | ||||
\(125\) | 11.1460 | − | 0.875196i | 0.996931 | − | 0.0782799i | ||||
\(126\) | −0.686471 | + | 1.32781i | −0.0611557 | + | 0.118291i | ||||
\(127\) | −9.61338 | + | 9.61338i | −0.853050 | + | 0.853050i | −0.990508 | − | 0.137458i | \(-0.956107\pi\) |
0.137458 | + | 0.990508i | \(0.456107\pi\) | |||||||
\(128\) | −9.42021 | + | 6.26575i | −0.832637 | + | 0.553819i | ||||
\(129\) | 5.22869i | 0.460360i | ||||||||
\(130\) | 2.97651 | − | 1.03408i | 0.261057 | − | 0.0906948i | ||||
\(131\) | 5.60184 | + | 5.60184i | 0.489435 | + | 0.489435i | 0.908128 | − | 0.418693i | \(-0.137512\pi\) |
−0.418693 | + | 0.908128i | \(0.637512\pi\) | |||||||
\(132\) | 0.437567 | − | 2.56599i | 0.0380854 | − | 0.223341i | ||||
\(133\) | −1.54646 | −0.134095 | ||||||||
\(134\) | −12.1149 | + | 3.85736i | −1.04657 | + | 0.333225i | ||||
\(135\) | 2.23531 | − | 0.0583995i | 0.192384 | − | 0.00502623i | ||||
\(136\) | 0.545772 | + | 3.89124i | 0.0467996 | + | 0.333671i | ||||
\(137\) | −4.68373 | + | 4.68373i | −0.400158 | + | 0.400158i | −0.878289 | − | 0.478130i | \(-0.841315\pi\) |
0.478130 | + | 0.878289i | \(0.341315\pi\) | |||||||
\(138\) | −8.48146 | − | 4.38486i | −0.721990 | − | 0.373264i | ||||
\(139\) | −1.64971 | − | 1.64971i | −0.139926 | − | 0.139926i | 0.633674 | − | 0.773600i | \(-0.281546\pi\) |
−0.773600 | + | 0.633674i | \(0.781546\pi\) | |||||||
\(140\) | −4.67877 | − | 0.672616i | −0.395428 | − | 0.0568465i | ||||
\(141\) | 0.0548243 | − | 0.0548243i | 0.00461704 | − | 0.00461704i | ||||
\(142\) | −6.06780 | − | 19.0573i | −0.509198 | − | 1.59925i | ||||
\(143\) | 0.917036 | + | 0.917036i | 0.0766864 | + | 0.0766864i | ||||
\(144\) | 1.32566 | − | 3.77394i | 0.110471 | − | 0.314495i | ||||
\(145\) | −6.77827 | − | 6.43311i | −0.562905 | − | 0.534241i | ||||
\(146\) | −5.84018 | + | 11.2964i | −0.483337 | + | 0.934899i | ||||
\(147\) | − | 5.88283i | − | 0.485208i | ||||||
\(148\) | 9.51332 | + | 13.4249i | 0.781990 | + | 1.10352i | ||||
\(149\) | −12.0813 | + | 12.0813i | −0.989742 | + | 0.989742i | −0.999948 | − | 0.0102058i | \(-0.996751\pi\) |
0.0102058 | + | 0.999948i | \(0.496751\pi\) | |||||||
\(150\) | 2.49419 | + | 6.61657i | 0.203650 | + | 0.540241i | ||||
\(151\) | 12.6503 | 1.02947 | 0.514735 | − | 0.857350i | \(-0.327890\pi\) | ||||
0.514735 | + | 0.857350i | \(0.327890\pi\) | |||||||
\(152\) | 4.09821 | − | 0.574800i | 0.332408 | − | 0.0466225i | ||||
\(153\) | −0.982332 | − | 0.982332i | −0.0794169 | − | 0.0794169i | ||||
\(154\) | −0.590235 | − | 1.85377i | −0.0475625 | − | 0.149381i | ||||
\(155\) | −0.610537 | − | 23.3690i | −0.0490395 | − | 1.87704i | ||||
\(156\) | 1.15225 | + | 1.62601i | 0.0922535 | + | 0.130185i | ||||
\(157\) | −6.31279 | −0.503816 | −0.251908 | − | 0.967751i | \(-0.581058\pi\) | ||||
−0.251908 | + | 0.967751i | \(0.581058\pi\) | |||||||
\(158\) | −3.76107 | − | 11.8125i | −0.299215 | − | 0.939753i | ||||
\(159\) | 5.13957 | 0.407595 | ||||||||
\(160\) | 12.6490 | + | 0.0434293i | 0.999994 | + | 0.00343339i | ||||
\(161\) | −7.13593 | −0.562390 | ||||||||
\(162\) | 0.429059 | + | 1.34756i | 0.0337100 | + | 0.105874i | ||||
\(163\) | 14.6329 | 1.14613 | 0.573067 | − | 0.819508i | \(-0.305753\pi\) | ||||
0.573067 | + | 0.819508i | \(0.305753\pi\) | |||||||
\(164\) | −6.59172 | − | 9.30201i | −0.514727 | − | 0.726365i | ||||
\(165\) | −2.00343 | + | 2.11092i | −0.155967 | + | 0.164335i | ||||
\(166\) | 5.30270 | + | 16.6543i | 0.411569 | + | 1.29263i | ||||
\(167\) | 5.31380 | + | 5.31380i | 0.411194 | + | 0.411194i | 0.882155 | − | 0.470960i | \(-0.156092\pi\) |
−0.470960 | + | 0.882155i | \(0.656092\pi\) | |||||||
\(168\) | −0.415238 | − | 2.96056i | −0.0320363 | − | 0.228412i | ||||
\(169\) | 12.0071 | 0.923623 | ||||||||
\(170\) | 1.91493 | − | 3.95381i | 0.146868 | − | 0.303243i | ||||
\(171\) | −1.03458 | + | 1.03458i | −0.0791163 | + | 0.0791163i | ||||
\(172\) | −6.04625 | − | 8.53227i | −0.461023 | − | 0.650579i | ||||
\(173\) | 13.1537i | 1.00006i | 0.866008 | + | 0.500029i | \(0.166678\pi\) | ||||
−0.866008 | + | 0.500029i | \(0.833322\pi\) | |||||||
\(174\) | 2.71431 | − | 5.25018i | 0.205771 | − | 0.398015i | ||||
\(175\) | 3.92695 | + | 3.53669i | 0.296849 | + | 0.267349i | ||||
\(176\) | 2.25318 | + | 4.69322i | 0.169840 | + | 0.353764i | ||||
\(177\) | −2.30403 | − | 2.30403i | −0.173181 | − | 0.173181i | ||||
\(178\) | −7.74261 | − | 24.3174i | −0.580333 | − | 1.82267i | ||||
\(179\) | 12.2215 | − | 12.2215i | 0.913479 | − | 0.913479i | −0.0830647 | − | 0.996544i | \(-0.526471\pi\) |
0.996544 | + | 0.0830647i | \(0.0264708\pi\) | |||||||
\(180\) | −3.58008 | + | 2.68012i | −0.266843 | + | 0.199764i | ||||
\(181\) | 7.77734 | + | 7.77734i | 0.578085 | + | 0.578085i | 0.934375 | − | 0.356290i | \(-0.115959\pi\) |
−0.356290 | + | 0.934375i | \(0.615959\pi\) | |||||||
\(182\) | 1.32309 | + | 0.684027i | 0.0980738 | + | 0.0507035i | ||||
\(183\) | 10.8244 | − | 10.8244i | 0.800163 | − | 0.800163i | ||||
\(184\) | 18.9107 | − | 2.65235i | 1.39411 | − | 0.195534i | ||||
\(185\) | −0.480449 | − | 18.3897i | −0.0353233 | − | 1.35204i | ||||
\(186\) | 14.0880 | − | 4.48559i | 1.03298 | − | 0.328899i | ||||
\(187\) | 1.80810 | 0.132222 | ||||||||
\(188\) | −0.0260665 | + | 0.152860i | −0.00190110 | + | 0.0111485i | ||||
\(189\) | 0.747384 | + | 0.747384i | 0.0543642 | + | 0.0543642i | ||||
\(190\) | −4.16410 | − | 2.01678i | −0.302095 | − | 0.146313i | ||||
\(191\) | − | 18.2743i | − | 1.32228i | −0.750262 | − | 0.661141i | \(-0.770073\pi\) | ||
0.750262 | − | 0.661141i | \(-0.229927\pi\) | |||||||
\(192\) | 2.20081 | + | 7.69132i | 0.158830 | + | 0.555073i | ||||
\(193\) | −11.3061 | + | 11.3061i | −0.813832 | + | 0.813832i | −0.985206 | − | 0.171374i | \(-0.945179\pi\) |
0.171374 | + | 0.985206i | \(0.445179\pi\) | |||||||
\(194\) | −1.19209 | + | 2.30582i | −0.0855873 | + | 0.165548i | ||||
\(195\) | −0.0581916 | − | 2.22735i | −0.00416719 | − | 0.159504i | ||||
\(196\) | 6.80268 | + | 9.59971i | 0.485906 | + | 0.685694i | ||||
\(197\) | − | 11.1767i | − | 0.796305i | −0.917319 | − | 0.398153i | \(-0.869651\pi\) | ||
0.917319 | − | 0.398153i | \(-0.130349\pi\) | |||||||
\(198\) | −1.63504 | − | 0.845304i | −0.116197 | − | 0.0600731i | ||||
\(199\) | − | 18.8869i | − | 1.33886i | −0.742877 | − | 0.669428i | \(-0.766539\pi\) | ||
0.742877 | − | 0.669428i | \(-0.233461\pi\) | |||||||
\(200\) | −11.7212 | − | 7.91285i | −0.828815 | − | 0.559523i | ||||
\(201\) | 8.99029i | 0.634126i | ||||||||
\(202\) | −3.90477 | + | 7.55284i | −0.274738 | + | 0.531416i | ||||
\(203\) | − | 4.41728i | − | 0.310032i | ||||||
\(204\) | 2.73892 | + | 0.467056i | 0.191763 | + | 0.0327005i | ||||
\(205\) | 0.332900 | + | 12.7421i | 0.0232508 | + | 0.889949i | ||||
\(206\) | −10.5237 | − | 5.44069i | −0.733222 | − | 0.379071i | ||||
\(207\) | −4.77394 | + | 4.77394i | −0.331812 | + | 0.331812i | ||||
\(208\) | −3.76051 | − | 1.32094i | −0.260744 | − | 0.0915906i | ||||
\(209\) | − | 1.90427i | − | 0.131721i | ||||||
\(210\) | −1.45693 | + | 3.00816i | −0.100538 | + | 0.207583i | ||||
\(211\) | −7.95311 | − | 7.95311i | −0.547514 | − | 0.547514i | 0.378207 | − | 0.925721i | \(-0.376541\pi\) |
−0.925721 | + | 0.378207i | \(0.876541\pi\) | |||||||
\(212\) | −8.38684 | + | 5.94320i | −0.576011 | + | 0.408181i | ||||
\(213\) | −14.1421 | −0.969002 | ||||||||
\(214\) | −0.0238002 | − | 0.0747499i | −0.00162695 | − | 0.00510980i | ||||
\(215\) | 0.305353 | + | 11.6877i | 0.0208249 | + | 0.797096i | ||||
\(216\) | −2.25841 | − | 1.70282i | −0.153665 | − | 0.115862i | ||||
\(217\) | 7.81352 | − | 7.81352i | 0.530416 | − | 0.530416i | ||||
\(218\) | 0.870524 | − | 1.68382i | 0.0589593 | − | 0.114043i | ||||
\(219\) | 6.35840 | + | 6.35840i | 0.429661 | + | 0.429661i | ||||
\(220\) | 0.828244 | − | 5.76133i | 0.0558402 | − | 0.388429i | ||||
\(221\) | −0.978836 | + | 0.978836i | −0.0658437 | + | 0.0658437i | ||||
\(222\) | 11.0863 | − | 3.52984i | 0.744062 | − | 0.236907i | ||||
\(223\) | 4.22843 | + | 4.22843i | 0.283157 | + | 0.283157i | 0.834367 | − | 0.551210i | \(-0.185834\pi\) |
−0.551210 | + | 0.834367i | \(0.685834\pi\) | |||||||
\(224\) | 4.10107 | + | 4.35092i | 0.274014 | + | 0.290708i | ||||
\(225\) | 4.99318 | − | 0.261081i | 0.332879 | − | 0.0174054i | ||||
\(226\) | −19.3298 | − | 9.99336i | −1.28580 | − | 0.664748i | ||||
\(227\) | − | 15.7654i | − | 1.04639i | −0.852214 | − | 0.523193i | \(-0.824741\pi\) | ||
0.852214 | − | 0.523193i | \(-0.175259\pi\) | |||||||
\(228\) | 0.491897 | − | 2.88459i | 0.0325767 | − | 0.191037i | ||||
\(229\) | −0.746140 | + | 0.746140i | −0.0493063 | + | 0.0493063i | −0.731330 | − | 0.682024i | \(-0.761100\pi\) |
0.682024 | + | 0.731330i | \(0.261100\pi\) | |||||||
\(230\) | −19.2147 | − | 9.30618i | −1.26698 | − | 0.613631i | ||||
\(231\) | −1.37565 | −0.0905112 | ||||||||
\(232\) | 1.64185 | + | 11.7061i | 0.107793 | + | 0.768541i | ||||
\(233\) | −5.74517 | − | 5.74517i | −0.376379 | − | 0.376379i | 0.493415 | − | 0.869794i | \(-0.335748\pi\) |
−0.869794 | + | 0.493415i | \(0.835748\pi\) | |||||||
\(234\) | 1.34276 | − | 0.427532i | 0.0877790 | − | 0.0279486i | ||||
\(235\) | 0.119347 | − | 0.125751i | 0.00778536 | − | 0.00820308i | ||||
\(236\) | 6.42404 | + | 1.09546i | 0.418169 | + | 0.0713086i | ||||
\(237\) | −8.76588 | −0.569405 | ||||||||
\(238\) | 1.97870 | − | 0.630012i | 0.128260 | − | 0.0408376i | ||||
\(239\) | 27.9736 | 1.80946 | 0.904729 | − | 0.425987i | \(-0.140073\pi\) | ||||
0.904729 | + | 0.425987i | \(0.140073\pi\) | |||||||
\(240\) | 2.74285 | − | 8.51333i | 0.177050 | − | 0.549533i | ||||
\(241\) | −7.01072 | −0.451600 | −0.225800 | − | 0.974174i | \(-0.572500\pi\) | ||||
−0.225800 | + | 0.974174i | \(0.572500\pi\) | |||||||
\(242\) | −12.5404 | + | 3.99284i | −0.806130 | + | 0.256670i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.14653 | + | 30.1804i | −0.329473 | + | 1.93210i | ||||
\(245\) | −0.343555 | − | 13.1499i | −0.0219489 | − | 0.840118i | ||||
\(246\) | −7.68161 | + | 2.44581i | −0.489762 | + | 0.155939i | ||||
\(247\) | 1.03090 | + | 1.03090i | 0.0655945 | + | 0.0655945i | ||||
\(248\) | −17.8021 | + | 23.6105i | −1.13044 | + | 1.49927i | ||||
\(249\) | 12.3589 | 0.783215 | ||||||||
\(250\) | 5.96168 | + | 14.6444i | 0.377050 | + | 0.926193i | ||||
\(251\) | −5.41619 | + | 5.41619i | −0.341867 | + | 0.341867i | −0.857069 | − | 0.515202i | \(-0.827717\pi\) |
0.515202 | + | 0.857069i | \(0.327717\pi\) | |||||||
\(252\) | −2.08384 | − | 0.355348i | −0.131270 | − | 0.0223848i | ||||
\(253\) | − | 8.78702i | − | 0.552435i | ||||||
\(254\) | −17.0793 | − | 8.82987i | −1.07165 | − | 0.554036i | ||||
\(255\) | −2.25318 | − | 2.13845i | −0.141100 | − | 0.133915i | ||||
\(256\) | −12.4853 | − | 10.0059i | −0.780329 | − | 0.625369i | ||||
\(257\) | 17.0268 | + | 17.0268i | 1.06210 | + | 1.06210i | 0.997940 | + | 0.0641616i | \(0.0204373\pi\) |
0.0641616 | + | 0.997940i | \(0.479563\pi\) | |||||||
\(258\) | −7.04595 | + | 2.24341i | −0.438662 | + | 0.139669i | ||||
\(259\) | 6.14869 | − | 6.14869i | 0.382061 | − | 0.382061i | ||||
\(260\) | 2.67058 | + | 3.56734i | 0.165622 | + | 0.221237i | ||||
\(261\) | −2.95516 | − | 2.95516i | −0.182920 | − | 0.182920i | ||||
\(262\) | −5.14528 | + | 9.95232i | −0.317877 | + | 0.614856i | ||||
\(263\) | 7.04662 | − | 7.04662i | 0.434513 | − | 0.434513i | −0.455647 | − | 0.890160i | \(-0.650592\pi\) |
0.890160 | + | 0.455647i | \(0.150592\pi\) | |||||||
\(264\) | 3.64556 | − | 0.511314i | 0.224369 | − | 0.0314692i | ||||
\(265\) | 11.4885 | − | 0.300148i | 0.705734 | − | 0.0184380i | ||||
\(266\) | −0.663520 | − | 2.08394i | −0.0406830 | − | 0.127774i | ||||
\(267\) | −18.0456 | −1.10437 | ||||||||
\(268\) | −10.3960 | − | 14.6705i | −0.635038 | − | 0.896144i | ||||
\(269\) | 13.1762 | + | 13.1762i | 0.803366 | + | 0.803366i | 0.983620 | − | 0.180254i | \(-0.0576921\pi\) |
−0.180254 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(270\) | 1.03777 | + | 2.98714i | 0.0631569 | + | 0.181792i | ||||
\(271\) | − | 2.01115i | − | 0.122169i | −0.998133 | − | 0.0610845i | \(-0.980544\pi\) | ||
0.998133 | − | 0.0610845i | \(-0.0194559\pi\) | |||||||
\(272\) | −5.00950 | + | 2.40503i | −0.303746 | + | 0.145826i | ||||
\(273\) | 0.744724 | − | 0.744724i | 0.0450727 | − | 0.0450727i | ||||
\(274\) | −8.32119 | − | 4.30200i | −0.502702 | − | 0.259893i | ||||
\(275\) | −4.35500 | + | 4.83555i | −0.262616 | + | 0.291595i | ||||
\(276\) | 2.26980 | − | 13.3106i | 0.136626 | − | 0.801204i | ||||
\(277\) | − | 5.15280i | − | 0.309602i | −0.987946 | − | 0.154801i | \(-0.950526\pi\) | ||
0.987946 | − | 0.154801i | \(-0.0494736\pi\) | |||||||
\(278\) | 1.51525 | − | 2.93089i | 0.0908787 | − | 0.175783i | ||||
\(279\) | − | 10.4545i | − | 0.625894i | ||||||
\(280\) | −1.10108 | − | 6.59350i | −0.0658020 | − | 0.394037i | ||||
\(281\) | − | 14.7480i | − | 0.879791i | −0.898049 | − | 0.439895i | \(-0.855016\pi\) | ||
0.898049 | − | 0.439895i | \(-0.144984\pi\) | |||||||
\(282\) | 0.0974017 | + | 0.0503560i | 0.00580019 | + | 0.00299866i | ||||
\(283\) | 7.82068i | 0.464891i | 0.972609 | + | 0.232446i | \(0.0746728\pi\) | ||||
−0.972609 | + | 0.232446i | \(0.925327\pi\) | |||||||
\(284\) | 23.0774 | − | 16.3534i | 1.36939 | − | 0.970396i | ||||
\(285\) | −2.25218 | + | 2.37302i | −0.133408 | + | 0.140566i | ||||
\(286\) | −0.842295 | + | 1.62922i | −0.0498060 | + | 0.0963378i | ||||
\(287\) | −4.26039 | + | 4.26039i | −0.251483 | + | 0.251483i | ||||
\(288\) | 5.65438 | + | 0.167155i | 0.333188 | + | 0.00984970i | ||||
\(289\) | − | 15.0700i | − | 0.886473i | ||||||
\(290\) | 5.76070 | − | 11.8943i | 0.338280 | − | 0.698456i | ||||
\(291\) | 1.29787 | + | 1.29787i | 0.0760826 | + | 0.0760826i | ||||
\(292\) | −17.7284 | − | 3.02314i | −1.03747 | − | 0.176916i | ||||
\(293\) | 19.1115 | 1.11651 | 0.558254 | − | 0.829670i | \(-0.311471\pi\) | ||||
0.558254 | + | 0.829670i | \(0.311471\pi\) | |||||||
\(294\) | 7.92745 | − | 2.52408i | 0.462338 | − | 0.147207i | ||||
\(295\) | −5.28476 | − | 5.01565i | −0.307690 | − | 0.292022i | ||||
\(296\) | −14.0090 | + | 18.5798i | −0.814257 | + | 1.07993i | ||||
\(297\) | −0.920311 | + | 0.920311i | −0.0534019 | + | 0.0534019i | ||||
\(298\) | −21.4639 | − | 11.0967i | −1.24337 | − | 0.642814i | ||||
\(299\) | 4.75695 | + | 4.75695i | 0.275102 | + | 0.275102i | ||||
\(300\) | −7.84605 | + | 6.19996i | −0.452992 | + | 0.357955i | ||||
\(301\) | −3.90784 | + | 3.90784i | −0.225244 | + | 0.225244i | ||||
\(302\) | 5.42773 | + | 17.0470i | 0.312331 | + | 0.980947i | ||||
\(303\) | 4.25125 | + | 4.25125i | 0.244228 | + | 0.244228i | ||||
\(304\) | 2.53295 | + | 5.27594i | 0.145274 | + | 0.302596i | ||||
\(305\) | 23.5637 | − | 24.8280i | 1.34925 | − | 1.42165i | ||||
\(306\) | 0.902270 | − | 1.74523i | 0.0515794 | − | 0.0997680i | ||||
\(307\) | 3.29048i | 0.187798i | 0.995582 | + | 0.0938988i | \(0.0299330\pi\) | ||||
−0.995582 | + | 0.0938988i | \(0.970067\pi\) | |||||||
\(308\) | 2.24481 | − | 1.59075i | 0.127910 | − | 0.0906414i | ||||
\(309\) | −5.92346 | + | 5.92346i | −0.336974 | + | 0.336974i | ||||
\(310\) | 31.2291 | − | 10.8494i | 1.77369 | − | 0.616204i | ||||
\(311\) | −10.6744 | −0.605292 | −0.302646 | − | 0.953103i | \(-0.597870\pi\) | ||||
−0.302646 | + | 0.953103i | \(0.597870\pi\) | |||||||
\(312\) | −1.69676 | + | 2.25037i | −0.0960601 | + | 0.127402i | ||||
\(313\) | −21.5451 | − | 21.5451i | −1.21780 | − | 1.21780i | −0.968400 | − | 0.249401i | \(-0.919766\pi\) |
−0.249401 | − | 0.968400i | \(-0.580234\pi\) | |||||||
\(314\) | −2.70856 | − | 8.50684i | −0.152853 | − | 0.480069i | ||||
\(315\) | 1.71428 | + | 1.62698i | 0.0965886 | + | 0.0916702i | ||||
\(316\) | 14.3043 | − | 10.1365i | 0.804680 | − | 0.570224i | ||||
\(317\) | −16.1238 | −0.905603 | −0.452801 | − | 0.891611i | \(-0.649575\pi\) | ||||
−0.452801 | + | 0.891611i | \(0.649575\pi\) | |||||||
\(318\) | 2.20518 | + | 6.92586i | 0.123660 | + | 0.388383i | ||||
\(319\) | 5.43934 | 0.304544 | ||||||||
\(320\) | 5.36865 | + | 17.0639i | 0.300117 | + | 0.953902i | ||||
\(321\) | −0.0554707 | −0.00309607 | ||||||||
\(322\) | −3.06173 | − | 9.61607i | −0.170624 | − | 0.535883i | ||||
\(323\) | 2.03260 | 0.113097 | ||||||||
\(324\) | −1.63182 | + | 1.15636i | −0.0906565 | + | 0.0642423i | ||||
\(325\) | −0.260152 | − | 4.97541i | −0.0144306 | − | 0.275986i | ||||
\(326\) | 6.27835 | + | 19.7186i | 0.347726 | + | 1.09211i | ||||
\(327\) | −0.947769 | − | 0.947769i | −0.0524117 | − | 0.0524117i | ||||
\(328\) | 9.70675 | − | 12.8738i | 0.535966 | − | 0.710838i | ||||
\(329\) | 0.0819496 | 0.00451803 | ||||||||
\(330\) | −3.70418 | − | 1.79403i | −0.203908 | − | 0.0987579i | ||||
\(331\) | 1.97876 | − | 1.97876i | 0.108762 | − | 0.108762i | −0.650631 | − | 0.759394i | \(-0.725496\pi\) |
0.759394 | + | 0.650631i | \(0.225496\pi\) | |||||||
\(332\) | −20.1675 | + | 14.2914i | −1.10684 | + | 0.784341i | ||||
\(333\) | − | 8.22694i | − | 0.450834i | ||||||
\(334\) | −4.88072 | + | 9.44058i | −0.267061 | + | 0.516566i | ||||
\(335\) | 0.525028 | + | 20.0960i | 0.0286854 | + | 1.09796i | ||||
\(336\) | 3.81136 | − | 1.82981i | 0.207927 | − | 0.0998243i | ||||
\(337\) | 25.2423 | + | 25.2423i | 1.37503 | + | 1.37503i | 0.852806 | + | 0.522229i | \(0.174899\pi\) |
0.522229 | + | 0.852806i | \(0.325101\pi\) | |||||||
\(338\) | 5.15175 | + | 16.1803i | 0.280218 | + | 0.880090i | ||||
\(339\) | −10.8801 | + | 10.8801i | −0.590926 | + | 0.590926i | ||||
\(340\) | 6.14960 | + | 0.884061i | 0.333509 | + | 0.0479449i | ||||
\(341\) | 9.62138 | + | 9.62138i | 0.521027 | + | 0.521027i | ||||
\(342\) | −1.83805 | − | 0.950259i | −0.0993904 | − | 0.0513841i | ||||
\(343\) | 9.62842 | − | 9.62842i | 0.519886 | − | 0.519886i | ||||
\(344\) | 8.90351 | − | 11.8085i | 0.480045 | − | 0.636672i | ||||
\(345\) | −10.3924 | + | 10.9500i | −0.559509 | + | 0.589529i | ||||
\(346\) | −17.7254 | + | 5.64372i | −0.952923 | + | 0.303408i | ||||
\(347\) | 24.1967 | 1.29895 | 0.649475 | − | 0.760383i | \(-0.274989\pi\) | ||||
0.649475 | + | 0.760383i | \(0.274989\pi\) | |||||||
\(348\) | 8.23952 | + | 1.40505i | 0.441685 | + | 0.0753186i | ||||
\(349\) | 2.28867 | + | 2.28867i | 0.122510 | + | 0.122510i | 0.765704 | − | 0.643194i | \(-0.222391\pi\) |
−0.643194 | + | 0.765704i | \(0.722391\pi\) | |||||||
\(350\) | −3.08100 | + | 6.80924i | −0.164687 | + | 0.363969i | ||||
\(351\) | − | 0.996441i | − | 0.0531861i | ||||||
\(352\) | −5.35763 | + | 5.04996i | −0.285562 | + | 0.269164i | ||||
\(353\) | −9.70578 | + | 9.70578i | −0.516587 | + | 0.516587i | −0.916537 | − | 0.399950i | \(-0.869027\pi\) |
0.399950 | + | 0.916537i | \(0.369027\pi\) | |||||||
\(354\) | 2.11624 | − | 4.09337i | 0.112477 | − | 0.217560i | ||||
\(355\) | −31.6120 | + | 0.825893i | −1.67779 | + | 0.0438338i | ||||
\(356\) | 29.4471 | − | 20.8672i | 1.56069 | − | 1.10596i | ||||
\(357\) | − | 1.46836i | − | 0.0777138i | ||||||
\(358\) | 21.7129 | + | 11.2254i | 1.14756 | + | 0.593283i | ||||
\(359\) | 27.1463i | 1.43273i | 0.697726 | + | 0.716365i | \(0.254195\pi\) | ||||
−0.697726 | + | 0.716365i | \(0.745805\pi\) | |||||||
\(360\) | −5.14767 | − | 3.67443i | −0.271306 | − | 0.193660i | ||||
\(361\) | 16.8593i | 0.887331i | ||||||||
\(362\) | −7.14347 | + | 13.8173i | −0.375452 | + | 0.726223i | ||||
\(363\) | 9.30606i | 0.488441i | ||||||||
\(364\) | −0.354083 | + | 2.07642i | −0.0185590 | + | 0.108834i | ||||
\(365\) | 14.5843 | + | 13.8416i | 0.763377 | + | 0.724505i | ||||
\(366\) | 19.2308 | + | 9.94219i | 1.00521 | + | 0.519687i | ||||
\(367\) | −16.3750 | + | 16.3750i | −0.854769 | + | 0.854769i | −0.990716 | − | 0.135947i | \(-0.956592\pi\) |
0.135947 | + | 0.990716i | \(0.456592\pi\) | |||||||
\(368\) | 11.6880 | + | 24.3452i | 0.609278 | + | 1.26908i | ||||
\(369\) | 5.70040i | 0.296751i | ||||||||
\(370\) | 24.5751 | − | 8.53771i | 1.27760 | − | 0.443854i | ||||
\(371\) | 3.84123 | + | 3.84123i | 0.199427 | + | 0.199427i | ||||
\(372\) | 12.0892 | + | 17.0598i | 0.626794 | + | 0.884510i | ||||
\(373\) | −29.7473 | −1.54026 | −0.770129 | − | 0.637888i | \(-0.779808\pi\) | ||||
−0.770129 | + | 0.637888i | \(0.779808\pi\) | |||||||
\(374\) | 0.775782 | + | 2.43652i | 0.0401147 | + | 0.125989i | ||||
\(375\) | 11.1460 | − | 0.875196i | 0.575579 | − | 0.0451949i | ||||
\(376\) | −0.217172 | + | 0.0304597i | −0.0111998 | + | 0.00157084i | ||||
\(377\) | −2.94464 | + | 2.94464i | −0.151657 | + | 0.151657i | ||||
\(378\) | −0.686471 | + | 1.32781i | −0.0353082 | + | 0.0682954i | ||||
\(379\) | −11.0584 | − | 11.0584i | −0.568031 | − | 0.568031i | 0.363546 | − | 0.931576i | \(-0.381566\pi\) |
−0.931576 | + | 0.363546i | \(0.881566\pi\) | |||||||
\(380\) | 0.931082 | − | 6.47667i | 0.0477635 | − | 0.332246i | ||||
\(381\) | −9.61338 | + | 9.61338i | −0.492509 | + | 0.492509i | ||||
\(382\) | 24.6256 | − | 7.84074i | 1.25996 | − | 0.401167i | ||||
\(383\) | −16.2297 | − | 16.2297i | −0.829298 | − | 0.829298i | 0.158122 | − | 0.987420i | \(-0.449456\pi\) |
−0.987420 | + | 0.158122i | \(0.949456\pi\) | |||||||
\(384\) | −9.42021 | + | 6.26575i | −0.480723 | + | 0.319747i | ||||
\(385\) | −3.07500 | + | 0.0803373i | −0.156717 | + | 0.00409437i | ||||
\(386\) | −20.0866 | − | 10.3846i | −1.02238 | − | 0.528565i | ||||
\(387\) | 5.22869i | 0.265789i | ||||||||
\(388\) | −3.61870 | − | 0.617081i | −0.183712 | − | 0.0313276i | ||||
\(389\) | 12.6341 | − | 12.6341i | 0.640575 | − | 0.640575i | −0.310122 | − | 0.950697i | \(-0.600370\pi\) |
0.950697 | + | 0.310122i | \(0.100370\pi\) | |||||||
\(390\) | 2.97651 | − | 1.03408i | 0.150722 | − | 0.0523627i | ||||
\(391\) | 9.37920 | 0.474326 | ||||||||
\(392\) | −10.0174 | + | 13.2858i | −0.505955 | + | 0.671036i | ||||
\(393\) | 5.60184 | + | 5.60184i | 0.282576 | + | 0.282576i | ||||
\(394\) | 15.0612 | − | 4.79545i | 0.758773 | − | 0.241591i | ||||
\(395\) | −19.5944 | + | 0.511923i | −0.985902 | + | 0.0257576i | ||||
\(396\) | 0.437567 | − | 2.56599i | 0.0219886 | − | 0.128946i | ||||
\(397\) | −5.42044 | −0.272044 | −0.136022 | − | 0.990706i | \(-0.543432\pi\) | ||||
−0.136022 | + | 0.990706i | \(0.543432\pi\) | |||||||
\(398\) | 25.4512 | − | 8.10358i | 1.27575 | − | 0.406196i | ||||
\(399\) | −1.54646 | −0.0774197 | ||||||||
\(400\) | 5.63393 | − | 19.1901i | 0.281697 | − | 0.959504i | ||||
\(401\) | 15.7550 | 0.786765 | 0.393382 | − | 0.919375i | \(-0.371305\pi\) | ||||
0.393382 | + | 0.919375i | \(0.371305\pi\) | |||||||
\(402\) | −12.1149 | + | 3.85736i | −0.604238 | + | 0.192388i | ||||
\(403\) | −10.4173 | −0.518922 | ||||||||
\(404\) | −11.8533 | − | 2.02128i | −0.589721 | − | 0.100563i | ||||
\(405\) | 2.23531 | − | 0.0583995i | 0.111073 | − | 0.00290189i | ||||
\(406\) | 5.95254 | − | 1.89527i | 0.295419 | − | 0.0940608i | ||||
\(407\) | 7.57135 | + | 7.57135i | 0.375298 | + | 0.375298i | ||||
\(408\) | 0.545772 | + | 3.89124i | 0.0270198 | + | 0.192645i | ||||
\(409\) | −30.9442 | −1.53009 | −0.765046 | − | 0.643976i | \(-0.777284\pi\) | ||||
−0.765046 | + | 0.643976i | \(0.777284\pi\) | |||||||
\(410\) | −17.0279 | + | 5.91573i | −0.840949 | + | 0.292157i | ||||
\(411\) | −4.68373 | + | 4.68373i | −0.231032 | + | 0.231032i | ||||
\(412\) | 2.81635 | − | 16.5157i | 0.138751 | − | 0.813669i | ||||
\(413\) | − | 3.44398i | − | 0.169467i | ||||||
\(414\) | −8.48146 | − | 4.38486i | −0.416841 | − | 0.215504i | ||||
\(415\) | 27.6260 | − | 0.721754i | 1.35610 | − | 0.0354295i | ||||
\(416\) | 0.166560 | − | 5.63426i | 0.00816628 | − | 0.276242i | ||||
\(417\) | −1.64971 | − | 1.64971i | −0.0807864 | − | 0.0807864i | ||||
\(418\) | 2.56611 | − | 0.817043i | 0.125513 | − | 0.0399629i | ||||
\(419\) | −15.2385 | + | 15.2385i | −0.744451 | + | 0.744451i | −0.973431 | − | 0.228980i | \(-0.926461\pi\) |
0.228980 | + | 0.973431i | \(0.426461\pi\) | |||||||
\(420\) | −4.67877 | − | 0.672616i | −0.228301 | − | 0.0328203i | ||||
\(421\) | 14.4008 | + | 14.4008i | 0.701852 | + | 0.701852i | 0.964808 | − | 0.262956i | \(-0.0846974\pi\) |
−0.262956 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(422\) | 7.30491 | − | 14.1296i | 0.355598 | − | 0.687819i | ||||
\(423\) | 0.0548243 | − | 0.0548243i | 0.00266565 | − | 0.00266565i | ||||
\(424\) | −11.6072 | − | 8.75176i | −0.563698 | − | 0.425023i | ||||
\(425\) | −5.16143 | − | 4.64849i | −0.250366 | − | 0.225485i | ||||
\(426\) | −6.06780 | − | 19.0573i | −0.293986 | − | 0.923330i | ||||
\(427\) | 16.1800 | 0.783004 | ||||||||
\(428\) | 0.0905181 | − | 0.0641442i | 0.00437536 | − | 0.00310053i | ||||
\(429\) | 0.917036 | + | 0.917036i | 0.0442749 | + | 0.0442749i | ||||
\(430\) | −15.6188 | + | 5.42619i | −0.753208 | + | 0.261674i | ||||
\(431\) | 4.47310i | 0.215461i | 0.994180 | + | 0.107731i | \(0.0343584\pi\) | ||||
−0.994180 | + | 0.107731i | \(0.965642\pi\) | |||||||
\(432\) | 1.32566 | − | 3.77394i | 0.0637807 | − | 0.181574i | ||||
\(433\) | 20.8589 | − | 20.8589i | 1.00242 | − | 1.00242i | 0.00241793 | − | 0.999997i | \(-0.499230\pi\) |
0.999997 | − | 0.00241793i | \(-0.000769652\pi\) | |||||||
\(434\) | 13.8816 | + | 7.17670i | 0.666339 | + | 0.344493i | ||||
\(435\) | −6.77827 | − | 6.43311i | −0.324993 | − | 0.308444i | ||||
\(436\) | 2.64255 | + | 0.450622i | 0.126555 | + | 0.0215809i | ||||
\(437\) | − | 9.87805i | − | 0.472531i | ||||||
\(438\) | −5.84018 | + | 11.2964i | −0.279055 | + | 0.539764i | ||||
\(439\) | 0.257771i | 0.0123027i | 0.999981 | + | 0.00615136i | \(0.00195805\pi\) | ||||
−0.999981 | + | 0.00615136i | \(0.998042\pi\) | |||||||
\(440\) | 8.11908 | − | 1.35584i | 0.387062 | − | 0.0646372i | ||||
\(441\) | − | 5.88283i | − | 0.280135i | ||||||
\(442\) | −1.73902 | − | 0.899059i | −0.0827165 | − | 0.0427639i | ||||
\(443\) | − | 27.8275i | − | 1.32212i | −0.750331 | − | 0.661062i | \(-0.770106\pi\) | ||
0.750331 | − | 0.661062i | \(-0.229894\pi\) | |||||||
\(444\) | 9.51332 | + | 13.4249i | 0.451482 | + | 0.637116i | ||||
\(445\) | −40.3374 | + | 1.05385i | −1.91218 | + | 0.0499574i | ||||
\(446\) | −3.88380 | + | 7.51229i | −0.183903 | + | 0.355717i | ||||
\(447\) | −12.0813 | + | 12.0813i | −0.571428 | + | 0.571428i | ||||
\(448\) | −4.10352 | + | 7.39322i | −0.193873 | + | 0.349297i | ||||
\(449\) | 7.32170i | 0.345533i | 0.984963 | + | 0.172766i | \(0.0552705\pi\) | ||||
−0.984963 | + | 0.172766i | \(0.944729\pi\) | |||||||
\(450\) | 2.49419 | + | 6.61657i | 0.117577 | + | 0.311908i | ||||
\(451\) | −5.24614 | − | 5.24614i | −0.247031 | − | 0.247031i | ||||
\(452\) | 5.17301 | − | 30.3357i | 0.243318 | − | 1.42687i | ||||
\(453\) | 12.6503 | 0.594364 | ||||||||
\(454\) | 21.2448 | − | 6.76428i | 0.997066 | − | 0.317463i | ||||
\(455\) | 1.62119 | − | 1.70818i | 0.0760027 | − | 0.0800806i | ||||
\(456\) | 4.09821 | − | 0.574800i | 0.191916 | − | 0.0269175i | ||||
\(457\) | 13.1962 | − | 13.1962i | 0.617293 | − | 0.617293i | −0.327543 | − | 0.944836i | \(-0.606221\pi\) |
0.944836 | + | 0.327543i | \(0.106221\pi\) | |||||||
\(458\) | −1.32560 | − | 0.685328i | −0.0619414 | − | 0.0320233i | ||||
\(459\) | −0.982332 | − | 0.982332i | −0.0458514 | − | 0.0458514i | ||||
\(460\) | 4.29636 | − | 29.8858i | 0.200319 | − | 1.39343i | ||||
\(461\) | −19.6030 | + | 19.6030i | −0.913002 | + | 0.913002i | −0.996507 | − | 0.0835057i | \(-0.973388\pi\) |
0.0835057 | + | 0.996507i | \(0.473388\pi\) | |||||||
\(462\) | −0.590235 | − | 1.85377i | −0.0274602 | − | 0.0862451i | ||||
\(463\) | −17.2918 | − | 17.2918i | −0.803619 | − | 0.803619i | 0.180040 | − | 0.983659i | \(-0.442377\pi\) |
−0.983659 | + | 0.180040i | \(0.942377\pi\) | |||||||
\(464\) | −15.0701 | + | 7.23508i | −0.699614 | + | 0.335880i | ||||
\(465\) | −0.610537 | − | 23.3690i | −0.0283130 | − | 1.08371i | ||||
\(466\) | 5.27693 | − | 10.2070i | 0.244449 | − | 0.472828i | ||||
\(467\) | − | 31.3895i | − | 1.45253i | −0.687413 | − | 0.726267i | \(-0.741254\pi\) | ||
0.687413 | − | 0.726267i | \(-0.258746\pi\) | |||||||
\(468\) | 1.15225 | + | 1.62601i | 0.0532626 | + | 0.0751623i | ||||
\(469\) | −6.71920 | + | 6.71920i | −0.310264 | + | 0.310264i | ||||
\(470\) | 0.220663 | + | 0.106873i | 0.0101784 | + | 0.00492968i | ||||
\(471\) | −6.31279 | −0.290878 | ||||||||
\(472\) | 1.28009 | + | 9.12677i | 0.0589209 | + | 0.420094i | ||||
\(473\) | −4.81202 | − | 4.81202i | −0.221257 | − | 0.221257i | ||||
\(474\) | −3.76107 | − | 11.8125i | −0.172752 | − | 0.542567i | ||||
\(475\) | −4.89573 | + | 5.43595i | −0.224632 | + | 0.249419i | ||||
\(476\) | 1.69795 | + | 2.39609i | 0.0778256 | + | 0.109825i | ||||
\(477\) | 5.13957 | 0.235325 | ||||||||
\(478\) | 12.0023 | + | 37.6959i | 0.548972 | + | 1.72417i | ||||
\(479\) | 10.4863 | 0.479133 | 0.239566 | − | 0.970880i | \(-0.422995\pi\) | ||||
0.239566 | + | 0.970880i | \(0.422995\pi\) | |||||||
\(480\) | 12.6490 | + | 0.0434293i | 0.577347 | + | 0.00198227i | ||||
\(481\) | −8.19767 | −0.373781 | ||||||||
\(482\) | −3.00801 | − | 9.44735i | −0.137011 | − | 0.430315i | ||||
\(483\) | −7.13593 | −0.324696 | ||||||||
\(484\) | −10.7612 | − | 15.1858i | −0.489144 | − | 0.690263i | ||||
\(485\) | 2.97694 | + | 2.82535i | 0.135176 | + | 0.128292i | ||||
\(486\) | 0.429059 | + | 1.34756i | 0.0194625 | + | 0.0611264i | ||||
\(487\) | 4.72750 | + | 4.72750i | 0.214224 | + | 0.214224i | 0.806059 | − | 0.591835i | \(-0.201596\pi\) |
−0.591835 | + | 0.806059i | \(0.701596\pi\) | |||||||
\(488\) | −42.8779 | + | 6.01391i | −1.94099 | + | 0.272237i | ||||
\(489\) | 14.6329 | 0.661721 | ||||||||
\(490\) | 17.5729 | − | 6.10505i | 0.793861 | − | 0.275798i | ||||
\(491\) | −3.00877 | + | 3.00877i | −0.135784 | + | 0.135784i | −0.771732 | − | 0.635948i | \(-0.780609\pi\) |
0.635948 | + | 0.771732i | \(0.280609\pi\) | |||||||
\(492\) | −6.59172 | − | 9.30201i | −0.297178 | − | 0.419367i | ||||
\(493\) | 5.80590i | 0.261485i | ||||||||
\(494\) | −0.946877 | + | 1.83151i | −0.0426020 | + | 0.0824035i | ||||
\(495\) | −2.00343 | + | 2.11092i | −0.0900475 | + | 0.0948789i | ||||
\(496\) | −39.4546 | − | 13.8591i | −1.77157 | − | 0.622290i | ||||
\(497\) | −10.5696 | − | 10.5696i | −0.474111 | − | 0.474111i | ||||
\(498\) | 5.30270 | + | 16.6543i | 0.237620 | + | 0.746299i | ||||
\(499\) | −8.75769 | + | 8.75769i | −0.392048 | + | 0.392048i | −0.875417 | − | 0.483369i | \(-0.839413\pi\) |
0.483369 | + | 0.875417i | \(0.339413\pi\) | |||||||
\(500\) | −17.1762 | + | 14.3170i | −0.768145 | + | 0.640276i | ||||
\(501\) | 5.31380 | + | 5.31380i | 0.237403 | + | 0.237403i | ||||
\(502\) | −9.62249 | − | 4.97476i | −0.429473 | − | 0.222034i | ||||
\(503\) | −3.79393 | + | 3.79393i | −0.169163 | + | 0.169163i | −0.786611 | − | 0.617448i | \(-0.788166\pi\) |
0.617448 | + | 0.786611i | \(0.288166\pi\) | |||||||
\(504\) | −0.415238 | − | 2.96056i | −0.0184962 | − | 0.131874i | ||||
\(505\) | 9.75112 | + | 9.25457i | 0.433919 | + | 0.411823i | ||||
\(506\) | 11.8410 | − | 3.77015i | 0.526397 | − | 0.167603i | ||||
\(507\) | 12.0071 | 0.533254 | ||||||||
\(508\) | 4.57074 | − | 26.8038i | 0.202794 | − | 1.18923i | ||||
\(509\) | −9.92183 | − | 9.92183i | −0.439777 | − | 0.439777i | 0.452160 | − | 0.891937i | \(-0.350654\pi\) |
−0.891937 | + | 0.452160i | \(0.850654\pi\) | |||||||
\(510\) | 1.91493 | − | 3.95381i | 0.0847945 | − | 0.175078i | ||||
\(511\) | 9.50433i | 0.420447i | ||||||||
\(512\) | 8.12660 | − | 21.1177i | 0.359149 | − | 0.933280i | ||||
\(513\) | −1.03458 | + | 1.03458i | −0.0456778 | + | 0.0456778i | ||||
\(514\) | −15.6391 | + | 30.2500i | −0.689809 | + | 1.33427i | ||||
\(515\) | −12.8948 | + | 13.5867i | −0.568214 | + | 0.598701i | ||||
\(516\) | −6.04625 | − | 8.53227i | −0.266171 | − | 0.375612i | ||||
\(517\) | 0.100911i | 0.00443805i | ||||||||
\(518\) | 10.9238 | + | 5.64756i | 0.479966 | + | 0.248139i | ||||
\(519\) | 13.1537i | 0.577384i | ||||||||
\(520\) | −3.66135 | + | 5.12935i | −0.160561 | + | 0.224937i | ||||
\(521\) | − | 31.9555i | − | 1.39999i | −0.714146 | − | 0.699997i | \(-0.753185\pi\) | ||
0.714146 | − | 0.699997i | \(-0.246815\pi\) | |||||||
\(522\) | 2.71431 | − | 5.25018i | 0.118802 | − | 0.229794i | ||||
\(523\) | 24.3222i | 1.06354i | 0.846890 | + | 0.531768i | \(0.178472\pi\) | ||||
−0.846890 | + | 0.531768i | \(0.821528\pi\) | |||||||
\(524\) | −15.6189 | − | 2.66343i | −0.682317 | − | 0.116352i | ||||
\(525\) | 3.92695 | + | 3.53669i | 0.171386 | + | 0.154354i | ||||
\(526\) | 12.5191 | + | 6.47231i | 0.545860 | + | 0.282206i | ||||
\(527\) | −10.2698 | + | 10.2698i | −0.447359 | + | 0.447359i | ||||
\(528\) | 2.25318 | + | 4.69322i | 0.0980572 | + | 0.204246i | ||||
\(529\) | − | 22.5810i | − | 0.981784i | ||||||
\(530\) | 5.33371 | + | 15.3526i | 0.231682 | + | 0.666876i | ||||
\(531\) | −2.30403 | − | 2.30403i | −0.0999862 | − | 0.0999862i | ||||
\(532\) | 2.52353 | − | 1.78826i | 0.109409 | − | 0.0775310i | ||||
\(533\) | 5.68011 | 0.246033 | ||||||||
\(534\) | −7.74261 | − | 24.3174i | −0.335056 | − | 1.05232i | ||||
\(535\) | −0.123994 | + | 0.00323946i | −0.00536073 | + | 0.000140054i | ||||
\(536\) | 15.3088 | − | 20.3037i | 0.661241 | − | 0.876988i | ||||
\(537\) | 12.2215 | − | 12.2215i | 0.527398 | − | 0.527398i | ||||
\(538\) | −12.1023 | + | 23.4090i | −0.521767 | + | 1.00923i | ||||
\(539\) | 5.41404 | + | 5.41404i | 0.233199 | + | 0.233199i | ||||
\(540\) | −3.58008 | + | 2.68012i | −0.154062 | + | 0.115334i | ||||
\(541\) | 24.3708 | − | 24.3708i | 1.04778 | − | 1.04778i | 0.0489835 | − | 0.998800i | \(-0.484402\pi\) |
0.998800 | − | 0.0489835i | \(-0.0155982\pi\) | |||||||
\(542\) | 2.71015 | − | 0.862903i | 0.116411 | − | 0.0370649i | ||||
\(543\) | 7.77734 | + | 7.77734i | 0.333758 | + | 0.333758i | ||||
\(544\) | −5.39028 | − | 5.71869i | −0.231106 | − | 0.245187i | ||||
\(545\) | −2.17390 | − | 2.06320i | −0.0931197 | − | 0.0883779i | ||||
\(546\) | 1.32309 | + | 0.684027i | 0.0566229 | + | 0.0292737i | ||||
\(547\) | − | 46.2500i | − | 1.97751i | −0.149550 | − | 0.988754i | \(-0.547782\pi\) | ||
0.149550 | − | 0.988754i | \(-0.452218\pi\) | |||||||
\(548\) | 2.22691 | − | 13.0591i | 0.0951289 | − | 0.557857i | ||||
\(549\) | 10.8244 | − | 10.8244i | 0.461974 | − | 0.461974i | ||||
\(550\) | −8.38473 | − | 3.79387i | −0.357526 | − | 0.161771i | ||||
\(551\) | 6.11470 | 0.260495 | ||||||||
\(552\) | 18.9107 | − | 2.65235i | 0.804891 | − | 0.112891i | ||||
\(553\) | −6.55147 | − | 6.55147i | −0.278597 | − | 0.278597i | ||||
\(554\) | 6.94369 | − | 2.21085i | 0.295009 | − | 0.0939301i | ||||
\(555\) | −0.480449 | − | 18.3897i | −0.0203939 | − | 0.780601i | ||||
\(556\) | 4.59967 | + | 0.784362i | 0.195070 | + | 0.0332644i | ||||
\(557\) | −3.18081 | −0.134775 | −0.0673876 | − | 0.997727i | \(-0.521466\pi\) | ||||
−0.0673876 | + | 0.997727i | \(0.521466\pi\) | |||||||
\(558\) | 14.0880 | − | 4.48559i | 0.596393 | − | 0.189890i | ||||
\(559\) | 5.21008 | 0.220363 | ||||||||
\(560\) | 8.41269 | − | 4.31276i | 0.355501 | − | 0.182247i | ||||
\(561\) | 1.80810 | 0.0763382 | ||||||||
\(562\) | 19.8737 | − | 6.32775i | 0.838323 | − | 0.266920i | ||||
\(563\) | −26.5795 | −1.12019 | −0.560096 | − | 0.828427i | \(-0.689236\pi\) | ||||
−0.560096 | + | 0.828427i | \(0.689236\pi\) | |||||||
\(564\) | −0.0260665 | + | 0.152860i | −0.00109760 | + | 0.00643657i | ||||
\(565\) | −23.6850 | + | 24.9558i | −0.996434 | + | 1.04990i | ||||
\(566\) | −10.5388 | + | 3.35553i | −0.442979 | + | 0.141044i | ||||
\(567\) | 0.747384 | + | 0.747384i | 0.0313872 | + | 0.0313872i | ||||
\(568\) | 31.9387 | + | 24.0815i | 1.34012 | + | 1.01044i | ||||
\(569\) | −6.17442 | −0.258845 | −0.129423 | − | 0.991590i | \(-0.541312\pi\) | ||||
−0.129423 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(570\) | −4.16410 | − | 2.01678i | −0.174415 | − | 0.0844736i | ||||
\(571\) | −22.1640 | + | 22.1640i | −0.927533 | + | 0.927533i | −0.997546 | − | 0.0700130i | \(-0.977696\pi\) |
0.0700130 | + | 0.997546i | \(0.477696\pi\) | |||||||
\(572\) | −2.55686 | − | 0.436010i | −0.106908 | − | 0.0182305i | ||||
\(573\) | − | 18.2743i | − | 0.763419i | ||||||
\(574\) | −7.56907 | − | 3.91316i | −0.315927 | − | 0.163332i | ||||
\(575\) | −22.5908 | + | 25.0835i | −0.942100 | + | 1.04606i | ||||
\(576\) | 2.20081 | + | 7.69132i | 0.0917005 | + | 0.320472i | ||||
\(577\) | 16.5888 | + | 16.5888i | 0.690601 | + | 0.690601i | 0.962364 | − | 0.271764i | \(-0.0876068\pi\) |
−0.271764 | + | 0.962364i | \(0.587607\pi\) | |||||||
\(578\) | 20.3077 | − | 6.46593i | 0.844691 | − | 0.268947i | ||||
\(579\) | −11.3061 | + | 11.3061i | −0.469866 | + | 0.469866i | ||||
\(580\) | 18.4999 | + | 2.65953i | 0.768166 | + | 0.110431i | ||||
\(581\) | 9.23686 | + | 9.23686i | 0.383209 | + | 0.383209i | ||||
\(582\) | −1.19209 | + | 2.30582i | −0.0494139 | + | 0.0955793i | ||||
\(583\) | −4.73000 | + | 4.73000i | −0.195897 | + | 0.195897i | ||||
\(584\) | −3.53265 | − | 25.1871i | −0.146182 | − | 1.04225i | ||||
\(585\) | −0.0581916 | − | 2.22735i | −0.00240593 | − | 0.0920896i | ||||
\(586\) | 8.19997 | + | 25.7539i | 0.338738 | + | 1.06388i | ||||
\(587\) | 4.69495 | 0.193781 | 0.0968907 | − | 0.995295i | \(-0.469110\pi\) | ||||
0.0968907 | + | 0.995295i | \(0.469110\pi\) | |||||||
\(588\) | 6.80268 | + | 9.59971i | 0.280538 | + | 0.395885i | ||||
\(589\) | 10.8160 | + | 10.8160i | 0.445666 | + | 0.445666i | ||||
\(590\) | 4.49140 | − | 9.27351i | 0.184908 | − | 0.381785i | ||||
\(591\) | − | 11.1767i | − | 0.459747i | ||||||
\(592\) | −31.0480 | − | 10.9061i | −1.27607 | − | 0.448238i | ||||
\(593\) | 16.7482 | − | 16.7482i | 0.687765 | − | 0.687765i | −0.273972 | − | 0.961738i | \(-0.588338\pi\) |
0.961738 | + | 0.273972i | \(0.0883376\pi\) | |||||||
\(594\) | −1.63504 | − | 0.845304i | −0.0670864 | − | 0.0346832i | ||||
\(595\) | −0.0857514 | − | 3.28223i | −0.00351546 | − | 0.134558i | ||||
\(596\) | 5.74415 | − | 33.6849i | 0.235289 | − | 1.37979i | ||||
\(597\) | − | 18.8869i | − | 0.772989i | ||||||
\(598\) | −4.36925 | + | 8.45127i | −0.178672 | + | 0.345598i | ||||
\(599\) | 3.09289i | 0.126372i | 0.998002 | + | 0.0631860i | \(0.0201261\pi\) | ||||
−0.998002 | + | 0.0631860i | \(0.979874\pi\) | |||||||
\(600\) | −11.7212 | − | 7.91285i | −0.478516 | − | 0.323041i | ||||
\(601\) | 23.3900i | 0.954099i | 0.878876 | + | 0.477050i | \(0.158294\pi\) | ||||
−0.878876 | + | 0.477050i | \(0.841706\pi\) | |||||||
\(602\) | −6.94272 | − | 3.58934i | −0.282964 | − | 0.146291i | ||||
\(603\) | 8.99029i | 0.366113i | ||||||||
\(604\) | −20.6430 | + | 14.6284i | −0.839953 | + | 0.595219i | ||||
\(605\) | 0.543469 | + | 20.8019i | 0.0220952 | + | 0.845716i | ||||
\(606\) | −3.90477 | + | 7.55284i | −0.158620 | + | 0.306813i | ||||
\(607\) | 25.7183 | − | 25.7183i | 1.04387 | − | 1.04387i | 0.0448798 | − | 0.998992i | \(-0.485710\pi\) |
0.998992 | − | 0.0448798i | \(-0.0142905\pi\) | |||||||
\(608\) | −6.02285 | + | 5.67698i | −0.244259 | + | 0.230232i | ||||
\(609\) | − | 4.41728i | − | 0.178997i | ||||||
\(610\) | 43.5673 | + | 21.1008i | 1.76399 | + | 0.854345i | ||||
\(611\) | −0.0546292 | − | 0.0546292i | −0.00221006 | − | 0.00221006i | ||||
\(612\) | 2.73892 | + | 0.467056i | 0.110714 | + | 0.0188796i | ||||
\(613\) | 35.2830 | 1.42507 | 0.712533 | − | 0.701639i | \(-0.247548\pi\) | ||||
0.712533 | + | 0.701639i | \(0.247548\pi\) | |||||||
\(614\) | −4.43411 | + | 1.41181i | −0.178946 | + | 0.0569760i | ||||
\(615\) | 0.332900 | + | 12.7421i | 0.0134238 | + | 0.513813i | ||||
\(616\) | 3.10678 | + | 2.34249i | 0.125176 | + | 0.0943814i | ||||
\(617\) | 4.50814 | − | 4.50814i | 0.181491 | − | 0.181491i | −0.610514 | − | 0.792005i | \(-0.709037\pi\) |
0.792005 | + | 0.610514i | \(0.209037\pi\) | |||||||
\(618\) | −10.5237 | − | 5.44069i | −0.423326 | − | 0.218857i | ||||
\(619\) | 1.70323 | + | 1.70323i | 0.0684586 | + | 0.0684586i | 0.740507 | − | 0.672048i | \(-0.234585\pi\) |
−0.672048 | + | 0.740507i | \(0.734585\pi\) | |||||||
\(620\) | 28.0193 | + | 37.4279i | 1.12528 | + | 1.50314i | ||||
\(621\) | −4.77394 | + | 4.77394i | −0.191572 | + | 0.191572i | ||||
\(622\) | −4.57996 | − | 14.3844i | −0.183640 | − | 0.576763i | ||||
\(623\) | −13.4870 | − | 13.4870i | −0.540344 | − | 0.540344i | ||||
\(624\) | −3.76051 | − | 1.32094i | −0.150541 | − | 0.0528799i | ||||
\(625\) | 24.8637 | − | 2.60725i | 0.994547 | − | 0.104290i | ||||
\(626\) | 19.7891 | − | 38.2774i | 0.790933 | − | 1.52987i | ||||
\(627\) | − | 1.90427i | − | 0.0760492i | ||||||
\(628\) | 10.3013 | − | 7.29987i | 0.411068 | − | 0.291296i | ||||
\(629\) | −8.08159 | + | 8.08159i | −0.322234 | + | 0.322234i | ||||
\(630\) | −1.45693 | + | 3.00816i | −0.0580454 | + | 0.119848i | ||||
\(631\) | 16.8799 | 0.671980 | 0.335990 | − | 0.941866i | \(-0.390929\pi\) | ||||
0.335990 | + | 0.941866i | \(0.390929\pi\) | |||||||
\(632\) | 19.7969 | + | 14.9267i | 0.787479 | + | 0.593752i | ||||
\(633\) | −7.95311 | − | 7.95311i | −0.316108 | − | 0.316108i | ||||
\(634\) | −6.91805 | − | 21.7277i | −0.274751 | − | 0.862918i | ||||
\(635\) | −20.9274 | + | 22.0503i | −0.830480 | + | 0.875038i | ||||
\(636\) | −8.38684 | + | 5.94320i | −0.332560 | + | 0.235663i | ||||
\(637\) | −5.86190 | −0.232257 | ||||||||
\(638\) | 2.33379 | + | 7.32981i | 0.0923958 | + | 0.290190i | ||||
\(639\) | −14.1421 | −0.559454 | ||||||||
\(640\) | −20.6911 | + | 14.5560i | −0.817889 | + | 0.575376i | ||||
\(641\) | −36.2647 | −1.43237 | −0.716185 | − | 0.697911i | \(-0.754113\pi\) | ||||
−0.716185 | + | 0.697911i | \(0.754113\pi\) | |||||||
\(642\) | −0.0238002 | − | 0.0747499i | −0.000939319 | − | 0.00295014i | ||||
\(643\) | 43.9474 | 1.73312 | 0.866559 | − | 0.499074i | \(-0.166327\pi\) | ||||
0.866559 | + | 0.499074i | \(0.166327\pi\) | |||||||
\(644\) | 11.6445 | − | 8.25172i | 0.458859 | − | 0.325163i | ||||
\(645\) | 0.305353 | + | 11.6877i | 0.0120233 | + | 0.460203i | ||||
\(646\) | 0.872106 | + | 2.73905i | 0.0343125 | + | 0.107766i | ||||
\(647\) | −2.77825 | − | 2.77825i | −0.109224 | − | 0.109224i | 0.650382 | − | 0.759607i | \(-0.274609\pi\) |
−0.759607 | + | 0.650382i | \(0.774609\pi\) | |||||||
\(648\) | −2.25841 | − | 1.70282i | −0.0887186 | − | 0.0668931i | ||||
\(649\) | 4.24084 | 0.166468 | ||||||||
\(650\) | 6.59302 | − | 2.48531i | 0.258600 | − | 0.0974819i | ||||
\(651\) | 7.81352 | − | 7.81352i | 0.306236 | − | 0.306236i | ||||
\(652\) | −23.8782 | + | 16.9209i | −0.935141 | + | 0.662673i | ||||
\(653\) | − | 15.8532i | − | 0.620384i | −0.950674 | − | 0.310192i | \(-0.899607\pi\) | ||
0.950674 | − | 0.310192i | \(-0.100393\pi\) | |||||||
\(654\) | 0.870524 | − | 1.68382i | 0.0340402 | − | 0.0658426i | ||||
\(655\) | 12.8490 | + | 12.1947i | 0.502051 | + | 0.476486i | ||||
\(656\) | 21.5130 | + | 7.55677i | 0.839941 | + | 0.295042i | ||||
\(657\) | 6.35840 | + | 6.35840i | 0.248065 | + | 0.248065i | ||||
\(658\) | 0.0351612 | + | 0.110432i | 0.00137073 | + | 0.00430508i | ||||
\(659\) | 3.02357 | − | 3.02357i | 0.117781 | − | 0.117781i | −0.645759 | − | 0.763541i | \(-0.723459\pi\) |
0.763541 | + | 0.645759i | \(0.223459\pi\) | |||||||
\(660\) | 0.828244 | − | 5.76133i | 0.0322394 | − | 0.224259i | ||||
\(661\) | −14.5980 | − | 14.5980i | −0.567797 | − | 0.567797i | 0.363714 | − | 0.931511i | \(-0.381509\pi\) |
−0.931511 | + | 0.363714i | \(0.881509\pi\) | |||||||
\(662\) | 3.51549 | + | 1.81749i | 0.136634 | + | 0.0706386i | ||||
\(663\) | −0.978836 | + | 0.978836i | −0.0380149 | + | 0.0380149i | ||||
\(664\) | −27.9115 | − | 21.0450i | −1.08318 | − | 0.816705i | ||||
\(665\) | −3.45680 | + | 0.0903123i | −0.134049 | + | 0.00350216i | ||||
\(666\) | 11.0863 | − | 3.52984i | 0.429584 | − | 0.136779i | ||||
\(667\) | 28.2155 | 1.09251 | ||||||||
\(668\) | −14.8158 | − | 2.52648i | −0.573242 | − | 0.0977524i | ||||
\(669\) | 4.22843 | + | 4.22843i | 0.163480 | + | 0.163480i | ||||
\(670\) | −26.8553 | + | 9.32989i | −1.03751 | + | 0.360445i | ||||
\(671\) | 19.9236i | 0.769143i | ||||||||
\(672\) | 4.10107 | + | 4.35092i | 0.158202 | + | 0.167841i | ||||
\(673\) | −11.2973 | + | 11.2973i | −0.435481 | + | 0.435481i | −0.890488 | − | 0.455007i | \(-0.849637\pi\) |
0.455007 | + | 0.890488i | \(0.349637\pi\) | |||||||
\(674\) | −23.1850 | + | 44.8458i | −0.893052 | + | 1.72740i | ||||
\(675\) | 4.99318 | − | 0.261081i | 0.192188 | − | 0.0100490i | ||||
\(676\) | −19.5934 | + | 13.8846i | −0.753592 | + | 0.534021i | ||||
\(677\) | 9.23434i | 0.354905i | 0.984129 | + | 0.177452i | \(0.0567855\pi\) | ||||
−0.984129 | + | 0.177452i | \(0.943214\pi\) | |||||||
\(678\) | −19.3298 | − | 9.99336i | −0.742355 | − | 0.383793i | ||||
\(679\) | 1.94002i | 0.0744510i | ||||||||
\(680\) | 1.44721 | + | 8.66624i | 0.0554981 | + | 0.332335i | ||||
\(681\) | − | 15.7654i | − | 0.604131i | ||||||
\(682\) | −8.83722 | + | 17.0935i | −0.338395 | + | 0.654544i | ||||
\(683\) | − | 10.8971i | − | 0.416967i | −0.978026 | − | 0.208483i | \(-0.933147\pi\) | ||
0.978026 | − | 0.208483i | \(-0.0668527\pi\) | |||||||
\(684\) | 0.491897 | − | 2.88459i | 0.0188082 | − | 0.110295i | ||||
\(685\) | −10.1960 | + | 10.7431i | −0.389571 | + | 0.410473i | ||||
\(686\) | 17.1060 | + | 8.84369i | 0.653110 | + | 0.337654i | ||||
\(687\) | −0.746140 | + | 0.746140i | −0.0284670 | + | 0.0284670i | ||||
\(688\) | 19.7328 | + | 6.93144i | 0.752305 | + | 0.264259i | ||||
\(689\) | − | 5.12128i | − | 0.195105i | ||||||
\(690\) | −19.2147 | − | 9.30618i | −0.731492 | − | 0.354280i | ||||
\(691\) | −12.7458 | − | 12.7458i | −0.484873 | − | 0.484873i | 0.421811 | − | 0.906684i | \(-0.361395\pi\) |
−0.906684 | + | 0.421811i | \(0.861395\pi\) | |||||||
\(692\) | −15.2105 | − | 21.4645i | −0.578215 | − | 0.815957i | ||||
\(693\) | −1.37565 | −0.0522567 | ||||||||
\(694\) | 10.3818 | + | 32.6065i | 0.394089 | + | 1.23773i | ||||
\(695\) | −3.78394 | − | 3.59125i | −0.143533 | − | 0.136224i | ||||
\(696\) | 1.64185 | + | 11.7061i | 0.0622343 | + | 0.443717i | ||||
\(697\) | 5.59969 | − | 5.59969i | 0.212103 | − | 0.212103i | ||||
\(698\) | −2.10214 | + | 4.06609i | −0.0795673 | + | 0.153904i | ||||
\(699\) | −5.74517 | − | 5.74517i | −0.217302 | − | 0.217302i | ||||
\(700\) | −10.4978 | − | 1.23027i | −0.396778 | − | 0.0464997i | ||||
\(701\) | 28.0269 | − | 28.0269i | 1.05856 | − | 1.05856i | 0.0603853 | − | 0.998175i | \(-0.480767\pi\) |
0.998175 | − | 0.0603853i | \(-0.0192329\pi\) | |||||||
\(702\) | 1.34276 | − | 0.427532i | 0.0506792 | − | 0.0161361i | ||||
\(703\) | 8.51143 | + | 8.51143i | 0.321015 | + | 0.321015i | ||||
\(704\) | −9.10384 | − | 5.05298i | −0.343114 | − | 0.190441i | ||||
\(705\) | 0.119347 | − | 0.125751i | 0.00449488 | − | 0.00473605i | ||||
\(706\) | −17.2434 | − | 8.91474i | −0.648965 | − | 0.335511i | ||||
\(707\) | 6.35463i | 0.238991i | ||||||||
\(708\) | 6.42404 | + | 1.09546i | 0.241430 | + | 0.0411700i | ||||
\(709\) | 6.39995 | − | 6.39995i | 0.240355 | − | 0.240355i | −0.576642 | − | 0.816997i | \(-0.695637\pi\) |
0.816997 | + | 0.576642i | \(0.195637\pi\) | |||||||
\(710\) | −14.6763 | − | 42.2445i | −0.550792 | − | 1.58541i | ||||
\(711\) | −8.76588 | −0.328746 | ||||||||
\(712\) | 40.7543 | + | 30.7284i | 1.52733 | + | 1.15159i | ||||
\(713\) | 49.9091 | + | 49.9091i | 1.86911 | + | 1.86911i | ||||
\(714\) | 1.97870 | − | 0.630012i | 0.0740509 | − | 0.0235776i | ||||
\(715\) | 2.10341 | + | 1.99630i | 0.0786630 | + | 0.0746574i | ||||
\(716\) | −5.81080 | + | 34.0758i | −0.217160 | + | 1.27347i | ||||
\(717\) | 27.9736 | 1.04469 | ||||||||
\(718\) | −36.5812 | + | 11.6474i | −1.36520 | + | 0.434676i | ||||
\(719\) | 11.7136 | 0.436843 | 0.218422 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218422 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(720\) | 2.74285 | − | 8.51333i | 0.102220 | − | 0.317273i | ||||
\(721\) | −8.85420 | −0.329748 | ||||||||
\(722\) | −22.7188 | + | 7.23362i | −0.845508 | + | 0.269208i | ||||
\(723\) | −7.01072 | −0.260732 | ||||||||
\(724\) | −21.6846 | − | 3.69778i | −0.805902 | − | 0.137427i | ||||
\(725\) | −15.5272 | − | 13.9841i | −0.576665 | − | 0.519357i | ||||
\(726\) | −12.5404 | + | 3.99284i | −0.465419 | + | 0.148188i | ||||
\(727\) | −7.19783 | − | 7.19783i | −0.266953 | − | 0.266953i | 0.560918 | − | 0.827871i | \(-0.310448\pi\) |
−0.827871 | + | 0.560918i | \(0.810448\pi\) | |||||||
\(728\) | −2.95002 | + | 0.413760i | −0.109335 | + | 0.0153350i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.3949 | + | 25.5920i | −0.458755 | + | 0.947204i | ||||
\(731\) | 5.13631 | − | 5.13631i | 0.189973 | − | 0.189973i | ||||
\(732\) | −5.14653 | + | 30.1804i | −0.190221 | + | 1.11550i | ||||
\(733\) | 10.6158i | 0.392103i | 0.980594 | + | 0.196052i | \(0.0628120\pi\) | ||||
−0.980594 | + | 0.196052i | \(0.937188\pi\) | |||||||
\(734\) | −29.0921 | − | 15.0404i | −1.07381 | − | 0.555152i | ||||
\(735\) | −0.343555 | − | 13.1499i | −0.0126722 | − | 0.485043i | ||||
\(736\) | −27.7917 | + | 26.1957i | −1.02442 | + | 0.965587i | ||||
\(737\) | −8.27386 | − | 8.27386i | −0.304772 | − | 0.304772i | ||||
\(738\) | −7.68161 | + | 2.44581i | −0.282764 | + | 0.0900314i | ||||
\(739\) | 30.4725 | − | 30.4725i | 1.12095 | − | 1.12095i | 0.129349 | − | 0.991599i | \(-0.458711\pi\) |
0.991599 | − | 0.129349i | \(-0.0412888\pi\) | |||||||
\(740\) | 22.0492 | + | 29.4531i | 0.810544 | + | 1.08272i | ||||
\(741\) | 1.03090 | + | 1.03090i | 0.0378710 | + | 0.0378710i | ||||
\(742\) | −3.52816 | + | 6.82439i | −0.129523 | + | 0.250531i | ||||
\(743\) | 6.20995 | − | 6.20995i | 0.227821 | − | 0.227821i | −0.583961 | − | 0.811782i | \(-0.698498\pi\) |
0.811782 | + | 0.583961i | \(0.198498\pi\) | |||||||
\(744\) | −17.8021 | + | 23.6105i | −0.652657 | + | 0.865603i | ||||
\(745\) | −26.2999 | + | 27.7110i | −0.963555 | + | 1.01525i | ||||
\(746\) | −12.7634 | − | 40.0862i | −0.467299 | − | 1.46766i | ||||
\(747\) | 12.3589 | 0.452189 | ||||||||
\(748\) | −2.95049 | + | 2.09082i | −0.107881 | + | 0.0764480i | ||||
\(749\) | −0.0414579 | − | 0.0414579i | −0.00151484 | − | 0.00151484i | ||||
\(750\) | 5.96168 | + | 14.6444i | 0.217690 | + | 0.534738i | ||||
\(751\) | − | 11.3219i | − | 0.413143i | −0.978432 | − | 0.206571i | \(-0.933769\pi\) | ||
0.978432 | − | 0.206571i | \(-0.0662305\pi\) | |||||||
\(752\) | −0.134226 | − | 0.279582i | −0.00489470 | − | 0.0101953i | ||||
\(753\) | −5.41619 | + | 5.41619i | −0.197377 | + | 0.197377i | ||||
\(754\) | −5.23150 | − | 2.70465i | −0.190520 | − | 0.0984975i | ||||
\(755\) | 28.2774 | − | 0.738773i | 1.02912 | − | 0.0268867i | ||||
\(756\) | −2.08384 | − | 0.355348i | −0.0757885 | − | 0.0129239i | ||||
\(757\) | 11.1139i | 0.403942i | 0.979391 | + | 0.201971i | \(0.0647348\pi\) | ||||
−0.979391 | + | 0.201971i | \(0.935265\pi\) | |||||||
\(758\) | 10.1571 | − | 19.6465i | 0.368922 | − | 0.713592i | ||||
\(759\) | − | 8.78702i | − | 0.318949i | ||||||
\(760\) | 9.12717 | − | 1.52419i | 0.331077 | − | 0.0552881i | ||||
\(761\) | 4.08171i | 0.147962i | 0.997260 | + | 0.0739810i | \(0.0235704\pi\) | ||||
−0.997260 | + | 0.0739810i | \(0.976430\pi\) | |||||||
\(762\) | −17.0793 | − | 8.82987i | −0.618717 | − | 0.319873i | ||||
\(763\) | − | 1.41669i | − | 0.0512878i | ||||||
\(764\) | 21.1317 | + | 29.8203i | 0.764518 | + | 1.07886i | ||||
\(765\) | −2.25318 | − | 2.13845i | −0.0814639 | − | 0.0773156i | ||||
\(766\) | 14.9069 | − | 28.8339i | 0.538609 | − | 1.04181i | ||||
\(767\) | −2.29583 | + | 2.29583i | −0.0828975 | + | 0.0828975i | ||||
\(768\) | −12.4853 | − | 10.0059i | −0.450523 | − | 0.361057i | ||||
\(769\) | 31.6143i | 1.14004i | 0.821631 | + | 0.570020i | \(0.193065\pi\) | ||||
−0.821631 | + | 0.570020i | \(0.806935\pi\) | |||||||
\(770\) | −1.42761 | − | 4.10927i | −0.0514477 | − | 0.148088i | ||||
\(771\) | 17.0268 | + | 17.0268i | 0.613204 | + | 0.613204i | ||||
\(772\) | 5.37556 | − | 31.5235i | 0.193471 | − | 1.13455i | ||||
\(773\) | 22.3964 | 0.805542 | 0.402771 | − | 0.915301i | \(-0.368047\pi\) | ||||
0.402771 | + | 0.915301i | \(0.368047\pi\) | |||||||
\(774\) | −7.04595 | + | 2.24341i | −0.253262 | + | 0.0806378i | ||||
\(775\) | −2.72947 | − | 52.2011i | −0.0980455 | − | 1.87512i | ||||
\(776\) | −0.721083 | − | 5.14117i | −0.0258854 | − | 0.184557i | ||||
\(777\) | 6.14869 | − | 6.14869i | 0.220583 | − | 0.220583i | ||||
\(778\) | 22.4460 | + | 11.6044i | 0.804727 | + | 0.416038i | ||||
\(779\) | −5.89752 | − | 5.89752i | −0.211301 | − | 0.211301i | ||||
\(780\) | 2.67058 | + | 3.56734i | 0.0956221 | + | 0.127731i | ||||
\(781\) | 13.0151 | − | 13.0151i | 0.465719 | − | 0.465719i | ||||
\(782\) | 4.02422 | + | 12.6390i | 0.143906 | + | 0.451970i | ||||
\(783\) | −2.95516 | − | 2.95516i | −0.105609 | − | 0.105609i | ||||
\(784\) | −22.2015 | − | 7.79862i | −0.792910 | − | 0.278522i | ||||
\(785\) | −14.1110 | + | 0.368664i | −0.503644 | + | 0.0131582i | ||||
\(786\) | −5.14528 | + | 9.95232i | −0.183526 | + | 0.354987i | ||||
\(787\) | 45.2339i | 1.61242i | 0.591633 | + | 0.806208i | \(0.298484\pi\) | ||||
−0.591633 | + | 0.806208i | \(0.701516\pi\) | |||||||
\(788\) | 12.9243 | + | 18.2383i | 0.460408 | + | 0.649713i | ||||
\(789\) | 7.04662 | − | 7.04662i | 0.250866 | − | 0.250866i | ||||
\(790\) | −9.09699 | − | 26.1849i | −0.323656 | − | 0.931618i | ||||
\(791\) | −16.2632 | −0.578254 | ||||||||
\(792\) | 3.64556 | − | 0.511314i | 0.129539 | − | 0.0181687i | ||||
\(793\) | −10.7859 | − | 10.7859i | −0.383018 | − | 0.383018i | ||||
\(794\) | −2.32569 | − | 7.30435i | −0.0825356 | − | 0.259222i | ||||
\(795\) | 11.4885 | − | 0.300148i | 0.407456 | − | 0.0106452i | ||||
\(796\) | 21.8401 | + | 30.8200i | 0.774101 | + | 1.09238i | ||||
\(797\) | −33.6337 | −1.19137 | −0.595684 | − | 0.803219i | \(-0.703119\pi\) | ||||
−0.595684 | + | 0.803219i | \(0.703119\pi\) | |||||||
\(798\) | −0.663520 | − | 2.08394i | −0.0234884 | − | 0.0737706i | ||||
\(799\) | −0.107711 | −0.00381056 | ||||||||
\(800\) | 28.2770 | − | 0.641619i | 0.999743 | − | 0.0226847i | ||||
\(801\) | −18.0456 | −0.637609 | ||||||||
\(802\) | 6.75980 | + | 21.2307i | 0.238697 | + | 0.749682i | ||||
\(803\) | −11.7034 | −0.413004 | ||||||||
\(804\) | −10.3960 | − | 14.6705i | −0.366640 | − | 0.517389i | ||||
\(805\) | −15.9510 | + | 0.416735i | −0.562199 | + | 0.0146880i | ||||
\(806\) | −4.46962 | − | 14.0379i | −0.157436 | − | 0.494463i | ||||
\(807\) | 13.1762 | + | 13.1762i | 0.463823 | + | 0.463823i | ||||
\(808\) | −2.36195 | − | 16.8402i | −0.0830929 | − | 0.592435i | ||||
\(809\) | 7.75023 | 0.272483 | 0.136242 | − | 0.990676i | \(-0.456498\pi\) | ||||
0.136242 | + | 0.990676i | \(0.456498\pi\) | |||||||
\(810\) | 1.03777 | + | 2.98714i | 0.0364636 | + | 0.104958i | ||||
\(811\) | 15.5679 | − | 15.5679i | 0.546661 | − | 0.546661i | −0.378812 | − | 0.925474i | \(-0.623667\pi\) |
0.925474 | + | 0.378812i | \(0.123667\pi\) | |||||||
\(812\) | 5.10797 | + | 7.20820i | 0.179255 | + | 0.252958i | ||||
\(813\) | − | 2.01115i | − | 0.0705343i | ||||||
\(814\) | −6.95427 | + | 13.4514i | −0.243747 | + | 0.471470i | ||||
\(815\) | 32.7089 | − | 0.854552i | 1.14574 | − | 0.0299336i | ||||
\(816\) | −5.00950 | + | 2.40503i | −0.175368 | + | 0.0841929i | ||||
\(817\) | −5.40950 | − | 5.40950i | −0.189254 | − | 0.189254i | ||||
\(818\) | −13.2769 | − | 41.6990i | −0.464215 | − | 1.45797i | ||||
\(819\) | 0.744724 | − | 0.744724i | 0.0260228 | − | 0.0260228i | ||||
\(820\) | −15.2777 | − | 20.4079i | −0.533522 | − | 0.712674i | ||||
\(821\) | −25.2360 | − | 25.2360i | −0.880741 | − | 0.880741i | 0.112869 | − | 0.993610i | \(-0.463996\pi\) |
−0.993610 | + | 0.112869i | \(0.963996\pi\) | |||||||
\(822\) | −8.32119 | − | 4.30200i | −0.290235 | − | 0.150049i | ||||
\(823\) | −24.2751 | + | 24.2751i | −0.846178 | + | 0.846178i | −0.989654 | − | 0.143476i | \(-0.954172\pi\) |
0.143476 | + | 0.989654i | \(0.454172\pi\) | |||||||
\(824\) | 23.4642 | − | 3.29101i | 0.817414 | − | 0.114648i | ||||
\(825\) | −4.35500 | + | 4.83555i | −0.151622 | + | 0.168352i | ||||
\(826\) | 4.64096 | − | 1.47767i | 0.161480 | − | 0.0514147i | ||||
\(827\) | −8.03445 | −0.279385 | −0.139693 | − | 0.990195i | \(-0.544611\pi\) | ||||
−0.139693 | + | 0.990195i | \(0.544611\pi\) | |||||||
\(828\) | 2.26980 | − | 13.3106i | 0.0788810 | − | 0.462575i | ||||
\(829\) | 17.2385 | + | 17.2385i | 0.598718 | + | 0.598718i | 0.939971 | − | 0.341254i | \(-0.110852\pi\) |
−0.341254 | + | 0.939971i | \(0.610852\pi\) | |||||||
\(830\) | 12.8258 | + | 36.9179i | 0.445189 | + | 1.28144i | ||||
\(831\) | − | 5.15280i | − | 0.178749i | ||||||
\(832\) | 7.66395 | − | 2.19298i | 0.265700 | − | 0.0760279i | ||||
\(833\) | −5.77890 | + | 5.77890i | −0.200227 | + | 0.200227i | ||||
\(834\) | 1.51525 | − | 2.93089i | 0.0524689 | − | 0.101488i | ||||
\(835\) | 12.1883 | + | 11.5676i | 0.421793 | + | 0.400315i | ||||
\(836\) | 2.20202 | + | 3.10742i | 0.0761586 | + | 0.107472i | ||||
\(837\) | − | 10.4545i | − | 0.361360i | ||||||
\(838\) | −27.0730 | − | 13.9966i | −0.935221 | − | 0.483503i | ||||
\(839\) | − | 23.0026i | − | 0.794136i | −0.917789 | − | 0.397068i | \(-0.870028\pi\) | ||
0.917789 | − | 0.397068i | \(-0.129972\pi\) | |||||||
\(840\) | −1.10108 | − | 6.59350i | −0.0379908 | − | 0.227497i | ||||
\(841\) | − | 11.5340i | − | 0.397726i | ||||||
\(842\) | −13.2271 | + | 25.5847i | −0.455836 | + | 0.881706i | ||||
\(843\) | − | 14.7480i | − | 0.507947i | ||||||
\(844\) | 22.1747 | + | 3.78135i | 0.763284 | + | 0.130160i | ||||
\(845\) | 26.8395 | − | 0.701209i | 0.923308 | − | 0.0241223i | ||||
\(846\) | 0.0974017 | + | 0.0503560i | 0.00334874 | + | 0.00173128i | ||||
\(847\) | −6.95520 | + | 6.95520i | −0.238983 | + | 0.238983i | ||||
\(848\) | 6.81331 | − | 19.3964i | 0.233970 | − | 0.666077i | ||||
\(849\) | 7.82068i | 0.268405i | ||||||||
\(850\) | 4.04955 | − | 8.94980i | 0.138898 | − | 0.306975i | ||||
\(851\) | 39.2750 | + | 39.2750i | 1.34633 | + | 1.34633i | ||||
\(852\) | 23.0774 | − | 16.3534i | 0.790617 | − | 0.560258i | ||||
\(853\) | −17.9417 | −0.614312 | −0.307156 | − | 0.951659i | \(-0.599377\pi\) | ||||
−0.307156 | + | 0.951659i | \(0.599377\pi\) | |||||||
\(854\) | 6.94216 | + | 21.8034i | 0.237556 | + | 0.746098i | ||||
\(855\) | −2.25218 | + | 2.37302i | −0.0770230 | + | 0.0811556i | ||||
\(856\) | 0.125276 | + | 0.0944566i | 0.00428183 | + | 0.00322846i | ||||
\(857\) | −27.5741 | + | 27.5741i | −0.941914 | + | 0.941914i | −0.998403 | − | 0.0564890i | \(-0.982009\pi\) |
0.0564890 | + | 0.998403i | \(0.482009\pi\) | |||||||
\(858\) | −0.842295 | + | 1.62922i | −0.0287555 | + | 0.0556206i | ||||
\(859\) | −22.0003 | − | 22.0003i | −0.750640 | − | 0.750640i | 0.223959 | − | 0.974599i | \(-0.428102\pi\) |
−0.974599 | + | 0.223959i | \(0.928102\pi\) | |||||||
\(860\) | −14.0135 | − | 18.7191i | −0.477856 | − | 0.638317i | ||||
\(861\) | −4.26039 | + | 4.26039i | −0.145194 | + | 0.145194i | ||||
\(862\) | −6.02775 | + | 1.91922i | −0.205306 | + | 0.0653689i | ||||
\(863\) | −16.4456 | − | 16.4456i | −0.559814 | − | 0.559814i | 0.369440 | − | 0.929254i | \(-0.379549\pi\) |
−0.929254 | + | 0.369440i | \(0.879549\pi\) | |||||||
\(864\) | 5.65438 | + | 0.167155i | 0.192366 | + | 0.00568673i | ||||
\(865\) | 0.768171 | + | 29.4026i | 0.0261186 | + | 0.999718i | ||||
\(866\) | 37.0582 | + | 19.1589i | 1.25929 | + | 0.651045i | ||||
\(867\) | − | 15.0700i | − | 0.511806i | ||||||
\(868\) | −3.71498 | + | 21.7855i | −0.126095 | + | 0.739447i | ||||
\(869\) | 8.06733 | − | 8.06733i | 0.273665 | − | 0.273665i | ||||
\(870\) | 5.76070 | − | 11.8943i | 0.195306 | − | 0.403254i | ||||
\(871\) | 8.95830 | 0.303540 | ||||||||
\(872\) | 0.526569 | + | 3.75433i | 0.0178319 | + | 0.127138i | ||||
\(873\) | 1.29787 | + | 1.29787i | 0.0439263 | + | 0.0439263i | ||||
\(874\) | 13.3112 | − | 4.23826i | 0.450259 | − | 0.143361i | ||||
\(875\) | 8.98447 | + | 7.67626i | 0.303731 | + | 0.259505i | ||||
\(876\) | −17.7284 | − | 3.02314i | −0.598986 | − | 0.102142i | ||||
\(877\) | 6.59281 | 0.222623 | 0.111312 | − | 0.993786i | \(-0.464495\pi\) | ||||
0.111312 | + | 0.993786i | \(0.464495\pi\) | |||||||
\(878\) | −0.347360 | + | 0.110599i | −0.0117228 | + | 0.00373252i | ||||
\(879\) | 19.1115 | 0.644617 | ||||||||
\(880\) | 5.31063 | + | 10.3592i | 0.179021 | + | 0.349208i | ||||
\(881\) | 22.1698 | 0.746920 | 0.373460 | − | 0.927646i | \(-0.378171\pi\) | ||||
0.373460 | + | 0.927646i | \(0.378171\pi\) | |||||||
\(882\) | 7.92745 | − | 2.52408i | 0.266931 | − | 0.0849902i | ||||
\(883\) | 38.7205 | 1.30305 | 0.651524 | − | 0.758628i | \(-0.274130\pi\) | ||||
0.651524 | + | 0.758628i | \(0.274130\pi\) | |||||||
\(884\) | 0.465394 | − | 2.72917i | 0.0156529 | − | 0.0917920i | ||||
\(885\) | −5.28476 | − | 5.01565i | −0.177645 | − | 0.168599i | ||||
\(886\) | 37.4991 | − | 11.9396i | 1.25981 | − | 0.401120i | ||||
\(887\) | −25.2413 | − | 25.2413i | −0.847518 | − | 0.847518i | 0.142305 | − | 0.989823i | \(-0.454549\pi\) |
−0.989823 | + | 0.142305i | \(0.954549\pi\) | |||||||
\(888\) | −14.0090 | + | 18.5798i | −0.470111 | + | 0.623497i | ||||
\(889\) | −14.3698 | −0.481947 | ||||||||
\(890\) | −18.7272 | − | 53.9047i | −0.627738 | − | 1.80689i | ||||
\(891\) | −0.920311 | + | 0.920311i | −0.0308316 | + | 0.0308316i | ||||
\(892\) | −11.7896 | − | 2.01043i | −0.394746 | − | 0.0673142i | ||||
\(893\) | 0.113440i | 0.00379613i | ||||||||
\(894\) | −21.4639 | − | 11.0967i | −0.717860 | − | 0.371129i | ||||
\(895\) | 26.6051 | − | 28.0326i | 0.889310 | − | 0.937025i | ||||
\(896\) | −11.7234 | − | 2.35760i | −0.391652 | − | 0.0787619i | ||||
\(897\) | 4.75695 | + | 4.75695i | 0.158830 | + | 0.158830i | ||||
\(898\) | −9.86641 | + | 3.14144i | −0.329246 | + | 0.104831i | ||||
\(899\) | −30.8947 | + | 30.8947i | −1.03040 | + | 1.03040i | ||||
\(900\) | −7.84605 | + | 6.19996i | −0.261535 | + | 0.206665i | ||||
\(901\) | −5.04877 | − | 5.04877i | −0.168199 | − | 0.168199i | ||||
\(902\) | 4.81857 | − | 9.32037i | 0.160441 | − | 0.310335i | ||||
\(903\) | −3.90784 | + | 3.90784i | −0.130045 | + | 0.130045i | ||||
\(904\) | 43.0986 | − | 6.04486i | 1.43344 | − | 0.201049i | ||||
\(905\) | 17.8389 | + | 16.9305i | 0.592986 | + | 0.562790i | ||||
\(906\) | 5.42773 | + | 17.0470i | 0.180324 | + | 0.566350i | ||||
\(907\) | 9.44895 | 0.313747 | 0.156874 | − | 0.987619i | \(-0.449858\pi\) | ||||
0.156874 | + | 0.987619i | \(0.449858\pi\) | |||||||
\(908\) | 18.2305 | + | 25.7262i | 0.605000 | + | 0.853755i | ||||
\(909\) | 4.25125 | + | 4.25125i | 0.141005 | + | 0.141005i | ||||
\(910\) | 2.99745 | + | 1.45174i | 0.0993646 | + | 0.0481248i | ||||
\(911\) | − | 36.1798i | − | 1.19869i | −0.800490 | − | 0.599346i | \(-0.795427\pi\) | ||
0.800490 | − | 0.599346i | \(-0.204573\pi\) | |||||||
\(912\) | 2.53295 | + | 5.27594i | 0.0838742 | + | 0.174704i | ||||
\(913\) | −11.3740 | + | 11.3740i | −0.376426 | + | 0.376426i | ||||
\(914\) | 23.4446 | + | 12.1207i | 0.775478 | + | 0.400917i | ||||
\(915\) | 23.5637 | − | 24.8280i | 0.778992 | − | 0.820788i | ||||
\(916\) | 0.354757 | − | 2.08037i | 0.0117215 | − | 0.0687374i | ||||
\(917\) | 8.37345i | 0.276516i | ||||||||
\(918\) | 0.902270 | − | 1.74523i | 0.0297794 | − | 0.0576011i | ||||
\(919\) | 45.3587i | 1.49624i | 0.663561 | + | 0.748122i | \(0.269044\pi\) | ||||
−0.663561 | + | 0.748122i | \(0.730956\pi\) | |||||||
\(920\) | 42.1162 | − | 7.03318i | 1.38853 | − | 0.231877i | ||||
\(921\) | 3.29048i | 0.108425i | ||||||||
\(922\) | −34.8269 | − | 18.0053i | −1.14696 | − | 0.592973i | ||||
\(923\) | 14.0918i | 0.463837i | ||||||||
\(924\) | 2.24481 | − | 1.59075i | 0.0738489 | − | 0.0523318i | ||||
\(925\) | −2.14790 | − | 41.0786i | −0.0706226 | − | 1.35066i | ||||
\(926\) | 15.8825 | − | 30.7209i | 0.521932 | − | 1.00955i | ||||
\(927\) | −5.92346 | + | 5.92346i | −0.194552 | + | 0.194552i | ||||
\(928\) | −16.2156 | − | 17.2036i | −0.532305 | − | 0.564735i | ||||
\(929\) | − | 0.551101i | − | 0.0180810i | −0.999959 | − | 0.00904052i | \(-0.997122\pi\) | ||
0.999959 | − | 0.00904052i | \(-0.00287773\pi\) | |||||||
\(930\) | 31.2291 | − | 10.8494i | 1.02404 | − | 0.355766i | ||||
\(931\) | 6.08626 | + | 6.08626i | 0.199469 | + | 0.199469i | ||||
\(932\) | 16.0186 | + | 2.73158i | 0.524706 | + | 0.0894758i | ||||
\(933\) | −10.6744 | −0.349466 | ||||||||
\(934\) | 42.2992 | − | 13.4679i | 1.38407 | − | 0.440685i | ||||
\(935\) | 4.04166 | − | 0.105592i | 0.132176 | − | 0.00345324i | ||||
\(936\) | −1.69676 | + | 2.25037i | −0.0554603 | + | 0.0735556i | ||||
\(937\) | −10.4271 | + | 10.4271i | −0.340639 | + | 0.340639i | −0.856607 | − | 0.515969i | \(-0.827432\pi\) |
0.515969 | + | 0.856607i | \(0.327432\pi\) | |||||||
\(938\) | −11.9374 | − | 6.17157i | −0.389771 | − | 0.201509i | ||||
\(939\) | −21.5451 | − | 21.5451i | −0.703098 | − | 0.703098i | ||||
\(940\) | −0.0493397 | + | 0.343211i | −0.00160928 | + | 0.0111943i | ||||
\(941\) | 7.44442 | − | 7.44442i | 0.242681 | − | 0.242681i | −0.575277 | − | 0.817958i | \(-0.695106\pi\) |
0.817958 | + | 0.575277i | \(0.195106\pi\) | |||||||
\(942\) | −2.70856 | − | 8.50684i | −0.0882496 | − | 0.277168i | ||||
\(943\) | −27.2134 | − | 27.2134i | −0.886190 | − | 0.886190i | ||||
\(944\) | −11.7496 | + | 5.64091i | −0.382417 | + | 0.183596i | ||||
\(945\) | 1.71428 | + | 1.62698i | 0.0557655 | + | 0.0529258i | ||||
\(946\) | 4.41983 | − | 8.54911i | 0.143701 | − | 0.277955i | ||||
\(947\) | 15.8341i | 0.514539i | 0.966340 | + | 0.257270i | \(0.0828229\pi\) | ||||
−0.966340 | + | 0.257270i | \(0.917177\pi\) | |||||||
\(948\) | 14.3043 | − | 10.1365i | 0.464582 | − | 0.329219i | ||||
\(949\) | 6.33577 | − | 6.33577i | 0.205668 | − | 0.205668i | ||||
\(950\) | −9.42581 | − | 4.26493i | −0.305814 | − | 0.138373i | ||||
\(951\) | −16.1238 | −0.522850 | ||||||||
\(952\) | −2.50035 | + | 3.31615i | −0.0810368 | + | 0.107477i | ||||
\(953\) | 14.8928 | + | 14.8928i | 0.482424 | + | 0.482424i | 0.905905 | − | 0.423481i | \(-0.139192\pi\) |
−0.423481 | + | 0.905905i | \(0.639192\pi\) | |||||||
\(954\) | 2.20518 | + | 6.92586i | 0.0713953 | + | 0.224233i | ||||
\(955\) | −1.06721 | − | 40.8486i | −0.0345341 | − | 1.32183i | ||||
\(956\) | −45.6477 | + | 32.3475i | −1.47635 | + | 1.04619i | ||||
\(957\) | 5.43934 | 0.175829 | ||||||||
\(958\) | 4.49925 | + | 14.1309i | 0.145364 | + | 0.456549i | ||||
\(959\) | −7.00109 | −0.226077 | ||||||||
\(960\) | 5.36865 | + | 17.0639i | 0.173273 | + | 0.550736i | ||||
\(961\) | −78.2963 | −2.52569 | ||||||||
\(962\) | −3.51728 | − | 11.0468i | −0.113402 | − | 0.356164i | ||||
\(963\) | −0.0554707 | −0.00178752 | ||||||||
\(964\) | 11.4402 | − | 8.10693i | 0.368465 | − | 0.261107i | ||||
\(965\) | −24.6123 | + | 25.9329i | −0.792300 | + | 0.834809i | ||||
\(966\) | −3.06173 | − | 9.61607i | −0.0985097 | − | 0.309392i | ||||
\(967\) | −27.8728 | − | 27.8728i | −0.896330 | − | 0.896330i | 0.0987795 | − | 0.995109i | \(-0.468506\pi\) |
−0.995109 | + | 0.0987795i | \(0.968506\pi\) | |||||||
\(968\) | 15.8465 | − | 21.0169i | 0.509327 | − | 0.675508i | ||||
\(969\) | 2.03260 | 0.0652966 | ||||||||
\(970\) | −2.53003 | + | 5.22383i | −0.0812345 | + | 0.167727i | ||||
\(971\) | −30.0958 | + | 30.0958i | −0.965819 | + | 0.965819i | −0.999435 | − | 0.0336155i | \(-0.989298\pi\) |
0.0336155 | + | 0.999435i | \(0.489298\pi\) | |||||||
\(972\) | −1.63182 | + | 1.15636i | −0.0523406 | + | 0.0370903i | ||||
\(973\) | − | 2.46593i | − | 0.0790540i | ||||||
\(974\) | −4.34220 | + | 8.39895i | −0.139133 | + | 0.269120i | ||||
\(975\) | −0.260152 | − | 4.97541i | −0.00833154 | − | 0.159341i | ||||
\(976\) | −26.5012 | − | 55.2001i | −0.848284 | − | 1.76691i | ||||
\(977\) | −9.03427 | − | 9.03427i | −0.289032 | − | 0.289032i | 0.547666 | − | 0.836697i | \(-0.315517\pi\) |
−0.836697 | + | 0.547666i | \(0.815517\pi\) | |||||||
\(978\) | 6.27835 | + | 19.7186i | 0.200760 | + | 0.630532i | ||||
\(979\) | 16.6075 | − | 16.6075i | 0.530780 | − | 0.530780i | ||||
\(980\) | 15.7667 | + | 21.0610i | 0.503648 | + | 0.672769i | ||||
\(981\) | −0.947769 | − | 0.947769i | −0.0302599 | − | 0.0302599i | ||||
\(982\) | −5.34543 | − | 2.76355i | −0.170579 | − | 0.0881884i | ||||
\(983\) | 24.5191 | − | 24.5191i | 0.782039 | − | 0.782039i | −0.198135 | − | 0.980175i | \(-0.563489\pi\) |
0.980175 | + | 0.198135i | \(0.0634886\pi\) | |||||||
\(984\) | 9.70675 | − | 12.8738i | 0.309440 | − | 0.410403i | ||||
\(985\) | −0.652712 | − | 24.9833i | −0.0207971 | − | 0.796034i | ||||
\(986\) | −7.82378 | + | 2.49107i | −0.249160 | + | 0.0793319i | ||||
\(987\) | 0.0819496 | 0.00260848 | ||||||||
\(988\) | −2.87433 | − | 0.490147i | −0.0914445 | − | 0.0155936i | ||||
\(989\) | −24.9615 | − | 24.9615i | −0.793728 | − | 0.793728i | ||||
\(990\) | −3.70418 | − | 1.79403i | −0.117726 | − | 0.0570179i | ||||
\(991\) | 25.8872i | 0.822334i | 0.911560 | + | 0.411167i | \(0.134879\pi\) | ||||
−0.911560 | + | 0.411167i | \(0.865121\pi\) | |||||||
\(992\) | 1.74752 | − | 59.1137i | 0.0554838 | − | 1.87686i | ||||
\(993\) | 1.97876 | − | 1.97876i | 0.0627940 | − | 0.0627940i | ||||
\(994\) | 9.70815 | − | 18.7781i | 0.307924 | − | 0.595605i | ||||
\(995\) | −1.10298 | − | 42.2180i | −0.0349670 | − | 1.33840i | ||||
\(996\) | −20.1675 | + | 14.2914i | −0.639032 | + | 0.452840i | ||||
\(997\) | 16.7546i | 0.530624i | 0.964163 | + | 0.265312i | \(0.0854750\pi\) | ||||
−0.964163 | + | 0.265312i | \(0.914525\pi\) | |||||||
\(998\) | −15.5591 | − | 8.04392i | −0.492513 | − | 0.254626i | ||||
\(999\) | − | 8.22694i | − | 0.260289i |
(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 | 240.2.y.e.187.5 | yes | 16 | |
3.2 | odd | 2 | 720.2.z.f.667.4 | 16 | |||
4.3 | odd | 2 | 960.2.y.e.847.8 | 16 | |||
5.3 | odd | 4 | 240.2.bc.e.43.8 | yes | 16 | ||
8.3 | odd | 2 | 1920.2.y.j.1567.1 | 16 | |||
8.5 | even | 2 | 1920.2.y.i.1567.1 | 16 | |||
15.8 | even | 4 | 720.2.bd.f.523.1 | 16 | |||
16.3 | odd | 4 | 240.2.bc.e.67.8 | yes | 16 | ||
16.5 | even | 4 | 1920.2.bc.j.607.3 | 16 | |||
16.11 | odd | 4 | 1920.2.bc.i.607.3 | 16 | |||
16.13 | even | 4 | 960.2.bc.e.367.6 | 16 | |||
20.3 | even | 4 | 960.2.bc.e.463.6 | 16 | |||
40.3 | even | 4 | 1920.2.bc.j.1183.3 | 16 | |||
40.13 | odd | 4 | 1920.2.bc.i.1183.3 | 16 | |||
48.35 | even | 4 | 720.2.bd.f.307.1 | 16 | |||
80.3 | even | 4 | inner | 240.2.y.e.163.5 | ✓ | 16 | |
80.13 | odd | 4 | 960.2.y.e.943.8 | 16 | |||
80.43 | even | 4 | 1920.2.y.i.223.1 | 16 | |||
80.53 | odd | 4 | 1920.2.y.j.223.1 | 16 | |||
240.83 | odd | 4 | 720.2.z.f.163.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.y.e.163.5 | ✓ | 16 | 80.3 | even | 4 | inner | |
240.2.y.e.187.5 | yes | 16 | 1.1 | even | 1 | trivial | |
240.2.bc.e.43.8 | yes | 16 | 5.3 | odd | 4 | ||
240.2.bc.e.67.8 | yes | 16 | 16.3 | odd | 4 | ||
720.2.z.f.163.4 | 16 | 240.83 | odd | 4 | |||
720.2.z.f.667.4 | 16 | 3.2 | odd | 2 | |||
720.2.bd.f.307.1 | 16 | 48.35 | even | 4 | |||
720.2.bd.f.523.1 | 16 | 15.8 | even | 4 | |||
960.2.y.e.847.8 | 16 | 4.3 | odd | 2 | |||
960.2.y.e.943.8 | 16 | 80.13 | odd | 4 | |||
960.2.bc.e.367.6 | 16 | 16.13 | even | 4 | |||
960.2.bc.e.463.6 | 16 | 20.3 | even | 4 | |||
1920.2.y.i.223.1 | 16 | 80.43 | even | 4 | |||
1920.2.y.i.1567.1 | 16 | 8.5 | even | 2 | |||
1920.2.y.j.223.1 | 16 | 80.53 | odd | 4 | |||
1920.2.y.j.1567.1 | 16 | 8.3 | odd | 2 | |||
1920.2.bc.i.607.3 | 16 | 16.11 | odd | 4 | |||
1920.2.bc.i.1183.3 | 16 | 40.13 | odd | 4 | |||
1920.2.bc.j.607.3 | 16 | 16.5 | even | 4 | |||
1920.2.bc.j.1183.3 | 16 | 40.3 | even | 4 |