Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(267,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.267");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.k (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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.25 | ||
Character | \(\chi\) | \(=\) | 380.343 |
Dual form | 380.2.k.c.267.25 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38545 | + | 0.283752i | 0.979664 | + | 0.200643i | ||||
\(3\) | −1.20015 | + | 1.20015i | −0.692909 | + | 0.692909i | −0.962871 | − | 0.269962i | \(-0.912989\pi\) |
0.269962 | + | 0.962871i | \(0.412989\pi\) | |||||||
\(4\) | 1.83897 | + | 0.786251i | 0.919485 | + | 0.393126i | ||||
\(5\) | −2.06624 | − | 0.854787i | −0.924050 | − | 0.382272i | ||||
\(6\) | −2.00330 | + | 1.32221i | −0.817846 | + | 0.539791i | ||||
\(7\) | 1.52124 | + | 1.52124i | 0.574973 | + | 0.574973i | 0.933514 | − | 0.358541i | \(-0.116726\pi\) |
−0.358541 | + | 0.933514i | \(0.616726\pi\) | |||||||
\(8\) | 2.32471 | + | 1.61113i | 0.821908 | + | 0.569620i | ||||
\(9\) | 0.119262i | 0.0397539i | ||||||||
\(10\) | −2.62013 | − | 1.77057i | −0.828558 | − | 0.559903i | ||||
\(11\) | 4.01379i | 1.21020i | 0.796148 | + | 0.605102i | \(0.206868\pi\) | ||||
−0.796148 | + | 0.605102i | \(0.793132\pi\) | |||||||
\(12\) | −3.15067 | + | 1.26342i | −0.909520 | + | 0.364719i | ||||
\(13\) | −1.50202 | − | 1.50202i | −0.416585 | − | 0.416585i | 0.467440 | − | 0.884025i | \(-0.345176\pi\) |
−0.884025 | + | 0.467440i | \(0.845176\pi\) | |||||||
\(14\) | 1.67595 | + | 2.53926i | 0.447916 | + | 0.678645i | ||||
\(15\) | 3.50568 | − | 1.45393i | 0.905162 | − | 0.375403i | ||||
\(16\) | 2.76362 | + | 2.89178i | 0.690904 | + | 0.722946i | ||||
\(17\) | −3.94831 | + | 3.94831i | −0.957605 | + | 0.957605i | −0.999137 | − | 0.0415323i | \(-0.986776\pi\) |
0.0415323 | + | 0.999137i | \(0.486776\pi\) | |||||||
\(18\) | −0.0338407 | + | 0.165232i | −0.00797634 | + | 0.0389455i | ||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.12767 | − | 3.19651i | −0.699369 | − | 0.714761i | ||||
\(21\) | −3.65143 | −0.796808 | ||||||||
\(22\) | −1.13892 | + | 5.56092i | −0.242819 | + | 1.18559i | ||||
\(23\) | 4.78362 | − | 4.78362i | 0.997453 | − | 0.997453i | −0.00254405 | − | 0.999997i | \(-0.500810\pi\) |
0.999997 | + | 0.00254405i | \(0.000809798\pi\) | |||||||
\(24\) | −4.72361 | + | 0.856407i | −0.964202 | + | 0.174813i | ||||
\(25\) | 3.53868 | + | 3.53239i | 0.707736 | + | 0.706477i | ||||
\(26\) | −1.65478 | − | 2.50718i | −0.324528 | − | 0.491698i | ||||
\(27\) | −3.74359 | − | 3.74359i | −0.720455 | − | 0.720455i | ||||
\(28\) | 1.60143 | + | 3.99358i | 0.302642 | + | 0.754715i | ||||
\(29\) | − | 7.97836i | − | 1.48154i | −0.671757 | − | 0.740772i | \(-0.734460\pi\) | ||
0.671757 | − | 0.740772i | \(-0.265540\pi\) | |||||||
\(30\) | 5.26951 | − | 1.01961i | 0.962077 | − | 0.186154i | ||||
\(31\) | 10.3376i | 1.85669i | 0.371719 | + | 0.928345i | \(0.378768\pi\) | ||||
−0.371719 | + | 0.928345i | \(0.621232\pi\) | |||||||
\(32\) | 3.00832 | + | 4.79062i | 0.531800 | + | 0.846870i | ||||
\(33\) | −4.81717 | − | 4.81717i | −0.838561 | − | 0.838561i | ||||
\(34\) | −6.59054 | + | 4.34986i | −1.13027 | + | 0.745995i | ||||
\(35\) | −1.84290 | − | 4.44357i | −0.311507 | − | 0.751100i | ||||
\(36\) | −0.0937696 | + | 0.219318i | −0.0156283 | + | 0.0365531i | ||||
\(37\) | 6.01436 | − | 6.01436i | 0.988755 | − | 0.988755i | −0.0111828 | − | 0.999937i | \(-0.503560\pi\) |
0.999937 | + | 0.0111828i | \(0.00355967\pi\) | |||||||
\(38\) | 1.38545 | + | 0.283752i | 0.224750 | + | 0.0460307i | ||||
\(39\) | 3.60530 | 0.577311 | ||||||||
\(40\) | −3.42623 | − | 5.31610i | −0.541735 | − | 0.840550i | ||||
\(41\) | 4.47478 | 0.698844 | 0.349422 | − | 0.936965i | \(-0.386378\pi\) | ||||
0.349422 | + | 0.936965i | \(0.386378\pi\) | |||||||
\(42\) | −5.05889 | − | 1.03610i | −0.780604 | − | 0.159874i | ||||
\(43\) | 1.96095 | − | 1.96095i | 0.299042 | − | 0.299042i | −0.541597 | − | 0.840639i | \(-0.682180\pi\) |
0.840639 | + | 0.541597i | \(0.182180\pi\) | |||||||
\(44\) | −3.15585 | + | 7.38124i | −0.475762 | + | 1.11276i | ||||
\(45\) | 0.101943 | − | 0.246423i | 0.0151968 | − | 0.0367346i | ||||
\(46\) | 7.98484 | − | 5.27012i | 1.17730 | − | 0.777037i | ||||
\(47\) | −2.21501 | − | 2.21501i | −0.323093 | − | 0.323093i | 0.526860 | − | 0.849952i | \(-0.323369\pi\) |
−0.849952 | + | 0.526860i | \(0.823369\pi\) | |||||||
\(48\) | −6.78735 | − | 0.153821i | −0.979670 | − | 0.0222022i | ||||
\(49\) | − | 2.37169i | − | 0.338812i | ||||||
\(50\) | 3.90036 | + | 5.89807i | 0.551594 | + | 0.834113i | ||||
\(51\) | − | 9.47715i | − | 1.32707i | ||||||
\(52\) | −1.58120 | − | 3.94313i | −0.219273 | − | 0.546813i | ||||
\(53\) | −5.27852 | − | 5.27852i | −0.725060 | − | 0.725060i | 0.244571 | − | 0.969631i | \(-0.421353\pi\) |
−0.969631 | + | 0.244571i | \(0.921353\pi\) | |||||||
\(54\) | −4.12433 | − | 6.24883i | −0.561250 | − | 0.850358i | ||||
\(55\) | 3.43093 | − | 8.29345i | 0.462627 | − | 1.11829i | ||||
\(56\) | 1.08552 | + | 5.98733i | 0.145059 | + | 0.800091i | ||||
\(57\) | −1.20015 | + | 1.20015i | −0.158964 | + | 0.158964i | ||||
\(58\) | 2.26388 | − | 11.0537i | 0.297262 | − | 1.45142i | ||||
\(59\) | 5.37196 | 0.699370 | 0.349685 | − | 0.936867i | \(-0.386289\pi\) | ||||
0.349685 | + | 0.936867i | \(0.386289\pi\) | |||||||
\(60\) | 7.58999 | + | 0.0826166i | 0.979863 | + | 0.0106658i | ||||
\(61\) | 12.0386 | 1.54138 | 0.770692 | − | 0.637208i | \(-0.219911\pi\) | ||||
0.770692 | + | 0.637208i | \(0.219911\pi\) | |||||||
\(62\) | −2.93332 | + | 14.3223i | −0.372532 | + | 1.81893i | ||||
\(63\) | −0.181425 | + | 0.181425i | −0.0228574 | + | 0.0228574i | ||||
\(64\) | 2.80854 | + | 7.49080i | 0.351067 | + | 0.936350i | ||||
\(65\) | 1.81962 | + | 4.38743i | 0.225696 | + | 0.544194i | ||||
\(66\) | −5.30708 | − | 8.04085i | −0.653257 | − | 0.989760i | ||||
\(67\) | 0.631476 | + | 0.631476i | 0.0771471 | + | 0.0771471i | 0.744627 | − | 0.667480i | \(-0.232627\pi\) |
−0.667480 | + | 0.744627i | \(0.732627\pi\) | |||||||
\(68\) | −10.3652 | + | 4.15645i | −1.25696 | + | 0.504044i | ||||
\(69\) | 11.4821i | 1.38229i | ||||||||
\(70\) | −1.29239 | − | 6.67929i | −0.154470 | − | 0.798327i | ||||
\(71\) | 6.42369i | 0.762352i | 0.924502 | + | 0.381176i | \(0.124481\pi\) | ||||
−0.924502 | + | 0.381176i | \(0.875519\pi\) | |||||||
\(72\) | −0.192146 | + | 0.277248i | −0.0226446 | + | 0.0326740i | ||||
\(73\) | −2.26914 | − | 2.26914i | −0.265583 | − | 0.265583i | 0.561735 | − | 0.827317i | \(-0.310134\pi\) |
−0.827317 | + | 0.561735i | \(0.810134\pi\) | |||||||
\(74\) | 10.0392 | − | 6.62604i | 1.16703 | − | 0.770261i | ||||
\(75\) | −8.48637 | + | 0.00755284i | −0.979921 | + | 0.000872127i | ||||
\(76\) | 1.83897 | + | 0.786251i | 0.210944 | + | 0.0901892i | ||||
\(77\) | −6.10592 | + | 6.10592i | −0.695834 | + | 0.695834i | ||||
\(78\) | 4.99499 | + | 1.02301i | 0.565571 | + | 0.115833i | ||||
\(79\) | 4.54855 | 0.511751 | 0.255876 | − | 0.966710i | \(-0.417636\pi\) | ||||
0.255876 | + | 0.966710i | \(0.417636\pi\) | |||||||
\(80\) | −3.23843 | − | 8.33742i | −0.362068 | − | 0.932152i | ||||
\(81\) | 8.62799 | 0.958666 | ||||||||
\(82\) | 6.19961 | + | 1.26973i | 0.684632 | + | 0.140218i | ||||
\(83\) | −4.42714 | + | 4.42714i | −0.485942 | + | 0.485942i | −0.907023 | − | 0.421081i | \(-0.861651\pi\) |
0.421081 | + | 0.907023i | \(0.361651\pi\) | |||||||
\(84\) | −6.71487 | − | 2.87094i | −0.732653 | − | 0.313246i | ||||
\(85\) | 11.5331 | − | 4.78318i | 1.25094 | − | 0.518809i | ||||
\(86\) | 3.27323 | − | 2.16038i | 0.352961 | − | 0.232960i | ||||
\(87\) | 9.57526 | + | 9.57526i | 1.02658 | + | 1.02658i | ||||
\(88\) | −6.46673 | + | 9.33089i | −0.689355 | + | 0.994676i | ||||
\(89\) | − | 8.81939i | − | 0.934854i | −0.884032 | − | 0.467427i | \(-0.845181\pi\) | ||
0.884032 | − | 0.467427i | \(-0.154819\pi\) | |||||||
\(90\) | 0.211161 | − | 0.312481i | 0.0222583 | − | 0.0329384i | ||||
\(91\) | − | 4.56984i | − | 0.479050i | ||||||
\(92\) | 12.5580 | − | 5.03580i | 1.30927 | − | 0.525018i | ||||
\(93\) | −12.4067 | − | 12.4067i | −1.28652 | − | 1.28652i | ||||
\(94\) | −2.44029 | − | 3.69731i | −0.251696 | − | 0.381349i | ||||
\(95\) | −2.06624 | − | 0.854787i | −0.211992 | − | 0.0876993i | ||||
\(96\) | −9.35992 | − | 2.13904i | −0.955293 | − | 0.218315i | ||||
\(97\) | 8.06581 | − | 8.06581i | 0.818959 | − | 0.818959i | −0.166998 | − | 0.985957i | \(-0.553407\pi\) |
0.985957 | + | 0.166998i | \(0.0534074\pi\) | |||||||
\(98\) | 0.672971 | − | 3.28586i | 0.0679804 | − | 0.331922i | ||||
\(99\) | −0.478691 | −0.0481103 | ||||||||
\(100\) | 3.73018 | + | 9.27824i | 0.373018 | + | 0.927824i | ||||
\(101\) | −12.2526 | −1.21918 | −0.609589 | − | 0.792718i | \(-0.708666\pi\) | ||||
−0.609589 | + | 0.792718i | \(0.708666\pi\) | |||||||
\(102\) | 2.68916 | − | 13.1302i | 0.266267 | − | 1.30008i | ||||
\(103\) | −1.67647 | + | 1.67647i | −0.165187 | + | 0.165187i | −0.784860 | − | 0.619673i | \(-0.787265\pi\) |
0.619673 | + | 0.784860i | \(0.287265\pi\) | |||||||
\(104\) | −1.07181 | − | 5.91169i | −0.105100 | − | 0.579689i | ||||
\(105\) | 7.54473 | + | 3.12120i | 0.736290 | + | 0.304598i | ||||
\(106\) | −5.81536 | − | 8.81094i | −0.564837 | − | 0.855794i | ||||
\(107\) | −5.31906 | − | 5.31906i | −0.514212 | − | 0.514212i | 0.401602 | − | 0.915814i | \(-0.368454\pi\) |
−0.915814 | + | 0.401602i | \(0.868454\pi\) | |||||||
\(108\) | −3.94095 | − | 9.82776i | −0.379218 | − | 0.945677i | ||||
\(109\) | 14.3543i | 1.37489i | 0.726237 | + | 0.687444i | \(0.241267\pi\) | ||||
−0.726237 | + | 0.687444i | \(0.758733\pi\) | |||||||
\(110\) | 7.10669 | − | 10.5167i | 0.677596 | − | 1.00272i | ||||
\(111\) | 14.4363i | 1.37023i | ||||||||
\(112\) | −0.194973 | + | 8.60320i | −0.0184233 | + | 0.812926i | ||||
\(113\) | 1.96246 | + | 1.96246i | 0.184613 | + | 0.184613i | 0.793362 | − | 0.608750i | \(-0.208329\pi\) |
−0.608750 | + | 0.793362i | \(0.708329\pi\) | |||||||
\(114\) | −2.00330 | + | 1.32221i | −0.187627 | + | 0.123837i | ||||
\(115\) | −13.9731 | + | 5.79512i | −1.30299 | + | 0.540397i | ||||
\(116\) | 6.27300 | − | 14.6720i | 0.582433 | − | 1.36226i | ||||
\(117\) | 0.179133 | − | 0.179133i | 0.0165609 | − | 0.0165609i | ||||
\(118\) | 7.44261 | + | 1.52431i | 0.685148 | + | 0.140324i | ||||
\(119\) | −12.0126 | −1.10119 | ||||||||
\(120\) | 10.4921 | + | 2.26814i | 0.957797 | + | 0.207052i | ||||
\(121\) | −5.11051 | −0.464592 | ||||||||
\(122\) | 16.6789 | + | 3.41598i | 1.51004 | + | 0.309268i | ||||
\(123\) | −5.37043 | + | 5.37043i | −0.484235 | + | 0.484235i | ||||
\(124\) | −8.12796 | + | 19.0106i | −0.729913 | + | 1.70720i | ||||
\(125\) | −4.29232 | − | 10.3236i | −0.383916 | − | 0.923368i | ||||
\(126\) | −0.302836 | + | 0.199876i | −0.0269788 | + | 0.0178064i | ||||
\(127\) | −7.79354 | − | 7.79354i | −0.691565 | − | 0.691565i | 0.271012 | − | 0.962576i | \(-0.412642\pi\) |
−0.962576 | + | 0.271012i | \(0.912642\pi\) | |||||||
\(128\) | 1.76557 | + | 11.1751i | 0.156056 | + | 0.987748i | ||||
\(129\) | 4.70688i | 0.414418i | ||||||||
\(130\) | 1.27606 | + | 6.59491i | 0.111918 | + | 0.578412i | ||||
\(131\) | 3.57377i | 0.312242i | 0.987738 | + | 0.156121i | \(0.0498989\pi\) | ||||
−0.987738 | + | 0.156121i | \(0.950101\pi\) | |||||||
\(132\) | −5.07112 | − | 12.6461i | −0.441384 | − | 1.10070i | ||||
\(133\) | 1.52124 | + | 1.52124i | 0.131908 | + | 0.131908i | ||||
\(134\) | 0.695699 | + | 1.05406i | 0.0600992 | + | 0.0910573i | ||||
\(135\) | 4.53518 | + | 10.9351i | 0.390326 | + | 0.941146i | ||||
\(136\) | −15.5399 | + | 2.81744i | −1.33253 | + | 0.241593i | ||||
\(137\) | −15.5792 | + | 15.5792i | −1.33102 | + | 1.33102i | −0.426565 | + | 0.904457i | \(0.640276\pi\) |
−0.904457 | + | 0.426565i | \(0.859724\pi\) | |||||||
\(138\) | −3.25808 | + | 15.9080i | −0.277347 | + | 1.35418i | ||||
\(139\) | −6.05603 | −0.513666 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(140\) | 0.104719 | − | 9.62057i | 0.00885040 | − | 0.813086i | ||||
\(141\) | 5.31671 | 0.447748 | ||||||||
\(142\) | −1.82274 | + | 8.89973i | −0.152961 | + | 0.746849i | ||||
\(143\) | 6.02878 | − | 6.02878i | 0.504152 | − | 0.504152i | ||||
\(144\) | −0.344879 | + | 0.329593i | −0.0287399 | + | 0.0274661i | ||||
\(145\) | −6.81979 | + | 16.4852i | −0.566353 | + | 1.36902i | ||||
\(146\) | −2.49992 | − | 3.78766i | −0.206895 | − | 0.313469i | ||||
\(147\) | 2.84639 | + | 2.84639i | 0.234766 | + | 0.234766i | ||||
\(148\) | 15.7890 | − | 6.33142i | 1.29785 | − | 0.520440i | ||||
\(149\) | 4.53121i | 0.371211i | 0.982624 | + | 0.185606i | \(0.0594247\pi\) | ||||
−0.982624 | + | 0.185606i | \(0.940575\pi\) | |||||||
\(150\) | −11.7596 | − | 2.39756i | −0.960169 | − | 0.195760i | ||||
\(151\) | − | 14.4169i | − | 1.17323i | −0.809864 | − | 0.586617i | \(-0.800459\pi\) | ||
0.809864 | − | 0.586617i | \(-0.199541\pi\) | |||||||
\(152\) | 2.32471 | + | 1.61113i | 0.188559 | + | 0.130680i | ||||
\(153\) | −0.470881 | − | 0.470881i | −0.0380685 | − | 0.0380685i | ||||
\(154\) | −10.1920 | + | 6.72691i | −0.821298 | + | 0.542070i | ||||
\(155\) | 8.83646 | − | 21.3600i | 0.709761 | − | 1.71567i | ||||
\(156\) | 6.63004 | + | 2.83468i | 0.530828 | + | 0.226956i | ||||
\(157\) | 1.75431 | − | 1.75431i | 0.140009 | − | 0.140009i | −0.633629 | − | 0.773637i | \(-0.718435\pi\) |
0.773637 | + | 0.633629i | \(0.218435\pi\) | |||||||
\(158\) | 6.30181 | + | 1.29066i | 0.501345 | + | 0.102679i | ||||
\(159\) | 12.6701 | 1.00480 | ||||||||
\(160\) | −2.12094 | − | 12.4700i | −0.167675 | − | 0.985842i | ||||
\(161\) | 14.5540 | 1.14702 | ||||||||
\(162\) | 11.9537 | + | 2.44821i | 0.939171 | + | 0.192350i | ||||
\(163\) | −9.41490 | + | 9.41490i | −0.737432 | + | 0.737432i | −0.972080 | − | 0.234648i | \(-0.924606\pi\) |
0.234648 | + | 0.972080i | \(0.424606\pi\) | |||||||
\(164\) | 8.22899 | + | 3.51831i | 0.642576 | + | 0.274733i | ||||
\(165\) | 5.83576 | + | 14.0711i | 0.454313 | + | 1.09543i | ||||
\(166\) | −7.38981 | + | 4.87739i | −0.573561 | + | 0.378559i | ||||
\(167\) | 8.94130 | + | 8.94130i | 0.691899 | + | 0.691899i | 0.962649 | − | 0.270751i | \(-0.0872719\pi\) |
−0.270751 | + | 0.962649i | \(0.587272\pi\) | |||||||
\(168\) | −8.48852 | − | 5.88292i | −0.654903 | − | 0.453877i | ||||
\(169\) | − | 8.48789i | − | 0.652914i | ||||||
\(170\) | 17.3358 | − | 3.35434i | 1.32960 | − | 0.257266i | ||||
\(171\) | 0.119262i | 0.00912016i | ||||||||
\(172\) | 5.14793 | − | 2.06433i | 0.392526 | − | 0.157403i | ||||
\(173\) | −2.06373 | − | 2.06373i | −0.156902 | − | 0.156902i | 0.624290 | − | 0.781193i | \(-0.285388\pi\) |
−0.781193 | + | 0.624290i | \(0.785388\pi\) | |||||||
\(174\) | 10.5491 | + | 15.9831i | 0.799724 | + | 1.21167i | ||||
\(175\) | 0.00957348 | + | 10.7568i | 0.000723687 | + | 0.813134i | ||||
\(176\) | −11.6070 | + | 11.0926i | −0.874912 | + | 0.836135i | ||||
\(177\) | −6.44718 | + | 6.44718i | −0.484600 | + | 0.484600i | ||||
\(178\) | 2.50252 | − | 12.2189i | 0.187572 | − | 0.915843i | ||||
\(179\) | −1.70622 | −0.127529 | −0.0637645 | − | 0.997965i | \(-0.520311\pi\) | ||||
−0.0637645 | + | 0.997965i | \(0.520311\pi\) | |||||||
\(180\) | 0.381221 | − | 0.373011i | 0.0284145 | − | 0.0278026i | ||||
\(181\) | 20.1290 | 1.49618 | 0.748089 | − | 0.663599i | \(-0.230972\pi\) | ||||
0.748089 | + | 0.663599i | \(0.230972\pi\) | |||||||
\(182\) | 1.29670 | − | 6.33131i | 0.0961180 | − | 0.469308i | ||||
\(183\) | −14.4482 | + | 14.4482i | −1.06804 | + | 1.06804i | ||||
\(184\) | 18.8275 | − | 3.41350i | 1.38798 | − | 0.251646i | ||||
\(185\) | −17.5681 | + | 7.28610i | −1.29163 | + | 0.535685i | ||||
\(186\) | −13.6685 | − | 20.7094i | −1.00222 | − | 1.51849i | ||||
\(187\) | −15.8477 | − | 15.8477i | −1.15890 | − | 1.15890i | ||||
\(188\) | −2.33178 | − | 5.81490i | −0.170063 | − | 0.424095i | ||||
\(189\) | − | 11.3898i | − | 0.828484i | ||||||
\(190\) | −2.62013 | − | 1.77057i | −0.190084 | − | 0.128450i | ||||
\(191\) | − | 16.2481i | − | 1.17567i | −0.808980 | − | 0.587836i | \(-0.799980\pi\) | ||
0.808980 | − | 0.587836i | \(-0.200020\pi\) | |||||||
\(192\) | −12.3608 | − | 5.61944i | −0.892063 | − | 0.405548i | ||||
\(193\) | 6.47432 | + | 6.47432i | 0.466031 | + | 0.466031i | 0.900626 | − | 0.434595i | \(-0.143108\pi\) |
−0.434595 | + | 0.900626i | \(0.643108\pi\) | |||||||
\(194\) | 13.4635 | − | 8.88612i | 0.966623 | − | 0.637987i | ||||
\(195\) | −7.44942 | − | 3.08177i | −0.533464 | − | 0.220690i | ||||
\(196\) | 1.86474 | − | 4.36146i | 0.133196 | − | 0.311533i | ||||
\(197\) | −4.14788 | + | 4.14788i | −0.295524 | + | 0.295524i | −0.839258 | − | 0.543734i | \(-0.817010\pi\) |
0.543734 | + | 0.839258i | \(0.317010\pi\) | |||||||
\(198\) | −0.663205 | − | 0.135830i | −0.0471319 | − | 0.00965299i | ||||
\(199\) | 10.4993 | 0.744272 | 0.372136 | − | 0.928178i | \(-0.378625\pi\) | ||||
0.372136 | + | 0.928178i | \(0.378625\pi\) | |||||||
\(200\) | 2.53527 | + | 13.9130i | 0.179271 | + | 0.983800i | ||||
\(201\) | −1.51574 | −0.106912 | ||||||||
\(202\) | −16.9754 | − | 3.47670i | −1.19439 | − | 0.244620i | ||||
\(203\) | 12.1370 | − | 12.1370i | 0.851847 | − | 0.851847i | ||||
\(204\) | 7.45142 | − | 17.4282i | 0.521704 | − | 1.22022i | ||||
\(205\) | −9.24597 | − | 3.82499i | −0.645766 | − | 0.267149i | ||||
\(206\) | −2.79837 | + | 1.84697i | −0.194972 | + | 0.128685i | ||||
\(207\) | 0.570502 | + | 0.570502i | 0.0396526 | + | 0.0396526i | ||||
\(208\) | 0.192510 | − | 8.49451i | 0.0133482 | − | 0.588989i | ||||
\(209\) | 4.01379i | 0.277640i | ||||||||
\(210\) | 9.56723 | + | 6.46511i | 0.660202 | + | 0.446135i | ||||
\(211\) | 16.0916i | 1.10779i | 0.832585 | + | 0.553897i | \(0.186860\pi\) | ||||
−0.832585 | + | 0.553897i | \(0.813140\pi\) | |||||||
\(212\) | −5.55679 | − | 13.8573i | −0.381642 | − | 0.951721i | ||||
\(213\) | −7.70942 | − | 7.70942i | −0.528241 | − | 0.528241i | ||||
\(214\) | −5.86002 | − | 8.87860i | −0.400583 | − | 0.606929i | ||||
\(215\) | −5.72798 | + | 2.37559i | −0.390645 | + | 0.162014i | ||||
\(216\) | −2.67136 | − | 14.7342i | −0.181763 | − | 1.00253i | ||||
\(217\) | −15.7259 | + | 15.7259i | −1.06755 | + | 1.06755i | ||||
\(218\) | −4.07305 | + | 19.8872i | −0.275862 | + | 1.34693i | ||||
\(219\) | 5.44663 | 0.368049 | ||||||||
\(220\) | 12.8301 | − | 12.5538i | 0.865006 | − | 0.846378i | ||||
\(221\) | 11.8609 | 0.797847 | ||||||||
\(222\) | −4.09634 | + | 20.0009i | −0.274928 | + | 1.34237i | ||||
\(223\) | 11.4105 | − | 11.4105i | 0.764105 | − | 0.764105i | −0.212957 | − | 0.977062i | \(-0.568309\pi\) |
0.977062 | + | 0.212957i | \(0.0683094\pi\) | |||||||
\(224\) | −2.71130 | + | 11.8640i | −0.181157 | + | 0.792698i | ||||
\(225\) | −0.421278 | + | 0.422029i | −0.0280852 | + | 0.0281352i | ||||
\(226\) | 2.16205 | + | 3.27575i | 0.143817 | + | 0.217900i | ||||
\(227\) | 2.06920 | + | 2.06920i | 0.137338 | + | 0.137338i | 0.772433 | − | 0.635096i | \(-0.219039\pi\) |
−0.635096 | + | 0.772433i | \(0.719039\pi\) | |||||||
\(228\) | −3.15067 | + | 1.26342i | −0.208658 | + | 0.0836723i | ||||
\(229\) | 21.9098i | 1.44784i | 0.689885 | + | 0.723919i | \(0.257661\pi\) | ||||
−0.689885 | + | 0.723919i | \(0.742339\pi\) | |||||||
\(230\) | −21.0034 | + | 4.06399i | −1.38492 | + | 0.267971i | ||||
\(231\) | − | 14.6561i | − | 0.964299i | ||||||
\(232\) | 12.8542 | − | 18.5474i | 0.843916 | − | 1.21769i | ||||
\(233\) | 9.03376 | + | 9.03376i | 0.591821 | + | 0.591821i | 0.938123 | − | 0.346302i | \(-0.112563\pi\) |
−0.346302 | + | 0.938123i | \(0.612563\pi\) | |||||||
\(234\) | 0.299010 | − | 0.197351i | 0.0195469 | − | 0.0129013i | ||||
\(235\) | 2.68338 | + | 6.47011i | 0.175044 | + | 0.422063i | ||||
\(236\) | 9.87887 | + | 4.22371i | 0.643060 | + | 0.274940i | ||||
\(237\) | −5.45896 | + | 5.45896i | −0.354597 | + | 0.354597i | ||||
\(238\) | −16.6429 | − | 3.40860i | −1.07880 | − | 0.220947i | ||||
\(239\) | −8.80262 | −0.569394 | −0.284697 | − | 0.958618i | \(-0.591893\pi\) | ||||
−0.284697 | + | 0.958618i | \(0.591893\pi\) | |||||||
\(240\) | 13.8928 | + | 6.11957i | 0.896776 | + | 0.395017i | ||||
\(241\) | −2.16116 | −0.139212 | −0.0696062 | − | 0.997575i | \(-0.522174\pi\) | ||||
−0.0696062 | + | 0.997575i | \(0.522174\pi\) | |||||||
\(242\) | −7.08038 | − | 1.45012i | −0.455144 | − | 0.0932171i | ||||
\(243\) | 0.875864 | − | 0.875864i | 0.0561867 | − | 0.0561867i | ||||
\(244\) | 22.1386 | + | 9.46536i | 1.41728 | + | 0.605958i | ||||
\(245\) | −2.02729 | + | 4.90047i | −0.129519 | + | 0.313080i | ||||
\(246\) | −8.96436 | + | 5.91661i | −0.571546 | + | 0.377230i | ||||
\(247\) | −1.50202 | − | 1.50202i | −0.0955711 | − | 0.0955711i | ||||
\(248\) | −16.6552 | + | 24.0319i | −1.05761 | + | 1.52603i | ||||
\(249\) | − | 10.6265i | − | 0.673427i | ||||||
\(250\) | −3.01748 | − | 15.5208i | −0.190842 | − | 0.981621i | ||||
\(251\) | − | 19.5275i | − | 1.23256i | −0.787526 | − | 0.616282i | \(-0.788638\pi\) | ||
0.787526 | − | 0.616282i | \(-0.211362\pi\) | |||||||
\(252\) | −0.476281 | + | 0.190989i | −0.0300029 | + | 0.0120312i | ||||
\(253\) | 19.2004 | + | 19.2004i | 1.20712 | + | 1.20712i | ||||
\(254\) | −8.58616 | − | 13.0090i | −0.538744 | − | 0.816259i | ||||
\(255\) | −8.10094 | + | 19.5820i | −0.507301 | + | 1.22628i | ||||
\(256\) | −0.724840 | + | 15.9836i | −0.0453025 | + | 0.998973i | ||||
\(257\) | 9.86907 | − | 9.86907i | 0.615616 | − | 0.615616i | −0.328788 | − | 0.944404i | \(-0.606640\pi\) |
0.944404 | + | 0.328788i | \(0.106640\pi\) | |||||||
\(258\) | −1.33559 | + | 6.52117i | −0.0831501 | + | 0.405990i | ||||
\(259\) | 18.2985 | 1.13701 | ||||||||
\(260\) | −0.103396 | + | 9.49903i | −0.00641237 | + | 0.589105i | ||||
\(261\) | 0.951512 | 0.0588971 | ||||||||
\(262\) | −1.01406 | + | 4.95129i | −0.0626491 | + | 0.305892i | ||||
\(263\) | −4.12699 | + | 4.12699i | −0.254481 | + | 0.254481i | −0.822805 | − | 0.568324i | \(-0.807592\pi\) |
0.568324 | + | 0.822805i | \(0.307592\pi\) | |||||||
\(264\) | −3.43744 | − | 18.9596i | −0.211560 | − | 1.16688i | ||||
\(265\) | 6.39467 | + | 15.4187i | 0.392821 | + | 0.947162i | ||||
\(266\) | 1.67595 | + | 2.53926i | 0.102759 | + | 0.155692i | ||||
\(267\) | 10.5846 | + | 10.5846i | 0.647769 | + | 0.647769i | ||||
\(268\) | 0.664766 | + | 1.65776i | 0.0406070 | + | 0.101264i | ||||
\(269\) | − | 17.1547i | − | 1.04594i | −0.852351 | − | 0.522970i | \(-0.824824\pi\) | ||
0.852351 | − | 0.522970i | \(-0.175176\pi\) | |||||||
\(270\) | 3.18042 | + | 16.4370i | 0.193554 | + | 1.00032i | ||||
\(271\) | 24.3506i | 1.47919i | 0.673050 | + | 0.739597i | \(0.264984\pi\) | ||||
−0.673050 | + | 0.739597i | \(0.735016\pi\) | |||||||
\(272\) | −22.3293 | − | 0.506046i | −1.35391 | − | 0.0306835i | ||||
\(273\) | 5.48452 | + | 5.48452i | 0.331938 | + | 0.331938i | ||||
\(274\) | −26.0049 | + | 17.1637i | −1.57101 | + | 1.03689i | ||||
\(275\) | −14.1783 | + | 14.2035i | −0.854981 | + | 0.856504i | ||||
\(276\) | −9.02786 | + | 21.1153i | −0.543413 | + | 1.27099i | ||||
\(277\) | −10.5003 | + | 10.5003i | −0.630902 | + | 0.630902i | −0.948294 | − | 0.317393i | \(-0.897193\pi\) |
0.317393 | + | 0.948294i | \(0.397193\pi\) | |||||||
\(278\) | −8.39035 | − | 1.71841i | −0.503220 | − | 0.103063i | ||||
\(279\) | −1.23288 | −0.0738106 | ||||||||
\(280\) | 2.87494 | − | 13.2991i | 0.171811 | − | 0.794776i | ||||
\(281\) | −1.50845 | −0.0899866 | −0.0449933 | − | 0.998987i | \(-0.514327\pi\) | ||||
−0.0449933 | + | 0.998987i | \(0.514327\pi\) | |||||||
\(282\) | 7.36606 | + | 1.50863i | 0.438643 | + | 0.0898375i | ||||
\(283\) | 12.4817 | − | 12.4817i | 0.741959 | − | 0.741959i | −0.230996 | − | 0.972955i | \(-0.574198\pi\) |
0.972955 | + | 0.230996i | \(0.0741985\pi\) | |||||||
\(284\) | −5.05064 | + | 11.8130i | −0.299700 | + | 0.700971i | ||||
\(285\) | 3.50568 | − | 1.45393i | 0.207659 | − | 0.0861233i | ||||
\(286\) | 10.0633 | − | 6.64193i | 0.595055 | − | 0.392745i | ||||
\(287\) | 6.80720 | + | 6.80720i | 0.401816 | + | 0.401816i | ||||
\(288\) | −0.571337 | + | 0.358777i | −0.0336664 | + | 0.0211411i | ||||
\(289\) | − | 14.1782i | − | 0.834014i | ||||||
\(290\) | −14.1262 | + | 20.9043i | −0.829520 | + | 1.22755i | ||||
\(291\) | 19.3604i | 1.13493i | ||||||||
\(292\) | −2.38876 | − | 5.95699i | −0.139792 | − | 0.348607i | ||||
\(293\) | −0.143152 | − | 0.143152i | −0.00836306 | − | 0.00836306i | 0.702913 | − | 0.711276i | \(-0.251882\pi\) |
−0.711276 | + | 0.702913i | \(0.751882\pi\) | |||||||
\(294\) | 3.13587 | + | 4.75121i | 0.182888 | + | 0.277096i | ||||
\(295\) | −11.0997 | − | 4.59188i | −0.646252 | − | 0.267350i | ||||
\(296\) | 23.6715 | − | 4.29173i | 1.37588 | − | 0.249452i | ||||
\(297\) | 15.0260 | − | 15.0260i | 0.871897 | − | 0.871897i | ||||
\(298\) | −1.28574 | + | 6.27779i | −0.0744809 | + | 0.363662i | ||||
\(299\) | −14.3701 | −0.831047 | ||||||||
\(300\) | −15.6121 | − | 6.65853i | −0.901365 | − | 0.384430i | ||||
\(301\) | 5.96613 | 0.343882 | ||||||||
\(302\) | 4.09084 | − | 19.9740i | 0.235401 | − | 1.14938i | ||||
\(303\) | 14.7050 | − | 14.7050i | 0.844780 | − | 0.844780i | ||||
\(304\) | 2.76362 | + | 2.89178i | 0.158504 | + | 0.165855i | ||||
\(305\) | −24.8746 | − | 10.2904i | −1.42432 | − | 0.589228i | ||||
\(306\) | −0.518771 | − | 0.785999i | −0.0296562 | − | 0.0449325i | ||||
\(307\) | −22.5165 | − | 22.5165i | −1.28508 | − | 1.28508i | −0.937736 | − | 0.347348i | \(-0.887082\pi\) |
−0.347348 | − | 0.937736i | \(-0.612918\pi\) | |||||||
\(308\) | −16.0294 | + | 6.42781i | −0.913359 | + | 0.366258i | ||||
\(309\) | − | 4.02404i | − | 0.228920i | ||||||
\(310\) | 18.3034 | − | 27.0859i | 1.03957 | − | 1.53838i | ||||
\(311\) | 10.0019i | 0.567158i | 0.958949 | + | 0.283579i | \(0.0915219\pi\) | ||||
−0.958949 | + | 0.283579i | \(0.908478\pi\) | |||||||
\(312\) | 8.38128 | + | 5.80860i | 0.474497 | + | 0.328847i | ||||
\(313\) | −19.1644 | − | 19.1644i | −1.08324 | − | 1.08324i | −0.996206 | − | 0.0870306i | \(-0.972262\pi\) |
−0.0870306 | − | 0.996206i | \(-0.527738\pi\) | |||||||
\(314\) | 2.92830 | − | 1.93272i | 0.165253 | − | 0.109070i | ||||
\(315\) | 0.529947 | − | 0.219788i | 0.0298591 | − | 0.0123836i | ||||
\(316\) | 8.36464 | + | 3.57630i | 0.470548 | + | 0.201183i | ||||
\(317\) | 9.07885 | − | 9.07885i | 0.509919 | − | 0.509919i | −0.404583 | − | 0.914501i | \(-0.632583\pi\) |
0.914501 | + | 0.404583i | \(0.132583\pi\) | |||||||
\(318\) | 17.5538 | + | 3.59516i | 0.984368 | + | 0.201606i | ||||
\(319\) | 32.0235 | 1.79297 | ||||||||
\(320\) | 0.599932 | − | 17.8785i | 0.0335372 | − | 0.999437i | ||||
\(321\) | 12.7674 | 0.712605 | ||||||||
\(322\) | 20.1639 | + | 4.12973i | 1.12369 | + | 0.230141i | ||||
\(323\) | −3.94831 | + | 3.94831i | −0.219690 | + | 0.219690i | ||||
\(324\) | 15.8666 | + | 6.78377i | 0.881479 | + | 0.376876i | ||||
\(325\) | −0.00945254 | − | 10.6209i | −0.000524332 | − | 0.589140i | ||||
\(326\) | −15.7154 | + | 10.3724i | −0.870396 | + | 0.574475i | ||||
\(327\) | −17.2273 | − | 17.2273i | −0.952673 | − | 0.952673i | ||||
\(328\) | 10.4026 | + | 7.20945i | 0.574386 | + | 0.398075i | ||||
\(329\) | − | 6.73911i | − | 0.371539i | ||||||
\(330\) | 4.09249 | + | 21.1507i | 0.225284 | + | 1.16431i | ||||
\(331\) | 7.53646i | 0.414242i | 0.978315 | + | 0.207121i | \(0.0664093\pi\) | ||||
−0.978315 | + | 0.207121i | \(0.933591\pi\) | |||||||
\(332\) | −11.6222 | + | 4.66053i | −0.637852 | + | 0.255780i | ||||
\(333\) | 0.717282 | + | 0.717282i | 0.0393068 | + | 0.0393068i | ||||
\(334\) | 9.85066 | + | 14.9249i | 0.539004 | + | 0.816653i | ||||
\(335\) | −0.765002 | − | 1.84456i | −0.0417965 | − | 0.100779i | ||||
\(336\) | −10.0912 | − | 10.5592i | −0.550518 | − | 0.576049i | ||||
\(337\) | 7.14595 | − | 7.14595i | 0.389264 | − | 0.389264i | −0.485161 | − | 0.874425i | \(-0.661239\pi\) |
0.874425 | + | 0.485161i | \(0.161239\pi\) | |||||||
\(338\) | 2.40846 | − | 11.7596i | 0.131003 | − | 0.639637i | ||||
\(339\) | −4.71051 | −0.255840 | ||||||||
\(340\) | 24.9698 | + | 0.271795i | 1.35418 | + | 0.0147401i | ||||
\(341\) | −41.4930 | −2.24697 | ||||||||
\(342\) | −0.0338407 | + | 0.165232i | −0.00182990 | + | 0.00893470i | ||||
\(343\) | 14.2565 | − | 14.2565i | 0.769781 | − | 0.769781i | ||||
\(344\) | 7.71797 | − | 1.39930i | 0.416125 | − | 0.0754450i | ||||
\(345\) | 9.81479 | − | 23.7249i | 0.528410 | − | 1.27730i | ||||
\(346\) | −2.27362 | − | 3.44479i | −0.122230 | − | 0.185193i | ||||
\(347\) | −2.43847 | − | 2.43847i | −0.130904 | − | 0.130904i | 0.638619 | − | 0.769523i | \(-0.279506\pi\) |
−0.769523 | + | 0.638619i | \(0.779506\pi\) | |||||||
\(348\) | 10.0800 | + | 25.1372i | 0.540347 | + | 1.34749i | ||||
\(349\) | − | 25.9387i | − | 1.38847i | −0.719750 | − | 0.694233i | \(-0.755744\pi\) | ||
0.719750 | − | 0.694233i | \(-0.244256\pi\) | |||||||
\(350\) | −3.03899 | + | 14.9057i | −0.162441 | + | 0.796744i | ||||
\(351\) | 11.2459i | 0.600261i | ||||||||
\(352\) | −19.2285 | + | 12.0747i | −1.02488 | + | 0.643586i | ||||
\(353\) | −15.6893 | − | 15.6893i | −0.835056 | − | 0.835056i | 0.153148 | − | 0.988203i | \(-0.451059\pi\) |
−0.988203 | + | 0.153148i | \(0.951059\pi\) | |||||||
\(354\) | −10.7617 | + | 7.10287i | −0.571977 | + | 0.377513i | ||||
\(355\) | 5.49089 | − | 13.2729i | 0.291426 | − | 0.704451i | ||||
\(356\) | 6.93426 | − | 16.2186i | 0.367515 | − | 0.859584i | ||||
\(357\) | 14.4170 | − | 14.4170i | 0.763027 | − | 0.763027i | ||||
\(358\) | −2.36389 | − | 0.484144i | −0.124936 | − | 0.0255878i | ||||
\(359\) | −15.8725 | −0.837718 | −0.418859 | − | 0.908051i | \(-0.637570\pi\) | ||||
−0.418859 | + | 0.908051i | \(0.637570\pi\) | |||||||
\(360\) | 0.634007 | − | 0.408618i | 0.0334151 | − | 0.0215360i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 27.8878 | + | 5.71165i | 1.46575 | + | 0.300198i | ||||
\(363\) | 6.13340 | − | 6.13340i | 0.321920 | − | 0.321920i | ||||
\(364\) | 3.59305 | − | 8.40380i | 0.188327 | − | 0.440479i | ||||
\(365\) | 2.74895 | + | 6.62821i | 0.143887 | + | 0.346937i | ||||
\(366\) | −24.1170 | + | 15.9176i | −1.26061 | + | 0.832025i | ||||
\(367\) | 9.08519 | + | 9.08519i | 0.474243 | + | 0.474243i | 0.903285 | − | 0.429042i | \(-0.141149\pi\) |
−0.429042 | + | 0.903285i | \(0.641149\pi\) | |||||||
\(368\) | 27.0533 | + | 0.613105i | 1.41025 | + | 0.0319603i | ||||
\(369\) | 0.533670i | 0.0277817i | ||||||||
\(370\) | −26.4072 | + | 5.10958i | −1.37285 | + | 0.265635i | ||||
\(371\) | − | 16.0597i | − | 0.833780i | ||||||
\(372\) | −13.0608 | − | 32.5704i | −0.677170 | − | 1.68870i | ||||
\(373\) | −3.81246 | − | 3.81246i | −0.197402 | − | 0.197402i | 0.601483 | − | 0.798885i | \(-0.294577\pi\) |
−0.798885 | + | 0.601483i | \(0.794577\pi\) | |||||||
\(374\) | −17.4594 | − | 26.4530i | −0.902805 | − | 1.36785i | ||||
\(375\) | 17.5413 | + | 7.23843i | 0.905829 | + | 0.373791i | ||||
\(376\) | −1.58059 | − | 8.71793i | −0.0815128 | − | 0.449593i | ||||
\(377\) | −11.9836 | + | 11.9836i | −0.617189 | + | 0.617189i | ||||
\(378\) | 3.23187 | − | 15.7800i | 0.166230 | − | 0.811636i | ||||
\(379\) | −10.9007 | −0.559930 | −0.279965 | − | 0.960010i | \(-0.590323\pi\) | ||||
−0.279965 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(380\) | −3.12767 | − | 3.19651i | −0.160446 | − | 0.163977i | ||||
\(381\) | 18.7069 | 0.958383 | ||||||||
\(382\) | 4.61044 | − | 22.5110i | 0.235891 | − | 1.15176i | ||||
\(383\) | 14.5162 | − | 14.5162i | 0.741744 | − | 0.741744i | −0.231170 | − | 0.972913i | \(-0.574255\pi\) |
0.972913 | + | 0.231170i | \(0.0742553\pi\) | |||||||
\(384\) | −15.5308 | − | 11.2929i | −0.792552 | − | 0.576287i | ||||
\(385\) | 17.8355 | − | 7.39702i | 0.908983 | − | 0.376987i | ||||
\(386\) | 7.13277 | + | 10.8070i | 0.363048 | + | 0.550060i | ||||
\(387\) | 0.233866 | + | 0.233866i | 0.0118881 | + | 0.0118881i | ||||
\(388\) | 21.1745 | − | 8.49102i | 1.07497 | − | 0.431066i | ||||
\(389\) | − | 15.6390i | − | 0.792929i | −0.918050 | − | 0.396465i | \(-0.870237\pi\) | ||
0.918050 | − | 0.396465i | \(-0.129763\pi\) | |||||||
\(390\) | −9.44637 | − | 6.38344i | −0.478336 | − | 0.323238i | ||||
\(391\) | 37.7744i | 1.91033i | ||||||||
\(392\) | 3.82109 | − | 5.51348i | 0.192994 | − | 0.278473i | ||||
\(393\) | −4.28907 | − | 4.28907i | −0.216355 | − | 0.216355i | ||||
\(394\) | −6.92367 | + | 4.56973i | −0.348810 | + | 0.230220i | ||||
\(395\) | −9.39838 | − | 3.88804i | −0.472884 | − | 0.195628i | ||||
\(396\) | −0.880298 | − | 0.376372i | −0.0442367 | − | 0.0189134i | ||||
\(397\) | 4.42602 | − | 4.42602i | 0.222136 | − | 0.222136i | −0.587262 | − | 0.809397i | \(-0.699794\pi\) |
0.809397 | + | 0.587262i | \(0.199794\pi\) | |||||||
\(398\) | 14.5462 | + | 2.97919i | 0.729137 | + | 0.149333i | ||||
\(399\) | −3.65143 | −0.182800 | ||||||||
\(400\) | −0.435346 | + | 19.9953i | −0.0217673 | + | 0.999763i | ||||
\(401\) | 11.7922 | 0.588875 | 0.294438 | − | 0.955671i | \(-0.404868\pi\) | ||||
0.294438 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(402\) | −2.09998 | − | 0.430093i | −0.104738 | − | 0.0214511i | ||||
\(403\) | 15.5273 | − | 15.5273i | 0.773469 | − | 0.773469i | ||||
\(404\) | −22.5321 | − | 9.63362i | −1.12102 | − | 0.479290i | ||||
\(405\) | −17.8275 | − | 7.37509i | −0.885855 | − | 0.366471i | ||||
\(406\) | 20.2591 | − | 13.3713i | 1.00544 | − | 0.663607i | ||||
\(407\) | 24.1404 | + | 24.1404i | 1.19659 | + | 1.19659i | ||||
\(408\) | 15.2689 | − | 22.0316i | 0.755923 | − | 1.09073i | ||||
\(409\) | − | 23.9203i | − | 1.18278i | −0.806385 | − | 0.591391i | \(-0.798579\pi\) | ||
0.806385 | − | 0.591391i | \(-0.201421\pi\) | |||||||
\(410\) | −11.7245 | − | 7.92291i | −0.579033 | − | 0.391285i | ||||
\(411\) | − | 37.3949i | − | 1.84455i | ||||||
\(412\) | −4.40110 | + | 1.76485i | −0.216827 | + | 0.0869479i | ||||
\(413\) | 8.17202 | + | 8.17202i | 0.402119 | + | 0.402119i | ||||
\(414\) | 0.628523 | + | 0.952285i | 0.0308902 | + | 0.0468023i | ||||
\(415\) | 12.9318 | − | 5.36326i | 0.634796 | − | 0.263272i | ||||
\(416\) | 2.67705 | − | 11.7141i | 0.131253 | − | 0.574333i | ||||
\(417\) | 7.26816 | − | 7.26816i | 0.355924 | − | 0.355924i | ||||
\(418\) | −1.13892 | + | 5.56092i | −0.0557065 | + | 0.271994i | ||||
\(419\) | −23.7000 | −1.15782 | −0.578910 | − | 0.815391i | \(-0.696522\pi\) | ||||
−0.578910 | + | 0.815391i | \(0.696522\pi\) | |||||||
\(420\) | 11.4205 | + | 11.6718i | 0.557262 | + | 0.569527i | ||||
\(421\) | −27.6593 | −1.34803 | −0.674015 | − | 0.738718i | \(-0.735432\pi\) | ||||
−0.674015 | + | 0.738718i | \(0.735432\pi\) | |||||||
\(422\) | −4.56604 | + | 22.2942i | −0.222271 | + | 1.08527i | ||||
\(423\) | 0.264166 | − | 0.264166i | 0.0128442 | − | 0.0128442i | ||||
\(424\) | −3.76665 | − | 20.7754i | −0.182925 | − | 1.00894i | ||||
\(425\) | −27.9187 | + | 0.0248476i | −1.35426 | + | 0.00120528i | ||||
\(426\) | −8.49349 | − | 12.8686i | −0.411511 | − | 0.623486i | ||||
\(427\) | 18.3135 | + | 18.3135i | 0.886254 | + | 0.886254i | ||||
\(428\) | −5.59946 | − | 13.9637i | −0.270660 | − | 0.674961i | ||||
\(429\) | 14.4709i | 0.698663i | ||||||||
\(430\) | −8.60994 | + | 1.66595i | −0.415208 | + | 0.0803393i | ||||
\(431\) | − | 11.7110i | − | 0.564099i | −0.959400 | − | 0.282049i | \(-0.908986\pi\) | ||
0.959400 | − | 0.282049i | \(-0.0910142\pi\) | |||||||
\(432\) | 0.479808 | − | 21.1715i | 0.0230848 | − | 1.01862i | ||||
\(433\) | −4.06976 | − | 4.06976i | −0.195580 | − | 0.195580i | 0.602522 | − | 0.798102i | \(-0.294163\pi\) |
−0.798102 | + | 0.602522i | \(0.794163\pi\) | |||||||
\(434\) | −26.2498 | + | 17.3253i | −1.26003 | + | 0.831641i | ||||
\(435\) | −11.6000 | − | 27.9696i | −0.556175 | − | 1.34104i | ||||
\(436\) | −11.2861 | + | 26.3970i | −0.540504 | + | 1.26419i | ||||
\(437\) | 4.78362 | − | 4.78362i | 0.228831 | − | 0.228831i | ||||
\(438\) | 7.54607 | + | 1.54549i | 0.360565 | + | 0.0738466i | ||||
\(439\) | −25.7007 | −1.22663 | −0.613313 | − | 0.789840i | \(-0.710164\pi\) | ||||
−0.613313 | + | 0.789840i | \(0.710164\pi\) | |||||||
\(440\) | 21.3377 | − | 13.7522i | 1.01724 | − | 0.655609i | ||||
\(441\) | 0.282851 | 0.0134691 | ||||||||
\(442\) | 16.4327 | + | 3.36554i | 0.781622 | + | 0.160082i | ||||
\(443\) | −17.7355 | + | 17.7355i | −0.842640 | + | 0.842640i | −0.989202 | − | 0.146561i | \(-0.953179\pi\) |
0.146561 | + | 0.989202i | \(0.453179\pi\) | |||||||
\(444\) | −11.3506 | + | 26.5479i | −0.538674 | + | 1.25991i | ||||
\(445\) | −7.53870 | + | 18.2230i | −0.357369 | + | 0.863851i | ||||
\(446\) | 19.0465 | − | 12.5710i | 0.901878 | − | 0.595254i | ||||
\(447\) | −5.43815 | − | 5.43815i | −0.257216 | − | 0.257216i | ||||
\(448\) | −7.12283 | + | 15.6677i | −0.336522 | + | 0.740230i | ||||
\(449\) | 5.66338i | 0.267272i | 0.991031 | + | 0.133636i | \(0.0426652\pi\) | ||||
−0.991031 | + | 0.133636i | \(0.957335\pi\) | |||||||
\(450\) | −0.703413 | + | 0.465163i | −0.0331592 | + | 0.0219280i | ||||
\(451\) | 17.9608i | 0.845743i | ||||||||
\(452\) | 2.06592 | + | 5.15189i | 0.0971726 | + | 0.242325i | ||||
\(453\) | 17.3025 | + | 17.3025i | 0.812945 | + | 0.812945i | ||||
\(454\) | 2.27964 | + | 3.45392i | 0.106989 | + | 0.162101i | ||||
\(455\) | −3.90624 | + | 9.44239i | −0.183127 | + | 0.442666i | ||||
\(456\) | −4.72361 | + | 0.856407i | −0.221203 | + | 0.0401049i | ||||
\(457\) | 19.7589 | − | 19.7589i | 0.924284 | − | 0.924284i | −0.0730444 | − | 0.997329i | \(-0.523271\pi\) |
0.997329 | + | 0.0730444i | \(0.0232715\pi\) | |||||||
\(458\) | −6.21694 | + | 30.3550i | −0.290499 | + | 1.41840i | ||||
\(459\) | 29.5617 | 1.37982 | ||||||||
\(460\) | −30.2524 | − | 0.329296i | −1.41053 | − | 0.0153535i | ||||
\(461\) | 31.3335 | 1.45935 | 0.729674 | − | 0.683795i | \(-0.239672\pi\) | ||||
0.729674 | + | 0.683795i | \(0.239672\pi\) | |||||||
\(462\) | 4.15870 | − | 20.3053i | 0.193480 | − | 0.944690i | ||||
\(463\) | −9.54706 | + | 9.54706i | −0.443689 | + | 0.443689i | −0.893250 | − | 0.449560i | \(-0.851581\pi\) |
0.449560 | + | 0.893250i | \(0.351581\pi\) | |||||||
\(464\) | 23.0717 | − | 22.0491i | 1.07108 | − | 1.02360i | ||||
\(465\) | 15.0301 | + | 36.2404i | 0.697006 | + | 1.68061i | ||||
\(466\) | 9.95251 | + | 15.0792i | 0.461041 | + | 0.698531i | ||||
\(467\) | 17.6594 | + | 17.6594i | 0.817178 | + | 0.817178i | 0.985698 | − | 0.168520i | \(-0.0538989\pi\) |
−0.168520 | + | 0.985698i | \(0.553899\pi\) | |||||||
\(468\) | 0.470264 | − | 0.188577i | 0.0217380 | − | 0.00871696i | ||||
\(469\) | 1.92125i | 0.0887149i | ||||||||
\(470\) | 1.88179 | + | 9.72546i | 0.0868007 | + | 0.448602i | ||||
\(471\) | 4.21087i | 0.194027i | ||||||||
\(472\) | 12.4882 | + | 8.65491i | 0.574818 | + | 0.398375i | ||||
\(473\) | 7.87084 | + | 7.87084i | 0.361902 | + | 0.361902i | ||||
\(474\) | −9.11213 | + | 6.01415i | −0.418534 | + | 0.276239i | ||||
\(475\) | 3.53868 | + | 3.53239i | 0.162366 | + | 0.162077i | ||||
\(476\) | −22.0908 | − | 9.44493i | −1.01253 | − | 0.432908i | ||||
\(477\) | 0.629525 | − | 0.629525i | 0.0288239 | − | 0.0288239i | ||||
\(478\) | −12.1956 | − | 2.49776i | −0.557815 | − | 0.114245i | ||||
\(479\) | 21.7112 | 0.992010 | 0.496005 | − | 0.868320i | \(-0.334800\pi\) | ||||
0.496005 | + | 0.868320i | \(0.334800\pi\) | |||||||
\(480\) | 17.5114 | + | 12.4205i | 0.799283 | + | 0.566916i | ||||
\(481\) | −18.0673 | −0.823800 | ||||||||
\(482\) | −2.99418 | − | 0.613233i | −0.136381 | − | 0.0279320i | ||||
\(483\) | −17.4670 | + | 17.4670i | −0.794778 | + | 0.794778i | ||||
\(484\) | −9.39807 | − | 4.01815i | −0.427185 | − | 0.182643i | ||||
\(485\) | −23.5604 | + | 9.77134i | −1.06982 | + | 0.443694i | ||||
\(486\) | 1.46200 | − | 0.964942i | 0.0663176 | − | 0.0437706i | ||||
\(487\) | −11.2980 | − | 11.2980i | −0.511962 | − | 0.511962i | 0.403165 | − | 0.915127i | \(-0.367910\pi\) |
−0.915127 | + | 0.403165i | \(0.867910\pi\) | |||||||
\(488\) | 27.9862 | + | 19.3957i | 1.26688 | + | 0.878002i | ||||
\(489\) | − | 22.5987i | − | 1.02195i | ||||||
\(490\) | −4.19923 | + | 6.21413i | −0.189702 | + | 0.280726i | ||||
\(491\) | − | 21.1601i | − | 0.954942i | −0.878647 | − | 0.477471i | \(-0.841554\pi\) | ||
0.878647 | − | 0.477471i | \(-0.158446\pi\) | |||||||
\(492\) | −14.0986 | + | 5.65355i | −0.635612 | + | 0.254882i | ||||
\(493\) | 31.5010 | + | 31.5010i | 1.41873 | + | 1.41873i | ||||
\(494\) | −1.65478 | − | 2.50718i | −0.0744519 | − | 0.112803i | ||||
\(495\) | 0.989090 | + | 0.409179i | 0.0444563 | + | 0.0183912i | ||||
\(496\) | −29.8942 | + | 28.5692i | −1.34229 | + | 1.28280i | ||||
\(497\) | −9.77195 | + | 9.77195i | −0.438332 | + | 0.438332i | ||||
\(498\) | 3.01529 | − | 14.7225i | 0.135118 | − | 0.659732i | ||||
\(499\) | −24.0759 | −1.07778 | −0.538892 | − | 0.842375i | \(-0.681157\pi\) | ||||
−0.538892 | + | 0.842375i | \(0.681157\pi\) | |||||||
\(500\) | 0.223480 | − | 22.3596i | 0.00999435 | − | 0.999950i | ||||
\(501\) | −21.4619 | −0.958846 | ||||||||
\(502\) | 5.54097 | − | 27.0544i | 0.247305 | − | 1.20750i | ||||
\(503\) | 20.3664 | − | 20.3664i | 0.908093 | − | 0.908093i | −0.0880249 | − | 0.996118i | \(-0.528056\pi\) |
0.996118 | + | 0.0880249i | \(0.0280555\pi\) | |||||||
\(504\) | −0.714059 | + | 0.129461i | −0.0318067 | + | 0.00576667i | ||||
\(505\) | 25.3168 | + | 10.4734i | 1.12658 | + | 0.466058i | ||||
\(506\) | 21.1532 | + | 32.0495i | 0.940373 | + | 1.42477i | ||||
\(507\) | 10.1868 | + | 10.1868i | 0.452410 | + | 0.452410i | ||||
\(508\) | −8.20440 | − | 20.4598i | −0.364011 | − | 0.907755i | ||||
\(509\) | 28.6068i | 1.26798i | 0.773343 | + | 0.633988i | \(0.218583\pi\) | ||||
−0.773343 | + | 0.633988i | \(0.781417\pi\) | |||||||
\(510\) | −16.7799 | + | 24.8314i | −0.743028 | + | 1.09955i | ||||
\(511\) | − | 6.90379i | − | 0.305406i | ||||||
\(512\) | −5.53961 | + | 21.9388i | −0.244818 | + | 0.969569i | ||||
\(513\) | −3.74359 | − | 3.74359i | −0.165284 | − | 0.165284i | ||||
\(514\) | 16.4735 | − | 10.8728i | 0.726616 | − | 0.479578i | ||||
\(515\) | 4.89701 | − | 2.03096i | 0.215788 | − | 0.0894948i | ||||
\(516\) | −3.70079 | + | 8.65581i | −0.162918 | + | 0.381051i | ||||
\(517\) | 8.89060 | − | 8.89060i | 0.391008 | − | 0.391008i | ||||
\(518\) | 25.3518 | + | 5.19224i | 1.11389 | + | 0.228134i | ||||
\(519\) | 4.95359 | 0.217438 | ||||||||
\(520\) | −2.83862 | + | 13.1311i | −0.124482 | + | 0.575838i | ||||
\(521\) | −33.7509 | −1.47866 | −0.739328 | − | 0.673346i | \(-0.764857\pi\) | ||||
−0.739328 | + | 0.673346i | \(0.764857\pi\) | |||||||
\(522\) | 1.31828 | + | 0.269994i | 0.0576994 | + | 0.0118173i | ||||
\(523\) | −10.9977 | + | 10.9977i | −0.480897 | + | 0.480897i | −0.905418 | − | 0.424521i | \(-0.860442\pi\) |
0.424521 | + | 0.905418i | \(0.360442\pi\) | |||||||
\(524\) | −2.80988 | + | 6.57205i | −0.122750 | + | 0.287101i | ||||
\(525\) | −12.9212 | − | 12.8983i | −0.563929 | − | 0.562927i | ||||
\(526\) | −6.88880 | + | 4.54671i | −0.300366 | + | 0.198246i | ||||
\(527\) | −40.8161 | − | 40.8161i | −1.77798 | − | 1.77798i | ||||
\(528\) | 0.617405 | − | 27.2430i | 0.0268691 | − | 1.18560i | ||||
\(529\) | − | 22.7659i | − | 0.989824i | ||||||
\(530\) | 4.48444 | + | 23.1764i | 0.194791 | + | 1.00672i | ||||
\(531\) | 0.640669i | 0.0278027i | ||||||||
\(532\) | 1.60143 | + | 3.99358i | 0.0694309 | + | 0.173144i | ||||
\(533\) | −6.72120 | − | 6.72120i | −0.291128 | − | 0.291128i | ||||
\(534\) | 11.6611 | + | 17.6679i | 0.504626 | + | 0.764566i | ||||
\(535\) | 6.44378 | + | 15.5371i | 0.278589 | + | 0.671727i | ||||
\(536\) | 0.450609 | + | 2.48539i | 0.0194634 | + | 0.107352i | ||||
\(537\) | 2.04773 | − | 2.04773i | 0.0883660 | − | 0.0883660i | ||||
\(538\) | 4.86768 | − | 23.7671i | 0.209861 | − | 1.02467i | ||||
\(539\) | 9.51945 | 0.410032 | ||||||||
\(540\) | −0.257703 | + | 23.6752i | −0.0110898 | + | 1.01882i | ||||
\(541\) | −44.1197 | −1.89685 | −0.948427 | − | 0.316995i | \(-0.897326\pi\) | ||||
−0.948427 | + | 0.316995i | \(0.897326\pi\) | |||||||
\(542\) | −6.90954 | + | 33.7367i | −0.296790 | + | 1.44911i | ||||
\(543\) | −24.1579 | + | 24.1579i | −1.03671 | + | 1.03671i | ||||
\(544\) | −30.7926 | − | 7.03708i | −1.32022 | − | 0.301712i | ||||
\(545\) | 12.2698 | − | 29.6593i | 0.525582 | − | 1.27047i | ||||
\(546\) | 6.04230 | + | 9.15479i | 0.258587 | + | 0.391789i | ||||
\(547\) | 15.0359 | + | 15.0359i | 0.642887 | + | 0.642887i | 0.951264 | − | 0.308377i | \(-0.0997858\pi\) |
−0.308377 | + | 0.951264i | \(0.599786\pi\) | |||||||
\(548\) | −40.8989 | + | 16.4005i | −1.74711 | + | 0.700595i | ||||
\(549\) | 1.43574i | 0.0612760i | ||||||||
\(550\) | −23.6736 | + | 15.6552i | −1.00945 | + | 0.667541i | ||||
\(551\) | − | 7.97836i | − | 0.339889i | ||||||
\(552\) | −18.4992 | + | 26.6926i | −0.787378 | + | 1.13611i | ||||
\(553\) | 6.91941 | + | 6.91941i | 0.294243 | + | 0.294243i | ||||
\(554\) | −17.5272 | + | 11.5682i | −0.744658 | + | 0.491486i | ||||
\(555\) | 12.3400 | − | 29.8289i | 0.523803 | − | 1.26616i | ||||
\(556\) | −11.1368 | − | 4.76156i | −0.472308 | − | 0.201935i | ||||
\(557\) | −5.74079 | + | 5.74079i | −0.243245 | + | 0.243245i | −0.818191 | − | 0.574946i | \(-0.805023\pi\) |
0.574946 | + | 0.818191i | \(0.305023\pi\) | |||||||
\(558\) | −1.70810 | − | 0.349833i | −0.0723096 | − | 0.0148096i | ||||
\(559\) | −5.89076 | −0.249153 | ||||||||
\(560\) | 7.75676 | − | 17.6096i | 0.327783 | − | 0.744141i | ||||
\(561\) | 38.0393 | 1.60602 | ||||||||
\(562\) | −2.08989 | − | 0.428026i | −0.0881567 | − | 0.0180552i | ||||
\(563\) | −21.8581 | + | 21.8581i | −0.921210 | + | 0.921210i | −0.997115 | − | 0.0759053i | \(-0.975815\pi\) |
0.0759053 | + | 0.997115i | \(0.475815\pi\) | |||||||
\(564\) | 9.77727 | + | 4.18027i | 0.411697 | + | 0.176021i | ||||
\(565\) | −2.37742 | − | 5.73239i | −0.100019 | − | 0.241164i | ||||
\(566\) | 20.8345 | − | 13.7511i | 0.875739 | − | 0.578002i | ||||
\(567\) | 13.1252 | + | 13.1252i | 0.551207 | + | 0.551207i | ||||
\(568\) | −10.3494 | + | 14.9332i | −0.434251 | + | 0.626584i | ||||
\(569\) | 3.55621i | 0.149084i | 0.997218 | + | 0.0745421i | \(0.0237495\pi\) | ||||
−0.997218 | + | 0.0745421i | \(0.976250\pi\) | |||||||
\(570\) | 5.26951 | − | 1.01961i | 0.220716 | − | 0.0427066i | ||||
\(571\) | − | 33.7698i | − | 1.41322i | −0.707602 | − | 0.706611i | \(-0.750223\pi\) | ||
0.707602 | − | 0.706611i | \(-0.249777\pi\) | |||||||
\(572\) | 15.8269 | − | 6.34661i | 0.661755 | − | 0.265365i | ||||
\(573\) | 19.5002 | + | 19.5002i | 0.814634 | + | 0.814634i | ||||
\(574\) | 7.49951 | + | 11.3626i | 0.313023 | + | 0.474267i | ||||
\(575\) | 33.8253 | − | 0.0301044i | 1.41061 | − | 0.00125544i | ||||
\(576\) | −0.893365 | + | 0.334951i | −0.0372236 | + | 0.0139563i | ||||
\(577\) | 2.38287 | − | 2.38287i | 0.0992004 | − | 0.0992004i | −0.655765 | − | 0.754965i | \(-0.727654\pi\) |
0.754965 | + | 0.655765i | \(0.227654\pi\) | |||||||
\(578\) | 4.02311 | − | 19.6433i | 0.167339 | − | 0.817054i | ||||
\(579\) | −15.5403 | −0.645835 | ||||||||
\(580\) | −25.5029 | + | 24.9537i | −1.05895 | + | 1.03615i | ||||
\(581\) | −13.4694 | −0.558806 | ||||||||
\(582\) | −5.49356 | + | 26.8230i | −0.227716 | + | 1.11185i | ||||
\(583\) | 21.1869 | − | 21.1869i | 0.877470 | − | 0.877470i | ||||
\(584\) | −1.61922 | − | 8.93096i | −0.0670036 | − | 0.369566i | ||||
\(585\) | −0.523252 | + | 0.217011i | −0.0216338 | + | 0.00897230i | ||||
\(586\) | −0.157711 | − | 0.238951i | −0.00651500 | − | 0.00987098i | ||||
\(587\) | 18.4563 | + | 18.4563i | 0.761773 | + | 0.761773i | 0.976643 | − | 0.214870i | \(-0.0689327\pi\) |
−0.214870 | + | 0.976643i | \(0.568933\pi\) | |||||||
\(588\) | 2.99644 | + | 7.47240i | 0.123571 | + | 0.308157i | ||||
\(589\) | 10.3376i | 0.425954i | ||||||||
\(590\) | −14.0752 | − | 9.51142i | −0.579469 | − | 0.391579i | ||||
\(591\) | − | 9.95619i | − | 0.409543i | ||||||
\(592\) | 34.0136 | + | 0.770847i | 1.39795 | + | 0.0316816i | ||||
\(593\) | −21.7190 | − | 21.7190i | −0.891894 | − | 0.891894i | 0.102807 | − | 0.994701i | \(-0.467218\pi\) |
−0.994701 | + | 0.102807i | \(0.967218\pi\) | |||||||
\(594\) | 25.0815 | − | 16.5542i | 1.02911 | − | 0.679226i | ||||
\(595\) | 24.8209 | + | 10.2682i | 1.01756 | + | 0.420956i | ||||
\(596\) | −3.56267 | + | 8.33276i | −0.145933 | + | 0.341323i | ||||
\(597\) | −12.6007 | + | 12.6007i | −0.515713 | + | 0.515713i | ||||
\(598\) | −19.9092 | − | 4.07756i | −0.814147 | − | 0.166744i | ||||
\(599\) | −8.38180 | −0.342471 | −0.171236 | − | 0.985230i | \(-0.554776\pi\) | ||||
−0.171236 | + | 0.985230i | \(0.554776\pi\) | |||||||
\(600\) | −19.7405 | − | 13.6551i | −0.805902 | − | 0.557465i | ||||
\(601\) | 12.0065 | 0.489754 | 0.244877 | − | 0.969554i | \(-0.421252\pi\) | ||||
0.244877 | + | 0.969554i | \(0.421252\pi\) | |||||||
\(602\) | 8.26580 | + | 1.69290i | 0.336889 | + | 0.0689976i | ||||
\(603\) | −0.0753108 | + | 0.0753108i | −0.00306689 | + | 0.00306689i | ||||
\(604\) | 11.3353 | − | 26.5123i | 0.461229 | − | 1.07877i | ||||
\(605\) | 10.5595 | + | 4.36840i | 0.429306 | + | 0.177601i | ||||
\(606\) | 24.5457 | − | 16.2005i | 0.997100 | − | 0.658101i | ||||
\(607\) | 29.9324 | + | 29.9324i | 1.21492 | + | 1.21492i | 0.969389 | + | 0.245532i | \(0.0789626\pi\) |
0.245532 | + | 0.969389i | \(0.421037\pi\) | |||||||
\(608\) | 3.00832 | + | 4.79062i | 0.122003 | + | 0.194285i | ||||
\(609\) | 29.1324i | 1.18051i | ||||||||
\(610\) | −31.5427 | − | 21.3151i | −1.27713 | − | 0.863025i | ||||
\(611\) | 6.65398i | 0.269191i | ||||||||
\(612\) | −0.495705 | − | 1.23617i | −0.0200377 | − | 0.0499691i | ||||
\(613\) | 6.30403 | + | 6.30403i | 0.254617 | + | 0.254617i | 0.822861 | − | 0.568243i | \(-0.192377\pi\) |
−0.568243 | + | 0.822861i | \(0.692377\pi\) | |||||||
\(614\) | −24.8065 | − | 37.5847i | −1.00111 | − | 1.51679i | ||||
\(615\) | 15.6872 | − | 6.50601i | 0.632567 | − | 0.262348i | ||||
\(616\) | −24.0319 | + | 4.35707i | −0.968273 | + | 0.175551i | ||||
\(617\) | −9.96310 | + | 9.96310i | −0.401099 | + | 0.401099i | −0.878620 | − | 0.477521i | \(-0.841535\pi\) |
0.477521 | + | 0.878620i | \(0.341535\pi\) | |||||||
\(618\) | 1.14183 | − | 5.57513i | 0.0459312 | − | 0.224264i | ||||
\(619\) | 8.56649 | 0.344316 | 0.172158 | − | 0.985069i | \(-0.444926\pi\) | ||||
0.172158 | + | 0.985069i | \(0.444926\pi\) | |||||||
\(620\) | 33.0443 | − | 32.3327i | 1.32709 | − | 1.29851i | ||||
\(621\) | −35.8158 | −1.43724 | ||||||||
\(622\) | −2.83807 | + | 13.8572i | −0.113796 | + | 0.555625i | ||||
\(623\) | 13.4164 | − | 13.4164i | 0.537516 | − | 0.537516i | ||||
\(624\) | 9.96368 | + | 10.4258i | 0.398866 | + | 0.417365i | ||||
\(625\) | 0.0444998 | + | 25.0000i | 0.00177999 | + | 0.999998i | ||||
\(626\) | −21.1135 | − | 31.9894i | −0.843864 | − | 1.27855i | ||||
\(627\) | −4.81717 | − | 4.81717i | −0.192379 | − | 0.192379i | ||||
\(628\) | 4.60544 | − | 1.84679i | 0.183777 | − | 0.0736949i | ||||
\(629\) | 47.4931i | 1.89367i | ||||||||
\(630\) | 0.796583 | − | 0.154132i | 0.0317366 | − | 0.00614077i | ||||
\(631\) | 25.1719i | 1.00208i | 0.865425 | + | 0.501039i | \(0.167049\pi\) | ||||
−0.865425 | + | 0.501039i | \(0.832951\pi\) | |||||||
\(632\) | 10.5740 | + | 7.32829i | 0.420613 | + | 0.291504i | ||||
\(633\) | −19.3124 | − | 19.3124i | −0.767601 | − | 0.767601i | ||||
\(634\) | 15.1545 | − | 10.0022i | 0.601861 | − | 0.397238i | ||||
\(635\) | 9.44149 | + | 22.7651i | 0.374674 | + | 0.903406i | ||||
\(636\) | 23.2999 | + | 9.96186i | 0.923900 | + | 0.395013i | ||||
\(637\) | −3.56232 | + | 3.56232i | −0.141144 | + | 0.141144i | ||||
\(638\) | 44.3670 | + | 9.08672i | 1.75651 | + | 0.359747i | ||||
\(639\) | −0.766100 | −0.0303064 | ||||||||
\(640\) | 5.90424 | − | 24.5996i | 0.233385 | − | 0.972384i | ||||
\(641\) | 21.8637 | 0.863565 | 0.431783 | − | 0.901978i | \(-0.357885\pi\) | ||||
0.431783 | + | 0.901978i | \(0.357885\pi\) | |||||||
\(642\) | 17.6886 | + | 3.62277i | 0.698114 | + | 0.142979i | ||||
\(643\) | −22.8913 | + | 22.8913i | −0.902746 | + | 0.902746i | −0.995673 | − | 0.0929271i | \(-0.970378\pi\) |
0.0929271 | + | 0.995673i | \(0.470378\pi\) | |||||||
\(644\) | 26.7644 | + | 11.4431i | 1.05466 | + | 0.450922i | ||||
\(645\) | 4.02338 | − | 9.72554i | 0.158420 | − | 0.382943i | ||||
\(646\) | −6.59054 | + | 4.34986i | −0.259301 | + | 0.171143i | ||||
\(647\) | −6.94398 | − | 6.94398i | −0.272996 | − | 0.272996i | 0.557309 | − | 0.830305i | \(-0.311834\pi\) |
−0.830305 | + | 0.557309i | \(0.811834\pi\) | |||||||
\(648\) | 20.0576 | + | 13.9008i | 0.787936 | + | 0.546075i | ||||
\(649\) | 21.5619i | 0.846379i | ||||||||
\(650\) | 3.00060 | − | 14.7174i | 0.117693 | − | 0.577264i | ||||
\(651\) | − | 37.7471i | − | 1.47943i | ||||||
\(652\) | −24.7162 | + | 9.91123i | −0.967961 | + | 0.388154i | ||||
\(653\) | 3.48781 | + | 3.48781i | 0.136489 | + | 0.136489i | 0.772050 | − | 0.635562i | \(-0.219231\pi\) |
−0.635562 | + | 0.772050i | \(0.719231\pi\) | |||||||
\(654\) | −18.9794 | − | 28.7560i | −0.742153 | − | 1.12445i | ||||
\(655\) | 3.05481 | − | 7.38425i | 0.119361 | − | 0.288527i | ||||
\(656\) | 12.3666 | + | 12.9401i | 0.482834 | + | 0.505226i | ||||
\(657\) | 0.270621 | − | 0.270621i | 0.0105579 | − | 0.0105579i | ||||
\(658\) | 1.91224 | − | 9.33673i | 0.0745468 | − | 0.363984i | ||||
\(659\) | −20.3040 | −0.790932 | −0.395466 | − | 0.918481i | \(-0.629417\pi\) | ||||
−0.395466 | + | 0.918481i | \(0.629417\pi\) | |||||||
\(660\) | −0.331606 | + | 30.4646i | −0.0129077 | + | 1.18583i | ||||
\(661\) | −29.3931 | −1.14326 | −0.571629 | − | 0.820512i | \(-0.693688\pi\) | ||||
−0.571629 | + | 0.820512i | \(0.693688\pi\) | |||||||
\(662\) | −2.13849 | + | 10.4414i | −0.0831147 | + | 0.405818i | ||||
\(663\) | −14.2348 | + | 14.2348i | −0.552836 | + | 0.552836i | ||||
\(664\) | −17.4245 | + | 3.15912i | −0.676201 | + | 0.122598i | ||||
\(665\) | −1.84290 | − | 4.44357i | −0.0714647 | − | 0.172314i | ||||
\(666\) | 0.790232 | + | 1.19729i | 0.0306209 | + | 0.0463941i | ||||
\(667\) | −38.1654 | − | 38.1654i | −1.47777 | − | 1.47777i | ||||
\(668\) | 9.41267 | + | 23.4729i | 0.364187 | + | 0.908194i | ||||
\(669\) | 27.3887i | 1.05891i | ||||||||
\(670\) | −0.536479 | − | 2.77262i | −0.0207260 | − | 0.107116i | ||||
\(671\) | 48.3204i | 1.86539i | ||||||||
\(672\) | −10.9847 | − | 17.4926i | −0.423743 | − | 0.674793i | ||||
\(673\) | −22.6855 | − | 22.6855i | −0.874464 | − | 0.874464i | 0.118492 | − | 0.992955i | \(-0.462194\pi\) |
−0.992955 | + | 0.118492i | \(0.962194\pi\) | |||||||
\(674\) | 11.9281 | − | 7.87271i | 0.459452 | − | 0.303245i | ||||
\(675\) | −0.0235593 | − | 26.4712i | −0.000906797 | − | 1.01888i | ||||
\(676\) | 6.67361 | − | 15.6090i | 0.256677 | − | 0.600345i | ||||
\(677\) | 19.9465 | − | 19.9465i | 0.766605 | − | 0.766605i | −0.210902 | − | 0.977507i | \(-0.567640\pi\) |
0.977507 | + | 0.210902i | \(0.0676401\pi\) | |||||||
\(678\) | −6.52620 | − | 1.33662i | −0.250637 | − | 0.0513325i | ||||
\(679\) | 24.5400 | 0.941758 | ||||||||
\(680\) | 34.5174 | + | 7.46179i | 1.32368 | + | 0.286147i | ||||
\(681\) | −4.96672 | −0.190325 | ||||||||
\(682\) | −57.4867 | − | 11.7737i | −2.20128 | − | 0.450839i | ||||
\(683\) | −6.48834 | + | 6.48834i | −0.248270 | + | 0.248270i | −0.820260 | − | 0.571991i | \(-0.806171\pi\) |
0.571991 | + | 0.820260i | \(0.306171\pi\) | |||||||
\(684\) | −0.0937696 | + | 0.219318i | −0.00358537 | + | 0.00838585i | ||||
\(685\) | 45.5073 | − | 18.8735i | 1.73874 | − | 0.721118i | ||||
\(686\) | 23.7971 | − | 15.7065i | 0.908578 | − | 0.599676i | ||||
\(687\) | −26.2951 | − | 26.2951i | −1.00322 | − | 1.00322i | ||||
\(688\) | 11.0900 | + | 0.251331i | 0.422801 | + | 0.00958189i | ||||
\(689\) | 15.8569i | 0.604098i | ||||||||
\(690\) | 20.3299 | − | 30.0847i | 0.773947 | − | 1.14531i | ||||
\(691\) | 37.0957i | 1.41119i | 0.708617 | + | 0.705593i | \(0.249319\pi\) | ||||
−0.708617 | + | 0.705593i | \(0.750681\pi\) | |||||||
\(692\) | −2.17252 | − | 5.41775i | −0.0825870 | − | 0.205952i | ||||
\(693\) | −0.728202 | − | 0.728202i | −0.0276621 | − | 0.0276621i | ||||
\(694\) | −2.68647 | − | 4.07032i | −0.101977 | − | 0.154507i | ||||
\(695\) | 12.5132 | + | 5.17661i | 0.474652 | + | 0.196360i | ||||
\(696\) | 6.83272 | + | 37.6866i | 0.258994 | + | 1.42851i | ||||
\(697\) | −17.6678 | + | 17.6678i | −0.669216 | + | 0.669216i | ||||
\(698\) | 7.36016 | − | 35.9369i | 0.278586 | − | 1.36023i | ||||
\(699\) | −21.6838 | −0.820157 | ||||||||
\(700\) | −8.43991 | + | 19.7889i | −0.318999 | + | 0.747949i | ||||
\(701\) | 11.2588 | 0.425239 | 0.212619 | − | 0.977135i | \(-0.431801\pi\) | ||||
0.212619 | + | 0.977135i | \(0.431801\pi\) | |||||||
\(702\) | −3.19104 | + | 15.5807i | −0.120438 | + | 0.588054i | ||||
\(703\) | 6.01436 | − | 6.01436i | 0.226836 | − | 0.226836i | ||||
\(704\) | −30.0665 | + | 11.2729i | −1.13317 | + | 0.424863i | ||||
\(705\) | −10.9856 | − | 4.54466i | −0.413741 | − | 0.171162i | ||||
\(706\) | −17.2849 | − | 26.1886i | −0.650526 | − | 0.985622i | ||||
\(707\) | −18.6391 | − | 18.6391i | −0.700994 | − | 0.700994i | ||||
\(708\) | −16.9253 | + | 6.78706i | −0.636091 | + | 0.255073i | ||||
\(709\) | − | 14.2210i | − | 0.534080i | −0.963685 | − | 0.267040i | \(-0.913954\pi\) | ||
0.963685 | − | 0.267040i | \(-0.0860455\pi\) | |||||||
\(710\) | 11.3736 | − | 16.8309i | 0.426843 | − | 0.631653i | ||||
\(711\) | 0.542467i | 0.0203441i | ||||||||
\(712\) | 14.2092 | − | 20.5025i | 0.532511 | − | 0.768364i | ||||
\(713\) | 49.4512 | + | 49.4512i | 1.85196 | + | 1.85196i | ||||
\(714\) | 24.0649 | − | 15.8832i | 0.900607 | − | 0.594414i | ||||
\(715\) | −17.6102 | + | 7.30358i | −0.658585 | + | 0.273138i | ||||
\(716\) | −3.13769 | − | 1.34152i | −0.117261 | − | 0.0501349i | ||||
\(717\) | 10.5645 | − | 10.5645i | 0.394538 | − | 0.394538i | ||||
\(718\) | −21.9906 | − | 4.50385i | −0.820682 | − | 0.168082i | ||||
\(719\) | −14.7950 | −0.551761 | −0.275880 | − | 0.961192i | \(-0.588969\pi\) | ||||
−0.275880 | + | 0.961192i | \(0.588969\pi\) | |||||||
\(720\) | 0.994334 | − | 0.386221i | 0.0370566 | − | 0.0143936i | ||||
\(721\) | −5.10061 | −0.189957 | ||||||||
\(722\) | 1.38545 | + | 0.283752i | 0.0515613 | + | 0.0105602i | ||||
\(723\) | 2.59372 | − | 2.59372i | 0.0964615 | − | 0.0964615i | ||||
\(724\) | 37.0166 | + | 15.8265i | 1.37571 | + | 0.588186i | ||||
\(725\) | 28.1826 | − | 28.2328i | 1.04668 | − | 1.04854i | ||||
\(726\) | 10.2379 | − | 6.75718i | 0.379964 | − | 0.250782i | ||||
\(727\) | −18.6479 | − | 18.6479i | −0.691613 | − | 0.691613i | 0.270973 | − | 0.962587i | \(-0.412654\pi\) |
−0.962587 | + | 0.270973i | \(0.912654\pi\) | |||||||
\(728\) | 7.36260 | − | 10.6236i | 0.272876 | − | 0.393735i | ||||
\(729\) | 27.9863i | 1.03653i | ||||||||
\(730\) | 1.92778 | + | 9.96311i | 0.0713503 | + | 0.368751i | ||||
\(731\) | 15.4849i | 0.572728i | ||||||||
\(732\) | −37.9296 | + | 15.2098i | −1.40192 | + | 0.562172i | ||||
\(733\) | 4.09933 | + | 4.09933i | 0.151412 | + | 0.151412i | 0.778748 | − | 0.627336i | \(-0.215855\pi\) |
−0.627336 | + | 0.778748i | \(0.715855\pi\) | |||||||
\(734\) | 10.0092 | + | 15.1651i | 0.369446 | + | 0.559753i | ||||
\(735\) | −3.44826 | − | 8.31437i | −0.127191 | − | 0.306680i | ||||
\(736\) | 37.3071 | + | 8.52585i | 1.37516 | + | 0.314267i | ||||
\(737\) | −2.53461 | + | 2.53461i | −0.0933636 | + | 0.0933636i | ||||
\(738\) | −0.151430 | + | 0.739376i | −0.00557422 | + | 0.0272168i | ||||
\(739\) | 14.1367 | 0.520025 | 0.260013 | − | 0.965605i | \(-0.416273\pi\) | ||||
0.260013 | + | 0.965605i | \(0.416273\pi\) | |||||||
\(740\) | −38.0359 | − | 0.414018i | −1.39823 | − | 0.0152196i | ||||
\(741\) | 3.60530 | 0.132444 | ||||||||
\(742\) | 4.55698 | − | 22.2500i | 0.167292 | − | 0.816824i | ||||
\(743\) | 10.3395 | − | 10.3395i | 0.379321 | − | 0.379321i | −0.491536 | − | 0.870857i | \(-0.663565\pi\) |
0.870857 | + | 0.491536i | \(0.163565\pi\) | |||||||
\(744\) | −8.85320 | − | 48.8308i | −0.324574 | − | 1.79023i | ||||
\(745\) | 3.87322 | − | 9.36256i | 0.141904 | − | 0.343018i | ||||
\(746\) | −4.20020 | − | 6.36379i | −0.153780 | − | 0.232995i | ||||
\(747\) | −0.527988 | − | 0.527988i | −0.0193181 | − | 0.0193181i | ||||
\(748\) | −16.6831 | − | 41.6036i | −0.609996 | − | 1.52118i | ||||
\(749\) | − | 16.1831i | − | 0.591316i | ||||||
\(750\) | 22.2488 | + | 15.0059i | 0.812410 | + | 0.547938i | ||||
\(751\) | − | 31.7895i | − | 1.16002i | −0.814611 | − | 0.580008i | \(-0.803049\pi\) | ||
0.814611 | − | 0.580008i | \(-0.196951\pi\) | |||||||
\(752\) | 0.283893 | − | 12.5268i | 0.0103525 | − | 0.456805i | ||||
\(753\) | 23.4360 | + | 23.4360i | 0.854055 | + | 0.854055i | ||||
\(754\) | −20.0032 | + | 13.2024i | −0.728472 | + | 0.480803i | ||||
\(755\) | −12.3234 | + | 29.7888i | −0.448495 | + | 1.08413i | ||||
\(756\) | 8.95523 | − | 20.9454i | 0.325698 | − | 0.761778i | ||||
\(757\) | −3.32343 | + | 3.32343i | −0.120792 | + | 0.120792i | −0.764919 | − | 0.644127i | \(-0.777221\pi\) |
0.644127 | + | 0.764919i | \(0.277221\pi\) | |||||||
\(758\) | −15.1024 | − | 3.09309i | −0.548543 | − | 0.112346i | ||||
\(759\) | −46.0869 | −1.67285 | ||||||||
\(760\) | −3.42623 | − | 5.31610i | −0.124282 | − | 0.192835i | ||||
\(761\) | −7.45399 | −0.270207 | −0.135103 | − | 0.990831i | \(-0.543137\pi\) | ||||
−0.135103 | + | 0.990831i | \(0.543137\pi\) | |||||||
\(762\) | 25.9175 | + | 5.30812i | 0.938894 | + | 0.192293i | ||||
\(763\) | −21.8362 | + | 21.8362i | −0.790524 | + | 0.790524i | ||||
\(764\) | 12.7751 | − | 29.8798i | 0.462187 | − | 1.08101i | ||||
\(765\) | 0.570450 | + | 1.37546i | 0.0206247 | + | 0.0497297i | ||||
\(766\) | 24.2306 | − | 15.9925i | 0.875486 | − | 0.577834i | ||||
\(767\) | −8.06878 | − | 8.06878i | −0.291347 | − | 0.291347i | ||||
\(768\) | −18.3128 | − | 20.0527i | −0.660807 | − | 0.723588i | ||||
\(769\) | − | 2.73507i | − | 0.0986291i | −0.998783 | − | 0.0493145i | \(-0.984296\pi\) | ||
0.998783 | − | 0.0493145i | \(-0.0157037\pi\) | |||||||
\(770\) | 26.8093 | − | 5.18737i | 0.966138 | − | 0.186940i | ||||
\(771\) | 23.6888i | 0.853132i | ||||||||
\(772\) | 6.81563 | + | 16.9965i | 0.245300 | + | 0.611718i | ||||
\(773\) | 22.8002 | + | 22.8002i | 0.820068 | + | 0.820068i | 0.986117 | − | 0.166050i | \(-0.0531012\pi\) |
−0.166050 | + | 0.986117i | \(0.553101\pi\) | |||||||
\(774\) | 0.257651 | + | 0.390371i | 0.00926107 | + | 0.0140316i | ||||
\(775\) | −36.5164 | + | 36.5815i | −1.31171 | + | 1.31405i | ||||
\(776\) | 31.7457 | − | 5.75561i | 1.13960 | − | 0.206614i | ||||
\(777\) | −21.9610 | + | 21.9610i | −0.787848 | + | 0.787848i | ||||
\(778\) | 4.43760 | − | 21.6671i | 0.159096 | − | 0.776805i | ||||
\(779\) | 4.47478 | 0.160326 | ||||||||
\(780\) | −11.2762 | − | 11.5244i | −0.403753 | − | 0.412639i | ||||
\(781\) | −25.7834 | −0.922601 | ||||||||
\(782\) | −10.7186 | + | 52.3347i | −0.383295 | + | 1.87148i | ||||
\(783\) | −29.8677 | + | 29.8677i | −1.06739 | + | 1.06739i | ||||
\(784\) | 6.85841 | − | 6.55443i | 0.244943 | − | 0.234087i | ||||
\(785\) | −5.12437 | + | 2.12526i | −0.182897 | + | 0.0758536i | ||||
\(786\) | −4.72528 | − | 7.15935i | −0.168545 | − | 0.255365i | ||||
\(787\) | −7.21929 | − | 7.21929i | −0.257340 | − | 0.257340i | 0.566632 | − | 0.823971i | \(-0.308246\pi\) |
−0.823971 | + | 0.566632i | \(0.808246\pi\) | |||||||
\(788\) | −10.8891 | + | 4.36655i | −0.387908 | + | 0.155552i | ||||
\(789\) | − | 9.90604i | − | 0.352664i | ||||||
\(790\) | −11.9178 | − | 8.05351i | −0.424016 | − | 0.286531i | ||||
\(791\) | 5.97073i | 0.212295i | ||||||||
\(792\) | −1.11282 | − | 0.771232i | −0.0395422 | − | 0.0274045i | ||||
\(793\) | −18.0822 | − | 18.0822i | −0.642117 | − | 0.642117i | ||||
\(794\) | 7.38795 | − | 4.87616i | 0.262189 | − | 0.173048i | ||||
\(795\) | −26.1794 | − | 10.8302i | −0.928487 | − | 0.384108i | ||||
\(796\) | 19.3078 | + | 8.25505i | 0.684347 | + | 0.292593i | ||||
\(797\) | 24.0462 | − | 24.0462i | 0.851760 | − | 0.851760i | −0.138590 | − | 0.990350i | \(-0.544257\pi\) |
0.990350 | + | 0.138590i | \(0.0442569\pi\) | |||||||
\(798\) | −5.05889 | − | 1.03610i | −0.179083 | − | 0.0366776i | ||||
\(799\) | 17.4911 | 0.618791 | ||||||||
\(800\) | −6.27685 | + | 27.5790i | −0.221920 | + | 0.975065i | ||||
\(801\) | 1.05182 | 0.0371641 | ||||||||
\(802\) | 16.3376 | + | 3.34607i | 0.576900 | + | 0.118154i | ||||
\(803\) | 9.10785 | − | 9.10785i | 0.321409 | − | 0.321409i | ||||
\(804\) | −2.78739 | − | 1.19175i | −0.0983038 | − | 0.0420298i | ||||
\(805\) | −30.0720 | − | 12.4406i | −1.05990 | − | 0.438473i | ||||
\(806\) | 25.9182 | − | 17.1064i | 0.912931 | − | 0.602549i | ||||
\(807\) | 20.5883 | + | 20.5883i | 0.724742 | + | 0.724742i | ||||
\(808\) | −28.4837 | − | 19.7405i | −1.00205 | − | 0.694468i | ||||
\(809\) | 49.8101i | 1.75123i | 0.483009 | + | 0.875615i | \(0.339544\pi\) | ||||
−0.483009 | + | 0.875615i | \(0.660456\pi\) | |||||||
\(810\) | −22.6065 | − | 15.2764i | −0.794311 | − | 0.536760i | ||||
\(811\) | − | 21.6879i | − | 0.761564i | −0.924665 | − | 0.380782i | \(-0.875655\pi\) | ||
0.924665 | − | 0.380782i | \(-0.124345\pi\) | |||||||
\(812\) | 31.8622 | − | 12.7768i | 1.11814 | − | 0.448378i | ||||
\(813\) | −29.2245 | − | 29.2245i | −1.02495 | − | 1.02495i | ||||
\(814\) | 26.5955 | + | 40.2953i | 0.932172 | + | 1.41235i | ||||
\(815\) | 27.5012 | − | 11.4057i | 0.963324 | − | 0.399524i | ||||
\(816\) | 27.4059 | − | 26.1912i | 0.959398 | − | 0.916876i | ||||
\(817\) | 1.96095 | − | 1.96095i | 0.0686049 | − | 0.0686049i | ||||
\(818\) | 6.78743 | − | 33.1405i | 0.237317 | − | 1.15873i | ||||
\(819\) | 0.545007 | 0.0190441 | ||||||||
\(820\) | −13.9957 | − | 14.3037i | −0.488749 | − | 0.499506i | ||||
\(821\) | 33.5950 | 1.17247 | 0.586236 | − | 0.810140i | \(-0.300609\pi\) | ||||
0.586236 | + | 0.810140i | \(0.300609\pi\) | |||||||
\(822\) | 10.6109 | − | 51.8089i | 0.370097 | − | 1.80704i | ||||
\(823\) | −33.8797 | + | 33.8797i | −1.18097 | + | 1.18097i | −0.201479 | + | 0.979493i | \(0.564575\pi\) |
−0.979493 | + | 0.201479i | \(0.935425\pi\) | |||||||
\(824\) | −6.59831 | + | 1.19630i | −0.229863 | + | 0.0416750i | ||||
\(825\) | −0.0303155 | − | 34.0625i | −0.00105545 | − | 1.18590i | ||||
\(826\) | 9.00313 | + | 13.6408i | 0.313259 | + | 0.474624i | ||||
\(827\) | −25.8243 | − | 25.8243i | −0.897997 | − | 0.897997i | 0.0972616 | − | 0.995259i | \(-0.468992\pi\) |
−0.995259 | + | 0.0972616i | \(0.968992\pi\) | |||||||
\(828\) | 0.600577 | + | 1.49769i | 0.0208715 | + | 0.0520484i | ||||
\(829\) | − | 38.9493i | − | 1.35276i | −0.736551 | − | 0.676382i | \(-0.763547\pi\) | ||
0.736551 | − | 0.676382i | \(-0.236453\pi\) | |||||||
\(830\) | 19.4382 | − | 3.76114i | 0.674711 | − | 0.130551i | ||||
\(831\) | − | 25.2039i | − | 0.874315i | ||||||
\(832\) | 7.03284 | − | 15.4698i | 0.243820 | − | 0.536318i | ||||
\(833\) | 9.36415 | + | 9.36415i | 0.324448 | + | 0.324448i | ||||
\(834\) | 12.1321 | − | 8.00735i | 0.420099 | − | 0.277272i | ||||
\(835\) | −10.8320 | − | 26.1178i | −0.374855 | − | 0.903843i | ||||
\(836\) | −3.15585 | + | 7.38124i | −0.109147 | + | 0.255285i | ||||
\(837\) | 38.6998 | − | 38.6998i | 1.33766 | − | 1.33766i | ||||
\(838\) | −32.8353 | − | 6.72493i | −1.13428 | − | 0.232309i | ||||
\(839\) | −16.6669 | −0.575406 | −0.287703 | − | 0.957720i | \(-0.592892\pi\) | ||||
−0.287703 | + | 0.957720i | \(0.592892\pi\) | |||||||
\(840\) | 12.5106 | + | 19.4114i | 0.431658 | + | 0.669757i | ||||
\(841\) | −34.6542 | −1.19497 | ||||||||
\(842\) | −38.3207 | − | 7.84838i | −1.32062 | − | 0.270473i | ||||
\(843\) | 1.81037 | − | 1.81037i | 0.0623526 | − | 0.0623526i | ||||
\(844\) | −12.6521 | + | 29.5920i | −0.435502 | + | 1.01860i | ||||
\(845\) | −7.25533 | + | 17.5380i | −0.249591 | + | 0.603325i | ||||
\(846\) | 0.440948 | − | 0.291032i | 0.0151601 | − | 0.0100059i | ||||
\(847\) | −7.77429 | − | 7.77429i | −0.267128 | − | 0.267128i | ||||
\(848\) | 0.676536 | − | 29.8521i | 0.0232323 | − | 1.02513i | ||||
\(849\) | 29.9599i | 1.02822i | ||||||||
\(850\) | −38.6872 | − | 7.88757i | −1.32696 | − | 0.270542i | ||||
\(851\) | − | 57.5408i | − | 1.97247i | ||||||
\(852\) | −8.11584 | − | 20.2389i | −0.278044 | − | 0.693374i | ||||
\(853\) | 23.5705 | + | 23.5705i | 0.807039 | + | 0.807039i | 0.984185 | − | 0.177145i | \(-0.0566863\pi\) |
−0.177145 | + | 0.984185i | \(0.556686\pi\) | |||||||
\(854\) | 20.1761 | + | 30.5691i | 0.690411 | + | 1.04605i | ||||
\(855\) | 0.101943 | − | 0.246423i | 0.00348639 | − | 0.00842749i | ||||
\(856\) | −3.79558 | − | 20.9349i | −0.129730 | − | 0.715541i | ||||
\(857\) | −5.00669 | + | 5.00669i | −0.171025 | + | 0.171025i | −0.787430 | − | 0.616404i | \(-0.788589\pi\) |
0.616404 | + | 0.787430i | \(0.288589\pi\) | |||||||
\(858\) | −4.10616 | + | 20.0488i | −0.140182 | + | 0.684456i | ||||
\(859\) | 10.6947 | 0.364898 | 0.182449 | − | 0.983215i | \(-0.441598\pi\) | ||||
0.182449 | + | 0.983215i | \(0.441598\pi\) | |||||||
\(860\) | −12.4014 | − | 0.134988i | −0.422884 | − | 0.00460307i | ||||
\(861\) | −16.3394 | −0.556844 | ||||||||
\(862\) | 3.32302 | − | 16.2251i | 0.113182 | − | 0.552627i | ||||
\(863\) | 30.2137 | − | 30.2137i | 1.02849 | − | 1.02849i | 0.0289054 | − | 0.999582i | \(-0.490798\pi\) |
0.999582 | − | 0.0289054i | \(-0.00920215\pi\) | |||||||
\(864\) | 6.67222 | − | 29.1960i | 0.226994 | − | 0.993270i | ||||
\(865\) | 2.50011 | + | 6.02820i | 0.0850062 | + | 0.204965i | ||||
\(866\) | −4.48366 | − | 6.79327i | −0.152361 | − | 0.230845i | ||||
\(867\) | 17.0161 | + | 17.0161i | 0.577896 | + | 0.577896i | ||||
\(868\) | −41.2841 | + | 16.5550i | −1.40127 | + | 0.561913i | ||||
\(869\) | 18.2569i | 0.619323i | ||||||||
\(870\) | −8.13479 | − | 42.0421i | −0.275795 | − | 1.42536i | ||||
\(871\) | − | 1.89698i | − | 0.0642766i | ||||||
\(872\) | −23.1265 | + | 33.3695i | −0.783163 | + | 1.13003i | ||||
\(873\) | 0.961942 | + | 0.961942i | 0.0325568 | + | 0.0325568i | ||||
\(874\) | 7.98484 | − | 5.27012i | 0.270091 | − | 0.178265i | ||||
\(875\) | 9.17495 | − | 22.2342i | 0.310170 | − | 0.751653i | ||||
\(876\) | 10.0162 | + | 4.28242i | 0.338416 | + | 0.144690i | ||||
\(877\) | 6.44438 | − | 6.44438i | 0.217611 | − | 0.217611i | −0.589880 | − | 0.807491i | \(-0.700825\pi\) |
0.807491 | + | 0.589880i | \(0.200825\pi\) | |||||||
\(878\) | −35.6071 | − | 7.29262i | −1.20168 | − | 0.246114i | ||||
\(879\) | 0.343610 | 0.0115897 | ||||||||
\(880\) | 33.4647 | − | 12.9984i | 1.12809 | − | 0.438175i | ||||
\(881\) | 27.9286 | 0.940938 | 0.470469 | − | 0.882417i | \(-0.344085\pi\) | ||||
0.470469 | + | 0.882417i | \(0.344085\pi\) | |||||||
\(882\) | 0.391878 | + | 0.0802596i | 0.0131952 | + | 0.00270248i | ||||
\(883\) | −24.6095 | + | 24.6095i | −0.828175 | + | 0.828175i | −0.987264 | − | 0.159089i | \(-0.949144\pi\) |
0.159089 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(884\) | 21.8117 | + | 9.32561i | 0.733608 | + | 0.313654i | ||||
\(885\) | 18.8324 | − | 7.81044i | 0.633043 | − | 0.262545i | ||||
\(886\) | −29.6043 | + | 19.5393i | −0.994575 | + | 0.656435i | ||||
\(887\) | 12.1805 | + | 12.1805i | 0.408980 | + | 0.408980i | 0.881383 | − | 0.472403i | \(-0.156613\pi\) |
−0.472403 | + | 0.881383i | \(0.656613\pi\) | |||||||
\(888\) | −23.2587 | + | 33.5602i | −0.780512 | + | 1.12621i | ||||
\(889\) | − | 23.7116i | − | 0.795262i | ||||||
\(890\) | −15.6153 | + | 23.1080i | −0.523427 | + | 0.774581i | ||||
\(891\) | 34.6309i | 1.16018i | ||||||||
\(892\) | 29.9551 | − | 12.0121i | 1.00297 | − | 0.402193i | ||||
\(893\) | −2.21501 | − | 2.21501i | −0.0741226 | − | 0.0741226i | ||||
\(894\) | −5.99122 | − | 9.07739i | −0.200376 | − | 0.303593i | ||||
\(895\) | 3.52546 | + | 1.45846i | 0.117843 | + | 0.0487508i | ||||
\(896\) | −14.3141 | + | 19.6858i | −0.478201 | + | 0.657656i | ||||
\(897\) | 17.2464 | − | 17.2464i | 0.575840 | − | 0.575840i | ||||
\(898\) | −1.60700 | + | 7.84636i | −0.0536262 | + | 0.261836i | ||||
\(899\) | 82.4772 | 2.75077 | ||||||||
\(900\) | −1.10654 | + | 0.444867i | −0.0368846 | + | 0.0148289i | ||||
\(901\) | 41.6824 | 1.38864 | ||||||||
\(902\) | −5.09643 | + | 24.8839i | −0.169692 | + | 0.828544i | ||||
\(903\) | −7.16027 | + | 7.16027i | −0.238279 | + | 0.238279i | ||||
\(904\) | 1.40037 | + | 7.72392i | 0.0465757 | + | 0.256894i | ||||
\(905\) | −41.5913 | − | 17.2060i | −1.38254 | − | 0.571947i | ||||
\(906\) | 19.0623 | + | 28.8815i | 0.633301 | + | 0.959525i | ||||
\(907\) | 37.7176 | + | 37.7176i | 1.25239 | + | 1.25239i | 0.954644 | + | 0.297749i | \(0.0962360\pi\) |
0.297749 | + | 0.954644i | \(0.403764\pi\) | |||||||
\(908\) | 2.17828 | + | 5.43211i | 0.0722889 | + | 0.180271i | ||||
\(909\) | − | 1.46126i | − | 0.0484671i | ||||||
\(910\) | −8.09122 | + | 11.9736i | −0.268221 | + | 0.396921i | ||||
\(911\) | − | 47.4298i | − | 1.57142i | −0.618596 | − | 0.785709i | \(-0.712298\pi\) | ||
0.618596 | − | 0.785709i | \(-0.287702\pi\) | |||||||
\(912\) | −6.78735 | − | 0.153821i | −0.224752 | − | 0.00509352i | ||||
\(913\) | −17.7696 | − | 17.7696i | −0.588088 | − | 0.588088i | ||||
\(914\) | 32.9818 | − | 21.7685i | 1.09094 | − | 0.720037i | ||||
\(915\) | 42.2034 | − | 17.5032i | 1.39520 | − | 0.578639i | ||||
\(916\) | −17.2266 | + | 40.2914i | −0.569183 | + | 1.33127i | ||||
\(917\) | −5.43654 | + | 5.43654i | −0.179530 | + | 0.179530i | ||||
\(918\) | 40.9564 | + | 8.38820i | 1.35176 | + | 0.276852i | ||||
\(919\) | −24.1651 | −0.797132 | −0.398566 | − | 0.917140i | \(-0.630492\pi\) | ||||
−0.398566 | + | 0.917140i | \(0.630492\pi\) | |||||||
\(920\) | −41.8200 | − | 9.04042i | −1.37876 | − | 0.298054i | ||||
\(921\) | 54.0465 | 1.78089 | ||||||||
\(922\) | 43.4112 | + | 8.89096i | 1.42967 | + | 0.292808i | ||||
\(923\) | 9.64850 | − | 9.64850i | 0.317584 | − | 0.317584i | ||||
\(924\) | 11.5234 | − | 26.9521i | 0.379091 | − | 0.886659i | ||||
\(925\) | 42.5279 | − | 0.0378497i | 1.39831 | − | 0.00124449i | ||||
\(926\) | −15.9360 | + | 10.5180i | −0.523690 | + | 0.345644i | ||||
\(927\) | −0.199938 | − | 0.199938i | −0.00656684 | − | 0.00656684i | ||||
\(928\) | 38.2213 | − | 24.0014i | 1.25467 | − | 0.787885i | ||||
\(929\) | − | 52.8659i | − | 1.73447i | −0.497896 | − | 0.867237i | \(-0.665894\pi\) | ||
0.497896 | − | 0.867237i | \(-0.334106\pi\) | |||||||
\(930\) | 10.5403 | + | 54.4742i | 0.345630 | + | 1.78628i | ||||
\(931\) | − | 2.37169i | − | 0.0777289i | ||||||
\(932\) | 9.51000 | + | 23.7156i | 0.311510 | + | 0.776831i | ||||
\(933\) | −12.0039 | − | 12.0039i | −0.392989 | − | 0.392989i | ||||
\(934\) | 19.4554 | + | 29.4771i | 0.636599 | + | 0.964521i | ||||
\(935\) | 19.1987 | + | 46.2914i | 0.627864 | + | 1.51389i | ||||
\(936\) | 0.705038 | − | 0.127826i | 0.0230449 | − | 0.00417812i | ||||
\(937\) | −19.2914 | + | 19.2914i | −0.630222 | + | 0.630222i | −0.948124 | − | 0.317902i | \(-0.897022\pi\) |
0.317902 | + | 0.948124i | \(0.397022\pi\) | |||||||
\(938\) | −0.545158 | + | 2.66180i | −0.0178000 | + | 0.0869109i | ||||
\(939\) | 46.0005 | 1.50117 | ||||||||
\(940\) | −0.152478 | + | 14.0081i | −0.00497328 | + | 0.456895i | ||||
\(941\) | −57.1900 | −1.86434 | −0.932170 | − | 0.362020i | \(-0.882087\pi\) | ||||
−0.932170 | + | 0.362020i | \(0.882087\pi\) | |||||||
\(942\) | −1.19484 | + | 5.83397i | −0.0389301 | + | 0.190081i | ||||
\(943\) | 21.4056 | − | 21.4056i | 0.697064 | − | 0.697064i | ||||
\(944\) | 14.8460 | + | 15.5346i | 0.483197 | + | 0.505607i | ||||
\(945\) | −9.73583 | + | 23.5340i | −0.316706 | + | 0.765561i | ||||
\(946\) | 8.67132 | + | 13.1381i | 0.281929 | + | 0.427155i | ||||
\(947\) | 26.9305 | + | 26.9305i | 0.875124 | + | 0.875124i | 0.993025 | − | 0.117901i | \(-0.0376166\pi\) |
−0.117901 | + | 0.993025i | \(0.537617\pi\) | |||||||
\(948\) | −14.3310 | + | 5.74674i | −0.465448 | + | 0.186645i | ||||
\(949\) | 6.81658i | 0.221275i | ||||||||
\(950\) | 3.90036 | + | 5.89807i | 0.126544 | + | 0.191359i | ||||
\(951\) | 21.7920i | 0.706655i | ||||||||
\(952\) | −27.9258 | − | 19.3538i | −0.905080 | − | 0.627261i | ||||
\(953\) | −10.7214 | − | 10.7214i | −0.347301 | − | 0.347301i | 0.511802 | − | 0.859103i | \(-0.328978\pi\) |
−0.859103 | + | 0.511802i | \(0.828978\pi\) | |||||||
\(954\) | 1.05081 | − | 0.693549i | 0.0340211 | − | 0.0224545i | ||||
\(955\) | −13.8887 | + | 33.5725i | −0.449427 | + | 1.08638i | ||||
\(956\) | −16.1877 | − | 6.92107i | −0.523549 | − | 0.223843i | ||||
\(957\) | −38.4331 | + | 38.4331i | −1.24236 | + | 1.24236i | ||||
\(958\) | 30.0799 | + | 6.16060i | 0.971837 | + | 0.199040i | ||||
\(959\) | −47.3993 | −1.53060 | ||||||||
\(960\) | 20.7369 | + | 22.1769i | 0.669281 | + | 0.715758i | ||||
\(961\) | −75.8663 | −2.44730 | ||||||||
\(962\) | −25.0315 | − | 5.12665i | −0.807048 | − | 0.165290i | ||||
\(963\) | 0.634359 | − | 0.634359i | 0.0204419 | − | 0.0204419i | ||||
\(964\) | −3.97430 | − | 1.69921i | −0.128004 | − | 0.0547280i | ||||
\(965\) | −7.84332 | − | 18.9116i | −0.252485 | − | 0.608787i | ||||
\(966\) | −29.1561 | + | 19.2435i | −0.938083 | + | 0.619149i | ||||
\(967\) | −28.2118 | − | 28.2118i | −0.907231 | − | 0.907231i | 0.0888168 | − | 0.996048i | \(-0.471691\pi\) |
−0.996048 | + | 0.0888168i | \(0.971691\pi\) | |||||||
\(968\) | −11.8804 | − | 8.23368i | −0.381852 | − | 0.264641i | ||||
\(969\) | − | 9.47715i | − | 0.304450i | ||||||
\(970\) | −35.4146 | + | 6.85242i | −1.13709 | + | 0.220018i | ||||
\(971\) | 15.3403i | 0.492294i | 0.969232 | + | 0.246147i | \(0.0791646\pi\) | ||||
−0.969232 | + | 0.246147i | \(0.920835\pi\) | |||||||
\(972\) | 2.29934 | − | 0.922038i | 0.0737513 | − | 0.0295744i | ||||
\(973\) | −9.21264 | − | 9.21264i | −0.295344 | − | 0.295344i | ||||
\(974\) | −12.4470 | − | 18.8587i | −0.398829 | − | 0.604272i | ||||
\(975\) | 12.7580 | + | 12.7353i | 0.408583 | + | 0.407857i | ||||
\(976\) | 33.2701 | + | 34.8130i | 1.06495 | + | 1.11434i | ||||
\(977\) | 43.0518 | − | 43.0518i | 1.37735 | − | 1.37735i | 0.528276 | − | 0.849073i | \(-0.322839\pi\) |
0.849073 | − | 0.528276i | \(-0.177161\pi\) | |||||||
\(978\) | 6.41242 | − | 31.3094i | 0.205047 | − | 1.00116i | ||||
\(979\) | 35.3992 | 1.13136 | ||||||||
\(980\) | −7.58112 | + | 7.41786i | −0.242170 | + | 0.236955i | ||||
\(981\) | −1.71191 | −0.0546572 | ||||||||
\(982\) | 6.00423 | − | 29.3164i | 0.191603 | − | 0.935523i | ||||
\(983\) | −19.7481 | + | 19.7481i | −0.629867 | + | 0.629867i | −0.948034 | − | 0.318168i | \(-0.896932\pi\) |
0.318168 | + | 0.948034i | \(0.396932\pi\) | |||||||
\(984\) | −21.1371 | + | 3.83224i | −0.673827 | + | 0.122167i | ||||
\(985\) | 12.1161 | − | 5.02496i | 0.386050 | − | 0.160108i | ||||
\(986\) | 34.7047 | + | 52.5817i | 1.10522 | + | 1.67454i | ||||
\(987\) | 8.08797 | + | 8.08797i | 0.257443 | + | 0.257443i | ||||
\(988\) | −1.58120 | − | 3.94313i | −0.0503047 | − | 0.125448i | ||||
\(989\) | − | 18.7609i | − | 0.596560i | ||||||
\(990\) | 1.25423 | + | 0.847555i | 0.0398622 | + | 0.0269371i | ||||
\(991\) | − | 34.3112i | − | 1.08993i | −0.838458 | − | 0.544966i | \(-0.816543\pi\) | ||
0.838458 | − | 0.544966i | \(-0.183457\pi\) | |||||||
\(992\) | −49.5236 | + | 31.0988i | −1.57237 | + | 0.987388i | ||||
\(993\) | −9.04492 | − | 9.04492i | −0.287032 | − | 0.287032i | ||||
\(994\) | −16.3114 | + | 10.7658i | −0.517366 | + | 0.341470i | ||||
\(995\) | −21.6940 | − | 8.97462i | −0.687745 | − | 0.284515i | ||||
\(996\) | 8.35510 | − | 19.5418i | 0.264741 | − | 0.619206i | ||||
\(997\) | −5.61418 | + | 5.61418i | −0.177803 | + | 0.177803i | −0.790397 | − | 0.612594i | \(-0.790126\pi\) |
0.612594 | + | 0.790397i | \(0.290126\pi\) | |||||||
\(998\) | −33.3561 | − | 6.83159i | −1.05587 | − | 0.216250i | ||||
\(999\) | −45.0306 | −1.42471 |
(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 | 380.2.k.c.343.25 | yes | 52 | |
4.3 | odd | 2 | 380.2.k.d.343.11 | yes | 52 | ||
5.2 | odd | 4 | 380.2.k.d.267.11 | yes | 52 | ||
20.7 | even | 4 | inner | 380.2.k.c.267.25 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.k.c.267.25 | ✓ | 52 | 20.7 | even | 4 | inner | |
380.2.k.c.343.25 | yes | 52 | 1.1 | even | 1 | trivial | |
380.2.k.d.267.11 | yes | 52 | 5.2 | odd | 4 | ||
380.2.k.d.343.11 | yes | 52 | 4.3 | odd | 2 |