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: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.4 | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.z.372.4 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0371933 | − | 0.114469i | −0.0262996 | − | 0.0809418i | 0.937045 | − | 0.349208i | \(-0.113549\pi\) |
−0.963345 | + | 0.268266i | \(0.913549\pi\) | |||||||
\(3\) | −2.23923 | − | 1.62690i | −1.29282 | − | 0.939288i | −0.292961 | − | 0.956124i | \(-0.594641\pi\) |
−0.999858 | + | 0.0168358i | \(0.994641\pi\) | |||||||
\(4\) | 1.60631 | − | 1.16706i | 0.803157 | − | 0.583528i | ||||
\(5\) | −0.867882 | + | 2.67107i | −0.388129 | + | 1.19454i | 0.546056 | + | 0.837748i | \(0.316128\pi\) |
−0.934185 | + | 0.356789i | \(0.883872\pi\) | |||||||
\(6\) | −0.102945 | + | 0.316832i | −0.0420271 | + | 0.129346i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | −0.388082 | − | 0.281958i | −0.137208 | − | 0.0996873i | ||||
\(9\) | 1.44031 | + | 4.43281i | 0.480103 | + | 1.47760i | ||||
\(10\) | 0.338034 | 0.106896 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −5.49558 | −1.58644 | ||||||||
\(13\) | −0.333638 | − | 1.02683i | −0.0925344 | − | 0.284792i | 0.894069 | − | 0.447930i | \(-0.147838\pi\) |
−0.986603 | + | 0.163138i | \(0.947838\pi\) | |||||||
\(14\) | −0.0973732 | − | 0.0707458i | −0.0260241 | − | 0.0189076i | ||||
\(15\) | 6.28893 | − | 4.56918i | 1.62380 | − | 1.17976i | ||||
\(16\) | 1.20927 | − | 3.72176i | 0.302318 | − | 0.930440i | ||||
\(17\) | −2.15023 | + | 6.61772i | −0.521507 | + | 1.60503i | 0.249615 | + | 0.968345i | \(0.419696\pi\) |
−0.771122 | + | 0.636688i | \(0.780304\pi\) | |||||||
\(18\) | 0.453850 | − | 0.329741i | 0.106974 | − | 0.0777208i | ||||
\(19\) | 6.10332 | + | 4.43432i | 1.40020 | + | 1.01730i | 0.994658 | + | 0.103225i | \(0.0329161\pi\) |
0.405539 | + | 0.914078i | \(0.367084\pi\) | |||||||
\(20\) | 1.72319 | + | 5.30344i | 0.385317 | + | 1.18588i | ||||
\(21\) | −2.76784 | −0.603992 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.82552 | 1.00619 | 0.503095 | − | 0.864231i | \(-0.332194\pi\) | ||||
0.503095 | + | 0.864231i | \(0.332194\pi\) | |||||||
\(24\) | 0.410289 | + | 1.26274i | 0.0837498 | + | 0.257755i | ||||
\(25\) | −2.33629 | − | 1.69741i | −0.467258 | − | 0.339483i | ||||
\(26\) | −0.105131 | + | 0.0763824i | −0.0206179 | + | 0.0149798i | ||||
\(27\) | 1.42061 | − | 4.37220i | 0.273397 | − | 0.841431i | ||||
\(28\) | 0.613557 | − | 1.88834i | 0.115951 | − | 0.356862i | ||||
\(29\) | 0.992877 | − | 0.721367i | 0.184373 | − | 0.133955i | −0.491770 | − | 0.870725i | \(-0.663650\pi\) |
0.676143 | + | 0.736770i | \(0.263650\pi\) | |||||||
\(30\) | −0.756935 | − | 0.549946i | −0.138197 | − | 0.100406i | ||||
\(31\) | −2.49503 | − | 7.67891i | −0.448121 | − | 1.37917i | −0.879025 | − | 0.476776i | \(-0.841805\pi\) |
0.430904 | − | 0.902398i | \(-0.358195\pi\) | |||||||
\(32\) | −1.43040 | −0.252861 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.837498 | 0.143630 | ||||||||
\(35\) | 0.867882 | + | 2.67107i | 0.146699 | + | 0.451493i | ||||
\(36\) | 7.48693 | + | 5.43957i | 1.24782 | + | 0.906595i | ||||
\(37\) | −1.24205 | + | 0.902399i | −0.204191 | + | 0.148354i | −0.685182 | − | 0.728372i | \(-0.740277\pi\) |
0.480990 | + | 0.876726i | \(0.340277\pi\) | |||||||
\(38\) | 0.280590 | − | 0.863568i | 0.0455177 | − | 0.140089i | ||||
\(39\) | −0.923456 | + | 2.84210i | −0.147871 | + | 0.455101i | ||||
\(40\) | 1.08994 | − | 0.791887i | 0.172334 | − | 0.125208i | ||||
\(41\) | 7.52374 | + | 5.46632i | 1.17501 | + | 0.853696i | 0.991600 | − | 0.129341i | \(-0.0412861\pi\) |
0.183411 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(42\) | 0.102945 | + | 0.316832i | 0.0158848 | + | 0.0488882i | ||||
\(43\) | 5.23402 | 0.798181 | 0.399091 | − | 0.916912i | \(-0.369326\pi\) | ||||
0.399091 | + | 0.916912i | \(0.369326\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.0904 | −1.95140 | ||||||||
\(46\) | −0.179477 | − | 0.552373i | −0.0264624 | − | 0.0814429i | ||||
\(47\) | 1.53217 | + | 1.11319i | 0.223490 | + | 0.162375i | 0.693896 | − | 0.720075i | \(-0.255893\pi\) |
−0.470406 | + | 0.882450i | \(0.655893\pi\) | |||||||
\(48\) | −8.76276 | + | 6.36651i | −1.26479 | + | 0.918927i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | −0.107407 | + | 0.330565i | −0.0151897 | + | 0.0467490i | ||||
\(51\) | 15.5812 | − | 11.3204i | 2.18180 | − | 1.58517i | ||||
\(52\) | −1.73430 | − | 1.26004i | −0.240504 | − | 0.174736i | ||||
\(53\) | −1.18215 | − | 3.63829i | −0.162381 | − | 0.499757i | 0.836453 | − | 0.548039i | \(-0.184625\pi\) |
−0.998834 | + | 0.0482819i | \(0.984625\pi\) | |||||||
\(54\) | −0.553319 | −0.0752972 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.479696 | −0.0641021 | ||||||||
\(57\) | −6.45255 | − | 19.8589i | −0.854661 | − | 2.63038i | ||||
\(58\) | −0.119503 | − | 0.0868237i | −0.0156915 | − | 0.0114005i | ||||
\(59\) | 5.39088 | − | 3.91670i | 0.701832 | − | 0.509911i | −0.178696 | − | 0.983904i | \(-0.557188\pi\) |
0.880528 | + | 0.473993i | \(0.157188\pi\) | |||||||
\(60\) | 4.76952 | − | 14.6791i | 0.615742 | − | 1.89506i | ||||
\(61\) | 3.02822 | − | 9.31990i | 0.387724 | − | 1.19329i | −0.546761 | − | 0.837289i | \(-0.684139\pi\) |
0.934485 | − | 0.356002i | \(-0.115861\pi\) | |||||||
\(62\) | −0.786200 | + | 0.571207i | −0.0998474 | + | 0.0725434i | ||||
\(63\) | 3.77078 | + | 2.73963i | 0.475073 | + | 0.345161i | ||||
\(64\) | −2.36535 | − | 7.27979i | −0.295668 | − | 0.909973i | ||||
\(65\) | 3.03229 | 0.376110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.06100 | −0.251792 | −0.125896 | − | 0.992043i | \(-0.540181\pi\) | ||||
−0.125896 | + | 0.992043i | \(0.540181\pi\) | |||||||
\(68\) | 4.26931 | + | 13.1396i | 0.517729 | + | 1.59341i | ||||
\(69\) | −10.8054 | − | 7.85062i | −1.30082 | − | 0.945103i | ||||
\(70\) | 0.273475 | − | 0.198691i | 0.0326865 | − | 0.0237482i | ||||
\(71\) | 3.86926 | − | 11.9084i | 0.459197 | − | 1.41326i | −0.406940 | − | 0.913455i | \(-0.633404\pi\) |
0.866137 | − | 0.499808i | \(-0.166596\pi\) | |||||||
\(72\) | 0.690910 | − | 2.12640i | 0.0814245 | − | 0.250599i | ||||
\(73\) | 2.07681 | − | 1.50889i | 0.243073 | − | 0.176603i | −0.459579 | − | 0.888137i | \(-0.652000\pi\) |
0.702651 | + | 0.711535i | \(0.252000\pi\) | |||||||
\(74\) | 0.149493 | + | 0.108613i | 0.0173782 | + | 0.0126260i | ||||
\(75\) | 2.46997 | + | 7.60180i | 0.285208 | + | 0.877780i | ||||
\(76\) | 14.9789 | 1.71820 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.359679 | 0.0407257 | ||||||||
\(79\) | 4.73672 | + | 14.5781i | 0.532923 | + | 1.64017i | 0.748095 | + | 0.663591i | \(0.230969\pi\) |
−0.215173 | + | 0.976576i | \(0.569031\pi\) | |||||||
\(80\) | 8.89156 | + | 6.46010i | 0.994107 | + | 0.722261i | ||||
\(81\) | 1.01813 | − | 0.739718i | 0.113126 | − | 0.0821909i | ||||
\(82\) | 0.345892 | − | 1.06455i | 0.0381974 | − | 0.117559i | ||||
\(83\) | −0.632256 | + | 1.94588i | −0.0693991 | + | 0.213589i | −0.979741 | − | 0.200268i | \(-0.935819\pi\) |
0.910342 | + | 0.413857i | \(0.135819\pi\) | |||||||
\(84\) | −4.44602 | + | 3.23022i | −0.485101 | + | 0.352446i | ||||
\(85\) | −15.8102 | − | 11.4868i | −1.71486 | − | 1.24592i | ||||
\(86\) | −0.194670 | − | 0.599134i | −0.0209918 | − | 0.0646063i | ||||
\(87\) | −3.39687 | −0.364183 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.76119 | 0.504685 | 0.252342 | − | 0.967638i | \(-0.418799\pi\) | ||||
0.252342 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(90\) | 0.486873 | + | 1.49844i | 0.0513209 | + | 0.157950i | ||||
\(91\) | −0.873475 | − | 0.634617i | −0.0915650 | − | 0.0665259i | ||||
\(92\) | 7.75130 | − | 5.63165i | 0.808129 | − | 0.587140i | ||||
\(93\) | −6.90584 | + | 21.2540i | −0.716102 | + | 2.20394i | ||||
\(94\) | 0.0704390 | − | 0.216789i | 0.00726523 | − | 0.0223601i | ||||
\(95\) | −17.1413 | + | 12.4539i | −1.75866 | + | 1.27774i | ||||
\(96\) | 3.20298 | + | 2.32710i | 0.326903 | + | 0.237509i | ||||
\(97\) | 2.81673 | + | 8.66899i | 0.285995 | + | 0.880203i | 0.986099 | + | 0.166161i | \(0.0531373\pi\) |
−0.700103 | + | 0.714042i | \(0.746863\pi\) | |||||||
\(98\) | −0.120360 | −0.0121582 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.73379 | −0.573379 | ||||||||
\(101\) | 1.46593 | + | 4.51167i | 0.145866 | + | 0.448928i | 0.997121 | − | 0.0758231i | \(-0.0241584\pi\) |
−0.851256 | + | 0.524751i | \(0.824158\pi\) | |||||||
\(102\) | −1.87535 | − | 1.36252i | −0.185687 | − | 0.134910i | ||||
\(103\) | −0.283885 | + | 0.206254i | −0.0279720 | + | 0.0203228i | −0.601683 | − | 0.798735i | \(-0.705503\pi\) |
0.573711 | + | 0.819058i | \(0.305503\pi\) | |||||||
\(104\) | −0.160045 | + | 0.492567i | −0.0156937 | + | 0.0483001i | ||||
\(105\) | 2.40216 | − | 7.39308i | 0.234427 | − | 0.721491i | ||||
\(106\) | −0.372503 | + | 0.270639i | −0.0361807 | + | 0.0262868i | ||||
\(107\) | 2.06116 | + | 1.49752i | 0.199260 | + | 0.144771i | 0.682941 | − | 0.730473i | \(-0.260701\pi\) |
−0.483681 | + | 0.875244i | \(0.660701\pi\) | |||||||
\(108\) | −2.82065 | − | 8.68106i | −0.271417 | − | 0.835336i | ||||
\(109\) | 3.81522 | 0.365432 | 0.182716 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182716 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.24933 | 0.403329 | ||||||||
\(112\) | −1.20927 | − | 3.72176i | −0.114266 | − | 0.351673i | ||||
\(113\) | −1.87262 | − | 1.36054i | −0.176161 | − | 0.127988i | 0.496211 | − | 0.868202i | \(-0.334724\pi\) |
−0.672372 | + | 0.740214i | \(0.734724\pi\) | |||||||
\(114\) | −2.03324 | + | 1.47724i | −0.190430 | + | 0.138356i | ||||
\(115\) | −4.18798 | + | 12.8893i | −0.390531 | + | 1.20193i | ||||
\(116\) | 0.752997 | − | 2.31749i | 0.0699140 | − | 0.215173i | ||||
\(117\) | 4.07121 | − | 2.95791i | 0.376383 | − | 0.273459i | ||||
\(118\) | −0.648845 | − | 0.471414i | −0.0597311 | − | 0.0433972i | ||||
\(119\) | 2.15023 | + | 6.61772i | 0.197111 | + | 0.606646i | ||||
\(120\) | −3.72894 | −0.340404 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.17947 | −0.106784 | ||||||||
\(123\) | −7.95426 | − | 24.4807i | −0.717211 | − | 2.20735i | ||||
\(124\) | −12.9695 | − | 9.42291i | −1.16470 | − | 0.846202i | ||||
\(125\) | −4.79919 | + | 3.48682i | −0.429253 | + | 0.311870i | ||||
\(126\) | 0.173355 | − | 0.533533i | 0.0154437 | − | 0.0475309i | ||||
\(127\) | −3.04272 | + | 9.36452i | −0.269997 | + | 0.830967i | 0.720502 | + | 0.693453i | \(0.243911\pi\) |
−0.990500 | + | 0.137514i | \(0.956089\pi\) | |||||||
\(128\) | −3.05976 | + | 2.22305i | −0.270447 | + | 0.196492i | ||||
\(129\) | −11.7202 | − | 8.51521i | −1.03190 | − | 0.749722i | ||||
\(130\) | −0.112781 | − | 0.347104i | −0.00989153 | − | 0.0304430i | ||||
\(131\) | −16.3782 | −1.43097 | −0.715484 | − | 0.698629i | \(-0.753794\pi\) | ||||
−0.715484 | + | 0.698629i | \(0.753794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.54411 | 0.654158 | ||||||||
\(134\) | 0.0766554 | + | 0.235921i | 0.00662202 | + | 0.0203805i | ||||
\(135\) | 10.4455 | + | 7.58911i | 0.899007 | + | 0.653167i | ||||
\(136\) | 2.70039 | − | 1.96195i | 0.231556 | − | 0.168235i | ||||
\(137\) | −4.39242 | + | 13.5185i | −0.375270 | + | 1.15496i | 0.568027 | + | 0.823010i | \(0.307707\pi\) |
−0.943297 | + | 0.331951i | \(0.892293\pi\) | |||||||
\(138\) | −0.496763 | + | 1.52888i | −0.0422873 | + | 0.130147i | ||||
\(139\) | −7.42631 | + | 5.39553i | −0.629891 | + | 0.457643i | −0.856362 | − | 0.516375i | \(-0.827281\pi\) |
0.226471 | + | 0.974018i | \(0.427281\pi\) | |||||||
\(140\) | 4.51137 | + | 3.27771i | 0.381281 | + | 0.277017i | ||||
\(141\) | −1.61984 | − | 4.98536i | −0.136415 | − | 0.419843i | ||||
\(142\) | −1.50705 | −0.126469 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 18.2396 | 1.51997 | ||||||||
\(145\) | 1.06512 | + | 3.27810i | 0.0884534 | + | 0.272232i | ||||
\(146\) | −0.249965 | − | 0.181610i | −0.0206872 | − | 0.0150302i | ||||
\(147\) | −2.23923 | + | 1.62690i | −0.184689 | + | 0.134184i | ||||
\(148\) | −0.941966 | + | 2.89907i | −0.0774291 | + | 0.238302i | ||||
\(149\) | −3.59077 | + | 11.0513i | −0.294168 | + | 0.905355i | 0.689332 | + | 0.724446i | \(0.257904\pi\) |
−0.983500 | + | 0.180910i | \(0.942096\pi\) | |||||||
\(150\) | 0.778305 | − | 0.565471i | 0.0635483 | − | 0.0461705i | ||||
\(151\) | 14.4935 | + | 10.5302i | 1.17947 | + | 0.856934i | 0.992112 | − | 0.125358i | \(-0.0400080\pi\) |
0.187357 | + | 0.982292i | \(0.440008\pi\) | |||||||
\(152\) | −1.11830 | − | 3.44176i | −0.0907058 | − | 0.279164i | ||||
\(153\) | −32.4321 | −2.62198 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.6763 | 1.82140 | ||||||||
\(156\) | 1.83353 | + | 5.64304i | 0.146800 | + | 0.451804i | ||||
\(157\) | −6.00942 | − | 4.36610i | −0.479604 | − | 0.348453i | 0.321568 | − | 0.946886i | \(-0.395790\pi\) |
−0.801172 | + | 0.598434i | \(0.795790\pi\) | |||||||
\(158\) | 1.49257 | − | 1.08442i | 0.118743 | − | 0.0862715i | ||||
\(159\) | −3.27200 | + | 10.0702i | −0.259487 | + | 0.798618i | ||||
\(160\) | 1.24141 | − | 3.82068i | 0.0981424 | − | 0.302051i | ||||
\(161\) | 3.90393 | − | 2.83637i | 0.307673 | − | 0.223537i | ||||
\(162\) | −0.122543 | − | 0.0890324i | −0.00962785 | − | 0.00699505i | ||||
\(163\) | 2.42670 | + | 7.46861i | 0.190074 | + | 0.584987i | 0.999999 | − | 0.00154665i | \(-0.000492315\pi\) |
−0.809925 | + | 0.586533i | \(0.800492\pi\) | |||||||
\(164\) | 18.4650 | 1.44187 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.246259 | 0.0191134 | ||||||||
\(167\) | 1.66949 | + | 5.13817i | 0.129189 | + | 0.397603i | 0.994641 | − | 0.103389i | \(-0.0329686\pi\) |
−0.865452 | + | 0.500992i | \(0.832969\pi\) | |||||||
\(168\) | 1.07415 | + | 0.780415i | 0.0828724 | + | 0.0602103i | ||||
\(169\) | 9.57415 | − | 6.95603i | 0.736473 | − | 0.535079i | ||||
\(170\) | −0.726850 | + | 2.23701i | −0.0557468 | + | 0.171571i | ||||
\(171\) | −10.8659 | + | 33.4417i | −0.830932 | + | 2.55735i | ||||
\(172\) | 8.40749 | − | 6.10840i | 0.641065 | − | 0.465761i | ||||
\(173\) | −15.9547 | − | 11.5918i | −1.21302 | − | 0.881307i | −0.217515 | − | 0.976057i | \(-0.569795\pi\) |
−0.995501 | + | 0.0947496i | \(0.969795\pi\) | |||||||
\(174\) | 0.126341 | + | 0.388836i | 0.00957785 | + | 0.0294776i | ||||
\(175\) | −2.88781 | −0.218298 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.4435 | −1.38630 | ||||||||
\(178\) | −0.177084 | − | 0.545009i | −0.0132730 | − | 0.0408501i | ||||
\(179\) | 18.8737 | + | 13.7125i | 1.41069 | + | 1.02492i | 0.993222 | + | 0.116229i | \(0.0370806\pi\) |
0.417463 | + | 0.908694i | \(0.362919\pi\) | |||||||
\(180\) | −21.0272 | + | 15.2772i | −1.56728 | + | 1.13869i | ||||
\(181\) | 0.953318 | − | 2.93401i | 0.0708596 | − | 0.218083i | −0.909355 | − | 0.416021i | \(-0.863424\pi\) |
0.980215 | + | 0.197938i | \(0.0634243\pi\) | |||||||
\(182\) | −0.0401566 | + | 0.123589i | −0.00297660 | + | 0.00916105i | ||||
\(183\) | −21.9434 | + | 15.9428i | −1.62210 | + | 1.17853i | ||||
\(184\) | −1.87270 | − | 1.36060i | −0.138057 | − | 0.100304i | ||||
\(185\) | −1.33242 | − | 4.10076i | −0.0979614 | − | 0.301494i | ||||
\(186\) | 2.68978 | 0.197224 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.76030 | 0.274248 | ||||||||
\(189\) | −1.42061 | − | 4.37220i | −0.103334 | − | 0.318031i | ||||
\(190\) | 2.06313 | + | 1.49895i | 0.149675 | + | 0.108745i | ||||
\(191\) | −10.1705 | + | 7.38933i | −0.735914 | + | 0.534673i | −0.891429 | − | 0.453161i | \(-0.850296\pi\) |
0.155515 | + | 0.987834i | \(0.450296\pi\) | |||||||
\(192\) | −6.54690 | + | 20.1493i | −0.472482 | + | 1.45415i | ||||
\(193\) | 6.38693 | − | 19.6569i | 0.459741 | − | 1.41494i | −0.405737 | − | 0.913990i | \(-0.632985\pi\) |
0.865478 | − | 0.500947i | \(-0.167015\pi\) | |||||||
\(194\) | 0.887568 | − | 0.644856i | 0.0637237 | − | 0.0462980i | ||||
\(195\) | −6.79000 | − | 4.93322i | −0.486242 | − | 0.353275i | ||||
\(196\) | −0.613557 | − | 1.88834i | −0.0438255 | − | 0.134881i | ||||
\(197\) | −6.27954 | −0.447399 | −0.223699 | − | 0.974658i | \(-0.571813\pi\) | ||||
−0.223699 | + | 0.974658i | \(0.571813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.86896 | −0.486927 | −0.243464 | − | 0.969910i | \(-0.578284\pi\) | ||||
−0.243464 | + | 0.969910i | \(0.578284\pi\) | |||||||
\(200\) | 0.428073 | + | 1.31747i | 0.0302693 | + | 0.0931594i | ||||
\(201\) | 4.61506 | + | 3.35304i | 0.325521 | + | 0.236505i | ||||
\(202\) | 0.461924 | − | 0.335607i | 0.0325009 | − | 0.0236133i | ||||
\(203\) | 0.379245 | − | 1.16720i | 0.0266178 | − | 0.0819212i | ||||
\(204\) | 11.8168 | − | 36.3682i | 0.827338 | − | 2.54629i | ||||
\(205\) | −21.1306 | + | 15.3523i | −1.47583 | + | 1.07225i | ||||
\(206\) | 0.0341683 | + | 0.0248247i | 0.00238062 | + | 0.00172962i | ||||
\(207\) | 6.95024 | + | 21.3906i | 0.483075 | + | 1.48675i | ||||
\(208\) | −4.22508 | −0.292957 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.935623 | −0.0645641 | ||||||||
\(211\) | −3.17009 | − | 9.75652i | −0.218238 | − | 0.671667i | −0.998908 | − | 0.0467233i | \(-0.985122\pi\) |
0.780670 | − | 0.624943i | \(-0.214878\pi\) | |||||||
\(212\) | −6.14499 | − | 4.46459i | −0.422039 | − | 0.306630i | ||||
\(213\) | −28.0378 | + | 20.3707i | −1.92112 | + | 1.39578i | ||||
\(214\) | 0.0947586 | − | 0.291637i | 0.00647756 | − | 0.0199359i | ||||
\(215\) | −4.54252 | + | 13.9804i | −0.309797 | + | 0.953457i | ||||
\(216\) | −1.78409 | + | 1.29622i | −0.121392 | + | 0.0881966i | ||||
\(217\) | −6.53207 | − | 4.74583i | −0.443426 | − | 0.322168i | ||||
\(218\) | −0.141900 | − | 0.436724i | −0.00961070 | − | 0.0295787i | ||||
\(219\) | −7.10527 | −0.480130 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.51268 | 0.505358 | ||||||||
\(222\) | −0.158047 | − | 0.486417i | −0.0106074 | − | 0.0326462i | ||||
\(223\) | 10.9396 | + | 7.94808i | 0.732570 | + | 0.532243i | 0.890375 | − | 0.455227i | \(-0.150442\pi\) |
−0.157806 | + | 0.987470i | \(0.550442\pi\) | |||||||
\(224\) | −1.15721 | + | 0.840765i | −0.0773196 | + | 0.0561760i | ||||
\(225\) | 4.15934 | − | 12.8011i | 0.277290 | − | 0.853410i | ||||
\(226\) | −0.0860905 | + | 0.264959i | −0.00572666 | + | 0.0176248i | ||||
\(227\) | 10.9836 | − | 7.98003i | 0.729005 | − | 0.529653i | −0.160243 | − | 0.987078i | \(-0.551228\pi\) |
0.889249 | + | 0.457424i | \(0.151228\pi\) | |||||||
\(228\) | −33.5413 | − | 24.3692i | −2.22133 | − | 1.61389i | ||||
\(229\) | −0.448988 | − | 1.38184i | −0.0296700 | − | 0.0913148i | 0.935125 | − | 0.354318i | \(-0.115287\pi\) |
−0.964795 | + | 0.263003i | \(0.915287\pi\) | |||||||
\(230\) | 1.63119 | 0.107557 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.588713 | −0.0386509 | ||||||||
\(233\) | −2.53514 | − | 7.80234i | −0.166082 | − | 0.511149i | 0.833032 | − | 0.553225i | \(-0.186603\pi\) |
−0.999114 | + | 0.0420760i | \(0.986603\pi\) | |||||||
\(234\) | −0.490010 | − | 0.356013i | −0.0320330 | − | 0.0232733i | ||||
\(235\) | −4.30314 | + | 3.12641i | −0.280706 | + | 0.203945i | ||||
\(236\) | 4.08843 | − | 12.5829i | 0.266134 | − | 0.819077i | ||||
\(237\) | 13.1105 | − | 40.3499i | 0.851617 | − | 2.62101i | ||||
\(238\) | 0.677550 | − | 0.492269i | 0.0439191 | − | 0.0319091i | ||||
\(239\) | 8.40045 | + | 6.10329i | 0.543380 | + | 0.394789i | 0.825339 | − | 0.564638i | \(-0.190984\pi\) |
−0.281959 | + | 0.959427i | \(0.590984\pi\) | |||||||
\(240\) | −9.40034 | − | 28.9313i | −0.606790 | − | 1.86751i | ||||
\(241\) | 8.20445 | 0.528495 | 0.264248 | − | 0.964455i | \(-0.414876\pi\) | ||||
0.264248 | + | 0.964455i | \(0.414876\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.2749 | −1.10818 | ||||||||
\(244\) | −6.01257 | − | 18.5048i | −0.384915 | − | 1.18465i | ||||
\(245\) | 2.27214 | + | 1.65081i | 0.145162 | + | 0.105466i | ||||
\(246\) | −2.50644 | + | 1.82103i | −0.159805 | + | 0.116105i | ||||
\(247\) | 2.51700 | − | 7.74653i | 0.160153 | − | 0.492900i | ||||
\(248\) | −1.19686 | + | 3.68354i | −0.0760004 | + | 0.233905i | ||||
\(249\) | 4.58152 | − | 3.32867i | 0.290342 | − | 0.210946i | ||||
\(250\) | 0.577630 | + | 0.419673i | 0.0365325 | + | 0.0265424i | ||||
\(251\) | −5.08184 | − | 15.6403i | −0.320763 | − | 0.987207i | −0.973317 | − | 0.229465i | \(-0.926302\pi\) |
0.652554 | − | 0.757742i | \(-0.273698\pi\) | |||||||
\(252\) | 9.25435 | 0.582969 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.18512 | 0.0743608 | ||||||||
\(255\) | 16.7149 | + | 51.4432i | 1.04673 | + | 3.22150i | ||||
\(256\) | −12.0168 | − | 8.73074i | −0.751052 | − | 0.545671i | ||||
\(257\) | 9.74377 | − | 7.07926i | 0.607800 | − | 0.441592i | −0.240839 | − | 0.970565i | \(-0.577423\pi\) |
0.848639 | + | 0.528973i | \(0.177423\pi\) | |||||||
\(258\) | −0.538816 | + | 1.65831i | −0.0335452 | + | 0.103242i | ||||
\(259\) | −0.474419 | + | 1.46011i | −0.0294790 | + | 0.0907270i | ||||
\(260\) | 4.87081 | − | 3.53885i | 0.302075 | − | 0.219470i | ||||
\(261\) | 4.62774 | + | 3.36225i | 0.286450 | + | 0.208118i | ||||
\(262\) | 0.609157 | + | 1.87479i | 0.0376339 | + | 0.115825i | ||||
\(263\) | −1.87602 | −0.115681 | −0.0578403 | − | 0.998326i | \(-0.518421\pi\) | ||||
−0.0578403 | + | 0.998326i | \(0.518421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7441 | 0.660003 | ||||||||
\(266\) | −0.280590 | − | 0.863568i | −0.0172041 | − | 0.0529487i | ||||
\(267\) | −10.6614 | − | 7.74596i | −0.652467 | − | 0.474045i | ||||
\(268\) | −3.31062 | + | 2.40531i | −0.202228 | + | 0.146927i | ||||
\(269\) | −4.33520 | + | 13.3424i | −0.264322 | + | 0.813498i | 0.727527 | + | 0.686079i | \(0.240669\pi\) |
−0.991849 | + | 0.127419i | \(0.959331\pi\) | |||||||
\(270\) | 0.480216 | − | 1.47795i | 0.0292250 | − | 0.0899453i | ||||
\(271\) | 1.09482 | − | 0.795435i | 0.0665058 | − | 0.0483193i | −0.554036 | − | 0.832493i | \(-0.686913\pi\) |
0.620541 | + | 0.784174i | \(0.286913\pi\) | |||||||
\(272\) | 22.0294 | + | 16.0053i | 1.33573 | + | 0.970462i | ||||
\(273\) | 0.923456 | + | 2.84210i | 0.0558901 | + | 0.172012i | ||||
\(274\) | 1.71081 | 0.103354 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −26.5190 | −1.59626 | ||||||||
\(277\) | 4.13573 | + | 12.7285i | 0.248492 | + | 0.764780i | 0.995042 | + | 0.0994513i | \(0.0317087\pi\) |
−0.746550 | + | 0.665329i | \(0.768291\pi\) | |||||||
\(278\) | 0.893829 | + | 0.649405i | 0.0536083 | + | 0.0389487i | ||||
\(279\) | 30.4456 | − | 22.1200i | 1.82273 | − | 1.32429i | ||||
\(280\) | 0.416320 | − | 1.28130i | 0.0248798 | − | 0.0765723i | ||||
\(281\) | −0.716570 | + | 2.20538i | −0.0427470 | + | 0.131562i | −0.970152 | − | 0.242496i | \(-0.922034\pi\) |
0.927405 | + | 0.374058i | \(0.122034\pi\) | |||||||
\(282\) | −0.510422 | + | 0.370843i | −0.0303952 | + | 0.0220834i | ||||
\(283\) | −18.0151 | − | 13.0887i | −1.07089 | − | 0.778045i | −0.0948154 | − | 0.995495i | \(-0.530226\pi\) |
−0.976071 | + | 0.217450i | \(0.930226\pi\) | |||||||
\(284\) | −7.68247 | − | 23.6442i | −0.455871 | − | 1.40303i | ||||
\(285\) | 58.6445 | 3.47380 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.29986 | 0.548953 | ||||||||
\(288\) | −2.06021 | − | 6.34068i | −0.121399 | − | 0.373628i | ||||
\(289\) | −25.4175 | − | 18.4669i | −1.49515 | − | 1.08629i | ||||
\(290\) | 0.335626 | − | 0.243847i | 0.0197086 | − | 0.0143192i | ||||
\(291\) | 7.79625 | − | 23.9944i | 0.457024 | − | 1.40658i | ||||
\(292\) | 1.57505 | − | 4.84751i | 0.0921729 | − | 0.283679i | ||||
\(293\) | −1.97384 | + | 1.43408i | −0.115313 | + | 0.0837800i | −0.643947 | − | 0.765070i | \(-0.722704\pi\) |
0.528634 | + | 0.848850i | \(0.322704\pi\) | |||||||
\(294\) | 0.269513 | + | 0.195813i | 0.0157183 | + | 0.0114200i | ||||
\(295\) | 5.78312 | + | 17.7986i | 0.336706 | + | 1.03628i | ||||
\(296\) | 0.736455 | 0.0428056 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.39858 | 0.0810176 | ||||||||
\(299\) | −1.60998 | − | 4.95499i | −0.0931073 | − | 0.286555i | ||||
\(300\) | 12.8393 | + | 9.32828i | 0.741276 | + | 0.538569i | ||||
\(301\) | 4.23441 | − | 3.07648i | 0.244068 | − | 0.177325i | ||||
\(302\) | 0.666318 | − | 2.05071i | 0.0383423 | − | 0.118005i | ||||
\(303\) | 4.05746 | − | 12.4876i | 0.233095 | − | 0.717393i | ||||
\(304\) | 23.8841 | − | 17.3528i | 1.36984 | − | 0.995250i | ||||
\(305\) | 22.2659 | + | 16.1771i | 1.27494 | + | 0.926301i | ||||
\(306\) | 1.20626 | + | 3.71247i | 0.0689571 | + | 0.212228i | ||||
\(307\) | 8.89055 | 0.507410 | 0.253705 | − | 0.967282i | \(-0.418351\pi\) | ||||
0.253705 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.971237 | 0.0552517 | ||||||||
\(310\) | −0.843404 | − | 2.59573i | −0.0479021 | − | 0.147428i | ||||
\(311\) | 9.57449 | + | 6.95627i | 0.542919 | + | 0.394454i | 0.825168 | − | 0.564887i | \(-0.191080\pi\) |
−0.282249 | + | 0.959341i | \(0.591080\pi\) | |||||||
\(312\) | 1.15973 | − | 0.842594i | 0.0656569 | − | 0.0477025i | ||||
\(313\) | −9.12853 | + | 28.0947i | −0.515975 | + | 1.58801i | 0.265525 | + | 0.964104i | \(0.414455\pi\) |
−0.781501 | + | 0.623905i | \(0.785545\pi\) | |||||||
\(314\) | −0.276273 | + | 0.850282i | −0.0155910 | + | 0.0479842i | ||||
\(315\) | −10.5903 | + | 7.69432i | −0.596697 | + | 0.433526i | ||||
\(316\) | 24.6221 | + | 17.8890i | 1.38510 | + | 1.00634i | ||||
\(317\) | −7.77317 | − | 23.9233i | −0.436585 | − | 1.34367i | −0.891454 | − | 0.453111i | \(-0.850314\pi\) |
0.454870 | − | 0.890558i | \(-0.349686\pi\) | |||||||
\(318\) | 1.27442 | 0.0714660 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 21.4976 | 1.20175 | ||||||||
\(321\) | −2.17910 | − | 6.70659i | −0.121626 | − | 0.374325i | ||||
\(322\) | −0.469876 | − | 0.341385i | −0.0261852 | − | 0.0190246i | ||||
\(323\) | −42.4686 | + | 30.8553i | −2.36302 | + | 1.71683i | ||||
\(324\) | 0.772152 | − | 2.37644i | 0.0428973 | − | 0.132024i | ||||
\(325\) | −0.963484 | + | 2.96530i | −0.0534445 | + | 0.164485i | ||||
\(326\) | 0.764668 | − | 0.555564i | 0.0423510 | − | 0.0307698i | ||||
\(327\) | −8.54315 | − | 6.20696i | −0.472437 | − | 0.343246i | ||||
\(328\) | −1.37856 | − | 4.24276i | −0.0761181 | − | 0.234267i | ||||
\(329\) | 1.89387 | 0.104412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.46333 | −0.520152 | −0.260076 | − | 0.965588i | \(-0.583748\pi\) | ||||
−0.260076 | + | 0.965588i | \(0.583748\pi\) | |||||||
\(332\) | 1.25535 | + | 3.86358i | 0.0688964 | + | 0.212041i | ||||
\(333\) | −5.78910 | − | 4.20603i | −0.317241 | − | 0.230489i | ||||
\(334\) | 0.526067 | − | 0.382210i | 0.0287851 | − | 0.0209136i | ||||
\(335\) | 1.78871 | − | 5.50508i | 0.0977276 | − | 0.300775i | ||||
\(336\) | −3.34707 | + | 10.3012i | −0.182598 | + | 0.561979i | ||||
\(337\) | −13.9352 | + | 10.1245i | −0.759098 | + | 0.551517i | −0.898634 | − | 0.438700i | \(-0.855439\pi\) |
0.139535 | + | 0.990217i | \(0.455439\pi\) | |||||||
\(338\) | −1.15234 | − | 0.837227i | −0.0626792 | − | 0.0455391i | ||||
\(339\) | 1.97977 | + | 6.09310i | 0.107526 | + | 0.330932i | ||||
\(340\) | −38.8019 | −2.10433 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.23217 | 0.228850 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | −2.03123 | − | 1.47578i | −0.109517 | − | 0.0795685i | ||||
\(345\) | 30.3474 | − | 22.0487i | 1.63385 | − | 1.18706i | ||||
\(346\) | −0.733493 | + | 2.25746i | −0.0394328 | + | 0.121362i | ||||
\(347\) | 2.69922 | − | 8.30733i | 0.144902 | − | 0.445961i | −0.852097 | − | 0.523384i | \(-0.824669\pi\) |
0.996998 | + | 0.0774232i | \(0.0246693\pi\) | |||||||
\(348\) | −5.45644 | + | 3.96433i | −0.292496 | + | 0.212511i | ||||
\(349\) | −24.2584 | − | 17.6248i | −1.29852 | − | 0.943433i | −0.298584 | − | 0.954383i | \(-0.596514\pi\) |
−0.999940 | + | 0.0109508i | \(0.996514\pi\) | |||||||
\(350\) | 0.107407 | + | 0.330565i | 0.00574116 | + | 0.0176695i | ||||
\(351\) | −4.96348 | −0.264931 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.31999 | 0.389604 | 0.194802 | − | 0.980843i | \(-0.437594\pi\) | ||||
0.194802 | + | 0.980843i | \(0.437594\pi\) | |||||||
\(354\) | 0.685973 | + | 2.11121i | 0.0364590 | + | 0.112209i | ||||
\(355\) | 28.4500 | + | 20.6701i | 1.50997 | + | 1.09706i | ||||
\(356\) | 7.64796 | − | 5.55657i | 0.405341 | − | 0.294498i | ||||
\(357\) | 5.95149 | − | 18.3168i | 0.314986 | − | 0.969427i | ||||
\(358\) | 0.867687 | − | 2.67047i | 0.0458587 | − | 0.141139i | ||||
\(359\) | 4.02078 | − | 2.92127i | 0.212209 | − | 0.154179i | −0.476604 | − | 0.879118i | \(-0.658132\pi\) |
0.688812 | + | 0.724940i | \(0.258132\pi\) | |||||||
\(360\) | 5.08013 | + | 3.69093i | 0.267747 | + | 0.194529i | ||||
\(361\) | 11.7160 | + | 36.0580i | 0.616630 | + | 1.89779i | ||||
\(362\) | −0.371311 | −0.0195156 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.14371 | −0.112361 | ||||||||
\(365\) | 2.22792 | + | 6.85685i | 0.116615 | + | 0.358904i | ||||
\(366\) | 2.64110 | + | 1.91887i | 0.138053 | + | 0.100301i | ||||
\(367\) | 11.4915 | − | 8.34904i | 0.599850 | − | 0.435816i | −0.245976 | − | 0.969276i | \(-0.579108\pi\) |
0.845825 | + | 0.533460i | \(0.179108\pi\) | |||||||
\(368\) | 5.83537 | − | 17.9594i | 0.304190 | − | 0.936200i | ||||
\(369\) | −13.3947 | + | 41.2245i | −0.697298 | + | 2.14606i | ||||
\(370\) | −0.419854 | + | 0.305041i | −0.0218271 | + | 0.0158583i | ||||
\(371\) | −3.09491 | − | 2.24858i | −0.160680 | − | 0.116741i | ||||
\(372\) | 13.7116 | + | 42.2001i | 0.710916 | + | 2.18797i | ||||
\(373\) | −8.97781 | −0.464853 | −0.232427 | − | 0.972614i | \(-0.574667\pi\) | ||||
−0.232427 | + | 0.972614i | \(0.574667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.4192 | 0.847883 | ||||||||
\(376\) | −0.280736 | − | 0.864015i | −0.0144778 | − | 0.0445582i | ||||
\(377\) | −1.07198 | − | 0.778842i | −0.0552100 | − | 0.0401124i | ||||
\(378\) | −0.447644 | + | 0.325233i | −0.0230243 | + | 0.0167282i | ||||
\(379\) | 3.33416 | − | 10.2615i | 0.171264 | − | 0.527097i | −0.828179 | − | 0.560464i | \(-0.810623\pi\) |
0.999443 | + | 0.0333665i | \(0.0106228\pi\) | |||||||
\(380\) | −13.0000 | + | 40.0097i | −0.666884 | + | 2.05246i | ||||
\(381\) | 22.0484 | − | 16.0191i | 1.12958 | − | 0.820685i | ||||
\(382\) | 1.22412 | + | 0.889379i | 0.0626317 | + | 0.0455046i | ||||
\(383\) | −7.26498 | − | 22.3593i | −0.371223 | − | 1.14251i | −0.945991 | − | 0.324192i | \(-0.894908\pi\) |
0.574768 | − | 0.818316i | \(-0.305092\pi\) | |||||||
\(384\) | 10.4682 | 0.534202 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.48766 | −0.126619 | ||||||||
\(387\) | 7.53861 | + | 23.2015i | 0.383209 | + | 1.17940i | ||||
\(388\) | 14.6417 | + | 10.6379i | 0.743322 | + | 0.540055i | ||||
\(389\) | 9.60671 | − | 6.97968i | 0.487079 | − | 0.353884i | −0.316981 | − | 0.948432i | \(-0.602669\pi\) |
0.804060 | + | 0.594548i | \(0.202669\pi\) | |||||||
\(390\) | −0.312159 | + | 0.960727i | −0.0158068 | + | 0.0486483i | ||||
\(391\) | −10.3760 | + | 31.9339i | −0.524735 | + | 1.61497i | ||||
\(392\) | −0.388082 | + | 0.281958i | −0.0196011 | + | 0.0142410i | ||||
\(393\) | 36.6745 | + | 26.6456i | 1.84998 | + | 1.34409i | ||||
\(394\) | 0.233556 | + | 0.718813i | 0.0117664 | + | 0.0362133i | ||||
\(395\) | −43.0501 | −2.16608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7264 | −1.19079 | −0.595397 | − | 0.803431i | \(-0.703005\pi\) | ||||
−0.595397 | + | 0.803431i | \(0.703005\pi\) | |||||||
\(398\) | 0.255479 | + | 0.786283i | 0.0128060 | + | 0.0394128i | ||||
\(399\) | −16.8930 | − | 12.2735i | −0.845708 | − | 0.614443i | ||||
\(400\) | −9.14259 | + | 6.64248i | −0.457129 | + | 0.332124i | ||||
\(401\) | −1.17464 | + | 3.61517i | −0.0586587 | + | 0.180533i | −0.976092 | − | 0.217356i | \(-0.930257\pi\) |
0.917434 | + | 0.397888i | \(0.130257\pi\) | |||||||
\(402\) | 0.212170 | − | 0.652992i | 0.0105821 | − | 0.0325683i | ||||
\(403\) | −7.05251 | + | 5.12395i | −0.351311 | + | 0.255242i | ||||
\(404\) | 7.62011 | + | 5.53634i | 0.379115 | + | 0.275443i | ||||
\(405\) | 1.09222 | + | 3.36149i | 0.0542726 | + | 0.167034i | ||||
\(406\) | −0.147713 | −0.00733089 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.23866 | −0.457382 | ||||||||
\(409\) | 1.84882 | + | 5.69009i | 0.0914183 | + | 0.281357i | 0.986304 | − | 0.164939i | \(-0.0527428\pi\) |
−0.894885 | + | 0.446296i | \(0.852743\pi\) | |||||||
\(410\) | 2.54328 | + | 1.84780i | 0.125604 | + | 0.0912564i | ||||
\(411\) | 31.8288 | − | 23.1249i | 1.57000 | − | 1.14067i | ||||
\(412\) | −0.215298 | + | 0.662618i | −0.0106070 | + | 0.0326449i | ||||
\(413\) | 2.05913 | − | 6.33736i | 0.101323 | − | 0.311841i | ||||
\(414\) | 2.19006 | − | 1.59117i | 0.107636 | − | 0.0782019i | ||||
\(415\) | −4.64886 | − | 3.37760i | −0.228204 | − | 0.165800i | ||||
\(416\) | 0.477234 | + | 1.46877i | 0.0233983 | + | 0.0720126i | ||||
\(417\) | 25.4072 | 1.24419 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.16889 | −0.203664 | −0.101832 | − | 0.994802i | \(-0.532470\pi\) | ||||
−0.101832 | + | 0.994802i | \(0.532470\pi\) | |||||||
\(420\) | −4.76952 | − | 14.6791i | −0.232729 | − | 0.716265i | ||||
\(421\) | −18.9759 | − | 13.7868i | −0.924828 | − | 0.671927i | 0.0198933 | − | 0.999802i | \(-0.493667\pi\) |
−0.944721 | + | 0.327875i | \(0.893667\pi\) | |||||||
\(422\) | −0.998914 | + | 0.725753i | −0.0486264 | + | 0.0353291i | ||||
\(423\) | −2.72775 | + | 8.39515i | −0.132628 | + | 0.408186i | ||||
\(424\) | −0.567073 | + | 1.74527i | −0.0275395 | + | 0.0847579i | ||||
\(425\) | 16.2566 | − | 11.8111i | 0.788560 | − | 0.572922i | ||||
\(426\) | 3.37463 | + | 2.45181i | 0.163501 | + | 0.118791i | ||||
\(427\) | −3.02822 | − | 9.31990i | −0.146546 | − | 0.451022i | ||||
\(428\) | 5.05856 | 0.244515 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.76928 | 0.0853221 | ||||||||
\(431\) | −11.5180 | − | 35.4487i | −0.554802 | − | 1.70751i | −0.696465 | − | 0.717591i | \(-0.745245\pi\) |
0.141663 | − | 0.989915i | \(-0.454755\pi\) | |||||||
\(432\) | −14.5544 | − | 10.5744i | −0.700248 | − | 0.508760i | ||||
\(433\) | 18.4345 | − | 13.3935i | 0.885906 | − | 0.643648i | −0.0489013 | − | 0.998804i | \(-0.515572\pi\) |
0.934807 | + | 0.355155i | \(0.115572\pi\) | |||||||
\(434\) | −0.300302 | + | 0.924233i | −0.0144149 | + | 0.0443646i | ||||
\(435\) | 2.94808 | − | 9.07326i | 0.141350 | − | 0.435030i | ||||
\(436\) | 6.12844 | − | 4.45257i | 0.293499 | − | 0.213239i | ||||
\(437\) | 29.4517 | + | 21.3979i | 1.40886 | + | 1.02360i | ||||
\(438\) | 0.264268 | + | 0.813334i | 0.0126272 | + | 0.0388626i | ||||
\(439\) | 1.42974 | 0.0682379 | 0.0341189 | − | 0.999418i | \(-0.489137\pi\) | ||||
0.0341189 | + | 0.999418i | \(0.489137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.66094 | 0.221949 | ||||||||
\(442\) | −0.279421 | − | 0.859969i | −0.0132907 | − | 0.0409046i | ||||
\(443\) | 21.3824 | + | 15.5352i | 1.01591 | + | 0.738101i | 0.965440 | − | 0.260624i | \(-0.0839284\pi\) |
0.0504690 | + | 0.998726i | \(0.483928\pi\) | |||||||
\(444\) | 6.82577 | − | 4.95921i | 0.323937 | − | 0.235354i | ||||
\(445\) | −4.13215 | + | 12.7175i | −0.195883 | + | 0.602865i | ||||
\(446\) | 0.502930 | − | 1.54786i | 0.0238144 | − | 0.0732933i | ||||
\(447\) | 26.0198 | − | 18.9045i | 1.23070 | − | 0.894152i | ||||
\(448\) | −6.19256 | − | 4.49915i | −0.292571 | − | 0.212565i | ||||
\(449\) | 4.35312 | + | 13.3975i | 0.205436 | + | 0.632268i | 0.999695 | + | 0.0246886i | \(0.00785943\pi\) |
−0.794259 | + | 0.607580i | \(0.792141\pi\) | |||||||
\(450\) | −1.62003 | −0.0763691 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.59583 | −0.216170 | ||||||||
\(453\) | −15.3229 | − | 47.1590i | −0.719932 | − | 2.21572i | ||||
\(454\) | −1.32198 | − | 0.960476i | −0.0620437 | − | 0.0450774i | ||||
\(455\) | 2.45318 | − | 1.78234i | 0.115007 | − | 0.0835572i | ||||
\(456\) | −3.09526 | + | 9.52624i | −0.144949 | + | 0.446107i | ||||
\(457\) | −9.11071 | + | 28.0399i | −0.426181 | + | 1.31165i | 0.475678 | + | 0.879620i | \(0.342203\pi\) |
−0.901859 | + | 0.432031i | \(0.857797\pi\) | |||||||
\(458\) | −0.141479 | + | 0.102791i | −0.00661088 | + | 0.00480309i | ||||
\(459\) | 25.8794 | + | 18.8025i | 1.20795 | + | 0.877624i | ||||
\(460\) | 8.31530 | + | 25.5918i | 0.387703 | + | 1.19323i | ||||
\(461\) | −31.7282 | −1.47773 | −0.738866 | − | 0.673853i | \(-0.764638\pi\) | ||||
−0.738866 | + | 0.673853i | \(0.764638\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7839 | −0.594117 | −0.297059 | − | 0.954859i | \(-0.596006\pi\) | ||||
−0.297059 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(464\) | −1.48410 | − | 4.56758i | −0.0688975 | − | 0.212045i | ||||
\(465\) | −50.7774 | − | 36.8919i | −2.35474 | − | 1.71082i | ||||
\(466\) | −0.798837 | + | 0.580389i | −0.0370054 | + | 0.0268860i | ||||
\(467\) | 9.13972 | − | 28.1292i | 0.422936 | − | 1.30166i | −0.482021 | − | 0.876160i | \(-0.660097\pi\) |
0.904957 | − | 0.425503i | \(-0.139903\pi\) | |||||||
\(468\) | 3.08760 | − | 9.50266i | 0.142724 | − | 0.439260i | ||||
\(469\) | −1.66739 | + | 1.21143i | −0.0769928 | + | 0.0559385i | ||||
\(470\) | 0.517925 | + | 0.376295i | 0.0238901 | + | 0.0173572i | ||||
\(471\) | 6.35328 | + | 19.5534i | 0.292744 | + | 0.900973i | ||||
\(472\) | −3.19645 | −0.147129 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.10644 | −0.234546 | ||||||||
\(475\) | −6.73224 | − | 20.7197i | −0.308897 | − | 0.950686i | ||||
\(476\) | 11.1772 | + | 8.12070i | 0.512306 | + | 0.372212i | ||||
\(477\) | 14.4252 | − | 10.4805i | 0.660484 | − | 0.479869i | ||||
\(478\) | 0.386197 | − | 1.18859i | 0.0176643 | − | 0.0543650i | ||||
\(479\) | 8.82473 | − | 27.1597i | 0.403212 | − | 1.24096i | −0.519167 | − | 0.854673i | \(-0.673758\pi\) |
0.922379 | − | 0.386286i | \(-0.126242\pi\) | |||||||
\(480\) | −8.99566 | + | 6.53573i | −0.410594 | + | 0.298314i | ||||
\(481\) | 1.34101 | + | 0.974297i | 0.0611446 | + | 0.0444241i | ||||
\(482\) | −0.305150 | − | 0.939156i | −0.0138992 | − | 0.0427774i | ||||
\(483\) | −13.3563 | −0.607731 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.6000 | −1.16244 | ||||||||
\(486\) | 0.642509 | + | 1.97744i | 0.0291448 | + | 0.0896985i | ||||
\(487\) | −0.856166 | − | 0.622041i | −0.0387966 | − | 0.0281874i | 0.568218 | − | 0.822878i | \(-0.307633\pi\) |
−0.607015 | + | 0.794691i | \(0.707633\pi\) | |||||||
\(488\) | −3.80302 | + | 2.76306i | −0.172155 | + | 0.125078i | ||||
\(489\) | 6.71671 | − | 20.6719i | 0.303740 | − | 0.934816i | ||||
\(490\) | 0.104458 | − | 0.321489i | 0.00471894 | − | 0.0145234i | ||||
\(491\) | 14.9255 | − | 10.8440i | 0.673577 | − | 0.489382i | −0.197644 | − | 0.980274i | \(-0.563329\pi\) |
0.871221 | + | 0.490892i | \(0.163329\pi\) | |||||||
\(492\) | −41.3473 | − | 30.0406i | −1.86408 | − | 1.35434i | ||||
\(493\) | 2.63890 | + | 8.12169i | 0.118850 | + | 0.365782i | ||||
\(494\) | −0.980354 | −0.0441082 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.5962 | −1.41871 | ||||||||
\(497\) | −3.86926 | − | 11.9084i | −0.173560 | − | 0.534163i | ||||
\(498\) | −0.551431 | − | 0.400638i | −0.0247102 | − | 0.0179530i | ||||
\(499\) | −25.6695 | + | 18.6500i | −1.14913 | + | 0.834889i | −0.988365 | − | 0.152104i | \(-0.951395\pi\) |
−0.160762 | + | 0.986993i | \(0.551395\pi\) | |||||||
\(500\) | −3.63970 | + | 11.2018i | −0.162772 | + | 0.500962i | ||||
\(501\) | 4.62088 | − | 14.2216i | 0.206446 | − | 0.635375i | ||||
\(502\) | −1.60132 | + | 1.16343i | −0.0714704 | + | 0.0519263i | ||||
\(503\) | −23.4844 | − | 17.0624i | −1.04712 | − | 0.760775i | −0.0754549 | − | 0.997149i | \(-0.524041\pi\) |
−0.971662 | + | 0.236374i | \(0.924041\pi\) | |||||||
\(504\) | −0.690910 | − | 2.12640i | −0.0307756 | − | 0.0947175i | ||||
\(505\) | −13.3232 | −0.592876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.7555 | −1.45472 | ||||||||
\(508\) | 6.04136 | + | 18.5934i | 0.268042 | + | 0.824948i | ||||
\(509\) | −2.33669 | − | 1.69770i | −0.103572 | − | 0.0752494i | 0.534794 | − | 0.844983i | \(-0.320389\pi\) |
−0.638366 | + | 0.769733i | \(0.720389\pi\) | |||||||
\(510\) | 5.26697 | − | 3.82668i | 0.233225 | − | 0.169448i | ||||
\(511\) | 0.793272 | − | 2.44144i | 0.0350923 | − | 0.108003i | ||||
\(512\) | −2.88991 | + | 8.89422i | −0.127717 | + | 0.393073i | ||||
\(513\) | 28.0582 | − | 20.3855i | 1.23880 | − | 0.900041i | ||||
\(514\) | −1.17276 | − | 0.852059i | −0.0517282 | − | 0.0375827i | ||||
\(515\) | −0.304540 | − | 0.937279i | −0.0134197 | − | 0.0413014i | ||||
\(516\) | −28.7640 | −1.26626 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.184783 | 0.00811890 | ||||||||
\(519\) | 16.8677 | + | 51.9134i | 0.740409 | + | 2.27874i | ||||
\(520\) | −1.17678 | − | 0.854980i | −0.0516052 | − | 0.0374933i | ||||
\(521\) | −25.6222 | + | 18.6157i | −1.12253 | + | 0.815567i | −0.984591 | − | 0.174874i | \(-0.944048\pi\) |
−0.137940 | + | 0.990441i | \(0.544048\pi\) | |||||||
\(522\) | 0.212753 | − | 0.654786i | 0.00931193 | − | 0.0286592i | ||||
\(523\) | 4.95603 | − | 15.2531i | 0.216712 | − | 0.666971i | −0.782316 | − | 0.622882i | \(-0.785962\pi\) |
0.999028 | − | 0.0440888i | \(-0.0140384\pi\) | |||||||
\(524\) | −26.3085 | + | 19.1142i | −1.14929 | + | 0.835009i | ||||
\(525\) | 6.46648 | + | 4.69817i | 0.282220 | + | 0.205045i | ||||
\(526\) | 0.0697754 | + | 0.214747i | 0.00304235 | + | 0.00936340i | ||||
\(527\) | 56.1818 | 2.44732 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.285644 | 0.0124193 | ||||||||
\(530\) | −0.399607 | − | 1.22986i | −0.0173578 | − | 0.0534219i | ||||
\(531\) | 25.1265 | + | 18.2555i | 1.09040 | + | 0.792221i | ||||
\(532\) | 12.1182 | − | 8.80440i | 0.525391 | − | 0.381719i | ||||
\(533\) | 3.10278 | − | 9.54938i | 0.134396 | − | 0.413630i | ||||
\(534\) | −0.490140 | + | 1.50850i | −0.0212104 | + | 0.0652790i | ||||
\(535\) | −5.78882 | + | 4.20583i | −0.250273 | + | 0.181834i | ||||
\(536\) | 0.799839 | + | 0.581117i | 0.0345478 | + | 0.0251004i | ||||
\(537\) | −19.9536 | − | 61.4110i | −0.861063 | − | 2.65008i | ||||
\(538\) | 1.68853 | 0.0727976 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 25.6357 | 1.10318 | ||||||||
\(541\) | −4.20098 | − | 12.9293i | −0.180614 | − | 0.555873i | 0.819231 | − | 0.573463i | \(-0.194401\pi\) |
−0.999845 | + | 0.0175903i | \(0.994401\pi\) | |||||||
\(542\) | −0.131773 | − | 0.0957385i | −0.00566013 | − | 0.00411232i | ||||
\(543\) | −6.90803 | + | 5.01898i | −0.296452 | + | 0.215385i | ||||
\(544\) | 3.07568 | − | 9.46596i | 0.131869 | − | 0.405850i | ||||
\(545\) | −3.31116 | + | 10.1907i | −0.141834 | + | 0.436522i | ||||
\(546\) | 0.290987 | − | 0.211414i | 0.0124531 | − | 0.00904769i | ||||
\(547\) | −7.13946 | − | 5.18712i | −0.305261 | − | 0.221785i | 0.424599 | − | 0.905381i | \(-0.360415\pi\) |
−0.729861 | + | 0.683596i | \(0.760415\pi\) | |||||||
\(548\) | 8.72120 | + | 26.8411i | 0.372551 | + | 1.14660i | ||||
\(549\) | 45.6749 | 1.94936 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.25862 | 0.394430 | ||||||||
\(552\) | 1.97986 | + | 6.09337i | 0.0842682 | + | 0.259351i | ||||
\(553\) | 12.4009 | + | 9.00978i | 0.527340 | + | 0.383135i | ||||
\(554\) | 1.30320 | − | 0.946827i | 0.0553675 | − | 0.0402268i | ||||
\(555\) | −3.68792 | + | 11.3503i | −0.156544 | + | 0.481791i | ||||
\(556\) | −5.63210 | + | 17.3338i | −0.238854 | + | 0.735118i | ||||
\(557\) | 27.5001 | − | 19.9800i | 1.16522 | − | 0.846581i | 0.174790 | − | 0.984606i | \(-0.444075\pi\) |
0.990429 | + | 0.138025i | \(0.0440755\pi\) | |||||||
\(558\) | −3.66443 | − | 2.66236i | −0.155128 | − | 0.112707i | ||||
\(559\) | −1.74627 | − | 5.37446i | −0.0738592 | − | 0.227315i | ||||
\(560\) | 10.9906 | 0.464437 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.279099 | 0.0117731 | ||||||||
\(563\) | 6.25004 | + | 19.2357i | 0.263408 | + | 0.810686i | 0.992056 | + | 0.125798i | \(0.0401491\pi\) |
−0.728648 | + | 0.684888i | \(0.759851\pi\) | |||||||
\(564\) | −8.42016 | − | 6.11761i | −0.354553 | − | 0.257598i | ||||
\(565\) | 5.25929 | − | 3.82110i | 0.221260 | − | 0.160755i | ||||
\(566\) | −0.828215 | + | 2.54899i | −0.0348125 | + | 0.107142i | ||||
\(567\) | 0.388893 | − | 1.19689i | 0.0163320 | − | 0.0502646i | ||||
\(568\) | −4.85925 | + | 3.53045i | −0.203890 | + | 0.148135i | ||||
\(569\) | 23.4073 | + | 17.0064i | 0.981284 | + | 0.712944i | 0.957995 | − | 0.286784i | \(-0.0925864\pi\) |
0.0232885 | + | 0.999729i | \(0.492586\pi\) | |||||||
\(570\) | −2.18118 | − | 6.71298i | −0.0913596 | − | 0.281176i | ||||
\(571\) | 7.51312 | 0.314414 | 0.157207 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157207 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.7958 | 1.45362 | ||||||||
\(574\) | −0.345892 | − | 1.06455i | −0.0144372 | − | 0.0444333i | ||||
\(575\) | −11.2738 | − | 8.19091i | −0.470151 | − | 0.341585i | ||||
\(576\) | 28.8631 | − | 20.9703i | 1.20263 | − | 0.873761i | ||||
\(577\) | 10.6224 | − | 32.6924i | 0.442216 | − | 1.36100i | −0.443292 | − | 0.896377i | \(-0.646190\pi\) |
0.885508 | − | 0.464624i | \(-0.153810\pi\) | |||||||
\(578\) | −1.16853 | + | 3.59636i | −0.0486043 | + | 0.149589i | ||||
\(579\) | −46.2816 | + | 33.6255i | −1.92340 | + | 1.39743i | ||||
\(580\) | 5.53664 | + | 4.02261i | 0.229897 | + | 0.167030i | ||||
\(581\) | 0.632256 | + | 1.94588i | 0.0262304 | + | 0.0807289i | ||||
\(582\) | −3.03658 | −0.125870 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.23142 | −0.0509565 | ||||||||
\(585\) | 4.36744 | + | 13.4416i | 0.180571 | + | 0.555741i | ||||
\(586\) | 0.237572 | + | 0.172606i | 0.00981400 | + | 0.00713029i | ||||
\(587\) | −34.0104 | + | 24.7100i | −1.40376 | + | 1.01989i | −0.409566 | + | 0.912280i | \(0.634320\pi\) |
−0.994193 | + | 0.107611i | \(0.965680\pi\) | |||||||
\(588\) | −1.69823 | + | 5.22661i | −0.0700338 | + | 0.215542i | ||||
\(589\) | 18.8228 | − | 57.9306i | 0.775580 | − | 2.38699i | ||||
\(590\) | 1.82230 | − | 1.32398i | 0.0750228 | − | 0.0545073i | ||||
\(591\) | 14.0613 | + | 10.2162i | 0.578406 | + | 0.420236i | ||||
\(592\) | 1.85654 | + | 5.71385i | 0.0763034 | + | 0.234838i | ||||
\(593\) | −29.2867 | −1.20266 | −0.601331 | − | 0.799000i | \(-0.705363\pi\) | ||||
−0.601331 | + | 0.799000i | \(0.705363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5425 | −0.801165 | ||||||||
\(596\) | 7.12953 | + | 21.9424i | 0.292037 | + | 0.898797i | ||||
\(597\) | 15.3812 | + | 11.1751i | 0.629509 | + | 0.457365i | ||||
\(598\) | −0.507313 | + | 0.368585i | −0.0207456 | + | 0.0150725i | ||||
\(599\) | −4.68399 | + | 14.4158i | −0.191383 | + | 0.589015i | 0.808617 | + | 0.588335i | \(0.200216\pi\) |
−1.00000 | 0.000679814i | \(0.999784\pi\) | ||||||||
\(600\) | 1.18484 | − | 3.64655i | 0.0483708 | − | 0.148870i | ||||
\(601\) | 25.7862 | − | 18.7348i | 1.05184 | − | 0.764207i | 0.0792785 | − | 0.996853i | \(-0.474738\pi\) |
0.972561 | + | 0.232646i | \(0.0747384\pi\) | |||||||
\(602\) | −0.509654 | − | 0.370285i | −0.0207719 | − | 0.0150917i | ||||
\(603\) | −2.96848 | − | 9.13605i | −0.120886 | − | 0.372049i | ||||
\(604\) | 35.5705 | 1.44734 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.58035 | −0.0641974 | ||||||||
\(607\) | 6.22556 | + | 19.1603i | 0.252688 | + | 0.777693i | 0.994276 | + | 0.106838i | \(0.0340726\pi\) |
−0.741589 | + | 0.670855i | \(0.765927\pi\) | |||||||
\(608\) | −8.73016 | − | 6.34283i | −0.354055 | − | 0.257236i | ||||
\(609\) | −2.74812 | + | 1.99663i | −0.111360 | + | 0.0809075i | ||||
\(610\) | 1.02364 | − | 3.15044i | 0.0414460 | − | 0.127558i | ||||
\(611\) | 0.631865 | − | 1.94468i | 0.0255625 | − | 0.0786733i | ||||
\(612\) | −52.0962 | + | 37.8501i | −2.10586 | + | 1.53000i | ||||
\(613\) | −3.14814 | − | 2.28726i | −0.127152 | − | 0.0923815i | 0.522391 | − | 0.852706i | \(-0.325040\pi\) |
−0.649544 | + | 0.760324i | \(0.725040\pi\) | |||||||
\(614\) | −0.330668 | − | 1.01769i | −0.0133447 | − | 0.0410707i | ||||
\(615\) | 72.2929 | 2.91513 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6122 | 1.15189 | 0.575943 | − | 0.817490i | \(-0.304635\pi\) | ||||
0.575943 | + | 0.817490i | \(0.304635\pi\) | |||||||
\(618\) | −0.0361235 | − | 0.111177i | −0.00145310 | − | 0.00447218i | ||||
\(619\) | 21.1595 | + | 15.3733i | 0.850473 | + | 0.617905i | 0.925276 | − | 0.379293i | \(-0.123833\pi\) |
−0.0748032 | + | 0.997198i | \(0.523833\pi\) | |||||||
\(620\) | 36.4252 | − | 26.4645i | 1.46287 | − | 1.06284i | ||||
\(621\) | 6.85520 | − | 21.0981i | 0.275090 | − | 0.846639i | ||||
\(622\) | 0.440172 | − | 1.35471i | 0.0176493 | − | 0.0543189i | ||||
\(623\) | 3.85188 | − | 2.79856i | 0.154322 | − | 0.112122i | ||||
\(624\) | 9.46092 | + | 6.87376i | 0.378740 | + | 0.275171i | ||||
\(625\) | −9.61030 | − | 29.5775i | −0.384412 | − | 1.18310i | ||||
\(626\) | 3.55550 | 0.142106 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.7485 | −0.588529 | ||||||||
\(629\) | −3.30114 | − | 10.1599i | −0.131625 | − | 0.405101i | ||||
\(630\) | 1.27465 | + | 0.926087i | 0.0507833 | + | 0.0368962i | ||||
\(631\) | 4.59742 | − | 3.34022i | 0.183020 | − | 0.132972i | −0.492503 | − | 0.870311i | \(-0.663918\pi\) |
0.675523 | + | 0.737339i | \(0.263918\pi\) | |||||||
\(632\) | 2.27219 | − | 6.99307i | 0.0903827 | − | 0.278169i | ||||
\(633\) | −8.77429 | + | 27.0045i | −0.348747 | + | 1.07333i | ||||
\(634\) | −2.44937 | + | 1.77957i | −0.0972771 | + | 0.0706759i | ||||
\(635\) | −22.3725 | − | 16.2546i | −0.887827 | − | 0.645044i | ||||
\(636\) | 6.49661 | + | 19.9945i | 0.257607 | + | 0.792834i | ||||
\(637\) | −1.07967 | −0.0427782 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 58.3605 | 2.30870 | ||||||||
\(640\) | −3.28240 | − | 10.1022i | −0.129748 | − | 0.399324i | ||||
\(641\) | 16.7703 | + | 12.1843i | 0.662387 | + | 0.481252i | 0.867468 | − | 0.497493i | \(-0.165746\pi\) |
−0.205081 | + | 0.978745i | \(0.565746\pi\) | |||||||
\(642\) | −0.686649 | + | 0.498879i | −0.0270999 | + | 0.0196892i | ||||
\(643\) | 6.57453 | − | 20.2343i | 0.259274 | − | 0.797964i | −0.733683 | − | 0.679492i | \(-0.762200\pi\) |
0.992957 | − | 0.118472i | \(-0.0377997\pi\) | |||||||
\(644\) | 2.96073 | − | 9.11220i | 0.116669 | − | 0.359071i | ||||
\(645\) | 32.9164 | − | 23.9152i | 1.29608 | − | 0.941659i | ||||
\(646\) | 5.11152 | + | 3.71373i | 0.201110 | + | 0.146115i | ||||
\(647\) | −5.33727 | − | 16.4264i | −0.209830 | − | 0.645790i | −0.999480 | − | 0.0322329i | \(-0.989738\pi\) |
0.789651 | − | 0.613557i | \(-0.210262\pi\) | |||||||
\(648\) | −0.603690 | −0.0237152 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.375270 | 0.0147193 | ||||||||
\(651\) | 6.90584 | + | 21.2540i | 0.270661 | + | 0.833010i | ||||
\(652\) | 12.6143 | + | 9.16484i | 0.494015 | + | 0.358923i | ||||
\(653\) | −33.2334 | + | 24.1455i | −1.30052 | + | 0.944886i | −0.999961 | − | 0.00887528i | \(-0.997175\pi\) |
−0.300564 | + | 0.953762i | \(0.597175\pi\) | |||||||
\(654\) | −0.392757 | + | 1.20878i | −0.0153580 | + | 0.0472671i | ||||
\(655\) | 14.2143 | − | 43.7472i | 0.555399 | − | 1.70934i | ||||
\(656\) | 29.4426 | − | 21.3913i | 1.14954 | − | 0.835190i | ||||
\(657\) | 9.67989 | + | 7.03285i | 0.377649 | + | 0.274378i | ||||
\(658\) | −0.0704390 | − | 0.216789i | −0.00274600 | − | 0.00845132i | ||||
\(659\) | −6.00410 | −0.233887 | −0.116943 | − | 0.993139i | \(-0.537310\pi\) | ||||
−0.116943 | + | 0.993139i | \(0.537310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.83502 | −0.0713739 | −0.0356870 | − | 0.999363i | \(-0.511362\pi\) | ||||
−0.0356870 | + | 0.999363i | \(0.511362\pi\) | |||||||
\(662\) | 0.351972 | + | 1.08326i | 0.0136798 | + | 0.0421020i | ||||
\(663\) | −16.8226 | − | 12.2223i | −0.653336 | − | 0.474676i | ||||
\(664\) | 0.794025 | − | 0.576893i | 0.0308142 | − | 0.0223878i | ||||
\(665\) | −6.54740 | + | 20.1508i | −0.253897 | + | 0.781416i | ||||
\(666\) | −0.266144 | + | 0.819108i | −0.0103129 | + | 0.0317398i | ||||
\(667\) | 4.79115 | − | 3.48097i | 0.185514 | − | 0.134784i | ||||
\(668\) | 8.67825 | + | 6.30512i | 0.335772 | + | 0.243952i | ||||
\(669\) | −11.5656 | − | 35.5952i | −0.447151 | − | 1.37619i | ||||
\(670\) | −0.696689 | −0.0269154 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.95910 | 0.152726 | ||||||||
\(673\) | −13.7328 | − | 42.2653i | −0.529361 | − | 1.62921i | −0.755527 | − | 0.655117i | \(-0.772619\pi\) |
0.226166 | − | 0.974089i | \(-0.427381\pi\) | |||||||
\(674\) | 1.67724 | + | 1.21858i | 0.0646048 | + | 0.0469381i | ||||
\(675\) | −10.7404 | + | 7.80336i | −0.413398 | + | 0.300352i | ||||
\(676\) | 7.26102 | − | 22.3471i | 0.279270 | − | 0.859505i | ||||
\(677\) | −4.80433 | + | 14.7862i | −0.184645 | + | 0.568280i | −0.999942 | − | 0.0107634i | \(-0.996574\pi\) |
0.815297 | + | 0.579043i | \(0.196574\pi\) | |||||||
\(678\) | 0.623838 | − | 0.453245i | 0.0239583 | − | 0.0174068i | ||||
\(679\) | 7.37429 | + | 5.35773i | 0.282999 | + | 0.205611i | ||||
\(680\) | 2.89687 | + | 8.91565i | 0.111090 | + | 0.341899i | ||||
\(681\) | −37.5774 | −1.43997 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.8979 | −1.41186 | −0.705930 | − | 0.708282i | \(-0.749471\pi\) | ||||
−0.705930 | + | 0.708282i | \(0.749471\pi\) | |||||||
\(684\) | 21.5743 | + | 66.3989i | 0.824914 | + | 2.53882i | ||||
\(685\) | −32.2966 | − | 23.4649i | −1.23399 | − | 0.896547i | ||||
\(686\) | −0.0973732 | + | 0.0707458i | −0.00371773 | + | 0.00270109i | ||||
\(687\) | −1.24273 | + | 3.82472i | −0.0474130 | + | 0.145922i | ||||
\(688\) | 6.32937 | − | 19.4798i | 0.241305 | − | 0.742660i | ||||
\(689\) | −3.34150 | + | 2.42774i | −0.127301 | + | 0.0924895i | ||||
\(690\) | −3.65261 | − | 2.65377i | −0.139052 | − | 0.101027i | ||||
\(691\) | −5.77015 | − | 17.7587i | −0.219507 | − | 0.675572i | −0.998803 | − | 0.0489163i | \(-0.984423\pi\) |
0.779296 | − | 0.626656i | \(-0.215577\pi\) | |||||||
\(692\) | −39.1566 | −1.48851 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.05133 | −0.0399078 | ||||||||
\(695\) | −7.96665 | − | 24.5188i | −0.302192 | − | 0.930052i | ||||
\(696\) | 1.31826 | + | 0.957775i | 0.0499687 | + | 0.0363044i | ||||
\(697\) | −52.3523 | + | 38.0362i | −1.98299 | + | 1.44072i | ||||
\(698\) | −1.11524 | + | 3.43236i | −0.0422125 | + | 0.129917i | ||||
\(699\) | −7.01685 | + | 21.5956i | −0.265402 | + | 0.816822i | ||||
\(700\) | −4.63874 | + | 3.37024i | −0.175328 | + | 0.127383i | ||||
\(701\) | −21.1419 | − | 15.3605i | −0.798518 | − | 0.580157i | 0.111961 | − | 0.993713i | \(-0.464287\pi\) |
−0.910479 | + | 0.413555i | \(0.864287\pi\) | |||||||
\(702\) | 0.184608 | + | 0.568165i | 0.00696758 | + | 0.0214440i | ||||
\(703\) | −11.5821 | −0.436828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.7221 | 0.554465 | ||||||||
\(706\) | −0.272254 | − | 0.837913i | −0.0102464 | − | 0.0315353i | ||||
\(707\) | 3.83786 | + | 2.78837i | 0.144337 | + | 0.104867i | ||||
\(708\) | −29.6260 | + | 21.5246i | −1.11341 | + | 0.808942i | ||||
\(709\) | −5.08176 | + | 15.6401i | −0.190850 | + | 0.587375i | −1.00000 | 0.000226975i | \(-0.999928\pi\) | |
0.809150 | + | 0.587602i | \(0.199928\pi\) | |||||||
\(710\) | 1.30794 | − | 4.02543i | 0.0490862 | − | 0.151072i | ||||
\(711\) | −57.7998 | + | 41.9940i | −2.16766 | + | 1.57490i | ||||
\(712\) | −1.84773 | − | 1.34246i | −0.0692467 | − | 0.0503107i | ||||
\(713\) | −12.0398 | − | 37.0547i | −0.450895 | − | 1.38771i | ||||
\(714\) | −2.31806 | −0.0867513 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 46.3204 | 1.73107 | ||||||||
\(717\) | −8.88113 | − | 27.3333i | −0.331672 | − | 1.02078i | ||||
\(718\) | −0.483941 | − | 0.351604i | −0.0180605 | − | 0.0131217i | ||||
\(719\) | 7.56360 | − | 5.49528i | 0.282075 | − | 0.204939i | −0.437747 | − | 0.899098i | \(-0.644223\pi\) |
0.719822 | + | 0.694159i | \(0.244223\pi\) | |||||||
\(720\) | −15.8298 | + | 48.7192i | −0.589943 | + | 1.81566i | ||||
\(721\) | −0.108434 | + | 0.333726i | −0.00403830 | + | 0.0124286i | ||||
\(722\) | 3.69177 | − | 2.68223i | 0.137394 | − | 0.0998223i | ||||
\(723\) | −18.3716 | − | 13.3478i | −0.683249 | − | 0.496409i | ||||
\(724\) | −1.89283 | − | 5.82552i | −0.0703463 | − | 0.216504i | ||||
\(725\) | −3.54411 | −0.131625 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7523 | 1.02928 | 0.514638 | − | 0.857408i | \(-0.327927\pi\) | ||||
0.514638 | + | 0.857408i | \(0.327927\pi\) | |||||||
\(728\) | 0.160045 | + | 0.492567i | 0.00593165 | + | 0.0182557i | ||||
\(729\) | 35.6280 | + | 25.8853i | 1.31956 | + | 0.958714i | ||||
\(730\) | 0.702033 | − | 0.510057i | 0.0259834 | − | 0.0188780i | ||||
\(731\) | −11.2543 | + | 34.6373i | −0.416257 | + | 1.28111i | ||||
\(732\) | −16.6418 | + | 51.2183i | −0.615100 | + | 1.89308i | ||||
\(733\) | 1.17817 | − | 0.855990i | 0.0435167 | − | 0.0316167i | −0.565814 | − | 0.824533i | \(-0.691438\pi\) |
0.609331 | + | 0.792916i | \(0.291438\pi\) | |||||||
\(734\) | −1.38311 | − | 1.00489i | −0.0510516 | − | 0.0370911i | ||||
\(735\) | −2.40216 | − | 7.39308i | −0.0886049 | − | 0.272698i | ||||
\(736\) | −6.90240 | −0.254426 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 5.21712 | 0.192045 | ||||||||
\(739\) | 8.52782 | + | 26.2459i | 0.313701 | + | 0.965472i | 0.976286 | + | 0.216485i | \(0.0694594\pi\) |
−0.662585 | + | 0.748987i | \(0.730541\pi\) | |||||||
\(740\) | −6.92610 | − | 5.03211i | −0.254609 | − | 0.184984i | ||||
\(741\) | −18.2389 | + | 13.2514i | −0.670024 | + | 0.486801i | ||||
\(742\) | −0.142284 | + | 0.437904i | −0.00522339 | + | 0.0160759i | ||||
\(743\) | −8.64546 | + | 26.6080i | −0.317171 | + | 0.976153i | 0.657680 | + | 0.753297i | \(0.271538\pi\) |
−0.974851 | + | 0.222855i | \(0.928462\pi\) | |||||||
\(744\) | 8.67277 | − | 6.30114i | 0.317959 | − | 0.231011i | ||||
\(745\) | −26.4023 | − | 19.1824i | −0.967305 | − | 0.702788i | ||||
\(746\) | 0.333914 | + | 1.02768i | 0.0122255 | + | 0.0376261i | ||||
\(747\) | −9.53638 | −0.348918 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.54774 | 0.0930922 | ||||||||
\(750\) | −0.610683 | − | 1.87949i | −0.0222990 | − | 0.0686292i | ||||
\(751\) | −27.5840 | − | 20.0409i | −1.00655 | − | 0.731304i | −0.0430704 | − | 0.999072i | \(-0.513714\pi\) |
−0.963483 | + | 0.267768i | \(0.913714\pi\) | |||||||
\(752\) | 5.99582 | − | 4.35622i | 0.218645 | − | 0.158855i | ||||
\(753\) | −14.0657 | + | 43.2898i | −0.512583 | + | 1.57757i | ||||
\(754\) | −0.0492827 | + | 0.151677i | −0.00179477 | + | 0.00552374i | ||||
\(755\) | −40.7055 | + | 29.5743i | −1.48142 | + | 1.07632i | ||||
\(756\) | −7.38455 | − | 5.36519i | −0.268574 | − | 0.195130i | ||||
\(757\) | −12.2874 | − | 37.8168i | −0.446594 | − | 1.37447i | −0.880727 | − | 0.473625i | \(-0.842945\pi\) |
0.434133 | − | 0.900849i | \(-0.357055\pi\) | |||||||
\(758\) | −1.29863 | −0.0471684 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1637 | 0.368677 | ||||||||
\(761\) | 1.18173 | + | 3.63699i | 0.0428376 | + | 0.131841i | 0.970188 | − | 0.242353i | \(-0.0779194\pi\) |
−0.927350 | + | 0.374194i | \(0.877919\pi\) | |||||||
\(762\) | −2.65375 | − | 1.92806i | −0.0961351 | − | 0.0698462i | ||||
\(763\) | 3.08658 | − | 2.24253i | 0.111742 | − | 0.0811850i | ||||
\(764\) | −7.71332 | + | 23.7392i | −0.279058 | + | 0.858853i | ||||
\(765\) | 28.1473 | − | 86.6283i | 1.01767 | − | 3.13205i | ||||
\(766\) | −2.28924 | + | 1.66323i | −0.0827137 | + | 0.0600950i | ||||
\(767\) | −5.82039 | − | 4.22876i | −0.210162 | − | 0.152692i | ||||
\(768\) | 12.7044 | + | 39.1003i | 0.458432 | + | 1.41091i | ||||
\(769\) | 19.6583 | 0.708897 | 0.354449 | − | 0.935075i | \(-0.384669\pi\) | ||||
0.354449 | + | 0.935075i | \(0.384669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.3358 | −1.20056 | ||||||||
\(772\) | −12.6813 | − | 39.0291i | −0.456411 | − | 1.40469i | ||||
\(773\) | 14.2359 | + | 10.3430i | 0.512031 | + | 0.372012i | 0.813593 | − | 0.581434i | \(-0.197508\pi\) |
−0.301563 | + | 0.953446i | \(0.597508\pi\) | |||||||
\(774\) | 2.37546 | − | 1.72587i | 0.0853842 | − | 0.0620353i | ||||
\(775\) | −7.20518 | + | 22.1753i | −0.258818 | + | 0.796559i | ||||
\(776\) | 1.35117 | − | 4.15848i | 0.0485043 | − | 0.149281i | ||||
\(777\) | 3.43778 | − | 2.49770i | 0.123330 | − | 0.0896044i | ||||
\(778\) | −1.15626 | − | 0.840074i | −0.0414540 | − | 0.0301181i | ||||
\(779\) | 21.6804 | + | 66.7253i | 0.776780 | + | 2.39068i | ||||
\(780\) | −16.6642 | −0.596675 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.04136 | 0.144519 | ||||||||
\(783\) | −1.74347 | − | 5.36584i | −0.0623065 | − | 0.191760i | ||||
\(784\) | −3.16592 | − | 2.30017i | −0.113069 | − | 0.0821491i | ||||
\(785\) | 16.8776 | − | 12.2623i | 0.602388 | − | 0.437660i | ||||
\(786\) | 1.68605 | − | 5.18913i | 0.0601394 | − | 0.185090i | ||||
\(787\) | 16.7168 | − | 51.4490i | 0.595890 | − | 1.83396i | 0.0456418 | − | 0.998958i | \(-0.485467\pi\) |
0.550248 | − | 0.835001i | \(-0.314533\pi\) | |||||||
\(788\) | −10.0869 | + | 7.32857i | −0.359331 | + | 0.261069i | ||||
\(789\) | 4.20085 | + | 3.05209i | 0.149554 | + | 0.108657i | ||||
\(790\) | 1.60117 | + | 4.92790i | 0.0569671 | + | 0.175327i | ||||
\(791\) | −2.31468 | −0.0823006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.5803 | −0.375717 | ||||||||
\(794\) | 0.882462 | + | 2.71594i | 0.0313174 | + | 0.0963851i | ||||
\(795\) | −24.0584 | − | 17.4795i | −0.853265 | − | 0.619933i | ||||
\(796\) | −11.0337 | + | 8.01646i | −0.391079 | + | 0.284136i | ||||
\(797\) | 11.2867 | − | 34.7368i | 0.399794 | − | 1.23044i | −0.525370 | − | 0.850874i | \(-0.676073\pi\) |
0.925164 | − | 0.379566i | \(-0.123927\pi\) | |||||||
\(798\) | −0.776629 | + | 2.39022i | −0.0274924 | + | 0.0846128i | ||||
\(799\) | −10.6613 | + | 7.74587i | −0.377169 | + | 0.274029i | ||||
\(800\) | 3.34182 | + | 2.42797i | 0.118151 | + | 0.0858418i | ||||
\(801\) | 6.85758 | + | 21.1055i | 0.242301 | + | 0.745725i | ||||
\(802\) | 0.457513 | 0.0161554 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.3264 | 0.399452 | ||||||||
\(805\) | 4.18798 | + | 12.8893i | 0.147607 | + | 0.454288i | ||||
\(806\) | 0.848839 | + | 0.616718i | 0.0298991 | + | 0.0217230i | ||||
\(807\) | 31.4141 | − | 22.8237i | 1.10583 | − | 0.803432i | ||||
\(808\) | 0.703201 | − | 2.16423i | 0.0247385 | − | 0.0761373i | ||||
\(809\) | −14.5038 | + | 44.6382i | −0.509928 | + | 1.56940i | 0.282397 | + | 0.959298i | \(0.408870\pi\) |
−0.792325 | + | 0.610099i | \(0.791130\pi\) | |||||||
\(810\) | 0.344164 | − | 0.250050i | 0.0120927 | − | 0.00878585i | ||||
\(811\) | −10.2434 | − | 7.44224i | −0.359693 | − | 0.261332i | 0.393231 | − | 0.919440i | \(-0.371357\pi\) |
−0.752924 | + | 0.658107i | \(0.771357\pi\) | |||||||
\(812\) | −0.752997 | − | 2.31749i | −0.0264250 | − | 0.0813278i | ||||
\(813\) | −3.74565 | −0.131366 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0552 | −0.772561 | ||||||||
\(816\) | −23.2899 | − | 71.6789i | −0.815309 | − | 2.50926i | ||||
\(817\) | 31.9449 | + | 23.2093i | 1.11761 | + | 0.811992i | ||||
\(818\) | 0.582575 | − | 0.423266i | 0.0203693 | − | 0.0147991i | ||||
\(819\) | 1.55506 | − | 4.78599i | 0.0543383 | − | 0.167236i | ||||
\(820\) | −16.0254 | + | 49.3212i | −0.559632 | + | 1.72237i | ||||
\(821\) | −39.8795 | + | 28.9742i | −1.39180 | + | 1.01121i | −0.396140 | + | 0.918190i | \(0.629651\pi\) |
−0.995665 | + | 0.0930154i | \(0.970349\pi\) | |||||||
\(822\) | −3.83091 | − | 2.78332i | −0.133618 | − | 0.0970793i | ||||
\(823\) | 5.94113 | + | 18.2849i | 0.207095 | + | 0.637373i | 0.999621 | + | 0.0275344i | \(0.00876559\pi\) |
−0.792526 | + | 0.609838i | \(0.791234\pi\) | |||||||
\(824\) | 0.168326 | 0.00586390 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.802017 | −0.0279057 | ||||||||
\(827\) | −13.4861 | − | 41.5059i | −0.468957 | − | 1.44330i | −0.853937 | − | 0.520377i | \(-0.825792\pi\) |
0.384980 | − | 0.922925i | \(-0.374208\pi\) | |||||||
\(828\) | 36.1283 | + | 26.2488i | 1.25555 | + | 0.912207i | ||||
\(829\) | 29.6968 | − | 21.5760i | 1.03141 | − | 0.749364i | 0.0628205 | − | 0.998025i | \(-0.479990\pi\) |
0.968591 | + | 0.248661i | \(0.0799904\pi\) | |||||||
\(830\) | −0.213724 | + | 0.657775i | −0.00741846 | + | 0.0228317i | ||||
\(831\) | 11.4470 | − | 35.2304i | 0.397094 | − | 1.22213i | ||||
\(832\) | −6.68594 | + | 4.85762i | −0.231793 | + | 0.168408i | ||||
\(833\) | 5.62937 | + | 4.08998i | 0.195046 | + | 0.141709i | ||||
\(834\) | −0.944975 | − | 2.90833i | −0.0327218 | − | 0.100707i | ||||
\(835\) | −15.1733 | −0.525094 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −37.1182 | −1.28299 | ||||||||
\(838\) | 0.155055 | + | 0.477209i | 0.00535628 | + | 0.0164849i | ||||
\(839\) | −32.7284 | − | 23.7786i | −1.12991 | − | 0.820928i | −0.144228 | − | 0.989544i | \(-0.546070\pi\) |
−0.985682 | + | 0.168617i | \(0.946070\pi\) | |||||||
\(840\) | −3.01678 | + | 2.19182i | −0.104089 | + | 0.0756248i | ||||
\(841\) | −8.49606 | + | 26.1482i | −0.292968 | + | 0.901661i | ||||
\(842\) | −0.872385 | + | 2.68493i | −0.0300644 | + | 0.0925287i | ||||
\(843\) | 5.19248 | − | 3.77256i | 0.178839 | − | 0.129934i | ||||
\(844\) | −16.4786 | − | 11.9724i | −0.567215 | − | 0.412106i | ||||
\(845\) | 10.2708 | + | 31.6102i | 0.353326 | + | 1.08742i | ||||
\(846\) | 1.06244 | 0.0365274 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.9704 | −0.514085 | ||||||||
\(849\) | 19.0459 | + | 58.6174i | 0.653655 | + | 2.01174i | ||||
\(850\) | −1.95664 | − | 1.42158i | −0.0671122 | − | 0.0487599i | ||||
\(851\) | −5.99352 | + | 4.35455i | −0.205455 | + | 0.149272i | ||||
\(852\) | −21.2638 | + | 65.4434i | −0.728487 | + | 2.24205i | ||||
\(853\) | −7.87834 | + | 24.2470i | −0.269749 | + | 0.830203i | 0.720812 | + | 0.693131i | \(0.243769\pi\) |
−0.990561 | + | 0.137072i | \(0.956231\pi\) | |||||||
\(854\) | −0.954211 | + | 0.693275i | −0.0326524 | + | 0.0237234i | ||||
\(855\) | −79.8946 | − | 58.0468i | −2.73234 | − | 1.98516i | ||||
\(856\) | −0.377661 | − | 1.16232i | −0.0129082 | − | 0.0397274i | ||||
\(857\) | −49.4756 | −1.69005 | −0.845027 | − | 0.534723i | \(-0.820416\pi\) | ||||
−0.845027 | + | 0.534723i | \(0.820416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6779 | 0.739641 | 0.369821 | − | 0.929103i | \(-0.379419\pi\) | ||||
0.369821 | + | 0.929103i | \(0.379419\pi\) | |||||||
\(860\) | 9.01923 | + | 27.7583i | 0.307553 | + | 0.946551i | ||||
\(861\) | −20.8245 | − | 15.1299i | −0.709697 | − | 0.515625i | ||||
\(862\) | −3.62939 | + | 2.63691i | −0.123618 | + | 0.0898134i | ||||
\(863\) | 4.21494 | − | 12.9723i | 0.143478 | − | 0.441581i | −0.853334 | − | 0.521365i | \(-0.825423\pi\) |
0.996812 | + | 0.0797840i | \(0.0254231\pi\) | |||||||
\(864\) | −2.03204 | + | 6.25398i | −0.0691314 | + | 0.212765i | ||||
\(865\) | 44.8093 | − | 32.5558i | 1.52356 | − | 1.10693i | ||||
\(866\) | −2.21878 | − | 1.61203i | −0.0753971 | − | 0.0547792i | ||||
\(867\) | 26.8719 | + | 82.7031i | 0.912617 | + | 2.80875i | ||||
\(868\) | −16.0312 | −0.544135 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.14826 | −0.0389295 | ||||||||
\(871\) | 0.687629 | + | 2.11630i | 0.0232994 | + | 0.0717082i | ||||
\(872\) | −1.48062 | − | 1.07573i | −0.0501400 | − | 0.0364289i | ||||
\(873\) | −34.3711 | + | 24.9721i | −1.16328 | + | 0.845176i | ||||
\(874\) | 1.35399 | − | 4.16716i | 0.0457995 | − | 0.140956i | ||||
\(875\) | −1.83313 | + | 5.64179i | −0.0619710 | + | 0.190727i | ||||
\(876\) | −11.4133 | + | 8.29225i | −0.385620 | + | 0.280169i | ||||
\(877\) | 23.5659 | + | 17.1216i | 0.795763 | + | 0.578156i | 0.909668 | − | 0.415336i | \(-0.136336\pi\) |
−0.113905 | + | 0.993492i | \(0.536336\pi\) | |||||||
\(878\) | −0.0531768 | − | 0.163661i | −0.00179463 | − | 0.00552330i | ||||
\(879\) | 6.75299 | 0.227773 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.8256 | −1.64498 | −0.822488 | − | 0.568783i | \(-0.807414\pi\) | ||||
−0.822488 | + | 0.568783i | \(0.807414\pi\) | |||||||
\(882\) | −0.173355 | − | 0.533533i | −0.00583718 | − | 0.0179650i | ||||
\(883\) | 19.5888 | + | 14.2321i | 0.659217 | + | 0.478949i | 0.866398 | − | 0.499353i | \(-0.166429\pi\) |
−0.207181 | + | 0.978303i | \(0.566429\pi\) | |||||||
\(884\) | 12.0677 | − | 8.76771i | 0.405881 | − | 0.294890i | ||||
\(885\) | 16.0068 | − | 49.2637i | 0.538061 | − | 1.65598i | ||||
\(886\) | 0.983022 | − | 3.02543i | 0.0330253 | − | 0.101641i | ||||
\(887\) | 5.37793 | − | 3.90730i | 0.180573 | − | 0.131194i | −0.493827 | − | 0.869560i | \(-0.664402\pi\) |
0.674400 | + | 0.738366i | \(0.264402\pi\) | |||||||
\(888\) | −1.64909 | − | 1.19813i | −0.0553399 | − | 0.0402068i | ||||
\(889\) | 3.04272 | + | 9.36452i | 0.102049 | + | 0.314076i | ||||
\(890\) | 1.60944 | 0.0539486 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.8483 | 0.898947 | ||||||||
\(893\) | 4.41509 | + | 13.5883i | 0.147745 | + | 0.454714i | ||||
\(894\) | −3.13174 | − | 2.27534i | −0.104741 | − | 0.0760989i | ||||
\(895\) | −53.0072 | + | 38.5120i | −1.77184 | + | 1.28731i | ||||
\(896\) | −1.16873 | + | 3.59697i | −0.0390444 | + | 0.120166i | ||||
\(897\) | −4.45615 | + | 13.7146i | −0.148787 | + | 0.457918i | ||||
\(898\) | 1.37170 | − | 0.996595i | 0.0457741 | − | 0.0332568i | ||||
\(899\) | −8.01657 | − | 5.82438i | −0.267368 | − | 0.194254i | ||||
\(900\) | −8.25843 | − | 25.4168i | −0.275281 | − | 0.847228i | ||||
\(901\) | 26.6191 | 0.886809 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.4869 | −0.482095 | ||||||||
\(904\) | 0.343115 | + | 1.05600i | 0.0114118 | + | 0.0351220i | ||||
\(905\) | 7.00957 | + | 5.09275i | 0.233006 | + | 0.169289i | ||||
\(906\) | −4.82834 | + | 3.50799i | −0.160411 | + | 0.116545i | ||||
\(907\) | −2.58896 | + | 7.96801i | −0.0859651 | + | 0.264573i | −0.984794 | − | 0.173726i | \(-0.944419\pi\) |
0.898829 | + | 0.438300i | \(0.144419\pi\) | |||||||
\(908\) | 8.32992 | − | 25.6369i | 0.276438 | − | 0.850789i | ||||
\(909\) | −17.8880 | + | 12.9964i | −0.593308 | + | 0.431063i | ||||
\(910\) | −0.295264 | − | 0.214522i | −0.00978791 | − | 0.00711133i | ||||
\(911\) | −5.80543 | − | 17.8673i | −0.192343 | − | 0.591970i | −0.999997 | − | 0.00231392i | \(-0.999263\pi\) |
0.807655 | − | 0.589656i | \(-0.200737\pi\) | |||||||
\(912\) | −81.7130 | −2.70579 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.54856 | 0.117376 | ||||||||
\(915\) | −23.5400 | − | 72.4487i | −0.778209 | − | 2.39508i | ||||
\(916\) | −2.33390 | − | 1.69568i | −0.0771144 | − | 0.0560269i | ||||
\(917\) | −13.2502 | + | 9.62685i | −0.437561 | + | 0.317907i | ||||
\(918\) | 1.18976 | − | 3.66171i | 0.0392680 | − | 0.120854i | ||||
\(919\) | −5.56351 | + | 17.1227i | −0.183523 | + | 0.564827i | −0.999920 | − | 0.0126652i | \(-0.995968\pi\) |
0.816397 | + | 0.577492i | \(0.195968\pi\) | |||||||
\(920\) | 5.25952 | − | 3.82127i | 0.173401 | − | 0.125983i | ||||
\(921\) | −19.9080 | − | 14.4640i | −0.655990 | − | 0.476605i | ||||
\(922\) | 1.18008 | + | 3.63190i | 0.0388637 | + | 0.119610i | ||||
\(923\) | −13.5188 | −0.444977 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.43353 | 0.145773 | ||||||||
\(926\) | 0.475474 | + | 1.46336i | 0.0156250 | + | 0.0480890i | ||||
\(927\) | −1.32317 | − | 0.961338i | −0.0434585 | − | 0.0315745i | ||||
\(928\) | −1.42021 | + | 1.03184i | −0.0466206 | + | 0.0338718i | ||||
\(929\) | −3.12803 | + | 9.62708i | −0.102627 | + | 0.315854i | −0.989166 | − | 0.146800i | \(-0.953103\pi\) |
0.886539 | + | 0.462654i | \(0.153103\pi\) | |||||||
\(930\) | −2.33441 | + | 7.18457i | −0.0765483 | + | 0.235591i | ||||
\(931\) | 6.10332 | − | 4.43432i | 0.200028 | − | 0.145329i | ||||
\(932\) | −13.1780 | − | 9.57437i | −0.431659 | − | 0.313619i | ||||
\(933\) | −10.1223 | − | 31.1534i | −0.331391 | − | 1.01992i | ||||
\(934\) | −3.55986 | −0.116482 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.41397 | −0.0789031 | ||||||||
\(937\) | 8.71776 | + | 26.8305i | 0.284797 | + | 0.876515i | 0.986459 | + | 0.164005i | \(0.0524414\pi\) |
−0.701663 | + | 0.712509i | \(0.747559\pi\) | |||||||
\(938\) | 0.200687 | + | 0.145807i | 0.00655265 | + | 0.00476078i | ||||
\(939\) | 66.1481 | − | 48.0594i | 2.15866 | − | 1.56836i | ||||
\(940\) | −3.26349 | + | 10.0440i | −0.106443 | + | 0.327599i | ||||
\(941\) | 6.22672 | − | 19.1639i | 0.202985 | − | 0.624725i | −0.796805 | − | 0.604237i | \(-0.793478\pi\) |
0.999790 | − | 0.0204879i | \(-0.00652195\pi\) | |||||||
\(942\) | 2.00196 | − | 1.45451i | 0.0652274 | − | 0.0473905i | ||||
\(943\) | 36.3060 | + | 26.3778i | 1.18228 | + | 0.858980i | ||||
\(944\) | −8.05798 | − | 24.7999i | −0.262265 | − | 0.807169i | ||||
\(945\) | 12.9114 | 0.420007 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.125141 | 0.00406653 | 0.00203326 | − | 0.999998i | \(-0.499353\pi\) | ||||
0.00203326 | + | 0.999998i | \(0.499353\pi\) | |||||||
\(948\) | −26.0310 | − | 80.1153i | −0.845449 | − | 2.60202i | ||||
\(949\) | −2.24228 | − | 1.62911i | −0.0727875 | − | 0.0528832i | ||||
\(950\) | −2.12137 | + | 1.54127i | −0.0688264 | + | 0.0500053i | ||||
\(951\) | −21.5149 | + | 66.2160i | −0.697668 | + | 2.14720i | ||||
\(952\) | 1.03146 | − | 3.17449i | 0.0334297 | − | 0.102886i | ||||
\(953\) | −23.7442 | + | 17.2512i | −0.769151 | + | 0.558821i | −0.901704 | − | 0.432355i | \(-0.857683\pi\) |
0.132552 | + | 0.991176i | \(0.457683\pi\) | |||||||
\(954\) | −1.73621 | − | 1.26143i | −0.0562120 | − | 0.0408404i | ||||
\(955\) | −10.9106 | − | 33.5792i | −0.353057 | − | 1.08660i | ||||
\(956\) | 20.6166 | 0.666790 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.43717 | −0.111050 | ||||||||
\(959\) | 4.39242 | + | 13.5185i | 0.141839 | + | 0.436534i | ||||
\(960\) | −48.1381 | − | 34.9744i | −1.55365 | − | 1.12879i | ||||
\(961\) | −27.6610 | + | 20.0969i | −0.892290 | + | 0.648287i | ||||
\(962\) | 0.0616505 | − | 0.189741i | 0.00198769 | − | 0.00611749i | ||||
\(963\) | −3.66952 | + | 11.2936i | −0.118249 | + | 0.363932i | ||||
\(964\) | 13.1789 | − | 9.57505i | 0.424465 | − | 0.308392i | ||||
\(965\) | 46.9619 | + | 34.1198i | 1.51176 | + | 1.09836i | ||||
\(966\) | 0.496763 | + | 1.52888i | 0.0159831 | + | 0.0491909i | ||||
\(967\) | 51.9463 | 1.67048 | 0.835240 | − | 0.549885i | \(-0.185328\pi\) | ||||
0.835240 | + | 0.549885i | \(0.185328\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 145.295 | 4.66756 | ||||||||
\(970\) | 0.952149 | + | 2.93041i | 0.0305717 | + | 0.0940899i | ||||
\(971\) | 20.2308 | + | 14.6985i | 0.649236 | + | 0.471697i | 0.863011 | − | 0.505185i | \(-0.168576\pi\) |
−0.213775 | + | 0.976883i | \(0.568576\pi\) | |||||||
\(972\) | −27.7489 | + | 20.1608i | −0.890047 | + | 0.646657i | ||||
\(973\) | −2.83660 | + | 8.73015i | −0.0909371 | + | 0.279876i | ||||
\(974\) | −0.0393608 | + | 0.121140i | −0.00126120 | + | 0.00388158i | ||||
\(975\) | 6.98169 | − | 5.07249i | 0.223593 | − | 0.162450i | ||||
\(976\) | −31.0245 | − | 22.5406i | −0.993070 | − | 0.721507i | ||||
\(977\) | −5.38173 | − | 16.5633i | −0.172177 | − | 0.529906i | 0.827316 | − | 0.561736i | \(-0.189866\pi\) |
−0.999493 | + | 0.0318303i | \(0.989866\pi\) | |||||||
\(978\) | −2.61611 | −0.0836540 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.57636 | 0.178130 | ||||||||
\(981\) | 5.49509 | + | 16.9121i | 0.175445 | + | 0.539963i | ||||
\(982\) | −1.79643 | − | 1.30518i | −0.0573263 | − | 0.0416500i | ||||
\(983\) | 34.2497 | − | 24.8839i | 1.09240 | − | 0.793672i | 0.112593 | − | 0.993641i | \(-0.464084\pi\) |
0.979802 | + | 0.199969i | \(0.0640843\pi\) | |||||||
\(984\) | −3.81562 | + | 11.7433i | −0.121638 | + | 0.374362i | ||||
\(985\) | 5.44990 | − | 16.7731i | 0.173648 | − | 0.534434i | ||||
\(986\) | 0.831533 | − | 0.604144i | 0.0264814 | − | 0.0192399i | ||||
\(987\) | −4.24080 | − | 3.08112i | −0.134986 | − | 0.0980732i | ||||
\(988\) | −4.99754 | − | 15.3808i | −0.158993 | − | 0.489330i | ||||
\(989\) | 25.2569 | 0.803122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.6263 | 1.76703 | 0.883513 | − | 0.468406i | \(-0.155172\pi\) | ||||
0.883513 | + | 0.468406i | \(0.155172\pi\) | |||||||
\(992\) | 3.56888 | + | 10.9839i | 0.113312 | + | 0.348738i | ||||
\(993\) | 21.1906 | + | 15.3958i | 0.672462 | + | 0.488573i | ||||
\(994\) | −1.21923 | + | 0.885821i | −0.0386716 | + | 0.0280965i | ||||
\(995\) | 5.96144 | − | 18.3474i | 0.188991 | − | 0.581653i | ||||
\(996\) | 3.47462 | − | 10.6938i | 0.110097 | − | 0.338845i | ||||
\(997\) | −13.2895 | + | 9.65540i | −0.420883 | + | 0.305790i | −0.777993 | − | 0.628273i | \(-0.783762\pi\) |
0.357110 | + | 0.934062i | \(0.383762\pi\) | |||||||
\(998\) | 3.08958 | + | 2.24471i | 0.0977991 | + | 0.0710552i | ||||
\(999\) | 2.18100 | + | 6.71244i | 0.0690039 | + | 0.212372i |
(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.z.148.4 | 24 | ||
11.2 | odd | 10 | 847.2.f.y.372.3 | 24 | |||
11.3 | even | 5 | 847.2.a.m.1.4 | ✓ | 6 | ||
11.4 | even | 5 | inner | 847.2.f.z.729.3 | 24 | ||
11.5 | even | 5 | inner | 847.2.f.z.323.3 | 24 | ||
11.6 | odd | 10 | 847.2.f.y.323.4 | 24 | |||
11.7 | odd | 10 | 847.2.f.y.729.4 | 24 | |||
11.8 | odd | 10 | 847.2.a.n.1.3 | yes | 6 | ||
11.9 | even | 5 | inner | 847.2.f.z.372.4 | 24 | ||
11.10 | odd | 2 | 847.2.f.y.148.3 | 24 | |||
33.8 | even | 10 | 7623.2.a.cp.1.4 | 6 | |||
33.14 | odd | 10 | 7623.2.a.cs.1.3 | 6 | |||
77.41 | even | 10 | 5929.2.a.bm.1.3 | 6 | |||
77.69 | odd | 10 | 5929.2.a.bj.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.4 | ✓ | 6 | 11.3 | even | 5 | ||
847.2.a.n.1.3 | yes | 6 | 11.8 | odd | 10 | ||
847.2.f.y.148.3 | 24 | 11.10 | odd | 2 | |||
847.2.f.y.323.4 | 24 | 11.6 | odd | 10 | |||
847.2.f.y.372.3 | 24 | 11.2 | odd | 10 | |||
847.2.f.y.729.4 | 24 | 11.7 | odd | 10 | |||
847.2.f.z.148.4 | 24 | 1.1 | even | 1 | trivial | ||
847.2.f.z.323.3 | 24 | 11.5 | even | 5 | inner | ||
847.2.f.z.372.4 | 24 | 11.9 | even | 5 | inner | ||
847.2.f.z.729.3 | 24 | 11.4 | even | 5 | inner | ||
5929.2.a.bj.1.4 | 6 | 77.69 | odd | 10 | |||
5929.2.a.bm.1.3 | 6 | 77.41 | even | 10 | |||
7623.2.a.cp.1.4 | 6 | 33.8 | even | 10 | |||
7623.2.a.cs.1.3 | 6 | 33.14 | odd | 10 |