Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Root | \(-0.788594 - 2.42704i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.v.729.4 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.06456 | + | 1.49999i | 1.45987 | + | 1.06066i | 0.983397 | + | 0.181466i | \(0.0580841\pi\) |
0.476470 | + | 0.879190i | \(0.341916\pi\) | |||||||
\(3\) | −0.126882 | + | 0.390502i | −0.0732553 | + | 0.225457i | −0.980980 | − | 0.194110i | \(-0.937818\pi\) |
0.907724 | + | 0.419567i | \(0.137818\pi\) | |||||||
\(4\) | 1.39441 | + | 4.29156i | 0.697206 | + | 2.14578i | ||||
\(5\) | −2.77410 | + | 2.01550i | −1.24062 | + | 0.901360i | −0.997639 | − | 0.0686724i | \(-0.978124\pi\) |
−0.242976 | + | 0.970032i | \(0.578124\pi\) | |||||||
\(6\) | −0.847707 | + | 0.615895i | −0.346075 | + | 0.251438i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −1.98127 | + | 6.09772i | −0.700485 | + | 2.15587i | ||||
\(9\) | 2.29066 | + | 1.66426i | 0.763553 | + | 0.554754i | ||||
\(10\) | −8.75055 | −2.76717 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.85279 | −0.534854 | ||||||||
\(13\) | −1.75964 | − | 1.27845i | −0.488036 | − | 0.354579i | 0.316393 | − | 0.948628i | \(-0.397528\pi\) |
−0.804428 | + | 0.594050i | \(0.797528\pi\) | |||||||
\(14\) | 0.788594 | − | 2.42704i | 0.210760 | − | 0.648654i | ||||
\(15\) | −0.435075 | − | 1.33902i | −0.112336 | − | 0.345734i | ||||
\(16\) | −5.93578 | + | 4.31259i | −1.48394 | + | 1.07815i | ||||
\(17\) | −3.65445 | + | 2.65511i | −0.886334 | + | 0.643960i | −0.934920 | − | 0.354859i | \(-0.884529\pi\) |
0.0485852 | + | 0.998819i | \(0.484529\pi\) | |||||||
\(18\) | 2.23283 | + | 6.87195i | 0.526283 | + | 1.61973i | ||||
\(19\) | 0.748999 | − | 2.30518i | 0.171832 | − | 0.528845i | −0.827643 | − | 0.561256i | \(-0.810318\pi\) |
0.999475 | + | 0.0324108i | \(0.0103185\pi\) | |||||||
\(20\) | −12.5179 | − | 9.09477i | −2.79908 | − | 2.03365i | ||||
\(21\) | 0.410598 | 0.0895999 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.648403 | 0.135201 | 0.0676006 | − | 0.997712i | \(-0.478466\pi\) | ||||
0.0676006 | + | 0.997712i | \(0.478466\pi\) | |||||||
\(24\) | −2.12979 | − | 1.54738i | −0.434741 | − | 0.315858i | ||||
\(25\) | 2.08830 | − | 6.42713i | 0.417660 | − | 1.28543i | ||||
\(26\) | −1.71522 | − | 5.27889i | −0.336382 | − | 1.03528i | ||||
\(27\) | −1.93708 | + | 1.40737i | −0.372792 | + | 0.270849i | ||||
\(28\) | 3.65062 | − | 2.65233i | 0.689902 | − | 0.501243i | ||||
\(29\) | 0.387183 | + | 1.19163i | 0.0718981 | + | 0.221280i | 0.980548 | − | 0.196279i | \(-0.0628858\pi\) |
−0.908650 | + | 0.417559i | \(0.862886\pi\) | |||||||
\(30\) | 1.11029 | − | 3.41711i | 0.202710 | − | 0.623876i | ||||
\(31\) | 6.50406 | + | 4.72548i | 1.16816 | + | 0.848721i | 0.990788 | − | 0.135422i | \(-0.0432390\pi\) |
0.177376 | + | 0.984143i | \(0.443239\pi\) | |||||||
\(32\) | −5.90061 | −1.04309 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.5275 | −1.97695 | ||||||||
\(35\) | 2.77410 | + | 2.01550i | 0.468909 | + | 0.340682i | ||||
\(36\) | −3.94815 | + | 12.1512i | −0.658025 | + | 2.02519i | ||||
\(37\) | 1.54919 | + | 4.76792i | 0.254686 | + | 0.783842i | 0.993891 | + | 0.110362i | \(0.0352011\pi\) |
−0.739206 | + | 0.673480i | \(0.764799\pi\) | |||||||
\(38\) | 5.00411 | − | 3.63570i | 0.811775 | − | 0.589789i | ||||
\(39\) | 0.722504 | − | 0.524930i | 0.115693 | − | 0.0840561i | ||||
\(40\) | −6.79373 | − | 20.9090i | −1.07418 | − | 3.30600i | ||||
\(41\) | 0.810151 | − | 2.49339i | 0.126524 | − | 0.389402i | −0.867651 | − | 0.497173i | \(-0.834371\pi\) |
0.994176 | + | 0.107771i | \(0.0343714\pi\) | |||||||
\(42\) | 0.847707 | + | 0.615895i | 0.130804 | + | 0.0950347i | ||||
\(43\) | 1.46138 | 0.222858 | 0.111429 | − | 0.993772i | \(-0.464457\pi\) | ||||
0.111429 | + | 0.993772i | \(0.464457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.70884 | −1.44731 | ||||||||
\(46\) | 1.33867 | + | 0.972600i | 0.197376 | + | 0.143402i | ||||
\(47\) | −1.55757 | + | 4.79369i | −0.227194 | + | 0.699232i | 0.770867 | + | 0.636996i | \(0.219823\pi\) |
−0.998061 | + | 0.0622362i | \(0.980177\pi\) | |||||||
\(48\) | −0.930935 | − | 2.86512i | −0.134369 | − | 0.413545i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 13.9521 | − | 10.1368i | 1.97312 | − | 1.43356i | ||||
\(51\) | −0.573144 | − | 1.76396i | −0.0802562 | − | 0.247003i | ||||
\(52\) | 3.03289 | − | 9.33427i | 0.420586 | − | 1.29443i | ||||
\(53\) | −10.8392 | − | 7.87516i | −1.48888 | − | 1.08174i | −0.974556 | − | 0.224143i | \(-0.928042\pi\) |
−0.514327 | − | 0.857594i | \(-0.671958\pi\) | |||||||
\(54\) | −6.11028 | −0.831504 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.41153 | 0.856776 | ||||||||
\(57\) | 0.805144 | + | 0.584971i | 0.106644 | + | 0.0774813i | ||||
\(58\) | −0.988069 | + | 3.04096i | −0.129740 | + | 0.399298i | ||||
\(59\) | 2.37009 | + | 7.29440i | 0.308560 | + | 0.949649i | 0.978325 | + | 0.207076i | \(0.0663948\pi\) |
−0.669765 | + | 0.742573i | \(0.733605\pi\) | |||||||
\(60\) | 5.13982 | − | 3.73430i | 0.663548 | − | 0.482096i | ||||
\(61\) | 11.5971 | − | 8.42580i | 1.48486 | − | 1.07881i | 0.508908 | − | 0.860821i | \(-0.330049\pi\) |
0.975950 | − | 0.217992i | \(-0.0699508\pi\) | |||||||
\(62\) | 6.33987 | + | 19.5121i | 0.805164 | + | 2.47804i | ||||
\(63\) | 0.874954 | − | 2.69283i | 0.110234 | − | 0.339265i | ||||
\(64\) | −0.310639 | − | 0.225693i | −0.0388299 | − | 0.0282116i | ||||
\(65\) | 7.45814 | 0.925068 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.22696 | 0.760744 | 0.380372 | − | 0.924834i | \(-0.375796\pi\) | ||||
0.380372 | + | 0.924834i | \(0.375796\pi\) | |||||||
\(68\) | −16.4904 | − | 11.9810i | −1.99975 | − | 1.45291i | ||||
\(69\) | −0.0822705 | + | 0.253203i | −0.00990421 | + | 0.0304820i | ||||
\(70\) | 2.70407 | + | 8.32227i | 0.323198 | + | 0.994701i | ||||
\(71\) | −3.42211 | + | 2.48631i | −0.406130 | + | 0.295071i | −0.772033 | − | 0.635582i | \(-0.780760\pi\) |
0.365903 | + | 0.930653i | \(0.380760\pi\) | |||||||
\(72\) | −14.6866 | + | 10.6704i | −1.73083 | + | 1.25752i | ||||
\(73\) | 1.83098 | + | 5.63517i | 0.214300 | + | 0.659547i | 0.999203 | + | 0.0399280i | \(0.0127128\pi\) |
−0.784903 | + | 0.619619i | \(0.787287\pi\) | |||||||
\(74\) | −3.95345 | + | 12.1675i | −0.459579 | + | 1.41444i | ||||
\(75\) | 2.24484 | + | 1.63097i | 0.259212 | + | 0.188328i | ||||
\(76\) | 10.9372 | 1.25459 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.27905 | 0.258051 | ||||||||
\(79\) | 7.89858 | + | 5.73865i | 0.888660 | + | 0.645649i | 0.935528 | − | 0.353252i | \(-0.114924\pi\) |
−0.0468685 | + | 0.998901i | \(0.514924\pi\) | |||||||
\(80\) | 7.77440 | − | 23.9271i | 0.869204 | − | 2.67514i | ||||
\(81\) | 2.32106 | + | 7.14349i | 0.257895 | + | 0.793721i | ||||
\(82\) | 5.41268 | − | 3.93254i | 0.597730 | − | 0.434277i | ||||
\(83\) | −6.77759 | + | 4.92421i | −0.743937 | + | 0.540502i | −0.893942 | − | 0.448183i | \(-0.852071\pi\) |
0.150004 | + | 0.988685i | \(0.452071\pi\) | |||||||
\(84\) | 0.572543 | + | 1.76211i | 0.0624695 | + | 0.192261i | ||||
\(85\) | 4.78643 | − | 14.7311i | 0.519161 | − | 1.59781i | ||||
\(86\) | 3.01711 | + | 2.19206i | 0.325344 | + | 0.236376i | ||||
\(87\) | −0.514460 | −0.0551559 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.76249 | 0.504823 | 0.252412 | − | 0.967620i | \(-0.418776\pi\) | ||||
0.252412 | + | 0.967620i | \(0.418776\pi\) | |||||||
\(90\) | −20.0445 | − | 14.5632i | −2.11288 | − | 1.53510i | ||||
\(91\) | −0.672122 | + | 2.06858i | −0.0704575 | + | 0.216846i | ||||
\(92\) | 0.904140 | + | 2.78266i | 0.0942631 | + | 0.290112i | ||||
\(93\) | −2.67056 | + | 1.94027i | −0.276924 | + | 0.201197i | ||||
\(94\) | −10.4062 | + | 7.56055i | −1.07332 | + | 0.779812i | ||||
\(95\) | 2.56830 | + | 7.90441i | 0.263502 | + | 0.810976i | ||||
\(96\) | 0.748680 | − | 2.30420i | 0.0764119 | − | 0.235172i | ||||
\(97\) | 7.04306 | + | 5.11708i | 0.715115 | + | 0.519561i | 0.884820 | − | 0.465934i | \(-0.154281\pi\) |
−0.169705 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(98\) | −2.55194 | −0.257785 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 30.4943 | 3.04943 | ||||||||
\(101\) | −4.67177 | − | 3.39424i | −0.464858 | − | 0.337739i | 0.330576 | − | 0.943779i | \(-0.392757\pi\) |
−0.795434 | + | 0.606040i | \(0.792757\pi\) | |||||||
\(102\) | 1.46263 | − | 4.50152i | 0.144822 | − | 0.445716i | ||||
\(103\) | −1.43414 | − | 4.41383i | −0.141310 | − | 0.434908i | 0.855208 | − | 0.518285i | \(-0.173429\pi\) |
−0.996518 | + | 0.0833771i | \(0.973429\pi\) | |||||||
\(104\) | 11.2820 | − | 8.19683i | 1.10629 | − | 0.803765i | ||||
\(105\) | −1.13904 | + | 0.827562i | −0.111159 | + | 0.0807617i | ||||
\(106\) | −10.5656 | − | 32.5176i | −1.02622 | − | 3.15839i | ||||
\(107\) | 1.24287 | − | 3.82517i | 0.120153 | − | 0.369793i | −0.872834 | − | 0.488018i | \(-0.837720\pi\) |
0.992987 | + | 0.118224i | \(0.0377202\pi\) | |||||||
\(108\) | −8.74091 | − | 6.35064i | −0.841095 | − | 0.611091i | ||||
\(109\) | 6.14762 | 0.588835 | 0.294418 | − | 0.955677i | \(-0.404874\pi\) | ||||
0.294418 | + | 0.955677i | \(0.404874\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.05845 | −0.195379 | ||||||||
\(112\) | 5.93578 | + | 4.31259i | 0.560878 | + | 0.407502i | ||||
\(113\) | −0.765858 | + | 2.35707i | −0.0720458 | + | 0.221734i | −0.980595 | − | 0.196043i | \(-0.937191\pi\) |
0.908549 | + | 0.417777i | \(0.137191\pi\) | |||||||
\(114\) | 0.784818 | + | 2.41542i | 0.0735050 | + | 0.226225i | ||||
\(115\) | −1.79873 | + | 1.30686i | −0.167733 | + | 0.121865i | ||||
\(116\) | −4.57404 | + | 3.32324i | −0.424689 | + | 0.308555i | ||||
\(117\) | −1.90305 | − | 5.85699i | −0.175937 | − | 0.541479i | ||||
\(118\) | −6.04834 | + | 18.6149i | −0.556795 | + | 1.71364i | ||||
\(119\) | 3.65445 | + | 2.65511i | 0.335003 | + | 0.243394i | ||||
\(120\) | 9.02699 | 0.824048 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 36.5817 | 3.31195 | ||||||||
\(123\) | 0.870880 | + | 0.632732i | 0.0785246 | + | 0.0570515i | ||||
\(124\) | −11.2103 | + | 34.5018i | −1.00672 | + | 3.09835i | ||||
\(125\) | 1.86267 | + | 5.73272i | 0.166602 | + | 0.512750i | ||||
\(126\) | 5.84563 | − | 4.24710i | 0.520770 | − | 0.378361i | ||||
\(127\) | −5.62588 | + | 4.08744i | −0.499216 | + | 0.362702i | −0.808718 | − | 0.588197i | \(-0.799838\pi\) |
0.309501 | + | 0.950899i | \(0.399838\pi\) | |||||||
\(128\) | 3.34398 | + | 10.2917i | 0.295569 | + | 0.909668i | ||||
\(129\) | −0.185423 | + | 0.570672i | −0.0163255 | + | 0.0502449i | ||||
\(130\) | 15.3978 | + | 11.1872i | 1.35048 | + | 0.981179i | ||||
\(131\) | 20.9388 | 1.82943 | 0.914715 | − | 0.404101i | \(-0.132415\pi\) | ||||
0.914715 | + | 0.404101i | \(0.132415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.42381 | −0.210171 | ||||||||
\(134\) | 12.8560 | + | 9.34040i | 1.11059 | + | 0.806888i | ||||
\(135\) | 2.53710 | − | 7.80839i | 0.218359 | − | 0.672039i | ||||
\(136\) | −8.94969 | − | 27.5443i | −0.767430 | − | 2.36191i | ||||
\(137\) | −7.39154 | + | 5.37027i | −0.631502 | + | 0.458813i | −0.856920 | − | 0.515449i | \(-0.827625\pi\) |
0.225419 | + | 0.974262i | \(0.427625\pi\) | |||||||
\(138\) | −0.549655 | + | 0.399348i | −0.0467898 | + | 0.0339947i | ||||
\(139\) | −3.32251 | − | 10.2256i | −0.281811 | − | 0.867326i | −0.987336 | − | 0.158641i | \(-0.949289\pi\) |
0.705525 | − | 0.708685i | \(-0.250711\pi\) | |||||||
\(140\) | −4.78140 | + | 14.7156i | −0.404102 | + | 1.24370i | ||||
\(141\) | −1.67432 | − | 1.21647i | −0.141003 | − | 0.102445i | ||||
\(142\) | −10.7946 | −0.905865 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −20.7741 | −1.73118 | ||||||||
\(145\) | −3.47581 | − | 2.52533i | −0.288651 | − | 0.209717i | ||||
\(146\) | −4.67255 | + | 14.3806i | −0.386703 | + | 1.19015i | ||||
\(147\) | −0.126882 | − | 0.390502i | −0.0104650 | − | 0.0322081i | ||||
\(148\) | −18.3016 | + | 13.2969i | −1.50438 | + | 1.09300i | ||||
\(149\) | 8.70132 | − | 6.32188i | 0.712840 | − | 0.517908i | −0.171249 | − | 0.985228i | \(-0.554780\pi\) |
0.884089 | + | 0.467319i | \(0.154780\pi\) | |||||||
\(150\) | 2.18817 | + | 6.73449i | 0.178663 | + | 0.549869i | ||||
\(151\) | 2.36838 | − | 7.28911i | 0.192736 | − | 0.593179i | −0.807260 | − | 0.590196i | \(-0.799050\pi\) |
0.999996 | − | 0.00298318i | \(-0.000949578\pi\) | |||||||
\(152\) | 12.5724 | + | 9.13437i | 1.01976 | + | 0.740896i | ||||
\(153\) | −12.7899 | −1.03400 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.5671 | −2.21425 | ||||||||
\(156\) | 3.26024 | + | 2.36870i | 0.261028 | + | 0.189648i | ||||
\(157\) | 5.67016 | − | 17.4510i | 0.452528 | − | 1.39274i | −0.421485 | − | 0.906835i | \(-0.638491\pi\) |
0.874013 | − | 0.485903i | \(-0.161509\pi\) | |||||||
\(158\) | 7.69918 | + | 23.6956i | 0.612514 | + | 1.88512i | ||||
\(159\) | 4.45057 | − | 3.23353i | 0.352953 | − | 0.256435i | ||||
\(160\) | 16.3689 | − | 11.8927i | 1.29407 | − | 0.940200i | ||||
\(161\) | −0.200367 | − | 0.616668i | −0.0157912 | − | 0.0486002i | ||||
\(162\) | −5.92321 | + | 18.2298i | −0.465371 | + | 1.43227i | ||||
\(163\) | −0.305473 | − | 0.221939i | −0.0239265 | − | 0.0173836i | 0.575758 | − | 0.817620i | \(-0.304707\pi\) |
−0.599684 | + | 0.800237i | \(0.704707\pi\) | |||||||
\(164\) | 11.8302 | 0.923784 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.3791 | −1.65934 | ||||||||
\(167\) | −0.0923401 | − | 0.0670890i | −0.00714549 | − | 0.00519150i | 0.584207 | − | 0.811605i | \(-0.301406\pi\) |
−0.591352 | + | 0.806413i | \(0.701406\pi\) | |||||||
\(168\) | −0.813506 | + | 2.50371i | −0.0627634 | + | 0.193166i | ||||
\(169\) | −2.55533 | − | 7.86451i | −0.196564 | − | 0.604962i | ||||
\(170\) | 31.9785 | − | 23.2337i | 2.45264 | − | 1.78194i | ||||
\(171\) | 5.55212 | − | 4.03385i | 0.424581 | − | 0.308476i | ||||
\(172\) | 2.03777 | + | 6.27160i | 0.155378 | + | 0.478205i | ||||
\(173\) | 4.11024 | − | 12.6500i | 0.312496 | − | 0.961763i | −0.664277 | − | 0.747486i | \(-0.731260\pi\) |
0.976773 | − | 0.214277i | \(-0.0687395\pi\) | |||||||
\(174\) | −1.06214 | − | 0.771686i | −0.0805203 | − | 0.0585014i | ||||
\(175\) | −6.75788 | −0.510848 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.14920 | −0.236708 | ||||||||
\(178\) | 9.83248 | + | 7.14371i | 0.736975 | + | 0.535444i | ||||
\(179\) | 3.50456 | − | 10.7859i | 0.261943 | − | 0.806177i | −0.730439 | − | 0.682978i | \(-0.760685\pi\) |
0.992382 | − | 0.123199i | \(-0.0393154\pi\) | |||||||
\(180\) | −13.5381 | − | 41.6660i | −1.00907 | − | 3.10560i | ||||
\(181\) | −9.51149 | + | 6.91050i | −0.706984 | + | 0.513654i | −0.882199 | − | 0.470876i | \(-0.843938\pi\) |
0.175216 | + | 0.984530i | \(0.443938\pi\) | |||||||
\(182\) | −4.49050 | + | 3.26254i | −0.332858 | + | 0.241835i | ||||
\(183\) | 1.81883 | + | 5.59778i | 0.134452 | + | 0.413800i | ||||
\(184\) | −1.28466 | + | 3.95378i | −0.0947065 | + | 0.291476i | ||||
\(185\) | −13.9074 | − | 10.1043i | −1.02249 | − | 0.742883i | ||||
\(186\) | −8.42394 | −0.617673 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −22.7443 | −1.65880 | ||||||||
\(189\) | 1.93708 | + | 1.40737i | 0.140902 | + | 0.102371i | ||||
\(190\) | −6.55415 | + | 20.1716i | −0.475488 | + | 1.46340i | ||||
\(191\) | −6.96351 | − | 21.4315i | −0.503862 | − | 1.55073i | −0.802676 | − | 0.596416i | \(-0.796591\pi\) |
0.298814 | − | 0.954311i | \(-0.403409\pi\) | |||||||
\(192\) | 0.127548 | − | 0.0926690i | 0.00920498 | − | 0.00668781i | ||||
\(193\) | 2.78563 | − | 2.02388i | 0.200514 | − | 0.145682i | −0.482997 | − | 0.875622i | \(-0.660452\pi\) |
0.683511 | + | 0.729940i | \(0.260452\pi\) | |||||||
\(194\) | 6.86526 | + | 21.1291i | 0.492897 | + | 1.51698i | ||||
\(195\) | −0.946302 | + | 2.91242i | −0.0677661 | + | 0.208563i | ||||
\(196\) | −3.65062 | − | 2.65233i | −0.260758 | − | 0.189452i | ||||
\(197\) | 2.18213 | 0.155470 | 0.0777352 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777352 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.33434 | 0.165477 | 0.0827386 | − | 0.996571i | \(-0.473633\pi\) | ||||
0.0827386 | + | 0.996571i | \(0.473633\pi\) | |||||||
\(200\) | 35.0534 | + | 25.4678i | 2.47865 | + | 1.80084i | ||||
\(201\) | −0.790088 | + | 2.43164i | −0.0557285 | + | 0.171515i | ||||
\(202\) | −4.55383 | − | 14.0152i | −0.320406 | − | 0.986109i | ||||
\(203\) | 1.01366 | − | 0.736466i | 0.0711449 | − | 0.0516898i | ||||
\(204\) | 6.77092 | − | 4.91936i | 0.474059 | − | 0.344424i | ||||
\(205\) | 2.77799 | + | 8.54977i | 0.194023 | + | 0.597142i | ||||
\(206\) | 3.65985 | − | 11.2639i | 0.254994 | − | 0.784790i | ||||
\(207\) | 1.48527 | + | 1.07911i | 0.103233 | + | 0.0750034i | ||||
\(208\) | 15.9583 | 1.10651 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.59296 | −0.247938 | ||||||||
\(211\) | −11.0575 | − | 8.03377i | −0.761233 | − | 0.553068i | 0.138056 | − | 0.990424i | \(-0.455915\pi\) |
−0.899288 | + | 0.437357i | \(0.855915\pi\) | |||||||
\(212\) | 18.6824 | − | 57.4984i | 1.28311 | − | 3.94901i | ||||
\(213\) | −0.536706 | − | 1.65181i | −0.0367745 | − | 0.113180i | ||||
\(214\) | 8.30373 | − | 6.03301i | 0.567631 | − | 0.412408i | ||||
\(215\) | −4.05402 | + | 2.94541i | −0.276482 | + | 0.200876i | ||||
\(216\) | −4.74389 | − | 14.6002i | −0.322781 | − | 0.993417i | ||||
\(217\) | 2.48433 | − | 7.64599i | 0.168647 | − | 0.519043i | ||||
\(218\) | 12.6922 | + | 9.22140i | 0.859622 | + | 0.624552i | ||||
\(219\) | −2.43286 | −0.164398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.82495 | 0.660897 | ||||||||
\(222\) | −4.24980 | − | 3.08766i | −0.285228 | − | 0.207230i | ||||
\(223\) | −1.65900 | + | 5.10589i | −0.111095 | + | 0.341916i | −0.991113 | − | 0.133026i | \(-0.957531\pi\) |
0.880017 | + | 0.474941i | \(0.157531\pi\) | |||||||
\(224\) | 1.82339 | + | 5.61181i | 0.121830 | + | 0.374955i | ||||
\(225\) | 15.4800 | − | 11.2469i | 1.03200 | − | 0.749792i | ||||
\(226\) | −5.11675 | + | 3.71754i | −0.340361 | + | 0.247287i | ||||
\(227\) | −3.27959 | − | 10.0935i | −0.217674 | − | 0.669932i | −0.998953 | − | 0.0457497i | \(-0.985432\pi\) |
0.781279 | − | 0.624182i | \(-0.214568\pi\) | |||||||
\(228\) | −1.38774 | + | 4.27101i | −0.0919050 | + | 0.282855i | ||||
\(229\) | −18.3169 | − | 13.3080i | −1.21042 | − | 0.879419i | −0.215148 | − | 0.976581i | \(-0.569023\pi\) |
−0.995269 | + | 0.0971622i | \(0.969023\pi\) | |||||||
\(230\) | −5.67388 | −0.374125 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.03333 | −0.527414 | ||||||||
\(233\) | 11.9926 | + | 8.71311i | 0.785659 | + | 0.570815i | 0.906672 | − | 0.421836i | \(-0.138614\pi\) |
−0.121013 | + | 0.992651i | \(0.538614\pi\) | |||||||
\(234\) | 4.85648 | − | 14.9467i | 0.317478 | − | 0.977097i | ||||
\(235\) | −5.34086 | − | 16.4375i | −0.348399 | − | 1.07226i | ||||
\(236\) | −27.9994 | + | 20.3428i | −1.82261 | + | 1.32420i | ||||
\(237\) | −3.24314 | + | 2.35628i | −0.210665 | + | 0.153057i | ||||
\(238\) | 3.56219 | + | 10.9633i | 0.230903 | + | 0.710646i | ||||
\(239\) | −0.605456 | + | 1.86340i | −0.0391637 | + | 0.120534i | −0.968727 | − | 0.248129i | \(-0.920184\pi\) |
0.929563 | + | 0.368663i | \(0.120184\pi\) | |||||||
\(240\) | 8.35717 | + | 6.07184i | 0.539453 | + | 0.391935i | ||||
\(241\) | −0.790252 | −0.0509046 | −0.0254523 | − | 0.999676i | \(-0.508103\pi\) | ||||
−0.0254523 | + | 0.999676i | \(0.508103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.2671 | −0.658638 | ||||||||
\(244\) | 52.3309 | + | 38.0207i | 3.35015 | + | 2.43402i | ||||
\(245\) | 1.05961 | − | 3.26115i | 0.0676961 | − | 0.208347i | ||||
\(246\) | 0.848895 | + | 2.61263i | 0.0541236 | + | 0.166575i | ||||
\(247\) | −4.26503 | + | 3.09873i | −0.271377 | + | 0.197167i | ||||
\(248\) | −41.7010 | + | 30.2975i | −2.64801 | + | 1.92389i | ||||
\(249\) | −1.06296 | − | 3.27146i | −0.0673624 | − | 0.207320i | ||||
\(250\) | −4.75343 | + | 14.6296i | −0.300633 | + | 0.925255i | ||||
\(251\) | 16.6782 | + | 12.1174i | 1.05272 | + | 0.764845i | 0.972728 | − | 0.231950i | \(-0.0745107\pi\) |
0.0799915 | + | 0.996796i | \(0.474511\pi\) | |||||||
\(252\) | 12.7765 | 0.804842 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −17.7461 | −1.11349 | ||||||||
\(255\) | 5.14522 | + | 3.73822i | 0.322206 | + | 0.234096i | ||||
\(256\) | −8.77095 | + | 26.9942i | −0.548185 | + | 1.68714i | ||||
\(257\) | 1.60059 | + | 4.92610i | 0.0998419 | + | 0.307282i | 0.988485 | − | 0.151317i | \(-0.0483515\pi\) |
−0.888643 | + | 0.458599i | \(0.848351\pi\) | |||||||
\(258\) | −1.23882 | + | 0.900057i | −0.0771257 | + | 0.0560351i | ||||
\(259\) | 4.05584 | − | 2.94674i | 0.252018 | − | 0.183101i | ||||
\(260\) | 10.3997 | + | 32.0070i | 0.644963 | + | 1.98499i | ||||
\(261\) | −1.09627 | + | 3.37398i | −0.0678577 | + | 0.208844i | ||||
\(262\) | 43.2295 | + | 31.4080i | 2.67072 | + | 1.94039i | ||||
\(263\) | −23.1920 | −1.43008 | −0.715041 | − | 0.699083i | \(-0.753592\pi\) | ||||
−0.715041 | + | 0.699083i | \(0.753592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45.9415 | 2.82217 | ||||||||
\(266\) | −5.00411 | − | 3.63570i | −0.306822 | − | 0.222919i | ||||
\(267\) | −0.604274 | + | 1.85976i | −0.0369810 | + | 0.113816i | ||||
\(268\) | 8.68294 | + | 26.7234i | 0.530395 | + | 1.63239i | ||||
\(269\) | −15.0962 | + | 10.9681i | −0.920434 | + | 0.668735i | −0.943632 | − | 0.330996i | \(-0.892615\pi\) |
0.0231978 | + | 0.999731i | \(0.492615\pi\) | |||||||
\(270\) | 16.9505 | − | 12.3153i | 1.03158 | − | 0.749485i | ||||
\(271\) | −9.34120 | − | 28.7493i | −0.567437 | − | 1.74639i | −0.660596 | − | 0.750742i | \(-0.729696\pi\) |
0.0931585 | − | 0.995651i | \(-0.470304\pi\) | |||||||
\(272\) | 10.2416 | − | 31.5203i | 0.620987 | − | 1.91120i | ||||
\(273\) | −0.722504 | − | 0.524930i | −0.0437279 | − | 0.0317702i | ||||
\(274\) | −23.3157 | −1.40855 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.20135 | −0.0723129 | ||||||||
\(277\) | 10.9153 | + | 7.93044i | 0.655838 | + | 0.476494i | 0.865255 | − | 0.501332i | \(-0.167157\pi\) |
−0.209417 | + | 0.977826i | \(0.567157\pi\) | |||||||
\(278\) | 8.47885 | − | 26.0952i | 0.508528 | − | 1.56509i | ||||
\(279\) | 7.03416 | + | 21.6489i | 0.421124 | + | 1.29609i | ||||
\(280\) | −17.7862 | + | 12.9224i | −1.06293 | + | 0.772264i | ||||
\(281\) | 6.55523 | − | 4.76266i | 0.391052 | − | 0.284116i | −0.374834 | − | 0.927092i | \(-0.622300\pi\) |
0.765887 | + | 0.642976i | \(0.222300\pi\) | |||||||
\(282\) | −1.63205 | − | 5.02294i | −0.0971874 | − | 0.299112i | ||||
\(283\) | −3.08744 | + | 9.50217i | −0.183529 | + | 0.564845i | −0.999920 | − | 0.0126548i | \(-0.995972\pi\) |
0.816391 | + | 0.577500i | \(0.195972\pi\) | |||||||
\(284\) | −15.4420 | − | 11.2193i | −0.916313 | − | 0.665740i | ||||
\(285\) | −3.41256 | −0.202143 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.62170 | −0.154754 | ||||||||
\(288\) | −13.5163 | − | 9.82015i | −0.796455 | − | 0.578658i | ||||
\(289\) | 1.05209 | − | 3.23800i | 0.0618877 | − | 0.190471i | ||||
\(290\) | −3.38807 | − | 10.4274i | −0.198954 | − | 0.612318i | ||||
\(291\) | −2.89187 | + | 2.10107i | −0.169524 | + | 0.123167i | ||||
\(292\) | −21.6305 | + | 15.7155i | −1.26583 | + | 0.919680i | ||||
\(293\) | −9.49598 | − | 29.2256i | −0.554761 | − | 1.70738i | −0.696574 | − | 0.717485i | \(-0.745293\pi\) |
0.141813 | − | 0.989894i | \(-0.454707\pi\) | |||||||
\(294\) | 0.323795 | − | 0.996539i | 0.0188841 | − | 0.0581193i | ||||
\(295\) | −21.2767 | − | 15.4585i | −1.23878 | − | 0.900026i | ||||
\(296\) | −32.1429 | −1.86827 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.4472 | 1.58997 | ||||||||
\(299\) | −1.14095 | − | 0.828952i | −0.0659831 | − | 0.0479395i | ||||
\(300\) | −3.86918 | + | 11.9081i | −0.223387 | + | 0.687515i | ||||
\(301\) | −0.451591 | − | 1.38986i | −0.0260293 | − | 0.0801099i | ||||
\(302\) | 15.8233 | − | 11.4963i | 0.910528 | − | 0.661537i | ||||
\(303\) | 1.91822 | − | 1.39367i | 0.110199 | − | 0.0800641i | ||||
\(304\) | 5.49542 | + | 16.9132i | 0.315184 | + | 0.970037i | ||||
\(305\) | −15.1894 | + | 46.7480i | −0.869740 | + | 2.67678i | ||||
\(306\) | −26.4056 | − | 19.1848i | −1.50951 | − | 1.09672i | ||||
\(307\) | 20.0677 | 1.14532 | 0.572661 | − | 0.819792i | \(-0.305911\pi\) | ||||
0.572661 | + | 0.819792i | \(0.305911\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.90558 | 0.108405 | ||||||||
\(310\) | −56.9141 | − | 41.3505i | −3.23251 | − | 2.34855i | ||||
\(311\) | −7.25146 | + | 22.3177i | −0.411193 | + | 1.26552i | 0.504420 | + | 0.863458i | \(0.331706\pi\) |
−0.915612 | + | 0.402062i | \(0.868294\pi\) | |||||||
\(312\) | 1.76940 | + | 5.44566i | 0.100173 | + | 0.308300i | ||||
\(313\) | 11.8707 | − | 8.62457i | 0.670971 | − | 0.487489i | −0.199379 | − | 0.979922i | \(-0.563892\pi\) |
0.870350 | + | 0.492433i | \(0.163892\pi\) | |||||||
\(314\) | 37.8828 | − | 27.5234i | 2.13785 | − | 1.55324i | ||||
\(315\) | 3.00020 | + | 9.23365i | 0.169042 | + | 0.520257i | ||||
\(316\) | −13.6139 | + | 41.8993i | −0.765841 | + | 2.35702i | ||||
\(317\) | −14.6035 | − | 10.6101i | −0.820215 | − | 0.595921i | 0.0965592 | − | 0.995327i | \(-0.469216\pi\) |
−0.916774 | + | 0.399406i | \(0.869216\pi\) | |||||||
\(318\) | 14.0388 | 0.787255 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.31663 | 0.0736018 | ||||||||
\(321\) | 1.33604 | + | 0.970689i | 0.0745704 | + | 0.0541786i | ||||
\(322\) | 0.511326 | − | 1.57370i | 0.0284951 | − | 0.0876989i | ||||
\(323\) | 3.38334 | + | 10.4128i | 0.188254 | + | 0.579386i | ||||
\(324\) | −27.4202 | + | 19.9219i | −1.52334 | + | 1.10677i | ||||
\(325\) | −11.8914 | + | 8.63963i | −0.659618 | + | 0.479240i | ||||
\(326\) | −0.297761 | − | 0.916414i | −0.0164915 | − | 0.0507555i | ||||
\(327\) | −0.780022 | + | 2.40066i | −0.0431353 | + | 0.132757i | ||||
\(328\) | 13.5989 | + | 9.88016i | 0.750872 | + | 0.545540i | ||||
\(329\) | 5.04039 | 0.277886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8300 | −1.08996 | −0.544979 | − | 0.838450i | \(-0.683462\pi\) | ||||
−0.544979 | + | 0.838450i | \(0.683462\pi\) | |||||||
\(332\) | −30.5833 | − | 22.2200i | −1.67847 | − | 1.21948i | ||||
\(333\) | −4.38640 | + | 13.4999i | −0.240373 | + | 0.739792i | ||||
\(334\) | −0.0900090 | − | 0.277019i | −0.00492507 | − | 0.0151578i | ||||
\(335\) | −17.2742 | + | 12.5505i | −0.943791 | + | 0.685704i | ||||
\(336\) | −2.43722 | + | 1.77074i | −0.132961 | + | 0.0966020i | ||||
\(337\) | 6.02842 | + | 18.5536i | 0.328389 | + | 1.01068i | 0.969888 | + | 0.243553i | \(0.0783130\pi\) |
−0.641499 | + | 0.767124i | \(0.721687\pi\) | |||||||
\(338\) | 6.52107 | − | 20.0698i | 0.354699 | − | 1.09165i | ||||
\(339\) | −0.823267 | − | 0.598138i | −0.0447137 | − | 0.0324864i | ||||
\(340\) | 69.8936 | 3.79051 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 17.5135 | 0.947020 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −2.89539 | + | 8.91109i | −0.156109 | + | 0.480454i | ||||
\(345\) | −0.282104 | − | 0.868226i | −0.0151880 | − | 0.0467437i | ||||
\(346\) | 27.4608 | − | 19.9515i | 1.47630 | − | 1.07260i | ||||
\(347\) | −23.0126 | + | 16.7196i | −1.23538 | + | 0.897556i | −0.997282 | − | 0.0736845i | \(-0.976524\pi\) |
−0.238099 | + | 0.971241i | \(0.576524\pi\) | |||||||
\(348\) | −0.717368 | − | 2.20783i | −0.0384550 | − | 0.118352i | ||||
\(349\) | −6.20717 | + | 19.1037i | −0.332262 | + | 1.02260i | 0.635793 | + | 0.771860i | \(0.280673\pi\) |
−0.968055 | + | 0.250738i | \(0.919327\pi\) | |||||||
\(350\) | −13.9521 | − | 10.1368i | −0.745770 | − | 0.541834i | ||||
\(351\) | 5.20782 | 0.277973 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.99700 | 0.478862 | 0.239431 | − | 0.970913i | \(-0.423039\pi\) | ||||
0.239431 | + | 0.970913i | \(0.423039\pi\) | |||||||
\(354\) | −6.50172 | − | 4.72378i | −0.345563 | − | 0.251066i | ||||
\(355\) | 4.48212 | − | 13.7946i | 0.237886 | − | 0.732139i | ||||
\(356\) | 6.64088 | + | 20.4385i | 0.351966 | + | 1.08324i | ||||
\(357\) | −1.50051 | + | 1.09019i | −0.0794155 | + | 0.0576987i | ||||
\(358\) | 23.4142 | − | 17.0114i | 1.23748 | − | 0.899081i | ||||
\(359\) | −2.92516 | − | 9.00271i | −0.154384 | − | 0.475145i | 0.843714 | − | 0.536793i | \(-0.180364\pi\) |
−0.998098 | + | 0.0616480i | \(0.980364\pi\) | |||||||
\(360\) | 19.2358 | − | 59.2018i | 1.01382 | − | 3.12021i | ||||
\(361\) | 10.6185 | + | 7.71476i | 0.558866 | + | 0.406040i | ||||
\(362\) | −30.0028 | −1.57691 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.81464 | −0.514427 | ||||||||
\(365\) | −16.4370 | − | 11.9422i | −0.860353 | − | 0.625083i | ||||
\(366\) | −4.64155 | + | 14.2852i | −0.242618 | + | 0.746700i | ||||
\(367\) | 0.424939 | + | 1.30783i | 0.0221817 | + | 0.0682681i | 0.961535 | − | 0.274684i | \(-0.0885732\pi\) |
−0.939353 | + | 0.342952i | \(0.888573\pi\) | |||||||
\(368\) | −3.84877 | + | 2.79630i | −0.200631 | + | 0.145767i | ||||
\(369\) | 6.00543 | − | 4.36320i | 0.312630 | − | 0.227139i | ||||
\(370\) | −13.5563 | − | 41.7220i | −0.704758 | − | 2.16902i | ||||
\(371\) | −4.14022 | + | 12.7423i | −0.214949 | + | 0.661546i | ||||
\(372\) | −12.0506 | − | 8.75531i | −0.624797 | − | 0.453942i | ||||
\(373\) | −5.07180 | −0.262608 | −0.131304 | − | 0.991342i | \(-0.541916\pi\) | ||||
−0.131304 | + | 0.991342i | \(0.541916\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.47498 | −0.127807 | ||||||||
\(376\) | −26.1447 | − | 18.9952i | −1.34831 | − | 0.979603i | ||||
\(377\) | 0.842136 | − | 2.59183i | 0.0433722 | − | 0.133486i | ||||
\(378\) | 1.88818 | + | 5.81123i | 0.0971176 | + | 0.298897i | ||||
\(379\) | 22.6381 | − | 16.4475i | 1.16284 | − | 0.844853i | 0.172706 | − | 0.984973i | \(-0.444749\pi\) |
0.990135 | + | 0.140120i | \(0.0447489\pi\) | |||||||
\(380\) | −30.3410 | + | 22.0440i | −1.55646 | + | 1.13083i | ||||
\(381\) | −0.882333 | − | 2.71554i | −0.0452033 | − | 0.139121i | ||||
\(382\) | 17.7705 | − | 54.6919i | 0.909216 | − | 2.79828i | ||||
\(383\) | 25.3065 | + | 18.3862i | 1.29310 | + | 0.939493i | 0.999863 | − | 0.0165464i | \(-0.00526712\pi\) |
0.293238 | + | 0.956039i | \(0.405267\pi\) | |||||||
\(384\) | −4.44323 | −0.226742 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.78692 | 0.447243 | ||||||||
\(387\) | 3.34752 | + | 2.43212i | 0.170164 | + | 0.123631i | ||||
\(388\) | −12.1393 | + | 37.3610i | −0.616281 | + | 1.89672i | ||||
\(389\) | 3.29214 | + | 10.1322i | 0.166918 | + | 0.513721i | 0.999173 | − | 0.0406730i | \(-0.0129502\pi\) |
−0.832255 | + | 0.554394i | \(0.812950\pi\) | |||||||
\(390\) | −6.32231 | + | 4.59343i | −0.320143 | + | 0.232597i | ||||
\(391\) | −2.36956 | + | 1.72158i | −0.119834 | + | 0.0870642i | ||||
\(392\) | −1.98127 | − | 6.09772i | −0.100069 | − | 0.307982i | ||||
\(393\) | −2.65675 | + | 8.17664i | −0.134015 | + | 0.412457i | ||||
\(394\) | 4.50515 | + | 3.27319i | 0.226966 | + | 0.164901i | ||||
\(395\) | −33.4777 | −1.68445 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1755 | 1.06277 | 0.531385 | − | 0.847131i | \(-0.321672\pi\) | ||||
0.531385 | + | 0.847131i | \(0.321672\pi\) | |||||||
\(398\) | 4.81940 | + | 3.50150i | 0.241575 | + | 0.175514i | ||||
\(399\) | 0.307538 | − | 0.946503i | 0.0153961 | − | 0.0473844i | ||||
\(400\) | 15.3219 | + | 47.1560i | 0.766095 | + | 2.35780i | ||||
\(401\) | 27.2727 | − | 19.8148i | 1.36194 | − | 0.989504i | 0.363616 | − | 0.931549i | \(-0.381542\pi\) |
0.998319 | − | 0.0579548i | \(-0.0184579\pi\) | |||||||
\(402\) | −5.27864 | + | 3.83515i | −0.263274 | + | 0.191280i | ||||
\(403\) | −5.40350 | − | 16.6303i | −0.269168 | − | 0.828413i | ||||
\(404\) | 8.05220 | − | 24.7821i | 0.400612 | − | 1.23296i | ||||
\(405\) | −20.8366 | − | 15.1386i | −1.03538 | − | 0.752245i | ||||
\(406\) | 3.19746 | 0.158687 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 11.8917 | 0.588725 | ||||||||
\(409\) | −2.13907 | − | 1.55413i | −0.105770 | − | 0.0768466i | 0.533643 | − | 0.845710i | \(-0.320823\pi\) |
−0.639413 | + | 0.768863i | \(0.720823\pi\) | |||||||
\(410\) | −7.08927 | + | 21.8185i | −0.350114 | + | 1.07754i | ||||
\(411\) | −1.15925 | − | 3.56780i | −0.0571815 | − | 0.175987i | ||||
\(412\) | 16.9424 | − | 12.3094i | 0.834694 | − | 0.606441i | ||||
\(413\) | 6.20498 | − | 4.50818i | 0.305327 | − | 0.221833i | ||||
\(414\) | 1.44777 | + | 4.45579i | 0.0711542 | + | 0.218990i | ||||
\(415\) | 8.87697 | − | 27.3205i | 0.435753 | − | 1.34111i | ||||
\(416\) | 10.3829 | + | 7.54365i | 0.509065 | + | 0.369858i | ||||
\(417\) | 4.41470 | 0.216189 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.0757 | 1.61585 | 0.807926 | − | 0.589284i | \(-0.200590\pi\) | ||||
0.807926 | + | 0.589284i | \(0.200590\pi\) | |||||||
\(420\) | −5.13982 | − | 3.73430i | −0.250797 | − | 0.182215i | ||||
\(421\) | 10.4083 | − | 32.0334i | 0.507268 | − | 1.56121i | −0.289656 | − | 0.957131i | \(-0.593541\pi\) |
0.796924 | − | 0.604079i | \(-0.206459\pi\) | |||||||
\(422\) | −10.7784 | − | 33.1725i | −0.524684 | − | 1.61481i | ||||
\(423\) | −11.5458 | + | 8.38852i | −0.561376 | + | 0.407864i | ||||
\(424\) | 69.4960 | − | 50.4918i | 3.37503 | − | 2.45210i | ||||
\(425\) | 9.43316 | + | 29.0323i | 0.457576 | + | 1.40827i | ||||
\(426\) | 1.36964 | − | 4.21533i | 0.0663594 | − | 0.204233i | ||||
\(427\) | −11.5971 | − | 8.42580i | −0.561224 | − | 0.407753i | ||||
\(428\) | 18.1490 | 0.877266 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.7879 | −0.616686 | ||||||||
\(431\) | −24.0703 | − | 17.4881i | −1.15943 | − | 0.842374i | −0.169722 | − | 0.985492i | \(-0.554287\pi\) |
−0.989706 | + | 0.143118i | \(0.954287\pi\) | |||||||
\(432\) | 5.42866 | − | 16.7077i | 0.261187 | − | 0.803850i | ||||
\(433\) | −7.15404 | − | 22.0179i | −0.343801 | − | 1.05811i | −0.962222 | − | 0.272265i | \(-0.912227\pi\) |
0.618421 | − | 0.785847i | \(-0.287773\pi\) | |||||||
\(434\) | 16.5980 | − | 12.0591i | 0.796729 | − | 0.578858i | ||||
\(435\) | 1.42716 | − | 1.03689i | 0.0684272 | − | 0.0497153i | ||||
\(436\) | 8.57231 | + | 26.3829i | 0.410539 | + | 1.26351i | ||||
\(437\) | 0.485653 | − | 1.49469i | 0.0232319 | − | 0.0715005i | ||||
\(438\) | −5.02281 | − | 3.64928i | −0.239999 | − | 0.174369i | ||||
\(439\) | −15.8166 | −0.754884 | −0.377442 | − | 0.926033i | \(-0.623196\pi\) | ||||
−0.377442 | + | 0.926033i | \(0.623196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.83141 | −0.134829 | ||||||||
\(442\) | 20.2842 | + | 14.7374i | 0.964823 | + | 0.700985i | ||||
\(443\) | −3.09841 | + | 9.53592i | −0.147210 | + | 0.453065i | −0.997289 | − | 0.0735904i | \(-0.976554\pi\) |
0.850079 | + | 0.526656i | \(0.176554\pi\) | |||||||
\(444\) | −2.87032 | − | 8.83395i | −0.136220 | − | 0.419241i | ||||
\(445\) | −13.2116 | + | 9.59882i | −0.626292 | + | 0.455027i | ||||
\(446\) | −11.0839 | + | 8.05294i | −0.524839 | + | 0.381318i | ||||
\(447\) | 1.36467 | + | 4.20001i | 0.0645466 | + | 0.198654i | ||||
\(448\) | −0.118654 | + | 0.365178i | −0.00560586 | + | 0.0172531i | ||||
\(449\) | −1.29950 | − | 0.944139i | −0.0613270 | − | 0.0445567i | 0.556699 | − | 0.830714i | \(-0.312068\pi\) |
−0.618026 | + | 0.786157i | \(0.712068\pi\) | |||||||
\(450\) | 48.8297 | 2.30185 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −11.1834 | −0.526023 | ||||||||
\(453\) | 2.54591 | + | 1.84971i | 0.119617 | + | 0.0869070i | ||||
\(454\) | 8.36932 | − | 25.7581i | 0.392792 | − | 1.20889i | ||||
\(455\) | −2.30469 | − | 7.09311i | −0.108046 | − | 0.332530i | ||||
\(456\) | −5.16220 | + | 3.75056i | −0.241742 | + | 0.175636i | ||||
\(457\) | 3.03944 | − | 2.20828i | 0.142179 | − | 0.103299i | −0.514422 | − | 0.857537i | \(-0.671994\pi\) |
0.656601 | + | 0.754238i | \(0.271994\pi\) | |||||||
\(458\) | −17.8545 | − | 54.9506i | −0.834287 | − | 2.56767i | ||||
\(459\) | 3.34224 | − | 10.2864i | 0.156002 | − | 0.480126i | ||||
\(460\) | −8.11662 | − | 5.89707i | −0.378440 | − | 0.274952i | ||||
\(461\) | 14.1849 | 0.660657 | 0.330329 | − | 0.943866i | \(-0.392840\pi\) | ||||
0.330329 | + | 0.943866i | \(0.392840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.34265 | −0.248294 | −0.124147 | − | 0.992264i | \(-0.539619\pi\) | ||||
−0.124147 | + | 0.992264i | \(0.539619\pi\) | |||||||
\(464\) | −7.43724 | − | 5.40347i | −0.345265 | − | 0.250850i | ||||
\(465\) | 3.49777 | − | 10.7650i | 0.162205 | − | 0.499216i | ||||
\(466\) | 11.6898 | + | 35.9776i | 0.541520 | + | 1.66663i | ||||
\(467\) | 19.3109 | − | 14.0302i | 0.893601 | − | 0.649239i | −0.0432136 | − | 0.999066i | \(-0.513760\pi\) |
0.936814 | + | 0.349827i | \(0.113760\pi\) | |||||||
\(468\) | 22.4820 | − | 16.3341i | 1.03923 | − | 0.755045i | ||||
\(469\) | −1.92424 | − | 5.92219i | −0.0888530 | − | 0.273461i | ||||
\(470\) | 13.6296 | − | 41.9475i | 0.628685 | − | 1.93489i | ||||
\(471\) | 6.09520 | + | 4.42842i | 0.280852 | + | 0.204051i | ||||
\(472\) | −49.1750 | −2.26346 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.2301 | −0.469883 | ||||||||
\(475\) | −13.2516 | − | 9.62782i | −0.608023 | − | 0.441755i | ||||
\(476\) | −6.29876 | + | 19.3856i | −0.288703 | + | 0.888538i | ||||
\(477\) | −11.7227 | − | 36.0786i | −0.536743 | − | 1.65193i | ||||
\(478\) | −4.04510 | + | 2.93893i | −0.185018 | + | 0.134424i | ||||
\(479\) | −0.353149 | + | 0.256578i | −0.0161358 | + | 0.0117233i | −0.595824 | − | 0.803115i | \(-0.703174\pi\) |
0.579688 | + | 0.814838i | \(0.303174\pi\) | |||||||
\(480\) | 2.56721 | + | 7.90105i | 0.117176 | + | 0.360632i | ||||
\(481\) | 3.36954 | − | 10.3704i | 0.153638 | − | 0.472849i | ||||
\(482\) | −1.63153 | − | 1.18537i | −0.0743140 | − | 0.0539923i | ||||
\(483\) | 0.266233 | 0.0121140 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.8517 | −1.35549 | ||||||||
\(486\) | −21.1972 | − | 15.4007i | −0.961524 | − | 0.698588i | ||||
\(487\) | 0.226720 | − | 0.697771i | 0.0102736 | − | 0.0316190i | −0.945788 | − | 0.324784i | \(-0.894708\pi\) |
0.956062 | + | 0.293165i | \(0.0947085\pi\) | |||||||
\(488\) | 28.4012 | + | 87.4098i | 1.28566 | + | 3.95686i | ||||
\(489\) | 0.125426 | − | 0.0911277i | 0.00567198 | − | 0.00412094i | ||||
\(490\) | 7.07934 | − | 5.14344i | 0.319812 | − | 0.232357i | ||||
\(491\) | −0.805765 | − | 2.47989i | −0.0363637 | − | 0.111916i | 0.931227 | − | 0.364440i | \(-0.118739\pi\) |
−0.967591 | + | 0.252524i | \(0.918739\pi\) | |||||||
\(492\) | −1.50104 | + | 4.61972i | −0.0676720 | + | 0.208273i | ||||
\(493\) | −4.57885 | − | 3.32673i | −0.206221 | − | 0.149828i | ||||
\(494\) | −13.4535 | −0.605302 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −58.9857 | −2.64854 | ||||||||
\(497\) | 3.42211 | + | 2.48631i | 0.153503 | + | 0.111526i | ||||
\(498\) | 2.71261 | − | 8.34857i | 0.121555 | − | 0.374108i | ||||
\(499\) | −2.55186 | − | 7.85383i | −0.114237 | − | 0.351586i | 0.877550 | − | 0.479485i | \(-0.159177\pi\) |
−0.991787 | + | 0.127899i | \(0.959177\pi\) | |||||||
\(500\) | −22.0049 | + | 15.9875i | −0.984091 | + | 0.714984i | ||||
\(501\) | 0.0379147 | − | 0.0275466i | 0.00169390 | − | 0.00123069i | ||||
\(502\) | 16.2572 | + | 50.0344i | 0.725593 | + | 2.23315i | ||||
\(503\) | −10.4793 | + | 32.2519i | −0.467248 | + | 1.43804i | 0.388884 | + | 0.921287i | \(0.372861\pi\) |
−0.856133 | + | 0.516756i | \(0.827139\pi\) | |||||||
\(504\) | 14.6866 | + | 10.6704i | 0.654194 | + | 0.475300i | ||||
\(505\) | 19.8010 | 0.881135 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.39533 | 0.150792 | ||||||||
\(508\) | −25.3863 | − | 18.4442i | −1.12633 | − | 0.818330i | ||||
\(509\) | −9.03680 | + | 27.8124i | −0.400549 | + | 1.23276i | 0.524006 | + | 0.851714i | \(0.324437\pi\) |
−0.924555 | + | 0.381048i | \(0.875563\pi\) | |||||||
\(510\) | 5.01533 | + | 15.4356i | 0.222082 | + | 0.683499i | ||||
\(511\) | 4.79356 | − | 3.48273i | 0.212055 | − | 0.154067i | ||||
\(512\) | −41.0901 | + | 29.8537i | −1.81594 | + | 1.31936i | ||||
\(513\) | 1.79338 | + | 5.51945i | 0.0791795 | + | 0.243690i | ||||
\(514\) | −4.08461 | + | 12.5711i | −0.180164 | + | 0.554488i | ||||
\(515\) | 12.8745 | + | 9.35391i | 0.567320 | + | 0.412182i | ||||
\(516\) | −2.70763 | −0.119197 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 12.7936 | 0.562120 | ||||||||
\(519\) | 4.41835 | + | 3.21012i | 0.193944 | + | 0.140908i | ||||
\(520\) | −14.7766 | + | 45.4776i | −0.647996 | + | 1.99433i | ||||
\(521\) | −3.00226 | − | 9.23999i | −0.131531 | − | 0.404811i | 0.863503 | − | 0.504343i | \(-0.168265\pi\) |
−0.995034 | + | 0.0995320i | \(0.968265\pi\) | |||||||
\(522\) | −7.32429 | + | 5.32141i | −0.320575 | + | 0.232912i | ||||
\(523\) | −10.3762 | + | 7.53879i | −0.453722 | + | 0.329648i | −0.791063 | − | 0.611734i | \(-0.790472\pi\) |
0.337342 | + | 0.941382i | \(0.390472\pi\) | |||||||
\(524\) | 29.1973 | + | 89.8599i | 1.27549 | + | 3.92555i | ||||
\(525\) | 0.857452 | − | 2.63897i | 0.0374223 | − | 0.115174i | ||||
\(526\) | −47.8814 | − | 34.7879i | −2.08773 | − | 1.51682i | ||||
\(527\) | −36.3155 | −1.58193 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5796 | −0.981721 | ||||||||
\(530\) | 94.8493 | + | 68.9120i | 4.11999 | + | 2.99335i | ||||
\(531\) | −6.71070 | + | 20.6534i | −0.291220 | + | 0.896282i | ||||
\(532\) | −3.37979 | − | 10.4019i | −0.146532 | − | 0.450981i | ||||
\(533\) | −4.61325 | + | 3.35172i | −0.199822 | + | 0.145179i | ||||
\(534\) | −4.03720 | + | 2.93320i | −0.174707 | + | 0.126932i | ||||
\(535\) | 4.26178 | + | 13.1164i | 0.184253 | + | 0.567072i | ||||
\(536\) | −12.3373 | + | 37.9703i | −0.532890 | + | 1.64007i | ||||
\(537\) | 3.76726 | + | 2.73707i | 0.162569 | + | 0.118113i | ||||
\(538\) | −47.6192 | −2.05301 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 37.0479 | 1.59429 | ||||||||
\(541\) | −5.58323 | − | 4.05646i | −0.240042 | − | 0.174401i | 0.461260 | − | 0.887265i | \(-0.347398\pi\) |
−0.701302 | + | 0.712864i | \(0.747398\pi\) | |||||||
\(542\) | 23.8382 | − | 73.3664i | 1.02394 | − | 3.15136i | ||||
\(543\) | −1.49173 | − | 4.59108i | −0.0640163 | − | 0.197022i | ||||
\(544\) | 21.5635 | − | 15.6668i | 0.924527 | − | 0.671708i | ||||
\(545\) | −17.0541 | + | 12.3905i | −0.730518 | + | 0.530753i | ||||
\(546\) | −0.704265 | − | 2.16750i | −0.0301398 | − | 0.0927606i | ||||
\(547\) | 5.47634 | − | 16.8544i | 0.234151 | − | 0.720643i | −0.763082 | − | 0.646302i | \(-0.776315\pi\) |
0.997233 | − | 0.0743412i | \(-0.0236854\pi\) | |||||||
\(548\) | −33.3536 | − | 24.2328i | −1.42480 | − | 1.03518i | ||||
\(549\) | 40.5878 | 1.73224 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.03692 | 0.129377 | ||||||||
\(552\) | −1.38096 | − | 1.00333i | −0.0587775 | − | 0.0427044i | ||||
\(553\) | 3.01699 | − | 9.28534i | 0.128295 | − | 0.394853i | ||||
\(554\) | 10.6398 | + | 32.7458i | 0.452040 | + | 1.39124i | ||||
\(555\) | 5.71034 | − | 4.14881i | 0.242391 | − | 0.176107i | ||||
\(556\) | 39.2509 | − | 28.5175i | 1.66461 | − | 1.20941i | ||||
\(557\) | −13.4198 | − | 41.3018i | −0.568614 | − | 1.75001i | −0.656962 | − | 0.753924i | \(-0.728159\pi\) |
0.0883477 | − | 0.996090i | \(-0.471841\pi\) | |||||||
\(558\) | −17.9508 | + | 55.2468i | −0.759917 | + | 2.33878i | ||||
\(559\) | −2.57150 | − | 1.86830i | −0.108763 | − | 0.0790208i | ||||
\(560\) | −25.1585 | −1.06314 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.6777 | 0.872234 | ||||||||
\(563\) | 18.0522 | + | 13.1157i | 0.760809 | + | 0.552760i | 0.899158 | − | 0.437623i | \(-0.144180\pi\) |
−0.138349 | + | 0.990384i | \(0.544180\pi\) | |||||||
\(564\) | 2.88584 | − | 8.88170i | 0.121516 | − | 0.373987i | ||||
\(565\) | −2.62611 | − | 8.08233i | −0.110481 | − | 0.340026i | ||||
\(566\) | −20.6274 | + | 14.9867i | −0.867035 | + | 0.629938i | ||||
\(567\) | 6.07661 | − | 4.41492i | 0.255194 | − | 0.185409i | ||||
\(568\) | −8.38071 | − | 25.7932i | −0.351647 | − | 1.08226i | ||||
\(569\) | −7.00513 | + | 21.5596i | −0.293670 | + | 0.903824i | 0.689994 | + | 0.723815i | \(0.257613\pi\) |
−0.983665 | + | 0.180010i | \(0.942387\pi\) | |||||||
\(570\) | −7.04545 | − | 5.11882i | −0.295102 | − | 0.214404i | ||||
\(571\) | −35.0994 | −1.46886 | −0.734432 | − | 0.678683i | \(-0.762551\pi\) | ||||
−0.734432 | + | 0.678683i | \(0.762551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.25258 | 0.386532 | ||||||||
\(574\) | −5.41268 | − | 3.93254i | −0.225921 | − | 0.164141i | ||||
\(575\) | 1.35406 | − | 4.16737i | 0.0564682 | − | 0.173791i | ||||
\(576\) | −0.335957 | − | 1.03397i | −0.0139982 | − | 0.0430820i | ||||
\(577\) | 26.4029 | − | 19.1828i | 1.09917 | − | 0.798591i | 0.118243 | − | 0.992985i | \(-0.462274\pi\) |
0.980924 | + | 0.194393i | \(0.0622739\pi\) | |||||||
\(578\) | 7.02910 | − | 5.10694i | 0.292372 | − | 0.212421i | ||||
\(579\) | 0.436883 | + | 1.34459i | 0.0181562 | + | 0.0558792i | ||||
\(580\) | 5.99087 | − | 18.4380i | 0.248757 | − | 0.765596i | ||||
\(581\) | 6.77759 | + | 4.92421i | 0.281182 | + | 0.204291i | ||||
\(582\) | −9.12204 | −0.378121 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −37.9894 | −1.57201 | ||||||||
\(585\) | 17.0840 | + | 12.4123i | 0.706338 | + | 0.513185i | ||||
\(586\) | 24.2332 | − | 74.5821i | 1.00106 | − | 3.08096i | ||||
\(587\) | 11.4390 | + | 35.2057i | 0.472139 | + | 1.45309i | 0.849778 | + | 0.527140i | \(0.176736\pi\) |
−0.377640 | + | 0.925953i | \(0.623264\pi\) | |||||||
\(588\) | 1.49894 | − | 1.08904i | 0.0618151 | − | 0.0449113i | ||||
\(589\) | 15.7646 | − | 11.4537i | 0.649570 | − | 0.471940i | ||||
\(590\) | −20.7396 | − | 63.8300i | −0.853837 | − | 2.62784i | ||||
\(591\) | −0.276873 | + | 0.852127i | −0.0113890 | + | 0.0350518i | ||||
\(592\) | −29.7578 | − | 21.6203i | −1.22304 | − | 0.888589i | ||||
\(593\) | 16.2161 | 0.665915 | 0.332958 | − | 0.942942i | \(-0.391953\pi\) | ||||
0.332958 | + | 0.942942i | \(0.391953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.4892 | −0.634995 | ||||||||
\(596\) | 39.2639 | + | 28.5269i | 1.60831 | + | 1.16851i | ||||
\(597\) | −0.296186 | + | 0.911565i | −0.0121221 | + | 0.0373079i | ||||
\(598\) | −1.11215 | − | 3.42285i | −0.0454792 | − | 0.139971i | ||||
\(599\) | −8.53313 | + | 6.19968i | −0.348654 | + | 0.253312i | −0.748304 | − | 0.663356i | \(-0.769132\pi\) |
0.399650 | + | 0.916668i | \(0.369132\pi\) | |||||||
\(600\) | −14.3928 | + | 10.4570i | −0.587585 | + | 0.426906i | ||||
\(601\) | 11.2764 | + | 34.7051i | 0.459973 | + | 1.41565i | 0.865196 | + | 0.501434i | \(0.167194\pi\) |
−0.405222 | + | 0.914218i | \(0.632806\pi\) | |||||||
\(602\) | 1.15243 | − | 3.54683i | 0.0469697 | − | 0.144558i | ||||
\(603\) | 14.2638 | + | 10.3633i | 0.580868 | + | 0.422026i | ||||
\(604\) | 34.5841 | 1.40721 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.05078 | 0.245796 | ||||||||
\(607\) | −27.2731 | − | 19.8151i | −1.10698 | − | 0.804269i | −0.124796 | − | 0.992182i | \(-0.539827\pi\) |
−0.982186 | + | 0.187914i | \(0.939827\pi\) | |||||||
\(608\) | −4.41955 | + | 13.6020i | −0.179236 | + | 0.551633i | ||||
\(609\) | 0.158977 | + | 0.489280i | 0.00644206 | + | 0.0198266i | ||||
\(610\) | −101.481 | + | 73.7304i | −4.10885 | + | 2.98526i | ||||
\(611\) | 8.86926 | − | 6.44389i | 0.358812 | − | 0.260692i | ||||
\(612\) | −17.8344 | − | 54.8886i | −0.720912 | − | 2.21874i | ||||
\(613\) | −7.48027 | + | 23.0219i | −0.302125 | + | 0.929845i | 0.678609 | + | 0.734499i | \(0.262583\pi\) |
−0.980734 | + | 0.195346i | \(0.937417\pi\) | |||||||
\(614\) | 41.4310 | + | 30.1014i | 1.67202 | + | 1.21479i | ||||
\(615\) | −3.69118 | −0.148843 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.6040 | 0.708710 | 0.354355 | − | 0.935111i | \(-0.384700\pi\) | ||||
0.354355 | + | 0.935111i | \(0.384700\pi\) | |||||||
\(618\) | 3.93419 | + | 2.85836i | 0.158256 | + | 0.114980i | ||||
\(619\) | −7.51455 | + | 23.1274i | −0.302035 | + | 0.929569i | 0.678732 | + | 0.734386i | \(0.262530\pi\) |
−0.980767 | + | 0.195183i | \(0.937470\pi\) | |||||||
\(620\) | −38.4399 | − | 118.306i | −1.54378 | − | 4.75128i | ||||
\(621\) | −1.25601 | + | 0.912544i | −0.0504019 | + | 0.0366191i | ||||
\(622\) | −48.4475 | + | 35.1992i | −1.94257 | + | 1.41136i | ||||
\(623\) | −1.47169 | − | 4.52940i | −0.0589621 | − | 0.181467i | ||||
\(624\) | −2.02481 | + | 6.23174i | −0.0810574 | + | 0.249469i | ||||
\(625\) | 10.6147 | + | 7.71201i | 0.424587 | + | 0.308480i | ||||
\(626\) | 37.4446 | 1.49659 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 82.7983 | 3.30401 | ||||||||
\(629\) | −18.3208 | − | 13.3109i | −0.730499 | − | 0.530739i | ||||
\(630\) | −7.65633 | + | 23.5637i | −0.305035 | + | 0.938802i | ||||
\(631\) | 1.24857 | + | 3.84271i | 0.0497049 | + | 0.152976i | 0.972828 | − | 0.231528i | \(-0.0743725\pi\) |
−0.923123 | + | 0.384504i | \(0.874372\pi\) | |||||||
\(632\) | −50.6420 | + | 36.7935i | −2.01443 | + | 1.46357i | ||||
\(633\) | 4.54021 | − | 3.29865i | 0.180457 | − | 0.131110i | ||||
\(634\) | −14.2348 | − | 43.8104i | −0.565338 | − | 1.73993i | ||||
\(635\) | 7.36851 | − | 22.6779i | 0.292410 | − | 0.899947i | ||||
\(636\) | 20.0828 | + | 14.5910i | 0.796335 | + | 0.578571i | ||||
\(637\) | 2.17503 | 0.0861779 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.9768 | −0.473793 | ||||||||
\(640\) | −30.0195 | − | 21.8104i | −1.18663 | − | 0.862134i | ||||
\(641\) | −6.60314 | + | 20.3224i | −0.260808 | + | 0.802686i | 0.731821 | + | 0.681497i | \(0.238671\pi\) |
−0.992629 | + | 0.121189i | \(0.961329\pi\) | |||||||
\(642\) | 1.30231 | + | 4.00810i | 0.0513981 | + | 0.158187i | ||||
\(643\) | −18.2636 | + | 13.2693i | −0.720246 | + | 0.523289i | −0.886463 | − | 0.462800i | \(-0.846845\pi\) |
0.166217 | + | 0.986089i | \(0.446845\pi\) | |||||||
\(644\) | 2.36707 | − | 1.71978i | 0.0932756 | − | 0.0677687i | ||||
\(645\) | −0.635810 | − | 1.95682i | −0.0250350 | − | 0.0770498i | ||||
\(646\) | −8.63409 | + | 26.5730i | −0.339704 | + | 1.04550i | ||||
\(647\) | −13.8480 | − | 10.0612i | −0.544422 | − | 0.395546i | 0.281303 | − | 0.959619i | \(-0.409233\pi\) |
−0.825725 | + | 0.564073i | \(0.809233\pi\) | |||||||
\(648\) | −48.1576 | −1.89181 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −37.5100 | −1.47126 | ||||||||
\(651\) | 2.67056 | + | 1.94027i | 0.104667 | + | 0.0760453i | ||||
\(652\) | 0.526509 | − | 1.62043i | 0.0206197 | − | 0.0634608i | ||||
\(653\) | −4.09173 | − | 12.5930i | −0.160122 | − | 0.492804i | 0.838522 | − | 0.544868i | \(-0.183420\pi\) |
−0.998644 | + | 0.0520637i | \(0.983420\pi\) | |||||||
\(654\) | −5.21138 | + | 3.78629i | −0.203781 | + | 0.148056i | ||||
\(655\) | −58.0863 | + | 42.2021i | −2.26962 | + | 1.64897i | ||||
\(656\) | 5.94410 | + | 18.2941i | 0.232078 | + | 0.714263i | ||||
\(657\) | −5.18425 | + | 15.9555i | −0.202257 | + | 0.622482i | ||||
\(658\) | 10.4062 | + | 7.56055i | 0.405676 | + | 0.294741i | ||||
\(659\) | −28.3747 | −1.10532 | −0.552660 | − | 0.833407i | \(-0.686387\pi\) | ||||
−0.552660 | + | 0.833407i | \(0.686387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9657 | 0.737679 | 0.368840 | − | 0.929493i | \(-0.379755\pi\) | ||||
0.368840 | + | 0.929493i | \(0.379755\pi\) | |||||||
\(662\) | −40.9404 | − | 29.7449i | −1.59119 | − | 1.15607i | ||||
\(663\) | −1.24661 | + | 3.83666i | −0.0484142 | + | 0.149004i | ||||
\(664\) | −16.5982 | − | 51.0841i | −0.644136 | − | 1.98245i | ||||
\(665\) | 6.72389 | − | 4.88520i | 0.260741 | − | 0.189440i | ||||
\(666\) | −29.3058 | + | 21.2919i | −1.13558 | + | 0.825046i | ||||
\(667\) | 0.251051 | + | 0.772654i | 0.00972072 | + | 0.0299173i | ||||
\(668\) | 0.159156 | − | 0.489833i | 0.00615794 | − | 0.0189522i | ||||
\(669\) | −1.78336 | − | 1.29569i | −0.0689488 | − | 0.0500942i | ||||
\(670\) | −54.4893 | −2.10511 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.42278 | −0.0934608 | ||||||||
\(673\) | 37.6551 | + | 27.3580i | 1.45150 | + | 1.05458i | 0.985478 | + | 0.169801i | \(0.0543124\pi\) |
0.466020 | + | 0.884774i | \(0.345688\pi\) | |||||||
\(674\) | −15.3842 | + | 47.3476i | −0.592577 | + | 1.82376i | ||||
\(675\) | 5.00016 | + | 15.3889i | 0.192456 | + | 0.592319i | ||||
\(676\) | 30.1878 | − | 21.9327i | 1.16107 | − | 0.843566i | ||||
\(677\) | 23.1132 | − | 16.7927i | 0.888312 | − | 0.645396i | −0.0471255 | − | 0.998889i | \(-0.515006\pi\) |
0.935437 | + | 0.353493i | \(0.115006\pi\) | |||||||
\(678\) | −0.802483 | − | 2.46979i | −0.0308192 | − | 0.0948517i | ||||
\(679\) | 2.69021 | − | 8.27962i | 0.103241 | − | 0.317743i | ||||
\(680\) | 80.3430 | + | 58.3726i | 3.08101 | + | 2.23849i | ||||
\(681\) | 4.35767 | 0.166986 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.9450 | −0.839704 | −0.419852 | − | 0.907593i | \(-0.637918\pi\) | ||||
−0.419852 | + | 0.907593i | \(0.637918\pi\) | |||||||
\(684\) | 25.0535 | + | 18.2024i | 0.957943 | + | 0.695986i | ||||
\(685\) | 9.68108 | − | 29.7953i | 0.369895 | − | 1.13842i | ||||
\(686\) | 0.788594 | + | 2.42704i | 0.0301086 | + | 0.0926649i | ||||
\(687\) | 7.52090 | − | 5.46425i | 0.286940 | − | 0.208474i | ||||
\(688\) | −8.67443 | + | 6.30234i | −0.330709 | + | 0.240274i | ||||
\(689\) | 9.00511 | + | 27.7149i | 0.343067 | + | 1.05585i | ||||
\(690\) | 0.719912 | − | 2.21566i | 0.0274066 | − | 0.0843488i | ||||
\(691\) | −9.00403 | − | 6.54181i | −0.342529 | − | 0.248862i | 0.403199 | − | 0.915112i | \(-0.367898\pi\) |
−0.745728 | + | 0.666250i | \(0.767898\pi\) | |||||||
\(692\) | 60.0197 | 2.28161 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −72.5903 | −2.75549 | ||||||||
\(695\) | 29.8267 | + | 21.6704i | 1.13139 | + | 0.822005i | ||||
\(696\) | 1.01928 | − | 3.13703i | 0.0386358 | − | 0.118909i | ||||
\(697\) | 3.65957 | + | 11.2630i | 0.138616 | + | 0.426617i | ||||
\(698\) | −41.4705 | + | 30.1301i | −1.56968 | + | 1.14044i | ||||
\(699\) | −4.92413 | + | 3.57759i | −0.186248 | + | 0.135317i | ||||
\(700\) | −9.42327 | − | 29.0018i | −0.356166 | − | 1.09617i | ||||
\(701\) | 11.8651 | − | 36.5170i | 0.448139 | − | 1.37923i | −0.430865 | − | 0.902416i | \(-0.641792\pi\) |
0.879004 | − | 0.476814i | \(-0.158208\pi\) | |||||||
\(702\) | 10.7519 | + | 7.81171i | 0.405804 | + | 0.294834i | ||||
\(703\) | 12.1513 | 0.458294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.09652 | 0.267271 | ||||||||
\(706\) | 18.5749 | + | 13.4954i | 0.699075 | + | 0.507908i | ||||
\(707\) | −1.78446 | + | 5.49199i | −0.0671114 | + | 0.206548i | ||||
\(708\) | −4.39128 | − | 13.5150i | −0.165034 | − | 0.507923i | ||||
\(709\) | 0.388734 | − | 0.282432i | 0.0145992 | − | 0.0106070i | −0.580462 | − | 0.814288i | \(-0.697128\pi\) |
0.595061 | + | 0.803681i | \(0.297128\pi\) | |||||||
\(710\) | 29.9454 | − | 21.7566i | 1.12383 | − | 0.816511i | ||||
\(711\) | 8.54233 | + | 26.2906i | 0.320362 | + | 0.985974i | ||||
\(712\) | −9.43579 | + | 29.0404i | −0.353621 | + | 1.08833i | ||||
\(713\) | 4.21725 | + | 3.06401i | 0.157937 | + | 0.114748i | ||||
\(714\) | −4.73317 | −0.177135 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 51.1752 | 1.91251 | ||||||||
\(717\) | −0.650841 | − | 0.472864i | −0.0243061 | − | 0.0176594i | ||||
\(718\) | 7.46483 | − | 22.9744i | 0.278585 | − | 0.857397i | ||||
\(719\) | 11.2698 | + | 34.6848i | 0.420292 | + | 1.29352i | 0.907431 | + | 0.420200i | \(0.138040\pi\) |
−0.487140 | + | 0.873324i | \(0.661960\pi\) | |||||||
\(720\) | 57.6295 | − | 41.8703i | 2.14772 | − | 1.56041i | ||||
\(721\) | −3.75463 | + | 2.72790i | −0.139830 | + | 0.101592i | ||||
\(722\) | 10.3504 | + | 31.8553i | 0.385202 | + | 1.18553i | ||||
\(723\) | 0.100269 | − | 0.308595i | 0.00372903 | − | 0.0114768i | ||||
\(724\) | −42.9198 | − | 31.1830i | −1.59510 | − | 1.15891i | ||||
\(725\) | 8.46730 | 0.314467 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.6867 | −1.24937 | −0.624686 | − | 0.780876i | \(-0.714773\pi\) | ||||
−0.624686 | + | 0.780876i | \(0.714773\pi\) | |||||||
\(728\) | −11.2820 | − | 8.19683i | −0.418137 | − | 0.303795i | ||||
\(729\) | −5.66046 | + | 17.4211i | −0.209647 | + | 0.645226i | ||||
\(730\) | −16.0221 | − | 49.3109i | −0.593003 | − | 1.82508i | ||||
\(731\) | −5.34054 | + | 3.88013i | −0.197527 | + | 0.143512i | ||||
\(732\) | −21.4870 | + | 15.6112i | −0.794182 | + | 0.577007i | ||||
\(733\) | 8.36313 | + | 25.7391i | 0.308899 | + | 0.950694i | 0.978193 | + | 0.207697i | \(0.0665967\pi\) |
−0.669294 | + | 0.742998i | \(0.733403\pi\) | |||||||
\(734\) | −1.08442 | + | 3.33750i | −0.0400267 | + | 0.123190i | ||||
\(735\) | 1.13904 | + | 0.827562i | 0.0420142 | + | 0.0305251i | ||||
\(736\) | −3.82597 | −0.141027 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 18.9434 | 0.697315 | ||||||||
\(739\) | −8.42399 | − | 6.12039i | −0.309882 | − | 0.225142i | 0.421964 | − | 0.906613i | \(-0.361341\pi\) |
−0.731846 | + | 0.681470i | \(0.761341\pi\) | |||||||
\(740\) | 23.9706 | − | 73.7739i | 0.881176 | − | 2.71198i | ||||
\(741\) | −0.668904 | − | 2.05868i | −0.0245728 | − | 0.0756273i | ||||
\(742\) | −27.6611 | + | 20.0970i | −1.01547 | + | 0.737783i | ||||
\(743\) | 38.4705 | − | 27.9505i | 1.41135 | − | 1.02540i | 0.418220 | − | 0.908346i | \(-0.362654\pi\) |
0.993125 | − | 0.117057i | \(-0.0373461\pi\) | |||||||
\(744\) | −6.54015 | − | 20.1285i | −0.239774 | − | 0.737947i | ||||
\(745\) | −11.3966 | + | 35.0750i | −0.417538 | + | 1.28505i | ||||
\(746\) | −10.4710 | − | 7.60766i | −0.383372 | − | 0.278536i | ||||
\(747\) | −23.7203 | −0.867881 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.02202 | −0.146961 | ||||||||
\(750\) | −5.10975 | − | 3.71245i | −0.186582 | − | 0.135560i | ||||
\(751\) | −9.17002 | + | 28.2224i | −0.334619 | + | 1.02985i | 0.632291 | + | 0.774731i | \(0.282115\pi\) |
−0.966910 | + | 0.255119i | \(0.917885\pi\) | |||||||
\(752\) | −11.4279 | − | 35.1715i | −0.416733 | − | 1.28257i | ||||
\(753\) | −6.84804 | + | 4.97539i | −0.249557 | + | 0.181313i | ||||
\(754\) | 5.62637 | − | 4.08780i | 0.204900 | − | 0.148869i | ||||
\(755\) | 8.12110 | + | 24.9942i | 0.295557 | + | 0.909632i | ||||
\(756\) | −3.33873 | + | 10.2756i | −0.121428 | + | 0.373718i | ||||
\(757\) | 25.0626 | + | 18.2090i | 0.910915 | + | 0.661818i | 0.941246 | − | 0.337722i | \(-0.109656\pi\) |
−0.0303313 | + | 0.999540i | \(0.509656\pi\) | |||||||
\(758\) | 71.4090 | 2.59369 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −53.2874 | −1.93294 | ||||||||
\(761\) | 9.51993 | + | 6.91663i | 0.345097 | + | 0.250728i | 0.746809 | − | 0.665038i | \(-0.231585\pi\) |
−0.401712 | + | 0.915766i | \(0.631585\pi\) | |||||||
\(762\) | 2.25166 | − | 6.92990i | 0.0815691 | − | 0.251044i | ||||
\(763\) | −1.89972 | − | 5.84674i | −0.0687745 | − | 0.211666i | ||||
\(764\) | 82.2644 | − | 59.7686i | 2.97622 | − | 2.16235i | ||||
\(765\) | 35.4805 | − | 25.7781i | 1.28280 | − | 0.932008i | ||||
\(766\) | 24.6676 | + | 75.9192i | 0.891278 | + | 2.74307i | ||||
\(767\) | 5.15503 | − | 15.8655i | 0.186137 | − | 0.572872i | ||||
\(768\) | −9.42843 | − | 6.85015i | −0.340219 | − | 0.247184i | ||||
\(769\) | −4.17897 | −0.150697 | −0.0753487 | − | 0.997157i | \(-0.524007\pi\) | ||||
−0.0753487 | + | 0.997157i | \(0.524007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.12674 | −0.0765926 | ||||||||
\(772\) | 12.5699 | + | 9.13257i | 0.452401 | + | 0.328689i | ||||
\(773\) | 0.0258938 | − | 0.0796928i | 0.000931334 | − | 0.00286635i | −0.950590 | − | 0.310450i | \(-0.899520\pi\) |
0.951521 | + | 0.307583i | \(0.0995203\pi\) | |||||||
\(774\) | 3.26301 | + | 10.0425i | 0.117287 | + | 0.360971i | ||||
\(775\) | 43.9537 | − | 31.9342i | 1.57886 | − | 1.14711i | ||||
\(776\) | −45.1568 | + | 32.8083i | −1.62103 | + | 1.17775i | ||||
\(777\) | 0.636096 | + | 1.95770i | 0.0228198 | + | 0.0702322i | ||||
\(778\) | −8.40135 | + | 25.8567i | −0.301203 | + | 0.927007i | ||||
\(779\) | −5.14091 | − | 3.73509i | −0.184192 | − | 0.133824i | ||||
\(780\) | −13.8183 | −0.494776 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −7.47446 | −0.267286 | ||||||||
\(783\) | −2.42707 | − | 1.76337i | −0.0867364 | − | 0.0630177i | ||||
\(784\) | 2.26726 | − | 6.97792i | 0.0809737 | − | 0.249212i | ||||
\(785\) | 19.4428 | + | 59.8389i | 0.693945 | + | 2.13574i | ||||
\(786\) | −17.7499 | + | 12.8961i | −0.633119 | + | 0.459988i | ||||
\(787\) | 10.8728 | − | 7.89952i | 0.387572 | − | 0.281588i | −0.376888 | − | 0.926259i | \(-0.623006\pi\) |
0.764460 | + | 0.644671i | \(0.223006\pi\) | |||||||
\(788\) | 3.04279 | + | 9.36474i | 0.108395 | + | 0.333605i | ||||
\(789\) | 2.94265 | − | 9.05653i | 0.104761 | − | 0.322421i | ||||
\(790\) | −69.1169 | − | 50.2164i | −2.45907 | − | 1.78662i | ||||
\(791\) | 2.47837 | 0.0881206 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.1787 | −1.10719 | ||||||||
\(794\) | 43.7183 | + | 31.7632i | 1.55150 | + | 1.12723i | ||||
\(795\) | −5.82915 | + | 17.9403i | −0.206738 | + | 0.636276i | ||||
\(796\) | 3.25503 | + | 10.0180i | 0.115372 | + | 0.355077i | ||||
\(797\) | 11.0009 | − | 7.99263i | 0.389672 | − | 0.283113i | −0.375649 | − | 0.926762i | \(-0.622580\pi\) |
0.765321 | + | 0.643649i | \(0.222580\pi\) | |||||||
\(798\) | 2.05468 | − | 1.49281i | 0.0727349 | − | 0.0528450i | ||||
\(799\) | −7.03576 | − | 21.6538i | −0.248907 | − | 0.766058i | ||||
\(800\) | −12.3222 | + | 37.9240i | −0.435657 | + | 1.34081i | ||||
\(801\) | 10.9092 | + | 7.92603i | 0.385459 | + | 0.280053i | ||||
\(802\) | 86.0284 | 3.03777 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −11.5372 | −0.406887 | ||||||||
\(805\) | 1.79873 | + | 1.30686i | 0.0633970 | + | 0.0460606i | ||||
\(806\) | 13.7894 | − | 42.4395i | 0.485712 | − | 1.49487i | ||||
\(807\) | −2.36761 | − | 7.28676i | −0.0833439 | − | 0.256506i | ||||
\(808\) | 29.9532 | − | 21.7622i | 1.05375 | − | 0.765593i | ||||
\(809\) | 36.0013 | − | 26.1565i | 1.26574 | − | 0.919612i | 0.266713 | − | 0.963776i | \(-0.414062\pi\) |
0.999024 | + | 0.0441638i | \(0.0140623\pi\) | |||||||
\(810\) | −20.3105 | − | 62.5094i | −0.713640 | − | 2.19636i | ||||
\(811\) | 7.47960 | − | 23.0199i | 0.262644 | − | 0.808336i | −0.729582 | − | 0.683893i | \(-0.760285\pi\) |
0.992227 | − | 0.124443i | \(-0.0397145\pi\) | |||||||
\(812\) | 4.57404 | + | 3.32324i | 0.160517 | + | 0.116623i | ||||
\(813\) | 12.4119 | 0.435303 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.29473 | 0.0453524 | ||||||||
\(816\) | 11.0093 | + | 7.99871i | 0.385402 | + | 0.280011i | ||||
\(817\) | 1.09457 | − | 3.36875i | 0.0382942 | − | 0.117857i | ||||
\(818\) | −2.08507 | − | 6.41719i | −0.0729028 | − | 0.224372i | ||||
\(819\) | −4.98226 | + | 3.61982i | −0.174094 | + | 0.126487i | ||||
\(820\) | −32.8182 | + | 23.8438i | −1.14606 | + | 0.832662i | ||||
\(821\) | 2.86779 | + | 8.82615i | 0.100087 | + | 0.308035i | 0.988546 | − | 0.150921i | \(-0.0482238\pi\) |
−0.888459 | + | 0.458955i | \(0.848224\pi\) | |||||||
\(822\) | 2.95834 | − | 9.10482i | 0.103184 | − | 0.317567i | ||||
\(823\) | 18.9984 | + | 13.8031i | 0.662242 | + | 0.481147i | 0.867419 | − | 0.497578i | \(-0.165777\pi\) |
−0.205177 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(824\) | 29.7558 | 1.03659 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.5728 | 0.681026 | ||||||||
\(827\) | −15.9690 | − | 11.6022i | −0.555297 | − | 0.403447i | 0.274438 | − | 0.961605i | \(-0.411508\pi\) |
−0.829735 | + | 0.558158i | \(0.811508\pi\) | |||||||
\(828\) | −2.55999 | + | 7.87884i | −0.0889658 | + | 0.273809i | ||||
\(829\) | −12.3588 | − | 38.0364i | −0.429238 | − | 1.32106i | −0.898878 | − | 0.438200i | \(-0.855616\pi\) |
0.469640 | − | 0.882858i | \(-0.344384\pi\) | |||||||
\(830\) | 59.3077 | − | 43.0895i | 2.05860 | − | 1.49566i | ||||
\(831\) | −4.48181 | + | 3.25622i | −0.155472 | + | 0.112957i | ||||
\(832\) | 0.258075 | + | 0.794275i | 0.00894716 | + | 0.0275365i | ||||
\(833\) | 1.39588 | − | 4.29606i | 0.0483642 | − | 0.148850i | ||||
\(834\) | 9.11442 | + | 6.62202i | 0.315607 | + | 0.229302i | ||||
\(835\) | 0.391379 | 0.0135442 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.2494 | −0.665357 | ||||||||
\(838\) | 68.2869 | + | 49.6133i | 2.35893 | + | 1.71386i | ||||
\(839\) | −2.42521 | + | 7.46403i | −0.0837276 | + | 0.257687i | −0.984152 | − | 0.177325i | \(-0.943256\pi\) |
0.900425 | + | 0.435012i | \(0.143256\pi\) | |||||||
\(840\) | −2.78949 | − | 8.58518i | −0.0962467 | − | 0.296217i | ||||
\(841\) | 22.1914 | − | 16.1230i | 0.765222 | − | 0.555966i | ||||
\(842\) | 69.5384 | − | 50.5226i | 2.39645 | − | 1.74112i | ||||
\(843\) | 1.02809 | + | 3.16413i | 0.0354092 | + | 0.108978i | ||||
\(844\) | 19.0586 | − | 58.6565i | 0.656025 | − | 2.01904i | ||||
\(845\) | 22.9397 | + | 16.6667i | 0.789149 | + | 0.573350i | ||||
\(846\) | −36.4198 | −1.25214 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 98.3017 | 3.37569 | ||||||||
\(849\) | −3.31888 | − | 2.41131i | −0.113904 | − | 0.0827558i | ||||
\(850\) | −24.0729 | + | 74.0887i | −0.825693 | + | 2.54122i | ||||
\(851\) | 1.00450 | + | 3.09153i | 0.0344338 | + | 0.105976i | ||||
\(852\) | 6.34045 | − | 4.60661i | 0.217220 | − | 0.157820i | ||||
\(853\) | −33.1689 | + | 24.0986i | −1.13568 | + | 0.825121i | −0.986512 | − | 0.163691i | \(-0.947660\pi\) |
−0.149170 | + | 0.988812i | \(0.547660\pi\) | |||||||
\(854\) | −11.3044 | − | 34.7912i | −0.386827 | − | 1.19053i | ||||
\(855\) | −7.27191 | + | 22.3806i | −0.248694 | + | 0.765401i | ||||
\(856\) | 20.8624 | + | 15.1574i | 0.713061 | + | 0.518069i | ||||
\(857\) | −31.1892 | −1.06540 | −0.532702 | − | 0.846303i | \(-0.678823\pi\) | ||||
−0.532702 | + | 0.846303i | \(0.678823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.95825 | 0.271532 | 0.135766 | − | 0.990741i | \(-0.456650\pi\) | ||||
0.135766 | + | 0.990741i | \(0.456650\pi\) | |||||||
\(860\) | −18.2934 | − | 13.2909i | −0.623799 | − | 0.453217i | ||||
\(861\) | 0.332647 | − | 1.02378i | 0.0113366 | − | 0.0348904i | ||||
\(862\) | −23.4627 | − | 72.2107i | −0.799143 | − | 2.45951i | ||||
\(863\) | −25.1639 | + | 18.2826i | −0.856588 | + | 0.622347i | −0.926954 | − | 0.375174i | \(-0.877583\pi\) |
0.0703669 | + | 0.997521i | \(0.477583\pi\) | |||||||
\(864\) | 11.4300 | − | 8.30436i | 0.388856 | − | 0.282520i | ||||
\(865\) | 14.0939 | + | 43.3766i | 0.479208 | + | 1.47485i | ||||
\(866\) | 18.2567 | − | 56.1883i | 0.620388 | − | 1.90936i | ||||
\(867\) | 1.13096 | + | 0.821688i | 0.0384093 | + | 0.0279060i | ||||
\(868\) | 36.2774 | 1.23133 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.50180 | 0.152625 | ||||||||
\(871\) | −10.9572 | − | 7.96087i | −0.371270 | − | 0.269744i | ||||
\(872\) | −12.1801 | + | 37.4865i | −0.412470 | + | 1.26945i | ||||
\(873\) | 7.61709 | + | 23.4430i | 0.257799 | + | 0.793425i | ||||
\(874\) | 3.24468 | − | 2.35740i | 0.109753 | − | 0.0797402i | ||||
\(875\) | 4.87654 | − | 3.54301i | 0.164857 | − | 0.119776i | ||||
\(876\) | −3.39241 | − | 10.4408i | −0.114619 | − | 0.352761i | ||||
\(877\) | 16.0371 | − | 49.3571i | 0.541534 | − | 1.66667i | −0.187556 | − | 0.982254i | \(-0.560057\pi\) |
0.729090 | − | 0.684417i | \(-0.239943\pi\) | |||||||
\(878\) | −32.6544 | − | 23.7248i | −1.10203 | − | 0.800672i | ||||
\(879\) | 12.6175 | 0.425579 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.1448 | 1.41989 | 0.709947 | − | 0.704256i | \(-0.248719\pi\) | ||||
0.709947 | + | 0.704256i | \(0.248719\pi\) | |||||||
\(882\) | −5.84563 | − | 4.24710i | −0.196833 | − | 0.143007i | ||||
\(883\) | −5.45656 | + | 16.7936i | −0.183628 | + | 0.565149i | −0.999922 | − | 0.0124878i | \(-0.996025\pi\) |
0.816294 | + | 0.577637i | \(0.196025\pi\) | |||||||
\(884\) | 13.7000 | + | 42.1643i | 0.460781 | + | 1.41814i | ||||
\(885\) | 8.73619 | − | 6.34722i | 0.293664 | − | 0.213359i | ||||
\(886\) | −20.7007 | + | 15.0399i | −0.695453 | + | 0.505276i | ||||
\(887\) | 3.29195 | + | 10.1316i | 0.110533 | + | 0.340185i | 0.990989 | − | 0.133942i | \(-0.0427636\pi\) |
−0.880456 | + | 0.474127i | \(0.842764\pi\) | |||||||
\(888\) | 4.07834 | − | 12.5519i | 0.136860 | − | 0.421213i | ||||
\(889\) | 5.62588 | + | 4.08744i | 0.188686 | + | 0.137088i | ||||
\(890\) | −41.6744 | −1.39693 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.2255 | −0.811131 | ||||||||
\(893\) | 9.88372 | + | 7.18094i | 0.330746 | + | 0.240301i | ||||
\(894\) | −3.48255 | + | 10.7182i | −0.116474 | + | 0.358470i | ||||
\(895\) | 12.0170 | + | 36.9846i | 0.401685 | + | 1.23626i | ||||
\(896\) | 8.75466 | − | 6.36063i | 0.292473 | − | 0.212494i | ||||
\(897\) | 0.468474 | − | 0.340366i | 0.0156419 | − | 0.0113645i | ||||
\(898\) | −1.26669 | − | 3.89847i | −0.0422700 | − | 0.130094i | ||||
\(899\) | −3.11275 | + | 9.58005i | −0.103816 | + | 0.319512i | ||||
\(900\) | 69.8521 | + | 50.7505i | 2.32840 | + | 1.69168i | ||||
\(901\) | 60.5209 | 2.01624 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.600040 | 0.0199681 | ||||||||
\(904\) | −12.8554 | − | 9.33998i | −0.427563 | − | 0.310643i | ||||
\(905\) | 12.4577 | − | 38.3409i | 0.414108 | − | 1.27449i | ||||
\(906\) | 2.48164 | + | 7.63770i | 0.0824469 | + | 0.253745i | ||||
\(907\) | −40.6939 | + | 29.5659i | −1.35122 | + | 0.981719i | −0.352270 | + | 0.935898i | \(0.614590\pi\) |
−0.998950 | + | 0.0458205i | \(0.985410\pi\) | |||||||
\(908\) | 38.7439 | − | 28.1491i | 1.28576 | − | 0.934160i | ||||
\(909\) | −5.05253 | − | 15.5501i | −0.167582 | − | 0.515763i | ||||
\(910\) | 5.88144 | − | 18.1012i | 0.194968 | − | 0.600049i | ||||
\(911\) | 18.6375 | + | 13.5410i | 0.617489 | + | 0.448632i | 0.852044 | − | 0.523471i | \(-0.175363\pi\) |
−0.234554 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(912\) | −7.30190 | −0.241790 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.58753 | 0.317127 | ||||||||
\(915\) | −16.3280 | − | 11.8630i | −0.539785 | − | 0.392177i | ||||
\(916\) | 31.5708 | − | 97.1650i | 1.04313 | − | 3.21042i | ||||
\(917\) | −6.47044 | − | 19.9140i | −0.213673 | − | 0.657617i | ||||
\(918\) | 22.3297 | − | 16.2235i | 0.736991 | − | 0.535455i | ||||
\(919\) | −30.7956 | + | 22.3743i | −1.01585 | + | 0.738061i | −0.965429 | − | 0.260667i | \(-0.916058\pi\) |
−0.0504252 | + | 0.998728i | \(0.516058\pi\) | |||||||
\(920\) | −4.40507 | − | 13.5574i | −0.145231 | − | 0.446975i | ||||
\(921\) | −2.54622 | + | 7.83647i | −0.0839009 | + | 0.258220i | ||||
\(922\) | 29.2857 | + | 21.2773i | 0.964472 | + | 0.700730i | ||||
\(923\) | 9.20031 | 0.302832 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.8792 | 1.11394 | ||||||||
\(926\) | −11.0302 | − | 8.01394i | −0.362476 | − | 0.263354i | ||||
\(927\) | 4.06064 | − | 12.4974i | 0.133369 | − | 0.410468i | ||||
\(928\) | −2.28462 | − | 7.03133i | −0.0749962 | − | 0.230815i | ||||
\(929\) | 14.1887 | − | 10.3087i | 0.465516 | − | 0.338217i | −0.330175 | − | 0.943920i | \(-0.607108\pi\) |
0.795691 | + | 0.605703i | \(0.207108\pi\) | |||||||
\(930\) | 23.3688 | − | 16.9785i | 0.766295 | − | 0.556746i | ||||
\(931\) | 0.748999 | + | 2.30518i | 0.0245474 | + | 0.0755493i | ||||
\(932\) | −20.6702 | + | 63.6164i | −0.677076 | + | 2.08383i | ||||
\(933\) | −7.79503 | − | 5.66342i | −0.255198 | − | 0.185412i | ||||
\(934\) | 60.9137 | 1.99316 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 39.4848 | 1.29060 | ||||||||
\(937\) | −45.9190 | − | 33.3621i | −1.50011 | − | 1.08989i | −0.970339 | − | 0.241749i | \(-0.922279\pi\) |
−0.529768 | − | 0.848142i | \(-0.677721\pi\) | |||||||
\(938\) | 4.91054 | − | 15.1131i | 0.160335 | − | 0.493460i | ||||
\(939\) | 1.86174 | + | 5.72983i | 0.0607554 | + | 0.186986i | ||||
\(940\) | 63.0950 | − | 45.8412i | 2.05793 | − | 1.49517i | ||||
\(941\) | −18.0399 | + | 13.1068i | −0.588084 | + | 0.427268i | −0.841630 | − | 0.540055i | \(-0.818403\pi\) |
0.253545 | + | 0.967324i | \(0.418403\pi\) | |||||||
\(942\) | 5.94133 | + | 18.2855i | 0.193579 | + | 0.595774i | ||||
\(943\) | 0.525304 | − | 1.61672i | 0.0171063 | − | 0.0526477i | ||||
\(944\) | −45.5261 | − | 33.0767i | −1.48175 | − | 1.07655i | ||||
\(945\) | −8.21023 | −0.267079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.7782 | 1.45510 | 0.727548 | − | 0.686057i | \(-0.240660\pi\) | ||||
0.727548 | + | 0.686057i | \(0.240660\pi\) | |||||||
\(948\) | −14.6344 | − | 10.6325i | −0.475303 | − | 0.345328i | ||||
\(949\) | 3.98244 | − | 12.2567i | 0.129275 | − | 0.397869i | ||||
\(950\) | −12.9170 | − | 39.7545i | −0.419084 | − | 1.28981i | ||||
\(951\) | 5.99617 | − | 4.35648i | 0.194439 | − | 0.141268i | ||||
\(952\) | −23.4306 | + | 17.0233i | −0.759390 | + | 0.551729i | ||||
\(953\) | −0.572242 | − | 1.76118i | −0.0185367 | − | 0.0570502i | 0.941360 | − | 0.337403i | \(-0.109549\pi\) |
−0.959897 | + | 0.280353i | \(0.909549\pi\) | |||||||
\(954\) | 29.9155 | − | 92.0706i | 0.968551 | − | 2.98089i | ||||
\(955\) | 62.5126 | + | 45.4181i | 2.02286 | + | 1.46970i | ||||
\(956\) | −8.84115 | −0.285943 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.11396 | −0.0359906 | ||||||||
\(959\) | 7.39154 | + | 5.37027i | 0.238685 | + | 0.173415i | ||||
\(960\) | −0.167056 | + | 0.514146i | −0.00539172 | + | 0.0165940i | ||||
\(961\) | 10.3932 | + | 31.9869i | 0.335263 | + | 1.03183i | ||||
\(962\) | 22.5122 | − | 16.3560i | 0.725821 | − | 0.527340i | ||||
\(963\) | 9.21308 | − | 6.69369i | 0.296887 | − | 0.215701i | ||||
\(964\) | −1.10194 | − | 3.39141i | −0.0354910 | − | 0.109230i | ||||
\(965\) | −3.64849 | + | 11.2289i | −0.117449 | + | 0.361471i | ||||
\(966\) | 0.549655 | + | 0.399348i | 0.0176849 | + | 0.0128488i | ||||
\(967\) | 33.5800 | 1.07986 | 0.539930 | − | 0.841710i | \(-0.318451\pi\) | ||||
0.539930 | + | 0.841710i | \(0.318451\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.49552 | −0.144417 | ||||||||
\(970\) | −61.6307 | − | 44.7773i | −1.97884 | − | 1.43771i | ||||
\(971\) | 13.1253 | − | 40.3955i | 0.421210 | − | 1.29635i | −0.485366 | − | 0.874311i | \(-0.661314\pi\) |
0.906577 | − | 0.422041i | \(-0.138686\pi\) | |||||||
\(972\) | −14.3166 | − | 44.0620i | −0.459206 | − | 1.41329i | ||||
\(973\) | −8.69844 | + | 6.31979i | −0.278859 | + | 0.202603i | ||||
\(974\) | 1.51473 | − | 1.10052i | 0.0485351 | − | 0.0352628i | ||||
\(975\) | −1.86499 | − | 5.73984i | −0.0597274 | − | 0.183822i | ||||
\(976\) | −32.5008 | + | 100.027i | −1.04033 | + | 3.20180i | ||||
\(977\) | −37.4839 | − | 27.2337i | −1.19922 | − | 0.871282i | −0.205009 | − | 0.978760i | \(-0.565722\pi\) |
−0.994207 | + | 0.107478i | \(0.965722\pi\) | |||||||
\(978\) | 0.395642 | 0.0126512 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 15.4729 | 0.494265 | ||||||||
\(981\) | 14.0821 | + | 10.2312i | 0.449607 | + | 0.326659i | ||||
\(982\) | 2.05627 | − | 6.32854i | 0.0656181 | − | 0.201952i | ||||
\(983\) | 7.75344 | + | 23.8626i | 0.247296 | + | 0.761100i | 0.995250 | + | 0.0973492i | \(0.0310364\pi\) |
−0.747954 | + | 0.663751i | \(0.768964\pi\) | |||||||
\(984\) | −5.58367 | + | 4.05677i | −0.178001 | + | 0.129325i | ||||
\(985\) | −6.05345 | + | 4.39809i | −0.192879 | + | 0.140135i | ||||
\(986\) | −4.46326 | − | 13.7365i | −0.142139 | − | 0.437459i | ||||
\(987\) | −0.639534 | + | 1.96828i | −0.0203566 | + | 0.0626511i | ||||
\(988\) | −19.2456 | − | 13.9827i | −0.612283 | − | 0.444850i | ||||
\(989\) | 0.947563 | 0.0301307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.5645 | 1.19328 | 0.596638 | − | 0.802510i | \(-0.296503\pi\) | ||||
0.596638 | + | 0.802510i | \(0.296503\pi\) | |||||||
\(992\) | −38.3779 | − | 27.8832i | −1.21850 | − | 0.885293i | ||||
\(993\) | 2.51607 | − | 7.74367i | 0.0798451 | − | 0.245738i | ||||
\(994\) | 3.33572 | + | 10.2663i | 0.105803 | + | 0.325627i | ||||
\(995\) | −6.47570 | + | 4.70487i | −0.205293 | + | 0.149154i | ||||
\(996\) | 12.5574 | − | 9.12351i | 0.397898 | − | 0.289090i | ||||
\(997\) | −11.0749 | − | 34.0849i | −0.350745 | − | 1.07948i | −0.958436 | − | 0.285308i | \(-0.907904\pi\) |
0.607691 | − | 0.794173i | \(-0.292096\pi\) | |||||||
\(998\) | 6.51221 | − | 20.0425i | 0.206140 | − | 0.634435i | ||||
\(999\) | −9.71116 | − | 7.05557i | −0.307248 | − | 0.223228i |
(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 | 847.2.f.v.323.4 | 16 | ||
11.2 | odd | 10 | 77.2.f.b.71.4 | yes | 16 | ||
11.3 | even | 5 | inner | 847.2.f.v.729.4 | 16 | ||
11.4 | even | 5 | 847.2.f.x.372.1 | 16 | |||
11.5 | even | 5 | 847.2.a.o.1.1 | 8 | |||
11.6 | odd | 10 | 847.2.a.p.1.8 | 8 | |||
11.7 | odd | 10 | 77.2.f.b.64.4 | ✓ | 16 | ||
11.8 | odd | 10 | 847.2.f.w.729.1 | 16 | |||
11.9 | even | 5 | 847.2.f.x.148.1 | 16 | |||
11.10 | odd | 2 | 847.2.f.w.323.1 | 16 | |||
33.2 | even | 10 | 693.2.m.i.379.1 | 16 | |||
33.5 | odd | 10 | 7623.2.a.cw.1.8 | 8 | |||
33.17 | even | 10 | 7623.2.a.ct.1.1 | 8 | |||
33.29 | even | 10 | 693.2.m.i.64.1 | 16 | |||
77.2 | odd | 30 | 539.2.q.g.214.4 | 32 | |||
77.6 | even | 10 | 5929.2.a.bt.1.8 | 8 | |||
77.13 | even | 10 | 539.2.f.e.148.4 | 16 | |||
77.18 | odd | 30 | 539.2.q.g.471.4 | 32 | |||
77.24 | even | 30 | 539.2.q.f.324.1 | 32 | |||
77.27 | odd | 10 | 5929.2.a.bs.1.1 | 8 | |||
77.40 | even | 30 | 539.2.q.f.361.1 | 32 | |||
77.46 | odd | 30 | 539.2.q.g.324.1 | 32 | |||
77.51 | odd | 30 | 539.2.q.g.361.1 | 32 | |||
77.62 | even | 10 | 539.2.f.e.295.4 | 16 | |||
77.68 | even | 30 | 539.2.q.f.214.4 | 32 | |||
77.73 | even | 30 | 539.2.q.f.471.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.64.4 | ✓ | 16 | 11.7 | odd | 10 | ||
77.2.f.b.71.4 | yes | 16 | 11.2 | odd | 10 | ||
539.2.f.e.148.4 | 16 | 77.13 | even | 10 | |||
539.2.f.e.295.4 | 16 | 77.62 | even | 10 | |||
539.2.q.f.214.4 | 32 | 77.68 | even | 30 | |||
539.2.q.f.324.1 | 32 | 77.24 | even | 30 | |||
539.2.q.f.361.1 | 32 | 77.40 | even | 30 | |||
539.2.q.f.471.4 | 32 | 77.73 | even | 30 | |||
539.2.q.g.214.4 | 32 | 77.2 | odd | 30 | |||
539.2.q.g.324.1 | 32 | 77.46 | odd | 30 | |||
539.2.q.g.361.1 | 32 | 77.51 | odd | 30 | |||
539.2.q.g.471.4 | 32 | 77.18 | odd | 30 | |||
693.2.m.i.64.1 | 16 | 33.29 | even | 10 | |||
693.2.m.i.379.1 | 16 | 33.2 | even | 10 | |||
847.2.a.o.1.1 | 8 | 11.5 | even | 5 | |||
847.2.a.p.1.8 | 8 | 11.6 | odd | 10 | |||
847.2.f.v.323.4 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.v.729.4 | 16 | 11.3 | even | 5 | inner | ||
847.2.f.w.323.1 | 16 | 11.10 | odd | 2 | |||
847.2.f.w.729.1 | 16 | 11.8 | odd | 10 | |||
847.2.f.x.148.1 | 16 | 11.9 | even | 5 | |||
847.2.f.x.372.1 | 16 | 11.4 | even | 5 | |||
5929.2.a.bs.1.1 | 8 | 77.27 | odd | 10 | |||
5929.2.a.bt.1.8 | 8 | 77.6 | even | 10 | |||
7623.2.a.ct.1.1 | 8 | 33.17 | even | 10 | |||
7623.2.a.cw.1.8 | 8 | 33.5 | odd | 10 |