Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 161.20 | ||
Character | \(\chi\) | \(=\) | 930.161 |
Dual form | 930.2.o.e.491.10 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.68621 | + | 0.395836i | 0.973535 | + | 0.228536i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | −0.395836 | + | 1.68621i | −0.161600 | + | 0.688393i | ||||
\(7\) | −1.28701 | − | 2.22916i | −0.486443 | − | 0.842543i | 0.513436 | − | 0.858128i | \(-0.328372\pi\) |
−0.999879 | + | 0.0155847i | \(0.995039\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.68663 | + | 1.33493i | 0.895542 | + | 0.444976i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −2.56707 | + | 4.44629i | −0.774000 | + | 1.34061i | 0.161355 | + | 0.986897i | \(0.448414\pi\) |
−0.935355 | + | 0.353711i | \(0.884920\pi\) | |||||||
\(12\) | −1.68621 | − | 0.395836i | −0.486768 | − | 0.114268i | ||||
\(13\) | 4.59412 | + | 2.65242i | 1.27418 | + | 0.735648i | 0.975772 | − | 0.218790i | \(-0.0702109\pi\) |
0.298408 | + | 0.954438i | \(0.403544\pi\) | |||||||
\(14\) | 2.22916 | − | 1.28701i | 0.595768 | − | 0.343967i | ||||
\(15\) | −1.26238 | − | 1.18591i | −0.325946 | − | 0.306201i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.59376 | + | 4.49252i | 0.629079 | + | 1.08960i | 0.987737 | + | 0.156127i | \(0.0499011\pi\) |
−0.358658 | + | 0.933469i | \(0.616766\pi\) | |||||||
\(18\) | −1.33493 | + | 2.68663i | −0.314646 | + | 0.633244i | ||||
\(19\) | −0.264764 | − | 0.458584i | −0.0607410 | − | 0.105206i | 0.834056 | − | 0.551680i | \(-0.186013\pi\) |
−0.894797 | + | 0.446474i | \(0.852680\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | −1.28778 | − | 4.26828i | −0.281017 | − | 0.931415i | ||||
\(22\) | −4.44629 | − | 2.56707i | −0.947953 | − | 0.547301i | ||||
\(23\) | −3.03318 | −0.632462 | −0.316231 | − | 0.948682i | \(-0.602417\pi\) | ||||
−0.316231 | + | 0.948682i | \(0.602417\pi\) | |||||||
\(24\) | 0.395836 | − | 1.68621i | 0.0807998 | − | 0.344197i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −2.65242 | + | 4.59412i | −0.520182 | + | 0.900982i | ||||
\(27\) | 4.00181 | + | 3.31444i | 0.770149 | + | 0.637864i | ||||
\(28\) | 1.28701 | + | 2.22916i | 0.243221 | + | 0.421272i | ||||
\(29\) | 8.44680 | 1.56853 | 0.784265 | − | 0.620426i | \(-0.213040\pi\) | ||||
0.784265 | + | 0.620426i | \(0.213040\pi\) | |||||||
\(30\) | 1.18591 | − | 1.26238i | 0.216517 | − | 0.230479i | ||||
\(31\) | 0.790363 | + | 5.51138i | 0.141953 | + | 0.989873i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −6.08863 | + | 6.48126i | −1.05989 | + | 1.12824i | ||||
\(34\) | −4.49252 | + | 2.59376i | −0.770461 | + | 0.444826i | ||||
\(35\) | 2.57401i | 0.435087i | ||||||||
\(36\) | −2.68663 | − | 1.33493i | −0.447771 | − | 0.222488i | ||||
\(37\) | 0.580888 | − | 0.335376i | 0.0954974 | − | 0.0551355i | −0.451491 | − | 0.892276i | \(-0.649108\pi\) |
0.546988 | + | 0.837140i | \(0.315774\pi\) | |||||||
\(38\) | 0.458584 | − | 0.264764i | 0.0743922 | − | 0.0429504i | ||||
\(39\) | 6.69674 | + | 6.29106i | 1.07234 | + | 1.00738i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 9.85425 | + | 5.68936i | 1.53898 | + | 0.888528i | 0.998899 | + | 0.0469123i | \(0.0149381\pi\) |
0.540077 | + | 0.841616i | \(0.318395\pi\) | |||||||
\(42\) | 4.26828 | − | 1.28778i | 0.658610 | − | 0.198709i | ||||
\(43\) | −6.69156 | + | 3.86337i | −1.02045 | + | 0.589159i | −0.914235 | − | 0.405184i | \(-0.867207\pi\) |
−0.106218 | + | 0.994343i | \(0.533874\pi\) | |||||||
\(44\) | 2.56707 | − | 4.44629i | 0.387000 | − | 0.670304i | ||||
\(45\) | −1.65922 | − | 2.49940i | −0.247342 | − | 0.372588i | ||||
\(46\) | − | 3.03318i | − | 0.447218i | ||||||
\(47\) | − | 6.75256i | − | 0.984961i | −0.870323 | − | 0.492481i | \(-0.836090\pi\) | ||
0.870323 | − | 0.492481i | \(-0.163910\pi\) | |||||||
\(48\) | 1.68621 | + | 0.395836i | 0.243384 | + | 0.0571341i | ||||
\(49\) | 0.187231 | − | 0.324294i | 0.0267473 | − | 0.0463278i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 2.59533 | + | 8.60205i | 0.363418 | + | 1.20453i | ||||
\(52\) | −4.59412 | − | 2.65242i | −0.637090 | − | 0.367824i | ||||
\(53\) | −0.822328 | + | 1.42431i | −0.112955 | + | 0.195644i | −0.916961 | − | 0.398978i | \(-0.869365\pi\) |
0.804005 | + | 0.594622i | \(0.202698\pi\) | |||||||
\(54\) | −3.31444 | + | 4.00181i | −0.451038 | + | 0.544578i | ||||
\(55\) | 4.44629 | − | 2.56707i | 0.599538 | − | 0.346143i | ||||
\(56\) | −2.22916 | + | 1.28701i | −0.297884 | + | 0.171983i | ||||
\(57\) | −0.264924 | − | 0.878074i | −0.0350900 | − | 0.116304i | ||||
\(58\) | 8.44680i | 1.10912i | ||||||||
\(59\) | −10.4486 | + | 6.03251i | −1.36029 | + | 0.785366i | −0.989663 | − | 0.143414i | \(-0.954192\pi\) |
−0.370632 | + | 0.928780i | \(0.620859\pi\) | |||||||
\(60\) | 1.26238 | + | 1.18591i | 0.162973 | + | 0.153100i | ||||
\(61\) | − | 7.06279i | − | 0.904297i | −0.891943 | − | 0.452149i | \(-0.850658\pi\) | ||
0.891943 | − | 0.452149i | \(-0.149342\pi\) | |||||||
\(62\) | −5.51138 | + | 0.790363i | −0.699946 | + | 0.100376i | ||||
\(63\) | −0.481936 | − | 7.70698i | −0.0607182 | − | 0.970988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.65242 | − | 4.59412i | −0.328992 | − | 0.569831i | ||||
\(66\) | −6.48126 | − | 6.08863i | −0.797787 | − | 0.749458i | ||||
\(67\) | 3.98360 | − | 6.89980i | 0.486675 | − | 0.842945i | −0.513208 | − | 0.858264i | \(-0.671543\pi\) |
0.999883 | + | 0.0153191i | \(0.00487642\pi\) | |||||||
\(68\) | −2.59376 | − | 4.49252i | −0.314539 | − | 0.544798i | ||||
\(69\) | −5.11459 | − | 1.20064i | −0.615724 | − | 0.144540i | ||||
\(70\) | −2.57401 | −0.307653 | ||||||||
\(71\) | −8.45327 | − | 4.88050i | −1.00322 | − | 0.579208i | −0.0940192 | − | 0.995570i | \(-0.529972\pi\) |
−0.909199 | + | 0.416362i | \(0.863305\pi\) | |||||||
\(72\) | 1.33493 | − | 2.68663i | 0.157323 | − | 0.316622i | ||||
\(73\) | −3.21521 | − | 1.85630i | −0.376312 | − | 0.217264i | 0.299901 | − | 0.953970i | \(-0.403047\pi\) |
−0.676212 | + | 0.736707i | \(0.736380\pi\) | |||||||
\(74\) | 0.335376 | + | 0.580888i | 0.0389867 | + | 0.0675269i | ||||
\(75\) | 0.500302 | + | 1.65822i | 0.0577699 | + | 0.191475i | ||||
\(76\) | 0.264764 | + | 0.458584i | 0.0303705 | + | 0.0526032i | ||||
\(77\) | 13.2153 | 1.50603 | ||||||||
\(78\) | −6.29106 | + | 6.69674i | −0.712322 | + | 0.758257i | ||||
\(79\) | 8.75345 | − | 5.05381i | 0.984841 | − | 0.568598i | 0.0811125 | − | 0.996705i | \(-0.474153\pi\) |
0.903728 | + | 0.428107i | \(0.140819\pi\) | |||||||
\(80\) | −0.866025 | − | 0.500000i | −0.0968246 | − | 0.0559017i | ||||
\(81\) | 5.43593 | + | 7.17291i | 0.603992 | + | 0.796990i | ||||
\(82\) | −5.68936 | + | 9.85425i | −0.628284 | + | 1.08822i | ||||
\(83\) | 3.97145 | − | 6.87875i | 0.435923 | − | 0.755041i | −0.561447 | − | 0.827513i | \(-0.689755\pi\) |
0.997371 | + | 0.0724712i | \(0.0230886\pi\) | |||||||
\(84\) | 1.28778 | + | 4.26828i | 0.140509 | + | 0.465708i | ||||
\(85\) | − | 5.18752i | − | 0.562665i | ||||||
\(86\) | −3.86337 | − | 6.69156i | −0.416598 | − | 0.721569i | ||||
\(87\) | 14.2431 | + | 3.34355i | 1.52702 | + | 0.358466i | ||||
\(88\) | 4.44629 | + | 2.56707i | 0.473976 | + | 0.273650i | ||||
\(89\) | −14.8905 | −1.57839 | −0.789195 | − | 0.614143i | \(-0.789502\pi\) | ||||
−0.789195 | + | 0.614143i | \(0.789502\pi\) | |||||||
\(90\) | 2.49940 | − | 1.65922i | 0.263459 | − | 0.174897i | ||||
\(91\) | − | 13.6547i | − | 1.43140i | ||||||
\(92\) | 3.03318 | 0.316231 | ||||||||
\(93\) | −0.848884 | + | 9.60622i | −0.0880252 | + | 0.996118i | ||||
\(94\) | 6.75256 | 0.696473 | ||||||||
\(95\) | 0.529528i | 0.0543284i | ||||||||
\(96\) | −0.395836 | + | 1.68621i | −0.0403999 | + | 0.172098i | ||||
\(97\) | −6.46323 | −0.656242 | −0.328121 | − | 0.944636i | \(-0.606415\pi\) | ||||
−0.328121 | + | 0.944636i | \(0.606415\pi\) | |||||||
\(98\) | 0.324294 | + | 0.187231i | 0.0327587 | + | 0.0189132i | ||||
\(99\) | −12.8322 | + | 8.51868i | −1.28969 | + | 0.856159i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | − | 8.88476i | − | 0.884067i | −0.896999 | − | 0.442034i | \(-0.854257\pi\) | ||
0.896999 | − | 0.442034i | \(-0.145743\pi\) | |||||||
\(102\) | −8.60205 | + | 2.59533i | −0.851730 | + | 0.256975i | ||||
\(103\) | −5.26044 | + | 9.11135i | −0.518327 | + | 0.897768i | 0.481447 | + | 0.876475i | \(0.340111\pi\) |
−0.999773 | + | 0.0212926i | \(0.993222\pi\) | |||||||
\(104\) | 2.65242 | − | 4.59412i | 0.260091 | − | 0.450491i | ||||
\(105\) | −1.01889 | + | 4.34033i | −0.0994332 | + | 0.423573i | ||||
\(106\) | −1.42431 | − | 0.822328i | −0.138342 | − | 0.0798715i | ||||
\(107\) | 11.2096 | − | 6.47185i | 1.08367 | − | 0.625657i | 0.151786 | − | 0.988413i | \(-0.451497\pi\) |
0.931884 | + | 0.362756i | \(0.118164\pi\) | |||||||
\(108\) | −4.00181 | − | 3.31444i | −0.385075 | − | 0.318932i | ||||
\(109\) | −1.35138 | −0.129439 | −0.0647193 | − | 0.997904i | \(-0.520615\pi\) | ||||
−0.0647193 | + | 0.997904i | \(0.520615\pi\) | |||||||
\(110\) | 2.56707 | + | 4.44629i | 0.244760 | + | 0.423937i | ||||
\(111\) | 1.11225 | − | 0.335578i | 0.105571 | − | 0.0318517i | ||||
\(112\) | −1.28701 | − | 2.22916i | −0.121611 | − | 0.210636i | ||||
\(113\) | −4.08230 | − | 2.35692i | −0.384030 | − | 0.221720i | 0.295540 | − | 0.955330i | \(-0.404500\pi\) |
−0.679570 | + | 0.733610i | \(0.737834\pi\) | |||||||
\(114\) | 0.878074 | − | 0.264924i | 0.0822392 | − | 0.0248124i | ||||
\(115\) | 2.62681 | + | 1.51659i | 0.244951 | + | 0.141423i | ||||
\(116\) | −8.44680 | −0.784265 | ||||||||
\(117\) | 8.80191 | + | 13.2589i | 0.813736 | + | 1.22578i | ||||
\(118\) | −6.03251 | − | 10.4486i | −0.555338 | − | 0.961873i | ||||
\(119\) | 6.67636 | − | 11.5638i | 0.612021 | − | 1.06005i | ||||
\(120\) | −1.18591 | + | 1.26238i | −0.108258 | + | 0.115239i | ||||
\(121\) | −7.67968 | − | 13.3016i | −0.698152 | − | 1.20924i | ||||
\(122\) | 7.06279 | 0.639435 | ||||||||
\(123\) | 14.3643 | + | 13.4941i | 1.29519 | + | 1.21673i | ||||
\(124\) | −0.790363 | − | 5.51138i | −0.0709767 | − | 0.494937i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 7.70698 | − | 0.481936i | 0.686593 | − | 0.0429343i | ||||
\(127\) | 13.5026 | − | 7.79574i | 1.19816 | − | 0.691760i | 0.238018 | − | 0.971261i | \(-0.423502\pi\) |
0.960146 | + | 0.279500i | \(0.0901688\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −12.8127 | + | 3.86571i | −1.12809 | + | 0.340356i | ||||
\(130\) | 4.59412 | − | 2.65242i | 0.402931 | − | 0.232632i | ||||
\(131\) | −16.4069 | + | 9.47252i | −1.43348 | + | 0.827618i | −0.997384 | − | 0.0722837i | \(-0.976971\pi\) |
−0.436093 | + | 0.899902i | \(0.643638\pi\) | |||||||
\(132\) | 6.08863 | − | 6.48126i | 0.529947 | − | 0.564121i | ||||
\(133\) | −0.681505 | + | 1.18040i | −0.0590940 | + | 0.102354i | ||||
\(134\) | 6.89980 | + | 3.98360i | 0.596052 | + | 0.344131i | ||||
\(135\) | −1.80845 | − | 4.87129i | −0.155647 | − | 0.419254i | ||||
\(136\) | 4.49252 | − | 2.59376i | 0.385231 | − | 0.222413i | ||||
\(137\) | 2.98906 | − | 5.17720i | 0.255373 | − | 0.442318i | −0.709624 | − | 0.704580i | \(-0.751135\pi\) |
0.964997 | + | 0.262262i | \(0.0844686\pi\) | |||||||
\(138\) | 1.20064 | − | 5.11459i | 0.102206 | − | 0.435383i | ||||
\(139\) | − | 20.6001i | − | 1.74728i | −0.486573 | − | 0.873640i | \(-0.661753\pi\) | ||
0.486573 | − | 0.873640i | \(-0.338247\pi\) | |||||||
\(140\) | − | 2.57401i | − | 0.217544i | ||||||
\(141\) | 2.67291 | − | 11.3862i | 0.225099 | − | 0.958895i | ||||
\(142\) | 4.88050 | − | 8.45327i | 0.409562 | − | 0.709382i | ||||
\(143\) | −23.5869 | + | 13.6179i | −1.97243 | + | 1.13878i | ||||
\(144\) | 2.68663 | + | 1.33493i | 0.223886 | + | 0.111244i | ||||
\(145\) | −7.31514 | − | 4.22340i | −0.607489 | − | 0.350734i | ||||
\(146\) | 1.85630 | − | 3.21521i | 0.153629 | − | 0.266093i | ||||
\(147\) | 0.444079 | − | 0.472716i | 0.0366271 | − | 0.0389890i | ||||
\(148\) | −0.580888 | + | 0.335376i | −0.0477487 | + | 0.0275677i | ||||
\(149\) | −20.8920 | + | 12.0620i | −1.71154 | + | 0.988160i | −0.779057 | + | 0.626953i | \(0.784302\pi\) |
−0.932486 | + | 0.361206i | \(0.882365\pi\) | |||||||
\(150\) | −1.65822 | + | 0.500302i | −0.135393 | + | 0.0408495i | ||||
\(151\) | 16.5788i | 1.34916i | 0.738201 | + | 0.674581i | \(0.235676\pi\) | ||||
−0.738201 | + | 0.674581i | \(0.764324\pi\) | |||||||
\(152\) | −0.458584 | + | 0.264764i | −0.0371961 | + | 0.0214752i | ||||
\(153\) | 0.971266 | + | 15.5322i | 0.0785222 | + | 1.25570i | ||||
\(154\) | 13.2153i | 1.06492i | ||||||||
\(155\) | 2.07122 | − | 5.16818i | 0.166364 | − | 0.415118i | ||||
\(156\) | −6.69674 | − | 6.29106i | −0.536169 | − | 0.503688i | ||||
\(157\) | 14.6508 | 1.16926 | 0.584631 | − | 0.811300i | \(-0.301239\pi\) | ||||
0.584631 | + | 0.811300i | \(0.301239\pi\) | |||||||
\(158\) | 5.05381 | + | 8.75345i | 0.402059 | + | 0.696387i | ||||
\(159\) | −1.95041 | + | 2.07619i | −0.154678 | + | 0.164652i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 3.90372 | + | 6.76144i | 0.307656 | + | 0.532876i | ||||
\(162\) | −7.17291 | + | 5.43593i | −0.563557 | + | 0.427087i | ||||
\(163\) | 22.4774 | 1.76056 | 0.880281 | − | 0.474452i | \(-0.157354\pi\) | ||||
0.880281 | + | 0.474452i | \(0.157354\pi\) | |||||||
\(164\) | −9.85425 | − | 5.68936i | −0.769488 | − | 0.444264i | ||||
\(165\) | 8.51353 | − | 2.56862i | 0.662778 | − | 0.199967i | ||||
\(166\) | 6.87875 | + | 3.97145i | 0.533895 | + | 0.308244i | ||||
\(167\) | 8.21327 | + | 14.2258i | 0.635562 | + | 1.10083i | 0.986396 | + | 0.164388i | \(0.0525650\pi\) |
−0.350833 | + | 0.936438i | \(0.614102\pi\) | |||||||
\(168\) | −4.26828 | + | 1.28778i | −0.329305 | + | 0.0993546i | ||||
\(169\) | 7.57064 | + | 13.1127i | 0.582357 | + | 1.00867i | ||||
\(170\) | 5.18752 | 0.397864 | ||||||||
\(171\) | −0.0991442 | − | 1.58549i | −0.00758174 | − | 0.121245i | ||||
\(172\) | 6.69156 | − | 3.86337i | 0.510226 | − | 0.294579i | ||||
\(173\) | 2.51861 | + | 1.45412i | 0.191486 | + | 0.110554i | 0.592678 | − | 0.805439i | \(-0.298071\pi\) |
−0.401192 | + | 0.915994i | \(0.631404\pi\) | |||||||
\(174\) | −3.34355 | + | 14.2431i | −0.253474 | + | 1.07977i | ||||
\(175\) | 1.28701 | − | 2.22916i | 0.0972885 | − | 0.168509i | ||||
\(176\) | −2.56707 | + | 4.44629i | −0.193500 | + | 0.335152i | ||||
\(177\) | −20.0065 | + | 6.03616i | −1.50378 | + | 0.453705i | ||||
\(178\) | − | 14.8905i | − | 1.11609i | ||||||
\(179\) | 2.85826 | + | 4.95065i | 0.213637 | + | 0.370029i | 0.952850 | − | 0.303442i | \(-0.0981358\pi\) |
−0.739213 | + | 0.673471i | \(0.764803\pi\) | |||||||
\(180\) | 1.65922 | + | 2.49940i | 0.123671 | + | 0.186294i | ||||
\(181\) | −13.2525 | − | 7.65134i | −0.985051 | − | 0.568719i | −0.0812595 | − | 0.996693i | \(-0.525894\pi\) |
−0.903791 | + | 0.427974i | \(0.859228\pi\) | |||||||
\(182\) | 13.6547 | 1.01215 | ||||||||
\(183\) | 2.79571 | − | 11.9094i | 0.206665 | − | 0.880365i | ||||
\(184\) | 3.03318i | 0.223609i | ||||||||
\(185\) | −0.670752 | −0.0493146 | ||||||||
\(186\) | −9.60622 | − | 0.848884i | −0.704362 | − | 0.0622432i | ||||
\(187\) | −26.6334 | −1.94763 | ||||||||
\(188\) | 6.75256i | 0.492481i | ||||||||
\(189\) | 2.23806 | − | 13.1864i | 0.162795 | − | 0.959168i | ||||
\(190\) | −0.529528 | −0.0384160 | ||||||||
\(191\) | −4.31841 | − | 2.49324i | −0.312470 | − | 0.180404i | 0.335562 | − | 0.942018i | \(-0.391074\pi\) |
−0.648031 | + | 0.761614i | \(0.724407\pi\) | |||||||
\(192\) | −1.68621 | − | 0.395836i | −0.121692 | − | 0.0285670i | ||||
\(193\) | 8.08463 | + | 14.0030i | 0.581945 | + | 1.00796i | 0.995249 | + | 0.0973645i | \(0.0310413\pi\) |
−0.413304 | + | 0.910593i | \(0.635625\pi\) | |||||||
\(194\) | − | 6.46323i | − | 0.464033i | ||||||
\(195\) | −2.65402 | − | 8.79659i | −0.190058 | − | 0.629937i | ||||
\(196\) | −0.187231 | + | 0.324294i | −0.0133737 | + | 0.0231639i | ||||
\(197\) | 4.30925 | − | 7.46384i | 0.307021 | − | 0.531777i | −0.670688 | − | 0.741740i | \(-0.734001\pi\) |
0.977709 | + | 0.209963i | \(0.0673343\pi\) | |||||||
\(198\) | −8.51868 | − | 12.8322i | −0.605396 | − | 0.911947i | ||||
\(199\) | 4.91862 | + | 2.83976i | 0.348671 | + | 0.201306i | 0.664100 | − | 0.747644i | \(-0.268815\pi\) |
−0.315429 | + | 0.948949i | \(0.602148\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | 9.44840 | − | 10.0577i | 0.666438 | − | 0.709414i | ||||
\(202\) | 8.88476 | 0.625130 | ||||||||
\(203\) | −10.8711 | − | 18.8293i | −0.763000 | − | 1.32155i | ||||
\(204\) | −2.59533 | − | 8.60205i | −0.181709 | − | 0.602264i | ||||
\(205\) | −5.68936 | − | 9.85425i | −0.397362 | − | 0.688251i | ||||
\(206\) | −9.11135 | − | 5.26044i | −0.634818 | − | 0.366512i | ||||
\(207\) | −8.14902 | − | 4.04908i | −0.566396 | − | 0.281430i | ||||
\(208\) | 4.59412 | + | 2.65242i | 0.318545 | + | 0.183912i | ||||
\(209\) | 2.71867 | 0.188054 | ||||||||
\(210\) | −4.34033 | − | 1.01889i | −0.299511 | − | 0.0703099i | ||||
\(211\) | 0.695561 | + | 1.20475i | 0.0478844 | + | 0.0829382i | 0.888974 | − | 0.457957i | \(-0.151419\pi\) |
−0.841090 | + | 0.540896i | \(0.818085\pi\) | |||||||
\(212\) | 0.822328 | − | 1.42431i | 0.0564777 | − | 0.0978222i | ||||
\(213\) | −12.3221 | − | 11.5757i | −0.844298 | − | 0.793151i | ||||
\(214\) | 6.47185 | + | 11.2096i | 0.442407 | + | 0.766271i | ||||
\(215\) | 7.72674 | 0.526960 | ||||||||
\(216\) | 3.31444 | − | 4.00181i | 0.225519 | − | 0.272289i | ||||
\(217\) | 11.2685 | − | 8.85503i | 0.764959 | − | 0.601118i | ||||
\(218\) | − | 1.35138i | − | 0.0915269i | ||||||
\(219\) | −4.68674 | − | 4.40282i | −0.316700 | − | 0.297515i | ||||
\(220\) | −4.44629 | + | 2.56707i | −0.299769 | + | 0.173072i | ||||
\(221\) | 27.5189i | 1.85112i | ||||||||
\(222\) | 0.335578 | + | 1.11225i | 0.0225226 | + | 0.0746497i | ||||
\(223\) | 11.5712 | − | 6.68062i | 0.774863 | − | 0.447368i | −0.0597434 | − | 0.998214i | \(-0.519028\pi\) |
0.834607 | + | 0.550846i | \(0.185695\pi\) | |||||||
\(224\) | 2.22916 | − | 1.28701i | 0.148942 | − | 0.0859917i | ||||
\(225\) | 0.187231 | + | 2.99415i | 0.0124821 | + | 0.199610i | ||||
\(226\) | 2.35692 | − | 4.08230i | 0.156780 | − | 0.271550i | ||||
\(227\) | −13.4583 | − | 7.77017i | −0.893261 | − | 0.515724i | −0.0182532 | − | 0.999833i | \(-0.505810\pi\) |
−0.875008 | + | 0.484109i | \(0.839144\pi\) | |||||||
\(228\) | 0.264924 | + | 0.878074i | 0.0175450 | + | 0.0581519i | ||||
\(229\) | 12.6066 | − | 7.27845i | 0.833071 | − | 0.480974i | −0.0218323 | − | 0.999762i | \(-0.506950\pi\) |
0.854903 | + | 0.518788i | \(0.173617\pi\) | |||||||
\(230\) | −1.51659 | + | 2.62681i | −0.100001 | + | 0.173207i | ||||
\(231\) | 22.2839 | + | 5.23111i | 1.46617 | + | 0.344182i | ||||
\(232\) | − | 8.44680i | − | 0.554559i | ||||||
\(233\) | − | 2.89624i | − | 0.189739i | −0.995490 | − | 0.0948694i | \(-0.969757\pi\) | ||
0.995490 | − | 0.0948694i | \(-0.0302434\pi\) | |||||||
\(234\) | −13.2589 | + | 8.80191i | −0.866760 | + | 0.575399i | ||||
\(235\) | −3.37628 | + | 5.84788i | −0.220244 | + | 0.381474i | ||||
\(236\) | 10.4486 | − | 6.03251i | 0.680147 | − | 0.392683i | ||||
\(237\) | 16.7607 | − | 5.05686i | 1.08872 | − | 0.328479i | ||||
\(238\) | 11.5638 | + | 6.67636i | 0.749570 | + | 0.432764i | ||||
\(239\) | 2.74446 | − | 4.75354i | 0.177524 | − | 0.307481i | −0.763508 | − | 0.645799i | \(-0.776524\pi\) |
0.941032 | + | 0.338318i | \(0.109858\pi\) | |||||||
\(240\) | −1.26238 | − | 1.18591i | −0.0814866 | − | 0.0765502i | ||||
\(241\) | −4.61436 | + | 2.66410i | −0.297237 | + | 0.171610i | −0.641201 | − | 0.767373i | \(-0.721564\pi\) |
0.343964 | + | 0.938983i | \(0.388230\pi\) | |||||||
\(242\) | 13.3016 | − | 7.67968i | 0.855059 | − | 0.493668i | ||||
\(243\) | 6.32684 | + | 14.2468i | 0.405867 | + | 0.913932i | ||||
\(244\) | 7.06279i | 0.452149i | ||||||||
\(245\) | −0.324294 | + | 0.187231i | −0.0207184 | + | 0.0119618i | ||||
\(246\) | −13.4941 | + | 14.3643i | −0.860355 | + | 0.915835i | ||||
\(247\) | − | 2.80906i | − | 0.178736i | ||||||
\(248\) | 5.51138 | − | 0.790363i | 0.349973 | − | 0.0501881i | ||||
\(249\) | 9.41957 | − | 10.0270i | 0.596941 | − | 0.635435i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −0.392937 | − | 0.680586i | −0.0248019 | − | 0.0429582i | 0.853358 | − | 0.521325i | \(-0.174562\pi\) |
−0.878160 | + | 0.478367i | \(0.841229\pi\) | |||||||
\(252\) | 0.481936 | + | 7.70698i | 0.0303591 | + | 0.485494i | ||||
\(253\) | 7.78638 | − | 13.4864i | 0.489526 | − | 0.847883i | ||||
\(254\) | 7.79574 | + | 13.5026i | 0.489148 | + | 0.847230i | ||||
\(255\) | 2.05341 | − | 8.74726i | 0.128589 | − | 0.547774i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.4435 | + | 6.02954i | 0.651446 | + | 0.376113i | 0.789010 | − | 0.614380i | \(-0.210594\pi\) |
−0.137564 | + | 0.990493i | \(0.543927\pi\) | |||||||
\(258\) | −3.86571 | − | 12.8127i | −0.240668 | − | 0.797681i | ||||
\(259\) | −1.49521 | − | 0.863261i | −0.0929080 | − | 0.0536405i | ||||
\(260\) | 2.65242 | + | 4.59412i | 0.164496 | + | 0.284915i | ||||
\(261\) | 22.6934 | + | 11.2759i | 1.40469 | + | 0.697959i | ||||
\(262\) | −9.47252 | − | 16.4069i | −0.585214 | − | 1.01362i | ||||
\(263\) | 2.04756 | 0.126258 | 0.0631291 | − | 0.998005i | \(-0.479892\pi\) | ||||
0.0631291 | + | 0.998005i | \(0.479892\pi\) | |||||||
\(264\) | 6.48126 | + | 6.08863i | 0.398894 | + | 0.374729i | ||||
\(265\) | 1.42431 | − | 0.822328i | 0.0874949 | − | 0.0505152i | ||||
\(266\) | −1.18040 | − | 0.681505i | −0.0723751 | − | 0.0417858i | ||||
\(267\) | −25.1085 | − | 5.89420i | −1.53662 | − | 0.360719i | ||||
\(268\) | −3.98360 | + | 6.89980i | −0.243337 | + | 0.421473i | ||||
\(269\) | 13.5077 | − | 23.3961i | 0.823581 | − | 1.42648i | −0.0794184 | − | 0.996841i | \(-0.525306\pi\) |
0.902999 | − | 0.429642i | \(-0.141360\pi\) | |||||||
\(270\) | 4.87129 | − | 1.80845i | 0.296458 | − | 0.110059i | ||||
\(271\) | − | 3.17938i | − | 0.193134i | −0.995327 | − | 0.0965668i | \(-0.969214\pi\) | ||
0.995327 | − | 0.0965668i | \(-0.0307861\pi\) | |||||||
\(272\) | 2.59376 | + | 4.49252i | 0.157270 | + | 0.272399i | ||||
\(273\) | 5.40503 | − | 23.0247i | 0.327127 | − | 1.39352i | ||||
\(274\) | 5.17720 | + | 2.98906i | 0.312766 | + | 0.180576i | ||||
\(275\) | −5.13414 | −0.309600 | ||||||||
\(276\) | 5.11459 | + | 1.20064i | 0.307862 | + | 0.0722702i | ||||
\(277\) | − | 16.5427i | − | 0.993955i | −0.867763 | − | 0.496978i | \(-0.834443\pi\) | ||
0.867763 | − | 0.496978i | \(-0.165557\pi\) | |||||||
\(278\) | 20.6001 | 1.23551 | ||||||||
\(279\) | −5.23389 | + | 15.8621i | −0.313345 | + | 0.949639i | ||||
\(280\) | 2.57401 | 0.153827 | ||||||||
\(281\) | − | 1.55339i | − | 0.0926672i | −0.998926 | − | 0.0463336i | \(-0.985246\pi\) | ||
0.998926 | − | 0.0463336i | \(-0.0147537\pi\) | |||||||
\(282\) | 11.3862 | + | 2.67291i | 0.678041 | + | 0.159169i | ||||
\(283\) | −3.03122 | −0.180187 | −0.0900936 | − | 0.995933i | \(-0.528717\pi\) | ||||
−0.0900936 | + | 0.995933i | \(0.528717\pi\) | |||||||
\(284\) | 8.45327 | + | 4.88050i | 0.501609 | + | 0.289604i | ||||
\(285\) | −0.209606 | + | 0.892896i | −0.0124160 | + | 0.0528906i | ||||
\(286\) | −13.6179 | − | 23.5869i | −0.805242 | − | 1.39472i | ||||
\(287\) | − | 29.2889i | − | 1.72887i | ||||||
\(288\) | −1.33493 | + | 2.68663i | −0.0786614 | + | 0.158311i | ||||
\(289\) | −4.95516 | + | 8.58260i | −0.291480 | + | 0.504859i | ||||
\(290\) | 4.22340 | − | 7.31514i | 0.248006 | − | 0.429560i | ||||
\(291\) | −10.8984 | − | 2.55838i | −0.638875 | − | 0.149975i | ||||
\(292\) | 3.21521 | + | 1.85630i | 0.188156 | + | 0.108632i | ||||
\(293\) | 6.74006 | − | 3.89138i | 0.393759 | − | 0.227337i | −0.290029 | − | 0.957018i | \(-0.593665\pi\) |
0.683787 | + | 0.729681i | \(0.260332\pi\) | |||||||
\(294\) | 0.472716 | + | 0.444079i | 0.0275694 | + | 0.0258992i | ||||
\(295\) | 12.0650 | 0.702453 | ||||||||
\(296\) | −0.335376 | − | 0.580888i | −0.0194933 | − | 0.0337634i | ||||
\(297\) | −25.0099 | + | 9.28484i | −1.45122 | + | 0.538761i | ||||
\(298\) | −12.0620 | − | 20.8920i | −0.698734 | − | 1.21024i | ||||
\(299\) | −13.9348 | − | 8.04526i | −0.805870 | − | 0.465270i | ||||
\(300\) | −0.500302 | − | 1.65822i | −0.0288850 | − | 0.0957375i | ||||
\(301\) | 17.2241 | + | 9.94437i | 0.992783 | + | 0.573184i | ||||
\(302\) | −16.5788 | −0.954002 | ||||||||
\(303\) | 3.51691 | − | 14.9816i | 0.202041 | − | 0.860671i | ||||
\(304\) | −0.264764 | − | 0.458584i | −0.0151852 | − | 0.0263016i | ||||
\(305\) | −3.53139 | + | 6.11655i | −0.202207 | + | 0.350233i | ||||
\(306\) | −15.5322 | + | 0.971266i | −0.887917 | + | 0.0555236i | ||||
\(307\) | −5.71957 | − | 9.90659i | −0.326433 | − | 0.565399i | 0.655368 | − | 0.755310i | \(-0.272513\pi\) |
−0.981801 | + | 0.189911i | \(0.939180\pi\) | |||||||
\(308\) | −13.2153 | −0.753013 | ||||||||
\(309\) | −12.4768 | + | 13.2814i | −0.709782 | + | 0.755552i | ||||
\(310\) | 5.16818 | + | 2.07122i | 0.293533 | + | 0.117637i | ||||
\(311\) | 7.22744i | 0.409831i | 0.978780 | + | 0.204915i | \(0.0656919\pi\) | ||||
−0.978780 | + | 0.204915i | \(0.934308\pi\) | |||||||
\(312\) | 6.29106 | − | 6.69674i | 0.356161 | − | 0.379129i | ||||
\(313\) | 11.2641 | − | 6.50334i | 0.636686 | − | 0.367591i | −0.146651 | − | 0.989188i | \(-0.546849\pi\) |
0.783337 | + | 0.621598i | \(0.213516\pi\) | |||||||
\(314\) | 14.6508i | 0.826793i | ||||||||
\(315\) | −3.43612 | + | 6.91541i | −0.193604 | + | 0.389639i | ||||
\(316\) | −8.75345 | + | 5.05381i | −0.492420 | + | 0.284299i | ||||
\(317\) | 19.7129 | − | 11.3812i | 1.10718 | − | 0.639233i | 0.169086 | − | 0.985601i | \(-0.445918\pi\) |
0.938099 | + | 0.346368i | \(0.112585\pi\) | |||||||
\(318\) | −2.07619 | − | 1.95041i | −0.116427 | − | 0.109374i | ||||
\(319\) | −21.6835 | + | 37.5569i | −1.21404 | + | 2.10278i | ||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | 21.4635 | − | 6.47576i | 1.19798 | − | 0.361442i | ||||
\(322\) | −6.76144 | + | 3.90372i | −0.376801 | + | 0.217546i | ||||
\(323\) | 1.37347 | − | 2.37891i | 0.0764217 | − | 0.132366i | ||||
\(324\) | −5.43593 | − | 7.17291i | −0.301996 | − | 0.398495i | ||||
\(325\) | 5.30484i | 0.294259i | ||||||||
\(326\) | 22.4774i | 1.24491i | ||||||||
\(327\) | −2.27871 | − | 0.534925i | −0.126013 | − | 0.0295814i | ||||
\(328\) | 5.68936 | − | 9.85425i | 0.314142 | − | 0.544110i | ||||
\(329\) | −15.0525 | + | 8.69058i | −0.829873 | + | 0.479127i | ||||
\(330\) | 2.56862 | + | 8.51353i | 0.141398 | + | 0.468655i | ||||
\(331\) | 4.25023 | + | 2.45387i | 0.233614 | + | 0.134877i | 0.612238 | − | 0.790673i | \(-0.290269\pi\) |
−0.378624 | + | 0.925550i | \(0.623603\pi\) | |||||||
\(332\) | −3.97145 | + | 6.87875i | −0.217962 | + | 0.377521i | ||||
\(333\) | 2.00833 | − | 0.125586i | 0.110056 | − | 0.00688206i | ||||
\(334\) | −14.2258 | + | 8.21327i | −0.778402 | + | 0.449410i | ||||
\(335\) | −6.89980 | + | 3.98360i | −0.376977 | + | 0.217647i | ||||
\(336\) | −1.28778 | − | 4.26828i | −0.0702543 | − | 0.232854i | ||||
\(337\) | 27.0752i | 1.47488i | 0.675414 | + | 0.737439i | \(0.263965\pi\) | ||||
−0.675414 | + | 0.737439i | \(0.736035\pi\) | |||||||
\(338\) | −13.1127 | + | 7.57064i | −0.713239 | + | 0.411789i | ||||
\(339\) | −5.95067 | − | 5.59018i | −0.323196 | − | 0.303617i | ||||
\(340\) | 5.18752i | 0.281333i | ||||||||
\(341\) | −26.5341 | − | 10.6339i | −1.43690 | − | 0.575858i | ||||
\(342\) | 1.58549 | − | 0.0991442i | 0.0857333 | − | 0.00536110i | ||||
\(343\) | −18.9820 | −1.02493 | ||||||||
\(344\) | 3.86337 | + | 6.69156i | 0.208299 | + | 0.360785i | ||||
\(345\) | 3.82904 | + | 3.59708i | 0.206149 | + | 0.193660i | ||||
\(346\) | −1.45412 | + | 2.51861i | −0.0781738 | + | 0.135401i | ||||
\(347\) | −10.2487 | − | 17.7512i | −0.550178 | − | 0.952936i | −0.998261 | − | 0.0589439i | \(-0.981227\pi\) |
0.448084 | − | 0.893992i | \(-0.352107\pi\) | |||||||
\(348\) | −14.2431 | − | 3.34355i | −0.763510 | − | 0.179233i | ||||
\(349\) | −20.0539 | −1.07346 | −0.536732 | − | 0.843753i | \(-0.680341\pi\) | ||||
−0.536732 | + | 0.843753i | \(0.680341\pi\) | |||||||
\(350\) | 2.22916 | + | 1.28701i | 0.119154 | + | 0.0687934i | ||||
\(351\) | 9.59354 | + | 25.8414i | 0.512065 | + | 1.37931i | ||||
\(352\) | −4.44629 | − | 2.56707i | −0.236988 | − | 0.136825i | ||||
\(353\) | 4.20458 | + | 7.28255i | 0.223787 | + | 0.387611i | 0.955955 | − | 0.293513i | \(-0.0948246\pi\) |
−0.732168 | + | 0.681125i | \(0.761491\pi\) | |||||||
\(354\) | −6.03616 | − | 20.0065i | −0.320818 | − | 1.06333i | ||||
\(355\) | 4.88050 | + | 8.45327i | 0.259030 | + | 0.448653i | ||||
\(356\) | 14.8905 | 0.789195 | ||||||||
\(357\) | 15.8351 | − | 16.8563i | 0.838085 | − | 0.892129i | ||||
\(358\) | −4.95065 | + | 2.85826i | −0.261650 | + | 0.151064i | ||||
\(359\) | −22.0093 | − | 12.7070i | −1.16160 | − | 0.670652i | −0.209916 | − | 0.977719i | \(-0.567319\pi\) |
−0.951688 | + | 0.307067i | \(0.900652\pi\) | |||||||
\(360\) | −2.49940 | + | 1.65922i | −0.131730 | + | 0.0874487i | ||||
\(361\) | 9.35980 | − | 16.2116i | 0.492621 | − | 0.853245i | ||||
\(362\) | 7.65134 | − | 13.2525i | 0.402145 | − | 0.696536i | ||||
\(363\) | −7.68432 | − | 25.4692i | −0.403322 | − | 1.33679i | ||||
\(364\) | 13.6547i | 0.715701i | ||||||||
\(365\) | 1.85630 | + | 3.21521i | 0.0971633 | + | 0.168292i | ||||
\(366\) | 11.9094 | + | 2.79571i | 0.622512 | + | 0.146134i | ||||
\(367\) | 14.9832 | + | 8.65053i | 0.782114 | + | 0.451554i | 0.837179 | − | 0.546929i | \(-0.184203\pi\) |
−0.0550648 | + | 0.998483i | \(0.517537\pi\) | |||||||
\(368\) | −3.03318 | −0.158115 | ||||||||
\(369\) | 18.8798 | + | 28.4399i | 0.982844 | + | 1.48052i | ||||
\(370\) | − | 0.670752i | − | 0.0348707i | ||||||
\(371\) | 4.23336 | 0.219785 | ||||||||
\(372\) | 0.848884 | − | 9.60622i | 0.0440126 | − | 0.498059i | ||||
\(373\) | −14.4940 | −0.750471 | −0.375236 | − | 0.926929i | \(-0.622438\pi\) | ||||
−0.375236 | + | 0.926929i | \(0.622438\pi\) | |||||||
\(374\) | − | 26.6334i | − | 1.37718i | ||||||
\(375\) | 0.395836 | − | 1.68621i | 0.0204409 | − | 0.0870757i | ||||
\(376\) | −6.75256 | −0.348236 | ||||||||
\(377\) | 38.8056 | + | 22.4044i | 1.99859 | + | 1.15389i | ||||
\(378\) | 13.1864 | + | 2.23806i | 0.678234 | + | 0.115113i | ||||
\(379\) | −9.90778 | − | 17.1608i | −0.508929 | − | 0.881490i | −0.999947 | − | 0.0103407i | \(-0.996708\pi\) |
0.491018 | − | 0.871149i | \(-0.336625\pi\) | |||||||
\(380\) | − | 0.529528i | − | 0.0271642i | ||||||
\(381\) | 25.8541 | − | 7.80045i | 1.32455 | − | 0.399629i | ||||
\(382\) | 2.49324 | − | 4.31841i | 0.127565 | − | 0.220949i | ||||
\(383\) | 1.97590 | − | 3.42236i | 0.100964 | − | 0.174874i | −0.811118 | − | 0.584882i | \(-0.801141\pi\) |
0.912082 | + | 0.410008i | \(0.134474\pi\) | |||||||
\(384\) | 0.395836 | − | 1.68621i | 0.0201999 | − | 0.0860492i | ||||
\(385\) | −11.4448 | − | 6.60766i | −0.583282 | − | 0.336758i | ||||
\(386\) | −14.0030 | + | 8.08463i | −0.712734 | + | 0.411497i | ||||
\(387\) | −23.1350 | + | 1.44669i | −1.17602 | + | 0.0735393i | ||||
\(388\) | 6.46323 | 0.328121 | ||||||||
\(389\) | 9.71945 | + | 16.8346i | 0.492796 | + | 0.853547i | 0.999966 | − | 0.00829898i | \(-0.00264168\pi\) |
−0.507170 | + | 0.861846i | \(0.669308\pi\) | |||||||
\(390\) | 8.79659 | − | 2.65402i | 0.445433 | − | 0.134392i | ||||
\(391\) | −7.86734 | − | 13.6266i | −0.397868 | − | 0.689128i | ||||
\(392\) | −0.324294 | − | 0.187231i | −0.0163793 | − | 0.00945661i | ||||
\(393\) | −31.4151 | + | 9.47824i | −1.58468 | + | 0.478114i | ||||
\(394\) | 7.46384 | + | 4.30925i | 0.376023 | + | 0.217097i | ||||
\(395\) | −10.1076 | −0.508569 | ||||||||
\(396\) | 12.8322 | − | 8.51868i | 0.644844 | − | 0.428080i | ||||
\(397\) | 11.9703 | + | 20.7332i | 0.600772 | + | 1.04057i | 0.992704 | + | 0.120574i | \(0.0384735\pi\) |
−0.391932 | + | 0.919994i | \(0.628193\pi\) | |||||||
\(398\) | −2.83976 | + | 4.91862i | −0.142344 | + | 0.246548i | ||||
\(399\) | −1.61641 | + | 1.72064i | −0.0809216 | + | 0.0861399i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −20.4973 | −1.02359 | −0.511793 | − | 0.859109i | \(-0.671019\pi\) | ||||
−0.511793 | + | 0.859109i | \(0.671019\pi\) | |||||||
\(402\) | 10.0577 | + | 9.44840i | 0.501632 | + | 0.471243i | ||||
\(403\) | −10.9875 | + | 27.4163i | −0.547324 | + | 1.36571i | ||||
\(404\) | 8.88476i | 0.442034i | ||||||||
\(405\) | −1.12120 | − | 8.92989i | −0.0557128 | − | 0.443730i | ||||
\(406\) | 18.8293 | − | 10.8711i | 0.934480 | − | 0.539522i | ||||
\(407\) | 3.44373i | 0.170699i | ||||||||
\(408\) | 8.60205 | − | 2.59533i | 0.425865 | − | 0.128488i | ||||
\(409\) | 7.58719 | − | 4.38047i | 0.375163 | − | 0.216600i | −0.300549 | − | 0.953766i | \(-0.597170\pi\) |
0.675712 | + | 0.737166i | \(0.263837\pi\) | |||||||
\(410\) | 9.85425 | − | 5.68936i | 0.486667 | − | 0.280977i | ||||
\(411\) | 7.08951 | − | 7.54669i | 0.349700 | − | 0.372251i | ||||
\(412\) | 5.26044 | − | 9.11135i | 0.259163 | − | 0.448884i | ||||
\(413\) | 26.8949 | + | 15.5278i | 1.32341 | + | 0.764071i | ||||
\(414\) | 4.04908 | − | 8.14902i | 0.199001 | − | 0.400503i | ||||
\(415\) | −6.87875 | + | 3.97145i | −0.337665 | + | 0.194951i | ||||
\(416\) | −2.65242 | + | 4.59412i | −0.130045 | + | 0.225245i | ||||
\(417\) | 8.15428 | − | 34.7362i | 0.399317 | − | 1.70104i | ||||
\(418\) | 2.71867i | 0.132974i | ||||||||
\(419\) | 17.8444i | 0.871754i | 0.900006 | + | 0.435877i | \(0.143562\pi\) | ||||
−0.900006 | + | 0.435877i | \(0.856438\pi\) | |||||||
\(420\) | 1.01889 | − | 4.34033i | 0.0497166 | − | 0.211787i | ||||
\(421\) | −8.25775 | + | 14.3028i | −0.402458 | + | 0.697078i | −0.994022 | − | 0.109180i | \(-0.965177\pi\) |
0.591564 | + | 0.806258i | \(0.298511\pi\) | |||||||
\(422\) | −1.20475 | + | 0.695561i | −0.0586462 | + | 0.0338594i | ||||
\(423\) | 9.01418 | − | 18.1416i | 0.438284 | − | 0.882075i | ||||
\(424\) | 1.42431 | + | 0.822328i | 0.0691708 | + | 0.0399358i | ||||
\(425\) | −2.59376 | + | 4.49252i | −0.125816 | + | 0.217919i | ||||
\(426\) | 11.5757 | − | 12.3221i | 0.560843 | − | 0.597009i | ||||
\(427\) | −15.7441 | + | 9.08985i | −0.761909 | + | 0.439889i | ||||
\(428\) | −11.2096 | + | 6.47185i | −0.541835 | + | 0.312829i | ||||
\(429\) | −45.1629 | + | 13.6261i | −2.18049 | + | 0.657874i | ||||
\(430\) | 7.72674i | 0.372617i | ||||||||
\(431\) | 10.7198 | − | 6.18908i | 0.516354 | − | 0.298117i | −0.219087 | − | 0.975705i | \(-0.570308\pi\) |
0.735442 | + | 0.677588i | \(0.236975\pi\) | |||||||
\(432\) | 4.00181 | + | 3.31444i | 0.192537 | + | 0.159466i | ||||
\(433\) | 1.18613i | 0.0570017i | 0.999594 | + | 0.0285008i | \(0.00907333\pi\) | ||||
−0.999594 | + | 0.0285008i | \(0.990927\pi\) | |||||||
\(434\) | 8.85503 | + | 11.2685i | 0.425055 | + | 0.540908i | ||||
\(435\) | −10.6631 | − | 10.0171i | −0.511257 | − | 0.480285i | ||||
\(436\) | 1.35138 | 0.0647193 | ||||||||
\(437\) | 0.803076 | + | 1.39097i | 0.0384163 | + | 0.0665391i | ||||
\(438\) | 4.40282 | − | 4.68674i | 0.210375 | − | 0.223941i | ||||
\(439\) | 8.22962 | − | 14.2541i | 0.392778 | − | 0.680312i | −0.600036 | − | 0.799973i | \(-0.704847\pi\) |
0.992815 | + | 0.119660i | \(0.0381806\pi\) | |||||||
\(440\) | −2.56707 | − | 4.44629i | −0.122380 | − | 0.211969i | ||||
\(441\) | 0.935931 | − | 0.621317i | 0.0445681 | − | 0.0295865i | ||||
\(442\) | −27.5189 | −1.30894 | ||||||||
\(443\) | 20.9565 | + | 12.0992i | 0.995671 | + | 0.574851i | 0.906965 | − | 0.421207i | \(-0.138393\pi\) |
0.0887065 | + | 0.996058i | \(0.471727\pi\) | |||||||
\(444\) | −1.11225 | + | 0.335578i | −0.0527853 | + | 0.0159258i | ||||
\(445\) | 12.8955 | + | 7.44525i | 0.611308 | + | 0.352939i | ||||
\(446\) | 6.68062 | + | 11.5712i | 0.316337 | + | 0.547911i | ||||
\(447\) | −40.0030 | + | 12.0693i | −1.89208 | + | 0.570859i | ||||
\(448\) | 1.28701 | + | 2.22916i | 0.0608053 | + | 0.105318i | ||||
\(449\) | −32.2944 | −1.52406 | −0.762032 | − | 0.647539i | \(-0.775798\pi\) | ||||
−0.762032 | + | 0.647539i | \(0.775798\pi\) | |||||||
\(450\) | −2.99415 | + | 0.187231i | −0.141146 | + | 0.00882617i | ||||
\(451\) | −50.5931 | + | 29.2099i | −2.38233 | + | 1.37544i | ||||
\(452\) | 4.08230 | + | 2.35692i | 0.192015 | + | 0.110860i | ||||
\(453\) | −6.56248 | + | 27.9553i | −0.308332 | + | 1.31346i | ||||
\(454\) | 7.77017 | − | 13.4583i | 0.364672 | − | 0.631631i | ||||
\(455\) | −6.82736 | + | 11.8253i | −0.320071 | + | 0.554380i | ||||
\(456\) | −0.878074 | + | 0.264924i | −0.0411196 | + | 0.0124062i | ||||
\(457\) | − | 19.0886i | − | 0.892929i | −0.894801 | − | 0.446464i | \(-0.852683\pi\) | ||
0.894801 | − | 0.446464i | \(-0.147317\pi\) | |||||||
\(458\) | 7.27845 | + | 12.6066i | 0.340100 | + | 0.589070i | ||||
\(459\) | −4.51045 | + | 26.5751i | −0.210530 | + | 1.24042i | ||||
\(460\) | −2.62681 | − | 1.51659i | −0.122476 | − | 0.0707114i | ||||
\(461\) | −12.8115 | −0.596691 | −0.298345 | − | 0.954458i | \(-0.596435\pi\) | ||||
−0.298345 | + | 0.954458i | \(0.596435\pi\) | |||||||
\(462\) | −5.23111 | + | 22.2839i | −0.243373 | + | 1.03674i | ||||
\(463\) | 20.6891i | 0.961503i | 0.876857 | + | 0.480751i | \(0.159636\pi\) | ||||
−0.876857 | + | 0.480751i | \(0.840364\pi\) | |||||||
\(464\) | 8.44680 | 0.392133 | ||||||||
\(465\) | 5.53826 | − | 7.89479i | 0.256831 | − | 0.366112i | ||||
\(466\) | 2.89624 | 0.134166 | ||||||||
\(467\) | − | 23.8528i | − | 1.10378i | −0.833918 | − | 0.551889i | \(-0.813907\pi\) | ||
0.833918 | − | 0.551889i | \(-0.186093\pi\) | |||||||
\(468\) | −8.80191 | − | 13.2589i | −0.406868 | − | 0.612892i | ||||
\(469\) | −20.5077 | −0.946957 | ||||||||
\(470\) | −5.84788 | − | 3.37628i | −0.269743 | − | 0.155736i | ||||
\(471\) | 24.7044 | + | 5.79932i | 1.13832 | + | 0.267219i | ||||
\(472\) | 6.03251 | + | 10.4486i | 0.277669 | + | 0.480937i | ||||
\(473\) | − | 39.6702i | − | 1.82404i | ||||||
\(474\) | 5.05686 | + | 16.7607i | 0.232269 | + | 0.769843i | ||||
\(475\) | 0.264764 | − | 0.458584i | 0.0121482 | − | 0.0210413i | ||||
\(476\) | −6.67636 | + | 11.5638i | −0.306011 | + | 0.530026i | ||||
\(477\) | −4.11064 | + | 2.72885i | −0.188213 | + | 0.124945i | ||||
\(478\) | 4.75354 | + | 2.74446i | 0.217422 | + | 0.125529i | ||||
\(479\) | 2.62035 | − | 1.51286i | 0.119727 | − | 0.0691243i | −0.438941 | − | 0.898516i | \(-0.644646\pi\) |
0.558667 | + | 0.829392i | \(0.311313\pi\) | |||||||
\(480\) | 1.18591 | − | 1.26238i | 0.0541292 | − | 0.0576197i | ||||
\(481\) | 3.55823 | 0.162241 | ||||||||
\(482\) | −2.66410 | − | 4.61436i | −0.121347 | − | 0.210178i | ||||
\(483\) | 3.90608 | + | 12.9465i | 0.177733 | + | 0.589085i | ||||
\(484\) | 7.67968 | + | 13.3016i | 0.349076 | + | 0.604618i | ||||
\(485\) | 5.59732 | + | 3.23162i | 0.254161 | + | 0.146740i | ||||
\(486\) | −14.2468 | + | 6.32684i | −0.646248 | + | 0.286991i | ||||
\(487\) | −33.0749 | − | 19.0958i | −1.49877 | − | 0.865314i | −0.498768 | − | 0.866735i | \(-0.666214\pi\) |
−0.999999 | + | 0.00142186i | \(0.999547\pi\) | |||||||
\(488\) | −7.06279 | −0.319717 | ||||||||
\(489\) | 37.9016 | + | 8.89736i | 1.71397 | + | 0.402352i | ||||
\(490\) | −0.187231 | − | 0.324294i | −0.00845825 | − | 0.0146501i | ||||
\(491\) | 12.7244 | − | 22.0394i | 0.574245 | − | 0.994622i | −0.421878 | − | 0.906653i | \(-0.638629\pi\) |
0.996123 | − | 0.0879695i | \(-0.0280378\pi\) | |||||||
\(492\) | −14.3643 | − | 13.4941i | −0.647593 | − | 0.608363i | ||||
\(493\) | 21.9089 | + | 37.9474i | 0.986729 | + | 1.70907i | ||||
\(494\) | 2.80906 | 0.126385 | ||||||||
\(495\) | 15.3724 | − | 0.961271i | 0.690937 | − | 0.0432059i | ||||
\(496\) | 0.790363 | + | 5.51138i | 0.0354884 | + | 0.247468i | ||||
\(497\) | 25.1249i | 1.12701i | ||||||||
\(498\) | 10.0270 | + | 9.41957i | 0.449321 | + | 0.422101i | ||||
\(499\) | −7.16472 | + | 4.13656i | −0.320737 | + | 0.185178i | −0.651721 | − | 0.758459i | \(-0.725953\pi\) |
0.330984 | + | 0.943636i | \(0.392619\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 8.21824 | + | 27.2389i | 0.367164 | + | 1.21694i | ||||
\(502\) | 0.680586 | − | 0.392937i | 0.0303760 | − | 0.0175376i | ||||
\(503\) | −12.4153 | + | 7.16797i | −0.553570 | + | 0.319604i | −0.750561 | − | 0.660802i | \(-0.770216\pi\) |
0.196991 | + | 0.980405i | \(0.436883\pi\) | |||||||
\(504\) | −7.70698 | + | 0.481936i | −0.343296 | + | 0.0214671i | ||||
\(505\) | −4.44238 | + | 7.69443i | −0.197683 | + | 0.342398i | ||||
\(506\) | 13.4864 | + | 7.78638i | 0.599544 | + | 0.346147i | ||||
\(507\) | 7.57522 | + | 25.1076i | 0.336427 | + | 1.11507i | ||||
\(508\) | −13.5026 | + | 7.79574i | −0.599082 | + | 0.345880i | ||||
\(509\) | 17.7292 | − | 30.7078i | 0.785832 | − | 1.36110i | −0.142668 | − | 0.989771i | \(-0.545568\pi\) |
0.928501 | − | 0.371331i | \(-0.121098\pi\) | |||||||
\(510\) | 8.74726 | + | 2.05341i | 0.387335 | + | 0.0909264i | ||||
\(511\) | 9.55629i | 0.422745i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.460415 | − | 2.71271i | 0.0203278 | − | 0.119769i | ||||
\(514\) | −6.02954 | + | 10.4435i | −0.265952 | + | 0.460642i | ||||
\(515\) | 9.11135 | − | 5.26044i | 0.401494 | − | 0.231803i | ||||
\(516\) | 12.8127 | − | 3.86571i | 0.564046 | − | 0.170178i | ||||
\(517\) | 30.0238 | + | 17.3343i | 1.32045 | + | 0.762360i | ||||
\(518\) | 0.863261 | − | 1.49521i | 0.0379295 | − | 0.0656959i | ||||
\(519\) | 3.67131 | + | 3.44891i | 0.161153 | + | 0.151390i | ||||
\(520\) | −4.59412 | + | 2.65242i | −0.201466 | + | 0.116316i | ||||
\(521\) | 13.5448 | − | 7.82011i | 0.593410 | − | 0.342605i | −0.173035 | − | 0.984916i | \(-0.555357\pi\) |
0.766445 | + | 0.642310i | \(0.222024\pi\) | |||||||
\(522\) | −11.2759 | + | 22.6934i | −0.493531 | + | 0.993263i | ||||
\(523\) | 26.2117i | 1.14616i | 0.819500 | + | 0.573078i | \(0.194251\pi\) | ||||
−0.819500 | + | 0.573078i | \(0.805749\pi\) | |||||||
\(524\) | 16.4069 | − | 9.47252i | 0.716738 | − | 0.413809i | ||||
\(525\) | 3.05255 | − | 3.24939i | 0.133224 | − | 0.141815i | ||||
\(526\) | 2.04756i | 0.0892780i | ||||||||
\(527\) | −22.7100 | + | 17.8459i | −0.989263 | + | 0.777380i | ||||
\(528\) | −6.08863 | + | 6.48126i | −0.264973 | + | 0.282060i | ||||
\(529\) | −13.7998 | −0.599992 | ||||||||
\(530\) | 0.822328 | + | 1.42431i | 0.0357196 | + | 0.0618682i | ||||
\(531\) | −36.1245 | + | 2.25895i | −1.56767 | + | 0.0980302i | ||||
\(532\) | 0.681505 | − | 1.18040i | 0.0295470 | − | 0.0511769i | ||||
\(533\) | 30.1811 | + | 52.2752i | 1.30729 | + | 2.26429i | ||||
\(534\) | 5.89420 | − | 25.1085i | 0.255067 | − | 1.08655i | ||||
\(535\) | −12.9437 | −0.559605 | ||||||||
\(536\) | −6.89980 | − | 3.98360i | −0.298026 | − | 0.172065i | ||||
\(537\) | 2.85999 | + | 9.47926i | 0.123418 | + | 0.409060i | ||||
\(538\) | 23.3961 | + | 13.5077i | 1.00868 | + | 0.582360i | ||||
\(539\) | 0.961271 | + | 1.66497i | 0.0414049 | + | 0.0717154i | ||||
\(540\) | 1.80845 | + | 4.87129i | 0.0778234 | + | 0.209627i | ||||
\(541\) | −2.17123 | − | 3.76069i | −0.0933487 | − | 0.161685i | 0.815570 | − | 0.578659i | \(-0.196424\pi\) |
−0.908918 | + | 0.416974i | \(0.863090\pi\) | |||||||
\(542\) | 3.17938 | 0.136566 | ||||||||
\(543\) | −19.3179 | − | 18.1476i | −0.829009 | − | 0.778788i | ||||
\(544\) | −4.49252 | + | 2.59376i | −0.192615 | + | 0.111206i | ||||
\(545\) | 1.17033 | + | 0.675690i | 0.0501314 | + | 0.0289434i | ||||
\(546\) | 23.0247 | + | 5.40503i | 0.985368 | + | 0.231314i | ||||
\(547\) | −3.95664 | + | 6.85310i | −0.169174 | + | 0.293017i | −0.938130 | − | 0.346285i | \(-0.887443\pi\) |
0.768956 | + | 0.639302i | \(0.220777\pi\) | |||||||
\(548\) | −2.98906 | + | 5.17720i | −0.127686 | + | 0.221159i | ||||
\(549\) | 9.42832 | − | 18.9751i | 0.402391 | − | 0.809836i | ||||
\(550\) | − | 5.13414i | − | 0.218920i | ||||||
\(551\) | −2.23641 | − | 3.87357i | −0.0952741 | − | 0.165020i | ||||
\(552\) | −1.20064 | + | 5.11459i | −0.0511028 | + | 0.217691i | ||||
\(553\) | −22.5315 | − | 13.0086i | −0.958137 | − | 0.553180i | ||||
\(554\) | 16.5427 | 0.702833 | ||||||||
\(555\) | −1.13103 | − | 0.265508i | −0.0480096 | − | 0.0112702i | ||||
\(556\) | 20.6001i | 0.873640i | ||||||||
\(557\) | −23.6372 | −1.00154 | −0.500770 | − | 0.865580i | \(-0.666950\pi\) | ||||
−0.500770 | + | 0.865580i | \(0.666950\pi\) | |||||||
\(558\) | −15.8621 | − | 5.23389i | −0.671496 | − | 0.221568i | ||||
\(559\) | −40.9891 | −1.73365 | ||||||||
\(560\) | 2.57401i | 0.108772i | ||||||||
\(561\) | −44.9096 | − | 10.5425i | −1.89609 | − | 0.445104i | ||||
\(562\) | 1.55339 | 0.0655256 | ||||||||
\(563\) | −9.05588 | − | 5.22841i | −0.381660 | − | 0.220351i | 0.296880 | − | 0.954915i | \(-0.404054\pi\) |
−0.678540 | + | 0.734563i | \(0.737387\pi\) | |||||||
\(564\) | −2.67291 | + | 11.3862i | −0.112550 | + | 0.479447i | ||||
\(565\) | 2.35692 | + | 4.08230i | 0.0991562 | + | 0.171744i | ||||
\(566\) | − | 3.03122i | − | 0.127412i | ||||||
\(567\) | 8.99349 | − | 21.3491i | 0.377691 | − | 0.896579i | ||||
\(568\) | −4.88050 | + | 8.45327i | −0.204781 | + | 0.354691i | ||||
\(569\) | 5.12252 | − | 8.87246i | 0.214747 | − | 0.371953i | −0.738447 | − | 0.674311i | \(-0.764441\pi\) |
0.953194 | + | 0.302358i | \(0.0977739\pi\) | |||||||
\(570\) | −0.892896 | − | 0.209606i | −0.0373993 | − | 0.00877944i | ||||
\(571\) | 27.0944 | + | 15.6430i | 1.13387 | + | 0.654638i | 0.944904 | − | 0.327346i | \(-0.106154\pi\) |
0.188962 | + | 0.981984i | \(0.439488\pi\) | |||||||
\(572\) | 23.5869 | − | 13.6179i | 0.986216 | − | 0.569392i | ||||
\(573\) | −6.29485 | − | 5.91352i | −0.262971 | − | 0.247041i | ||||
\(574\) | 29.2889 | 1.22250 | ||||||||
\(575\) | −1.51659 | − | 2.62681i | −0.0632462 | − | 0.109546i | ||||
\(576\) | −2.68663 | − | 1.33493i | −0.111943 | − | 0.0556220i | ||||
\(577\) | −12.2866 | − | 21.2810i | −0.511498 | − | 0.885941i | −0.999911 | − | 0.0133282i | \(-0.995757\pi\) |
0.488413 | − | 0.872613i | \(-0.337576\pi\) | |||||||
\(578\) | −8.58260 | − | 4.95516i | −0.356989 | − | 0.206108i | ||||
\(579\) | 8.08952 | + | 26.8122i | 0.336189 | + | 1.11428i | ||||
\(580\) | 7.31514 | + | 4.22340i | 0.303745 | + | 0.175367i | ||||
\(581\) | −20.4451 | −0.848207 | ||||||||
\(582\) | 2.55838 | − | 10.8984i | 0.106048 | − | 0.451753i | ||||
\(583\) | −4.22194 | − | 7.31262i | −0.174855 | − | 0.302858i | ||||
\(584\) | −1.85630 | + | 3.21521i | −0.0768143 | + | 0.133046i | ||||
\(585\) | −0.993232 | − | 15.8835i | −0.0410651 | − | 0.656701i | ||||
\(586\) | 3.89138 | + | 6.74006i | 0.160751 | + | 0.278429i | ||||
\(587\) | −28.3116 | −1.16855 | −0.584273 | − | 0.811557i | \(-0.698620\pi\) | ||||
−0.584273 | + | 0.811557i | \(0.698620\pi\) | |||||||
\(588\) | −0.444079 | + | 0.472716i | −0.0183135 | + | 0.0194945i | ||||
\(589\) | 2.31817 | − | 1.82166i | 0.0955187 | − | 0.0750603i | ||||
\(590\) | 12.0650i | 0.496709i | ||||||||
\(591\) | 10.2208 | − | 10.8799i | 0.420426 | − | 0.447538i | ||||
\(592\) | 0.580888 | − | 0.335376i | 0.0238744 | − | 0.0137839i | ||||
\(593\) | − | 26.2219i | − | 1.07680i | −0.842689 | − | 0.538401i | \(-0.819028\pi\) | ||
0.842689 | − | 0.538401i | \(-0.180972\pi\) | |||||||
\(594\) | −9.28484 | − | 25.0099i | −0.380961 | − | 1.02617i | ||||
\(595\) | −11.5638 | + | 6.67636i | −0.474070 | + | 0.273704i | ||||
\(596\) | 20.8920 | − | 12.0620i | 0.855771 | − | 0.494080i | ||||
\(597\) | 7.16975 | + | 6.73541i | 0.293438 | + | 0.275662i | ||||
\(598\) | 8.04526 | − | 13.9348i | 0.328995 | − | 0.569836i | ||||
\(599\) | 29.8917 | + | 17.2580i | 1.22134 | + | 0.705141i | 0.965204 | − | 0.261500i | \(-0.0842171\pi\) |
0.256136 | + | 0.966641i | \(0.417550\pi\) | |||||||
\(600\) | 1.65822 | − | 0.500302i | 0.0676966 | − | 0.0204247i | ||||
\(601\) | −23.6671 | + | 13.6642i | −0.965403 | + | 0.557375i | −0.897832 | − | 0.440339i | \(-0.854858\pi\) |
−0.0675710 | + | 0.997714i | \(0.521525\pi\) | |||||||
\(602\) | −9.94437 | + | 17.2241i | −0.405302 | + | 0.702004i | ||||
\(603\) | 19.9132 | − | 13.2194i | 0.810928 | − | 0.538334i | ||||
\(604\) | − | 16.5788i | − | 0.674581i | ||||||
\(605\) | 15.3594i | 0.624447i | ||||||||
\(606\) | 14.9816 | + | 3.51691i | 0.608586 | + | 0.142865i | ||||
\(607\) | 11.0332 | − | 19.1100i | 0.447822 | − | 0.775651i | −0.550422 | − | 0.834887i | \(-0.685533\pi\) |
0.998244 | + | 0.0592358i | \(0.0188664\pi\) | |||||||
\(608\) | 0.458584 | − | 0.264764i | 0.0185980 | − | 0.0107376i | ||||
\(609\) | −10.8776 | − | 36.0533i | −0.440784 | − | 1.46095i | ||||
\(610\) | −6.11655 | − | 3.53139i | −0.247652 | − | 0.142982i | ||||
\(611\) | 17.9106 | − | 31.0221i | 0.724585 | − | 1.25502i | ||||
\(612\) | −0.971266 | − | 15.5322i | −0.0392611 | − | 0.627852i | ||||
\(613\) | 24.3755 | − | 14.0732i | 0.984517 | − | 0.568411i | 0.0808859 | − | 0.996723i | \(-0.474225\pi\) |
0.903631 | + | 0.428312i | \(0.140892\pi\) | |||||||
\(614\) | 9.90659 | − | 5.71957i | 0.399797 | − | 0.230823i | ||||
\(615\) | −5.69279 | − | 18.8684i | −0.229556 | − | 0.760848i | ||||
\(616\) | − | 13.2153i | − | 0.532461i | ||||||
\(617\) | 24.9200 | − | 14.3875i | 1.00324 | − | 0.579221i | 0.0940345 | − | 0.995569i | \(-0.470024\pi\) |
0.909205 | + | 0.416348i | \(0.136690\pi\) | |||||||
\(618\) | −13.2814 | − | 12.4768i | −0.534256 | − | 0.501891i | ||||
\(619\) | − | 14.4354i | − | 0.580208i | −0.956995 | − | 0.290104i | \(-0.906310\pi\) | ||
0.956995 | − | 0.290104i | \(-0.0936899\pi\) | |||||||
\(620\) | −2.07122 | + | 5.16818i | −0.0831820 | + | 0.207559i | ||||
\(621\) | −12.1382 | − | 10.0533i | −0.487090 | − | 0.403425i | ||||
\(622\) | −7.22744 | −0.289794 | ||||||||
\(623\) | 19.1642 | + | 33.1933i | 0.767796 | + | 1.32986i | ||||
\(624\) | 6.69674 | + | 6.29106i | 0.268084 | + | 0.251844i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 6.50334 | + | 11.2641i | 0.259926 | + | 0.450205i | ||||
\(627\) | 4.58425 | + | 1.07615i | 0.183077 | + | 0.0429772i | ||||
\(628\) | −14.6508 | −0.584631 | ||||||||
\(629\) | 3.01337 | + | 1.73977i | 0.120151 | + | 0.0693691i | ||||
\(630\) | −6.91541 | − | 3.43612i | −0.275517 | − | 0.136898i | ||||
\(631\) | 18.2779 | + | 10.5528i | 0.727633 | + | 0.420099i | 0.817556 | − | 0.575850i | \(-0.195329\pi\) |
−0.0899227 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(632\) | −5.05381 | − | 8.75345i | −0.201030 | − | 0.348194i | ||||
\(633\) | 0.695981 | + | 2.30679i | 0.0276628 | + | 0.0916866i | ||||
\(634\) | 11.3812 | + | 19.7129i | 0.452006 | + | 0.782898i | ||||
\(635\) | −15.5915 | −0.618729 | ||||||||
\(636\) | 1.95041 | − | 2.07619i | 0.0773390 | − | 0.0823262i | ||||
\(637\) | 1.72033 | − | 0.993232i | 0.0681619 | − | 0.0393533i | ||||
\(638\) | −37.5569 | − | 21.6835i | −1.48689 | − | 0.858458i | ||||
\(639\) | −16.1957 | − | 24.3966i | −0.640690 | − | 0.965114i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −13.7198 | + | 23.7633i | −0.541898 | + | 0.938594i | 0.456898 | + | 0.889519i | \(0.348961\pi\) |
−0.998795 | + | 0.0490748i | \(0.984373\pi\) | |||||||
\(642\) | 6.47576 | + | 21.4635i | 0.255578 | + | 0.847098i | ||||
\(643\) | 34.0135i | 1.34136i | 0.741747 | + | 0.670680i | \(0.233998\pi\) | ||||
−0.741747 | + | 0.670680i | \(0.766002\pi\) | |||||||
\(644\) | −3.90372 | − | 6.76144i | −0.153828 | − | 0.266438i | ||||
\(645\) | 13.0289 | + | 3.05853i | 0.513014 | + | 0.120429i | ||||
\(646\) | 2.37891 | + | 1.37347i | 0.0935971 | + | 0.0540383i | ||||
\(647\) | −12.8461 | −0.505031 | −0.252516 | − | 0.967593i | \(-0.581258\pi\) | ||||
−0.252516 | + | 0.967593i | \(0.581258\pi\) | |||||||
\(648\) | 7.17291 | − | 5.43593i | 0.281779 | − | 0.213544i | ||||
\(649\) | − | 61.9435i | − | 2.43149i | ||||||
\(650\) | −5.30484 | −0.208073 | ||||||||
\(651\) | 22.5063 | − | 10.4710i | 0.882092 | − | 0.410389i | ||||
\(652\) | −22.4774 | −0.880281 | ||||||||
\(653\) | − | 0.0217666i | − | 0.000851794i | −1.00000 | 0.000425897i | \(-0.999864\pi\) | |||
1.00000 | 0.000425897i | \(-0.000135567\pi\) | ||||||||
\(654\) | 0.534925 | − | 2.27871i | 0.0209172 | − | 0.0891047i | ||||
\(655\) | 18.9450 | 0.740244 | ||||||||
\(656\) | 9.85425 | + | 5.68936i | 0.384744 | + | 0.222132i | ||||
\(657\) | −6.16004 | − | 9.27927i | −0.240326 | − | 0.362019i | ||||
\(658\) | −8.69058 | − | 15.0525i | −0.338794 | − | 0.586808i | ||||
\(659\) | − | 42.3998i | − | 1.65166i | −0.563917 | − | 0.825832i | \(-0.690706\pi\) | ||
0.563917 | − | 0.825832i | \(-0.309294\pi\) | |||||||
\(660\) | −8.51353 | + | 2.56862i | −0.331389 | + | 0.0999834i | ||||
\(661\) | 3.57820 | − | 6.19762i | 0.139176 | − | 0.241059i | −0.788009 | − | 0.615664i | \(-0.788888\pi\) |
0.927185 | + | 0.374604i | \(0.122221\pi\) | |||||||
\(662\) | −2.45387 | + | 4.25023i | −0.0953724 | + | 0.165190i | ||||
\(663\) | −10.8930 | + | 46.4028i | −0.423049 | + | 1.80213i | ||||
\(664\) | −6.87875 | − | 3.97145i | −0.266947 | − | 0.154122i | ||||
\(665\) | 1.18040 | − | 0.681505i | 0.0457740 | − | 0.0264276i | ||||
\(666\) | 0.125586 | + | 2.00833i | 0.00486635 | + | 0.0778213i | ||||
\(667\) | −25.6207 | −0.992036 | ||||||||
\(668\) | −8.21327 | − | 14.2258i | −0.317781 | − | 0.550413i | ||||
\(669\) | 22.1559 | − | 6.68466i | 0.856597 | − | 0.258444i | ||||
\(670\) | −3.98360 | − | 6.89980i | −0.153900 | − | 0.266563i | ||||
\(671\) | 31.4032 | + | 18.1307i | 1.21231 | + | 0.699926i | ||||
\(672\) | 4.26828 | − | 1.28778i | 0.164653 | − | 0.0496773i | ||||
\(673\) | −15.4883 | − | 8.94220i | −0.597032 | − | 0.344696i | 0.170841 | − | 0.985299i | \(-0.445351\pi\) |
−0.767873 | + | 0.640602i | \(0.778685\pi\) | |||||||
\(674\) | −27.0752 | −1.04290 | ||||||||
\(675\) | −0.869482 | + | 5.12289i | −0.0334664 | + | 0.197180i | ||||
\(676\) | −7.57064 | − | 13.1127i | −0.291179 | − | 0.504336i | ||||
\(677\) | 16.7056 | − | 28.9349i | 0.642048 | − | 1.11206i | −0.342927 | − | 0.939362i | \(-0.611418\pi\) |
0.984975 | − | 0.172698i | \(-0.0552483\pi\) | |||||||
\(678\) | 5.59018 | − | 5.95067i | 0.214690 | − | 0.228534i | ||||
\(679\) | 8.31822 | + | 14.4076i | 0.319224 | + | 0.552912i | ||||
\(680\) | −5.18752 | −0.198932 | ||||||||
\(681\) | −19.6179 | − | 18.4295i | −0.751759 | − | 0.706218i | ||||
\(682\) | 10.6339 | − | 26.5341i | 0.407193 | − | 1.01604i | ||||
\(683\) | − | 19.4433i | − | 0.743979i | −0.928237 | − | 0.371990i | \(-0.878676\pi\) | ||
0.928237 | − | 0.371990i | \(-0.121324\pi\) | |||||||
\(684\) | 0.0991442 | + | 1.58549i | 0.00379087 | + | 0.0606226i | ||||
\(685\) | −5.17720 | + | 2.98906i | −0.197811 | + | 0.114206i | ||||
\(686\) | − | 18.9820i | − | 0.724734i | ||||||
\(687\) | 24.1386 | − | 7.28285i | 0.920944 | − | 0.277858i | ||||
\(688\) | −6.69156 | + | 3.86337i | −0.255113 | + | 0.147290i | ||||
\(689\) | −7.55575 | + | 4.36231i | −0.287851 | + | 0.166191i | ||||
\(690\) | −3.59708 | + | 3.82904i | −0.136939 | + | 0.145769i | ||||
\(691\) | −10.6087 | + | 18.3747i | −0.403572 | + | 0.699007i | −0.994154 | − | 0.107970i | \(-0.965565\pi\) |
0.590582 | + | 0.806978i | \(0.298898\pi\) | |||||||
\(692\) | −2.51861 | − | 1.45412i | −0.0957430 | − | 0.0552772i | ||||
\(693\) | 35.5047 | + | 17.6415i | 1.34871 | + | 0.670146i | ||||
\(694\) | 17.7512 | − | 10.2487i | 0.673827 | − | 0.389034i | ||||
\(695\) | −10.3001 | + | 17.8402i | −0.390704 | + | 0.676718i | ||||
\(696\) | 3.34355 | − | 14.2431i | 0.126737 | − | 0.539883i | ||||
\(697\) | 59.0273i | 2.23582i | ||||||||
\(698\) | − | 20.0539i | − | 0.759053i | ||||||
\(699\) | 1.14644 | − | 4.88367i | 0.0433622 | − | 0.184718i | ||||
\(700\) | −1.28701 | + | 2.22916i | −0.0486443 | + | 0.0842543i | ||||
\(701\) | −28.4019 | + | 16.3979i | −1.07273 | + | 0.619338i | −0.928925 | − | 0.370268i | \(-0.879266\pi\) |
−0.143801 | + | 0.989607i | \(0.545932\pi\) | |||||||
\(702\) | −25.8414 | + | 9.59354i | −0.975321 | + | 0.362085i | ||||
\(703\) | −0.307596 | − | 0.177591i | −0.0116012 | − | 0.00669796i | ||||
\(704\) | 2.56707 | − | 4.44629i | 0.0967500 | − | 0.167576i | ||||
\(705\) | −8.00793 | + | 8.52432i | −0.301596 | + | 0.321045i | ||||
\(706\) | −7.28255 | + | 4.20458i | −0.274082 | + | 0.158242i | ||||
\(707\) | −19.8056 | + | 11.4347i | −0.744865 | + | 0.430048i | ||||
\(708\) | 20.0065 | − | 6.03616i | 0.751890 | − | 0.226853i | ||||
\(709\) | − | 49.3472i | − | 1.85327i | −0.375960 | − | 0.926636i | \(-0.622687\pi\) | ||
0.375960 | − | 0.926636i | \(-0.377313\pi\) | |||||||
\(710\) | −8.45327 | + | 4.88050i | −0.317245 | + | 0.183162i | ||||
\(711\) | 30.2637 | − | 1.89246i | 1.13498 | − | 0.0709729i | ||||
\(712\) | 14.8905i | 0.558045i | ||||||||
\(713\) | −2.39732 | − | 16.7170i | −0.0897802 | − | 0.626057i | ||||
\(714\) | 16.8563 | + | 15.8351i | 0.630831 | + | 0.592615i | ||||
\(715\) | 27.2358 | 1.01856 | ||||||||
\(716\) | −2.85826 | − | 4.95065i | −0.106818 | − | 0.185015i | ||||
\(717\) | 6.50937 | − | 6.92913i | 0.243097 | − | 0.258773i | ||||
\(718\) | 12.7070 | − | 22.0093i | 0.474223 | − | 0.821378i | ||||
\(719\) | −3.77117 | − | 6.53187i | −0.140641 | − | 0.243598i | 0.787097 | − | 0.616829i | \(-0.211583\pi\) |
−0.927738 | + | 0.373232i | \(0.878250\pi\) | |||||||
\(720\) | −1.65922 | − | 2.49940i | −0.0618356 | − | 0.0931470i | ||||
\(721\) | 27.0809 | 1.00854 | ||||||||
\(722\) | 16.2116 | + | 9.35980i | 0.603335 | + | 0.348336i | ||||
\(723\) | −8.83535 | + | 2.66571i | −0.328590 | + | 0.0991389i | ||||
\(724\) | 13.2525 | + | 7.65134i | 0.492525 | + | 0.284360i | ||||
\(725\) | 4.22340 | + | 7.31514i | 0.156853 | + | 0.271677i | ||||
\(726\) | 25.4692 | − | 7.68432i | 0.945251 | − | 0.285192i | ||||
\(727\) | 20.0826 | + | 34.7841i | 0.744822 | + | 1.29007i | 0.950278 | + | 0.311403i | \(0.100799\pi\) |
−0.205456 | + | 0.978666i | \(0.565868\pi\) | |||||||
\(728\) | −13.6547 | −0.506077 | ||||||||
\(729\) | 5.02899 | + | 26.5275i | 0.186259 | + | 0.982501i | ||||
\(730\) | −3.21521 | + | 1.85630i | −0.119000 | + | 0.0687048i | ||||
\(731\) | −34.7126 | − | 20.0413i | −1.28389 | − | 0.741255i | ||||
\(732\) | −2.79571 | + | 11.9094i | −0.103332 | + | 0.440183i | ||||
\(733\) | 7.73727 | − | 13.4013i | 0.285783 | − | 0.494990i | −0.687016 | − | 0.726642i | \(-0.741080\pi\) |
0.972799 | + | 0.231652i | \(0.0744132\pi\) | |||||||
\(734\) | −8.65053 | + | 14.9832i | −0.319297 | + | 0.553038i | ||||
\(735\) | −0.620942 | + | 0.187344i | −0.0229038 | + | 0.00691031i | ||||
\(736\) | − | 3.03318i | − | 0.111805i | ||||||
\(737\) | 20.4524 | + | 35.4245i | 0.753372 | + | 1.30488i | ||||
\(738\) | −28.4399 | + | 18.8798i | −1.04689 | + | 0.694976i | ||||
\(739\) | 20.8170 | + | 12.0187i | 0.765767 | + | 0.442116i | 0.831362 | − | 0.555731i | \(-0.187561\pi\) |
−0.0655955 | + | 0.997846i | \(0.520895\pi\) | |||||||
\(740\) | 0.670752 | 0.0246573 | ||||||||
\(741\) | 1.11193 | − | 4.73667i | 0.0408477 | − | 0.174006i | ||||
\(742\) | 4.23336i | 0.155412i | ||||||||
\(743\) | −16.5869 | −0.608516 | −0.304258 | − | 0.952590i | \(-0.598409\pi\) | ||||
−0.304258 | + | 0.952590i | \(0.598409\pi\) | |||||||
\(744\) | 9.60622 | + | 0.848884i | 0.352181 | + | 0.0311216i | ||||
\(745\) | 24.1241 | 0.883837 | ||||||||
\(746\) | − | 14.4940i | − | 0.530663i | ||||||
\(747\) | 19.8525 | − | 13.1790i | 0.726363 | − | 0.482196i | ||||
\(748\) | 26.6334 | 0.973814 | ||||||||
\(749\) | −28.8536 | − | 16.6586i | −1.05429 | − | 0.608693i | ||||
\(750\) | 1.68621 | + | 0.395836i | 0.0615718 | + | 0.0144539i | ||||
\(751\) | −15.3278 | − | 26.5485i | −0.559318 | − | 0.968768i | −0.997553 | − | 0.0699074i | \(-0.977730\pi\) |
0.438235 | − | 0.898860i | \(-0.355604\pi\) | |||||||
\(752\) | − | 6.75256i | − | 0.246240i | ||||||
\(753\) | −0.393174 | − | 1.30315i | −0.0143281 | − | 0.0474895i | ||||
\(754\) | −22.4044 | + | 38.8056i | −0.815921 | + | 1.41322i | ||||
\(755\) | 8.28939 | − | 14.3576i | 0.301682 | − | 0.522528i | ||||
\(756\) | −2.23806 | + | 13.1864i | −0.0813974 | + | 0.479584i | ||||
\(757\) | 15.7629 | + | 9.10072i | 0.572913 | + | 0.330771i | 0.758312 | − | 0.651892i | \(-0.226024\pi\) |
−0.185399 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(758\) | 17.1608 | − | 9.90778i | 0.623308 | − | 0.359867i | ||||
\(759\) | 18.4679 | − | 19.6588i | 0.670343 | − | 0.713570i | ||||
\(760\) | 0.529528 | 0.0192080 | ||||||||
\(761\) | 18.2034 | + | 31.5292i | 0.659873 | + | 1.14293i | 0.980648 | + | 0.195778i | \(0.0627232\pi\) |
−0.320775 | + | 0.947155i | \(0.603943\pi\) | |||||||
\(762\) | 7.80045 | + | 25.8541i | 0.282581 | + | 0.936596i | ||||
\(763\) | 1.73923 | + | 3.01244i | 0.0629645 | + | 0.109058i | ||||
\(764\) | 4.31841 | + | 2.49324i | 0.156235 | + | 0.0902022i | ||||
\(765\) | 6.92496 | − | 13.9369i | 0.250373 | − | 0.503891i | ||||
\(766\) | 3.42236 | + | 1.97590i | 0.123655 | + | 0.0713922i | ||||
\(767\) | −64.0030 | −2.31101 | ||||||||
\(768\) | 1.68621 | + | 0.395836i | 0.0608460 | + | 0.0142835i | ||||
\(769\) | 15.0861 | + | 26.1298i | 0.544017 | + | 0.942265i | 0.998668 | + | 0.0515956i | \(0.0164307\pi\) |
−0.454651 | + | 0.890670i | \(0.650236\pi\) | |||||||
\(770\) | 6.60766 | − | 11.4448i | 0.238124 | − | 0.412442i | ||||
\(771\) | 15.2232 | + | 14.3010i | 0.548251 | + | 0.515038i | ||||
\(772\) | −8.08463 | − | 14.0030i | −0.290972 | − | 0.503979i | ||||
\(773\) | 14.9673 | 0.538336 | 0.269168 | − | 0.963093i | \(-0.413251\pi\) | ||||
0.269168 | + | 0.963093i | \(0.413251\pi\) | |||||||
\(774\) | −1.44669 | − | 23.1350i | −0.0520002 | − | 0.831572i | ||||
\(775\) | −4.37781 | + | 3.44017i | −0.157256 | + | 0.123574i | ||||
\(776\) | 6.46323i | 0.232016i | ||||||||
\(777\) | −2.17954 | − | 2.04750i | −0.0781904 | − | 0.0734537i | ||||
\(778\) | −16.8346 | + | 9.71945i | −0.603549 | + | 0.348459i | ||||
\(779\) | − | 6.02534i | − | 0.215880i | ||||||
\(780\) | 2.65402 | + | 8.79659i | 0.0950292 | + | 0.314969i | ||||
\(781\) | 43.4002 | − | 25.0571i | 1.55298 | − | 0.896615i | ||||
\(782\) | 13.6266 | − | 7.86734i | 0.487287 | − | 0.281335i | ||||
\(783\) | 33.8025 | + | 27.9964i | 1.20800 | + | 1.00051i | ||||
\(784\) | 0.187231 | − | 0.324294i | 0.00668684 | − | 0.0115819i | ||||
\(785\) | −12.6880 | − | 7.32540i | −0.452853 | − | 0.261455i | ||||
\(786\) | −9.47824 | − | 31.4151i | −0.338078 | − | 1.12054i | ||||
\(787\) | −0.227315 | + | 0.131240i | −0.00810290 | + | 0.00467821i | −0.504046 | − | 0.863677i | \(-0.668156\pi\) |
0.495943 | + | 0.868355i | \(0.334822\pi\) | |||||||
\(788\) | −4.30925 | + | 7.46384i | −0.153511 | + | 0.265888i | ||||
\(789\) | 3.45263 | + | 0.810500i | 0.122917 | + | 0.0288546i | ||||
\(790\) | − | 10.1076i | − | 0.359613i | ||||||
\(791\) | 12.1335i | 0.431416i | ||||||||
\(792\) | 8.51868 | + | 12.8322i | 0.302698 | + | 0.455974i | ||||
\(793\) | 18.7335 | − | 32.4473i | 0.665245 | − | 1.15224i | ||||
\(794\) | −20.7332 | + | 11.9703i | −0.735793 | + | 0.424810i | ||||
\(795\) | 2.72720 | − | 0.822824i | 0.0967239 | − | 0.0291826i | ||||
\(796\) | −4.91862 | − | 2.83976i | −0.174336 | − | 0.100653i | ||||
\(797\) | 4.06441 | − | 7.03976i | 0.143969 | − | 0.249361i | −0.785019 | − | 0.619472i | \(-0.787347\pi\) |
0.928988 | + | 0.370111i | \(0.120680\pi\) | |||||||
\(798\) | −1.72064 | − | 1.61641i | −0.0609101 | − | 0.0572202i | ||||
\(799\) | 30.3360 | − | 17.5145i | 1.07321 | − | 0.619618i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | −40.0052 | − | 19.8778i | −1.41351 | − | 0.702346i | ||||
\(802\) | − | 20.4973i | − | 0.723785i | ||||||
\(803\) | 16.5073 | − | 9.53051i | 0.582531 | − | 0.336324i | ||||
\(804\) | −9.44840 | + | 10.0577i | −0.333219 | + | 0.354707i | ||||
\(805\) | − | 7.80744i | − | 0.275176i | ||||||
\(806\) | −27.4163 | − | 10.9875i | −0.965699 | − | 0.387017i | ||||
\(807\) | 32.0379 | − | 34.1039i | 1.12779 | − | 1.20051i | ||||
\(808\) | −8.88476 | −0.312565 | ||||||||
\(809\) | 1.67849 | + | 2.90724i | 0.0590127 | + | 0.102213i | 0.894022 | − | 0.448022i | \(-0.147871\pi\) |
−0.835010 | + | 0.550235i | \(0.814538\pi\) | |||||||
\(810\) | 8.92989 | − | 1.12120i | 0.313764 | − | 0.0393949i | ||||
\(811\) | −17.9731 | + | 31.1303i | −0.631120 | + | 1.09313i | 0.356203 | + | 0.934409i | \(0.384071\pi\) |
−0.987323 | + | 0.158724i | \(0.949262\pi\) | |||||||
\(812\) | 10.8711 | + | 18.8293i | 0.381500 | + | 0.660777i | ||||
\(813\) | 1.25851 | − | 5.36111i | 0.0441380 | − | 0.188022i | ||||
\(814\) | −3.44373 | −0.120703 | ||||||||
\(815\) | −19.4660 | − | 11.2387i | −0.681863 | − | 0.393674i | ||||
\(816\) | 2.59533 | + | 8.60205i | 0.0908546 | + | 0.301132i | ||||
\(817\) | 3.54336 | + | 2.04576i | 0.123967 | + | 0.0715722i | ||||
\(818\) | 4.38047 | + | 7.58719i | 0.153160 | + | 0.265280i | ||||
\(819\) | 18.2281 | − | 36.6851i | 0.636940 | − | 1.28188i | ||||
\(820\) | 5.68936 | + | 9.85425i | 0.198681 | + | 0.344125i | ||||
\(821\) | −21.8066 | −0.761056 | −0.380528 | − | 0.924769i | \(-0.624258\pi\) | ||||
−0.380528 | + | 0.924769i | \(0.624258\pi\) | |||||||
\(822\) | 7.54669 | + | 7.08951i | 0.263221 | + | 0.247275i | ||||
\(823\) | 18.4662 | − | 10.6615i | 0.643692 | − | 0.371636i | −0.142343 | − | 0.989817i | \(-0.545464\pi\) |
0.786035 | + | 0.618181i | \(0.212130\pi\) | |||||||
\(824\) | 9.11135 | + | 5.26044i | 0.317409 | + | 0.183256i | ||||
\(825\) | −8.65725 | − | 2.03228i | −0.301407 | − | 0.0707548i | ||||
\(826\) | −15.5278 | + | 26.8949i | −0.540280 | + | 0.935792i | ||||
\(827\) | −12.4338 | + | 21.5359i | −0.432364 | + | 0.748877i | −0.997076 | − | 0.0764112i | \(-0.975654\pi\) |
0.564712 | + | 0.825288i | \(0.308987\pi\) | |||||||
\(828\) | 8.14902 | + | 4.04908i | 0.283198 | + | 0.140715i | ||||
\(829\) | 1.77571i | 0.0616728i | 0.999524 | + | 0.0308364i | \(0.00981709\pi\) | ||||
−0.999524 | + | 0.0308364i | \(0.990183\pi\) | |||||||
\(830\) | −3.97145 | − | 6.87875i | −0.137851 | − | 0.238765i | ||||
\(831\) | 6.54821 | − | 27.8945i | 0.227155 | − | 0.967651i | ||||
\(832\) | −4.59412 | − | 2.65242i | −0.159273 | − | 0.0919560i | ||||
\(833\) | 1.94253 | 0.0673047 | ||||||||
\(834\) | 34.7362 | + | 8.15428i | 1.20282 | + | 0.282360i | ||||
\(835\) | − | 16.4265i | − | 0.568464i | ||||||
\(836\) | −2.71867 | −0.0940270 | ||||||||
\(837\) | −15.1042 | + | 24.6751i | −0.522079 | + | 0.852897i | ||||
\(838\) | −17.8444 | −0.616423 | ||||||||
\(839\) | 2.30549i | 0.0795945i | 0.999208 | + | 0.0397973i | \(0.0126712\pi\) | ||||
−0.999208 | + | 0.0397973i | \(0.987329\pi\) | |||||||
\(840\) | 4.34033 | + | 1.01889i | 0.149756 | + | 0.0351550i | ||||
\(841\) | 42.3483 | 1.46029 | ||||||||
\(842\) | −14.3028 | − | 8.25775i | −0.492909 | − | 0.284581i | ||||
\(843\) | 0.614886 | − | 2.61934i | 0.0211778 | − | 0.0902148i | ||||
\(844\) | −0.695561 | − | 1.20475i | −0.0239422 | − | 0.0414691i | ||||
\(845\) | − | 15.1413i | − | 0.520876i | ||||||
\(846\) | 18.1416 | + | 9.01418i | 0.623721 | + | 0.309914i | ||||
\(847\) | −19.7676 | + | 34.2385i | −0.679222 | + | 1.17645i | ||||
\(848\) | −0.822328 | + | 1.42431i | −0.0282388 | + | 0.0489111i | ||||
\(849\) | −5.11128 | − | 1.19987i | −0.175419 | − | 0.0411793i | ||||
\(850\) | −4.49252 | − | 2.59376i | −0.154092 | − | 0.0889652i | ||||
\(851\) | −1.76194 | + | 1.01726i | −0.0603985 | + | 0.0348711i | ||||
\(852\) | 12.3221 | + | 11.5757i | 0.422149 | + | 0.396576i | ||||
\(853\) | −28.9723 | −0.991991 | −0.495996 | − | 0.868325i | \(-0.665197\pi\) | ||||
−0.495996 | + | 0.868325i | \(0.665197\pi\) | |||||||
\(854\) | −9.08985 | − | 15.7441i | −0.311048 | − | 0.538751i | ||||
\(855\) | −0.706882 | + | 1.42264i | −0.0241748 | + | 0.0486534i | ||||
\(856\) | −6.47185 | − | 11.2096i | −0.221203 | − | 0.383135i | ||||
\(857\) | −3.20393 | − | 1.84979i | −0.109444 | − | 0.0631877i | 0.444279 | − | 0.895889i | \(-0.353460\pi\) |
−0.553723 | + | 0.832701i | \(0.686793\pi\) | |||||||
\(858\) | −13.6261 | − | 45.1629i | −0.465187 | − | 1.54184i | ||||
\(859\) | −37.3943 | − | 21.5896i | −1.27588 | − | 0.736629i | −0.299791 | − | 0.954005i | \(-0.596917\pi\) |
−0.976088 | + | 0.217376i | \(0.930250\pi\) | |||||||
\(860\) | −7.72674 | −0.263480 | ||||||||
\(861\) | 11.5936 | − | 49.3874i | 0.395110 | − | 1.68312i | ||||
\(862\) | 6.18908 | + | 10.7198i | 0.210801 | + | 0.365118i | ||||
\(863\) | 7.65540 | − | 13.2595i | 0.260593 | − | 0.451360i | −0.705807 | − | 0.708405i | \(-0.749415\pi\) |
0.966400 | + | 0.257044i | \(0.0827486\pi\) | |||||||
\(864\) | −3.31444 | + | 4.00181i | −0.112759 | + | 0.136144i | ||||
\(865\) | −1.45412 | − | 2.51861i | −0.0494415 | − | 0.0856351i | ||||
\(866\) | −1.18613 | −0.0403063 | ||||||||
\(867\) | −11.7528 | + | 12.5107i | −0.399145 | + | 0.424884i | ||||
\(868\) | −11.2685 | + | 8.85503i | −0.382479 | + | 0.300559i | ||||
\(869\) | 51.8939i | 1.76038i | ||||||||
\(870\) | 10.0171 | − | 10.6631i | 0.339613 | − | 0.361513i | ||||
\(871\) | 36.6023 | − | 21.1324i | 1.24022 | − | 0.716043i | ||||
\(872\) | 1.35138i | 0.0457635i | ||||||||
\(873\) | −17.3643 | − | 8.62795i | −0.587692 | − | 0.292012i | ||||
\(874\) | −1.39097 | + | 0.803076i | −0.0470502 | + | 0.0271645i | ||||
\(875\) | −2.22916 | + | 1.28701i | −0.0753594 | + | 0.0435087i | ||||
\(876\) | 4.68674 | + | 4.40282i | 0.158350 | + | 0.148757i | ||||
\(877\) | −19.7173 | + | 34.1513i | −0.665805 | + | 1.15321i | 0.313262 | + | 0.949667i | \(0.398578\pi\) |
−0.979066 | + | 0.203541i | \(0.934755\pi\) | |||||||
\(878\) | 14.2541 | + | 8.22962i | 0.481053 | + | 0.277736i | ||||
\(879\) | 12.9055 | − | 3.89373i | 0.435293 | − | 0.131332i | ||||
\(880\) | 4.44629 | − | 2.56707i | 0.149884 | − | 0.0865358i | ||||
\(881\) | −9.28944 | + | 16.0898i | −0.312969 | + | 0.542079i | −0.979004 | − | 0.203842i | \(-0.934657\pi\) |
0.666035 | + | 0.745921i | \(0.267990\pi\) | |||||||
\(882\) | 0.621317 | + | 0.935931i | 0.0209208 | + | 0.0315144i | ||||
\(883\) | − | 17.4530i | − | 0.587339i | −0.955907 | − | 0.293669i | \(-0.905123\pi\) | ||
0.955907 | − | 0.293669i | \(-0.0948765\pi\) | |||||||
\(884\) | − | 27.5189i | − | 0.925562i | ||||||
\(885\) | 20.3442 | + | 4.77578i | 0.683863 | + | 0.160536i | ||||
\(886\) | −12.0992 | + | 20.9565i | −0.406481 | + | 0.704046i | ||||
\(887\) | 43.3396 | − | 25.0221i | 1.45520 | − | 0.840161i | 0.456433 | − | 0.889758i | \(-0.349127\pi\) |
0.998769 | + | 0.0495968i | \(0.0157936\pi\) | |||||||
\(888\) | −0.335578 | − | 1.11225i | −0.0112613 | − | 0.0373248i | ||||
\(889\) | −34.7559 | − | 20.0663i | −1.16568 | − | 0.673003i | ||||
\(890\) | −7.44525 | + | 12.8955i | −0.249565 | + | 0.432260i | ||||
\(891\) | −45.8473 | + | 5.75638i | −1.53594 | + | 0.192846i | ||||
\(892\) | −11.5712 | + | 6.68062i | −0.387432 | + | 0.223684i | ||||
\(893\) | −3.09662 | + | 1.78783i | −0.103624 | + | 0.0598275i | ||||
\(894\) | −12.0693 | − | 40.0030i | −0.403658 | − | 1.33790i | ||||
\(895\) | − | 5.71652i | − | 0.191082i | ||||||
\(896\) | −2.22916 | + | 1.28701i | −0.0744710 | + | 0.0429959i | ||||
\(897\) | −20.3124 | − | 19.0819i | −0.678212 | − | 0.637127i | ||||
\(898\) | − | 32.2944i | − | 1.07768i | ||||||
\(899\) | 6.67604 | + | 46.5535i | 0.222658 | + | 1.55265i | ||||
\(900\) | −0.187231 | − | 2.99415i | −0.00624105 | − | 0.0998051i | ||||
\(901\) | −8.53168 | −0.284231 | ||||||||
\(902\) | −29.2099 | − | 50.5931i | −0.972584 | − | 1.68457i | ||||
\(903\) | 25.1072 | + | 23.5863i | 0.835516 | + | 0.784902i | ||||
\(904\) | −2.35692 | + | 4.08230i | −0.0783899 | + | 0.135775i | ||||
\(905\) | 7.65134 | + | 13.2525i | 0.254339 | + | 0.440528i | ||||
\(906\) | −27.9553 | − | 6.56248i | −0.928754 | − | 0.218024i | ||||
\(907\) | 10.6428 | 0.353387 | 0.176693 | − | 0.984266i | \(-0.443460\pi\) | ||||
0.176693 | + | 0.984266i | \(0.443460\pi\) | |||||||
\(908\) | 13.4583 | + | 7.77017i | 0.446630 | + | 0.257862i | ||||
\(909\) | 11.8605 | − | 23.8700i | 0.393389 | − | 0.791720i | ||||
\(910\) | −11.8253 | − | 6.82736i | −0.392006 | − | 0.226325i | ||||
\(911\) | −0.881044 | − | 1.52601i | −0.0291903 | − | 0.0505591i | 0.851061 | − | 0.525066i | \(-0.175960\pi\) |
−0.880252 | + | 0.474507i | \(0.842626\pi\) | |||||||
\(912\) | −0.264924 | − | 0.878074i | −0.00877250 | − | 0.0290759i | ||||
\(913\) | 20.3900 | + | 35.3165i | 0.674809 | + | 1.16880i | ||||
\(914\) | 19.0886 | 0.631396 | ||||||||
\(915\) | −8.37583 | + | 8.91595i | −0.276897 | + | 0.294752i | ||||
\(916\) | −12.6066 | + | 7.27845i | −0.416535 | + | 0.240487i | ||||
\(917\) | 42.2315 | + | 24.3824i | 1.39461 | + | 0.805177i | ||||
\(918\) | −26.5751 | − | 4.51045i | −0.877108 | − | 0.148867i | ||||
\(919\) | 3.39521 | − | 5.88068i | 0.111998 | − | 0.193986i | −0.804578 | − | 0.593847i | \(-0.797608\pi\) |
0.916576 | + | 0.399861i | \(0.130942\pi\) | |||||||
\(920\) | 1.51659 | − | 2.62681i | 0.0500005 | − | 0.0866034i | ||||
\(921\) | −5.72303 | − | 18.9686i | −0.188580 | − | 0.625038i | ||||
\(922\) | − | 12.8115i | − | 0.421924i | ||||||
\(923\) | −25.8902 | − | 44.8432i | −0.852187 | − | 1.47603i | ||||
\(924\) | −22.2839 | − | 5.23111i | −0.733085 | − | 0.172091i | ||||
\(925\) | 0.580888 | + | 0.335376i | 0.0190995 | + | 0.0110271i | ||||
\(926\) | −20.6891 | −0.679885 | ||||||||
\(927\) | −26.2958 | + | 17.4565i | −0.863669 | + | 0.573346i | ||||
\(928\) | 8.44680i | 0.277280i | ||||||||
\(929\) | 59.0112 | 1.93610 | 0.968048 | − | 0.250766i | \(-0.0806824\pi\) | ||||
0.968048 | + | 0.250766i | \(0.0806824\pi\) | |||||||
\(930\) | 7.89479 | + | 5.53826i | 0.258880 | + | 0.181607i | ||||
\(931\) | −0.198288 | −0.00649864 | ||||||||
\(932\) | 2.89624i | 0.0948694i | ||||||||
\(933\) | −2.86089 | + | 12.1870i | −0.0936612 | + | 0.398985i | ||||
\(934\) | 23.8528 | 0.780489 | ||||||||
\(935\) | 23.0652 | + | 13.3167i | 0.754313 | + | 0.435503i | ||||
\(936\) | 13.2589 | − | 8.80191i | 0.433380 | − | 0.287699i | ||||
\(937\) | 1.34945 | + | 2.33732i | 0.0440847 | + | 0.0763569i | 0.887226 | − | 0.461335i | \(-0.152630\pi\) |
−0.843141 | + | 0.537692i | \(0.819296\pi\) | |||||||
\(938\) | − | 20.5077i | − | 0.669600i | ||||||
\(939\) | 21.5680 | − | 6.50727i | 0.703844 | − | 0.212357i | ||||
\(940\) | 3.37628 | − | 5.84788i | 0.110122 | − | 0.190737i | ||||
\(941\) | −4.89303 | + | 8.47498i | −0.159508 | + | 0.276276i | −0.934691 | − | 0.355460i | \(-0.884324\pi\) |
0.775183 | + | 0.631737i | \(0.217658\pi\) | |||||||
\(942\) | −5.79932 | + | 24.7044i | −0.188952 | + | 0.804912i | ||||
\(943\) | −29.8897 | − | 17.2568i | −0.973343 | − | 0.561960i | ||||
\(944\) | −10.4486 | + | 6.03251i | −0.340074 | + | 0.196342i | ||||
\(945\) | −8.53140 | + | 10.3007i | −0.277527 | + | 0.335082i | ||||
\(946\) | 39.6702 | 1.28979 | ||||||||
\(947\) | −16.6868 | − | 28.9023i | −0.542247 | − | 0.939199i | −0.998775 | − | 0.0494896i | \(-0.984241\pi\) |
0.456528 | − | 0.889709i | \(-0.349093\pi\) | |||||||
\(948\) | −16.7607 | + | 5.05686i | −0.544361 | + | 0.164239i | ||||
\(949\) | −9.84738 | − | 17.0562i | −0.319659 | − | 0.553666i | ||||
\(950\) | 0.458584 | + | 0.264764i | 0.0148784 | + | 0.00859007i | ||||
\(951\) | 37.7452 | − | 11.3881i | 1.22397 | − | 0.369284i | ||||
\(952\) | −11.5638 | − | 6.67636i | −0.374785 | − | 0.216382i | ||||
\(953\) | 12.6811 | 0.410781 | 0.205391 | − | 0.978680i | \(-0.434153\pi\) | ||||
0.205391 | + | 0.978680i | \(0.434153\pi\) | |||||||
\(954\) | −2.72885 | − | 4.11064i | −0.0883498 | − | 0.133087i | ||||
\(955\) | 2.49324 | + | 4.31841i | 0.0806793 | + | 0.139741i | ||||
\(956\) | −2.74446 | + | 4.75354i | −0.0887622 | + | 0.153741i | ||||
\(957\) | −51.4294 | + | 54.7458i | −1.66248 | + | 1.76968i | ||||
\(958\) | 1.51286 | + | 2.62035i | 0.0488783 | + | 0.0846596i | ||||
\(959\) | −15.3877 | −0.496896 | ||||||||
\(960\) | 1.26238 | + | 1.18591i | 0.0407433 | + | 0.0382751i | ||||
\(961\) | −29.7507 | + | 8.71199i | −0.959698 | + | 0.281032i | ||||
\(962\) | 3.55823i | 0.114722i | ||||||||
\(963\) | 38.7554 | − | 2.42347i | 1.24888 | − | 0.0780951i | ||||
\(964\) | 4.61436 | − | 2.66410i | 0.148619 | − | 0.0858050i | ||||
\(965\) | − | 16.1693i | − | 0.520507i | ||||||
\(966\) | −12.9465 | + | 3.90608i | −0.416546 | + | 0.125676i | ||||
\(967\) | 33.0932 | − | 19.1063i | 1.06420 | − | 0.614419i | 0.137612 | − | 0.990486i | \(-0.456057\pi\) |
0.926592 | + | 0.376068i | \(0.122724\pi\) | |||||||
\(968\) | −13.3016 | + | 7.67968i | −0.427529 | + | 0.246834i | ||||
\(969\) | 3.25762 | − | 3.46769i | 0.104650 | − | 0.111398i | ||||
\(970\) | −3.23162 | + | 5.59732i | −0.103761 | + | 0.179719i | ||||
\(971\) | 6.71435 | + | 3.87653i | 0.215474 | + | 0.124404i | 0.603853 | − | 0.797096i | \(-0.293632\pi\) |
−0.388379 | + | 0.921500i | \(0.626965\pi\) | |||||||
\(972\) | −6.32684 | − | 14.2468i | −0.202933 | − | 0.456966i | ||||
\(973\) | −45.9210 | + | 26.5125i | −1.47216 | + | 0.849951i | ||||
\(974\) | 19.0958 | − | 33.0749i | 0.611869 | − | 1.05979i | ||||
\(975\) | −2.09985 | + | 8.94508i | −0.0672489 | + | 0.286472i | ||||
\(976\) | − | 7.06279i | − | 0.226074i | ||||||
\(977\) | − | 45.6238i | − | 1.45963i | −0.683643 | − | 0.729817i | \(-0.739605\pi\) | ||
0.683643 | − | 0.729817i | \(-0.260395\pi\) | |||||||
\(978\) | −8.89736 | + | 37.9016i | −0.284506 | + | 1.21196i | ||||
\(979\) | 38.2249 | − | 66.2075i | 1.22167 | − | 2.11600i | ||||
\(980\) | 0.324294 | − | 0.187231i | 0.0103592 | − | 0.00598089i | ||||
\(981\) | −3.63065 | − | 1.80399i | −0.115918 | − | 0.0575971i | ||||
\(982\) | 22.0394 | + | 12.7244i | 0.703304 | + | 0.406053i | ||||
\(983\) | 1.48950 | − | 2.57989i | 0.0475077 | − | 0.0822858i | −0.841294 | − | 0.540578i | \(-0.818205\pi\) |
0.888801 | + | 0.458293i | \(0.151539\pi\) | |||||||
\(984\) | 13.4941 | − | 14.3643i | 0.430177 | − | 0.457918i | ||||
\(985\) | −7.46384 | + | 4.30925i | −0.237818 | + | 0.137304i | ||||
\(986\) | −37.9474 | + | 21.9089i | −1.20849 | + | 0.697723i | ||||
\(987\) | −28.8218 | + | 8.69583i | −0.917408 | + | 0.276791i | ||||
\(988\) | 2.80906i | 0.0893680i | ||||||||
\(989\) | 20.2967 | − | 11.7183i | 0.645398 | − | 0.372620i | ||||
\(990\) | 0.961271 | + | 15.3724i | 0.0305512 | + | 0.488566i | ||||
\(991\) | 3.63959i | 0.115615i | 0.998328 | + | 0.0578077i | \(0.0184110\pi\) | ||||
−0.998328 | + | 0.0578077i | \(0.981589\pi\) | |||||||
\(992\) | −5.51138 | + | 0.790363i | −0.174987 | + | 0.0250941i | ||||
\(993\) | 6.19546 | + | 5.82014i | 0.196607 | + | 0.184697i | ||||
\(994\) | −25.1249 | −0.796914 | ||||||||
\(995\) | −2.83976 | − | 4.91862i | −0.0900266 | − | 0.155931i | ||||
\(996\) | −9.41957 | + | 10.0270i | −0.298471 | + | 0.317718i | ||||
\(997\) | −23.0520 | + | 39.9272i | −0.730064 | + | 1.26451i | 0.226792 | + | 0.973943i | \(0.427176\pi\) |
−0.956855 | + | 0.290564i | \(0.906157\pi\) | |||||||
\(998\) | −4.13656 | − | 7.16472i | −0.130940 | − | 0.226795i | ||||
\(999\) | 3.43619 | + | 0.583207i | 0.108716 | + | 0.0184518i |
(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 | 930.2.o.e.161.20 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.161.7 | ✓ | 40 | |
31.26 | odd | 6 | inner | 930.2.o.e.491.17 | yes | 40 | |
93.26 | even | 6 | inner | 930.2.o.e.491.10 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.7 | ✓ | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.161.20 | yes | 40 | 1.1 | even | 1 | trivial | |
930.2.o.e.491.10 | yes | 40 | 93.26 | even | 6 | inner | |
930.2.o.e.491.17 | yes | 40 | 31.26 | odd | 6 | inner |