Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(101,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bk (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.14 | ||
Character | \(\chi\) | \(=\) | 630.101 |
Dual form | 630.2.bk.c.131.6 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0.661104 | + | 1.60092i | 0.381689 | + | 0.924291i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −1.60092 | + | 0.661104i | −0.653572 | + | 0.269895i | ||||
\(7\) | −2.57921 | + | 0.589657i | −0.974848 | + | 0.222869i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.12588 | + | 2.11675i | −0.708628 | + | 0.705583i | ||||
\(10\) | 0.866025 | + | 0.500000i | 0.273861 | + | 0.158114i | ||||
\(11\) | −2.51862 | + | 1.45413i | −0.759392 | + | 0.438435i | −0.829077 | − | 0.559134i | \(-0.811134\pi\) |
0.0696854 | + | 0.997569i | \(0.477800\pi\) | |||||||
\(12\) | −0.661104 | − | 1.60092i | −0.190844 | − | 0.462145i | ||||
\(13\) | 1.69585 | − | 0.979098i | 0.470344 | − | 0.271553i | −0.246040 | − | 0.969260i | \(-0.579129\pi\) |
0.716384 | + | 0.697707i | \(0.245796\pi\) | |||||||
\(14\) | −0.589657 | − | 2.57921i | −0.157592 | − | 0.689322i | ||||
\(15\) | 1.71699 | + | 0.227927i | 0.443325 | + | 0.0588504i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.68420 | + | 2.91713i | −0.408479 | + | 0.707507i | −0.994720 | − | 0.102630i | \(-0.967274\pi\) |
0.586240 | + | 0.810137i | \(0.300607\pi\) | |||||||
\(18\) | −2.11675 | − | 2.12588i | −0.498922 | − | 0.501075i | ||||
\(19\) | −6.97993 | + | 4.02986i | −1.60131 | + | 0.924514i | −0.610079 | + | 0.792341i | \(0.708862\pi\) |
−0.991227 | + | 0.132173i | \(0.957804\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | −2.64912 | − | 3.73928i | −0.578084 | − | 0.815977i | ||||
\(22\) | −1.45413 | − | 2.51862i | −0.310020 | − | 0.536971i | ||||
\(23\) | −2.47278 | − | 1.42766i | −0.515609 | − | 0.297687i | 0.219527 | − | 0.975606i | \(-0.429549\pi\) |
−0.735136 | + | 0.677919i | \(0.762882\pi\) | |||||||
\(24\) | 1.60092 | − | 0.661104i | 0.326786 | − | 0.134947i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0.979098 | + | 1.69585i | 0.192017 | + | 0.332583i | ||||
\(27\) | −4.79417 | − | 2.00398i | −0.922639 | − | 0.385665i | ||||
\(28\) | 2.57921 | − | 0.589657i | 0.487424 | − | 0.111435i | ||||
\(29\) | 1.87671 | + | 1.08352i | 0.348496 | + | 0.201204i | 0.664023 | − | 0.747712i | \(-0.268848\pi\) |
−0.315527 | + | 0.948917i | \(0.602181\pi\) | |||||||
\(30\) | −0.227927 | + | 1.71699i | −0.0416135 | + | 0.313478i | ||||
\(31\) | − | 2.20521i | − | 0.396067i | −0.980195 | − | 0.198034i | \(-0.936544\pi\) | ||
0.980195 | − | 0.198034i | \(-0.0634555\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −3.99300 | − | 3.07078i | −0.695093 | − | 0.534554i | ||||
\(34\) | −2.91713 | − | 1.68420i | −0.500283 | − | 0.288839i | ||||
\(35\) | −0.778946 | + | 2.52849i | −0.131666 | + | 0.427392i | ||||
\(36\) | 2.12588 | − | 2.11675i | 0.354314 | − | 0.352791i | ||||
\(37\) | 1.68075 | + | 2.91115i | 0.276314 | + | 0.478590i | 0.970466 | − | 0.241239i | \(-0.0775537\pi\) |
−0.694152 | + | 0.719829i | \(0.744220\pi\) | |||||||
\(38\) | −4.02986 | − | 6.97993i | −0.653730 | − | 1.13229i | ||||
\(39\) | 2.68859 | + | 2.06763i | 0.430519 | + | 0.331086i | ||||
\(40\) | −0.866025 | − | 0.500000i | −0.136931 | − | 0.0790569i | ||||
\(41\) | 4.24814 | + | 7.35799i | 0.663448 | + | 1.14912i | 0.979704 | + | 0.200451i | \(0.0642407\pi\) |
−0.316256 | + | 0.948674i | \(0.602426\pi\) | |||||||
\(42\) | 3.73928 | − | 2.64912i | 0.576983 | − | 0.408767i | ||||
\(43\) | 0.991430 | − | 1.71721i | 0.151192 | − | 0.261872i | −0.780474 | − | 0.625188i | \(-0.785022\pi\) |
0.931666 | + | 0.363316i | \(0.118356\pi\) | |||||||
\(44\) | 2.51862 | − | 1.45413i | 0.379696 | − | 0.219218i | ||||
\(45\) | 0.770216 | + | 2.89944i | 0.114817 | + | 0.432223i | ||||
\(46\) | 1.42766 | − | 2.47278i | 0.210497 | − | 0.364591i | ||||
\(47\) | −0.647198 | −0.0944035 | −0.0472018 | − | 0.998885i | \(-0.515030\pi\) | ||||
−0.0472018 | + | 0.998885i | \(0.515030\pi\) | |||||||
\(48\) | 0.661104 | + | 1.60092i | 0.0954221 | + | 0.231073i | ||||
\(49\) | 6.30461 | − | 3.04169i | 0.900659 | − | 0.434527i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | −5.78352 | − | 0.767750i | −0.809854 | − | 0.107506i | ||||
\(52\) | −1.69585 | + | 0.979098i | −0.235172 | + | 0.135776i | ||||
\(53\) | 9.25368 | + | 5.34261i | 1.27109 | + | 0.733865i | 0.975193 | − | 0.221355i | \(-0.0710480\pi\) |
0.295897 | + | 0.955220i | \(0.404381\pi\) | |||||||
\(54\) | 2.00398 | − | 4.79417i | 0.272707 | − | 0.652404i | ||||
\(55\) | 2.90825i | 0.392148i | ||||||||
\(56\) | 0.589657 | + | 2.57921i | 0.0787962 | + | 0.344661i | ||||
\(57\) | −11.0659 | − | 8.51014i | −1.46572 | − | 1.12720i | ||||
\(58\) | −1.08352 | + | 1.87671i | −0.142273 | + | 0.246424i | ||||
\(59\) | 9.11655 | 1.18687 | 0.593437 | − | 0.804881i | \(-0.297771\pi\) | ||||
0.593437 | + | 0.804881i | \(0.297771\pi\) | |||||||
\(60\) | −1.71699 | − | 0.227927i | −0.221662 | − | 0.0294252i | ||||
\(61\) | − | 3.03785i | − | 0.388957i | −0.980907 | − | 0.194478i | \(-0.937699\pi\) | ||
0.980907 | − | 0.194478i | \(-0.0623014\pi\) | |||||||
\(62\) | 2.20521 | 0.280062 | ||||||||
\(63\) | 4.23494 | − | 6.71307i | 0.533552 | − | 0.845767i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 1.95820i | − | 0.242884i | ||||||
\(66\) | 3.07078 | − | 3.99300i | 0.377986 | − | 0.491505i | ||||
\(67\) | −15.1391 | −1.84954 | −0.924769 | − | 0.380529i | \(-0.875742\pi\) | ||||
−0.924769 | + | 0.380529i | \(0.875742\pi\) | |||||||
\(68\) | 1.68420 | − | 2.91713i | 0.204240 | − | 0.353754i | ||||
\(69\) | 0.650802 | − | 4.90254i | 0.0783474 | − | 0.590197i | ||||
\(70\) | −2.52849 | − | 0.778946i | −0.302212 | − | 0.0931018i | ||||
\(71\) | 7.94202i | 0.942544i | 0.881988 | + | 0.471272i | \(0.156205\pi\) | ||||
−0.881988 | + | 0.471272i | \(0.843795\pi\) | |||||||
\(72\) | 2.11675 | + | 2.12588i | 0.249461 | + | 0.250538i | ||||
\(73\) | −12.5756 | − | 7.26053i | −1.47186 | − | 0.849780i | −0.472363 | − | 0.881404i | \(-0.656599\pi\) |
−0.999500 | + | 0.0316238i | \(0.989932\pi\) | |||||||
\(74\) | −2.91115 | + | 1.68075i | −0.338414 | + | 0.195384i | ||||
\(75\) | 1.05588 | − | 1.37299i | 0.121923 | − | 0.158539i | ||||
\(76\) | 6.97993 | − | 4.02986i | 0.800653 | − | 0.462257i | ||||
\(77\) | 5.63860 | − | 5.23561i | 0.642578 | − | 0.596653i | ||||
\(78\) | −2.06763 | + | 2.68859i | −0.234113 | + | 0.304423i | ||||
\(79\) | 4.29504 | 0.483230 | 0.241615 | − | 0.970372i | \(-0.422323\pi\) | ||||
0.241615 | + | 0.970372i | \(0.422323\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 0.0387579 | − | 8.99992i | 0.00430643 | − | 0.999991i | ||||
\(82\) | −7.35799 | + | 4.24814i | −0.812554 | + | 0.469128i | ||||
\(83\) | 6.87362 | − | 11.9055i | 0.754477 | − | 1.30679i | −0.191156 | − | 0.981560i | \(-0.561224\pi\) |
0.945634 | − | 0.325233i | \(-0.105443\pi\) | |||||||
\(84\) | 2.64912 | + | 3.73928i | 0.289042 | + | 0.407988i | ||||
\(85\) | 1.68420 | + | 2.91713i | 0.182678 | + | 0.316407i | ||||
\(86\) | 1.71721 | + | 0.991430i | 0.185171 | + | 0.106909i | ||||
\(87\) | −0.493925 | + | 3.72078i | −0.0529544 | + | 0.398909i | ||||
\(88\) | 1.45413 | + | 2.51862i | 0.155010 | + | 0.268486i | ||||
\(89\) | 8.43872 | + | 14.6163i | 0.894502 | + | 1.54932i | 0.834420 | + | 0.551130i | \(0.185803\pi\) |
0.0600826 | + | 0.998193i | \(0.480864\pi\) | |||||||
\(90\) | −2.89944 | + | 0.770216i | −0.305628 | + | 0.0811879i | ||||
\(91\) | −3.79661 | + | 3.52526i | −0.397993 | + | 0.369548i | ||||
\(92\) | 2.47278 | + | 1.42766i | 0.257805 | + | 0.148844i | ||||
\(93\) | 3.53036 | − | 1.45787i | 0.366081 | − | 0.151174i | ||||
\(94\) | − | 0.647198i | − | 0.0667534i | ||||||
\(95\) | 8.05973i | 0.826911i | ||||||||
\(96\) | −1.60092 | + | 0.661104i | −0.163393 | + | 0.0674736i | ||||
\(97\) | 5.21536 | + | 3.01109i | 0.529539 | + | 0.305730i | 0.740829 | − | 0.671694i | \(-0.234433\pi\) |
−0.211289 | + | 0.977424i | \(0.567766\pi\) | |||||||
\(98\) | 3.04169 | + | 6.30461i | 0.307257 | + | 0.636862i | ||||
\(99\) | 2.27627 | − | 8.42258i | 0.228774 | − | 0.846501i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 7.83797 | + | 13.5758i | 0.779907 | + | 1.35084i | 0.931995 | + | 0.362471i | \(0.118067\pi\) |
−0.152088 | + | 0.988367i | \(0.548600\pi\) | |||||||
\(102\) | 0.767750 | − | 5.78352i | 0.0760186 | − | 0.572654i | ||||
\(103\) | −3.19529 | − | 1.84480i | −0.314841 | − | 0.181774i | 0.334250 | − | 0.942485i | \(-0.391517\pi\) |
−0.649091 | + | 0.760711i | \(0.724850\pi\) | |||||||
\(104\) | −0.979098 | − | 1.69585i | −0.0960085 | − | 0.166292i | ||||
\(105\) | −4.56287 | + | 0.424564i | −0.445290 | + | 0.0414332i | ||||
\(106\) | −5.34261 | + | 9.25368i | −0.518921 | + | 0.898797i | ||||
\(107\) | −10.6841 | + | 6.16845i | −1.03287 | + | 0.596327i | −0.917805 | − | 0.397031i | \(-0.870040\pi\) |
−0.115063 | + | 0.993358i | \(0.536707\pi\) | |||||||
\(108\) | 4.79417 | + | 2.00398i | 0.461319 | + | 0.192833i | ||||
\(109\) | −3.48038 | + | 6.02819i | −0.333360 | + | 0.577396i | −0.983168 | − | 0.182702i | \(-0.941516\pi\) |
0.649809 | + | 0.760098i | \(0.274849\pi\) | |||||||
\(110\) | −2.90825 | −0.277291 | ||||||||
\(111\) | −3.54936 | + | 4.61532i | −0.336890 | + | 0.438067i | ||||
\(112\) | −2.57921 | + | 0.589657i | −0.243712 | + | 0.0557173i | ||||
\(113\) | 2.35912 | − | 1.36204i | 0.221927 | − | 0.128130i | −0.384915 | − | 0.922952i | \(-0.625769\pi\) |
0.606842 | + | 0.794822i | \(0.292436\pi\) | |||||||
\(114\) | 8.51014 | − | 11.0659i | 0.797048 | − | 1.03642i | ||||
\(115\) | −2.47278 | + | 1.42766i | −0.230587 | + | 0.133130i | ||||
\(116\) | −1.87671 | − | 1.08352i | −0.174248 | − | 0.100602i | ||||
\(117\) | −1.53267 | + | 5.67113i | −0.141695 | + | 0.524296i | ||||
\(118\) | 9.11655i | 0.839246i | ||||||||
\(119\) | 2.62381 | − | 8.51697i | 0.240524 | − | 0.780750i | ||||
\(120\) | 0.227927 | − | 1.71699i | 0.0208068 | − | 0.156739i | ||||
\(121\) | −1.27104 | + | 2.20151i | −0.115549 | + | 0.200137i | ||||
\(122\) | 3.03785 | 0.275034 | ||||||||
\(123\) | −8.97108 | + | 11.6653i | −0.808895 | + | 1.05183i | ||||
\(124\) | 2.20521i | 0.198034i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.71307 | + | 4.23494i | 0.598048 | + | 0.377278i | ||||
\(127\) | −6.59858 | −0.585529 | −0.292765 | − | 0.956185i | \(-0.594575\pi\) | ||||
−0.292765 | + | 0.956185i | \(0.594575\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 3.40455 | + | 0.451947i | 0.299754 | + | 0.0397917i | ||||
\(130\) | 1.95820 | 0.171745 | ||||||||
\(131\) | −2.20506 | + | 3.81928i | −0.192657 | + | 0.333692i | −0.946130 | − | 0.323787i | \(-0.895044\pi\) |
0.753473 | + | 0.657479i | \(0.228377\pi\) | |||||||
\(132\) | 3.99300 | + | 3.07078i | 0.347546 | + | 0.267277i | ||||
\(133\) | 15.6264 | − | 14.5096i | 1.35498 | − | 1.25814i | ||||
\(134\) | − | 15.1391i | − | 1.30782i | ||||||
\(135\) | −4.13258 | + | 3.14989i | −0.355676 | + | 0.271099i | ||||
\(136\) | 2.91713 | + | 1.68420i | 0.250142 | + | 0.144419i | ||||
\(137\) | −4.23640 | + | 2.44589i | −0.361940 | + | 0.208966i | −0.669932 | − | 0.742423i | \(-0.733677\pi\) |
0.307991 | + | 0.951389i | \(0.400343\pi\) | |||||||
\(138\) | 4.90254 | + | 0.650802i | 0.417332 | + | 0.0554000i | ||||
\(139\) | 13.7982 | − | 7.96639i | 1.17035 | − | 0.675701i | 0.216586 | − | 0.976264i | \(-0.430508\pi\) |
0.953762 | + | 0.300563i | \(0.0971745\pi\) | |||||||
\(140\) | 0.778946 | − | 2.52849i | 0.0658329 | − | 0.213696i | ||||
\(141\) | −0.427865 | − | 1.03611i | −0.0360327 | − | 0.0872563i | ||||
\(142\) | −7.94202 | −0.666479 | ||||||||
\(143\) | −2.84746 | + | 4.93195i | −0.238117 | + | 0.412430i | ||||
\(144\) | −2.12588 | + | 2.11675i | −0.177157 | + | 0.176396i | ||||
\(145\) | 1.87671 | − | 1.08352i | 0.155852 | − | 0.0899813i | ||||
\(146\) | 7.26053 | − | 12.5756i | 0.600885 | − | 1.04076i | ||||
\(147\) | 9.03750 | + | 8.08230i | 0.745401 | + | 0.666617i | ||||
\(148\) | −1.68075 | − | 2.91115i | −0.138157 | − | 0.239295i | ||||
\(149\) | −6.20631 | − | 3.58321i | −0.508441 | − | 0.293548i | 0.223752 | − | 0.974646i | \(-0.428170\pi\) |
−0.732192 | + | 0.681098i | \(0.761503\pi\) | |||||||
\(150\) | 1.37299 | + | 1.05588i | 0.112104 | + | 0.0862126i | ||||
\(151\) | 3.38348 | + | 5.86035i | 0.275343 | + | 0.476909i | 0.970222 | − | 0.242218i | \(-0.0778751\pi\) |
−0.694878 | + | 0.719127i | \(0.744542\pi\) | |||||||
\(152\) | 4.02986 | + | 6.97993i | 0.326865 | + | 0.566147i | ||||
\(153\) | −2.59440 | − | 9.76650i | −0.209745 | − | 0.789575i | ||||
\(154\) | 5.23561 | + | 5.63860i | 0.421897 | + | 0.454372i | ||||
\(155\) | −1.90977 | − | 1.10260i | −0.153396 | − | 0.0885634i | ||||
\(156\) | −2.68859 | − | 2.06763i | −0.215259 | − | 0.165543i | ||||
\(157\) | 10.0931i | 0.805514i | 0.915307 | + | 0.402757i | \(0.131948\pi\) | ||||
−0.915307 | + | 0.402757i | \(0.868052\pi\) | |||||||
\(158\) | 4.29504i | 0.341695i | ||||||||
\(159\) | −2.43545 | + | 18.3464i | −0.193144 | + | 1.45497i | ||||
\(160\) | 0.866025 | + | 0.500000i | 0.0684653 | + | 0.0395285i | ||||
\(161\) | 7.21962 | + | 2.22413i | 0.568986 | + | 0.175286i | ||||
\(162\) | 8.99992 | + | 0.0387579i | 0.707100 | + | 0.00304511i | ||||
\(163\) | 11.7073 | + | 20.2777i | 0.916989 | + | 1.58827i | 0.803963 | + | 0.594679i | \(0.202721\pi\) |
0.113026 | + | 0.993592i | \(0.463946\pi\) | |||||||
\(164\) | −4.24814 | − | 7.35799i | −0.331724 | − | 0.574562i | ||||
\(165\) | −4.65587 | + | 1.92266i | −0.362459 | + | 0.149679i | ||||
\(166\) | 11.9055 | + | 6.87362i | 0.924042 | + | 0.533496i | ||||
\(167\) | −5.38906 | − | 9.33412i | −0.417018 | − | 0.722296i | 0.578620 | − | 0.815597i | \(-0.303591\pi\) |
−0.995638 | + | 0.0933010i | \(0.970258\pi\) | |||||||
\(168\) | −3.73928 | + | 2.64912i | −0.288491 | + | 0.204384i | ||||
\(169\) | −4.58273 | + | 7.93753i | −0.352518 | + | 0.610579i | ||||
\(170\) | −2.91713 | + | 1.68420i | −0.223733 | + | 0.129173i | ||||
\(171\) | 6.30831 | − | 23.3418i | 0.482408 | − | 1.78499i | ||||
\(172\) | −0.991430 | + | 1.71721i | −0.0755958 | + | 0.130936i | ||||
\(173\) | 2.57885 | 0.196067 | 0.0980333 | − | 0.995183i | \(-0.468745\pi\) | ||||
0.0980333 | + | 0.995183i | \(0.468745\pi\) | |||||||
\(174\) | −3.72078 | − | 0.493925i | −0.282071 | − | 0.0374444i | ||||
\(175\) | 1.80026 | + | 1.93883i | 0.136087 | + | 0.146562i | ||||
\(176\) | −2.51862 | + | 1.45413i | −0.189848 | + | 0.109609i | ||||
\(177\) | 6.02699 | + | 14.5949i | 0.453016 | + | 1.09702i | ||||
\(178\) | −14.6163 | + | 8.43872i | −1.09554 | + | 0.632509i | ||||
\(179\) | 0.461274 | + | 0.266316i | 0.0344772 | + | 0.0199054i | 0.517140 | − | 0.855901i | \(-0.326997\pi\) |
−0.482662 | + | 0.875807i | \(0.660330\pi\) | |||||||
\(180\) | −0.770216 | − | 2.89944i | −0.0574085 | − | 0.216112i | ||||
\(181\) | − | 25.2946i | − | 1.88013i | −0.340993 | − | 0.940066i | \(-0.610763\pi\) | ||
0.340993 | − | 0.940066i | \(-0.389237\pi\) | |||||||
\(182\) | −3.52526 | − | 3.79661i | −0.261310 | − | 0.281423i | ||||
\(183\) | 4.86335 | − | 2.00834i | 0.359509 | − | 0.148460i | ||||
\(184\) | −1.42766 | + | 2.47278i | −0.105248 | + | 0.182295i | ||||
\(185\) | 3.36151 | 0.247143 | ||||||||
\(186\) | 1.45787 | + | 3.53036i | 0.106896 | + | 0.258859i | ||||
\(187\) | − | 9.79617i | − | 0.716367i | ||||||
\(188\) | 0.647198 | 0.0472018 | ||||||||
\(189\) | 13.5468 | + | 2.34175i | 0.985386 | + | 0.170338i | ||||
\(190\) | −8.05973 | −0.584714 | ||||||||
\(191\) | 23.3473i | 1.68935i | 0.535276 | + | 0.844677i | \(0.320208\pi\) | ||||
−0.535276 | + | 0.844677i | \(0.679792\pi\) | |||||||
\(192\) | −0.661104 | − | 1.60092i | −0.0477111 | − | 0.115536i | ||||
\(193\) | 4.17857 | 0.300780 | 0.150390 | − | 0.988627i | \(-0.451947\pi\) | ||||
0.150390 | + | 0.988627i | \(0.451947\pi\) | |||||||
\(194\) | −3.01109 | + | 5.21536i | −0.216184 | + | 0.374441i | ||||
\(195\) | 3.13491 | − | 1.29457i | 0.224496 | − | 0.0927062i | ||||
\(196\) | −6.30461 | + | 3.04169i | −0.450329 | + | 0.217264i | ||||
\(197\) | 2.79573i | 0.199187i | 0.995028 | + | 0.0995936i | \(0.0317543\pi\) | ||||
−0.995028 | + | 0.0995936i | \(0.968246\pi\) | |||||||
\(198\) | 8.42258 | + | 2.27627i | 0.598567 | + | 0.161768i | ||||
\(199\) | −3.02178 | − | 1.74463i | −0.214208 | − | 0.123673i | 0.389057 | − | 0.921214i | \(-0.372801\pi\) |
−0.603266 | + | 0.797540i | \(0.706134\pi\) | |||||||
\(200\) | −0.866025 | + | 0.500000i | −0.0612372 | + | 0.0353553i | ||||
\(201\) | −10.0085 | − | 24.2365i | −0.705947 | − | 1.70951i | ||||
\(202\) | −13.5758 | + | 7.83797i | −0.955187 | + | 0.551477i | ||||
\(203\) | −5.47932 | − | 1.68800i | −0.384573 | − | 0.118475i | ||||
\(204\) | 5.78352 | + | 0.767750i | 0.404927 | + | 0.0537532i | ||||
\(205\) | 8.49627 | 0.593405 | ||||||||
\(206\) | 1.84480 | − | 3.19529i | 0.128533 | − | 0.222626i | ||||
\(207\) | 8.27882 | − | 2.19921i | 0.575418 | − | 0.152856i | ||||
\(208\) | 1.69585 | − | 0.979098i | 0.117586 | − | 0.0678882i | ||||
\(209\) | 11.7199 | − | 20.2994i | 0.810679 | − | 1.40414i | ||||
\(210\) | −0.424564 | − | 4.56287i | −0.0292977 | − | 0.314868i | ||||
\(211\) | −4.69846 | − | 8.13798i | −0.323455 | − | 0.560241i | 0.657743 | − | 0.753242i | \(-0.271511\pi\) |
−0.981199 | + | 0.193001i | \(0.938178\pi\) | |||||||
\(212\) | −9.25368 | − | 5.34261i | −0.635545 | − | 0.366932i | ||||
\(213\) | −12.7145 | + | 5.25050i | −0.871185 | + | 0.359758i | ||||
\(214\) | −6.16845 | − | 10.6841i | −0.421667 | − | 0.730348i | ||||
\(215\) | −0.991430 | − | 1.71721i | −0.0676150 | − | 0.117113i | ||||
\(216\) | −2.00398 | + | 4.79417i | −0.136353 | + | 0.326202i | ||||
\(217\) | 1.30032 | + | 5.68769i | 0.0882712 | + | 0.386106i | ||||
\(218\) | −6.02819 | − | 3.48038i | −0.408281 | − | 0.235721i | ||||
\(219\) | 3.30974 | − | 24.9325i | 0.223651 | − | 1.68478i | ||||
\(220\) | − | 2.90825i | − | 0.196074i | ||||||
\(221\) | 6.59600i | 0.443695i | ||||||||
\(222\) | −4.61532 | − | 3.54936i | −0.309760 | − | 0.238218i | ||||
\(223\) | 14.4132 | + | 8.32148i | 0.965181 | + | 0.557248i | 0.897764 | − | 0.440477i | \(-0.145191\pi\) |
0.0674174 | + | 0.997725i | \(0.478524\pi\) | |||||||
\(224\) | −0.589657 | − | 2.57921i | −0.0393981 | − | 0.172330i | ||||
\(225\) | 2.89610 | + | 0.782695i | 0.193073 | + | 0.0521797i | ||||
\(226\) | 1.36204 | + | 2.35912i | 0.0906013 | + | 0.156926i | ||||
\(227\) | −0.765073 | − | 1.32514i | −0.0507796 | − | 0.0879529i | 0.839518 | − | 0.543331i | \(-0.182837\pi\) |
−0.890298 | + | 0.455378i | \(0.849504\pi\) | |||||||
\(228\) | 11.0659 | + | 8.51014i | 0.732860 | + | 0.563598i | ||||
\(229\) | −19.5572 | − | 11.2914i | −1.29238 | − | 0.746154i | −0.313302 | − | 0.949654i | \(-0.601435\pi\) |
−0.979075 | + | 0.203500i | \(0.934768\pi\) | |||||||
\(230\) | −1.42766 | − | 2.47278i | −0.0941369 | − | 0.163050i | ||||
\(231\) | 12.1095 | + | 5.56566i | 0.796746 | + | 0.366194i | ||||
\(232\) | 1.08352 | − | 1.87671i | 0.0711365 | − | 0.123212i | ||||
\(233\) | −1.52031 | + | 0.877750i | −0.0995986 | + | 0.0575033i | −0.548972 | − | 0.835841i | \(-0.684981\pi\) |
0.449373 | + | 0.893344i | \(0.351647\pi\) | |||||||
\(234\) | −5.67113 | − | 1.53267i | −0.370733 | − | 0.100194i | ||||
\(235\) | −0.323599 | + | 0.560490i | −0.0211093 | + | 0.0365623i | ||||
\(236\) | −9.11655 | −0.593437 | ||||||||
\(237\) | 2.83947 | + | 6.87602i | 0.184443 | + | 0.446645i | ||||
\(238\) | 8.51697 | + | 2.62381i | 0.552073 | + | 0.170076i | ||||
\(239\) | 13.5333 | − | 7.81348i | 0.875399 | − | 0.505412i | 0.00626059 | − | 0.999980i | \(-0.498007\pi\) |
0.869139 | + | 0.494568i | \(0.164674\pi\) | |||||||
\(240\) | 1.71699 | + | 0.227927i | 0.110831 | + | 0.0147126i | ||||
\(241\) | −6.76393 | + | 3.90516i | −0.435703 | + | 0.251553i | −0.701773 | − | 0.712400i | \(-0.747608\pi\) |
0.266070 | + | 0.963954i | \(0.414275\pi\) | |||||||
\(242\) | −2.20151 | − | 1.27104i | −0.141518 | − | 0.0817056i | ||||
\(243\) | 14.4338 | − | 5.88783i | 0.925926 | − | 0.377705i | ||||
\(244\) | 3.03785i | 0.194478i | ||||||||
\(245\) | 0.518123 | − | 6.98080i | 0.0331017 | − | 0.445987i | ||||
\(246\) | −11.6653 | − | 8.97108i | −0.743754 | − | 0.571975i | ||||
\(247\) | −7.89126 | + | 13.6681i | −0.502109 | + | 0.869678i | ||||
\(248\) | −2.20521 | −0.140031 | ||||||||
\(249\) | 23.6038 | + | 3.13336i | 1.49583 | + | 0.198569i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 12.4166 | 0.783726 | 0.391863 | − | 0.920024i | \(-0.371831\pi\) | ||||
0.391863 | + | 0.920024i | \(0.371831\pi\) | |||||||
\(252\) | −4.23494 | + | 6.71307i | −0.266776 | + | 0.422884i | ||||
\(253\) | 8.30397 | 0.522066 | ||||||||
\(254\) | − | 6.59858i | − | 0.414032i | ||||||
\(255\) | −3.55665 | + | 4.62480i | −0.222726 | + | 0.289616i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.7065 | − | 25.4724i | 0.917367 | − | 1.58893i | 0.113969 | − | 0.993484i | \(-0.463644\pi\) |
0.803398 | − | 0.595442i | \(-0.203023\pi\) | |||||||
\(258\) | −0.451947 | + | 3.40455i | −0.0281370 | + | 0.211958i | ||||
\(259\) | −6.05159 | − | 6.51739i | −0.376027 | − | 0.404971i | ||||
\(260\) | 1.95820i | 0.121442i | ||||||||
\(261\) | −6.28320 | + | 1.66909i | −0.388920 | + | 0.103314i | ||||
\(262\) | −3.81928 | − | 2.20506i | −0.235956 | − | 0.136229i | ||||
\(263\) | −22.6005 | + | 13.0484i | −1.39360 | + | 0.804598i | −0.993712 | − | 0.111964i | \(-0.964286\pi\) |
−0.399892 | + | 0.916562i | \(0.630952\pi\) | |||||||
\(264\) | −3.07078 | + | 3.99300i | −0.188993 | + | 0.245752i | ||||
\(265\) | 9.25368 | − | 5.34261i | 0.568449 | − | 0.328194i | ||||
\(266\) | 14.5096 | + | 15.6264i | 0.889641 | + | 0.958119i | ||||
\(267\) | −17.8206 | + | 23.1726i | −1.09060 | + | 1.41814i | ||||
\(268\) | 15.1391 | 0.924769 | ||||||||
\(269\) | −7.78339 | + | 13.4812i | −0.474562 | + | 0.821965i | −0.999576 | − | 0.0291286i | \(-0.990727\pi\) |
0.525014 | + | 0.851094i | \(0.324060\pi\) | |||||||
\(270\) | −3.14989 | − | 4.13258i | −0.191696 | − | 0.251501i | ||||
\(271\) | 10.2838 | − | 5.93737i | 0.624698 | − | 0.360670i | −0.153998 | − | 0.988071i | \(-0.549215\pi\) |
0.778696 | + | 0.627402i | \(0.215882\pi\) | |||||||
\(272\) | −1.68420 | + | 2.91713i | −0.102120 | + | 0.176877i | ||||
\(273\) | −8.15361 | − | 3.74750i | −0.493479 | − | 0.226809i | ||||
\(274\) | −2.44589 | − | 4.23640i | −0.147762 | − | 0.255931i | ||||
\(275\) | 2.51862 | + | 1.45413i | 0.151878 | + | 0.0876870i | ||||
\(276\) | −0.650802 | + | 4.90254i | −0.0391737 | + | 0.295098i | ||||
\(277\) | −13.7278 | − | 23.7773i | −0.824825 | − | 1.42864i | −0.902053 | − | 0.431626i | \(-0.857940\pi\) |
0.0772275 | − | 0.997013i | \(-0.475393\pi\) | |||||||
\(278\) | 7.96639 | + | 13.7982i | 0.477793 | + | 0.827561i | ||||
\(279\) | 4.66787 | + | 4.68802i | 0.279458 | + | 0.280664i | ||||
\(280\) | 2.52849 | + | 0.778946i | 0.151106 | + | 0.0465509i | ||||
\(281\) | −22.5302 | − | 13.0078i | −1.34404 | − | 0.775980i | −0.356639 | − | 0.934242i | \(-0.616077\pi\) |
−0.987397 | + | 0.158263i | \(0.949411\pi\) | |||||||
\(282\) | 1.03611 | − | 0.427865i | 0.0616995 | − | 0.0254790i | ||||
\(283\) | 0.865094i | 0.0514245i | 0.999669 | + | 0.0257123i | \(0.00818537\pi\) | ||||
−0.999669 | + | 0.0257123i | \(0.991815\pi\) | |||||||
\(284\) | − | 7.94202i | − | 0.471272i | ||||||
\(285\) | −12.9030 | + | 5.32832i | −0.764306 | + | 0.315622i | ||||
\(286\) | −4.93195 | − | 2.84746i | −0.291632 | − | 0.168374i | ||||
\(287\) | −15.2955 | − | 16.4728i | −0.902865 | − | 0.972360i | ||||
\(288\) | −2.11675 | − | 2.12588i | −0.124731 | − | 0.125269i | ||||
\(289\) | 2.82692 | + | 4.89636i | 0.166289 | + | 0.288021i | ||||
\(290\) | 1.08352 | + | 1.87671i | 0.0636264 | + | 0.110204i | ||||
\(291\) | −1.37261 | + | 10.3400i | −0.0804641 | + | 0.606142i | ||||
\(292\) | 12.5756 | + | 7.26053i | 0.735931 | + | 0.424890i | ||||
\(293\) | −11.3934 | − | 19.7339i | −0.665608 | − | 1.15287i | −0.979120 | − | 0.203283i | \(-0.934839\pi\) |
0.313512 | − | 0.949584i | \(-0.398495\pi\) | |||||||
\(294\) | −8.08230 | + | 9.03750i | −0.471369 | + | 0.527078i | ||||
\(295\) | 4.55827 | − | 7.89516i | 0.265393 | − | 0.459674i | ||||
\(296\) | 2.91115 | − | 1.68075i | 0.169207 | − | 0.0976918i | ||||
\(297\) | 14.9887 | − | 1.92407i | 0.869734 | − | 0.111646i | ||||
\(298\) | 3.58321 | − | 6.20631i | 0.207570 | − | 0.359522i | ||||
\(299\) | −5.59127 | −0.323351 | ||||||||
\(300\) | −1.05588 | + | 1.37299i | −0.0609615 | + | 0.0792697i | ||||
\(301\) | −1.54454 | + | 5.01364i | −0.0890258 | + | 0.288981i | ||||
\(302\) | −5.86035 | + | 3.38348i | −0.337226 | + | 0.194697i | ||||
\(303\) | −16.5520 | + | 21.5229i | −0.950886 | + | 1.23646i | ||||
\(304\) | −6.97993 | + | 4.02986i | −0.400326 | + | 0.231129i | ||||
\(305\) | −2.63086 | − | 1.51893i | −0.150642 | − | 0.0869734i | ||||
\(306\) | 9.76650 | − | 2.59440i | 0.558314 | − | 0.148312i | ||||
\(307\) | 19.5794i | 1.11745i | 0.829352 | + | 0.558726i | \(0.188710\pi\) | ||||
−0.829352 | + | 0.558726i | \(0.811290\pi\) | |||||||
\(308\) | −5.63860 | + | 5.23561i | −0.321289 | + | 0.298326i | ||||
\(309\) | 0.840958 | − | 6.33500i | 0.0478404 | − | 0.360386i | ||||
\(310\) | 1.10260 | − | 1.90977i | 0.0626237 | − | 0.108468i | ||||
\(311\) | 24.7602 | 1.40402 | 0.702010 | − | 0.712167i | \(-0.252286\pi\) | ||||
0.702010 | + | 0.712167i | \(0.252286\pi\) | |||||||
\(312\) | 2.06763 | − | 2.68859i | 0.117056 | − | 0.152211i | ||||
\(313\) | − | 29.7074i | − | 1.67916i | −0.543233 | − | 0.839582i | \(-0.682800\pi\) | ||
0.543233 | − | 0.839582i | \(-0.317200\pi\) | |||||||
\(314\) | −10.0931 | −0.569585 | ||||||||
\(315\) | −3.69622 | − | 7.02410i | −0.208258 | − | 0.395763i | ||||
\(316\) | −4.29504 | −0.241615 | ||||||||
\(317\) | 5.98746i | 0.336289i | 0.985762 | + | 0.168144i | \(0.0537775\pi\) | ||||
−0.985762 | + | 0.168144i | \(0.946222\pi\) | |||||||
\(318\) | −18.3464 | − | 2.43545i | −1.02882 | − | 0.136573i | ||||
\(319\) | −6.30228 | −0.352860 | ||||||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −16.9385 | − | 13.0263i | −0.945414 | − | 0.727060i | ||||
\(322\) | −2.22413 | + | 7.21962i | −0.123946 | + | 0.402334i | ||||
\(323\) | − | 27.1484i | − | 1.51058i | ||||||
\(324\) | −0.0387579 | + | 8.99992i | −0.00215322 | + | 0.499995i | ||||
\(325\) | −1.69585 | − | 0.979098i | −0.0940687 | − | 0.0543106i | ||||
\(326\) | −20.2777 | + | 11.7073i | −1.12308 | + | 0.648409i | ||||
\(327\) | −11.9515 | − | 1.58654i | −0.660922 | − | 0.0877360i | ||||
\(328\) | 7.35799 | − | 4.24814i | 0.406277 | − | 0.234564i | ||||
\(329\) | 1.66926 | − | 0.381624i | 0.0920291 | − | 0.0210396i | ||||
\(330\) | −1.92266 | − | 4.65587i | −0.105839 | − | 0.256297i | ||||
\(331\) | 7.70669 | 0.423598 | 0.211799 | − | 0.977313i | \(-0.432068\pi\) | ||||
0.211799 | + | 0.977313i | \(0.432068\pi\) | |||||||
\(332\) | −6.87362 | + | 11.9055i | −0.377239 | + | 0.653396i | ||||
\(333\) | −9.73525 | − | 2.63103i | −0.533488 | − | 0.144180i | ||||
\(334\) | 9.33412 | − | 5.38906i | 0.510741 | − | 0.294876i | ||||
\(335\) | −7.56956 | + | 13.1109i | −0.413569 | + | 0.716323i | ||||
\(336\) | −2.64912 | − | 3.73928i | −0.144521 | − | 0.203994i | ||||
\(337\) | 3.29935 | + | 5.71465i | 0.179727 | + | 0.311297i | 0.941787 | − | 0.336210i | \(-0.109145\pi\) |
−0.762060 | + | 0.647507i | \(0.775812\pi\) | |||||||
\(338\) | −7.93753 | − | 4.58273i | −0.431745 | − | 0.249268i | ||||
\(339\) | 3.74013 | + | 2.87631i | 0.203136 | + | 0.156220i | ||||
\(340\) | −1.68420 | − | 2.91713i | −0.0913388 | − | 0.158203i | ||||
\(341\) | 3.20665 | + | 5.55408i | 0.173650 | + | 0.300770i | ||||
\(342\) | 23.3418 | + | 6.30831i | 1.26218 | + | 0.341114i | ||||
\(343\) | −14.4673 | + | 11.5627i | −0.781163 | + | 0.624327i | ||||
\(344\) | −1.71721 | − | 0.991430i | −0.0925856 | − | 0.0534543i | ||||
\(345\) | −3.92033 | − | 3.01488i | −0.211063 | − | 0.162316i | ||||
\(346\) | 2.57885i | 0.138640i | ||||||||
\(347\) | − | 12.1162i | − | 0.650431i | −0.945640 | − | 0.325216i | \(-0.894563\pi\) | ||
0.945640 | − | 0.325216i | \(-0.105437\pi\) | |||||||
\(348\) | 0.493925 | − | 3.72078i | 0.0264772 | − | 0.199455i | ||||
\(349\) | −0.214315 | − | 0.123735i | −0.0114720 | − | 0.00662337i | 0.494253 | − | 0.869318i | \(-0.335442\pi\) |
−0.505725 | + | 0.862695i | \(0.668775\pi\) | |||||||
\(350\) | −1.93883 | + | 1.80026i | −0.103635 | + | 0.0962280i | ||||
\(351\) | −10.0923 | + | 1.29553i | −0.538686 | + | 0.0691500i | ||||
\(352\) | −1.45413 | − | 2.51862i | −0.0775051 | − | 0.134243i | ||||
\(353\) | −0.0652598 | − | 0.113033i | −0.00347343 | − | 0.00601615i | 0.864283 | − | 0.503005i | \(-0.167772\pi\) |
−0.867757 | + | 0.496989i | \(0.834439\pi\) | |||||||
\(354\) | −14.5949 | + | 6.02699i | −0.775708 | + | 0.320331i | ||||
\(355\) | 6.87799 | + | 3.97101i | 0.365046 | + | 0.210759i | ||||
\(356\) | −8.43872 | − | 14.6163i | −0.447251 | − | 0.774662i | ||||
\(357\) | 15.3696 | − | 1.43010i | 0.813445 | − | 0.0756891i | ||||
\(358\) | −0.266316 | + | 0.461274i | −0.0140753 | + | 0.0243791i | ||||
\(359\) | −8.88009 | + | 5.12692i | −0.468673 | + | 0.270589i | −0.715684 | − | 0.698424i | \(-0.753885\pi\) |
0.247011 | + | 0.969013i | \(0.420552\pi\) | |||||||
\(360\) | 2.89944 | − | 0.770216i | 0.152814 | − | 0.0405939i | ||||
\(361\) | 22.9796 | − | 39.8018i | 1.20945 | − | 2.09483i | ||||
\(362\) | 25.2946 | 1.32945 | ||||||||
\(363\) | −4.36473 | − | 0.579408i | −0.229089 | − | 0.0304110i | ||||
\(364\) | 3.79661 | − | 3.52526i | 0.198996 | − | 0.184774i | ||||
\(365\) | −12.5756 | + | 7.26053i | −0.658237 | + | 0.380033i | ||||
\(366\) | 2.00834 | + | 4.86335i | 0.104977 | + | 0.254212i | ||||
\(367\) | 0.374347 | − | 0.216129i | 0.0195407 | − | 0.0112818i | −0.490198 | − | 0.871611i | \(-0.663075\pi\) |
0.509739 | + | 0.860329i | \(0.329742\pi\) | |||||||
\(368\) | −2.47278 | − | 1.42766i | −0.128902 | − | 0.0744218i | ||||
\(369\) | −24.6060 | − | 6.64999i | −1.28094 | − | 0.346185i | ||||
\(370\) | 3.36151i | 0.174756i | ||||||||
\(371\) | −27.0175 | − | 8.32321i | −1.40268 | − | 0.432120i | ||||
\(372\) | −3.53036 | + | 1.45787i | −0.183041 | + | 0.0755872i | ||||
\(373\) | −1.54641 | + | 2.67846i | −0.0800700 | + | 0.138685i | −0.903280 | − | 0.429052i | \(-0.858848\pi\) |
0.823210 | + | 0.567737i | \(0.192181\pi\) | |||||||
\(374\) | 9.79617 | 0.506548 | ||||||||
\(375\) | −0.661104 | − | 1.60092i | −0.0341393 | − | 0.0826711i | ||||
\(376\) | 0.647198i | 0.0333767i | ||||||||
\(377\) | 4.24348 | 0.218550 | ||||||||
\(378\) | −2.34175 | + | 13.5468i | −0.120447 | + | 0.696773i | ||||
\(379\) | −9.20781 | −0.472973 | −0.236487 | − | 0.971635i | \(-0.575996\pi\) | ||||
−0.236487 | + | 0.971635i | \(0.575996\pi\) | |||||||
\(380\) | − | 8.05973i | − | 0.413455i | ||||||
\(381\) | −4.36235 | − | 10.5638i | −0.223490 | − | 0.541199i | ||||
\(382\) | −23.3473 | −1.19455 | ||||||||
\(383\) | 12.2460 | − | 21.2108i | 0.625743 | − | 1.08382i | −0.362653 | − | 0.931924i | \(-0.618129\pi\) |
0.988397 | − | 0.151895i | \(-0.0485376\pi\) | |||||||
\(384\) | 1.60092 | − | 0.661104i | 0.0816966 | − | 0.0337368i | ||||
\(385\) | −1.71487 | − | 7.50098i | −0.0873978 | − | 0.382285i | ||||
\(386\) | 4.17857i | 0.212684i | ||||||||
\(387\) | 1.52723 | + | 5.74919i | 0.0776335 | + | 0.292248i | ||||
\(388\) | −5.21536 | − | 3.01109i | −0.264770 | − | 0.152865i | ||||
\(389\) | −4.52023 | + | 2.60976i | −0.229185 | + | 0.132320i | −0.610196 | − | 0.792251i | \(-0.708909\pi\) |
0.381011 | + | 0.924570i | \(0.375576\pi\) | |||||||
\(390\) | 1.29457 | + | 3.13491i | 0.0655532 | + | 0.158743i | ||||
\(391\) | 8.32931 | − | 4.80893i | 0.421232 | − | 0.243198i | ||||
\(392\) | −3.04169 | − | 6.30461i | −0.153629 | − | 0.318431i | ||||
\(393\) | −7.57213 | − | 1.00518i | −0.381963 | − | 0.0507048i | ||||
\(394\) | −2.79573 | −0.140847 | ||||||||
\(395\) | 2.14752 | − | 3.71962i | 0.108054 | − | 0.187154i | ||||
\(396\) | −2.27627 | + | 8.42258i | −0.114387 | + | 0.423251i | ||||
\(397\) | 8.32819 | − | 4.80828i | 0.417980 | − | 0.241321i | −0.276233 | − | 0.961091i | \(-0.589086\pi\) |
0.694213 | + | 0.719770i | \(0.255753\pi\) | |||||||
\(398\) | 1.74463 | − | 3.02178i | 0.0874502 | − | 0.151468i | ||||
\(399\) | 33.5594 | + | 15.4243i | 1.68007 | + | 0.772181i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −15.8370 | − | 9.14348i | −0.790861 | − | 0.456604i | 0.0494047 | − | 0.998779i | \(-0.484268\pi\) |
−0.840266 | + | 0.542175i | \(0.817601\pi\) | |||||||
\(402\) | 24.2365 | − | 10.0085i | 1.20881 | − | 0.499180i | ||||
\(403\) | −2.15912 | − | 3.73970i | −0.107553 | − | 0.186288i | ||||
\(404\) | −7.83797 | − | 13.5758i | −0.389953 | − | 0.675419i | ||||
\(405\) | −7.77478 | − | 4.53352i | −0.386332 | − | 0.225273i | ||||
\(406\) | 1.68800 | − | 5.47932i | 0.0837742 | − | 0.271934i | ||||
\(407\) | −8.46635 | − | 4.88805i | −0.419661 | − | 0.242292i | ||||
\(408\) | −0.767750 | + | 5.78352i | −0.0380093 | + | 0.286327i | ||||
\(409\) | 4.06433i | 0.200968i | 0.994939 | + | 0.100484i | \(0.0320391\pi\) | ||||
−0.994939 | + | 0.100484i | \(0.967961\pi\) | |||||||
\(410\) | 8.49627i | 0.419601i | ||||||||
\(411\) | −6.71637 | − | 5.16515i | −0.331294 | − | 0.254778i | ||||
\(412\) | 3.19529 | + | 1.84480i | 0.157421 | + | 0.0908868i | ||||
\(413\) | −23.5135 | + | 5.37563i | −1.15702 | + | 0.264518i | ||||
\(414\) | 2.19921 | + | 8.27882i | 0.108085 | + | 0.406882i | ||||
\(415\) | −6.87362 | − | 11.9055i | −0.337412 | − | 0.584416i | ||||
\(416\) | 0.979098 | + | 1.69585i | 0.0480042 | + | 0.0831458i | ||||
\(417\) | 21.8756 | + | 16.8232i | 1.07125 | + | 0.823835i | ||||
\(418\) | 20.2994 | + | 11.7199i | 0.992875 | + | 0.573237i | ||||
\(419\) | 6.00474 | + | 10.4005i | 0.293351 | + | 0.508098i | 0.974600 | − | 0.223953i | \(-0.0718963\pi\) |
−0.681249 | + | 0.732052i | \(0.738563\pi\) | |||||||
\(420\) | 4.56287 | − | 0.424564i | 0.222645 | − | 0.0207166i | ||||
\(421\) | −6.01384 | + | 10.4163i | −0.293097 | + | 0.507658i | −0.974540 | − | 0.224212i | \(-0.928019\pi\) |
0.681444 | + | 0.731871i | \(0.261352\pi\) | |||||||
\(422\) | 8.13798 | − | 4.69846i | 0.396150 | − | 0.228718i | ||||
\(423\) | 1.37587 | − | 1.36995i | 0.0668970 | − | 0.0666095i | ||||
\(424\) | 5.34261 | − | 9.25368i | 0.259460 | − | 0.449398i | ||||
\(425\) | 3.36841 | 0.163392 | ||||||||
\(426\) | −5.25050 | − | 12.7145i | −0.254387 | − | 0.616021i | ||||
\(427\) | 1.79129 | + | 7.83525i | 0.0866865 | + | 0.379174i | ||||
\(428\) | 10.6841 | − | 6.16845i | 0.516434 | − | 0.298163i | ||||
\(429\) | −9.77812 | − | 1.29802i | −0.472092 | − | 0.0626692i | ||||
\(430\) | 1.71721 | − | 0.991430i | 0.0828111 | − | 0.0478110i | ||||
\(431\) | −8.15790 | − | 4.70997i | −0.392952 | − | 0.226871i | 0.290486 | − | 0.956879i | \(-0.406183\pi\) |
−0.683439 | + | 0.730008i | \(0.739516\pi\) | |||||||
\(432\) | −4.79417 | − | 2.00398i | −0.230660 | − | 0.0964164i | ||||
\(433\) | − | 28.8287i | − | 1.38542i | −0.721216 | − | 0.692710i | \(-0.756417\pi\) | ||
0.721216 | − | 0.692710i | \(-0.243583\pi\) | |||||||
\(434\) | −5.68769 | + | 1.30032i | −0.273018 | + | 0.0624172i | ||||
\(435\) | 2.97532 | + | 2.28814i | 0.142656 | + | 0.109708i | ||||
\(436\) | 3.48038 | − | 6.02819i | 0.166680 | − | 0.288698i | ||||
\(437\) | 23.0131 | 1.10086 | ||||||||
\(438\) | 24.9325 | + | 3.30974i | 1.19132 | + | 0.158145i | ||||
\(439\) | 35.2441i | 1.68211i | 0.540949 | + | 0.841055i | \(0.318065\pi\) | ||||
−0.540949 | + | 0.841055i | \(0.681935\pi\) | |||||||
\(440\) | 2.90825 | 0.138645 | ||||||||
\(441\) | −6.96437 | + | 19.8116i | −0.331637 | + | 0.943407i | ||||
\(442\) | −6.59600 | −0.313740 | ||||||||
\(443\) | 21.2414i | 1.00921i | 0.863350 | + | 0.504605i | \(0.168362\pi\) | ||||
−0.863350 | + | 0.504605i | \(0.831638\pi\) | |||||||
\(444\) | 3.54936 | − | 4.61532i | 0.168445 | − | 0.219033i | ||||
\(445\) | 16.8774 | 0.800067 | ||||||||
\(446\) | −8.32148 | + | 14.4132i | −0.394034 | + | 0.682486i | ||||
\(447\) | 1.63342 | − | 12.3047i | 0.0772581 | − | 0.581991i | ||||
\(448\) | 2.57921 | − | 0.589657i | 0.121856 | − | 0.0278587i | ||||
\(449\) | 16.9305i | 0.799002i | 0.916733 | + | 0.399501i | \(0.130817\pi\) | ||||
−0.916733 | + | 0.399501i | \(0.869183\pi\) | |||||||
\(450\) | −0.782695 | + | 2.89610i | −0.0368966 | + | 0.136523i | ||||
\(451\) | −21.3989 | − | 12.3546i | −1.00763 | − | 0.581757i | ||||
\(452\) | −2.35912 | + | 1.36204i | −0.110964 | + | 0.0640648i | ||||
\(453\) | −7.14512 | + | 9.29098i | −0.335707 | + | 0.436528i | ||||
\(454\) | 1.32514 | − | 0.765073i | 0.0621921 | − | 0.0359066i | ||||
\(455\) | 1.15466 | + | 5.05059i | 0.0541314 | + | 0.236775i | ||||
\(456\) | −8.51014 | + | 11.0659i | −0.398524 | + | 0.518210i | ||||
\(457\) | 33.2351 | 1.55467 | 0.777335 | − | 0.629086i | \(-0.216571\pi\) | ||||
0.777335 | + | 0.629086i | \(0.216571\pi\) | |||||||
\(458\) | 11.2914 | − | 19.5572i | 0.527610 | − | 0.913848i | ||||
\(459\) | 13.9202 | − | 10.6101i | 0.649740 | − | 0.495237i | ||||
\(460\) | 2.47278 | − | 1.42766i | 0.115294 | − | 0.0665649i | ||||
\(461\) | −13.2679 | + | 22.9806i | −0.617946 | + | 1.07031i | 0.371914 | + | 0.928267i | \(0.378702\pi\) |
−0.989860 | + | 0.142047i | \(0.954632\pi\) | |||||||
\(462\) | −5.56566 | + | 12.1095i | −0.258938 | + | 0.563384i | ||||
\(463\) | −5.25467 | − | 9.10135i | −0.244205 | − | 0.422976i | 0.717703 | − | 0.696350i | \(-0.245194\pi\) |
−0.961908 | + | 0.273374i | \(0.911860\pi\) | |||||||
\(464\) | 1.87671 | + | 1.08352i | 0.0871240 | + | 0.0503011i | ||||
\(465\) | 0.502626 | − | 3.78632i | 0.0233087 | − | 0.175586i | ||||
\(466\) | −0.877750 | − | 1.52031i | −0.0406610 | − | 0.0704269i | ||||
\(467\) | −6.14519 | − | 10.6438i | −0.284366 | − | 0.492536i | 0.688089 | − | 0.725626i | \(-0.258450\pi\) |
−0.972455 | + | 0.233090i | \(0.925116\pi\) | |||||||
\(468\) | 1.53267 | − | 5.67113i | 0.0708477 | − | 0.262148i | ||||
\(469\) | 39.0469 | − | 8.92688i | 1.80302 | − | 0.412205i | ||||
\(470\) | −0.560490 | − | 0.323599i | −0.0258535 | − | 0.0149265i | ||||
\(471\) | −16.1582 | + | 6.67256i | −0.744529 | + | 0.307456i | ||||
\(472\) | − | 9.11655i | − | 0.419623i | ||||||
\(473\) | 5.76665i | 0.265151i | ||||||||
\(474\) | −6.87602 | + | 2.83947i | −0.315826 | + | 0.130421i | ||||
\(475\) | 6.97993 | + | 4.02986i | 0.320261 | + | 0.184903i | ||||
\(476\) | −2.62381 | + | 8.51697i | −0.120262 | + | 0.390375i | ||||
\(477\) | −30.9812 | + | 8.22993i | −1.41853 | + | 0.376823i | ||||
\(478\) | 7.81348 | + | 13.5333i | 0.357380 | + | 0.619001i | ||||
\(479\) | 15.8696 | + | 27.4869i | 0.725100 | + | 1.25591i | 0.958933 | + | 0.283633i | \(0.0915399\pi\) |
−0.233833 | + | 0.972277i | \(0.575127\pi\) | |||||||
\(480\) | −0.227927 | + | 1.71699i | −0.0104034 | + | 0.0783694i | ||||
\(481\) | 5.70060 | + | 3.29124i | 0.259925 | + | 0.150068i | ||||
\(482\) | −3.90516 | − | 6.76393i | −0.177875 | − | 0.308089i | ||||
\(483\) | 1.21226 | + | 13.0284i | 0.0551599 | + | 0.592814i | ||||
\(484\) | 1.27104 | − | 2.20151i | 0.0577746 | − | 0.100069i | ||||
\(485\) | 5.21536 | − | 3.01109i | 0.236817 | − | 0.136726i | ||||
\(486\) | 5.88783 | + | 14.4338i | 0.267077 | + | 0.654729i | ||||
\(487\) | 20.7358 | − | 35.9155i | 0.939630 | − | 1.62749i | 0.173468 | − | 0.984840i | \(-0.444503\pi\) |
0.766162 | − | 0.642647i | \(-0.222164\pi\) | |||||||
\(488\) | −3.03785 | −0.137517 | ||||||||
\(489\) | −24.7232 | + | 32.1481i | −1.11802 | + | 1.45379i | ||||
\(490\) | 6.98080 | + | 0.518123i | 0.315360 | + | 0.0234064i | ||||
\(491\) | 9.34197 | − | 5.39359i | 0.421597 | − | 0.243409i | −0.274163 | − | 0.961683i | \(-0.588401\pi\) |
0.695760 | + | 0.718274i | \(0.255068\pi\) | |||||||
\(492\) | 8.97108 | − | 11.6653i | 0.404448 | − | 0.525913i | ||||
\(493\) | −6.32152 | + | 3.64973i | −0.284707 | + | 0.164376i | ||||
\(494\) | −13.6681 | − | 7.89126i | −0.614956 | − | 0.355045i | ||||
\(495\) | −6.15603 | − | 6.18260i | −0.276693 | − | 0.277887i | ||||
\(496\) | − | 2.20521i | − | 0.0990168i | ||||||
\(497\) | −4.68306 | − | 20.4841i | −0.210064 | − | 0.918837i | ||||
\(498\) | −3.13336 | + | 23.6038i | −0.140409 | + | 1.05771i | ||||
\(499\) | −13.4335 | + | 23.2675i | −0.601365 | + | 1.04159i | 0.391250 | + | 0.920285i | \(0.372043\pi\) |
−0.992615 | + | 0.121310i | \(0.961290\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 11.3804 | − | 14.7983i | 0.508441 | − | 0.661138i | ||||
\(502\) | 12.4166i | 0.554178i | ||||||||
\(503\) | 36.7424 | 1.63826 | 0.819131 | − | 0.573606i | \(-0.194456\pi\) | ||||
0.819131 | + | 0.573606i | \(0.194456\pi\) | |||||||
\(504\) | −6.71307 | − | 4.23494i | −0.299024 | − | 0.188639i | ||||
\(505\) | 15.6759 | 0.697570 | ||||||||
\(506\) | 8.30397i | 0.369156i | ||||||||
\(507\) | −15.7370 | − | 2.08905i | −0.698905 | − | 0.0927782i | ||||
\(508\) | 6.59858 | 0.292765 | ||||||||
\(509\) | −6.13530 | + | 10.6266i | −0.271942 | + | 0.471018i | −0.969359 | − | 0.245648i | \(-0.920999\pi\) |
0.697417 | + | 0.716666i | \(0.254333\pi\) | |||||||
\(510\) | −4.62480 | − | 3.55665i | −0.204789 | − | 0.157491i | ||||
\(511\) | 36.7163 | + | 11.3111i | 1.62423 | + | 0.500374i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 41.5387 | − | 5.33225i | 1.83398 | − | 0.235424i | ||||
\(514\) | 25.4724 | + | 14.7065i | 1.12354 | + | 0.648676i | ||||
\(515\) | −3.19529 | + | 1.84480i | −0.140801 | + | 0.0812916i | ||||
\(516\) | −3.40455 | − | 0.451947i | −0.149877 | − | 0.0198958i | ||||
\(517\) | 1.63004 | − | 0.941107i | 0.0716893 | − | 0.0413898i | ||||
\(518\) | 6.51739 | − | 6.05159i | 0.286358 | − | 0.265891i | ||||
\(519\) | 1.70489 | + | 4.12853i | 0.0748363 | + | 0.181223i | ||||
\(520\) | −1.95820 | −0.0858726 | ||||||||
\(521\) | 14.0346 | − | 24.3087i | 0.614868 | − | 1.06498i | −0.375540 | − | 0.926806i | \(-0.622543\pi\) |
0.990408 | − | 0.138176i | \(-0.0441239\pi\) | |||||||
\(522\) | −1.66909 | − | 6.28320i | −0.0730539 | − | 0.275008i | ||||
\(523\) | −15.2468 | + | 8.80274i | −0.666696 | + | 0.384917i | −0.794824 | − | 0.606841i | \(-0.792437\pi\) |
0.128128 | + | 0.991758i | \(0.459103\pi\) | |||||||
\(524\) | 2.20506 | − | 3.81928i | 0.0963285 | − | 0.166846i | ||||
\(525\) | −1.91375 | + | 4.16384i | −0.0835229 | + | 0.181725i | ||||
\(526\) | −13.0484 | − | 22.6005i | −0.568937 | − | 0.985427i | ||||
\(527\) | 6.43288 | + | 3.71402i | 0.280220 | + | 0.161785i | ||||
\(528\) | −3.99300 | − | 3.07078i | −0.173773 | − | 0.133638i | ||||
\(529\) | −7.42359 | − | 12.8580i | −0.322765 | − | 0.559045i | ||||
\(530\) | 5.34261 | + | 9.25368i | 0.232068 | + | 0.401954i | ||||
\(531\) | −19.3807 | + | 19.2974i | −0.841051 | + | 0.837437i | ||||
\(532\) | −15.6264 | + | 14.5096i | −0.677492 | + | 0.629071i | ||||
\(533\) | 14.4084 | + | 8.31869i | 0.624096 | + | 0.360322i | ||||
\(534\) | −23.1726 | − | 17.8206i | −1.00278 | − | 0.771174i | ||||
\(535\) | 12.3369i | 0.533371i | ||||||||
\(536\) | 15.1391i | 0.653910i | ||||||||
\(537\) | −0.121401 | + | 0.914525i | −0.00523885 | + | 0.0394646i | ||||
\(538\) | −13.4812 | − | 7.78339i | −0.581217 | − | 0.335566i | ||||
\(539\) | −11.4559 | + | 16.8286i | −0.493441 | + | 0.724857i | ||||
\(540\) | 4.13258 | − | 3.14989i | 0.177838 | − | 0.135550i | ||||
\(541\) | −11.8477 | − | 20.5208i | −0.509372 | − | 0.882258i | −0.999941 | − | 0.0108558i | \(-0.996544\pi\) |
0.490569 | − | 0.871402i | \(-0.336789\pi\) | |||||||
\(542\) | 5.93737 | + | 10.2838i | 0.255032 | + | 0.441728i | ||||
\(543\) | 40.4946 | − | 16.7223i | 1.73779 | − | 0.717625i | ||||
\(544\) | −2.91713 | − | 1.68420i | −0.125071 | − | 0.0722096i | ||||
\(545\) | 3.48038 | + | 6.02819i | 0.149083 | + | 0.258219i | ||||
\(546\) | 3.74750 | − | 8.15361i | 0.160378 | − | 0.348942i | ||||
\(547\) | −16.4082 | + | 28.4199i | −0.701566 | + | 1.21515i | 0.266351 | + | 0.963876i | \(0.414182\pi\) |
−0.967917 | + | 0.251271i | \(0.919151\pi\) | |||||||
\(548\) | 4.23640 | − | 2.44589i | 0.180970 | − | 0.104483i | ||||
\(549\) | 6.43036 | + | 6.45812i | 0.274441 | + | 0.275626i | ||||
\(550\) | −1.45413 | + | 2.51862i | −0.0620041 | + | 0.107394i | ||||
\(551\) | −17.4657 | −0.744065 | ||||||||
\(552\) | −4.90254 | − | 0.650802i | −0.208666 | − | 0.0277000i | ||||
\(553\) | −11.0778 | + | 2.53260i | −0.471076 | + | 0.107697i | ||||
\(554\) | 23.7773 | − | 13.7278i | 1.01020 | − | 0.583240i | ||||
\(555\) | 2.22230 | + | 5.38150i | 0.0943316 | + | 0.228432i | ||||
\(556\) | −13.7982 | + | 7.96639i | −0.585174 | + | 0.337850i | ||||
\(557\) | 20.6283 | + | 11.9097i | 0.874048 | + | 0.504632i | 0.868691 | − | 0.495354i | \(-0.164962\pi\) |
0.00535689 | + | 0.999986i | \(0.498295\pi\) | |||||||
\(558\) | −4.68802 | + | 4.66787i | −0.198460 | + | 0.197607i | ||||
\(559\) | − | 3.88283i | − | 0.164226i | ||||||
\(560\) | −0.778946 | + | 2.52849i | −0.0329165 | + | 0.106848i | ||||
\(561\) | 15.6829 | − | 6.47629i | 0.662132 | − | 0.273429i | ||||
\(562\) | 13.0078 | − | 22.5302i | 0.548700 | − | 0.950377i | ||||
\(563\) | −18.0130 | −0.759157 | −0.379579 | − | 0.925159i | \(-0.623931\pi\) | ||||
−0.379579 | + | 0.925159i | \(0.623931\pi\) | |||||||
\(564\) | 0.427865 | + | 1.03611i | 0.0180164 | + | 0.0436282i | ||||
\(565\) | − | 2.72407i | − | 0.114603i | ||||||
\(566\) | −0.865094 | −0.0363626 | ||||||||
\(567\) | 5.20689 | + | 23.2355i | 0.218669 | + | 0.975799i | ||||
\(568\) | 7.94202 | 0.333240 | ||||||||
\(569\) | − | 15.9044i | − | 0.666747i | −0.942795 | − | 0.333374i | \(-0.891813\pi\) | ||
0.942795 | − | 0.333374i | \(-0.108187\pi\) | |||||||
\(570\) | −5.32832 | − | 12.9030i | −0.223179 | − | 0.540446i | ||||
\(571\) | 27.5270 | 1.15197 | 0.575985 | − | 0.817461i | \(-0.304619\pi\) | ||||
0.575985 | + | 0.817461i | \(0.304619\pi\) | |||||||
\(572\) | 2.84746 | − | 4.93195i | 0.119058 | − | 0.206215i | ||||
\(573\) | −37.3772 | + | 15.4350i | −1.56146 | + | 0.644807i | ||||
\(574\) | 16.4728 | − | 15.2955i | 0.687563 | − | 0.638422i | ||||
\(575\) | 2.85531i | 0.119075i | ||||||||
\(576\) | 2.12588 | − | 2.11675i | 0.0885785 | − | 0.0881978i | ||||
\(577\) | −17.2512 | − | 9.95997i | −0.718176 | − | 0.414639i | 0.0959051 | − | 0.995390i | \(-0.469425\pi\) |
−0.814081 | + | 0.580752i | \(0.802759\pi\) | |||||||
\(578\) | −4.89636 | + | 2.82692i | −0.203662 | + | 0.117584i | ||||
\(579\) | 2.76247 | + | 6.68955i | 0.114804 | + | 0.278008i | ||||
\(580\) | −1.87671 | + | 1.08352i | −0.0779261 | + | 0.0449907i | ||||
\(581\) | −10.7083 | + | 34.7597i | −0.444257 | + | 1.44207i | ||||
\(582\) | −10.3400 | − | 1.37261i | −0.428607 | − | 0.0568967i | ||||
\(583\) | −31.0753 | −1.28701 | ||||||||
\(584\) | −7.26053 | + | 12.5756i | −0.300443 | + | 0.520382i | ||||
\(585\) | 4.14501 | + | 4.16290i | 0.171375 | + | 0.172115i | ||||
\(586\) | 19.7339 | − | 11.3934i | 0.815200 | − | 0.470656i | ||||
\(587\) | 17.0018 | − | 29.4479i | 0.701739 | − | 1.21545i | −0.266117 | − | 0.963941i | \(-0.585741\pi\) |
0.967856 | − | 0.251506i | \(-0.0809259\pi\) | |||||||
\(588\) | −9.03750 | − | 8.08230i | −0.372700 | − | 0.333308i | ||||
\(589\) | 8.88669 | + | 15.3922i | 0.366170 | + | 0.634225i | ||||
\(590\) | 7.89516 | + | 4.55827i | 0.325039 | + | 0.187661i | ||||
\(591\) | −4.47573 | + | 1.84827i | −0.184107 | + | 0.0760275i | ||||
\(592\) | 1.68075 | + | 2.91115i | 0.0690785 | + | 0.119647i | ||||
\(593\) | 5.23235 | + | 9.06270i | 0.214867 | + | 0.372160i | 0.953231 | − | 0.302241i | \(-0.0977349\pi\) |
−0.738364 | + | 0.674402i | \(0.764402\pi\) | |||||||
\(594\) | 1.92407 | + | 14.9887i | 0.0789457 | + | 0.614995i | ||||
\(595\) | −6.06401 | − | 6.53077i | −0.248600 | − | 0.267735i | ||||
\(596\) | 6.20631 | + | 3.58321i | 0.254220 | + | 0.146774i | ||||
\(597\) | 0.795294 | − | 5.99101i | 0.0325492 | − | 0.245196i | ||||
\(598\) | − | 5.59127i | − | 0.228644i | ||||||
\(599\) | 15.9493i | 0.651672i | 0.945426 | + | 0.325836i | \(0.105646\pi\) | ||||
−0.945426 | + | 0.325836i | \(0.894354\pi\) | |||||||
\(600\) | −1.37299 | − | 1.05588i | −0.0560522 | − | 0.0431063i | ||||
\(601\) | 14.6089 | + | 8.43447i | 0.595911 | + | 0.344049i | 0.767431 | − | 0.641131i | \(-0.221535\pi\) |
−0.171520 | + | 0.985181i | \(0.554868\pi\) | |||||||
\(602\) | −5.01364 | − | 1.54454i | −0.204341 | − | 0.0629508i | ||||
\(603\) | 32.1840 | − | 32.0457i | 1.31063 | − | 1.30500i | ||||
\(604\) | −3.38348 | − | 5.86035i | −0.137672 | − | 0.238454i | ||||
\(605\) | 1.27104 | + | 2.20151i | 0.0516752 | + | 0.0895040i | ||||
\(606\) | −21.5229 | − | 16.5520i | −0.874310 | − | 0.672378i | ||||
\(607\) | −8.28479 | − | 4.78322i | −0.336269 | − | 0.194145i | 0.322352 | − | 0.946620i | \(-0.395527\pi\) |
−0.658621 | + | 0.752475i | \(0.728860\pi\) | |||||||
\(608\) | −4.02986 | − | 6.97993i | −0.163433 | − | 0.283073i | ||||
\(609\) | −0.920045 | − | 9.88790i | −0.0372821 | − | 0.400678i | ||||
\(610\) | 1.51893 | − | 2.63086i | 0.0614995 | − | 0.106520i | ||||
\(611\) | −1.09755 | + | 0.633670i | −0.0444021 | + | 0.0256356i | ||||
\(612\) | 2.59440 | + | 9.76650i | 0.104872 | + | 0.394788i | ||||
\(613\) | −19.3430 | + | 33.5030i | −0.781255 | + | 1.35317i | 0.149956 | + | 0.988693i | \(0.452087\pi\) |
−0.931211 | + | 0.364480i | \(0.881247\pi\) | |||||||
\(614\) | −19.5794 | −0.790158 | ||||||||
\(615\) | 5.61692 | + | 13.6018i | 0.226496 | + | 0.548479i | ||||
\(616\) | −5.23561 | − | 5.63860i | −0.210949 | − | 0.227186i | ||||
\(617\) | −26.6003 | + | 15.3577i | −1.07089 | + | 0.618277i | −0.928424 | − | 0.371523i | \(-0.878836\pi\) |
−0.142464 | + | 0.989800i | \(0.545502\pi\) | |||||||
\(618\) | 6.33500 | + | 0.840958i | 0.254831 | + | 0.0338283i | ||||
\(619\) | 3.13100 | − | 1.80768i | 0.125845 | − | 0.0726569i | −0.435756 | − | 0.900065i | \(-0.643519\pi\) |
0.561601 | + | 0.827408i | \(0.310186\pi\) | |||||||
\(620\) | 1.90977 | + | 1.10260i | 0.0766981 | + | 0.0442817i | ||||
\(621\) | 8.99392 | + | 11.7998i | 0.360913 | + | 0.473510i | ||||
\(622\) | 24.7602i | 0.992793i | ||||||||
\(623\) | −30.3838 | − | 32.7225i | −1.21730 | − | 1.31100i | ||||
\(624\) | 2.68859 | + | 2.06763i | 0.107630 | + | 0.0827714i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 29.7074 | 1.18735 | ||||||||
\(627\) | 40.2457 | + | 5.34253i | 1.60726 | + | 0.213360i | ||||
\(628\) | − | 10.0931i | − | 0.402757i | ||||||
\(629\) | −11.3229 | −0.451474 | ||||||||
\(630\) | 7.02410 | − | 3.69622i | 0.279847 | − | 0.147261i | ||||
\(631\) | 40.5503 | 1.61428 | 0.807142 | − | 0.590358i | \(-0.201013\pi\) | ||||
0.807142 | + | 0.590358i | \(0.201013\pi\) | |||||||
\(632\) | − | 4.29504i | − | 0.170848i | ||||||
\(633\) | 9.92207 | − | 12.9019i | 0.394367 | − | 0.512805i | ||||
\(634\) | −5.98746 | −0.237792 | ||||||||
\(635\) | −3.29929 | + | 5.71454i | −0.130928 | + | 0.226774i | ||||
\(636\) | 2.43545 | − | 18.3464i | 0.0965718 | − | 0.727483i | ||||
\(637\) | 7.71354 | − | 11.3311i | 0.305622 | − | 0.448954i | ||||
\(638\) | − | 6.30228i | − | 0.249510i | ||||||
\(639\) | −16.8112 | − | 16.8838i | −0.665043 | − | 0.667913i | ||||
\(640\) | −0.866025 | − | 0.500000i | −0.0342327 | − | 0.0197642i | ||||
\(641\) | 30.1024 | − | 17.3796i | 1.18897 | − | 0.686453i | 0.230899 | − | 0.972978i | \(-0.425833\pi\) |
0.958073 | + | 0.286524i | \(0.0924999\pi\) | |||||||
\(642\) | 13.0263 | − | 16.9385i | 0.514109 | − | 0.668508i | ||||
\(643\) | −0.969046 | + | 0.559479i | −0.0382154 | + | 0.0220637i | −0.518986 | − | 0.854783i | \(-0.673690\pi\) |
0.480771 | + | 0.876846i | \(0.340357\pi\) | |||||||
\(644\) | −7.21962 | − | 2.22413i | −0.284493 | − | 0.0876432i | ||||
\(645\) | 2.09367 | − | 2.72245i | 0.0824382 | − | 0.107196i | ||||
\(646\) | 27.1484 | 1.06814 | ||||||||
\(647\) | 8.00562 | − | 13.8661i | 0.314734 | − | 0.545134i | −0.664647 | − | 0.747157i | \(-0.731418\pi\) |
0.979381 | + | 0.202023i | \(0.0647515\pi\) | |||||||
\(648\) | −8.99992 | − | 0.0387579i | −0.353550 | − | 0.00152255i | ||||
\(649\) | −22.9611 | + | 13.2566i | −0.901302 | + | 0.520367i | ||||
\(650\) | 0.979098 | − | 1.69585i | 0.0384034 | − | 0.0665166i | ||||
\(651\) | −8.24589 | + | 5.84186i | −0.323182 | + | 0.228960i | ||||
\(652\) | −11.7073 | − | 20.2777i | −0.458494 | − | 0.794136i | ||||
\(653\) | 18.0245 | + | 10.4064i | 0.705352 | + | 0.407235i | 0.809338 | − | 0.587344i | \(-0.199826\pi\) |
−0.103986 | + | 0.994579i | \(0.533160\pi\) | |||||||
\(654\) | 1.58654 | − | 11.9515i | 0.0620387 | − | 0.467342i | ||||
\(655\) | 2.20506 | + | 3.81928i | 0.0861588 | + | 0.149232i | ||||
\(656\) | 4.24814 | + | 7.35799i | 0.165862 | + | 0.287281i | ||||
\(657\) | 42.1030 | − | 11.1843i | 1.64259 | − | 0.436343i | ||||
\(658\) | 0.381624 | + | 1.66926i | 0.0148773 | + | 0.0650744i | ||||
\(659\) | 1.89741 | + | 1.09547i | 0.0739127 | + | 0.0426735i | 0.536501 | − | 0.843900i | \(-0.319746\pi\) |
−0.462588 | + | 0.886573i | \(0.653079\pi\) | |||||||
\(660\) | 4.65587 | − | 1.92266i | 0.181230 | − | 0.0748393i | ||||
\(661\) | 18.8074i | 0.731524i | 0.930708 | + | 0.365762i | \(0.119192\pi\) | ||||
−0.930708 | + | 0.365762i | \(0.880808\pi\) | |||||||
\(662\) | 7.70669i | 0.299529i | ||||||||
\(663\) | −10.5597 | + | 4.36064i | −0.410103 | + | 0.169353i | ||||
\(664\) | −11.9055 | − | 6.87362i | −0.462021 | − | 0.266748i | ||||
\(665\) | −4.75247 | − | 20.7877i | −0.184293 | − | 0.806112i | ||||
\(666\) | 2.63103 | − | 9.73525i | 0.101950 | − | 0.377233i | ||||
\(667\) | −3.09379 | − | 5.35859i | −0.119792 | − | 0.207486i | ||||
\(668\) | 5.38906 | + | 9.33412i | 0.208509 | + | 0.361148i | ||||
\(669\) | −3.79338 | + | 28.5758i | −0.146660 | + | 1.10480i | ||||
\(670\) | −13.1109 | − | 7.56956i | −0.506517 | − | 0.292438i | ||||
\(671\) | 4.41742 | + | 7.65119i | 0.170532 | + | 0.295371i | ||||
\(672\) | 3.73928 | − | 2.64912i | 0.144246 | − | 0.102192i | ||||
\(673\) | −18.6100 | + | 32.2335i | −0.717364 | + | 1.24251i | 0.244676 | + | 0.969605i | \(0.421318\pi\) |
−0.962041 | + | 0.272906i | \(0.912015\pi\) | |||||||
\(674\) | −5.71465 | + | 3.29935i | −0.220120 | + | 0.127086i | ||||
\(675\) | 0.661591 | + | 5.15386i | 0.0254647 | + | 0.198372i | ||||
\(676\) | 4.58273 | − | 7.93753i | 0.176259 | − | 0.305290i | ||||
\(677\) | −41.0092 | −1.57611 | −0.788056 | − | 0.615604i | \(-0.788912\pi\) | ||||
−0.788056 | + | 0.615604i | \(0.788912\pi\) | |||||||
\(678\) | −2.87631 | + | 3.74013i | −0.110464 | + | 0.143639i | ||||
\(679\) | −15.2270 | − | 4.69095i | −0.584358 | − | 0.180022i | ||||
\(680\) | 2.91713 | − | 1.68420i | 0.111867 | − | 0.0645863i | ||||
\(681\) | 1.61566 | − | 2.10088i | 0.0619121 | − | 0.0805058i | ||||
\(682\) | −5.55408 | + | 3.20665i | −0.212677 | + | 0.122789i | ||||
\(683\) | −28.9807 | − | 16.7320i | −1.10892 | − | 0.640233i | −0.170368 | − | 0.985380i | \(-0.554496\pi\) |
−0.938549 | + | 0.345147i | \(0.887829\pi\) | |||||||
\(684\) | −6.30831 | + | 23.3418i | −0.241204 | + | 0.892495i | ||||
\(685\) | 4.89178i | 0.186905i | ||||||||
\(686\) | −11.5627 | − | 14.4673i | −0.441466 | − | 0.552366i | ||||
\(687\) | 5.14720 | − | 38.7743i | 0.196378 | − | 1.47933i | ||||
\(688\) | 0.991430 | − | 1.71721i | 0.0377979 | − | 0.0654679i | ||||
\(689\) | 20.9238 | 0.797132 | ||||||||
\(690\) | 3.01488 | − | 3.92033i | 0.114775 | − | 0.149244i | ||||
\(691\) | 43.1762i | 1.64250i | 0.570569 | + | 0.821250i | \(0.306723\pi\) | ||||
−0.570569 | + | 0.821250i | \(0.693277\pi\) | |||||||
\(692\) | −2.57885 | −0.0980333 | ||||||||
\(693\) | −0.904547 | + | 23.0658i | −0.0343609 | + | 0.876197i | ||||
\(694\) | 12.1162 | 0.459924 | ||||||||
\(695\) | − | 15.9328i | − | 0.604365i | ||||||
\(696\) | 3.72078 | + | 0.493925i | 0.141036 | + | 0.0187222i | ||||
\(697\) | −28.6189 | −1.08402 | ||||||||
\(698\) | 0.123735 | − | 0.214315i | 0.00468343 | − | 0.00811194i | ||||
\(699\) | −2.41029 | − | 1.85360i | −0.0911655 | − | 0.0701098i | ||||
\(700\) | −1.80026 | − | 1.93883i | −0.0680435 | − | 0.0732809i | ||||
\(701\) | 23.1589i | 0.874701i | 0.899291 | + | 0.437350i | \(0.144083\pi\) | ||||
−0.899291 | + | 0.437350i | \(0.855917\pi\) | |||||||
\(702\) | −1.29553 | − | 10.0923i | −0.0488965 | − | 0.380908i | ||||
\(703\) | −23.4631 | − | 13.5464i | −0.884926 | − | 0.510912i | ||||
\(704\) | 2.51862 | − | 1.45413i | 0.0949240 | − | 0.0548044i | ||||
\(705\) | −1.11123 | − | 0.147514i | −0.0418514 | − | 0.00555569i | ||||
\(706\) | 0.113033 | − | 0.0652598i | 0.00425406 | − | 0.00245608i | ||||
\(707\) | −28.2208 | − | 30.3930i | −1.06135 | − | 1.14305i | ||||
\(708\) | −6.02699 | − | 14.5949i | −0.226508 | − | 0.548508i | ||||
\(709\) | 25.4831 | 0.957038 | 0.478519 | − | 0.878077i | \(-0.341174\pi\) | ||||
0.478519 | + | 0.878077i | \(0.341174\pi\) | |||||||
\(710\) | −3.97101 | + | 6.87799i | −0.149029 | + | 0.258126i | ||||
\(711\) | −9.13076 | + | 9.09153i | −0.342430 | + | 0.340959i | ||||
\(712\) | 14.6163 | − | 8.43872i | 0.547768 | − | 0.316254i | ||||
\(713\) | −3.14828 | + | 5.45299i | −0.117904 | + | 0.204216i | ||||
\(714\) | 1.43010 | + | 15.3696i | 0.0535203 | + | 0.575193i | ||||
\(715\) | 2.84746 | + | 4.93195i | 0.106489 | + | 0.184444i | ||||
\(716\) | −0.461274 | − | 0.266316i | −0.0172386 | − | 0.00995271i | ||||
\(717\) | 21.4557 | + | 16.5003i | 0.801278 | + | 0.616214i | ||||
\(718\) | −5.12692 | − | 8.88009i | −0.191335 | − | 0.331402i | ||||
\(719\) | 1.20759 | + | 2.09160i | 0.0450354 | + | 0.0780036i | 0.887664 | − | 0.460491i | \(-0.152327\pi\) |
−0.842629 | + | 0.538495i | \(0.818993\pi\) | |||||||
\(720\) | 0.770216 | + | 2.89944i | 0.0287042 | + | 0.108056i | ||||
\(721\) | 9.32911 | + | 2.87400i | 0.347434 | + | 0.107033i | ||||
\(722\) | 39.8018 | + | 22.9796i | 1.48127 | + | 0.855212i | ||||
\(723\) | −10.7235 | − | 8.24679i | −0.398811 | − | 0.306702i | ||||
\(724\) | 25.2946i | 0.940066i | ||||||||
\(725\) | − | 2.16704i | − | 0.0804817i | ||||||
\(726\) | 0.579408 | − | 4.36473i | 0.0215039 | − | 0.161990i | ||||
\(727\) | 23.7545 | + | 13.7147i | 0.881006 | + | 0.508649i | 0.870990 | − | 0.491301i | \(-0.163478\pi\) |
0.0100163 | + | 0.999950i | \(0.496812\pi\) | |||||||
\(728\) | 3.52526 | + | 3.79661i | 0.130655 | + | 0.140712i | ||||
\(729\) | 18.9682 | + | 19.2148i | 0.702524 | + | 0.711660i | ||||
\(730\) | −7.26053 | − | 12.5756i | −0.268724 | − | 0.465444i | ||||
\(731\) | 3.33954 | + | 5.78425i | 0.123517 | + | 0.213938i | ||||
\(732\) | −4.86335 | + | 2.00834i | −0.179755 | + | 0.0742302i | ||||
\(733\) | 36.8669 | + | 21.2851i | 1.36171 | + | 0.786184i | 0.989852 | − | 0.142105i | \(-0.0453871\pi\) |
0.371859 | + | 0.928289i | \(0.378720\pi\) | |||||||
\(734\) | 0.216129 | + | 0.374347i | 0.00797747 | + | 0.0138174i | ||||
\(735\) | 11.5182 | − | 3.78556i | 0.424856 | − | 0.139633i | ||||
\(736\) | 1.42766 | − | 2.47278i | 0.0526241 | − | 0.0911477i | ||||
\(737\) | 38.1297 | − | 22.0142i | 1.40452 | − | 0.810903i | ||||
\(738\) | 6.64999 | − | 24.6060i | 0.244790 | − | 0.905761i | ||||
\(739\) | −17.3740 | + | 30.0927i | −0.639113 | + | 1.10698i | 0.346514 | + | 0.938045i | \(0.387365\pi\) |
−0.985628 | + | 0.168932i | \(0.945968\pi\) | |||||||
\(740\) | −3.36151 | −0.123571 | ||||||||
\(741\) | −27.0984 | − | 3.59726i | −0.995485 | − | 0.132149i | ||||
\(742\) | 8.32321 | − | 27.0175i | 0.305555 | − | 0.991842i | ||||
\(743\) | −30.6126 | + | 17.6742i | −1.12307 | + | 0.648404i | −0.942183 | − | 0.335100i | \(-0.891230\pi\) |
−0.180886 | + | 0.983504i | \(0.557897\pi\) | |||||||
\(744\) | −1.45787 | − | 3.53036i | −0.0534482 | − | 0.129429i | ||||
\(745\) | −6.20631 | + | 3.58321i | −0.227382 | + | 0.131279i | ||||
\(746\) | −2.67846 | − | 1.54641i | −0.0980654 | − | 0.0566181i | ||||
\(747\) | 10.5883 | + | 39.8593i | 0.387407 | + | 1.45838i | ||||
\(748\) | 9.79617i | 0.358183i | ||||||||
\(749\) | 23.9192 | − | 22.2096i | 0.873987 | − | 0.811523i | ||||
\(750\) | 1.60092 | − | 0.661104i | 0.0584573 | − | 0.0241401i | ||||
\(751\) | 17.3461 | − | 30.0443i | 0.632968 | − | 1.09633i | −0.353974 | − | 0.935255i | \(-0.615170\pi\) |
0.986942 | − | 0.161077i | \(-0.0514968\pi\) | |||||||
\(752\) | −0.647198 | −0.0236009 | ||||||||
\(753\) | 8.20863 | + | 19.8779i | 0.299139 | + | 0.724391i | ||||
\(754\) | 4.24348i | 0.154539i | ||||||||
\(755\) | 6.76696 | 0.246275 | ||||||||
\(756\) | −13.5468 | − | 2.34175i | −0.492693 | − | 0.0851688i | ||||
\(757\) | 39.4586 | 1.43415 | 0.717074 | − | 0.696997i | \(-0.245481\pi\) | ||||
0.717074 | + | 0.696997i | \(0.245481\pi\) | |||||||
\(758\) | − | 9.20781i | − | 0.334443i | ||||||
\(759\) | 5.48979 | + | 13.2940i | 0.199267 | + | 0.482541i | ||||
\(760\) | 8.05973 | 0.292357 | ||||||||
\(761\) | 5.67608 | − | 9.83125i | 0.205758 | − | 0.356383i | −0.744616 | − | 0.667493i | \(-0.767367\pi\) |
0.950374 | + | 0.311110i | \(0.100701\pi\) | |||||||
\(762\) | 10.5638 | − | 4.36235i | 0.382686 | − | 0.158031i | ||||
\(763\) | 5.42205 | − | 17.6002i | 0.196291 | − | 0.637169i | ||||
\(764\) | − | 23.3473i | − | 0.844677i | ||||||
\(765\) | −9.75524 | − | 2.63644i | −0.352701 | − | 0.0953205i | ||||
\(766\) | 21.2108 | + | 12.2460i | 0.766376 | + | 0.442467i | ||||
\(767\) | 15.4603 | − | 8.92600i | 0.558238 | − | 0.322299i | ||||
\(768\) | 0.661104 | + | 1.60092i | 0.0238555 | + | 0.0577682i | ||||
\(769\) | −25.0365 | + | 14.4549i | −0.902841 | + | 0.521255i | −0.878121 | − | 0.478439i | \(-0.841203\pi\) |
−0.0247199 | + | 0.999694i | \(0.507869\pi\) | |||||||
\(770\) | 7.50098 | − | 1.71487i | 0.270316 | − | 0.0617996i | ||||
\(771\) | 50.5018 | + | 6.70401i | 1.81878 | + | 0.241439i | ||||
\(772\) | −4.17857 | −0.150390 | ||||||||
\(773\) | −15.3683 | + | 26.6187i | −0.552761 | + | 0.957410i | 0.445313 | + | 0.895375i | \(0.353092\pi\) |
−0.998074 | + | 0.0620349i | \(0.980241\pi\) | |||||||
\(774\) | −5.74919 | + | 1.52723i | −0.206650 | + | 0.0548952i | ||||
\(775\) | −1.90977 | + | 1.10260i | −0.0686009 | + | 0.0396067i | ||||
\(776\) | 3.01109 | − | 5.21536i | 0.108092 | − | 0.187220i | ||||
\(777\) | 6.43308 | − | 13.9968i | 0.230785 | − | 0.502131i | ||||
\(778\) | −2.60976 | − | 4.52023i | −0.0935643 | − | 0.162058i | ||||
\(779\) | −59.3034 | − | 34.2388i | −2.12476 | − | 1.22673i | ||||
\(780\) | −3.13491 | + | 1.29457i | −0.112248 | + | 0.0463531i | ||||
\(781\) | −11.5487 | − | 20.0029i | −0.413244 | − | 0.715760i | ||||
\(782\) | 4.80893 | + | 8.32931i | 0.171967 | + | 0.297856i | ||||
\(783\) | −6.82592 | − | 8.95545i | −0.243938 | − | 0.320042i | ||||
\(784\) | 6.30461 | − | 3.04169i | 0.225165 | − | 0.108632i | ||||
\(785\) | 8.74085 | + | 5.04653i | 0.311974 | + | 0.180118i | ||||
\(786\) | 1.00518 | − | 7.57213i | 0.0358537 | − | 0.270089i | ||||
\(787\) | − | 26.2583i | − | 0.936007i | −0.883727 | − | 0.468004i | \(-0.844973\pi\) | ||
0.883727 | − | 0.468004i | \(-0.155027\pi\) | |||||||
\(788\) | − | 2.79573i | − | 0.0995936i | ||||||
\(789\) | −35.8307 | − | 27.5552i | −1.27561 | − | 0.980990i | ||||
\(790\) | 3.71962 | + | 2.14752i | 0.132338 | + | 0.0764054i | ||||
\(791\) | −5.28152 | + | 4.90404i | −0.187789 | + | 0.174368i | ||||
\(792\) | −8.42258 | − | 2.27627i | −0.299283 | − | 0.0808838i | ||||
\(793\) | −2.97435 | − | 5.15173i | −0.105622 | − | 0.182943i | ||||
\(794\) | 4.80828 | + | 8.32819i | 0.170640 | + | 0.295556i | ||||
\(795\) | 14.6707 | + | 11.2824i | 0.520317 | + | 0.400144i | ||||
\(796\) | 3.02178 | + | 1.74463i | 0.107104 | + | 0.0618366i | ||||
\(797\) | 5.45013 | + | 9.43990i | 0.193054 | + | 0.334379i | 0.946261 | − | 0.323405i | \(-0.104828\pi\) |
−0.753207 | + | 0.657783i | \(0.771494\pi\) | |||||||
\(798\) | −15.4243 | + | 33.5594i | −0.546014 | + | 1.18799i | ||||
\(799\) | 1.09001 | − | 1.88796i | 0.0385619 | − | 0.0667912i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | −48.8787 | − | 13.2099i | −1.72704 | − | 0.466748i | ||||
\(802\) | 9.14348 | − | 15.8370i | 0.322868 | − | 0.559223i | ||||
\(803\) | 42.2309 | 1.49029 | ||||||||
\(804\) | 10.0085 | + | 24.2365i | 0.352974 | + | 0.854756i | ||||
\(805\) | 5.53597 | − | 5.14031i | 0.195117 | − | 0.181172i | ||||
\(806\) | 3.73970 | − | 2.15912i | 0.131725 | − | 0.0760516i | ||||
\(807\) | −26.7280 | − | 3.54808i | −0.940870 | − | 0.124898i | ||||
\(808\) | 13.5758 | − | 7.83797i | 0.477594 | − | 0.275739i | ||||
\(809\) | −14.0577 | − | 8.11622i | −0.494243 | − | 0.285351i | 0.232090 | − | 0.972694i | \(-0.425444\pi\) |
−0.726333 | + | 0.687343i | \(0.758777\pi\) | |||||||
\(810\) | 4.53352 | − | 7.77478i | 0.159292 | − | 0.273178i | ||||
\(811\) | 34.0263i | 1.19482i | 0.801934 | + | 0.597412i | \(0.203804\pi\) | ||||
−0.801934 | + | 0.597412i | \(0.796196\pi\) | |||||||
\(812\) | 5.47932 | + | 1.68800i | 0.192287 | + | 0.0592373i | ||||
\(813\) | 16.3039 | + | 12.5384i | 0.571804 | + | 0.439739i | ||||
\(814\) | 4.88805 | − | 8.46635i | 0.171326 | − | 0.296745i | ||||
\(815\) | 23.4147 | 0.820180 | ||||||||
\(816\) | −5.78352 | − | 0.767750i | −0.202464 | − | 0.0268766i | ||||
\(817\) | 15.9813i | 0.559115i | ||||||||
\(818\) | −4.06433 | −0.142106 | ||||||||
\(819\) | 0.609054 | − | 15.5308i | 0.0212821 | − | 0.542689i | ||||
\(820\) | −8.49627 | −0.296703 | ||||||||
\(821\) | 34.9843i | 1.22096i | 0.792031 | + | 0.610480i | \(0.209024\pi\) | ||||
−0.792031 | + | 0.610480i | \(0.790976\pi\) | |||||||
\(822\) | 5.16515 | − | 6.71637i | 0.180155 | − | 0.234260i | ||||
\(823\) | −1.46588 | −0.0510975 | −0.0255487 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255487 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(824\) | −1.84480 | + | 3.19529i | −0.0642667 | + | 0.111313i | ||||
\(825\) | −0.662868 | + | 4.99343i | −0.0230781 | + | 0.173849i | ||||
\(826\) | −5.37563 | − | 23.5135i | −0.187042 | − | 0.818138i | ||||
\(827\) | − | 3.05294i | − | 0.106161i | −0.998590 | − | 0.0530805i | \(-0.983096\pi\) | ||
0.998590 | − | 0.0530805i | \(-0.0169040\pi\) | |||||||
\(828\) | −8.27882 | + | 2.19921i | −0.287709 | + | 0.0764278i | ||||
\(829\) | −45.1011 | − | 26.0391i | −1.56643 | − | 0.904377i | −0.996581 | − | 0.0826248i | \(-0.973670\pi\) |
−0.569846 | − | 0.821752i | \(-0.692997\pi\) | |||||||
\(830\) | 11.9055 | − | 6.87362i | 0.413244 | − | 0.238587i | ||||
\(831\) | 28.9900 | − | 37.6964i | 1.00565 | − | 1.30767i | ||||
\(832\) | −1.69585 | + | 0.979098i | −0.0587929 | + | 0.0339441i | ||||
\(833\) | −1.74525 | + | 23.5142i | −0.0604693 | + | 0.814718i | ||||
\(834\) | −16.8232 | + | 21.8756i | −0.582539 | + | 0.757490i | ||||
\(835\) | −10.7781 | −0.372992 | ||||||||
\(836\) | −11.7199 | + | 20.2994i | −0.405340 | + | 0.702069i | ||||
\(837\) | −4.41919 | + | 10.5722i | −0.152749 | + | 0.365427i | ||||
\(838\) | −10.4005 | + | 6.00474i | −0.359280 | + | 0.207430i | ||||
\(839\) | 1.17639 | − | 2.03757i | 0.0406135 | − | 0.0703447i | −0.845004 | − | 0.534760i | \(-0.820402\pi\) |
0.885618 | + | 0.464415i | \(0.153735\pi\) | |||||||
\(840\) | 0.424564 | + | 4.56287i | 0.0146488 | + | 0.157434i | ||||
\(841\) | −12.1520 | − | 21.0478i | −0.419034 | − | 0.725788i | ||||
\(842\) | −10.4163 | − | 6.01384i | −0.358969 | − | 0.207251i | ||||
\(843\) | 5.92964 | − | 44.6684i | 0.204228 | − | 1.53846i | ||||
\(844\) | 4.69846 | + | 8.13798i | 0.161728 | + | 0.280121i | ||||
\(845\) | 4.58273 | + | 7.93753i | 0.157651 | + | 0.273059i | ||||
\(846\) | 1.36995 | + | 1.37587i | 0.0471000 | + | 0.0473033i | ||||
\(847\) | 1.98014 | − | 6.42762i | 0.0680385 | − | 0.220856i | ||||
\(848\) | 9.25368 | + | 5.34261i | 0.317773 | + | 0.183466i | ||||
\(849\) | −1.38495 | + | 0.571917i | −0.0475312 | + | 0.0196281i | ||||
\(850\) | 3.36841i | 0.115535i | ||||||||
\(851\) | − | 9.59815i | − | 0.329021i | ||||||
\(852\) | 12.7145 | − | 5.25050i | 0.435592 | − | 0.179879i | ||||
\(853\) | −24.1341 | − | 13.9338i | −0.826334 | − | 0.477084i | 0.0262617 | − | 0.999655i | \(-0.491640\pi\) |
−0.852596 | + | 0.522571i | \(0.824973\pi\) | |||||||
\(854\) | −7.83525 | + | 1.79129i | −0.268117 | + | 0.0612966i | ||||
\(855\) | −17.0604 | − | 17.1340i | −0.583454 | − | 0.585972i | ||||
\(856\) | 6.16845 | + | 10.6841i | 0.210833 | + | 0.365174i | ||||
\(857\) | −14.5780 | − | 25.2499i | −0.497975 | − | 0.862519i | 0.502022 | − | 0.864855i | \(-0.332590\pi\) |
−0.999997 | + | 0.00233623i | \(0.999256\pi\) | |||||||
\(858\) | 1.29802 | − | 9.77812i | 0.0443138 | − | 0.333819i | ||||
\(859\) | −49.7500 | − | 28.7232i | −1.69745 | − | 0.980022i | −0.948169 | − | 0.317767i | \(-0.897067\pi\) |
−0.749279 | − | 0.662255i | \(-0.769600\pi\) | |||||||
\(860\) | 0.991430 | + | 1.71721i | 0.0338075 | + | 0.0585563i | ||||
\(861\) | 16.2597 | − | 35.3771i | 0.554131 | − | 1.20565i | ||||
\(862\) | 4.70997 | − | 8.15790i | 0.160422 | − | 0.277859i | ||||
\(863\) | 16.5615 | − | 9.56179i | 0.563761 | − | 0.325487i | −0.190893 | − | 0.981611i | \(-0.561138\pi\) |
0.754653 | + | 0.656124i | \(0.227805\pi\) | |||||||
\(864\) | 2.00398 | − | 4.79417i | 0.0681767 | − | 0.163101i | ||||
\(865\) | 1.28943 | − | 2.23335i | 0.0438418 | − | 0.0759362i | ||||
\(866\) | 28.8287 | 0.979640 | ||||||||
\(867\) | −5.96979 | + | 7.76267i | −0.202745 | + | 0.263634i | ||||
\(868\) | −1.30032 | − | 5.68769i | −0.0441356 | − | 0.193053i | ||||
\(869\) | −10.8176 | + | 6.24553i | −0.366961 | + | 0.211865i | ||||
\(870\) | −2.28814 | + | 2.97532i | −0.0775752 | + | 0.100873i | ||||
\(871\) | −25.6736 | + | 14.8227i | −0.869918 | + | 0.502248i | ||||
\(872\) | 6.02819 | + | 3.48038i | 0.204140 | + | 0.117860i | ||||
\(873\) | −17.4610 | + | 4.63838i | −0.590964 | + | 0.156985i | ||||
\(874\) | 23.0131i | 0.778428i | ||||||||
\(875\) | 2.57921 | − | 0.589657i | 0.0871931 | − | 0.0199340i | ||||
\(876\) | −3.30974 | + | 24.9325i | −0.111826 | + | 0.842390i | ||||
\(877\) | −14.3773 | + | 24.9022i | −0.485487 | + | 0.840888i | −0.999861 | − | 0.0166782i | \(-0.994691\pi\) |
0.514374 | + | 0.857566i | \(0.328024\pi\) | |||||||
\(878\) | −35.2441 | −1.18943 | ||||||||
\(879\) | 24.0602 | − | 31.2860i | 0.811530 | − | 1.05525i | ||||
\(880\) | 2.90825i | 0.0980371i | ||||||||
\(881\) | −9.79497 | −0.330001 | −0.165001 | − | 0.986293i | \(-0.552763\pi\) | ||||
−0.165001 | + | 0.986293i | \(0.552763\pi\) | |||||||
\(882\) | −19.8116 | − | 6.96437i | −0.667090 | − | 0.234503i | ||||
\(883\) | −22.0390 | −0.741670 | −0.370835 | − | 0.928699i | \(-0.620929\pi\) | ||||
−0.370835 | + | 0.928699i | \(0.620929\pi\) | |||||||
\(884\) | − | 6.59600i | − | 0.221848i | ||||||
\(885\) | 15.6530 | + | 2.07790i | 0.526170 | + | 0.0698480i | ||||
\(886\) | −21.2414 | −0.713619 | ||||||||
\(887\) | 23.8142 | − | 41.2474i | 0.799603 | − | 1.38495i | −0.120272 | − | 0.992741i | \(-0.538377\pi\) |
0.919875 | − | 0.392212i | \(-0.128290\pi\) | |||||||
\(888\) | 4.61532 | + | 3.54936i | 0.154880 | + | 0.119109i | ||||
\(889\) | 17.0191 | − | 3.89089i | 0.570802 | − | 0.130496i | ||||
\(890\) | 16.8774i | 0.565733i | ||||||||
\(891\) | 12.9894 | + | 22.7237i | 0.435161 | + | 0.761273i | ||||
\(892\) | −14.4132 | − | 8.32148i | −0.482591 | − | 0.278624i | ||||
\(893\) | 4.51740 | − | 2.60812i | 0.151169 | − | 0.0872774i | ||||
\(894\) | 12.3047 | + | 1.63342i | 0.411530 | + | 0.0546298i | ||||
\(895\) | 0.461274 | − | 0.266316i | 0.0154187 | − | 0.00890198i | ||||
\(896\) | 0.589657 | + | 2.57921i | 0.0196990 | + | 0.0861652i | ||||
\(897\) | −3.69641 | − | 8.95116i | −0.123419 | − | 0.298871i | ||||
\(898\) | −16.9305 | −0.564980 | ||||||||
\(899\) | 2.38939 | − | 4.13854i | 0.0796905 | − | 0.138028i | ||||
\(900\) | −2.89610 | − | 0.782695i | −0.0965366 | − | 0.0260898i | ||||
\(901\) | −31.1702 | + | 17.9961i | −1.03843 | + | 0.599537i | ||||
\(902\) | 12.3546 | − | 21.3989i | 0.411365 | − | 0.712504i | ||||
\(903\) | −9.04753 | + | 0.841850i | −0.301083 | + | 0.0280150i | ||||
\(904\) | −1.36204 | − | 2.35912i | −0.0453007 | − | 0.0784631i | ||||
\(905\) | −21.9057 | − | 12.6473i | −0.728172 | − | 0.420410i | ||||
\(906\) | −9.29098 | − | 7.14512i | −0.308672 | − | 0.237381i | ||||
\(907\) | 3.17593 | + | 5.50087i | 0.105455 | + | 0.182653i | 0.913924 | − | 0.405885i | \(-0.133037\pi\) |
−0.808469 | + | 0.588539i | \(0.799703\pi\) | |||||||
\(908\) | 0.765073 | + | 1.32514i | 0.0253898 | + | 0.0439765i | ||||
\(909\) | −45.3991 | − | 12.2695i | −1.50579 | − | 0.406953i | ||||
\(910\) | −5.05059 | + | 1.15466i | −0.167425 | + | 0.0382767i | ||||
\(911\) | 23.4087 | + | 13.5150i | 0.775563 | + | 0.447772i | 0.834856 | − | 0.550469i | \(-0.185551\pi\) |
−0.0592924 | + | 0.998241i | \(0.518884\pi\) | |||||||
\(912\) | −11.0659 | − | 8.51014i | −0.366430 | − | 0.281799i | ||||
\(913\) | 39.9804i | 1.32316i | ||||||||
\(914\) | 33.2351i | 1.09932i | ||||||||
\(915\) | 0.692407 | − | 5.21596i | 0.0228903 | − | 0.172434i | ||||
\(916\) | 19.5572 | + | 11.2914i | 0.646188 | + | 0.373077i | ||||
\(917\) | 3.43524 | − | 11.1509i | 0.113442 | − | 0.368236i | ||||
\(918\) | 10.6101 | + | 13.9202i | 0.350185 | + | 0.459436i | ||||
\(919\) | −18.7122 | − | 32.4104i | −0.617257 | − | 1.06912i | −0.989984 | − | 0.141179i | \(-0.954911\pi\) |
0.372727 | − | 0.927941i | \(-0.378423\pi\) | |||||||
\(920\) | 1.42766 | + | 2.47278i | 0.0470685 | + | 0.0815250i | ||||
\(921\) | −31.3450 | + | 12.9440i | −1.03285 | + | 0.426519i | ||||
\(922\) | −22.9806 | − | 13.2679i | −0.756827 | − | 0.436954i | ||||
\(923\) | 7.77601 | + | 13.4684i | 0.255951 | + | 0.443319i | ||||
\(924\) | −12.1095 | − | 5.56566i | −0.398373 | − | 0.183097i | ||||
\(925\) | 1.68075 | − | 2.91115i | 0.0552628 | − | 0.0957180i | ||||
\(926\) | 9.10135 | − | 5.25467i | 0.299089 | − | 0.172679i | ||||
\(927\) | 10.6978 | − | 2.84179i | 0.351361 | − | 0.0933366i | ||||
\(928\) | −1.08352 | + | 1.87671i | −0.0355682 | + | 0.0616060i | ||||
\(929\) | −7.79487 | −0.255741 | −0.127871 | − | 0.991791i | \(-0.540814\pi\) | ||||
−0.127871 | + | 0.991791i | \(0.540814\pi\) | |||||||
\(930\) | 3.78632 | + | 0.502626i | 0.124158 | + | 0.0164818i | ||||
\(931\) | −31.7481 | + | 46.6375i | −1.04050 | + | 1.52848i | ||||
\(932\) | 1.52031 | − | 0.877750i | 0.0497993 | − | 0.0287517i | ||||
\(933\) | 16.3691 | + | 39.6390i | 0.535899 | + | 1.29772i | ||||
\(934\) | 10.6438 | − | 6.14519i | 0.348275 | − | 0.201077i | ||||
\(935\) | −8.48373 | − | 4.89809i | −0.277448 | − | 0.160185i | ||||
\(936\) | 5.67113 | + | 1.53267i | 0.185367 | + | 0.0500969i | ||||
\(937\) | 55.3757i | 1.80905i | 0.426424 | + | 0.904523i | \(0.359773\pi\) | ||||
−0.426424 | + | 0.904523i | \(0.640227\pi\) | |||||||
\(938\) | 8.92688 | + | 39.0469i | 0.291473 | + | 1.27493i | ||||
\(939\) | 47.5592 | − | 19.6397i | 1.55204 | − | 0.640918i | ||||
\(940\) | 0.323599 | − | 0.560490i | 0.0105546 | − | 0.0182812i | ||||
\(941\) | −29.2725 | −0.954256 | −0.477128 | − | 0.878834i | \(-0.658322\pi\) | ||||
−0.477128 | + | 0.878834i | \(0.658322\pi\) | |||||||
\(942\) | −6.67256 | − | 16.1582i | −0.217404 | − | 0.526462i | ||||
\(943\) | − | 24.2595i | − | 0.789999i | ||||||
\(944\) | 9.11655 | 0.296718 | ||||||||
\(945\) | 8.80143 | − | 10.5610i | 0.286310 | − | 0.343550i | ||||
\(946\) | −5.76665 | −0.187490 | ||||||||
\(947\) | − | 43.5322i | − | 1.41461i | −0.706911 | − | 0.707303i | \(-0.749912\pi\) | ||
0.706911 | − | 0.707303i | \(-0.250088\pi\) | |||||||
\(948\) | −2.83947 | − | 6.87602i | −0.0922217 | − | 0.223323i | ||||
\(949\) | −28.4351 | −0.923041 | ||||||||
\(950\) | −4.02986 | + | 6.97993i | −0.130746 | + | 0.226459i | ||||
\(951\) | −9.58543 | + | 3.95833i | −0.310829 | + | 0.128358i | ||||
\(952\) | −8.51697 | − | 2.62381i | −0.276037 | − | 0.0850381i | ||||
\(953\) | − | 19.9323i | − | 0.645672i | −0.946455 | − | 0.322836i | \(-0.895364\pi\) | ||
0.946455 | − | 0.322836i | \(-0.104636\pi\) | |||||||
\(954\) | −8.22993 | − | 30.9812i | −0.266454 | − | 1.00305i | ||||
\(955\) | 20.2194 | + | 11.6737i | 0.654284 | + | 0.377751i | ||||
\(956\) | −13.5333 | + | 7.81348i | −0.437700 | + | 0.252706i | ||||
\(957\) | −4.16647 | − | 10.0894i | −0.134683 | − | 0.326146i | ||||
\(958\) | −27.4869 | + | 15.8696i | −0.888063 | + | 0.512723i | ||||
\(959\) | 9.48433 | − | 8.80648i | 0.306265 | − | 0.284376i | ||||
\(960\) | −1.71699 | − | 0.227927i | −0.0554156 | − | 0.00735630i | ||||
\(961\) | 26.1370 | 0.843131 | ||||||||
\(962\) | −3.29124 | + | 5.70060i | −0.106114 | + | 0.183795i | ||||
\(963\) | 9.65603 | − | 35.7289i | 0.311161 | − | 1.15135i | ||||
\(964\) | 6.76393 | − | 3.90516i | 0.217852 | − | 0.125777i | ||||
\(965\) | 2.08929 | − | 3.61875i | 0.0672565 | − | 0.116492i | ||||
\(966\) | −13.0284 | + | 1.21226i | −0.419182 | + | 0.0390039i | ||||
\(967\) | 13.3577 | + | 23.1362i | 0.429555 | + | 0.744011i | 0.996834 | − | 0.0795148i | \(-0.0253371\pi\) |
−0.567279 | + | 0.823526i | \(0.692004\pi\) | |||||||
\(968\) | 2.20151 | + | 1.27104i | 0.0707591 | + | 0.0408528i | ||||
\(969\) | 43.4625 | − | 17.9479i | 1.39622 | − | 0.576571i | ||||
\(970\) | 3.01109 | + | 5.21536i | 0.0966802 | + | 0.167455i | ||||
\(971\) | −1.77474 | − | 3.07394i | −0.0569541 | − | 0.0986475i | 0.836143 | − | 0.548512i | \(-0.184806\pi\) |
−0.893097 | + | 0.449865i | \(0.851472\pi\) | |||||||
\(972\) | −14.4338 | + | 5.88783i | −0.462963 | + | 0.188852i | ||||
\(973\) | −30.8910 | + | 28.6832i | −0.990319 | + | 0.919540i | ||||
\(974\) | 35.9155 | + | 20.7358i | 1.15081 | + | 0.664419i | ||||
\(975\) | 0.446325 | − | 3.36220i | 0.0142938 | − | 0.107677i | ||||
\(976\) | − | 3.03785i | − | 0.0972392i | ||||||
\(977\) | 51.3465i | 1.64272i | 0.570411 | + | 0.821360i | \(0.306784\pi\) | ||||
−0.570411 | + | 0.821360i | \(0.693216\pi\) | |||||||
\(978\) | −32.1481 | − | 24.7232i | −1.02798 | − | 0.790560i | ||||
\(979\) | −42.5078 | − | 24.5419i | −1.35856 | − | 0.784362i | ||||
\(980\) | −0.518123 | + | 6.98080i | −0.0165508 | + | 0.222993i | ||||
\(981\) | −5.36128 | − | 20.1823i | −0.171173 | − | 0.644372i | ||||
\(982\) | 5.39359 | + | 9.34197i | 0.172116 | + | 0.298114i | ||||
\(983\) | 20.7452 | + | 35.9317i | 0.661669 | + | 1.14604i | 0.980177 | + | 0.198124i | \(0.0634850\pi\) |
−0.318508 | + | 0.947920i | \(0.603182\pi\) | |||||||
\(984\) | 11.6653 | + | 8.97108i | 0.371877 | + | 0.285988i | ||||
\(985\) | 2.42117 | + | 1.39786i | 0.0771449 | + | 0.0445396i | ||||
\(986\) | −3.64973 | − | 6.32152i | −0.116231 | − | 0.201318i | ||||
\(987\) | 1.71450 | + | 2.42005i | 0.0545732 | + | 0.0770311i | ||||
\(988\) | 7.89126 | − | 13.6681i | 0.251055 | − | 0.434839i | ||||
\(989\) | −4.90317 | + | 2.83085i | −0.155912 | + | 0.0900156i | ||||
\(990\) | 6.18260 | − | 6.15603i | 0.196496 | − | 0.195652i | ||||
\(991\) | 12.9670 | − | 22.4595i | 0.411911 | − | 0.713451i | −0.583188 | − | 0.812337i | \(-0.698195\pi\) |
0.995099 | + | 0.0988866i | \(0.0315281\pi\) | |||||||
\(992\) | 2.20521 | 0.0700155 | ||||||||
\(993\) | 5.09492 | + | 12.3378i | 0.161682 | + | 0.391528i | ||||
\(994\) | 20.4841 | − | 4.68306i | 0.649716 | − | 0.148538i | ||||
\(995\) | −3.02178 | + | 1.74463i | −0.0957969 | + | 0.0553084i | ||||
\(996\) | −23.6038 | − | 3.13336i | −0.747916 | − | 0.0992843i | ||||
\(997\) | 18.3703 | − | 10.6061i | 0.581792 | − | 0.335898i | −0.180053 | − | 0.983657i | \(-0.557627\pi\) |
0.761845 | + | 0.647759i | \(0.224294\pi\) | |||||||
\(998\) | −23.2675 | − | 13.4335i | −0.736519 | − | 0.425229i | ||||
\(999\) | −2.22394 | − | 17.3247i | −0.0703624 | − | 0.548130i |
(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 | 630.2.bk.c.101.14 | yes | 32 | |
3.2 | odd | 2 | 1890.2.bk.c.521.13 | 32 | |||
7.5 | odd | 6 | 630.2.t.c.551.16 | yes | 32 | ||
9.4 | even | 3 | 1890.2.t.c.1151.6 | 32 | |||
9.5 | odd | 6 | 630.2.t.c.311.16 | ✓ | 32 | ||
21.5 | even | 6 | 1890.2.t.c.1601.6 | 32 | |||
63.5 | even | 6 | inner | 630.2.bk.c.131.6 | yes | 32 | |
63.40 | odd | 6 | 1890.2.bk.c.341.13 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.c.311.16 | ✓ | 32 | 9.5 | odd | 6 | ||
630.2.t.c.551.16 | yes | 32 | 7.5 | odd | 6 | ||
630.2.bk.c.101.14 | yes | 32 | 1.1 | even | 1 | trivial | |
630.2.bk.c.131.6 | yes | 32 | 63.5 | even | 6 | inner | |
1890.2.t.c.1151.6 | 32 | 9.4 | even | 3 | |||
1890.2.t.c.1601.6 | 32 | 21.5 | even | 6 | |||
1890.2.bk.c.341.13 | 32 | 63.40 | odd | 6 | |||
1890.2.bk.c.521.13 | 32 | 3.2 | odd | 2 |