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 | 323.4 | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.z.729.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.03276 | + | 0.750346i | 0.730273 | + | 0.530574i | 0.889650 | − | 0.456643i | \(-0.150948\pi\) |
−0.159377 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(3\) | −0.796038 | + | 2.44995i | −0.459593 | + | 1.41448i | 0.406064 | + | 0.913844i | \(0.366901\pi\) |
−0.865657 | + | 0.500637i | \(0.833099\pi\) | |||||||
\(4\) | −0.114455 | − | 0.352256i | −0.0572275 | − | 0.176128i | ||||
\(5\) | 3.31004 | − | 2.40489i | 1.48030 | − | 1.07550i | 0.502835 | − | 0.864382i | \(-0.332290\pi\) |
0.977461 | − | 0.211115i | \(-0.0677096\pi\) | |||||||
\(6\) | −2.66043 | + | 1.93292i | −1.08612 | + | 0.789109i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0.935069 | − | 2.87785i | 0.330597 | − | 1.01747i | ||||
\(9\) | −2.94155 | − | 2.13716i | −0.980515 | − | 0.712386i | ||||
\(10\) | 5.22298 | 1.65165 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.954122 | 0.275431 | ||||||||
\(13\) | −3.55232 | − | 2.58091i | −0.985236 | − | 0.715816i | −0.0263633 | − | 0.999652i | \(-0.508393\pi\) |
−0.958873 | + | 0.283837i | \(0.908393\pi\) | |||||||
\(14\) | 0.394480 | − | 1.21408i | 0.105429 | − | 0.324478i | ||||
\(15\) | 3.25694 | + | 10.0238i | 0.840938 | + | 2.58814i | ||||
\(16\) | 2.52579 | − | 1.83509i | 0.631447 | − | 0.458773i | ||||
\(17\) | 3.39096 | − | 2.46368i | 0.822429 | − | 0.597530i | −0.0949779 | − | 0.995479i | \(-0.530278\pi\) |
0.917407 | + | 0.397949i | \(0.130278\pi\) | |||||||
\(18\) | −1.43431 | − | 4.41435i | −0.338070 | − | 1.04047i | ||||
\(19\) | 0.385900 | − | 1.18768i | 0.0885315 | − | 0.272472i | −0.896982 | − | 0.442066i | \(-0.854246\pi\) |
0.985514 | + | 0.169594i | \(0.0542457\pi\) | |||||||
\(20\) | −1.22599 | − | 0.890732i | −0.274139 | − | 0.199174i | ||||
\(21\) | 2.57603 | 0.562137 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.97180 | 1.03669 | 0.518346 | − | 0.855171i | \(-0.326548\pi\) | ||||
0.518346 | + | 0.855171i | \(0.326548\pi\) | |||||||
\(24\) | 6.30624 | + | 4.58175i | 1.28726 | + | 0.935246i | ||||
\(25\) | 3.62782 | − | 11.1653i | 0.725563 | − | 2.23305i | ||||
\(26\) | −1.73213 | − | 5.33093i | −0.339698 | − | 1.04548i | ||||
\(27\) | 1.32536 | − | 0.962928i | 0.255065 | − | 0.185316i | ||||
\(28\) | −0.299647 | + | 0.217706i | −0.0566280 | + | 0.0411426i | ||||
\(29\) | 0.598078 | + | 1.84069i | 0.111060 | + | 0.341808i | 0.991105 | − | 0.133083i | \(-0.0424875\pi\) |
−0.880045 | + | 0.474891i | \(0.842488\pi\) | |||||||
\(30\) | −4.15769 | + | 12.7961i | −0.759088 | + | 2.33623i | ||||
\(31\) | 1.26432 | + | 0.918580i | 0.227078 | + | 0.164982i | 0.695507 | − | 0.718519i | \(-0.255180\pi\) |
−0.468429 | + | 0.883501i | \(0.655180\pi\) | |||||||
\(32\) | −2.06640 | −0.365292 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.35067 | 0.917632 | ||||||||
\(35\) | −3.31004 | − | 2.40489i | −0.559499 | − | 0.406500i | ||||
\(36\) | −0.416153 | + | 1.28079i | −0.0693588 | + | 0.213464i | ||||
\(37\) | −0.221348 | − | 0.681238i | −0.0363893 | − | 0.111995i | 0.931212 | − | 0.364478i | \(-0.118753\pi\) |
−0.967601 | + | 0.252483i | \(0.918753\pi\) | |||||||
\(38\) | 1.28971 | − | 0.937030i | 0.209219 | − | 0.152006i | ||||
\(39\) | 9.15089 | − | 6.64851i | 1.46532 | − | 1.06461i | ||||
\(40\) | −3.82578 | − | 11.7745i | −0.604908 | − | 1.86172i | ||||
\(41\) | −1.48522 | + | 4.57102i | −0.231952 | + | 0.713874i | 0.765559 | + | 0.643365i | \(0.222462\pi\) |
−0.997511 | + | 0.0705088i | \(0.977538\pi\) | |||||||
\(42\) | 2.66043 | + | 1.93292i | 0.410513 | + | 0.298255i | ||||
\(43\) | −1.35362 | −0.206424 | −0.103212 | − | 0.994659i | \(-0.532912\pi\) | ||||
−0.103212 | + | 0.994659i | \(0.532912\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.8763 | −2.21762 | ||||||||
\(46\) | 5.13469 | + | 3.73057i | 0.757068 | + | 0.550042i | ||||
\(47\) | −3.23424 | + | 9.95395i | −0.471762 | + | 1.45193i | 0.378514 | + | 0.925596i | \(0.376435\pi\) |
−0.850276 | + | 0.526338i | \(0.823565\pi\) | |||||||
\(48\) | 2.48527 | + | 7.64887i | 0.358718 | + | 1.10402i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 12.1245 | − | 8.80895i | 1.71466 | − | 1.24577i | ||||
\(51\) | 3.33656 | + | 10.2689i | 0.467212 | + | 1.43793i | ||||
\(52\) | −0.502561 | + | 1.54672i | −0.0696927 | + | 0.214492i | ||||
\(53\) | 3.21325 | + | 2.33457i | 0.441374 | + | 0.320677i | 0.786181 | − | 0.617997i | \(-0.212055\pi\) |
−0.344806 | + | 0.938674i | \(0.612055\pi\) | |||||||
\(54\) | 2.09131 | 0.284591 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.02595 | −0.404359 | ||||||||
\(57\) | 2.60256 | + | 1.89087i | 0.344718 | + | 0.250452i | ||||
\(58\) | −0.763485 | + | 2.34976i | −0.100250 | + | 0.308539i | ||||
\(59\) | 4.25172 | + | 13.0854i | 0.553526 | + | 1.70358i | 0.699804 | + | 0.714335i | \(0.253271\pi\) |
−0.146277 | + | 0.989244i | \(0.546729\pi\) | |||||||
\(60\) | 3.15818 | − | 2.29456i | 0.407720 | − | 0.296226i | ||||
\(61\) | −9.48745 | + | 6.89304i | −1.21474 | + | 0.882563i | −0.995653 | − | 0.0931414i | \(-0.970309\pi\) |
−0.219091 | + | 0.975704i | \(0.570309\pi\) | |||||||
\(62\) | 0.616486 | + | 1.89735i | 0.0782938 | + | 0.240964i | ||||
\(63\) | −1.12357 | + | 3.45799i | −0.141557 | + | 0.435666i | ||||
\(64\) | −7.18568 | − | 5.22070i | −0.898210 | − | 0.652588i | ||||
\(65\) | −17.9651 | −2.22830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.59274 | 0.927600 | 0.463800 | − | 0.885940i | \(-0.346486\pi\) | ||||
0.463800 | + | 0.885940i | \(0.346486\pi\) | |||||||
\(68\) | −1.25596 | − | 0.912508i | −0.152307 | − | 0.110658i | ||||
\(69\) | −3.95774 | + | 12.1807i | −0.476456 | + | 1.46638i | ||||
\(70\) | −1.61399 | − | 4.96735i | −0.192909 | − | 0.593712i | ||||
\(71\) | −0.176622 | + | 0.128323i | −0.0209611 | + | 0.0152292i | −0.598216 | − | 0.801335i | \(-0.704124\pi\) |
0.577255 | + | 0.816564i | \(0.304124\pi\) | |||||||
\(72\) | −8.90096 | + | 6.46693i | −1.04899 | + | 0.762135i | ||||
\(73\) | −3.39036 | − | 10.4344i | −0.396811 | − | 1.22126i | −0.927542 | − | 0.373719i | \(-0.878082\pi\) |
0.530730 | − | 0.847541i | \(-0.321918\pi\) | |||||||
\(74\) | 0.282564 | − | 0.869644i | 0.0328475 | − | 0.101094i | ||||
\(75\) | 24.4665 | + | 17.7760i | 2.82515 | + | 2.05259i | ||||
\(76\) | −0.462535 | −0.0530564 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 14.4394 | 1.63494 | ||||||||
\(79\) | −3.69112 | − | 2.68176i | −0.415284 | − | 0.301721i | 0.360454 | − | 0.932777i | \(-0.382622\pi\) |
−0.775737 | + | 0.631056i | \(0.782622\pi\) | |||||||
\(80\) | 3.94728 | − | 12.1485i | 0.441319 | − | 1.35824i | ||||
\(81\) | −2.06662 | − | 6.36039i | −0.229624 | − | 0.706710i | ||||
\(82\) | −4.96372 | + | 3.60635i | −0.548151 | + | 0.398255i | ||||
\(83\) | 1.98579 | − | 1.44276i | 0.217969 | − | 0.158364i | −0.473443 | − | 0.880825i | \(-0.656989\pi\) |
0.691412 | + | 0.722461i | \(0.256989\pi\) | |||||||
\(84\) | −0.294840 | − | 0.907424i | −0.0321697 | − | 0.0990081i | ||||
\(85\) | 5.29936 | − | 16.3098i | 0.574797 | − | 1.76904i | ||||
\(86\) | −1.39796 | − | 1.01568i | −0.150746 | − | 0.109524i | ||||
\(87\) | −4.98571 | −0.534524 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.20456 | 0.445683 | 0.222841 | − | 0.974855i | \(-0.428467\pi\) | ||||
0.222841 | + | 0.974855i | \(0.428467\pi\) | |||||||
\(90\) | −15.3636 | − | 11.1623i | −1.61947 | − | 1.17661i | ||||
\(91\) | −1.35686 | + | 4.17600i | −0.142238 | + | 0.437764i | ||||
\(92\) | −0.569047 | − | 1.75135i | −0.0593273 | − | 0.182591i | ||||
\(93\) | −3.25692 | + | 2.36629i | −0.337727 | + | 0.245373i | ||||
\(94\) | −10.8091 | + | 7.85327i | −1.11487 | + | 0.810003i | ||||
\(95\) | −1.57889 | − | 4.85931i | −0.161990 | − | 0.498555i | ||||
\(96\) | 1.64493 | − | 5.06259i | 0.167885 | − | 0.516698i | ||||
\(97\) | 8.83842 | + | 6.42149i | 0.897405 | + | 0.652003i | 0.937798 | − | 0.347181i | \(-0.112861\pi\) |
−0.0403929 | + | 0.999184i | \(0.512861\pi\) | |||||||
\(98\) | −1.27656 | −0.128952 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.34826 | −0.434826 | ||||||||
\(101\) | 5.95905 | + | 4.32950i | 0.592948 | + | 0.430802i | 0.843369 | − | 0.537335i | \(-0.180569\pi\) |
−0.250421 | + | 0.968137i | \(0.580569\pi\) | |||||||
\(102\) | −4.25934 | + | 13.1089i | −0.421737 | + | 1.29797i | ||||
\(103\) | −0.0475535 | − | 0.146354i | −0.00468558 | − | 0.0144207i | 0.948686 | − | 0.316218i | \(-0.102413\pi\) |
−0.953372 | + | 0.301798i | \(0.902413\pi\) | |||||||
\(104\) | −10.7491 | + | 7.80970i | −1.05404 | + | 0.765804i | ||||
\(105\) | 8.52678 | − | 6.19507i | 0.832129 | − | 0.604577i | ||||
\(106\) | 1.56680 | + | 4.82210i | 0.152181 | + | 0.468364i | ||||
\(107\) | −2.45550 | + | 7.55725i | −0.237382 | + | 0.730587i | 0.759414 | + | 0.650607i | \(0.225486\pi\) |
−0.996796 | + | 0.0799799i | \(0.974514\pi\) | |||||||
\(108\) | −0.490891 | − | 0.356653i | −0.0472360 | − | 0.0343190i | ||||
\(109\) | 4.91440 | 0.470714 | 0.235357 | − | 0.971909i | \(-0.424374\pi\) | ||||
0.235357 | + | 0.971909i | \(0.424374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.84520 | 0.175139 | ||||||||
\(112\) | −2.52579 | − | 1.83509i | −0.238665 | − | 0.173400i | ||||
\(113\) | 0.940056 | − | 2.89319i | 0.0884330 | − | 0.272169i | −0.897054 | − | 0.441922i | \(-0.854297\pi\) |
0.985487 | + | 0.169753i | \(0.0542969\pi\) | |||||||
\(114\) | 1.26902 | + | 3.90565i | 0.118855 | + | 0.365797i | ||||
\(115\) | 16.4569 | − | 11.9566i | 1.53461 | − | 1.11496i | ||||
\(116\) | 0.579943 | − | 0.421353i | 0.0538464 | − | 0.0391217i | ||||
\(117\) | 4.93349 | + | 15.1837i | 0.456102 | + | 1.40374i | ||||
\(118\) | −5.42759 | + | 16.7044i | −0.499650 | + | 1.53776i | ||||
\(119\) | −3.39096 | − | 2.46368i | −0.310849 | − | 0.225845i | ||||
\(120\) | 31.8925 | 2.91138 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −14.9704 | −1.35536 | ||||||||
\(123\) | −10.0165 | − | 7.27742i | −0.903158 | − | 0.656183i | ||||
\(124\) | 0.178868 | − | 0.550500i | 0.0160628 | − | 0.0494363i | ||||
\(125\) | −8.52137 | − | 26.2261i | −0.762174 | − | 2.34573i | ||||
\(126\) | −3.75507 | + | 2.72822i | −0.334528 | + | 0.243049i | ||||
\(127\) | −8.73362 | + | 6.34535i | −0.774984 | + | 0.563059i | −0.903469 | − | 0.428653i | \(-0.858988\pi\) |
0.128486 | + | 0.991711i | \(0.458988\pi\) | |||||||
\(128\) | −2.22666 | − | 6.85296i | −0.196811 | − | 0.605721i | ||||
\(129\) | 1.07753 | − | 3.31630i | 0.0948712 | − | 0.291984i | ||||
\(130\) | −18.5537 | − | 13.4800i | −1.62727 | − | 1.18228i | ||||
\(131\) | 8.70429 | 0.760497 | 0.380249 | − | 0.924884i | \(-0.375838\pi\) | ||||
0.380249 | + | 0.924884i | \(0.375838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.24880 | −0.108285 | ||||||||
\(134\) | 7.84149 | + | 5.69718i | 0.677401 | + | 0.492161i | ||||
\(135\) | 2.07125 | − | 6.37466i | 0.178265 | − | 0.548644i | ||||
\(136\) | −3.91931 | − | 12.0624i | −0.336078 | − | 1.03434i | ||||
\(137\) | −9.70634 | + | 7.05207i | −0.829269 | + | 0.602499i | −0.919352 | − | 0.393435i | \(-0.871287\pi\) |
0.0900835 | + | 0.995934i | \(0.471287\pi\) | |||||||
\(138\) | −13.2271 | + | 9.61007i | −1.12597 | + | 0.818064i | ||||
\(139\) | −2.53075 | − | 7.78884i | −0.214655 | − | 0.660641i | −0.999178 | − | 0.0405407i | \(-0.987092\pi\) |
0.784523 | − | 0.620100i | \(-0.212908\pi\) | |||||||
\(140\) | −0.468285 | + | 1.44123i | −0.0395773 | + | 0.121807i | ||||
\(141\) | −21.8122 | − | 15.8475i | −1.83691 | − | 1.33460i | ||||
\(142\) | −0.278695 | −0.0233875 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −11.3516 | −0.945968 | ||||||||
\(145\) | 6.40632 | + | 4.65447i | 0.532016 | + | 0.386532i | ||||
\(146\) | 4.32801 | − | 13.3202i | 0.358189 | − | 1.10239i | ||||
\(147\) | −0.796038 | − | 2.44995i | −0.0656561 | − | 0.202069i | ||||
\(148\) | −0.214636 | + | 0.155942i | −0.0176430 | + | 0.0128184i | ||||
\(149\) | 9.77425 | − | 7.10141i | 0.800738 | − | 0.581770i | −0.110393 | − | 0.993888i | \(-0.535211\pi\) |
0.911130 | + | 0.412118i | \(0.135211\pi\) | |||||||
\(150\) | 11.9300 | + | 36.7167i | 0.974078 | + | 2.99790i | ||||
\(151\) | 2.14720 | − | 6.60842i | 0.174737 | − | 0.537785i | −0.824884 | − | 0.565302i | \(-0.808760\pi\) |
0.999621 | + | 0.0275162i | \(0.00875980\pi\) | |||||||
\(152\) | −3.05711 | − | 2.22112i | −0.247965 | − | 0.180157i | ||||
\(153\) | −15.2399 | −1.23208 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.39402 | 0.513580 | ||||||||
\(156\) | −3.38935 | − | 2.46250i | −0.271365 | − | 0.197158i | ||||
\(157\) | 3.24253 | − | 9.97947i | 0.258782 | − | 0.796449i | −0.734279 | − | 0.678848i | \(-0.762480\pi\) |
0.993061 | − | 0.117601i | \(-0.0375203\pi\) | |||||||
\(158\) | −1.79981 | − | 5.53923i | −0.143185 | − | 0.440678i | ||||
\(159\) | −8.27745 | + | 6.01392i | −0.656445 | + | 0.476935i | ||||
\(160\) | −6.83988 | + | 4.96946i | −0.540740 | + | 0.392870i | ||||
\(161\) | −1.53637 | − | 4.72846i | −0.121083 | − | 0.372655i | ||||
\(162\) | 2.63817 | − | 8.11945i | 0.207274 | − | 0.637924i | ||||
\(163\) | 6.32444 | + | 4.59497i | 0.495368 | + | 0.359906i | 0.807245 | − | 0.590217i | \(-0.200958\pi\) |
−0.311877 | + | 0.950123i | \(0.600958\pi\) | |||||||
\(164\) | 1.78016 | 0.139007 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.13342 | 0.243201 | ||||||||
\(167\) | 17.2728 | + | 12.5494i | 1.33661 | + | 0.971101i | 0.999561 | + | 0.0296124i | \(0.00942730\pi\) |
0.337045 | + | 0.941489i | \(0.390573\pi\) | |||||||
\(168\) | 2.40877 | − | 7.41343i | 0.185841 | − | 0.571959i | ||||
\(169\) | 1.94065 | + | 5.97270i | 0.149281 | + | 0.459438i | ||||
\(170\) | 17.7109 | − | 12.8678i | 1.35837 | − | 0.986912i | ||||
\(171\) | −3.67340 | + | 2.66888i | −0.280912 | + | 0.204094i | ||||
\(172\) | 0.154928 | + | 0.476820i | 0.0118132 | + | 0.0363572i | ||||
\(173\) | −6.00679 | + | 18.4870i | −0.456688 | + | 1.40554i | 0.412455 | + | 0.910978i | \(0.364671\pi\) |
−0.869142 | + | 0.494562i | \(0.835329\pi\) | |||||||
\(174\) | −5.14905 | − | 3.74100i | −0.390349 | − | 0.283605i | ||||
\(175\) | −11.7399 | −0.887450 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35.4432 | −2.66408 | ||||||||
\(178\) | 4.34231 | + | 3.15488i | 0.325470 | + | 0.236468i | ||||
\(179\) | 5.56120 | − | 17.1156i | 0.415663 | − | 1.27928i | −0.495993 | − | 0.868327i | \(-0.665196\pi\) |
0.911656 | − | 0.410954i | \(-0.134804\pi\) | |||||||
\(180\) | 1.70266 | + | 5.24026i | 0.126909 | + | 0.390586i | ||||
\(181\) | −12.2627 | + | 8.90938i | −0.911480 | + | 0.662229i | −0.941389 | − | 0.337324i | \(-0.890478\pi\) |
0.0299086 | + | 0.999553i | \(0.490478\pi\) | |||||||
\(182\) | −4.53476 | + | 3.29470i | −0.336139 | + | 0.244219i | ||||
\(183\) | −9.33525 | − | 28.7309i | −0.690081 | − | 2.12385i | ||||
\(184\) | 4.64898 | − | 14.3081i | 0.342727 | − | 1.05481i | ||||
\(185\) | −2.37097 | − | 1.72261i | −0.174317 | − | 0.126649i | ||||
\(186\) | −5.13916 | −0.376822 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.87652 | 0.282724 | ||||||||
\(189\) | −1.32536 | − | 0.962928i | −0.0964055 | − | 0.0700427i | ||||
\(190\) | 2.01555 | − | 6.20322i | 0.146223 | − | 0.450029i | ||||
\(191\) | −7.34144 | − | 22.5946i | −0.531208 | − | 1.63489i | −0.751703 | − | 0.659502i | \(-0.770767\pi\) |
0.220495 | − | 0.975388i | \(-0.429233\pi\) | |||||||
\(192\) | 18.5106 | − | 13.4487i | 1.33588 | − | 0.970577i | ||||
\(193\) | 11.3733 | − | 8.26319i | 0.818668 | − | 0.594797i | −0.0976625 | − | 0.995220i | \(-0.531137\pi\) |
0.916331 | + | 0.400422i | \(0.131137\pi\) | |||||||
\(194\) | 4.30965 | + | 13.2637i | 0.309415 | + | 0.952281i | ||||
\(195\) | 14.3009 | − | 44.0137i | 1.02411 | − | 3.15189i | ||||
\(196\) | 0.299647 | + | 0.217706i | 0.0214034 | + | 0.0155505i | ||||
\(197\) | −18.0665 | −1.28718 | −0.643591 | − | 0.765369i | \(-0.722556\pi\) | ||||
−0.643591 | + | 0.765369i | \(0.722556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.54374 | 0.109433 | 0.0547163 | − | 0.998502i | \(-0.482575\pi\) | ||||
0.0547163 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(200\) | −28.7397 | − | 20.8806i | −2.03220 | − | 1.47648i | ||||
\(201\) | −6.04411 | + | 18.6019i | −0.426319 | + | 1.31207i | ||||
\(202\) | 2.90566 | + | 8.94270i | 0.204441 | + | 0.629206i | ||||
\(203\) | 1.56579 | − | 1.13761i | 0.109897 | − | 0.0798447i | ||||
\(204\) | 3.23539 | − | 2.35065i | 0.226523 | − | 0.164578i | ||||
\(205\) | 6.07667 | + | 18.7021i | 0.424413 | + | 1.30621i | ||||
\(206\) | 0.0607050 | − | 0.186831i | 0.00422952 | − | 0.0130171i | ||||
\(207\) | −14.6248 | − | 10.6255i | −1.01649 | − | 0.738525i | ||||
\(208\) | −13.7086 | −0.950522 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 13.4546 | 0.928454 | ||||||||
\(211\) | −17.8660 | − | 12.9804i | −1.22995 | − | 0.893608i | −0.233060 | − | 0.972462i | \(-0.574874\pi\) |
−0.996886 | + | 0.0788540i | \(0.974874\pi\) | |||||||
\(212\) | 0.454592 | − | 1.39909i | 0.0312215 | − | 0.0960900i | ||||
\(213\) | −0.173788 | − | 0.534865i | −0.0119078 | − | 0.0366483i | ||||
\(214\) | −8.20650 | + | 5.96237i | −0.560985 | + | 0.407579i | ||||
\(215\) | −4.48053 | + | 3.25529i | −0.305569 | + | 0.222009i | ||||
\(216\) | −1.53186 | − | 4.71458i | −0.104230 | − | 0.320786i | ||||
\(217\) | 0.482926 | − | 1.48629i | 0.0327832 | − | 0.100896i | ||||
\(218\) | 5.07540 | + | 3.68750i | 0.343750 | + | 0.249749i | ||||
\(219\) | 28.2628 | 1.90982 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.4043 | −1.23801 | ||||||||
\(222\) | 1.90566 | + | 1.38454i | 0.127899 | + | 0.0929242i | ||||
\(223\) | −2.64955 | + | 8.15449i | −0.177427 | + | 0.546065i | −0.999736 | − | 0.0229766i | \(-0.992686\pi\) |
0.822309 | + | 0.569042i | \(0.192686\pi\) | |||||||
\(224\) | 0.638553 | + | 1.96526i | 0.0426651 | + | 0.131310i | ||||
\(225\) | −34.5333 | + | 25.0899i | −2.30222 | + | 1.67266i | ||||
\(226\) | 3.14175 | − | 2.28261i | 0.208986 | − | 0.151837i | ||||
\(227\) | 8.21085 | + | 25.2704i | 0.544974 | + | 1.67726i | 0.721053 | + | 0.692880i | \(0.243659\pi\) |
−0.176079 | + | 0.984376i | \(0.556341\pi\) | |||||||
\(228\) | 0.368196 | − | 1.13319i | 0.0243844 | − | 0.0750473i | ||||
\(229\) | −9.23194 | − | 6.70740i | −0.610064 | − | 0.443237i | 0.239373 | − | 0.970928i | \(-0.423058\pi\) |
−0.849437 | + | 0.527690i | \(0.823058\pi\) | |||||||
\(230\) | 25.9676 | 1.71225 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.85648 | 0.384497 | ||||||||
\(233\) | 21.5304 | + | 15.6427i | 1.41050 | + | 1.02479i | 0.993249 | + | 0.115999i | \(0.0370069\pi\) |
0.417252 | + | 0.908791i | \(0.362993\pi\) | |||||||
\(234\) | −6.29792 | + | 19.3830i | −0.411708 | + | 1.26711i | ||||
\(235\) | 13.2327 | + | 40.7260i | 0.863204 | + | 2.65667i | ||||
\(236\) | 4.12280 | − | 2.99539i | 0.268371 | − | 0.194983i | ||||
\(237\) | 9.50845 | − | 6.90830i | 0.617640 | − | 0.448742i | ||||
\(238\) | −1.65345 | − | 5.08879i | −0.107177 | − | 0.329857i | ||||
\(239\) | 2.32158 | − | 7.14510i | 0.150171 | − | 0.462178i | −0.847469 | − | 0.530845i | \(-0.821875\pi\) |
0.997640 | + | 0.0686671i | \(0.0218746\pi\) | |||||||
\(240\) | 26.6210 | + | 19.3413i | 1.71838 | + | 1.24848i | ||||
\(241\) | −27.4388 | −1.76749 | −0.883744 | − | 0.467971i | \(-0.844985\pi\) | ||||
−0.883744 | + | 0.467971i | \(0.844985\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1425 | 1.42044 | ||||||||
\(244\) | 3.51400 | + | 2.55307i | 0.224961 | + | 0.163444i | ||||
\(245\) | −1.26432 | + | 3.89119i | −0.0807747 | + | 0.248599i | ||||
\(246\) | −4.88409 | − | 15.0317i | −0.311398 | − | 0.958385i | ||||
\(247\) | −4.43613 | + | 3.22304i | −0.282264 | + | 0.205077i | ||||
\(248\) | 3.82576 | − | 2.77957i | 0.242936 | − | 0.176503i | ||||
\(249\) | 1.95394 | + | 6.01360i | 0.123826 | + | 0.381096i | ||||
\(250\) | 10.8781 | − | 33.4793i | 0.687990 | − | 2.11741i | ||||
\(251\) | −1.55747 | − | 1.13157i | −0.0983065 | − | 0.0714239i | 0.537546 | − | 0.843234i | \(-0.319351\pi\) |
−0.635853 | + | 0.771810i | \(0.719351\pi\) | |||||||
\(252\) | 1.34670 | 0.0848340 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.7810 | −0.864694 | ||||||||
\(255\) | 35.7397 | + | 25.9664i | 2.23811 | + | 1.62608i | ||||
\(256\) | −2.64690 | + | 8.14631i | −0.165431 | + | 0.509144i | ||||
\(257\) | 3.13975 | + | 9.66315i | 0.195852 | + | 0.602771i | 0.999966 | + | 0.00829511i | \(0.00264044\pi\) |
−0.804113 | + | 0.594476i | \(0.797360\pi\) | |||||||
\(258\) | 3.60120 | − | 2.61643i | 0.224201 | − | 0.162892i | ||||
\(259\) | −0.579496 | + | 0.421028i | −0.0360081 | + | 0.0261614i | ||||
\(260\) | 2.05620 | + | 6.32833i | 0.127520 | + | 0.392466i | ||||
\(261\) | 2.17458 | − | 6.69267i | 0.134603 | − | 0.414266i | ||||
\(262\) | 8.98946 | + | 6.53122i | 0.555371 | + | 0.403500i | ||||
\(263\) | 4.38774 | 0.270560 | 0.135280 | − | 0.990807i | \(-0.456807\pi\) | ||||
0.135280 | + | 0.990807i | \(0.456807\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.2504 | 0.998253 | ||||||||
\(266\) | −1.28971 | − | 0.937030i | −0.0790773 | − | 0.0574530i | ||||
\(267\) | −3.34699 | + | 10.3010i | −0.204833 | + | 0.630410i | ||||
\(268\) | −0.869027 | − | 2.67459i | −0.0530842 | − | 0.163377i | ||||
\(269\) | −0.505942 | + | 0.367588i | −0.0308478 | + | 0.0224123i | −0.603102 | − | 0.797664i | \(-0.706069\pi\) |
0.572255 | + | 0.820076i | \(0.306069\pi\) | |||||||
\(270\) | 6.92231 | − | 5.02936i | 0.421279 | − | 0.306077i | ||||
\(271\) | 3.68889 | + | 11.3532i | 0.224084 | + | 0.689659i | 0.998383 | + | 0.0568398i | \(0.0181024\pi\) |
−0.774299 | + | 0.632819i | \(0.781898\pi\) | |||||||
\(272\) | 4.04378 | − | 12.4455i | 0.245190 | − | 0.754617i | ||||
\(273\) | −9.15089 | − | 6.64851i | −0.553837 | − | 0.402386i | ||||
\(274\) | −15.3158 | −0.925263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.74371 | 0.285538 | ||||||||
\(277\) | 23.1032 | + | 16.7854i | 1.38814 | + | 1.00854i | 0.996067 | + | 0.0886037i | \(0.0282405\pi\) |
0.392069 | + | 0.919936i | \(0.371760\pi\) | |||||||
\(278\) | 3.23066 | − | 9.94295i | 0.193762 | − | 0.596339i | ||||
\(279\) | −1.75590 | − | 5.40409i | −0.105123 | − | 0.323534i | ||||
\(280\) | −10.0160 | + | 7.27706i | −0.598571 | + | 0.434888i | ||||
\(281\) | 11.8910 | − | 8.63932i | 0.709357 | − | 0.515378i | −0.173609 | − | 0.984815i | \(-0.555543\pi\) |
0.882966 | + | 0.469436i | \(0.155543\pi\) | |||||||
\(282\) | −10.6357 | − | 32.7333i | −0.633346 | − | 1.94924i | ||||
\(283\) | −6.96513 | + | 21.4365i | −0.414034 | + | 1.27426i | 0.499079 | + | 0.866557i | \(0.333672\pi\) |
−0.913112 | + | 0.407708i | \(0.866328\pi\) | |||||||
\(284\) | 0.0654178 | + | 0.0475288i | 0.00388183 | + | 0.00282032i | ||||
\(285\) | 13.1619 | 0.779646 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.80626 | 0.283704 | ||||||||
\(288\) | 6.07841 | + | 4.41623i | 0.358174 | + | 0.260229i | ||||
\(289\) | 0.175630 | − | 0.540533i | 0.0103312 | − | 0.0317960i | ||||
\(290\) | 3.12375 | + | 9.61391i | 0.183433 | + | 0.564548i | ||||
\(291\) | −22.7681 | + | 16.5420i | −1.33469 | + | 0.969707i | ||||
\(292\) | −3.28756 | + | 2.38855i | −0.192390 | + | 0.139779i | ||||
\(293\) | −5.20015 | − | 16.0044i | −0.303796 | − | 0.934988i | −0.980124 | − | 0.198387i | \(-0.936430\pi\) |
0.676328 | − | 0.736601i | \(-0.263570\pi\) | |||||||
\(294\) | 1.01619 | − | 3.12752i | 0.0592656 | − | 0.182401i | ||||
\(295\) | 45.5424 | + | 33.0885i | 2.65158 | + | 1.92648i | ||||
\(296\) | −2.16747 | −0.125982 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.4230 | 0.893429 | ||||||||
\(299\) | −17.6614 | − | 12.8318i | −1.02139 | − | 0.742081i | ||||
\(300\) | 3.46138 | − | 10.6530i | 0.199843 | − | 0.615053i | ||||
\(301\) | 0.418290 | + | 1.28737i | 0.0241099 | + | 0.0742025i | ||||
\(302\) | 7.17615 | − | 5.21378i | 0.412941 | − | 0.300019i | ||||
\(303\) | −15.3507 | + | 11.1530i | −0.881876 | + | 0.640720i | ||||
\(304\) | −1.20480 | − | 3.70799i | −0.0690999 | − | 0.212668i | ||||
\(305\) | −14.8269 | + | 45.6325i | −0.848986 | + | 2.61291i | ||||
\(306\) | −15.7392 | − | 11.4352i | −0.899752 | − | 0.653708i | ||||
\(307\) | −0.238354 | −0.0136036 | −0.00680179 | − | 0.999977i | \(-0.502165\pi\) | ||||
−0.00680179 | + | 0.999977i | \(0.502165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.396416 | 0.0225513 | ||||||||
\(310\) | 6.60350 | + | 4.79773i | 0.375054 | + | 0.272493i | ||||
\(311\) | −0.202877 | + | 0.624391i | −0.0115041 | + | 0.0354059i | −0.956644 | − | 0.291260i | \(-0.905925\pi\) |
0.945140 | + | 0.326666i | \(0.105925\pi\) | |||||||
\(312\) | −10.5767 | − | 32.5517i | −0.598787 | − | 1.84288i | ||||
\(313\) | 6.02930 | − | 4.38054i | 0.340796 | − | 0.247603i | −0.404202 | − | 0.914670i | \(-0.632451\pi\) |
0.744998 | + | 0.667067i | \(0.232451\pi\) | |||||||
\(314\) | 10.8368 | − | 7.87340i | 0.611557 | − | 0.444322i | ||||
\(315\) | 4.59702 | + | 14.1482i | 0.259013 | + | 0.797159i | ||||
\(316\) | −0.522198 | + | 1.60716i | −0.0293759 | + | 0.0904099i | ||||
\(317\) | −14.1102 | − | 10.2517i | −0.792509 | − | 0.575791i | 0.116198 | − | 0.993226i | \(-0.462929\pi\) |
−0.908707 | + | 0.417435i | \(0.862929\pi\) | |||||||
\(318\) | −13.0612 | −0.732433 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −36.3401 | −2.03147 | ||||||||
\(321\) | −16.5602 | − | 12.0317i | −0.924303 | − | 0.671545i | ||||
\(322\) | 1.96128 | − | 6.03619i | 0.109298 | − | 0.336384i | ||||
\(323\) | −1.61748 | − | 4.97811i | −0.0899993 | − | 0.276989i | ||||
\(324\) | −2.00395 | + | 1.45596i | −0.111331 | + | 0.0808865i | ||||
\(325\) | −41.7037 | + | 30.2995i | −2.31331 | + | 1.68072i | ||||
\(326\) | 3.08382 | + | 9.49103i | 0.170797 | + | 0.525659i | ||||
\(327\) | −3.91205 | + | 12.0400i | −0.216337 | + | 0.665816i | ||||
\(328\) | 11.7659 | + | 8.54845i | 0.649665 | + | 0.472009i | ||||
\(329\) | 10.4662 | 0.577021 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.6146 | −1.57280 | −0.786399 | − | 0.617719i | \(-0.788057\pi\) | ||||
−0.786399 | + | 0.617719i | \(0.788057\pi\) | |||||||
\(332\) | −0.735506 | − | 0.534377i | −0.0403662 | − | 0.0293277i | ||||
\(333\) | −0.804809 | + | 2.47695i | −0.0441033 | + | 0.135736i | ||||
\(334\) | 8.42227 | + | 25.9211i | 0.460846 | + | 1.41834i | ||||
\(335\) | 25.1323 | − | 18.2597i | 1.37312 | − | 0.997632i | ||||
\(336\) | 6.50652 | − | 4.72726i | 0.354960 | − | 0.257893i | ||||
\(337\) | −0.534762 | − | 1.64583i | −0.0291304 | − | 0.0896541i | 0.935434 | − | 0.353501i | \(-0.115009\pi\) |
−0.964565 | + | 0.263847i | \(0.915009\pi\) | |||||||
\(338\) | −2.47736 | + | 7.62453i | −0.134751 | + | 0.414720i | ||||
\(339\) | 6.33987 | + | 4.60619i | 0.344335 | + | 0.250174i | ||||
\(340\) | −6.35176 | −0.344472 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.79633 | −0.313430 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −1.26572 | + | 3.89550i | −0.0682433 | + | 0.210031i | ||||
\(345\) | 16.1929 | + | 49.8365i | 0.871794 | + | 2.68311i | ||||
\(346\) | −20.0752 | + | 14.5855i | −1.07925 | + | 0.784121i | ||||
\(347\) | 2.20869 | − | 1.60471i | 0.118569 | − | 0.0861453i | −0.526921 | − | 0.849915i | \(-0.676653\pi\) |
0.645489 | + | 0.763769i | \(0.276653\pi\) | |||||||
\(348\) | 0.570639 | + | 1.75625i | 0.0305895 | + | 0.0941447i | ||||
\(349\) | −9.55056 | + | 29.3936i | −0.511230 | + | 1.57340i | 0.278809 | + | 0.960347i | \(0.410060\pi\) |
−0.790039 | + | 0.613057i | \(0.789940\pi\) | |||||||
\(350\) | −12.1245 | − | 8.80895i | −0.648081 | − | 0.470858i | ||||
\(351\) | −7.19332 | −0.383951 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.9543 | −1.27496 | −0.637480 | − | 0.770467i | \(-0.720023\pi\) | ||||
−0.637480 | + | 0.770467i | \(0.720023\pi\) | |||||||
\(354\) | −36.6044 | − | 26.5947i | −1.94550 | − | 1.41349i | ||||
\(355\) | −0.276022 | + | 0.849510i | −0.0146498 | + | 0.0450873i | ||||
\(356\) | −0.481233 | − | 1.48108i | −0.0255053 | − | 0.0784973i | ||||
\(357\) | 8.73524 | − | 6.34652i | 0.462318 | − | 0.335894i | ||||
\(358\) | 18.5860 | − | 13.5035i | 0.982301 | − | 0.713684i | ||||
\(359\) | 0.468502 | + | 1.44190i | 0.0247266 | + | 0.0761007i | 0.962658 | − | 0.270719i | \(-0.0872615\pi\) |
−0.937932 | + | 0.346820i | \(0.887261\pi\) | |||||||
\(360\) | −13.9103 | + | 42.8116i | −0.733139 | + | 2.25637i | ||||
\(361\) | 14.1097 | + | 10.2513i | 0.742614 | + | 0.539541i | ||||
\(362\) | −19.3496 | −1.01699 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.62632 | 0.0852425 | ||||||||
\(365\) | −36.3159 | − | 26.3850i | −1.90086 | − | 1.38106i | ||||
\(366\) | 11.9170 | − | 36.6769i | 0.622914 | − | 1.91713i | ||||
\(367\) | 2.69527 | + | 8.29518i | 0.140692 | + | 0.433005i | 0.996432 | − | 0.0844010i | \(-0.0268977\pi\) |
−0.855740 | + | 0.517406i | \(0.826898\pi\) | |||||||
\(368\) | 12.5577 | − | 9.12372i | 0.654617 | − | 0.475607i | ||||
\(369\) | 14.1378 | − | 10.2717i | 0.735986 | − | 0.534725i | ||||
\(370\) | −1.15609 | − | 3.55809i | −0.0601025 | − | 0.184977i | ||||
\(371\) | 1.22735 | − | 3.77741i | 0.0637210 | − | 0.196113i | ||||
\(372\) | 1.20631 | + | 0.876437i | 0.0625444 | + | 0.0454412i | ||||
\(373\) | 36.8111 | 1.90601 | 0.953004 | − | 0.302957i | \(-0.0979739\pi\) | ||||
0.953004 | + | 0.302957i | \(0.0979739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 71.0360 | 3.66828 | ||||||||
\(376\) | 25.6217 | + | 18.6153i | 1.32134 | + | 0.960009i | ||||
\(377\) | 2.62610 | − | 8.08232i | 0.135251 | − | 0.416261i | ||||
\(378\) | −0.646249 | − | 1.98895i | −0.0332395 | − | 0.102301i | ||||
\(379\) | −2.10213 | + | 1.52729i | −0.107979 | + | 0.0784516i | −0.640465 | − | 0.767988i | \(-0.721258\pi\) |
0.532485 | + | 0.846439i | \(0.321258\pi\) | |||||||
\(380\) | −1.53101 | + | 1.11234i | −0.0785392 | + | 0.0570621i | ||||
\(381\) | −8.59351 | − | 26.4481i | −0.440259 | − | 1.35498i | ||||
\(382\) | 9.37182 | − | 28.8435i | 0.479504 | − | 1.47576i | ||||
\(383\) | −15.5649 | − | 11.3085i | −0.795327 | − | 0.577839i | 0.114213 | − | 0.993456i | \(-0.463565\pi\) |
−0.909539 | + | 0.415618i | \(0.863565\pi\) | |||||||
\(384\) | 18.5619 | 0.947235 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.9462 | 0.913435 | ||||||||
\(387\) | 3.98172 | + | 2.89289i | 0.202402 | + | 0.147054i | ||||
\(388\) | 1.25041 | − | 3.84836i | 0.0634798 | − | 0.195371i | ||||
\(389\) | −8.75540 | − | 26.9464i | −0.443917 | − | 1.36623i | −0.883668 | − | 0.468115i | \(-0.844933\pi\) |
0.439751 | − | 0.898120i | \(-0.355067\pi\) | |||||||
\(390\) | 47.7950 | − | 34.7251i | 2.42019 | − | 1.75837i | ||||
\(391\) | 16.8592 | − | 12.2489i | 0.852606 | − | 0.619455i | ||||
\(392\) | 0.935069 | + | 2.87785i | 0.0472281 | + | 0.145353i | ||||
\(393\) | −6.92895 | + | 21.3251i | −0.349519 | + | 1.07571i | ||||
\(394\) | −18.6584 | − | 13.5561i | −0.939995 | − | 0.682946i | ||||
\(395\) | −18.6671 | −0.939243 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3666 | −0.520287 | −0.260143 | − | 0.965570i | \(-0.583770\pi\) | ||||
−0.260143 | + | 0.965570i | \(0.583770\pi\) | |||||||
\(398\) | 1.59431 | + | 1.15834i | 0.0799157 | + | 0.0580621i | ||||
\(399\) | 0.994091 | − | 3.05950i | 0.0497668 | − | 0.153167i | ||||
\(400\) | −11.3262 | − | 34.8585i | −0.566311 | − | 1.74293i | ||||
\(401\) | 10.3455 | − | 7.51648i | 0.516632 | − | 0.375355i | −0.298702 | − | 0.954347i | \(-0.596554\pi\) |
0.815334 | + | 0.578992i | \(0.196554\pi\) | |||||||
\(402\) | −20.1999 | + | 14.6761i | −1.00748 | + | 0.731978i | ||||
\(403\) | −2.12048 | − | 6.52618i | −0.105629 | − | 0.325092i | ||||
\(404\) | 0.843052 | − | 2.59465i | 0.0419434 | − | 0.129089i | ||||
\(405\) | −22.1366 | − | 16.0832i | −1.09998 | − | 0.799180i | ||||
\(406\) | 2.47069 | 0.122618 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 32.6722 | 1.61752 | ||||||||
\(409\) | −25.9061 | − | 18.8219i | −1.28098 | − | 0.930683i | −0.281393 | − | 0.959592i | \(-0.590797\pi\) |
−0.999582 | + | 0.0289093i | \(0.990797\pi\) | |||||||
\(410\) | −7.75725 | + | 23.8744i | −0.383103 | + | 1.17907i | ||||
\(411\) | −9.55063 | − | 29.3938i | −0.471098 | − | 1.44989i | ||||
\(412\) | −0.0461116 | + | 0.0335020i | −0.00227175 | + | 0.00165053i | ||||
\(413\) | 11.1311 | − | 8.08724i | 0.547727 | − | 0.397947i | ||||
\(414\) | −7.13110 | − | 21.9473i | −0.350475 | − | 1.07865i | ||||
\(415\) | 3.10338 | − | 9.55122i | 0.152339 | − | 0.468851i | ||||
\(416\) | 7.34052 | + | 5.33320i | 0.359898 | + | 0.261481i | ||||
\(417\) | 21.0969 | 1.03312 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.0934 | −0.981629 | −0.490815 | − | 0.871264i | \(-0.663301\pi\) | ||||
−0.490815 | + | 0.871264i | \(0.663301\pi\) | |||||||
\(420\) | −3.15818 | − | 2.29456i | −0.154104 | − | 0.111963i | ||||
\(421\) | −6.92949 | + | 21.3268i | −0.337722 | + | 1.03940i | 0.627643 | + | 0.778501i | \(0.284020\pi\) |
−0.965365 | + | 0.260902i | \(0.915980\pi\) | |||||||
\(422\) | −8.71154 | − | 26.8113i | −0.424071 | − | 1.30516i | ||||
\(423\) | 30.7868 | − | 22.3679i | 1.49691 | − | 1.08757i | ||||
\(424\) | 9.72314 | − | 7.06427i | 0.472197 | − | 0.343071i | ||||
\(425\) | −15.2059 | − | 46.7988i | −0.737592 | − | 2.27008i | ||||
\(426\) | 0.221852 | − | 0.682789i | 0.0107487 | − | 0.0330812i | ||||
\(427\) | 9.48745 | + | 6.89304i | 0.459130 | + | 0.333577i | ||||
\(428\) | 2.94313 | 0.142262 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.06991 | −0.340941 | ||||||||
\(431\) | 9.77748 | + | 7.10375i | 0.470965 | + | 0.342176i | 0.797817 | − | 0.602900i | \(-0.205988\pi\) |
−0.326853 | + | 0.945075i | \(0.605988\pi\) | |||||||
\(432\) | 1.58051 | − | 4.86431i | 0.0760423 | − | 0.234034i | ||||
\(433\) | −0.0934633 | − | 0.287650i | −0.00449156 | − | 0.0138236i | 0.948786 | − | 0.315921i | \(-0.102313\pi\) |
−0.953277 | + | 0.302097i | \(0.902313\pi\) | |||||||
\(434\) | 1.61398 | − | 1.17263i | 0.0774736 | − | 0.0562879i | ||||
\(435\) | −16.5029 | + | 11.9901i | −0.791254 | + | 0.574880i | ||||
\(436\) | −0.562477 | − | 1.73113i | −0.0269378 | − | 0.0829060i | ||||
\(437\) | 1.91862 | − | 5.90490i | 0.0917799 | − | 0.282470i | ||||
\(438\) | 29.1887 | + | 21.2068i | 1.39469 | + | 1.01330i | ||||
\(439\) | 3.52592 | 0.168283 | 0.0841416 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841416 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.63595 | 0.173141 | ||||||||
\(442\) | −19.0073 | − | 13.8096i | −0.904084 | − | 0.656856i | ||||
\(443\) | −6.75027 | + | 20.7752i | −0.320715 | + | 0.987059i | 0.652623 | + | 0.757683i | \(0.273669\pi\) |
−0.973338 | + | 0.229376i | \(0.926331\pi\) | |||||||
\(444\) | −0.211193 | − | 0.649984i | −0.0100228 | − | 0.0308469i | ||||
\(445\) | 13.9173 | − | 10.1115i | 0.659743 | − | 0.479331i | ||||
\(446\) | −8.85504 | + | 6.43357i | −0.419298 | + | 0.304638i | ||||
\(447\) | 9.61744 | + | 29.5994i | 0.454889 | + | 1.40001i | ||||
\(448\) | −2.74469 | + | 8.44727i | −0.129674 | + | 0.399096i | ||||
\(449\) | −7.52525 | − | 5.46741i | −0.355138 | − | 0.258023i | 0.395883 | − | 0.918301i | \(-0.370439\pi\) |
−0.751022 | + | 0.660278i | \(0.770439\pi\) | |||||||
\(450\) | −54.4908 | −2.56872 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.12674 | −0.0529974 | ||||||||
\(453\) | 14.4811 | + | 10.5211i | 0.680380 | + | 0.494325i | ||||
\(454\) | −10.4817 | + | 32.2593i | −0.491930 | + | 1.51400i | ||||
\(455\) | 5.55153 | + | 17.0858i | 0.260260 | + | 0.800997i | ||||
\(456\) | 7.87522 | − | 5.72169i | 0.368791 | − | 0.267942i | ||||
\(457\) | −9.15527 | + | 6.65169i | −0.428266 | + | 0.311153i | −0.780955 | − | 0.624587i | \(-0.785267\pi\) |
0.352689 | + | 0.935740i | \(0.385267\pi\) | |||||||
\(458\) | −4.50153 | − | 13.8543i | −0.210343 | − | 0.647369i | ||||
\(459\) | 2.12189 | − | 6.53051i | 0.0990414 | − | 0.304818i | ||||
\(460\) | −6.09536 | − | 4.42854i | −0.284198 | − | 0.206482i | ||||
\(461\) | 0.678821 | 0.0316158 | 0.0158079 | − | 0.999875i | \(-0.494968\pi\) | ||||
0.0158079 | + | 0.999875i | \(0.494968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4936 | −0.627103 | −0.313551 | − | 0.949571i | \(-0.601519\pi\) | ||||
−0.313551 | + | 0.949571i | \(0.601519\pi\) | |||||||
\(464\) | 4.88846 | + | 3.55168i | 0.226941 | + | 0.164882i | ||||
\(465\) | −5.08989 | + | 15.6651i | −0.236038 | + | 0.726450i | ||||
\(466\) | 10.4983 | + | 32.3104i | 0.486324 | + | 1.49675i | ||||
\(467\) | −23.9928 | + | 17.4318i | −1.11026 | + | 0.806649i | −0.982704 | − | 0.185183i | \(-0.940712\pi\) |
−0.127552 | + | 0.991832i | \(0.540712\pi\) | |||||||
\(468\) | 4.78390 | − | 3.47571i | 0.221136 | − | 0.160665i | ||||
\(469\) | −2.34628 | − | 7.22112i | −0.108341 | − | 0.333440i | ||||
\(470\) | −16.8924 | + | 51.9893i | −0.779186 | + | 2.39809i | ||||
\(471\) | 21.8681 | + | 15.8881i | 1.00763 | + | 0.732084i | ||||
\(472\) | 41.6335 | 1.91634 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 15.0036 | 0.689137 | ||||||||
\(475\) | −11.8608 | − | 8.61735i | −0.544210 | − | 0.395391i | ||||
\(476\) | −0.479734 | + | 1.47647i | −0.0219886 | + | 0.0676738i | ||||
\(477\) | −4.46260 | − | 13.7345i | −0.204328 | − | 0.628858i | ||||
\(478\) | 7.75893 | − | 5.63719i | 0.354885 | − | 0.257839i | ||||
\(479\) | 3.80348 | − | 2.76339i | 0.173785 | − | 0.126262i | −0.497492 | − | 0.867468i | \(-0.665746\pi\) |
0.671278 | + | 0.741206i | \(0.265746\pi\) | |||||||
\(480\) | −6.73015 | − | 20.7133i | −0.307188 | − | 0.945427i | ||||
\(481\) | −0.971917 | + | 2.99125i | −0.0443156 | + | 0.136389i | ||||
\(482\) | −28.3377 | − | 20.5886i | −1.29075 | − | 0.937784i | ||||
\(483\) | 12.8075 | 0.582763 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.6985 | 2.02965 | ||||||||
\(486\) | 22.8679 | + | 16.6145i | 1.03731 | + | 0.753649i | ||||
\(487\) | 10.0040 | − | 30.7893i | 0.453327 | − | 1.39520i | −0.419762 | − | 0.907634i | \(-0.637886\pi\) |
0.873089 | − | 0.487562i | \(-0.162114\pi\) | |||||||
\(488\) | 10.9657 | + | 33.7489i | 0.496393 | + | 1.52774i | ||||
\(489\) | −16.2920 | + | 11.8368i | −0.736748 | + | 0.535279i | ||||
\(490\) | −4.22548 | + | 3.06999i | −0.190888 | + | 0.138688i | ||||
\(491\) | 2.11860 | + | 6.52038i | 0.0956111 | + | 0.294261i | 0.987412 | − | 0.158166i | \(-0.0505582\pi\) |
−0.891801 | + | 0.452427i | \(0.850558\pi\) | |||||||
\(492\) | −1.41708 | + | 4.36131i | −0.0638868 | + | 0.196623i | ||||
\(493\) | 6.56294 | + | 4.76826i | 0.295580 | + | 0.214751i | ||||
\(494\) | −6.99986 | −0.314939 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.87908 | 0.219077 | ||||||||
\(497\) | 0.176622 | + | 0.128323i | 0.00792256 | + | 0.00575608i | ||||
\(498\) | −2.49432 | + | 7.67674i | −0.111773 | + | 0.344003i | ||||
\(499\) | 3.38900 | + | 10.4303i | 0.151713 | + | 0.466923i | 0.997813 | − | 0.0661003i | \(-0.0210557\pi\) |
−0.846100 | + | 0.533023i | \(0.821056\pi\) | |||||||
\(500\) | −8.26298 | + | 6.00341i | −0.369532 | + | 0.268481i | ||||
\(501\) | −44.4952 | + | 32.3277i | −1.98790 | + | 1.44429i | ||||
\(502\) | −0.759428 | − | 2.33728i | −0.0338949 | − | 0.104318i | ||||
\(503\) | 8.32288 | − | 25.6152i | 0.371099 | − | 1.14213i | −0.574974 | − | 0.818172i | \(-0.694988\pi\) |
0.946073 | − | 0.323954i | \(-0.105012\pi\) | |||||||
\(504\) | 8.90096 | + | 6.46693i | 0.396480 | + | 0.288060i | ||||
\(505\) | 30.1367 | 1.34106 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.1777 | −0.718475 | ||||||||
\(508\) | 3.23480 | + | 2.35022i | 0.143521 | + | 0.104274i | ||||
\(509\) | 9.39282 | − | 28.9081i | 0.416330 | − | 1.28133i | −0.494727 | − | 0.869049i | \(-0.664732\pi\) |
0.911056 | − | 0.412282i | \(-0.135268\pi\) | |||||||
\(510\) | 17.4268 | + | 53.6342i | 0.771672 | + | 2.37496i | ||||
\(511\) | −8.87607 | + | 6.44884i | −0.392654 | + | 0.285280i | ||||
\(512\) | −20.5051 | + | 14.8978i | −0.906206 | + | 0.658397i | ||||
\(513\) | −0.632193 | − | 1.94569i | −0.0279120 | − | 0.0859043i | ||||
\(514\) | −4.00809 | + | 12.3356i | −0.176789 | + | 0.544102i | ||||
\(515\) | −0.509370 | − | 0.370079i | −0.0224455 | − | 0.0163076i | ||||
\(516\) | −1.29151 | −0.0568558 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.914398 | −0.0401763 | ||||||||
\(519\) | −40.5106 | − | 29.4327i | −1.77822 | − | 1.29195i | ||||
\(520\) | −16.7986 | + | 51.7009i | −0.736669 | + | 2.26723i | ||||
\(521\) | −0.289063 | − | 0.889643i | −0.0126641 | − | 0.0389760i | 0.944525 | − | 0.328440i | \(-0.106523\pi\) |
−0.957189 | + | 0.289464i | \(0.906523\pi\) | |||||||
\(522\) | 7.26764 | − | 5.28025i | 0.318096 | − | 0.231110i | ||||
\(523\) | 21.1844 | − | 15.3913i | 0.926328 | − | 0.673017i | −0.0187630 | − | 0.999824i | \(-0.505973\pi\) |
0.945091 | + | 0.326807i | \(0.105973\pi\) | |||||||
\(524\) | −0.996249 | − | 3.06614i | −0.0435214 | − | 0.133945i | ||||
\(525\) | 9.34538 | − | 28.7621i | 0.407866 | − | 1.25528i | ||||
\(526\) | 4.53150 | + | 3.29232i | 0.197583 | + | 0.143552i | ||||
\(527\) | 6.55034 | 0.285337 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.71881 | 0.0747307 | ||||||||
\(530\) | 16.7828 | + | 12.1934i | 0.728997 | + | 0.529647i | ||||
\(531\) | 15.4590 | − | 47.5780i | 0.670865 | − | 2.06471i | ||||
\(532\) | 0.142931 | + | 0.439897i | 0.00619685 | + | 0.0190720i | ||||
\(533\) | 17.0734 | − | 12.4045i | 0.739529 | − | 0.537300i | ||||
\(534\) | −11.1859 | + | 8.12707i | −0.484063 | + | 0.351693i | ||||
\(535\) | 10.0465 | + | 30.9200i | 0.434349 | + | 1.33679i | ||||
\(536\) | 7.09973 | − | 21.8507i | 0.306662 | − | 0.943808i | ||||
\(537\) | 37.5055 | + | 27.2493i | 1.61848 | + | 1.17590i | ||||
\(538\) | −0.798336 | −0.0344187 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.48258 | −0.106833 | ||||||||
\(541\) | 21.6465 | + | 15.7271i | 0.930656 | + | 0.676161i | 0.946153 | − | 0.323719i | \(-0.104933\pi\) |
−0.0154971 | + | 0.999880i | \(0.504933\pi\) | |||||||
\(542\) | −4.70910 | + | 14.4931i | −0.202273 | + | 0.622533i | ||||
\(543\) | −12.0660 | − | 37.1353i | −0.517801 | − | 1.59363i | ||||
\(544\) | −7.00709 | + | 5.09095i | −0.300427 | + | 0.218273i | ||||
\(545\) | 16.2669 | − | 11.8186i | 0.696796 | − | 0.506252i | ||||
\(546\) | −4.46201 | − | 13.7327i | −0.190957 | − | 0.587704i | ||||
\(547\) | −14.3563 | + | 44.1843i | −0.613833 | + | 1.88918i | −0.196216 | + | 0.980561i | \(0.562865\pi\) |
−0.417617 | + | 0.908623i | \(0.637135\pi\) | |||||||
\(548\) | 3.59508 | + | 2.61198i | 0.153574 | + | 0.111578i | ||||
\(549\) | 42.6393 | 1.81980 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.41695 | 0.102966 | ||||||||
\(552\) | 31.3534 | + | 22.7796i | 1.33449 | + | 0.969563i | ||||
\(553\) | −1.40988 | + | 4.33917i | −0.0599543 | + | 0.184520i | ||||
\(554\) | 11.2652 | + | 34.6707i | 0.478613 | + | 1.47302i | ||||
\(555\) | 6.10770 | − | 4.43750i | 0.259257 | − | 0.188362i | ||||
\(556\) | −2.45401 | + | 1.78294i | −0.104073 | + | 0.0756136i | ||||
\(557\) | −10.8457 | − | 33.3796i | −0.459546 | − | 1.41434i | −0.865714 | − | 0.500539i | \(-0.833135\pi\) |
0.406167 | − | 0.913799i | \(-0.366865\pi\) | |||||||
\(558\) | 2.24151 | − | 6.89867i | 0.0948908 | − | 0.292044i | ||||
\(559\) | 4.80848 | + | 3.49356i | 0.203377 | + | 0.147762i | ||||
\(560\) | −12.7737 | −0.539786 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.7630 | 0.791471 | ||||||||
\(563\) | −7.23901 | − | 5.25945i | −0.305088 | − | 0.221659i | 0.424698 | − | 0.905335i | \(-0.360380\pi\) |
−0.729786 | + | 0.683676i | \(0.760380\pi\) | |||||||
\(564\) | −3.08586 | + | 9.49729i | −0.129938 | + | 0.399908i | ||||
\(565\) | −3.84618 | − | 11.8373i | −0.161810 | − | 0.498000i | ||||
\(566\) | −23.2781 | + | 16.9125i | −0.978450 | + | 0.710885i | ||||
\(567\) | −5.41047 | + | 3.93094i | −0.227219 | + | 0.165084i | ||||
\(568\) | 0.204141 | + | 0.628281i | 0.00856556 | + | 0.0263621i | ||||
\(569\) | −6.00285 | + | 18.4749i | −0.251653 | + | 0.774507i | 0.742818 | + | 0.669493i | \(0.233489\pi\) |
−0.994471 | + | 0.105014i | \(0.966511\pi\) | |||||||
\(570\) | 13.5932 | + | 9.87600i | 0.569354 | + | 0.413660i | ||||
\(571\) | −16.0171 | −0.670295 | −0.335148 | − | 0.942166i | \(-0.608786\pi\) | ||||
−0.335148 | + | 0.942166i | \(0.608786\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 61.1999 | 2.55666 | ||||||||
\(574\) | 4.96372 | + | 3.60635i | 0.207182 | + | 0.150526i | ||||
\(575\) | 18.0368 | − | 55.5115i | 0.752186 | − | 2.31499i | ||||
\(576\) | 9.97954 | + | 30.7139i | 0.415814 | + | 1.27974i | ||||
\(577\) | 26.6322 | − | 19.3494i | 1.10871 | − | 0.805526i | 0.126251 | − | 0.991998i | \(-0.459705\pi\) |
0.982460 | + | 0.186472i | \(0.0597054\pi\) | |||||||
\(578\) | 0.586970 | − | 0.426459i | 0.0244147 | − | 0.0177383i | ||||
\(579\) | 11.1908 | + | 34.4419i | 0.465076 | + | 1.43136i | ||||
\(580\) | 0.906329 | − | 2.78939i | 0.0376333 | − | 0.115823i | ||||
\(581\) | −1.98579 | − | 1.44276i | −0.0823846 | − | 0.0598559i | ||||
\(582\) | −35.9262 | −1.48919 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −33.1990 | −1.37378 | ||||||||
\(585\) | 52.8452 | + | 38.3943i | 2.18488 | + | 1.58741i | ||||
\(586\) | 6.63833 | − | 20.4307i | 0.274227 | − | 0.843983i | ||||
\(587\) | 8.47857 | + | 26.0944i | 0.349948 | + | 1.07703i | 0.958881 | + | 0.283808i | \(0.0915978\pi\) |
−0.608933 | + | 0.793222i | \(0.708402\pi\) | |||||||
\(588\) | −0.771901 | + | 0.560819i | −0.0318327 | + | 0.0231278i | ||||
\(589\) | 1.57888 | − | 1.14712i | 0.0650565 | − | 0.0472663i | ||||
\(590\) | 22.2066 | + | 68.3450i | 0.914233 | + | 2.81372i | ||||
\(591\) | 14.3816 | − | 44.2620i | 0.591580 | − | 1.82070i | ||||
\(592\) | −1.80921 | − | 1.31447i | −0.0743582 | − | 0.0540244i | ||||
\(593\) | −14.6132 | −0.600092 | −0.300046 | − | 0.953925i | \(-0.597002\pi\) | ||||
−0.300046 | + | 0.953925i | \(0.597002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.1491 | −0.703045 | ||||||||
\(596\) | −3.62023 | − | 2.63025i | −0.148290 | − | 0.107739i | ||||
\(597\) | −1.22887 | + | 3.78208i | −0.0502944 | + | 0.154790i | ||||
\(598\) | −8.61178 | − | 26.5043i | −0.352162 | − | 1.08384i | ||||
\(599\) | −20.4491 | + | 14.8571i | −0.835527 | + | 0.607046i | −0.921118 | − | 0.389284i | \(-0.872722\pi\) |
0.0855904 | + | 0.996330i | \(0.472722\pi\) | |||||||
\(600\) | 74.0344 | − | 53.7891i | 3.02244 | − | 2.19593i | ||||
\(601\) | 2.87416 | + | 8.84576i | 0.117239 | + | 0.360826i | 0.992408 | − | 0.122993i | \(-0.0392493\pi\) |
−0.875168 | + | 0.483819i | \(0.839249\pi\) | |||||||
\(602\) | −0.533974 | + | 1.64340i | −0.0217632 | + | 0.0669802i | ||||
\(603\) | −22.3344 | − | 16.2269i | −0.909526 | − | 0.660810i | ||||
\(604\) | −2.57361 | −0.104719 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −24.2222 | −0.983960 | ||||||||
\(607\) | −1.72055 | − | 1.25005i | −0.0698349 | − | 0.0507380i | 0.552320 | − | 0.833632i | \(-0.313743\pi\) |
−0.622155 | + | 0.782894i | \(0.713743\pi\) | |||||||
\(608\) | −0.797424 | + | 2.45422i | −0.0323398 | + | 0.0995317i | ||||
\(609\) | 1.54067 | + | 4.74169i | 0.0624311 | + | 0.192143i | ||||
\(610\) | −49.5528 | + | 36.0022i | −2.00633 | + | 1.45769i | ||||
\(611\) | 37.1793 | − | 27.0123i | 1.50411 | − | 1.09280i | ||||
\(612\) | 1.74429 | + | 5.36837i | 0.0705087 | + | 0.217003i | ||||
\(613\) | 12.6526 | − | 38.9408i | 0.511035 | − | 1.57280i | −0.279347 | − | 0.960190i | \(-0.590118\pi\) |
0.790382 | − | 0.612614i | \(-0.209882\pi\) | |||||||
\(614\) | −0.246163 | − | 0.178848i | −0.00993433 | − | 0.00721771i | ||||
\(615\) | −50.6564 | −2.04266 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.53813 | −0.303474 | −0.151737 | − | 0.988421i | \(-0.548487\pi\) | ||||
−0.151737 | + | 0.988421i | \(0.548487\pi\) | |||||||
\(618\) | 0.409404 | + | 0.297449i | 0.0164686 | + | 0.0119652i | ||||
\(619\) | −6.02754 | + | 18.5509i | −0.242267 | + | 0.745623i | 0.753806 | + | 0.657097i | \(0.228216\pi\) |
−0.996074 | + | 0.0885260i | \(0.971784\pi\) | |||||||
\(620\) | −0.731828 | − | 2.25233i | −0.0293909 | − | 0.0904559i | ||||
\(621\) | 6.58941 | − | 4.78749i | 0.264424 | − | 0.192115i | ||||
\(622\) | −0.678032 | + | 0.492619i | −0.0271866 | + | 0.0197522i | ||||
\(623\) | −1.29928 | − | 3.99878i | −0.0520546 | − | 0.160208i | ||||
\(624\) | 10.9126 | − | 33.5855i | 0.436853 | − | 1.34450i | ||||
\(625\) | −43.7881 | − | 31.8139i | −1.75152 | − | 1.27256i | ||||
\(626\) | 9.51375 | 0.380246 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.88645 | −0.155086 | ||||||||
\(629\) | −2.42893 | − | 1.76472i | −0.0968479 | − | 0.0703641i | ||||
\(630\) | −5.86839 | + | 18.0610i | −0.233802 | + | 0.719569i | ||||
\(631\) | −3.29578 | − | 10.1434i | −0.131203 | − | 0.403801i | 0.863777 | − | 0.503874i | \(-0.168092\pi\) |
−0.994980 | + | 0.100073i | \(0.968092\pi\) | |||||||
\(632\) | −11.1691 | + | 8.11485i | −0.444284 | + | 0.322792i | ||||
\(633\) | 46.0234 | − | 33.4380i | 1.82927 | − | 1.32904i | ||||
\(634\) | −6.88020 | − | 21.1751i | −0.273248 | − | 0.840970i | ||||
\(635\) | −13.6488 | + | 42.0067i | −0.541637 | + | 1.66699i | ||||
\(636\) | 3.06584 | + | 2.22746i | 0.121568 | + | 0.0883246i | ||||
\(637\) | 4.39091 | 0.173974 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.793787 | 0.0314017 | ||||||||
\(640\) | −23.8509 | − | 17.3287i | −0.942791 | − | 0.684977i | ||||
\(641\) | 0.138547 | − | 0.426405i | 0.00547230 | − | 0.0168420i | −0.948283 | − | 0.317426i | \(-0.897182\pi\) |
0.953755 | + | 0.300584i | \(0.0971815\pi\) | |||||||
\(642\) | −8.07485 | − | 24.8518i | −0.318689 | − | 0.980823i | ||||
\(643\) | 25.6005 | − | 18.5999i | 1.00959 | − | 0.733507i | 0.0454636 | − | 0.998966i | \(-0.485524\pi\) |
0.964122 | + | 0.265459i | \(0.0855235\pi\) | |||||||
\(644\) | −1.48979 | + | 1.08239i | −0.0587058 | + | 0.0426522i | ||||
\(645\) | −4.40865 | − | 13.5684i | −0.173590 | − | 0.534256i | ||||
\(646\) | 2.06482 | − | 6.35487i | 0.0812394 | − | 0.250029i | ||||
\(647\) | 24.3710 | + | 17.7065i | 0.958122 | + | 0.696116i | 0.952714 | − | 0.303869i | \(-0.0982786\pi\) |
0.00540790 | + | 0.999985i | \(0.498279\pi\) | |||||||
\(648\) | −20.2367 | −0.794972 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −65.8051 | −2.58109 | ||||||||
\(651\) | 3.25692 | + | 2.36629i | 0.127649 | + | 0.0927423i | ||||
\(652\) | 0.894744 | − | 2.75374i | 0.0350409 | − | 0.107845i | ||||
\(653\) | 10.6954 | + | 32.9170i | 0.418543 | + | 1.28814i | 0.909043 | + | 0.416702i | \(0.136814\pi\) |
−0.490500 | + | 0.871441i | \(0.663186\pi\) | |||||||
\(654\) | −13.0744 | + | 9.49912i | −0.511250 | + | 0.371445i | ||||
\(655\) | 28.8116 | − | 20.9328i | 1.12576 | − | 0.817913i | ||||
\(656\) | 4.63691 | + | 14.2710i | 0.181041 | + | 0.557187i | ||||
\(657\) | −12.3272 | + | 37.9391i | −0.480929 | + | 1.48015i | ||||
\(658\) | 10.8091 | + | 7.85327i | 0.421383 | + | 0.306152i | ||||
\(659\) | 20.2587 | 0.789167 | 0.394584 | − | 0.918860i | \(-0.370889\pi\) | ||||
0.394584 | + | 0.918860i | \(0.370889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.6737 | 1.58202 | 0.791012 | − | 0.611801i | \(-0.209555\pi\) | ||||
0.791012 | + | 0.611801i | \(0.209555\pi\) | |||||||
\(662\) | −29.5520 | − | 21.4708i | −1.14857 | − | 0.834487i | ||||
\(663\) | 14.6505 | − | 45.0897i | 0.568980 | − | 1.75114i | ||||
\(664\) | −2.29520 | − | 7.06389i | −0.0890710 | − | 0.274132i | ||||
\(665\) | −4.13358 | + | 3.00322i | −0.160293 | + | 0.116460i | ||||
\(666\) | −2.68974 | + | 1.95421i | −0.104225 | + | 0.0757242i | ||||
\(667\) | 2.97352 | + | 9.15157i | 0.115135 | + | 0.354350i | ||||
\(668\) | 2.44365 | − | 7.52078i | 0.0945476 | − | 0.290988i | ||||
\(669\) | −17.8690 | − | 12.9826i | −0.690854 | − | 0.501935i | ||||
\(670\) | 39.6567 | 1.53207 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −5.32312 | −0.205344 | ||||||||
\(673\) | 20.0219 | + | 14.5467i | 0.771786 | + | 0.560735i | 0.902503 | − | 0.430685i | \(-0.141728\pi\) |
−0.130717 | + | 0.991420i | \(0.541728\pi\) | |||||||
\(674\) | 0.682659 | − | 2.10101i | 0.0262950 | − | 0.0809278i | ||||
\(675\) | −5.94320 | − | 18.2913i | −0.228754 | − | 0.704032i | ||||
\(676\) | 1.88180 | − | 1.36721i | 0.0723771 | − | 0.0525850i | ||||
\(677\) | −9.20835 | + | 6.69026i | −0.353906 | + | 0.257128i | −0.750506 | − | 0.660864i | \(-0.770190\pi\) |
0.396600 | + | 0.917992i | \(0.370190\pi\) | |||||||
\(678\) | 3.09135 | + | 9.51419i | 0.118723 | + | 0.365390i | ||||
\(679\) | 3.37598 | − | 10.3902i | 0.129558 | − | 0.398739i | ||||
\(680\) | −41.9817 | − | 30.5015i | −1.60993 | − | 1.16968i | ||||
\(681\) | −68.4475 | −2.62291 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.212700 | −0.00813875 | −0.00406938 | − | 0.999992i | \(-0.501295\pi\) | ||||
−0.00406938 | + | 0.999992i | \(0.501295\pi\) | |||||||
\(684\) | 1.36057 | + | 0.988511i | 0.0520226 | + | 0.0377967i | ||||
\(685\) | −15.1690 | + | 46.6853i | −0.579577 | + | 1.78375i | ||||
\(686\) | 0.394480 | + | 1.21408i | 0.0150613 | + | 0.0463540i | ||||
\(687\) | 23.7818 | − | 17.2785i | 0.907332 | − | 0.659215i | ||||
\(688\) | −3.41895 | + | 2.48401i | −0.130346 | + | 0.0947021i | ||||
\(689\) | −5.38920 | − | 16.5862i | −0.205312 | − | 0.631886i | ||||
\(690\) | −20.6712 | + | 63.6195i | −0.786940 | + | 2.42195i | ||||
\(691\) | −29.4324 | − | 21.3839i | −1.11966 | − | 0.813481i | −0.135503 | − | 0.990777i | \(-0.543265\pi\) |
−0.984158 | + | 0.177296i | \(0.943265\pi\) | |||||||
\(692\) | 7.19966 | 0.273690 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.48514 | 0.132294 | ||||||||
\(695\) | −27.1082 | − | 19.6952i | −1.02827 | − | 0.747083i | ||||
\(696\) | −4.66198 | + | 14.3481i | −0.176712 | + | 0.543864i | ||||
\(697\) | 6.22522 | + | 19.1593i | 0.235797 | + | 0.725709i | ||||
\(698\) | −31.9188 | + | 23.1904i | −1.20814 | + | 0.877769i | ||||
\(699\) | −55.4630 | + | 40.2962i | −2.09780 | + | 1.52414i | ||||
\(700\) | 1.34369 | + | 4.13544i | 0.0507865 | + | 0.156305i | ||||
\(701\) | 5.79080 | − | 17.8223i | 0.218716 | − | 0.673138i | −0.780153 | − | 0.625588i | \(-0.784859\pi\) |
0.998869 | − | 0.0475491i | \(-0.0151411\pi\) | |||||||
\(702\) | −7.42899 | − | 5.39748i | −0.280389 | − | 0.203715i | ||||
\(703\) | −0.894509 | −0.0337371 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −110.310 | −4.15453 | ||||||||
\(706\) | −24.7391 | − | 17.9740i | −0.931068 | − | 0.676461i | ||||
\(707\) | 2.27616 | − | 7.00529i | 0.0856036 | − | 0.263461i | ||||
\(708\) | 4.05666 | + | 12.4851i | 0.152458 | + | 0.469219i | ||||
\(709\) | 10.3227 | − | 7.49988i | 0.387677 | − | 0.281664i | −0.376826 | − | 0.926284i | \(-0.622985\pi\) |
0.764503 | + | 0.644620i | \(0.222985\pi\) | |||||||
\(710\) | −0.922491 | + | 0.670229i | −0.0346205 | + | 0.0251533i | ||||
\(711\) | 5.12626 | + | 15.7770i | 0.192250 | + | 0.591684i | ||||
\(712\) | 3.93156 | − | 12.1001i | 0.147341 | − | 0.453470i | ||||
\(713\) | 6.28593 | + | 4.56700i | 0.235410 | + | 0.171035i | ||||
\(714\) | 13.7835 | 0.515835 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.66558 | −0.249105 | ||||||||
\(717\) | 15.6571 | + | 11.3755i | 0.584725 | + | 0.424827i | ||||
\(718\) | −0.598073 | + | 1.84068i | −0.0223199 | + | 0.0686936i | ||||
\(719\) | −5.29123 | − | 16.2847i | −0.197329 | − | 0.607318i | −0.999942 | − | 0.0108162i | \(-0.996557\pi\) |
0.802612 | − | 0.596501i | \(-0.203443\pi\) | |||||||
\(720\) | −37.5743 | + | 27.2993i | −1.40031 | + | 1.01739i | ||||
\(721\) | −0.124497 | + | 0.0904521i | −0.00463649 | + | 0.00336861i | ||||
\(722\) | 6.87993 | + | 21.1742i | 0.256044 | + | 0.788024i | ||||
\(723\) | 21.8423 | − | 67.2238i | 0.812325 | − | 2.50008i | ||||
\(724\) | 4.54191 | + | 3.29989i | 0.168799 | + | 0.122640i | ||||
\(725\) | 22.7216 | 0.843858 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.65786 | −0.321102 | −0.160551 | − | 0.987028i | \(-0.551327\pi\) | ||||
−0.160551 | + | 0.987028i | \(0.551327\pi\) | |||||||
\(728\) | 10.7491 | + | 7.80970i | 0.398389 | + | 0.289447i | ||||
\(729\) | −11.4264 | + | 35.1668i | −0.423200 | + | 1.30248i | ||||
\(730\) | −17.7078 | − | 54.4989i | −0.655394 | − | 2.01710i | ||||
\(731\) | −4.59006 | + | 3.33488i | −0.169770 | + | 0.123345i | ||||
\(732\) | −9.05219 | + | 6.57680i | −0.334579 | + | 0.243086i | ||||
\(733\) | −8.67924 | − | 26.7120i | −0.320575 | − | 0.986629i | −0.973398 | − | 0.229119i | \(-0.926416\pi\) |
0.652823 | − | 0.757510i | \(-0.273584\pi\) | |||||||
\(734\) | −3.44068 | + | 10.5893i | −0.126998 | + | 0.390859i | ||||
\(735\) | −8.52678 | − | 6.19507i | −0.314515 | − | 0.228509i | ||||
\(736\) | −10.2737 | −0.378695 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 22.3084 | 0.821182 | ||||||||
\(739\) | −27.4228 | − | 19.9239i | −1.00877 | − | 0.732911i | −0.0448155 | − | 0.998995i | \(-0.514270\pi\) |
−0.963950 | + | 0.266084i | \(0.914270\pi\) | |||||||
\(740\) | −0.335431 | + | 1.03235i | −0.0123307 | + | 0.0379500i | ||||
\(741\) | −4.36496 | − | 13.4340i | −0.160351 | − | 0.493509i | ||||
\(742\) | 4.10193 | − | 2.98022i | 0.150586 | − | 0.109407i | ||||
\(743\) | −4.57354 | + | 3.32287i | −0.167787 | + | 0.121904i | −0.668510 | − | 0.743703i | \(-0.733068\pi\) |
0.500723 | + | 0.865608i | \(0.333068\pi\) | |||||||
\(744\) | 3.76438 | + | 11.5856i | 0.138009 | + | 0.424748i | ||||
\(745\) | 15.2751 | − | 47.0119i | 0.559636 | − | 1.72238i | ||||
\(746\) | 38.0171 | + | 27.6211i | 1.39191 | + | 1.01128i | ||||
\(747\) | −8.92472 | −0.326538 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.94617 | 0.290347 | ||||||||
\(750\) | 73.3633 | + | 53.3015i | 2.67885 | + | 1.94630i | ||||
\(751\) | 13.7021 | − | 42.1707i | 0.499997 | − | 1.53883i | −0.309025 | − | 0.951054i | \(-0.600003\pi\) |
0.809022 | − | 0.587778i | \(-0.199997\pi\) | |||||||
\(752\) | 10.0974 | + | 31.0767i | 0.368216 | + | 1.13325i | ||||
\(753\) | 4.01209 | − | 2.91495i | 0.146209 | − | 0.106227i | ||||
\(754\) | 8.77667 | − | 6.37663i | 0.319628 | − | 0.232223i | ||||
\(755\) | −8.78515 | − | 27.0379i | −0.319724 | − | 0.984011i | ||||
\(756\) | −0.187504 | + | 0.577077i | −0.00681944 | + | 0.0209881i | ||||
\(757\) | 17.2953 | + | 12.5657i | 0.628607 | + | 0.456710i | 0.855917 | − | 0.517113i | \(-0.172993\pi\) |
−0.227311 | + | 0.973822i | \(0.572993\pi\) | |||||||
\(758\) | −3.31700 | −0.120479 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.4607 | −0.560819 | ||||||||
\(761\) | −3.70994 | − | 2.69543i | −0.134485 | − | 0.0977092i | 0.518509 | − | 0.855072i | \(-0.326487\pi\) |
−0.652994 | + | 0.757363i | \(0.726487\pi\) | |||||||
\(762\) | 10.9702 | − | 33.7627i | 0.397407 | − | 1.22309i | ||||
\(763\) | −1.51863 | − | 4.67387i | −0.0549782 | − | 0.169205i | ||||
\(764\) | −7.11883 | + | 5.17214i | −0.257550 | + | 0.187121i | ||||
\(765\) | −50.4449 | + | 36.6503i | −1.82384 | + | 1.32510i | ||||
\(766\) | −7.58948 | − | 23.3580i | −0.274219 | − | 0.843960i | ||||
\(767\) | 18.6689 | − | 57.4569i | 0.674095 | − | 2.07465i | ||||
\(768\) | −17.8510 | − | 12.9695i | −0.644144 | − | 0.467998i | ||||
\(769\) | −12.8223 | −0.462385 | −0.231193 | − | 0.972908i | \(-0.574263\pi\) | ||||
−0.231193 | + | 0.972908i | \(0.574263\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.1736 | −0.942621 | ||||||||
\(772\) | −4.21249 | − | 3.06055i | −0.151611 | − | 0.110152i | ||||
\(773\) | 16.7067 | − | 51.4178i | 0.600897 | − | 1.84937i | 0.0780395 | − | 0.996950i | \(-0.475134\pi\) |
0.522857 | − | 0.852420i | \(-0.324866\pi\) | |||||||
\(774\) | 1.94150 | + | 5.97534i | 0.0697859 | + | 0.214779i | ||||
\(775\) | 14.8429 | − | 10.7840i | 0.533173 | − | 0.387373i | ||||
\(776\) | 26.7446 | − | 19.4311i | 0.960075 | − | 0.697535i | ||||
\(777\) | −0.570199 | − | 1.75489i | −0.0204558 | − | 0.0629564i | ||||
\(778\) | 11.1768 | − | 34.3988i | 0.400709 | − | 1.23326i | ||||
\(779\) | 4.85576 | + | 3.52792i | 0.173976 | + | 0.126401i | ||||
\(780\) | −17.1409 | −0.613743 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.6025 | 0.951302 | ||||||||
\(783\) | 2.56512 | + | 1.86367i | 0.0916700 | + | 0.0666021i | ||||
\(784\) | −0.964766 | + | 2.96924i | −0.0344559 | + | 0.106044i | ||||
\(785\) | −13.2666 | − | 40.8304i | −0.473505 | − | 1.45730i | ||||
\(786\) | −23.1572 | + | 16.8247i | −0.825988 | + | 0.600116i | ||||
\(787\) | −35.4766 | + | 25.7752i | −1.26460 | + | 0.918788i | −0.998974 | − | 0.0452876i | \(-0.985580\pi\) |
−0.265629 | + | 0.964075i | \(0.585580\pi\) | |||||||
\(788\) | 2.06780 | + | 6.36403i | 0.0736622 | + | 0.226709i | ||||
\(789\) | −3.49281 | + | 10.7498i | −0.124347 | + | 0.382702i | ||||
\(790\) | −19.2787 | − | 14.0068i | −0.685904 | − | 0.498338i | ||||
\(791\) | −3.04208 | −0.108164 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.4928 | 1.82856 | ||||||||
\(794\) | −10.7063 | − | 7.77856i | −0.379951 | − | 0.276051i | ||||
\(795\) | −12.9359 | + | 39.8127i | −0.458790 | + | 1.41201i | ||||
\(796\) | −0.176688 | − | 0.543791i | −0.00626255 | − | 0.0192742i | ||||
\(797\) | 28.9383 | − | 21.0249i | 1.02505 | − | 0.744740i | 0.0577359 | − | 0.998332i | \(-0.481612\pi\) |
0.967311 | + | 0.253591i | \(0.0816119\pi\) | |||||||
\(798\) | 3.32234 | − | 2.41382i | 0.117610 | − | 0.0854484i | ||||
\(799\) | 13.5562 | + | 41.7216i | 0.479583 | + | 1.47600i | ||||
\(800\) | −7.49652 | + | 23.0719i | −0.265042 | + | 0.815716i | ||||
\(801\) | −12.3679 | − | 8.98582i | −0.436999 | − | 0.317498i | ||||
\(802\) | 16.3244 | 0.576436 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.24440 | 0.255490 | ||||||||
\(805\) | −16.4569 | − | 11.9566i | −0.580029 | − | 0.421415i | ||||
\(806\) | 2.70693 | − | 8.33108i | 0.0953477 | − | 0.293450i | ||||
\(807\) | −0.497825 | − | 1.53215i | −0.0175243 | − | 0.0539342i | ||||
\(808\) | 18.0318 | − | 13.1009i | 0.634356 | − | 0.460886i | ||||
\(809\) | −24.8424 | + | 18.0490i | −0.873411 | + | 0.634570i | −0.931500 | − | 0.363741i | \(-0.881499\pi\) |
0.0580894 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(810\) | −10.7939 | − | 33.2202i | −0.379259 | − | 1.16724i | ||||
\(811\) | −5.28368 | + | 16.2615i | −0.185535 | + | 0.571019i | −0.999957 | − | 0.00925442i | \(-0.997054\pi\) |
0.814422 | + | 0.580273i | \(0.197054\pi\) | |||||||
\(812\) | −0.579943 | − | 0.421353i | −0.0203520 | − | 0.0147866i | ||||
\(813\) | −30.7514 | −1.07850 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.9845 | 1.12037 | ||||||||
\(816\) | 27.2718 | + | 19.8141i | 0.954705 | + | 0.693634i | ||||
\(817\) | −0.522360 | + | 1.60766i | −0.0182751 | + | 0.0562449i | ||||
\(818\) | −12.6319 | − | 38.8771i | −0.441665 | − | 1.35931i | ||||
\(819\) | 12.9161 | − | 9.38406i | 0.451324 | − | 0.327906i | ||||
\(820\) | 5.89241 | − | 4.28109i | 0.205772 | − | 0.149502i | ||||
\(821\) | 3.82631 | + | 11.7762i | 0.133539 | + | 0.410991i | 0.995360 | − | 0.0962218i | \(-0.0306758\pi\) |
−0.861821 | + | 0.507213i | \(0.830676\pi\) | |||||||
\(822\) | 12.1920 | − | 37.5231i | 0.425244 | − | 1.30877i | ||||
\(823\) | −37.3268 | − | 27.1195i | −1.30113 | − | 0.945326i | −0.301164 | − | 0.953572i | \(-0.597375\pi\) |
−0.999966 | + | 0.00824607i | \(0.997375\pi\) | |||||||
\(824\) | −0.465652 | −0.0162217 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.5640 | 0.611131 | ||||||||
\(827\) | 37.7894 | + | 27.4556i | 1.31407 | + | 0.954725i | 0.999986 | + | 0.00532868i | \(0.00169618\pi\) |
0.314080 | + | 0.949396i | \(0.398304\pi\) | |||||||
\(828\) | −2.06903 | + | 6.36782i | −0.0719037 | + | 0.221297i | ||||
\(829\) | 1.24396 | + | 3.82852i | 0.0432046 | + | 0.132970i | 0.970332 | − | 0.241776i | \(-0.0777299\pi\) |
−0.927127 | + | 0.374746i | \(0.877730\pi\) | |||||||
\(830\) | 10.3718 | − | 7.53553i | 0.360009 | − | 0.261562i | ||||
\(831\) | −59.5146 | + | 43.2399i | −2.06454 | + | 1.49997i | ||||
\(832\) | 12.0517 | + | 37.0912i | 0.417816 | + | 1.28591i | ||||
\(833\) | −1.29523 | + | 3.98632i | −0.0448772 | + | 0.138118i | ||||
\(834\) | 21.7880 | + | 15.8299i | 0.754458 | + | 0.548146i | ||||
\(835\) | 87.3534 | 3.02299 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.56020 | 0.0884933 | ||||||||
\(838\) | −20.7517 | − | 15.0770i | −0.716857 | − | 0.520827i | ||||
\(839\) | −4.41960 | + | 13.6021i | −0.152582 | + | 0.469598i | −0.997908 | − | 0.0646525i | \(-0.979406\pi\) |
0.845326 | + | 0.534250i | \(0.179406\pi\) | |||||||
\(840\) | −9.85533 | − | 30.3316i | −0.340041 | − | 1.04654i | ||||
\(841\) | 20.4310 | − | 14.8440i | 0.704518 | − | 0.511863i | ||||
\(842\) | −23.1590 | + | 16.8260i | −0.798110 | + | 0.579861i | ||||
\(843\) | 11.7002 | + | 36.0096i | 0.402977 | + | 1.24024i | ||||
\(844\) | −2.52758 | + | 7.77908i | −0.0870028 | + | 0.267767i | ||||
\(845\) | 20.7873 | + | 15.1028i | 0.715104 | + | 0.519554i | ||||
\(846\) | 48.5792 | 1.67019 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.4002 | 0.425823 | ||||||||
\(849\) | −46.9738 | − | 34.1285i | −1.61214 | − | 1.17129i | ||||
\(850\) | 19.4112 | − | 59.7417i | 0.665800 | − | 2.04912i | ||||
\(851\) | −1.10050 | − | 3.38698i | −0.0377245 | − | 0.116104i | ||||
\(852\) | −0.168519 | + | 0.122436i | −0.00577335 | + | 0.00419459i | ||||
\(853\) | −26.1318 | + | 18.9859i | −0.894735 | + | 0.650063i | −0.937108 | − | 0.349038i | \(-0.886508\pi\) |
0.0423729 | + | 0.999102i | \(0.486508\pi\) | |||||||
\(854\) | 4.62612 | + | 14.2377i | 0.158303 | + | 0.487205i | ||||
\(855\) | −5.74075 | + | 17.6682i | −0.196330 | + | 0.604240i | ||||
\(856\) | 19.4526 | + | 14.1331i | 0.664875 | + | 0.483060i | ||||
\(857\) | −16.2318 | −0.554468 | −0.277234 | − | 0.960802i | \(-0.589418\pi\) | ||||
−0.277234 | + | 0.960802i | \(0.589418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2893 | −0.965220 | −0.482610 | − | 0.875835i | \(-0.660311\pi\) | ||||
−0.482610 | + | 0.875835i | \(0.660311\pi\) | |||||||
\(860\) | 1.65952 | + | 1.20571i | 0.0565890 | + | 0.0411143i | ||||
\(861\) | −3.82597 | + | 11.7751i | −0.130389 | + | 0.401295i | ||||
\(862\) | 4.76754 | + | 14.6730i | 0.162383 | + | 0.499764i | ||||
\(863\) | −25.8776 | + | 18.8012i | −0.880885 | + | 0.640001i | −0.933486 | − | 0.358615i | \(-0.883249\pi\) |
0.0526003 | + | 0.998616i | \(0.483249\pi\) | |||||||
\(864\) | −2.73872 | + | 1.98980i | −0.0931731 | + | 0.0676942i | ||||
\(865\) | 24.5764 | + | 75.6384i | 0.835622 | + | 2.57178i | ||||
\(866\) | 0.119312 | − | 0.367204i | 0.00405438 | − | 0.0124781i | ||||
\(867\) | 1.18447 | + | 0.860569i | 0.0402268 | + | 0.0292265i | ||||
\(868\) | −0.578830 | −0.0196468 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −26.0403 | −0.882848 | ||||||||
\(871\) | −26.9718 | − | 19.5962i | −0.913905 | − | 0.663991i | ||||
\(872\) | 4.59530 | − | 14.1429i | 0.155617 | − | 0.478938i | ||||
\(873\) | −12.2749 | − | 37.7782i | −0.415442 | − | 1.27860i | ||||
\(874\) | 6.41219 | − | 4.65873i | 0.216896 | − | 0.157584i | ||||
\(875\) | −22.3092 | + | 16.2086i | −0.754189 | + | 0.547951i | ||||
\(876\) | −3.23482 | − | 9.95574i | −0.109294 | − | 0.336373i | ||||
\(877\) | −14.1520 | + | 43.5553i | −0.477878 | + | 1.47076i | 0.364157 | + | 0.931337i | \(0.381357\pi\) |
−0.842036 | + | 0.539421i | \(0.818643\pi\) | |||||||
\(878\) | 3.64144 | + | 2.64566i | 0.122893 | + | 0.0892867i | ||||
\(879\) | 43.3496 | 1.46215 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.7142 | 0.900025 | 0.450012 | − | 0.893022i | \(-0.351420\pi\) | ||||
0.450012 | + | 0.893022i | \(0.351420\pi\) | |||||||
\(882\) | 3.75507 | + | 2.72822i | 0.126440 | + | 0.0918639i | ||||
\(883\) | −8.80295 | + | 27.0927i | −0.296243 | + | 0.911742i | 0.686558 | + | 0.727075i | \(0.259121\pi\) |
−0.982801 | + | 0.184667i | \(0.940879\pi\) | |||||||
\(884\) | 2.10647 | + | 6.48304i | 0.0708481 | + | 0.218048i | ||||
\(885\) | −117.319 | + | 85.2370i | −3.94362 | + | 2.86521i | ||||
\(886\) | −22.5600 | + | 16.3908i | −0.757918 | + | 0.550660i | ||||
\(887\) | 7.29711 | + | 22.4582i | 0.245013 | + | 0.754072i | 0.995634 | + | 0.0933398i | \(0.0297543\pi\) |
−0.750621 | + | 0.660733i | \(0.770246\pi\) | |||||||
\(888\) | 1.72539 | − | 5.31021i | 0.0579004 | − | 0.178199i | ||||
\(889\) | 8.73362 | + | 6.34535i | 0.292916 | + | 0.212816i | ||||
\(890\) | 21.9604 | 0.736113 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.17572 | 0.106331 | ||||||||
\(893\) | 10.5740 | + | 7.68246i | 0.353845 | + | 0.257084i | ||||
\(894\) | −12.2773 | + | 37.7856i | −0.410614 | + | 1.26374i | ||||
\(895\) | −22.7533 | − | 70.0274i | −0.760559 | − | 2.34076i | ||||
\(896\) | −5.82947 | + | 4.23536i | −0.194749 | + | 0.141493i | ||||
\(897\) | 45.4964 | − | 33.0551i | 1.51908 | − | 1.10368i | ||||
\(898\) | −3.66934 | − | 11.2931i | −0.122448 | − | 0.376855i | ||||
\(899\) | −0.934665 | + | 2.87660i | −0.0311728 | + | 0.0959401i | ||||
\(900\) | 12.7906 | + | 9.29292i | 0.426353 | + | 0.309764i | ||||
\(901\) | 16.6477 | 0.554614 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.48696 | −0.116039 | ||||||||
\(904\) | −7.44715 | − | 5.41067i | −0.247689 | − | 0.179956i | ||||
\(905\) | −19.1640 | + | 58.9809i | −0.637034 | + | 1.96059i | ||||
\(906\) | 7.06102 | + | 21.7316i | 0.234587 | + | 0.721984i | ||||
\(907\) | −19.3706 | + | 14.0736i | −0.643192 | + | 0.467306i | −0.860945 | − | 0.508698i | \(-0.830127\pi\) |
0.217754 | + | 0.976004i | \(0.430127\pi\) | |||||||
\(908\) | 7.96189 | − | 5.78465i | 0.264225 | − | 0.191970i | ||||
\(909\) | −8.27599 | − | 25.4709i | −0.274497 | − | 0.844816i | ||||
\(910\) | −7.08688 | + | 21.8112i | −0.234928 | + | 0.723034i | ||||
\(911\) | −14.7555 | − | 10.7205i | −0.488873 | − | 0.355187i | 0.315878 | − | 0.948800i | \(-0.397701\pi\) |
−0.804751 | + | 0.593613i | \(0.797701\pi\) | |||||||
\(912\) | 10.0435 | 0.332572 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −14.4463 | −0.477841 | ||||||||
\(915\) | −99.9947 | − | 72.6504i | −3.30572 | − | 2.40175i | ||||
\(916\) | −1.30608 | + | 4.01971i | −0.0431541 | + | 0.132815i | ||||
\(917\) | −2.68977 | − | 8.27827i | −0.0888241 | − | 0.273373i | ||||
\(918\) | 7.09154 | − | 5.15231i | 0.234056 | − | 0.170052i | ||||
\(919\) | 22.9780 | − | 16.6945i | 0.757975 | − | 0.550701i | −0.140313 | − | 0.990107i | \(-0.544811\pi\) |
0.898289 | + | 0.439406i | \(0.144811\pi\) | |||||||
\(920\) | −19.0210 | − | 58.5406i | −0.627104 | − | 1.93003i | ||||
\(921\) | 0.189739 | − | 0.583956i | 0.00625211 | − | 0.0192420i | ||||
\(922\) | 0.701061 | + | 0.509350i | 0.0230882 | + | 0.0167746i | ||||
\(923\) | 0.958607 | 0.0315529 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.40922 | −0.276493 | ||||||||
\(926\) | −13.9357 | − | 10.1249i | −0.457956 | − | 0.332725i | ||||
\(927\) | −0.172902 | + | 0.532138i | −0.00567885 | + | 0.0174777i | ||||
\(928\) | −1.23587 | − | 3.80361i | −0.0405694 | − | 0.124860i | ||||
\(929\) | −2.74227 | + | 1.99237i | −0.0899709 | + | 0.0653677i | −0.631861 | − | 0.775081i | \(-0.717709\pi\) |
0.541890 | + | 0.840449i | \(0.317709\pi\) | |||||||
\(930\) | −17.0109 | + | 12.3591i | −0.557808 | + | 0.405271i | ||||
\(931\) | 0.385900 | + | 1.18768i | 0.0126474 | + | 0.0389246i | ||||
\(932\) | 3.04599 | − | 9.37460i | 0.0997748 | − | 0.307075i | ||||
\(933\) | −1.36823 | − | 0.994078i | −0.0447939 | − | 0.0325446i | ||||
\(934\) | −37.8588 | −1.23878 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 48.3096 | 1.57905 | ||||||||
\(937\) | 36.7190 | + | 26.6779i | 1.19956 | + | 0.871529i | 0.994241 | − | 0.107167i | \(-0.0341780\pi\) |
0.205315 | + | 0.978696i | \(0.434178\pi\) | |||||||
\(938\) | 2.99518 | − | 9.21822i | 0.0977962 | − | 0.300986i | ||||
\(939\) | 5.93257 | + | 18.2586i | 0.193602 | + | 0.595846i | ||||
\(940\) | 12.8314 | − | 9.32258i | 0.418515 | − | 0.304069i | ||||
\(941\) | 17.4164 | − | 12.6538i | 0.567759 | − | 0.412501i | −0.266531 | − | 0.963826i | \(-0.585878\pi\) |
0.834291 | + | 0.551325i | \(0.185878\pi\) | |||||||
\(942\) | 10.6630 | + | 32.8172i | 0.347418 | + | 1.06924i | ||||
\(943\) | −7.38420 | + | 22.7262i | −0.240463 | + | 0.740068i | ||||
\(944\) | 34.7519 | + | 25.2488i | 1.13108 | + | 0.821777i | ||||
\(945\) | −6.70272 | −0.218039 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.2673 | −0.366140 | −0.183070 | − | 0.983100i | \(-0.558603\pi\) | ||||
−0.183070 | + | 0.983100i | \(0.558603\pi\) | |||||||
\(948\) | −3.52178 | − | 2.55872i | −0.114382 | − | 0.0831035i | ||||
\(949\) | −14.8867 | + | 45.8167i | −0.483244 | + | 1.48727i | ||||
\(950\) | −5.78336 | − | 17.7994i | −0.187637 | − | 0.577487i | ||||
\(951\) | 36.3484 | − | 26.4087i | 1.17868 | − | 0.856359i | ||||
\(952\) | −10.2609 | + | 7.45496i | −0.332557 | + | 0.241617i | ||||
\(953\) | 7.37612 | + | 22.7014i | 0.238936 | + | 0.735370i | 0.996575 | + | 0.0826956i | \(0.0263529\pi\) |
−0.757639 | + | 0.652674i | \(0.773647\pi\) | |||||||
\(954\) | 5.69679 | − | 17.5329i | 0.184440 | − | 0.567649i | ||||
\(955\) | −78.6380 | − | 57.1339i | −2.54467 | − | 1.84881i | ||||
\(956\) | −2.78262 | −0.0899964 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.00159 | 0.193902 | ||||||||
\(959\) | 9.70634 | + | 7.05207i | 0.313434 | + | 0.227723i | ||||
\(960\) | 28.9281 | − | 89.0316i | 0.933651 | − | 2.87348i | ||||
\(961\) | −8.82482 | − | 27.1600i | −0.284672 | − | 0.876129i | ||||
\(962\) | −3.24823 | + | 2.35998i | −0.104727 | + | 0.0760888i | ||||
\(963\) | 23.3740 | − | 16.9822i | 0.753217 | − | 0.547244i | ||||
\(964\) | 3.14051 | + | 9.66548i | 0.101149 | + | 0.311304i | ||||
\(965\) | 17.7741 | − | 54.7030i | 0.572168 | − | 1.76095i | ||||
\(966\) | 13.2271 | + | 9.61007i | 0.425576 | + | 0.309199i | ||||
\(967\) | −20.5165 | −0.659765 | −0.329882 | − | 0.944022i | \(-0.607009\pi\) | ||||
−0.329882 | + | 0.944022i | \(0.607009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.4837 | 0.433159 | ||||||||
\(970\) | 46.1629 | + | 33.5393i | 1.48220 | + | 1.07688i | ||||
\(971\) | −10.7428 | + | 33.0630i | −0.344754 | + | 1.06104i | 0.616962 | + | 0.786993i | \(0.288363\pi\) |
−0.961715 | + | 0.274050i | \(0.911637\pi\) | |||||||
\(972\) | −2.53432 | − | 7.79982i | −0.0812882 | − | 0.250179i | ||||
\(973\) | −6.62558 | + | 4.81377i | −0.212406 | + | 0.154322i | ||||
\(974\) | 33.4344 | − | 24.2915i | 1.07131 | − | 0.778350i | ||||
\(975\) | −41.0347 | − | 126.292i | −1.31416 | − | 4.04457i | ||||
\(976\) | −11.3139 | + | 34.8207i | −0.362150 | + | 1.11458i | ||||
\(977\) | −4.67850 | − | 3.39913i | −0.149678 | − | 0.108748i | 0.510426 | − | 0.859922i | \(-0.329488\pi\) |
−0.660104 | + | 0.751174i | \(0.729488\pi\) | |||||||
\(978\) | −25.7074 | −0.822032 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.51540 | 0.0484078 | ||||||||
\(981\) | −14.4559 | − | 10.5028i | −0.461542 | − | 0.335330i | ||||
\(982\) | −2.70453 | + | 8.32369i | −0.0863050 | + | 0.265620i | ||||
\(983\) | −5.32500 | − | 16.3887i | −0.169841 | − | 0.522718i | 0.829519 | − | 0.558478i | \(-0.188615\pi\) |
−0.999360 | + | 0.0357606i | \(0.988615\pi\) | |||||||
\(984\) | −30.3094 | + | 22.0211i | −0.966229 | + | 0.702007i | ||||
\(985\) | −59.8008 | + | 43.4478i | −1.90541 | + | 1.38436i | ||||
\(986\) | 3.20012 | + | 9.84895i | 0.101912 | + | 0.313654i | ||||
\(987\) | −8.33150 | + | 25.6417i | −0.265195 | + | 0.816185i | ||||
\(988\) | 1.64307 | + | 1.19376i | 0.0522731 | + | 0.0379786i | ||||
\(989\) | −6.72991 | −0.213999 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0077 | −0.762630 | −0.381315 | − | 0.924445i | \(-0.624529\pi\) | ||||
−0.381315 | + | 0.924445i | \(0.624529\pi\) | |||||||
\(992\) | −2.61259 | − | 1.89815i | −0.0829497 | − | 0.0602665i | ||||
\(993\) | 22.7783 | − | 70.1044i | 0.722847 | − | 2.22469i | ||||
\(994\) | 0.0861214 | + | 0.265054i | 0.00273161 | + | 0.00840702i | ||||
\(995\) | 5.10983 | − | 3.71251i | 0.161993 | − | 0.117695i | ||||
\(996\) | 1.89469 | − | 1.37657i | 0.0600355 | − | 0.0436184i | ||||
\(997\) | −11.1350 | − | 34.2699i | −0.352648 | − | 1.08534i | −0.957361 | − | 0.288895i | \(-0.906712\pi\) |
0.604713 | − | 0.796443i | \(-0.293288\pi\) | |||||||
\(998\) | −4.32628 | + | 13.3149i | −0.136946 | + | 0.421476i | ||||
\(999\) | −0.949348 | − | 0.689741i | −0.0300360 | − | 0.0218225i |
(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.323.4 | 24 | ||
11.2 | odd | 10 | 847.2.f.y.148.4 | 24 | |||
11.3 | even | 5 | inner | 847.2.f.z.729.4 | 24 | ||
11.4 | even | 5 | inner | 847.2.f.z.372.3 | 24 | ||
11.5 | even | 5 | 847.2.a.m.1.3 | ✓ | 6 | ||
11.6 | odd | 10 | 847.2.a.n.1.4 | yes | 6 | ||
11.7 | odd | 10 | 847.2.f.y.372.4 | 24 | |||
11.8 | odd | 10 | 847.2.f.y.729.3 | 24 | |||
11.9 | even | 5 | inner | 847.2.f.z.148.3 | 24 | ||
11.10 | odd | 2 | 847.2.f.y.323.3 | 24 | |||
33.5 | odd | 10 | 7623.2.a.cs.1.4 | 6 | |||
33.17 | even | 10 | 7623.2.a.cp.1.3 | 6 | |||
77.6 | even | 10 | 5929.2.a.bm.1.4 | 6 | |||
77.27 | odd | 10 | 5929.2.a.bj.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.3 | ✓ | 6 | 11.5 | even | 5 | ||
847.2.a.n.1.4 | yes | 6 | 11.6 | odd | 10 | ||
847.2.f.y.148.4 | 24 | 11.2 | odd | 10 | |||
847.2.f.y.323.3 | 24 | 11.10 | odd | 2 | |||
847.2.f.y.372.4 | 24 | 11.7 | odd | 10 | |||
847.2.f.y.729.3 | 24 | 11.8 | odd | 10 | |||
847.2.f.z.148.3 | 24 | 11.9 | even | 5 | inner | ||
847.2.f.z.323.4 | 24 | 1.1 | even | 1 | trivial | ||
847.2.f.z.372.3 | 24 | 11.4 | even | 5 | inner | ||
847.2.f.z.729.4 | 24 | 11.3 | even | 5 | inner | ||
5929.2.a.bj.1.3 | 6 | 77.27 | odd | 10 | |||
5929.2.a.bm.1.4 | 6 | 77.6 | even | 10 | |||
7623.2.a.cp.1.3 | 6 | 33.17 | even | 10 | |||
7623.2.a.cs.1.4 | 6 | 33.5 | odd | 10 |