Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(43,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(0.323042 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.127 |
Dual form | 210.3.l.a.43.3 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 0.578661 | − | 4.96640i | 0.115732 | − | 0.993280i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −1.87083 | − | 1.87083i | −0.267261 | − | 0.267261i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 5.54506 | − | 4.38774i | 0.554506 | − | 0.438774i | ||||
\(11\) | 19.5717 | 1.77924 | 0.889622 | − | 0.456698i | \(-0.150968\pi\) | ||||
0.889622 | + | 0.456698i | \(0.150968\pi\) | |||||||
\(12\) | 2.44949 | + | 2.44949i | 0.204124 | + | 0.204124i | ||||
\(13\) | 8.03207 | − | 8.03207i | 0.617851 | − | 0.617851i | −0.327129 | − | 0.944980i | \(-0.606081\pi\) |
0.944980 | + | 0.327129i | \(0.106081\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | −5.37386 | − | 6.79129i | −0.358258 | − | 0.452753i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −2.19659 | − | 2.19659i | −0.129211 | − | 0.129211i | 0.639543 | − | 0.768755i | \(-0.279123\pi\) |
−0.768755 | + | 0.639543i | \(0.779123\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | − | 8.25097i | − | 0.434261i | −0.976143 | − | 0.217131i | \(-0.930330\pi\) | ||
0.976143 | − | 0.217131i | \(-0.0696698\pi\) | |||||||
\(20\) | 9.93280 | + | 1.15732i | 0.496640 | + | 0.0578661i | ||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | 19.5717 | + | 19.5717i | 0.889622 | + | 0.889622i | ||||
\(23\) | −17.9068 | + | 17.9068i | −0.778557 | + | 0.778557i | −0.979585 | − | 0.201028i | \(-0.935572\pi\) |
0.201028 | + | 0.979585i | \(0.435572\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −24.3303 | − | 5.74773i | −0.973212 | − | 0.229909i | ||||
\(26\) | 16.0641 | 0.617851 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 3.74166 | − | 3.74166i | 0.133631 | − | 0.133631i | ||||
\(29\) | 19.7495i | 0.681017i | 0.940241 | + | 0.340508i | \(0.110599\pi\) | ||||
−0.940241 | + | 0.340508i | \(0.889401\pi\) | |||||||
\(30\) | 1.41742 | − | 12.1652i | 0.0472475 | − | 0.405505i | ||||
\(31\) | 30.0043 | 0.967881 | 0.483940 | − | 0.875101i | \(-0.339205\pi\) | ||||
0.483940 | + | 0.875101i | \(0.339205\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 23.9703 | − | 23.9703i | 0.726373 | − | 0.726373i | ||||
\(34\) | − | 4.39319i | − | 0.129211i | ||||||
\(35\) | −10.3739 | + | 8.20871i | −0.296396 | + | 0.234535i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 37.2346 | + | 37.2346i | 1.00634 | + | 1.00634i | 0.999980 | + | 0.00635971i | \(0.00202437\pi\) |
0.00635971 | + | 0.999980i | \(0.497976\pi\) | |||||||
\(38\) | 8.25097 | − | 8.25097i | 0.217131 | − | 0.217131i | ||||
\(39\) | − | 19.6745i | − | 0.504473i | ||||||
\(40\) | 8.77548 | + | 11.0901i | 0.219387 | + | 0.277253i | ||||
\(41\) | −80.8620 | −1.97224 | −0.986122 | − | 0.166023i | \(-0.946907\pi\) | ||||
−0.986122 | + | 0.166023i | \(0.946907\pi\) | |||||||
\(42\) | −4.58258 | − | 4.58258i | −0.109109 | − | 0.109109i | ||||
\(43\) | −13.6780 | + | 13.6780i | −0.318093 | + | 0.318093i | −0.848034 | − | 0.529942i | \(-0.822214\pi\) |
0.529942 | + | 0.848034i | \(0.322214\pi\) | |||||||
\(44\) | 39.1434i | 0.889622i | ||||||||
\(45\) | −14.8992 | − | 1.73598i | −0.331093 | − | 0.0385774i | ||||
\(46\) | −35.8136 | −0.778557 | ||||||||
\(47\) | −8.17549 | − | 8.17549i | −0.173947 | − | 0.173947i | 0.614764 | − | 0.788711i | \(-0.289251\pi\) |
−0.788711 | + | 0.614764i | \(0.789251\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.102062 | + | 0.102062i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −18.5826 | − | 30.0780i | −0.371652 | − | 0.601561i | ||||
\(51\) | −5.38053 | −0.105501 | ||||||||
\(52\) | 16.0641 | + | 16.0641i | 0.308926 | + | 0.308926i | ||||
\(53\) | −38.8560 | + | 38.8560i | −0.733132 | + | 0.733132i | −0.971239 | − | 0.238107i | \(-0.923473\pi\) |
0.238107 | + | 0.971239i | \(0.423473\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 11.3254 | − | 97.2008i | 0.205916 | − | 1.76729i | ||||
\(56\) | 7.48331 | 0.133631 | ||||||||
\(57\) | −10.1053 | − | 10.1053i | −0.177287 | − | 0.177287i | ||||
\(58\) | −19.7495 | + | 19.7495i | −0.340508 | + | 0.340508i | ||||
\(59\) | 74.3773i | 1.26063i | 0.776339 | + | 0.630316i | \(0.217075\pi\) | ||||
−0.776339 | + | 0.630316i | \(0.782925\pi\) | |||||||
\(60\) | 13.5826 | − | 10.7477i | 0.226376 | − | 0.179129i | ||||
\(61\) | 97.8414 | 1.60396 | 0.801979 | − | 0.597352i | \(-0.203781\pi\) | ||||
0.801979 | + | 0.597352i | \(0.203781\pi\) | |||||||
\(62\) | 30.0043 | + | 30.0043i | 0.483940 | + | 0.483940i | ||||
\(63\) | −5.61249 | + | 5.61249i | −0.0890871 | + | 0.0890871i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −35.2426 | − | 44.5383i | −0.542194 | − | 0.685205i | ||||
\(66\) | 47.9406 | 0.726373 | ||||||||
\(67\) | −67.1712 | − | 67.1712i | −1.00255 | − | 1.00255i | −0.999997 | − | 0.00255792i | \(-0.999186\pi\) |
−0.00255792 | − | 0.999997i | \(-0.500814\pi\) | |||||||
\(68\) | 4.39319 | − | 4.39319i | 0.0646057 | − | 0.0646057i | ||||
\(69\) | 43.8625i | 0.635689i | ||||||||
\(70\) | −18.5826 | − | 2.16515i | −0.265465 | − | 0.0309307i | ||||
\(71\) | −13.3793 | −0.188441 | −0.0942203 | − | 0.995551i | \(-0.530036\pi\) | ||||
−0.0942203 | + | 0.995551i | \(0.530036\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −48.2738 | + | 48.2738i | −0.661285 | + | 0.661285i | −0.955683 | − | 0.294398i | \(-0.904881\pi\) |
0.294398 | + | 0.955683i | \(0.404881\pi\) | |||||||
\(74\) | 74.4691i | 1.00634i | ||||||||
\(75\) | −36.8379 | + | 22.7589i | −0.491172 | + | 0.303452i | ||||
\(76\) | 16.5019 | 0.217131 | ||||||||
\(77\) | −36.6153 | − | 36.6153i | −0.475523 | − | 0.475523i | ||||
\(78\) | 19.6745 | − | 19.6745i | 0.252237 | − | 0.252237i | ||||
\(79\) | − | 40.2089i | − | 0.508973i | −0.967076 | − | 0.254487i | \(-0.918094\pi\) | ||
0.967076 | − | 0.254487i | \(-0.0819065\pi\) | |||||||
\(80\) | −2.31464 | + | 19.8656i | −0.0289331 | + | 0.248320i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −80.8620 | − | 80.8620i | −0.986122 | − | 0.986122i | ||||
\(83\) | 34.4137 | − | 34.4137i | 0.414623 | − | 0.414623i | −0.468722 | − | 0.883346i | \(-0.655285\pi\) |
0.883346 | + | 0.468722i | \(0.155285\pi\) | |||||||
\(84\) | − | 9.16515i | − | 0.109109i | ||||||
\(85\) | −12.1803 | + | 9.63809i | −0.143297 | + | 0.113389i | ||||
\(86\) | −27.3560 | −0.318093 | ||||||||
\(87\) | 24.1881 | + | 24.1881i | 0.278024 | + | 0.278024i | ||||
\(88\) | −39.1434 | + | 39.1434i | −0.444811 | + | 0.444811i | ||||
\(89\) | 157.941i | 1.77462i | 0.461176 | + | 0.887309i | \(0.347428\pi\) | ||||
−0.461176 | + | 0.887309i | \(0.652572\pi\) | |||||||
\(90\) | −13.1632 | − | 16.6352i | −0.146258 | − | 0.184835i | ||||
\(91\) | −30.0532 | −0.330255 | ||||||||
\(92\) | −35.8136 | − | 35.8136i | −0.389278 | − | 0.389278i | ||||
\(93\) | 36.7476 | − | 36.7476i | 0.395136 | − | 0.395136i | ||||
\(94\) | − | 16.3510i | − | 0.173947i | ||||||
\(95\) | −40.9776 | − | 4.77451i | −0.431343 | − | 0.0502580i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −73.2856 | − | 73.2856i | −0.755522 | − | 0.755522i | 0.219982 | − | 0.975504i | \(-0.429400\pi\) |
−0.975504 | + | 0.219982i | \(0.929400\pi\) | |||||||
\(98\) | −7.00000 | + | 7.00000i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | − | 58.7150i | − | 0.593081i | ||||||
\(100\) | 11.4955 | − | 48.6606i | 0.114955 | − | 0.486606i | ||||
\(101\) | 121.236 | 1.20035 | 0.600176 | − | 0.799868i | \(-0.295097\pi\) | ||||
0.600176 | + | 0.799868i | \(0.295097\pi\) | |||||||
\(102\) | −5.38053 | − | 5.38053i | −0.0527503 | − | 0.0527503i | ||||
\(103\) | 23.5614 | − | 23.5614i | 0.228751 | − | 0.228751i | −0.583419 | − | 0.812171i | \(-0.698286\pi\) |
0.812171 | + | 0.583419i | \(0.198286\pi\) | |||||||
\(104\) | 32.1283i | 0.308926i | ||||||||
\(105\) | −2.65176 | + | 22.7589i | −0.0252548 | + | 0.216752i | ||||
\(106\) | −77.7120 | −0.733132 | ||||||||
\(107\) | −14.4314 | − | 14.4314i | −0.134873 | − | 0.134873i | 0.636447 | − | 0.771320i | \(-0.280403\pi\) |
−0.771320 | + | 0.636447i | \(0.780403\pi\) | |||||||
\(108\) | 7.34847 | − | 7.34847i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 34.6374i | − | 0.317775i | −0.987297 | − | 0.158887i | \(-0.949209\pi\) | ||
0.987297 | − | 0.158887i | \(-0.0507907\pi\) | |||||||
\(110\) | 108.526 | − | 85.8755i | 0.986602 | − | 0.780686i | ||||
\(111\) | 91.2057 | 0.821673 | ||||||||
\(112\) | 7.48331 | + | 7.48331i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | −19.9430 | + | 19.9430i | −0.176486 | + | 0.176486i | −0.789822 | − | 0.613336i | \(-0.789827\pi\) |
0.613336 | + | 0.789822i | \(0.289827\pi\) | |||||||
\(114\) | − | 20.2107i | − | 0.177287i | ||||||
\(115\) | 78.5704 | + | 99.2944i | 0.683221 | + | 0.863429i | ||||
\(116\) | −39.4990 | −0.340508 | ||||||||
\(117\) | −24.0962 | − | 24.0962i | −0.205950 | − | 0.205950i | ||||
\(118\) | −74.3773 | + | 74.3773i | −0.630316 | + | 0.630316i | ||||
\(119\) | 8.21890i | 0.0690664i | ||||||||
\(120\) | 24.3303 | + | 2.83485i | 0.202753 | + | 0.0236237i | ||||
\(121\) | 262.051 | 2.16571 | ||||||||
\(122\) | 97.8414 | + | 97.8414i | 0.801979 | + | 0.801979i | ||||
\(123\) | −99.0353 | + | 99.0353i | −0.805165 | + | 0.805165i | ||||
\(124\) | 60.0086i | 0.483940i | ||||||||
\(125\) | −42.6245 | + | 117.508i | −0.340996 | + | 0.940065i | ||||
\(126\) | −11.2250 | −0.0890871 | ||||||||
\(127\) | 13.8950 | + | 13.8950i | 0.109410 | + | 0.109410i | 0.759692 | − | 0.650283i | \(-0.225350\pi\) |
−0.650283 | + | 0.759692i | \(0.725350\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 33.5041i | 0.259722i | ||||||||
\(130\) | 9.29569 | − | 79.7809i | 0.0715053 | − | 0.613700i | ||||
\(131\) | 161.799 | 1.23511 | 0.617554 | − | 0.786528i | \(-0.288124\pi\) | ||||
0.617554 | + | 0.786528i | \(0.288124\pi\) | |||||||
\(132\) | 47.9406 | + | 47.9406i | 0.363187 | + | 0.363187i | ||||
\(133\) | −15.4361 | + | 15.4361i | −0.116061 | + | 0.116061i | ||||
\(134\) | − | 134.342i | − | 1.00255i | ||||||
\(135\) | −20.3739 | + | 16.1216i | −0.150918 | + | 0.119419i | ||||
\(136\) | 8.78638 | 0.0646057 | ||||||||
\(137\) | −35.8023 | − | 35.8023i | −0.261331 | − | 0.261331i | 0.564264 | − | 0.825595i | \(-0.309160\pi\) |
−0.825595 | + | 0.564264i | \(0.809160\pi\) | |||||||
\(138\) | −43.8625 | + | 43.8625i | −0.317845 | + | 0.317845i | ||||
\(139\) | − | 89.7460i | − | 0.645654i | −0.946458 | − | 0.322827i | \(-0.895367\pi\) | ||
0.946458 | − | 0.322827i | \(-0.104633\pi\) | |||||||
\(140\) | −16.4174 | − | 20.7477i | −0.117267 | − | 0.148198i | ||||
\(141\) | −20.0258 | −0.142027 | ||||||||
\(142\) | −13.3793 | − | 13.3793i | −0.0942203 | − | 0.0942203i | ||||
\(143\) | 157.201 | − | 157.201i | 1.09931 | − | 1.09931i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 98.0839 | + | 11.4283i | 0.676441 | + | 0.0788156i | ||||
\(146\) | −96.5477 | −0.661285 | ||||||||
\(147\) | 8.57321 | + | 8.57321i | 0.0583212 | + | 0.0583212i | ||||
\(148\) | −74.4691 | + | 74.4691i | −0.503170 | + | 0.503170i | ||||
\(149\) | 293.641i | 1.97075i | 0.170408 | + | 0.985374i | \(0.445491\pi\) | ||||
−0.170408 | + | 0.985374i | \(0.554509\pi\) | |||||||
\(150\) | −59.5968 | − | 14.0790i | −0.397312 | − | 0.0938600i | ||||
\(151\) | 231.725 | 1.53461 | 0.767303 | − | 0.641285i | \(-0.221598\pi\) | ||||
0.767303 | + | 0.641285i | \(0.221598\pi\) | |||||||
\(152\) | 16.5019 | + | 16.5019i | 0.108565 | + | 0.108565i | ||||
\(153\) | −6.58978 | + | 6.58978i | −0.0430705 | + | 0.0430705i | ||||
\(154\) | − | 73.2305i | − | 0.475523i | ||||||
\(155\) | 17.3623 | − | 149.013i | 0.112015 | − | 0.961377i | ||||
\(156\) | 39.3489 | 0.252237 | ||||||||
\(157\) | 62.8204 | + | 62.8204i | 0.400130 | + | 0.400130i | 0.878279 | − | 0.478149i | \(-0.158692\pi\) |
−0.478149 | + | 0.878279i | \(0.658692\pi\) | |||||||
\(158\) | 40.2089 | − | 40.2089i | 0.254487 | − | 0.254487i | ||||
\(159\) | 95.1774i | 0.598600i | ||||||||
\(160\) | −22.1803 | + | 17.5510i | −0.138627 | + | 0.109694i | ||||
\(161\) | 67.0011 | 0.416156 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 97.0117 | − | 97.0117i | 0.595164 | − | 0.595164i | −0.343858 | − | 0.939022i | \(-0.611734\pi\) |
0.939022 | + | 0.343858i | \(0.111734\pi\) | |||||||
\(164\) | − | 161.724i | − | 0.986122i | ||||||
\(165\) | −105.176 | − | 132.917i | −0.637428 | − | 0.805557i | ||||
\(166\) | 68.8275 | 0.414623 | ||||||||
\(167\) | −135.497 | − | 135.497i | −0.811362 | − | 0.811362i | 0.173476 | − | 0.984838i | \(-0.444500\pi\) |
−0.984838 | + | 0.173476i | \(0.944500\pi\) | |||||||
\(168\) | 9.16515 | − | 9.16515i | 0.0545545 | − | 0.0545545i | ||||
\(169\) | 39.9718i | 0.236520i | ||||||||
\(170\) | −21.8183 | − | 2.54217i | −0.128343 | − | 0.0149539i | ||||
\(171\) | −24.7529 | −0.144754 | ||||||||
\(172\) | −27.3560 | − | 27.3560i | −0.159046 | − | 0.159046i | ||||
\(173\) | −66.1772 | + | 66.1772i | −0.382527 | + | 0.382527i | −0.872012 | − | 0.489485i | \(-0.837185\pi\) |
0.489485 | + | 0.872012i | \(0.337185\pi\) | |||||||
\(174\) | 48.3762i | 0.278024i | ||||||||
\(175\) | 34.7648 | + | 56.2708i | 0.198656 | + | 0.321548i | ||||
\(176\) | −78.2867 | −0.444811 | ||||||||
\(177\) | 91.0932 | + | 91.0932i | 0.514651 | + | 0.514651i | ||||
\(178\) | −157.941 | + | 157.941i | −0.887309 | + | 0.887309i | ||||
\(179\) | − | 274.045i | − | 1.53098i | −0.643450 | − | 0.765488i | \(-0.722497\pi\) | ||
0.643450 | − | 0.765488i | \(-0.277503\pi\) | |||||||
\(180\) | 3.47197 | − | 29.7984i | 0.0192887 | − | 0.165547i | ||||
\(181\) | −36.0493 | −0.199167 | −0.0995836 | − | 0.995029i | \(-0.531751\pi\) | ||||
−0.0995836 | + | 0.995029i | \(0.531751\pi\) | |||||||
\(182\) | −30.0532 | − | 30.0532i | −0.165128 | − | 0.165128i | ||||
\(183\) | 119.831 | − | 119.831i | 0.654813 | − | 0.654813i | ||||
\(184\) | − | 71.6272i | − | 0.389278i | ||||||
\(185\) | 206.468 | − | 163.376i | 1.11604 | − | 0.883111i | ||||
\(186\) | 73.4952 | 0.395136 | ||||||||
\(187\) | −42.9910 | − | 42.9910i | −0.229899 | − | 0.229899i | ||||
\(188\) | 16.3510 | − | 16.3510i | 0.0869733 | − | 0.0869733i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | −36.2031 | − | 45.7521i | −0.190543 | − | 0.240801i | ||||
\(191\) | 133.194 | 0.697352 | 0.348676 | − | 0.937243i | \(-0.386631\pi\) | ||||
0.348676 | + | 0.937243i | \(0.386631\pi\) | |||||||
\(192\) | −9.79796 | − | 9.79796i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | −236.565 | + | 236.565i | −1.22573 | + | 1.22573i | −0.260160 | + | 0.965566i | \(0.583775\pi\) |
−0.965566 | + | 0.260160i | \(0.916225\pi\) | |||||||
\(194\) | − | 146.571i | − | 0.755522i | ||||||
\(195\) | −97.7113 | − | 11.3848i | −0.501084 | − | 0.0583838i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −203.011 | − | 203.011i | −1.03051 | − | 1.03051i | −0.999520 | − | 0.0309909i | \(-0.990134\pi\) |
−0.0309909 | − | 0.999520i | \(-0.509866\pi\) | |||||||
\(198\) | 58.7150 | − | 58.7150i | 0.296541 | − | 0.296541i | ||||
\(199\) | − | 102.932i | − | 0.517244i | −0.965979 | − | 0.258622i | \(-0.916732\pi\) | ||
0.965979 | − | 0.258622i | \(-0.0832684\pi\) | |||||||
\(200\) | 60.1561 | − | 37.1652i | 0.300780 | − | 0.185826i | ||||
\(201\) | −164.535 | −0.818582 | ||||||||
\(202\) | 121.236 | + | 121.236i | 0.600176 | + | 0.600176i | ||||
\(203\) | 36.9479 | − | 36.9479i | 0.182009 | − | 0.182009i | ||||
\(204\) | − | 10.7611i | − | 0.0527503i | ||||||
\(205\) | −46.7917 | + | 401.593i | −0.228252 | + | 1.95899i | ||||
\(206\) | 47.1228 | 0.228751 | ||||||||
\(207\) | 53.7204 | + | 53.7204i | 0.259519 | + | 0.259519i | ||||
\(208\) | −32.1283 | + | 32.1283i | −0.154463 | + | 0.154463i | ||||
\(209\) | − | 161.485i | − | 0.772657i | ||||||
\(210\) | −25.4107 | + | 20.1072i | −0.121003 | + | 0.0957484i | ||||
\(211\) | −216.191 | −1.02460 | −0.512301 | − | 0.858806i | \(-0.671207\pi\) | ||||
−0.512301 | + | 0.858806i | \(0.671207\pi\) | |||||||
\(212\) | −77.7120 | − | 77.7120i | −0.366566 | − | 0.366566i | ||||
\(213\) | −16.3862 | + | 16.3862i | −0.0769306 | + | 0.0769306i | ||||
\(214\) | − | 28.8629i | − | 0.134873i | ||||||
\(215\) | 60.0154 | + | 75.8453i | 0.279142 | + | 0.352769i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −56.1329 | − | 56.1329i | −0.258677 | − | 0.258677i | ||||
\(218\) | 34.6374 | − | 34.6374i | 0.158887 | − | 0.158887i | ||||
\(219\) | 118.246i | 0.539937i | ||||||||
\(220\) | 194.402 | + | 22.6507i | 0.883644 | + | 0.102958i | ||||
\(221\) | −35.2864 | −0.159667 | ||||||||
\(222\) | 91.2057 | + | 91.2057i | 0.410836 | + | 0.410836i | ||||
\(223\) | 143.253 | − | 143.253i | 0.642390 | − | 0.642390i | −0.308752 | − | 0.951142i | \(-0.599911\pi\) |
0.951142 | + | 0.308752i | \(0.0999114\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | −17.2432 | + | 72.9909i | −0.0766364 | + | 0.324404i | ||||
\(226\) | −39.8859 | −0.176486 | ||||||||
\(227\) | 226.766 | + | 226.766i | 0.998969 | + | 0.998969i | 0.999999 | − | 0.00103000i | \(-0.000327858\pi\) |
−0.00103000 | + | 0.999999i | \(0.500328\pi\) | |||||||
\(228\) | 20.2107 | − | 20.2107i | 0.0886433 | − | 0.0886433i | ||||
\(229\) | 48.9068i | 0.213567i | 0.994282 | + | 0.106783i | \(0.0340552\pi\) | ||||
−0.994282 | + | 0.106783i | \(0.965945\pi\) | |||||||
\(230\) | −20.7239 | + | 177.865i | −0.0901041 | + | 0.773325i | ||||
\(231\) | −89.6887 | −0.388263 | ||||||||
\(232\) | −39.4990 | − | 39.4990i | −0.170254 | − | 0.170254i | ||||
\(233\) | −122.967 | + | 122.967i | −0.527755 | + | 0.527755i | −0.919902 | − | 0.392147i | \(-0.871732\pi\) |
0.392147 | + | 0.919902i | \(0.371732\pi\) | |||||||
\(234\) | − | 48.1924i | − | 0.205950i | ||||||
\(235\) | −45.3336 | + | 35.8719i | −0.192909 | + | 0.152647i | ||||
\(236\) | −148.755 | −0.630316 | ||||||||
\(237\) | −49.2456 | − | 49.2456i | −0.207787 | − | 0.207787i | ||||
\(238\) | −8.21890 | + | 8.21890i | −0.0345332 | + | 0.0345332i | ||||
\(239\) | 359.392i | 1.50373i | 0.659317 | + | 0.751865i | \(0.270846\pi\) | ||||
−0.659317 | + | 0.751865i | \(0.729154\pi\) | |||||||
\(240\) | 21.4955 | + | 27.1652i | 0.0895644 | + | 0.113188i | ||||
\(241\) | −96.4510 | −0.400212 | −0.200106 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200106 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(242\) | 262.051 | + | 262.051i | 1.08285 | + | 1.08285i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 195.683i | 0.801979i | ||||||||
\(245\) | 34.7648 | + | 4.05063i | 0.141897 | + | 0.0165332i | ||||
\(246\) | −198.071 | −0.805165 | ||||||||
\(247\) | −66.2723 | − | 66.2723i | −0.268309 | − | 0.268309i | ||||
\(248\) | −60.0086 | + | 60.0086i | −0.241970 | + | 0.241970i | ||||
\(249\) | − | 84.2961i | − | 0.338539i | ||||||
\(250\) | −160.133 | + | 74.8836i | −0.640530 | + | 0.299534i | ||||
\(251\) | −290.502 | −1.15738 | −0.578690 | − | 0.815548i | \(-0.696436\pi\) | ||||
−0.578690 | + | 0.815548i | \(0.696436\pi\) | |||||||
\(252\) | −11.2250 | − | 11.2250i | −0.0445435 | − | 0.0445435i | ||||
\(253\) | −350.466 | + | 350.466i | −1.38524 | + | 1.38524i | ||||
\(254\) | 27.7901i | 0.109410i | ||||||||
\(255\) | −3.11351 | + | 26.7219i | −0.0122098 | + | 0.104792i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −225.583 | − | 225.583i | −0.877755 | − | 0.877755i | 0.115547 | − | 0.993302i | \(-0.463138\pi\) |
−0.993302 | + | 0.115547i | \(0.963138\pi\) | |||||||
\(258\) | −33.5041 | + | 33.5041i | −0.129861 | + | 0.129861i | ||||
\(259\) | − | 139.319i | − | 0.537911i | ||||||
\(260\) | 89.0766 | − | 70.4852i | 0.342602 | − | 0.271097i | ||||
\(261\) | 59.2485 | 0.227006 | ||||||||
\(262\) | 161.799 | + | 161.799i | 0.617554 | + | 0.617554i | ||||
\(263\) | 245.931 | − | 245.931i | 0.935097 | − | 0.935097i | −0.0629214 | − | 0.998018i | \(-0.520042\pi\) |
0.998018 | + | 0.0629214i | \(0.0200417\pi\) | |||||||
\(264\) | 95.8813i | 0.363187i | ||||||||
\(265\) | 170.490 | + | 215.459i | 0.643359 | + | 0.813053i | ||||
\(266\) | −30.8723 | −0.116061 | ||||||||
\(267\) | 193.437 | + | 193.437i | 0.724485 | + | 0.724485i | ||||
\(268\) | 134.342 | − | 134.342i | 0.501277 | − | 0.501277i | ||||
\(269\) | − | 306.198i | − | 1.13828i | −0.822240 | − | 0.569142i | \(-0.807276\pi\) | ||
0.822240 | − | 0.569142i | \(-0.192724\pi\) | |||||||
\(270\) | −36.4955 | − | 4.25227i | −0.135168 | − | 0.0157492i | ||||
\(271\) | −370.284 | −1.36636 | −0.683180 | − | 0.730250i | \(-0.739404\pi\) | ||||
−0.683180 | + | 0.730250i | \(0.739404\pi\) | |||||||
\(272\) | 8.78638 | + | 8.78638i | 0.0323029 | + | 0.0323029i | ||||
\(273\) | −36.8075 | + | 36.8075i | −0.134826 | + | 0.134826i | ||||
\(274\) | − | 71.6046i | − | 0.261331i | ||||||
\(275\) | −476.185 | − | 112.493i | −1.73158 | − | 0.409064i | ||||
\(276\) | −87.7251 | −0.317845 | ||||||||
\(277\) | −161.817 | − | 161.817i | −0.584176 | − | 0.584176i | 0.351872 | − | 0.936048i | \(-0.385545\pi\) |
−0.936048 | + | 0.351872i | \(0.885545\pi\) | |||||||
\(278\) | 89.7460 | − | 89.7460i | 0.322827 | − | 0.322827i | ||||
\(279\) | − | 90.0129i | − | 0.322627i | ||||||
\(280\) | 4.33030 | − | 37.1652i | 0.0154654 | − | 0.132733i | ||||
\(281\) | −235.757 | −0.838994 | −0.419497 | − | 0.907757i | \(-0.637793\pi\) | ||||
−0.419497 | + | 0.907757i | \(0.637793\pi\) | |||||||
\(282\) | −20.0258 | − | 20.0258i | −0.0710134 | − | 0.0710134i | ||||
\(283\) | 2.26750 | − | 2.26750i | 0.00801238 | − | 0.00801238i | −0.703089 | − | 0.711102i | \(-0.748197\pi\) |
0.711102 | + | 0.703089i | \(0.248197\pi\) | |||||||
\(284\) | − | 26.7586i | − | 0.0942203i | ||||||
\(285\) | −56.0347 | + | 44.3396i | −0.196613 | + | 0.155577i | ||||
\(286\) | 314.402 | 1.09931 | ||||||||
\(287\) | 151.279 | + | 151.279i | 0.527104 | + | 0.527104i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 279.350i | − | 0.966609i | ||||||
\(290\) | 86.6556 | + | 109.512i | 0.298813 | + | 0.377628i | ||||
\(291\) | −179.512 | −0.616881 | ||||||||
\(292\) | −96.5477 | − | 96.5477i | −0.330643 | − | 0.330643i | ||||
\(293\) | 199.403 | − | 199.403i | 0.680556 | − | 0.680556i | −0.279570 | − | 0.960125i | \(-0.590192\pi\) |
0.960125 | + | 0.279570i | \(0.0901918\pi\) | |||||||
\(294\) | 17.1464i | 0.0583212i | ||||||||
\(295\) | 369.387 | + | 43.0392i | 1.25216 | + | 0.145896i | ||||
\(296\) | −148.938 | −0.503170 | ||||||||
\(297\) | −71.9110 | − | 71.9110i | −0.242124 | − | 0.242124i | ||||
\(298\) | −293.641 | + | 293.641i | −0.985374 | + | 0.985374i | ||||
\(299\) | 287.657i | 0.962065i | ||||||||
\(300\) | −45.5178 | − | 73.6758i | −0.151726 | − | 0.245586i | ||||
\(301\) | 51.1783 | 0.170028 | ||||||||
\(302\) | 231.725 | + | 231.725i | 0.767303 | + | 0.767303i | ||||
\(303\) | 148.483 | − | 148.483i | 0.490042 | − | 0.490042i | ||||
\(304\) | 33.0039i | 0.108565i | ||||||||
\(305\) | 56.6170 | − | 485.920i | 0.185630 | − | 1.59318i | ||||
\(306\) | −13.1796 | −0.0430705 | ||||||||
\(307\) | −381.514 | − | 381.514i | −1.24272 | − | 1.24272i | −0.958870 | − | 0.283847i | \(-0.908389\pi\) |
−0.283847 | − | 0.958870i | \(-0.591611\pi\) | |||||||
\(308\) | 73.2305 | − | 73.2305i | 0.237761 | − | 0.237761i | ||||
\(309\) | − | 57.7134i | − | 0.186775i | ||||||
\(310\) | 166.376 | − | 131.651i | 0.536696 | − | 0.424681i | ||||
\(311\) | −388.702 | −1.24985 | −0.624923 | − | 0.780686i | \(-0.714870\pi\) | ||||
−0.624923 | + | 0.780686i | \(0.714870\pi\) | |||||||
\(312\) | 39.3489 | + | 39.3489i | 0.126118 | + | 0.126118i | ||||
\(313\) | −50.5806 | + | 50.5806i | −0.161599 | + | 0.161599i | −0.783275 | − | 0.621675i | \(-0.786452\pi\) |
0.621675 | + | 0.783275i | \(0.286452\pi\) | |||||||
\(314\) | 125.641i | 0.400130i | ||||||||
\(315\) | 24.6261 | + | 31.1216i | 0.0781782 | + | 0.0987987i | ||||
\(316\) | 80.4178 | 0.254487 | ||||||||
\(317\) | 54.9675 | + | 54.9675i | 0.173399 | + | 0.173399i | 0.788471 | − | 0.615072i | \(-0.210873\pi\) |
−0.615072 | + | 0.788471i | \(0.710873\pi\) | |||||||
\(318\) | −95.1774 | + | 95.1774i | −0.299300 | + | 0.299300i | ||||
\(319\) | 386.531i | 1.21169i | ||||||||
\(320\) | −39.7312 | − | 4.62929i | −0.124160 | − | 0.0144665i | ||||
\(321\) | −35.3497 | −0.110124 | ||||||||
\(322\) | 67.0011 | + | 67.0011i | 0.208078 | + | 0.208078i | ||||
\(323\) | −18.1240 | + | 18.1240i | −0.0561115 | + | 0.0561115i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −241.589 | + | 149.256i | −0.743350 | + | 0.459251i | ||||
\(326\) | 194.023 | 0.595164 | ||||||||
\(327\) | −42.4220 | − | 42.4220i | −0.129731 | − | 0.129731i | ||||
\(328\) | 161.724 | − | 161.724i | 0.493061 | − | 0.493061i | ||||
\(329\) | 30.5899i | 0.0929783i | ||||||||
\(330\) | 27.7414 | − | 238.092i | 0.0840648 | − | 0.721492i | ||||
\(331\) | 195.576 | 0.590865 | 0.295433 | − | 0.955364i | \(-0.404536\pi\) | ||||
0.295433 | + | 0.955364i | \(0.404536\pi\) | |||||||
\(332\) | 68.8275 | + | 68.8275i | 0.207312 | + | 0.207312i | ||||
\(333\) | 111.704 | − | 111.704i | 0.335446 | − | 0.335446i | ||||
\(334\) | − | 270.995i | − | 0.811362i | ||||||
\(335\) | −372.468 | + | 294.730i | −1.11185 | + | 0.879790i | ||||
\(336\) | 18.3303 | 0.0545545 | ||||||||
\(337\) | 420.206 | + | 420.206i | 1.24690 | + | 1.24690i | 0.957081 | + | 0.289822i | \(0.0935961\pi\) |
0.289822 | + | 0.957081i | \(0.406404\pi\) | |||||||
\(338\) | −39.9718 | + | 39.9718i | −0.118260 | + | 0.118260i | ||||
\(339\) | 48.8501i | 0.144101i | ||||||||
\(340\) | −19.2762 | − | 24.3605i | −0.0566946 | − | 0.0716485i | ||||
\(341\) | 587.235 | 1.72210 | ||||||||
\(342\) | −24.7529 | − | 24.7529i | −0.0723769 | − | 0.0723769i | ||||
\(343\) | 13.0958 | − | 13.0958i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 54.7119i | − | 0.159046i | ||||||
\(345\) | 217.839 | + | 25.3815i | 0.631418 | + | 0.0735697i | ||||
\(346\) | −132.354 | −0.382527 | ||||||||
\(347\) | 21.4182 | + | 21.4182i | 0.0617238 | + | 0.0617238i | 0.737295 | − | 0.675571i | \(-0.236103\pi\) |
−0.675571 | + | 0.737295i | \(0.736103\pi\) | |||||||
\(348\) | −48.3762 | + | 48.3762i | −0.139012 | + | 0.139012i | ||||
\(349\) | − | 244.156i | − | 0.699588i | −0.936827 | − | 0.349794i | \(-0.886252\pi\) | ||
0.936827 | − | 0.349794i | \(-0.113748\pi\) | |||||||
\(350\) | −21.5060 | + | 91.0357i | −0.0614458 | + | 0.260102i | ||||
\(351\) | −59.0234 | −0.168158 | ||||||||
\(352\) | −78.2867 | − | 78.2867i | −0.222405 | − | 0.222405i | ||||
\(353\) | 228.969 | − | 228.969i | 0.648637 | − | 0.648637i | −0.304026 | − | 0.952664i | \(-0.598331\pi\) |
0.952664 | + | 0.304026i | \(0.0983311\pi\) | |||||||
\(354\) | 182.186i | 0.514651i | ||||||||
\(355\) | −7.74207 | + | 66.4469i | −0.0218087 | + | 0.187174i | ||||
\(356\) | −315.882 | −0.887309 | ||||||||
\(357\) | 10.0661 | + | 10.0661i | 0.0281962 | + | 0.0281962i | ||||
\(358\) | 274.045 | − | 274.045i | 0.765488 | − | 0.765488i | ||||
\(359\) | 165.483i | 0.460956i | 0.973078 | + | 0.230478i | \(0.0740290\pi\) | ||||
−0.973078 | + | 0.230478i | \(0.925971\pi\) | |||||||
\(360\) | 33.2704 | − | 26.3264i | 0.0924177 | − | 0.0731290i | ||||
\(361\) | 292.922 | 0.811417 | ||||||||
\(362\) | −36.0493 | − | 36.0493i | −0.0995836 | − | 0.0995836i | ||||
\(363\) | 320.945 | − | 320.945i | 0.884147 | − | 0.884147i | ||||
\(364\) | − | 60.1065i | − | 0.165128i | ||||||
\(365\) | 211.813 | + | 267.681i | 0.580310 | + | 0.733374i | ||||
\(366\) | 239.662 | 0.654813 | ||||||||
\(367\) | −225.601 | − | 225.601i | −0.614715 | − | 0.614715i | 0.329456 | − | 0.944171i | \(-0.393135\pi\) |
−0.944171 | + | 0.329456i | \(0.893135\pi\) | |||||||
\(368\) | 71.6272 | − | 71.6272i | 0.194639 | − | 0.194639i | ||||
\(369\) | 242.586i | 0.657415i | ||||||||
\(370\) | 369.844 | + | 43.0924i | 0.999577 | + | 0.116466i | ||||
\(371\) | 145.386 | 0.391876 | ||||||||
\(372\) | 73.4952 | + | 73.4952i | 0.197568 | + | 0.197568i | ||||
\(373\) | 279.406 | − | 279.406i | 0.749078 | − | 0.749078i | −0.225228 | − | 0.974306i | \(-0.572313\pi\) |
0.974306 | + | 0.225228i | \(0.0723128\pi\) | |||||||
\(374\) | − | 85.9821i | − | 0.229899i | ||||||
\(375\) | 91.7133 | + | 196.122i | 0.244569 | + | 0.522991i | ||||
\(376\) | 32.7020 | 0.0869733 | ||||||||
\(377\) | 158.629 | + | 158.629i | 0.420767 | + | 0.420767i | ||||
\(378\) | −13.7477 | + | 13.7477i | −0.0363696 | + | 0.0363696i | ||||
\(379\) | − | 746.946i | − | 1.97083i | −0.170158 | − | 0.985417i | \(-0.554428\pi\) | ||
0.170158 | − | 0.985417i | \(-0.445572\pi\) | |||||||
\(380\) | 9.54903 | − | 81.9553i | 0.0251290 | − | 0.215672i | ||||
\(381\) | 34.0357 | 0.0893327 | ||||||||
\(382\) | 133.194 | + | 133.194i | 0.348676 | + | 0.348676i | ||||
\(383\) | 359.176 | − | 359.176i | 0.937797 | − | 0.937797i | −0.0603788 | − | 0.998176i | \(-0.519231\pi\) |
0.998176 | + | 0.0603788i | \(0.0192309\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −203.034 | + | 160.658i | −0.527361 | + | 0.417294i | ||||
\(386\) | −473.130 | −1.22573 | ||||||||
\(387\) | 41.0339 | + | 41.0339i | 0.106031 | + | 0.106031i | ||||
\(388\) | 146.571 | − | 146.571i | 0.377761 | − | 0.377761i | ||||
\(389\) | 476.719i | 1.22550i | 0.790278 | + | 0.612749i | \(0.209936\pi\) | ||||
−0.790278 | + | 0.612749i | \(0.790064\pi\) | |||||||
\(390\) | −86.3264 | − | 109.096i | −0.221350 | − | 0.279734i | ||||
\(391\) | 78.6680 | 0.201197 | ||||||||
\(392\) | −14.0000 | − | 14.0000i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 198.163 | − | 198.163i | 0.504231 | − | 0.504231i | ||||
\(394\) | − | 406.021i | − | 1.03051i | ||||||
\(395\) | −199.693 | − | 23.2673i | −0.505553 | − | 0.0589046i | ||||
\(396\) | 117.430 | 0.296541 | ||||||||
\(397\) | −137.315 | − | 137.315i | −0.345883 | − | 0.345883i | 0.512691 | − | 0.858573i | \(-0.328649\pi\) |
−0.858573 | + | 0.512691i | \(0.828649\pi\) | |||||||
\(398\) | 102.932 | − | 102.932i | 0.258622 | − | 0.258622i | ||||
\(399\) | 37.8107i | 0.0947636i | ||||||||
\(400\) | 97.3212 | + | 22.9909i | 0.243303 | + | 0.0574773i | ||||
\(401\) | −691.294 | −1.72392 | −0.861962 | − | 0.506973i | \(-0.830765\pi\) | ||||
−0.861962 | + | 0.506973i | \(0.830765\pi\) | |||||||
\(402\) | −164.535 | − | 164.535i | −0.409291 | − | 0.409291i | ||||
\(403\) | 240.997 | − | 240.997i | 0.598006 | − | 0.598006i | ||||
\(404\) | 242.471i | 0.600176i | ||||||||
\(405\) | −5.20795 | + | 44.6976i | −0.0128591 | + | 0.110364i | ||||
\(406\) | 73.8958 | 0.182009 | ||||||||
\(407\) | 728.743 | + | 728.743i | 1.79052 | + | 1.79052i | ||||
\(408\) | 10.7611 | − | 10.7611i | 0.0263752 | − | 0.0263752i | ||||
\(409\) | − | 146.348i | − | 0.357818i | −0.983866 | − | 0.178909i | \(-0.942743\pi\) | ||
0.983866 | − | 0.178909i | \(-0.0572568\pi\) | |||||||
\(410\) | −448.385 | + | 354.801i | −1.09362 | + | 0.865369i | ||||
\(411\) | −87.6974 | −0.213376 | ||||||||
\(412\) | 47.1228 | + | 47.1228i | 0.114376 | + | 0.114376i | ||||
\(413\) | 139.147 | − | 139.147i | 0.336918 | − | 0.336918i | ||||
\(414\) | 107.441i | 0.259519i | ||||||||
\(415\) | −150.999 | − | 190.826i | −0.363852 | − | 0.459823i | ||||
\(416\) | −64.2565 | −0.154463 | ||||||||
\(417\) | −109.916 | − | 109.916i | −0.263587 | − | 0.263587i | ||||
\(418\) | 161.485 | − | 161.485i | 0.386329 | − | 0.386329i | ||||
\(419\) | 19.1814i | 0.0457790i | 0.999738 | + | 0.0228895i | \(0.00728659\pi\) | ||||
−0.999738 | + | 0.0228895i | \(0.992713\pi\) | |||||||
\(420\) | −45.5178 | − | 5.30352i | −0.108376 | − | 0.0126274i | ||||
\(421\) | −343.060 | −0.814870 | −0.407435 | − | 0.913234i | \(-0.633577\pi\) | ||||
−0.407435 | + | 0.913234i | \(0.633577\pi\) | |||||||
\(422\) | −216.191 | − | 216.191i | −0.512301 | − | 0.512301i | ||||
\(423\) | −24.5265 | + | 24.5265i | −0.0579822 | + | 0.0579822i | ||||
\(424\) | − | 155.424i | − | 0.366566i | ||||||
\(425\) | 40.8184 | + | 66.0692i | 0.0960432 | + | 0.155457i | ||||
\(426\) | −32.7724 | −0.0769306 | ||||||||
\(427\) | −183.045 | − | 183.045i | −0.428676 | − | 0.428676i | ||||
\(428\) | 28.8629 | − | 28.8629i | 0.0674366 | − | 0.0674366i | ||||
\(429\) | − | 385.062i | − | 0.897581i | ||||||
\(430\) | −15.8298 | + | 135.861i | −0.0368136 | + | 0.315955i | ||||
\(431\) | 251.794 | 0.584210 | 0.292105 | − | 0.956386i | \(-0.405644\pi\) | ||||
0.292105 | + | 0.956386i | \(0.405644\pi\) | |||||||
\(432\) | 14.6969 | + | 14.6969i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −125.195 | + | 125.195i | −0.289133 | + | 0.289133i | −0.836737 | − | 0.547604i | \(-0.815540\pi\) |
0.547604 | + | 0.836737i | \(0.315540\pi\) | |||||||
\(434\) | − | 112.266i | − | 0.258677i | ||||||
\(435\) | 134.124 | − | 106.131i | 0.308332 | − | 0.243979i | ||||
\(436\) | 69.2749 | 0.158887 | ||||||||
\(437\) | 147.749 | + | 147.749i | 0.338097 | + | 0.338097i | ||||
\(438\) | −118.246 | + | 118.246i | −0.269969 | + | 0.269969i | ||||
\(439\) | 37.5609i | 0.0855601i | 0.999085 | + | 0.0427801i | \(0.0136215\pi\) | ||||
−0.999085 | + | 0.0427801i | \(0.986379\pi\) | |||||||
\(440\) | 171.751 | + | 217.052i | 0.390343 | + | 0.493301i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −35.2864 | − | 35.2864i | −0.0798334 | − | 0.0798334i | ||||
\(443\) | −583.967 | + | 583.967i | −1.31821 | + | 1.31821i | −0.403019 | + | 0.915192i | \(0.632039\pi\) |
−0.915192 | + | 0.403019i | \(0.867961\pi\) | |||||||
\(444\) | 182.411i | 0.410836i | ||||||||
\(445\) | 784.398 | + | 91.3943i | 1.76269 | + | 0.205380i | ||||
\(446\) | 286.506 | 0.642390 | ||||||||
\(447\) | 359.636 | + | 359.636i | 0.804554 | + | 0.804554i | ||||
\(448\) | −14.9666 | + | 14.9666i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | − | 595.556i | − | 1.32640i | −0.748440 | − | 0.663202i | \(-0.769197\pi\) | ||
0.748440 | − | 0.663202i | \(-0.230803\pi\) | |||||||
\(450\) | −90.2341 | + | 55.7477i | −0.200520 | + | 0.123884i | ||||
\(451\) | −1582.61 | −3.50910 | ||||||||
\(452\) | −39.8859 | − | 39.8859i | −0.0882432 | − | 0.0882432i | ||||
\(453\) | 283.805 | − | 283.805i | 0.626500 | − | 0.626500i | ||||
\(454\) | 453.532i | 0.998969i | ||||||||
\(455\) | −17.3906 | + | 149.256i | −0.0382212 | + | 0.328036i | ||||
\(456\) | 40.4213 | 0.0886433 | ||||||||
\(457\) | 300.505 | + | 300.505i | 0.657560 | + | 0.657560i | 0.954802 | − | 0.297242i | \(-0.0960668\pi\) |
−0.297242 | + | 0.954802i | \(0.596067\pi\) | |||||||
\(458\) | −48.9068 | + | 48.9068i | −0.106783 | + | 0.106783i | ||||
\(459\) | 16.1416i | 0.0351669i | ||||||||
\(460\) | −198.589 | + | 157.141i | −0.431715 | + | 0.341611i | ||||
\(461\) | 565.424 | 1.22652 | 0.613258 | − | 0.789883i | \(-0.289859\pi\) | ||||
0.613258 | + | 0.789883i | \(0.289859\pi\) | |||||||
\(462\) | −89.6887 | − | 89.6887i | −0.194131 | − | 0.194131i | ||||
\(463\) | −247.619 | + | 247.619i | −0.534815 | + | 0.534815i | −0.922001 | − | 0.387186i | \(-0.873447\pi\) |
0.387186 | + | 0.922001i | \(0.373447\pi\) | |||||||
\(464\) | − | 78.9979i | − | 0.170254i | ||||||
\(465\) | −161.239 | − | 203.768i | −0.346751 | − | 0.438211i | ||||
\(466\) | −245.934 | −0.527755 | ||||||||
\(467\) | −310.936 | − | 310.936i | −0.665816 | − | 0.665816i | 0.290929 | − | 0.956745i | \(-0.406036\pi\) |
−0.956745 | + | 0.290929i | \(0.906036\pi\) | |||||||
\(468\) | 48.1924 | − | 48.1924i | 0.102975 | − | 0.102975i | ||||
\(469\) | 251.331i | 0.535888i | ||||||||
\(470\) | −81.2055 | − | 9.46167i | −0.172778 | − | 0.0201312i | ||||
\(471\) | 153.878 | 0.326705 | ||||||||
\(472\) | −148.755 | − | 148.755i | −0.315158 | − | 0.315158i | ||||
\(473\) | −267.701 | + | 267.701i | −0.565964 | + | 0.565964i | ||||
\(474\) | − | 98.4912i | − | 0.207787i | ||||||
\(475\) | −47.4243 | + | 200.749i | −0.0998407 | + | 0.422629i | ||||
\(476\) | −16.4378 | −0.0345332 | ||||||||
\(477\) | 116.568 | + | 116.568i | 0.244377 | + | 0.244377i | ||||
\(478\) | −359.392 | + | 359.392i | −0.751865 | + | 0.751865i | ||||
\(479\) | 337.547i | 0.704692i | 0.935870 | + | 0.352346i | \(0.114616\pi\) | ||||
−0.935870 | + | 0.352346i | \(0.885384\pi\) | |||||||
\(480\) | −5.66970 | + | 48.6606i | −0.0118119 | + | 0.101376i | ||||
\(481\) | 598.141 | 1.24354 | ||||||||
\(482\) | −96.4510 | − | 96.4510i | −0.200106 | − | 0.200106i | ||||
\(483\) | 82.0593 | − | 82.0593i | 0.169895 | − | 0.169895i | ||||
\(484\) | 524.101i | 1.08285i | ||||||||
\(485\) | −406.373 | + | 321.558i | −0.837883 | + | 0.663007i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 153.784 | + | 153.784i | 0.315778 | + | 0.315778i | 0.847143 | − | 0.531365i | \(-0.178321\pi\) |
−0.531365 | + | 0.847143i | \(0.678321\pi\) | |||||||
\(488\) | −195.683 | + | 195.683i | −0.400989 | + | 0.400989i | ||||
\(489\) | − | 237.629i | − | 0.485949i | ||||||
\(490\) | 30.7142 | + | 38.8154i | 0.0626820 | + | 0.0792152i | ||||
\(491\) | 320.910 | 0.653585 | 0.326792 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326792 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(492\) | −198.071 | − | 198.071i | −0.402583 | − | 0.402583i | ||||
\(493\) | 43.3816 | − | 43.3816i | 0.0879951 | − | 0.0879951i | ||||
\(494\) | − | 132.545i | − | 0.268309i | ||||||
\(495\) | −291.603 | − | 33.9761i | −0.589096 | − | 0.0686386i | ||||
\(496\) | −120.017 | −0.241970 | ||||||||
\(497\) | 25.0304 | + | 25.0304i | 0.0503629 | + | 0.0503629i | ||||
\(498\) | 84.2961 | − | 84.2961i | 0.169269 | − | 0.169269i | ||||
\(499\) | 284.928i | 0.570997i | 0.958379 | + | 0.285499i | \(0.0921592\pi\) | ||||
−0.958379 | + | 0.285499i | \(0.907841\pi\) | |||||||
\(500\) | −235.016 | − | 85.2490i | −0.470032 | − | 0.170498i | ||||
\(501\) | −331.900 | −0.662474 | ||||||||
\(502\) | −290.502 | − | 290.502i | −0.578690 | − | 0.578690i | ||||
\(503\) | −548.564 | + | 548.564i | −1.09058 | + | 1.09058i | −0.0951181 | + | 0.995466i | \(0.530323\pi\) |
−0.995466 | + | 0.0951181i | \(0.969677\pi\) | |||||||
\(504\) | − | 22.4499i | − | 0.0445435i | ||||||
\(505\) | 70.1543 | − | 602.105i | 0.138919 | − | 1.19229i | ||||
\(506\) | −700.933 | −1.38524 | ||||||||
\(507\) | 48.9553 | + | 48.9553i | 0.0965588 | + | 0.0965588i | ||||
\(508\) | −27.7901 | + | 27.7901i | −0.0547049 | + | 0.0547049i | ||||
\(509\) | − | 558.480i | − | 1.09721i | −0.836081 | − | 0.548606i | \(-0.815159\pi\) | ||
0.836081 | − | 0.548606i | \(-0.184841\pi\) | |||||||
\(510\) | −29.8354 | + | 23.6084i | −0.0585008 | + | 0.0462910i | ||||
\(511\) | 180.624 | 0.353472 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −30.3160 | + | 30.3160i | −0.0590955 | + | 0.0590955i | ||||
\(514\) | − | 451.166i | − | 0.877755i | ||||||
\(515\) | −103.381 | − | 130.649i | −0.200740 | − | 0.253688i | ||||
\(516\) | −67.0081 | −0.129861 | ||||||||
\(517\) | −160.008 | − | 160.008i | −0.309493 | − | 0.309493i | ||||
\(518\) | 139.319 | − | 139.319i | 0.268956 | − | 0.268956i | ||||
\(519\) | 162.100i | 0.312332i | ||||||||
\(520\) | 159.562 | + | 18.5914i | 0.306850 | + | 0.0357526i | ||||
\(521\) | 455.328 | 0.873949 | 0.436975 | − | 0.899474i | \(-0.356050\pi\) | ||||
0.436975 | + | 0.899474i | \(0.356050\pi\) | |||||||
\(522\) | 59.2485 | + | 59.2485i | 0.113503 | + | 0.113503i | ||||
\(523\) | 37.6920 | − | 37.6920i | 0.0720687 | − | 0.0720687i | −0.670154 | − | 0.742222i | \(-0.733772\pi\) |
0.742222 | + | 0.670154i | \(0.233772\pi\) | |||||||
\(524\) | 323.598i | 0.617554i | ||||||||
\(525\) | 111.495 | + | 26.3394i | 0.212372 | + | 0.0501703i | ||||
\(526\) | 491.861 | 0.935097 | ||||||||
\(527\) | −65.9073 | − | 65.9073i | −0.125061 | − | 0.125061i | ||||
\(528\) | −95.8813 | + | 95.8813i | −0.181593 | + | 0.181593i | ||||
\(529\) | − | 112.308i | − | 0.212302i | ||||||
\(530\) | −44.9689 | + | 385.949i | −0.0848470 | + | 0.728206i | ||||
\(531\) | 223.132 | 0.420211 | ||||||||
\(532\) | −30.8723 | − | 30.8723i | −0.0580306 | − | 0.0580306i | ||||
\(533\) | −649.489 | + | 649.489i | −1.21855 | + | 1.21855i | ||||
\(534\) | 386.875i | 0.724485i | ||||||||
\(535\) | −80.0233 | + | 63.3214i | −0.149576 | + | 0.118358i | ||||
\(536\) | 268.685 | 0.501277 | ||||||||
\(537\) | −335.635 | − | 335.635i | −0.625019 | − | 0.625019i | ||||
\(538\) | 306.198 | − | 306.198i | 0.569142 | − | 0.569142i | ||||
\(539\) | 137.002i | 0.254178i | ||||||||
\(540\) | −32.2432 | − | 40.7477i | −0.0597096 | − | 0.0754588i | ||||
\(541\) | 122.456 | 0.226352 | 0.113176 | − | 0.993575i | \(-0.463898\pi\) | ||||
0.113176 | + | 0.993575i | \(0.463898\pi\) | |||||||
\(542\) | −370.284 | − | 370.284i | −0.683180 | − | 0.683180i | ||||
\(543\) | −44.1512 | + | 44.1512i | −0.0813097 | + | 0.0813097i | ||||
\(544\) | 17.5728i | 0.0323029i | ||||||||
\(545\) | −172.023 | − | 20.0433i | −0.315639 | − | 0.0367768i | ||||
\(546\) | −73.6151 | −0.134826 | ||||||||
\(547\) | 630.975 | + | 630.975i | 1.15352 | + | 1.15352i | 0.985842 | + | 0.167676i | \(0.0536264\pi\) |
0.167676 | + | 0.985842i | \(0.446374\pi\) | |||||||
\(548\) | 71.6046 | − | 71.6046i | 0.130665 | − | 0.130665i | ||||
\(549\) | − | 293.524i | − | 0.534653i | ||||||
\(550\) | −363.692 | − | 588.678i | −0.661259 | − | 1.07032i | ||||
\(551\) | 162.952 | 0.295739 | ||||||||
\(552\) | −87.7251 | − | 87.7251i | −0.158922 | − | 0.158922i | ||||
\(553\) | −75.2239 | + | 75.2239i | −0.136029 | + | 0.136029i | ||||
\(554\) | − | 323.634i | − | 0.584176i | ||||||
\(555\) | 52.7772 | − | 452.964i | 0.0950940 | − | 0.816151i | ||||
\(556\) | 179.492 | 0.322827 | ||||||||
\(557\) | 89.6207 | + | 89.6207i | 0.160899 | + | 0.160899i | 0.782965 | − | 0.622066i | \(-0.213706\pi\) |
−0.622066 | + | 0.782965i | \(0.713706\pi\) | |||||||
\(558\) | 90.0129 | − | 90.0129i | 0.161313 | − | 0.161313i | ||||
\(559\) | 219.725i | 0.393068i | ||||||||
\(560\) | 41.4955 | − | 32.8348i | 0.0740990 | − | 0.0586337i | ||||
\(561\) | −105.306 | −0.187711 | ||||||||
\(562\) | −235.757 | − | 235.757i | −0.419497 | − | 0.419497i | ||||
\(563\) | −268.774 | + | 268.774i | −0.477396 | + | 0.477396i | −0.904298 | − | 0.426902i | \(-0.859605\pi\) |
0.426902 | + | 0.904298i | \(0.359605\pi\) | |||||||
\(564\) | − | 40.0516i | − | 0.0710134i | ||||||
\(565\) | 87.5046 | + | 110.585i | 0.154875 | + | 0.195726i | ||||
\(566\) | 4.53501 | 0.00801238 | ||||||||
\(567\) | 16.8375 | + | 16.8375i | 0.0296957 | + | 0.0296957i | ||||
\(568\) | 26.7586 | − | 26.7586i | 0.0471102 | − | 0.0471102i | ||||
\(569\) | − | 373.315i | − | 0.656089i | −0.944662 | − | 0.328045i | \(-0.893610\pi\) | ||
0.944662 | − | 0.328045i | \(-0.106390\pi\) | |||||||
\(570\) | −100.374 | − | 11.6951i | −0.176095 | − | 0.0205178i | ||||
\(571\) | 93.3963 | 0.163566 | 0.0817831 | − | 0.996650i | \(-0.473939\pi\) | ||||
0.0817831 | + | 0.996650i | \(0.473939\pi\) | |||||||
\(572\) | 314.402 | + | 314.402i | 0.549654 | + | 0.549654i | ||||
\(573\) | 163.129 | − | 163.129i | 0.284693 | − | 0.284693i | ||||
\(574\) | 302.558i | 0.527104i | ||||||||
\(575\) | 538.602 | − | 332.755i | 0.936698 | − | 0.578704i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −356.401 | − | 356.401i | −0.617679 | − | 0.617679i | 0.327257 | − | 0.944936i | \(-0.393876\pi\) |
−0.944936 | + | 0.327257i | \(0.893876\pi\) | |||||||
\(578\) | 279.350 | − | 279.350i | 0.483304 | − | 0.483304i | ||||
\(579\) | 579.464i | 1.00080i | ||||||||
\(580\) | −22.8565 | + | 196.168i | −0.0394078 | + | 0.338220i | ||||
\(581\) | −128.764 | −0.221626 | ||||||||
\(582\) | −179.512 | − | 179.512i | −0.308441 | − | 0.308441i | ||||
\(583\) | −760.478 | + | 760.478i | −1.30442 | + | 1.30442i | ||||
\(584\) | − | 193.095i | − | 0.330643i | ||||||
\(585\) | −133.615 | + | 105.728i | −0.228402 | + | 0.180731i | ||||
\(586\) | 398.806 | 0.680556 | ||||||||
\(587\) | −213.286 | − | 213.286i | −0.363349 | − | 0.363349i | 0.501695 | − | 0.865044i | \(-0.332710\pi\) |
−0.865044 | + | 0.501695i | \(0.832710\pi\) | |||||||
\(588\) | −17.1464 | + | 17.1464i | −0.0291606 | + | 0.0291606i | ||||
\(589\) | − | 247.565i | − | 0.420313i | ||||||
\(590\) | 326.348 | + | 412.427i | 0.553133 | + | 0.699028i | ||||
\(591\) | −497.272 | −0.841408 | ||||||||
\(592\) | −148.938 | − | 148.938i | −0.251585 | − | 0.251585i | ||||
\(593\) | 118.172 | − | 118.172i | 0.199279 | − | 0.199279i | −0.600412 | − | 0.799691i | \(-0.704997\pi\) |
0.799691 | + | 0.600412i | \(0.204997\pi\) | |||||||
\(594\) | − | 143.822i | − | 0.242124i | ||||||
\(595\) | 40.8184 | + | 4.75596i | 0.0686023 | + | 0.00799321i | ||||
\(596\) | −587.283 | −0.985374 | ||||||||
\(597\) | −126.065 | − | 126.065i | −0.211164 | − | 0.211164i | ||||
\(598\) | −287.657 | + | 287.657i | −0.481032 | + | 0.481032i | ||||
\(599\) | 210.890i | 0.352071i | 0.984384 | + | 0.176035i | \(0.0563273\pi\) | ||||
−0.984384 | + | 0.176035i | \(0.943673\pi\) | |||||||
\(600\) | 28.1580 | − | 119.194i | 0.0469300 | − | 0.198656i | ||||
\(601\) | −238.143 | −0.396244 | −0.198122 | − | 0.980177i | \(-0.563484\pi\) | ||||
−0.198122 | + | 0.980177i | \(0.563484\pi\) | |||||||
\(602\) | 51.1783 | + | 51.1783i | 0.0850138 | + | 0.0850138i | ||||
\(603\) | −201.513 | + | 201.513i | −0.334185 | + | 0.334185i | ||||
\(604\) | 463.451i | 0.767303i | ||||||||
\(605\) | 151.639 | − | 1301.45i | 0.250642 | − | 2.15116i | ||||
\(606\) | 296.965 | 0.490042 | ||||||||
\(607\) | 617.412 | + | 617.412i | 1.01715 | + | 1.01715i | 0.999850 | + | 0.0173035i | \(0.00550814\pi\) |
0.0173035 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(608\) | −33.0039 | + | 33.0039i | −0.0542827 | + | 0.0542827i | ||||
\(609\) | − | 90.5035i | − | 0.148610i | ||||||
\(610\) | 542.537 | − | 429.303i | 0.889405 | − | 0.703775i | ||||
\(611\) | −131.332 | −0.214946 | ||||||||
\(612\) | −13.1796 | − | 13.1796i | −0.0215352 | − | 0.0215352i | ||||
\(613\) | −765.627 | + | 765.627i | −1.24898 | + | 1.24898i | −0.292816 | + | 0.956169i | \(0.594592\pi\) |
−0.956169 | + | 0.292816i | \(0.905408\pi\) | |||||||
\(614\) | − | 763.028i | − | 1.24272i | ||||||
\(615\) | 434.541 | + | 549.157i | 0.706571 | + | 0.892938i | ||||
\(616\) | 146.461 | 0.237761 | ||||||||
\(617\) | 42.0185 | + | 42.0185i | 0.0681012 | + | 0.0681012i | 0.740337 | − | 0.672236i | \(-0.234666\pi\) |
−0.672236 | + | 0.740337i | \(0.734666\pi\) | |||||||
\(618\) | 57.7134 | − | 57.7134i | 0.0933874 | − | 0.0933874i | ||||
\(619\) | − | 564.440i | − | 0.911858i | −0.890016 | − | 0.455929i | \(-0.849307\pi\) | ||
0.890016 | − | 0.455929i | \(-0.150693\pi\) | |||||||
\(620\) | 298.027 | + | 34.7247i | 0.480689 | + | 0.0560075i | ||||
\(621\) | 131.588 | 0.211896 | ||||||||
\(622\) | −388.702 | − | 388.702i | −0.624923 | − | 0.624923i | ||||
\(623\) | 295.480 | − | 295.480i | 0.474287 | − | 0.474287i | ||||
\(624\) | 78.6978i | 0.126118i | ||||||||
\(625\) | 558.927 | + | 279.688i | 0.894284 | + | 0.447501i | ||||
\(626\) | −101.161 | −0.161599 | ||||||||
\(627\) | −197.778 | − | 197.778i | −0.315436 | − | 0.315436i | ||||
\(628\) | −125.641 | + | 125.641i | −0.200065 | + | 0.200065i | ||||
\(629\) | − | 163.578i | − | 0.260061i | ||||||
\(630\) | −6.49545 | + | 55.7477i | −0.0103102 | + | 0.0884885i | ||||
\(631\) | 498.286 | 0.789676 | 0.394838 | − | 0.918751i | \(-0.370801\pi\) | ||||
0.394838 | + | 0.918751i | \(0.370801\pi\) | |||||||
\(632\) | 80.4178 | + | 80.4178i | 0.127243 | + | 0.127243i | ||||
\(633\) | −264.779 | + | 264.779i | −0.418292 | + | 0.418292i | ||||
\(634\) | 109.935i | 0.173399i | ||||||||
\(635\) | 77.0489 | − | 60.9678i | 0.121337 | − | 0.0960123i | ||||
\(636\) | −190.355 | −0.299300 | ||||||||
\(637\) | 56.2245 | + | 56.2245i | 0.0882645 | + | 0.0882645i | ||||
\(638\) | −386.531 | + | 386.531i | −0.605847 | + | 0.605847i | ||||
\(639\) | 40.1379i | 0.0628136i | ||||||||
\(640\) | −35.1019 | − | 44.3605i | −0.0548468 | − | 0.0693133i | ||||
\(641\) | 145.183 | 0.226494 | 0.113247 | − | 0.993567i | \(-0.463875\pi\) | ||||
0.113247 | + | 0.993567i | \(0.463875\pi\) | |||||||
\(642\) | −35.3497 | − | 35.3497i | −0.0550618 | − | 0.0550618i | ||||
\(643\) | 646.724 | − | 646.724i | 1.00579 | − | 1.00579i | 0.00580843 | − | 0.999983i | \(-0.498151\pi\) |
0.999983 | − | 0.00580843i | \(-0.00184889\pi\) | |||||||
\(644\) | 134.002i | 0.208078i | ||||||||
\(645\) | 166.395 | + | 19.3875i | 0.257976 | + | 0.0300581i | ||||
\(646\) | −36.2481 | −0.0561115 | ||||||||
\(647\) | 190.030 | + | 190.030i | 0.293710 | + | 0.293710i | 0.838544 | − | 0.544834i | \(-0.183407\pi\) |
−0.544834 | + | 0.838544i | \(0.683407\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 1455.69i | 2.24297i | ||||||||
\(650\) | −390.845 | − | 92.3322i | −0.601300 | − | 0.142050i | ||||
\(651\) | −137.497 | −0.211209 | ||||||||
\(652\) | 194.023 | + | 194.023i | 0.297582 | + | 0.297582i | ||||
\(653\) | 416.099 | − | 416.099i | 0.637212 | − | 0.637212i | −0.312655 | − | 0.949867i | \(-0.601218\pi\) |
0.949867 | + | 0.312655i | \(0.101218\pi\) | |||||||
\(654\) | − | 84.8441i | − | 0.129731i | ||||||
\(655\) | 93.6269 | − | 803.560i | 0.142942 | − | 1.22681i | ||||
\(656\) | 323.448 | 0.493061 | ||||||||
\(657\) | 144.822 | + | 144.822i | 0.220428 | + | 0.220428i | ||||
\(658\) | −30.5899 | + | 30.5899i | −0.0464892 | + | 0.0464892i | ||||
\(659\) | − | 615.296i | − | 0.933682i | −0.884341 | − | 0.466841i | \(-0.845392\pi\) | ||
0.884341 | − | 0.466841i | \(-0.154608\pi\) | |||||||
\(660\) | 265.834 | − | 210.351i | 0.402779 | − | 0.318714i | ||||
\(661\) | −455.425 | −0.688994 | −0.344497 | − | 0.938787i | \(-0.611951\pi\) | ||||
−0.344497 | + | 0.938787i | \(0.611951\pi\) | |||||||
\(662\) | 195.576 | + | 195.576i | 0.295433 | + | 0.295433i | ||||
\(663\) | −43.2168 | + | 43.2168i | −0.0651837 | + | 0.0651837i | ||||
\(664\) | 137.655i | 0.207312i | ||||||||
\(665\) | 67.7298 | + | 85.5944i | 0.101849 | + | 0.128713i | ||||
\(666\) | 223.407 | 0.335446 | ||||||||
\(667\) | −353.650 | − | 353.650i | −0.530210 | − | 0.530210i | ||||
\(668\) | 270.995 | − | 270.995i | 0.405681 | − | 0.405681i | ||||
\(669\) | − | 350.897i | − | 0.524509i | ||||||
\(670\) | −667.198 | − | 77.7387i | −0.995818 | − | 0.116028i | ||||
\(671\) | 1914.92 | 2.85383 | ||||||||
\(672\) | 18.3303 | + | 18.3303i | 0.0272772 | + | 0.0272772i | ||||
\(673\) | 156.161 | − | 156.161i | 0.232037 | − | 0.232037i | −0.581505 | − | 0.813543i | \(-0.697536\pi\) |
0.813543 | + | 0.581505i | \(0.197536\pi\) | |||||||
\(674\) | 840.412i | 1.24690i | ||||||||
\(675\) | 68.2767 | + | 110.514i | 0.101151 | + | 0.163724i | ||||
\(676\) | −79.9437 | −0.118260 | ||||||||
\(677\) | −567.709 | − | 567.709i | −0.838566 | − | 0.838566i | 0.150104 | − | 0.988670i | \(-0.452039\pi\) |
−0.988670 | + | 0.150104i | \(0.952039\pi\) | |||||||
\(678\) | −48.8501 | + | 48.8501i | −0.0720503 | + | 0.0720503i | ||||
\(679\) | 274.210i | 0.403843i | ||||||||
\(680\) | 5.08433 | − | 43.6367i | 0.00747696 | − | 0.0641716i | ||||
\(681\) | 555.461 | 0.815655 | ||||||||
\(682\) | 587.235 | + | 587.235i | 0.861048 | + | 0.861048i | ||||
\(683\) | −124.523 | + | 124.523i | −0.182317 | + | 0.182317i | −0.792365 | − | 0.610047i | \(-0.791150\pi\) |
0.610047 | + | 0.792365i | \(0.291150\pi\) | |||||||
\(684\) | − | 49.5058i | − | 0.0723769i | ||||||
\(685\) | −198.526 | + | 157.091i | −0.289819 | + | 0.229330i | ||||
\(686\) | 26.1916 | 0.0381802 | ||||||||
\(687\) | 59.8984 | + | 59.8984i | 0.0871883 | + | 0.0871883i | ||||
\(688\) | 54.7119 | − | 54.7119i | 0.0795231 | − | 0.0795231i | ||||
\(689\) | 624.188i | 0.905934i | ||||||||
\(690\) | 192.457 | + | 243.221i | 0.278924 | + | 0.352494i | ||||
\(691\) | −1214.16 | −1.75710 | −0.878551 | − | 0.477648i | \(-0.841489\pi\) | ||||
−0.878551 | + | 0.477648i | \(0.841489\pi\) | |||||||
\(692\) | −132.354 | − | 132.354i | −0.191263 | − | 0.191263i | ||||
\(693\) | −109.846 | + | 109.846i | −0.158508 | + | 0.158508i | ||||
\(694\) | 42.8363i | 0.0617238i | ||||||||
\(695\) | −445.715 | − | 51.9325i | −0.641316 | − | 0.0747230i | ||||
\(696\) | −96.7523 | −0.139012 | ||||||||
\(697\) | 177.621 | + | 177.621i | 0.254836 | + | 0.254836i | ||||
\(698\) | 244.156 | − | 244.156i | 0.349794 | − | 0.349794i | ||||
\(699\) | 301.206i | 0.430910i | ||||||||
\(700\) | −112.542 | + | 69.5296i | −0.160774 | + | 0.0993280i | ||||
\(701\) | −788.147 | −1.12432 | −0.562159 | − | 0.827029i | \(-0.690029\pi\) | ||||
−0.562159 | + | 0.827029i | \(0.690029\pi\) | |||||||
\(702\) | −59.0234 | − | 59.0234i | −0.0840789 | − | 0.0840789i | ||||
\(703\) | 307.221 | − | 307.221i | 0.437014 | − | 0.437014i | ||||
\(704\) | − | 156.573i | − | 0.222405i | ||||||
\(705\) | −11.5881 | + | 99.4561i | −0.0164371 | + | 0.141072i | ||||
\(706\) | 457.938 | 0.648637 | ||||||||
\(707\) | −226.811 | − | 226.811i | −0.320808 | − | 0.320808i | ||||
\(708\) | −182.186 | + | 182.186i | −0.257325 | + | 0.257325i | ||||
\(709\) | − | 1230.75i | − | 1.73589i | −0.496660 | − | 0.867945i | \(-0.665440\pi\) | ||
0.496660 | − | 0.867945i | \(-0.334560\pi\) | |||||||
\(710\) | −74.1890 | + | 58.7049i | −0.104492 | + | 0.0826829i | ||||
\(711\) | −120.627 | −0.169658 | ||||||||
\(712\) | −315.882 | − | 315.882i | −0.443654 | − | 0.443654i | ||||
\(713\) | −537.281 | + | 537.281i | −0.753550 | + | 0.753550i | ||||
\(714\) | 20.1321i | 0.0281962i | ||||||||
\(715\) | −689.757 | − | 871.690i | −0.964696 | − | 1.21915i | ||||
\(716\) | 548.090 | 0.765488 | ||||||||
\(717\) | 440.163 | + | 440.163i | 0.613895 | + | 0.613895i | ||||
\(718\) | −165.483 | + | 165.483i | −0.230478 | + | 0.230478i | ||||
\(719\) | − | 251.624i | − | 0.349963i | −0.984572 | − | 0.174982i | \(-0.944013\pi\) | ||
0.984572 | − | 0.174982i | \(-0.0559866\pi\) | |||||||
\(720\) | 59.5968 | + | 6.94393i | 0.0827734 | + | 0.00964435i | ||||
\(721\) | −88.1587 | −0.122273 | ||||||||
\(722\) | 292.922 | + | 292.922i | 0.405708 | + | 0.405708i | ||||
\(723\) | −118.128 | + | 118.128i | −0.163386 | + | 0.163386i | ||||
\(724\) | − | 72.0985i | − | 0.0995836i | ||||||
\(725\) | 113.515 | − | 480.511i | 0.156572 | − | 0.662774i | ||||
\(726\) | 641.891 | 0.884147 | ||||||||
\(727\) | 254.322 | + | 254.322i | 0.349824 | + | 0.349824i | 0.860044 | − | 0.510220i | \(-0.170436\pi\) |
−0.510220 | + | 0.860044i | \(0.670436\pi\) | |||||||
\(728\) | 60.1065 | − | 60.1065i | 0.0825638 | − | 0.0825638i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −55.8684 | + | 479.495i | −0.0765320 | + | 0.656842i | ||||
\(731\) | 60.0899 | 0.0822024 | ||||||||
\(732\) | 239.662 | + | 239.662i | 0.327406 | + | 0.327406i | ||||
\(733\) | −27.6831 | + | 27.6831i | −0.0377668 | + | 0.0377668i | −0.725738 | − | 0.687971i | \(-0.758502\pi\) |
0.687971 | + | 0.725738i | \(0.258502\pi\) | |||||||
\(734\) | − | 451.201i | − | 0.614715i | ||||||
\(735\) | 47.5390 | − | 37.6170i | 0.0646789 | − | 0.0511797i | ||||
\(736\) | 143.254 | 0.194639 | ||||||||
\(737\) | −1314.65 | − | 1314.65i | −1.78379 | − | 1.78379i | ||||
\(738\) | −242.586 | + | 242.586i | −0.328707 | + | 0.328707i | ||||
\(739\) | 434.621i | 0.588121i | 0.955787 | + | 0.294060i | \(0.0950066\pi\) | ||||
−0.955787 | + | 0.294060i | \(0.904993\pi\) | |||||||
\(740\) | 326.751 | + | 412.936i | 0.441556 | + | 0.558022i | ||||
\(741\) | −162.333 | −0.219073 | ||||||||
\(742\) | 145.386 | + | 145.386i | 0.195938 | + | 0.195938i | ||||
\(743\) | 126.704 | − | 126.704i | 0.170530 | − | 0.170530i | −0.616682 | − | 0.787212i | \(-0.711524\pi\) |
0.787212 | + | 0.616682i | \(0.211524\pi\) | |||||||
\(744\) | 146.990i | 0.197568i | ||||||||
\(745\) | 1458.34 | + | 169.919i | 1.95750 | + | 0.228079i | ||||
\(746\) | 558.812 | 0.749078 | ||||||||
\(747\) | −103.241 | − | 103.241i | −0.138208 | − | 0.138208i | ||||
\(748\) | 85.9821 | − | 85.9821i | 0.114949 | − | 0.114949i | ||||
\(749\) | 53.9975i | 0.0720928i | ||||||||
\(750\) | −104.408 | + | 287.835i | −0.139211 | + | 0.383780i | ||||
\(751\) | 735.755 | 0.979701 | 0.489851 | − | 0.871806i | \(-0.337051\pi\) | ||||
0.489851 | + | 0.871806i | \(0.337051\pi\) | |||||||
\(752\) | 32.7020 | + | 32.7020i | 0.0434866 | + | 0.0434866i | ||||
\(753\) | −355.791 | + | 355.791i | −0.472498 | + | 0.472498i | ||||
\(754\) | 317.258i | 0.420767i | ||||||||
\(755\) | 134.090 | − | 1150.84i | 0.177603 | − | 1.52429i | ||||
\(756\) | −27.4955 | −0.0363696 | ||||||||
\(757\) | −255.322 | − | 255.322i | −0.337281 | − | 0.337281i | 0.518062 | − | 0.855343i | \(-0.326654\pi\) |
−0.855343 | + | 0.518062i | \(0.826654\pi\) | |||||||
\(758\) | 746.946 | − | 746.946i | 0.985417 | − | 0.985417i | ||||
\(759\) | 858.464i | 1.13105i | ||||||||
\(760\) | 91.5043 | − | 72.4062i | 0.120400 | − | 0.0952713i | ||||
\(761\) | 783.231 | 1.02921 | 0.514606 | − | 0.857427i | \(-0.327938\pi\) | ||||
0.514606 | + | 0.857427i | \(0.327938\pi\) | |||||||
\(762\) | 34.0357 | + | 34.0357i | 0.0446663 | + | 0.0446663i | ||||
\(763\) | −64.8007 | + | 64.8007i | −0.0849289 | + | 0.0849289i | ||||
\(764\) | 266.389i | 0.348676i | ||||||||
\(765\) | 28.9143 | + | 36.5408i | 0.0377964 | + | 0.0477657i | ||||
\(766\) | 718.352 | 0.937797 | ||||||||
\(767\) | 597.403 | + | 597.403i | 0.778883 | + | 0.778883i | ||||
\(768\) | 19.5959 | − | 19.5959i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 186.068i | − | 0.241961i | −0.992655 | − | 0.120980i | \(-0.961396\pi\) | ||
0.992655 | − | 0.120980i | \(-0.0386038\pi\) | |||||||
\(770\) | −363.692 | − | 42.3757i | −0.472328 | − | 0.0550333i | ||||
\(771\) | −552.564 | −0.716684 | ||||||||
\(772\) | −473.130 | − | 473.130i | −0.612863 | − | 0.612863i | ||||
\(773\) | −333.576 | + | 333.576i | −0.431534 | + | 0.431534i | −0.889150 | − | 0.457616i | \(-0.848703\pi\) |
0.457616 | + | 0.889150i | \(0.348703\pi\) | |||||||
\(774\) | 82.0679i | 0.106031i | ||||||||
\(775\) | −730.014 | − | 172.457i | −0.941953 | − | 0.222525i | ||||
\(776\) | 293.143 | 0.377761 | ||||||||
\(777\) | −170.630 | − | 170.630i | −0.219601 | − | 0.219601i | ||||
\(778\) | −476.719 | + | 476.719i | −0.612749 | + | 0.612749i | ||||
\(779\) | 667.190i | 0.856469i | ||||||||
\(780\) | 22.7697 | − | 195.423i | 0.0291919 | − | 0.250542i | ||||
\(781\) | −261.855 | −0.335282 | ||||||||
\(782\) | 78.6680 | + | 78.6680i | 0.100598 | + | 0.100598i | ||||
\(783\) | 72.5642 | − | 72.5642i | 0.0926746 | − | 0.0926746i | ||||
\(784\) | − | 28.0000i | − | 0.0357143i | ||||||
\(785\) | 348.343 | − | 275.639i | 0.443749 | − | 0.351133i | ||||
\(786\) | 396.326 | 0.504231 | ||||||||
\(787\) | 431.752 | + | 431.752i | 0.548605 | + | 0.548605i | 0.926037 | − | 0.377432i | \(-0.123193\pi\) |
−0.377432 | + | 0.926037i | \(0.623193\pi\) | |||||||
\(788\) | 406.021 | − | 406.021i | 0.515255 | − | 0.515255i | ||||
\(789\) | − | 602.404i | − | 0.763504i | ||||||
\(790\) | −176.426 | − | 222.961i | −0.223324 | − | 0.282229i | ||||
\(791\) | 74.6197 | 0.0943360 | ||||||||
\(792\) | 117.430 | + | 117.430i | 0.148270 | + | 0.148270i | ||||
\(793\) | 785.869 | − | 785.869i | 0.991007 | − | 0.991007i | ||||
\(794\) | − | 274.631i | − | 0.345883i | ||||||
\(795\) | 472.689 | + | 55.0755i | 0.594578 | + | 0.0692773i | ||||
\(796\) | 205.863 | 0.258622 | ||||||||
\(797\) | −67.9296 | − | 67.9296i | −0.0852316 | − | 0.0852316i | 0.663206 | − | 0.748437i | \(-0.269195\pi\) |
−0.748437 | + | 0.663206i | \(0.769195\pi\) | |||||||
\(798\) | −37.8107 | + | 37.8107i | −0.0473818 | + | 0.0473818i | ||||
\(799\) | 35.9165i | 0.0449518i | ||||||||
\(800\) | 74.3303 | + | 120.312i | 0.0929129 | + | 0.150390i | ||||
\(801\) | 473.823 | 0.591539 | ||||||||
\(802\) | −691.294 | − | 691.294i | −0.861962 | − | 0.861962i | ||||
\(803\) | −944.800 | + | 944.800i | −1.17659 | + | 1.17659i | ||||
\(804\) | − | 329.070i | − | 0.409291i | ||||||
\(805\) | 38.7710 | − | 332.755i | 0.0481627 | − | 0.413360i | ||||
\(806\) | 481.993 | 0.598006 | ||||||||
\(807\) | −375.015 | − | 375.015i | −0.464702 | − | 0.464702i | ||||
\(808\) | −242.471 | + | 242.471i | −0.300088 | + | 0.300088i | ||||
\(809\) | 375.281i | 0.463883i | 0.972730 | + | 0.231941i | \(0.0745078\pi\) | ||||
−0.972730 | + | 0.231941i | \(0.925492\pi\) | |||||||
\(810\) | −49.9056 | + | 39.4897i | −0.0616118 | + | 0.0487527i | ||||
\(811\) | 283.093 | 0.349066 | 0.174533 | − | 0.984651i | \(-0.444158\pi\) | ||||
0.174533 | + | 0.984651i | \(0.444158\pi\) | |||||||
\(812\) | 73.8958 | + | 73.8958i | 0.0910047 | + | 0.0910047i | ||||
\(813\) | −453.503 | + | 453.503i | −0.557814 | + | 0.557814i | ||||
\(814\) | 1457.49i | 1.79052i | ||||||||
\(815\) | −425.662 | − | 537.936i | −0.522285 | − | 0.660044i | ||||
\(816\) | 21.5221 | 0.0263752 | ||||||||
\(817\) | 112.857 | + | 112.857i | 0.138135 | + | 0.138135i | ||||
\(818\) | 146.348 | − | 146.348i | 0.178909 | − | 0.178909i | ||||
\(819\) | 90.1597i | 0.110085i | ||||||||
\(820\) | −803.186 | − | 93.5834i | −0.979496 | − | 0.114126i | ||||
\(821\) | 1325.60 | 1.61462 | 0.807308 | − | 0.590131i | \(-0.200924\pi\) | ||||
0.807308 | + | 0.590131i | \(0.200924\pi\) | |||||||
\(822\) | −87.6974 | − | 87.6974i | −0.106688 | − | 0.106688i | ||||
\(823\) | 794.494 | − | 794.494i | 0.965363 | − | 0.965363i | −0.0340566 | − | 0.999420i | \(-0.510843\pi\) |
0.999420 | + | 0.0340566i | \(0.0108427\pi\) | |||||||
\(824\) | 94.2456i | 0.114376i | ||||||||
\(825\) | −720.980 | + | 445.430i | −0.873915 | + | 0.539915i | ||||
\(826\) | 278.294 | 0.336918 | ||||||||
\(827\) | 361.128 | + | 361.128i | 0.436672 | + | 0.436672i | 0.890890 | − | 0.454218i | \(-0.150081\pi\) |
−0.454218 | + | 0.890890i | \(0.650081\pi\) | |||||||
\(828\) | −107.441 | + | 107.441i | −0.129759 | + | 0.129759i | ||||
\(829\) | 195.726i | 0.236099i | 0.993008 | + | 0.118049i | \(0.0376641\pi\) | ||||
−0.993008 | + | 0.118049i | \(0.962336\pi\) | |||||||
\(830\) | 39.8278 | − | 341.825i | 0.0479853 | − | 0.411837i | ||||
\(831\) | −396.368 | −0.476978 | ||||||||
\(832\) | −64.2565 | − | 64.2565i | −0.0772314 | − | 0.0772314i | ||||
\(833\) | 15.3762 | − | 15.3762i | 0.0184588 | − | 0.0184588i | ||||
\(834\) | − | 219.832i | − | 0.263587i | ||||||
\(835\) | −751.342 | + | 594.528i | −0.899811 | + | 0.712009i | ||||
\(836\) | 322.971 | 0.386329 | ||||||||
\(837\) | −110.243 | − | 110.243i | −0.131712 | − | 0.131712i | ||||
\(838\) | −19.1814 | + | 19.1814i | −0.0228895 | + | 0.0228895i | ||||
\(839\) | − | 10.5401i | − | 0.0125627i | −0.999980 | − | 0.00628133i | \(-0.998001\pi\) | ||
0.999980 | − | 0.00628133i | \(-0.00199942\pi\) | |||||||
\(840\) | −40.2143 | − | 50.8213i | −0.0478742 | − | 0.0605016i | ||||
\(841\) | 450.958 | 0.536216 | ||||||||
\(842\) | −343.060 | − | 343.060i | −0.407435 | − | 0.407435i | ||||
\(843\) | −288.742 | + | 288.742i | −0.342518 | + | 0.342518i | ||||
\(844\) | − | 432.382i | − | 0.512301i | ||||||
\(845\) | 198.516 | + | 23.1302i | 0.234931 | + | 0.0273730i | ||||
\(846\) | −49.0529 | −0.0579822 | ||||||||
\(847\) | −490.252 | − | 490.252i | −0.578810 | − | 0.578810i | ||||
\(848\) | 155.424 | − | 155.424i | 0.183283 | − | 0.183283i | ||||
\(849\) | − | 5.55423i | − | 0.00654208i | ||||||
\(850\) | −25.2508 | + | 106.888i | −0.0297069 | + | 0.125750i | ||||
\(851\) | −1333.50 | −1.56699 | ||||||||
\(852\) | −32.7724 | − | 32.7724i | −0.0384653 | − | 0.0384653i | ||||
\(853\) | −950.696 | + | 950.696i | −1.11453 | + | 1.11453i | −0.122002 | + | 0.992530i | \(0.538932\pi\) |
−0.992530 | + | 0.122002i | \(0.961068\pi\) | |||||||
\(854\) | − | 366.089i | − | 0.428676i | ||||||
\(855\) | −14.3235 | + | 122.933i | −0.0167527 | + | 0.143781i | ||||
\(856\) | 57.7258 | 0.0674366 | ||||||||
\(857\) | 628.392 | + | 628.392i | 0.733246 | + | 0.733246i | 0.971261 | − | 0.238016i | \(-0.0764969\pi\) |
−0.238016 | + | 0.971261i | \(0.576497\pi\) | |||||||
\(858\) | 385.062 | − | 385.062i | 0.448791 | − | 0.448791i | ||||
\(859\) | − | 832.998i | − | 0.969730i | −0.874589 | − | 0.484865i | \(-0.838869\pi\) | ||
0.874589 | − | 0.484865i | \(-0.161131\pi\) | |||||||
\(860\) | −151.691 | + | 120.031i | −0.176384 | + | 0.139571i | ||||
\(861\) | 370.556 | 0.430379 | ||||||||
\(862\) | 251.794 | + | 251.794i | 0.292105 | + | 0.292105i | ||||
\(863\) | 802.913 | − | 802.913i | 0.930374 | − | 0.930374i | −0.0673547 | − | 0.997729i | \(-0.521456\pi\) |
0.997729 | + | 0.0673547i | \(0.0214559\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 290.368 | + | 366.957i | 0.335686 | + | 0.424227i | ||||
\(866\) | −250.389 | −0.289133 | ||||||||
\(867\) | −342.132 | − | 342.132i | −0.394616 | − | 0.394616i | ||||
\(868\) | 112.266 | − | 112.266i | 0.129339 | − | 0.129339i | ||||
\(869\) | − | 786.955i | − | 0.905587i | ||||||
\(870\) | 240.255 | + | 27.9934i | 0.276156 | + | 0.0321763i | ||||
\(871\) | −1079.05 | −1.23886 | ||||||||
\(872\) | 69.2749 | + | 69.2749i | 0.0794437 | + | 0.0794437i | ||||
\(873\) | −219.857 | + | 219.857i | −0.251841 | + | 0.251841i | ||||
\(874\) | 295.497i | 0.338097i | ||||||||
\(875\) | 299.581 | − | 140.094i | 0.342378 | − | 0.160108i | ||||
\(876\) | −236.493 | −0.269969 | ||||||||
\(877\) | 483.085 | + | 483.085i | 0.550838 | + | 0.550838i | 0.926683 | − | 0.375845i | \(-0.122647\pi\) |
−0.375845 | + | 0.926683i | \(0.622647\pi\) | |||||||
\(878\) | −37.5609 | + | 37.5609i | −0.0427801 | + | 0.0427801i | ||||
\(879\) | − | 488.435i | − | 0.555671i | ||||||
\(880\) | −45.3015 | + | 388.803i | −0.0514790 | + | 0.441822i | ||||
\(881\) | −1190.88 | −1.35174 | −0.675868 | − | 0.737023i | \(-0.736231\pi\) | ||||
−0.675868 | + | 0.737023i | \(0.736231\pi\) | |||||||
\(882\) | 21.0000 | + | 21.0000i | 0.0238095 | + | 0.0238095i | ||||
\(883\) | −52.9133 | + | 52.9133i | −0.0599245 | + | 0.0599245i | −0.736434 | − | 0.676509i | \(-0.763492\pi\) |
0.676509 | + | 0.736434i | \(0.263492\pi\) | |||||||
\(884\) | − | 70.5727i | − | 0.0798334i | ||||||
\(885\) | 505.118 | − | 399.693i | 0.570754 | − | 0.451631i | ||||
\(886\) | −1167.93 | −1.31821 | ||||||||
\(887\) | −393.366 | − | 393.366i | −0.443479 | − | 0.443479i | 0.449700 | − | 0.893180i | \(-0.351531\pi\) |
−0.893180 | + | 0.449700i | \(0.851531\pi\) | |||||||
\(888\) | −182.411 | + | 182.411i | −0.205418 | + | 0.205418i | ||||
\(889\) | − | 51.9905i | − | 0.0584820i | ||||||
\(890\) | 693.004 | + | 875.793i | 0.778656 | + | 0.984037i | ||||
\(891\) | −176.145 | −0.197694 | ||||||||
\(892\) | 286.506 | + | 286.506i | 0.321195 | + | 0.321195i | ||||
\(893\) | −67.4557 | + | 67.4557i | −0.0755383 | + | 0.0755383i | ||||
\(894\) | 719.271i | 0.804554i | ||||||||
\(895\) | −1361.02 | − | 158.579i | −1.52069 | − | 0.177183i | ||||
\(896\) | −29.9333 | −0.0334077 | ||||||||
\(897\) | 352.307 | + | 352.307i | 0.392761 | + | 0.392761i | ||||
\(898\) | 595.556 | − | 595.556i | 0.663202 | − | 0.663202i | ||||
\(899\) | 592.570i | 0.659143i | ||||||||
\(900\) | −145.982 | − | 34.4864i | −0.162202 | − | 0.0383182i | ||||
\(901\) | 170.702 | 0.189458 | ||||||||
\(902\) | −1582.61 | − | 1582.61i | −1.75455 | − | 1.75455i | ||||
\(903\) | 62.6804 | − | 62.6804i | 0.0694135 | − | 0.0694135i | ||||
\(904\) | − | 79.7719i | − | 0.0882432i | ||||||
\(905\) | −20.8603 | + | 179.035i | −0.0230501 | + | 0.197829i | ||||
\(906\) | 567.609 | 0.626500 | ||||||||
\(907\) | 715.081 | + | 715.081i | 0.788403 | + | 0.788403i | 0.981232 | − | 0.192829i | \(-0.0617664\pi\) |
−0.192829 | + | 0.981232i | \(0.561766\pi\) | |||||||
\(908\) | −453.532 | + | 453.532i | −0.499485 | + | 0.499485i | ||||
\(909\) | − | 363.707i | − | 0.400118i | ||||||
\(910\) | −166.647 | + | 131.866i | −0.183129 | + | 0.144908i | ||||
\(911\) | −1440.70 | −1.58145 | −0.790727 | − | 0.612169i | \(-0.790297\pi\) | ||||
−0.790727 | + | 0.612169i | \(0.790297\pi\) | |||||||
\(912\) | 40.4213 | + | 40.4213i | 0.0443216 | + | 0.0443216i | ||||
\(913\) | 673.535 | − | 673.535i | 0.737716 | − | 0.737716i | ||||
\(914\) | 601.010i | 0.657560i | ||||||||
\(915\) | −525.786 | − | 664.469i | −0.574630 | − | 0.726196i | ||||
\(916\) | −97.8136 | −0.106783 | ||||||||
\(917\) | −302.699 | − | 302.699i | −0.330097 | − | 0.330097i | ||||
\(918\) | −16.1416 | + | 16.1416i | −0.0175834 | + | 0.0175834i | ||||
\(919\) | − | 139.961i | − | 0.152297i | −0.997096 | − | 0.0761485i | \(-0.975738\pi\) | ||
0.997096 | − | 0.0761485i | \(-0.0242623\pi\) | |||||||
\(920\) | −355.730 | − | 41.4479i | −0.386663 | − | 0.0450521i | ||||
\(921\) | −934.515 | −1.01467 | ||||||||
\(922\) | 565.424 | + | 565.424i | 0.613258 | + | 0.613258i | ||||
\(923\) | −107.463 | + | 107.463i | −0.116428 | + | 0.116428i | ||||
\(924\) | − | 179.377i | − | 0.194131i | ||||||
\(925\) | −691.914 | − | 1119.94i | −0.748015 | − | 1.21075i | ||||
\(926\) | −495.239 | −0.534815 | ||||||||
\(927\) | −70.6842 | − | 70.6842i | −0.0762505 | − | 0.0762505i | ||||
\(928\) | 78.9979 | − | 78.9979i | 0.0851271 | − | 0.0851271i | ||||
\(929\) | 268.303i | 0.288808i | 0.989519 | + | 0.144404i | \(0.0461265\pi\) | ||||
−0.989519 | + | 0.144404i | \(0.953874\pi\) | |||||||
\(930\) | 42.5288 | − | 365.007i | 0.0457299 | − | 0.392481i | ||||
\(931\) | 57.7568 | 0.0620374 | ||||||||
\(932\) | −245.934 | − | 245.934i | −0.263878 | − | 0.263878i | ||||
\(933\) | −476.061 | + | 476.061i | −0.510248 | + | 0.510248i | ||||
\(934\) | − | 621.872i | − | 0.665816i | ||||||
\(935\) | −238.388 | + | 188.634i | −0.254960 | + | 0.201747i | ||||
\(936\) | 96.3848 | 0.102975 | ||||||||
\(937\) | −750.288 | − | 750.288i | −0.800734 | − | 0.800734i | 0.182476 | − | 0.983210i | \(-0.441589\pi\) |
−0.983210 | + | 0.182476i | \(0.941589\pi\) | |||||||
\(938\) | −251.331 | + | 251.331i | −0.267944 | + | 0.267944i | ||||
\(939\) | 123.897i | 0.131945i | ||||||||
\(940\) | −71.7439 | − | 90.6672i | −0.0763233 | − | 0.0964545i | ||||
\(941\) | 858.370 | 0.912189 | 0.456095 | − | 0.889931i | \(-0.349248\pi\) | ||||
0.456095 | + | 0.889931i | \(0.349248\pi\) | |||||||
\(942\) | 153.878 | + | 153.878i | 0.163352 | + | 0.163352i | ||||
\(943\) | 1447.98 | − | 1447.98i | 1.53550 | − | 1.53550i | ||||
\(944\) | − | 297.509i | − | 0.315158i | ||||||
\(945\) | 68.2767 | + | 7.95527i | 0.0722505 | + | 0.00841828i | ||||
\(946\) | −535.402 | −0.565964 | ||||||||
\(947\) | 1103.38 | + | 1103.38i | 1.16513 | + | 1.16513i | 0.983336 | + | 0.181798i | \(0.0581917\pi\) |
0.181798 | + | 0.983336i | \(0.441808\pi\) | |||||||
\(948\) | 98.4912 | − | 98.4912i | 0.103894 | − | 0.103894i | ||||
\(949\) | 775.477i | 0.817152i | ||||||||
\(950\) | −248.173 | + | 153.324i | −0.261235 | + | 0.161394i | ||||
\(951\) | 134.642 | 0.141580 | ||||||||
\(952\) | −16.4378 | − | 16.4378i | −0.0172666 | − | 0.0172666i | ||||
\(953\) | −1277.56 | + | 1277.56i | −1.34056 | + | 1.34056i | −0.445064 | + | 0.895499i | \(0.646819\pi\) |
−0.895499 | + | 0.445064i | \(0.853181\pi\) | |||||||
\(954\) | 233.136i | 0.244377i | ||||||||
\(955\) | 77.0743 | − | 661.496i | 0.0807061 | − | 0.692666i | ||||
\(956\) | −718.783 | −0.751865 | ||||||||
\(957\) | 473.401 | + | 473.401i | 0.494672 | + | 0.494672i | ||||
\(958\) | −337.547 | + | 337.547i | −0.352346 | + | 0.352346i | ||||
\(959\) | 133.960i | 0.139687i | ||||||||
\(960\) | −54.3303 | + | 42.9909i | −0.0565941 | + | 0.0447822i | ||||
\(961\) | −60.7414 | −0.0632064 | ||||||||
\(962\) | 598.141 | + | 598.141i | 0.621768 | + | 0.621768i | ||||
\(963\) | −43.2943 | + | 43.2943i | −0.0449578 | + | 0.0449578i | ||||
\(964\) | − | 192.902i | − | 0.200106i | ||||||
\(965\) | 1037.99 | + | 1311.77i | 1.07563 | + | 1.35935i | ||||
\(966\) | 164.119 | 0.169895 | ||||||||
\(967\) | −478.601 | − | 478.601i | −0.494933 | − | 0.494933i | 0.414923 | − | 0.909857i | \(-0.363808\pi\) |
−0.909857 | + | 0.414923i | \(0.863808\pi\) | |||||||
\(968\) | −524.101 | + | 524.101i | −0.541427 | + | 0.541427i | ||||
\(969\) | 44.3946i | 0.0458149i | ||||||||
\(970\) | −727.932 | − | 84.8151i | −0.750445 | − | 0.0874382i | ||||
\(971\) | 97.1677 | 0.100070 | 0.0500349 | − | 0.998747i | \(-0.484067\pi\) | ||||
0.0500349 | + | 0.998747i | \(0.484067\pi\) | |||||||
\(972\) | −22.0454 | − | 22.0454i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −167.899 | + | 167.899i | −0.172558 | + | 0.172558i | ||||
\(974\) | 307.568i | 0.315778i | ||||||||
\(975\) | −113.083 | + | 478.686i | −0.115983 | + | 0.490960i | ||||
\(976\) | −391.366 | −0.400989 | ||||||||
\(977\) | −711.442 | − | 711.442i | −0.728191 | − | 0.728191i | 0.242068 | − | 0.970259i | \(-0.422174\pi\) |
−0.970259 | + | 0.242068i | \(0.922174\pi\) | |||||||
\(978\) | 237.629 | − | 237.629i | 0.242975 | − | 0.242975i | ||||
\(979\) | 3091.17i | 3.15748i | ||||||||
\(980\) | −8.10125 | + | 69.5296i | −0.00826659 | + | 0.0709486i | ||||
\(981\) | −103.912 | −0.105925 | ||||||||
\(982\) | 320.910 | + | 320.910i | 0.326792 | + | 0.326792i | ||||
\(983\) | −443.320 | + | 443.320i | −0.450986 | + | 0.450986i | −0.895682 | − | 0.444695i | \(-0.853312\pi\) |
0.444695 | + | 0.895682i | \(0.353312\pi\) | |||||||
\(984\) | − | 396.141i | − | 0.402583i | ||||||
\(985\) | −1125.71 | + | 890.758i | −1.14285 | + | 0.904323i | ||||
\(986\) | 86.7632 | 0.0879951 | ||||||||
\(987\) | 37.4648 | + | 37.4648i | 0.0379583 | + | 0.0379583i | ||||
\(988\) | 132.545 | − | 132.545i | 0.134154 | − | 0.134154i | ||||
\(989\) | − | 489.858i | − | 0.495306i | ||||||
\(990\) | −257.626 | − | 325.579i | −0.260229 | − | 0.328867i | ||||
\(991\) | 1708.27 | 1.72378 | 0.861890 | − | 0.507095i | \(-0.169281\pi\) | ||||
0.861890 | + | 0.507095i | \(0.169281\pi\) | |||||||
\(992\) | −120.017 | − | 120.017i | −0.120985 | − | 0.120985i | ||||
\(993\) | 239.531 | − | 239.531i | 0.241220 | − | 0.241220i | ||||
\(994\) | 50.0607i | 0.0503629i | ||||||||
\(995\) | −511.200 | − | 59.5625i | −0.513768 | − | 0.0598618i | ||||
\(996\) | 168.592 | 0.169269 | ||||||||
\(997\) | 1363.41 | + | 1363.41i | 1.36752 | + | 1.36752i | 0.863967 | + | 0.503548i | \(0.167972\pi\) |
0.503548 | + | 0.863967i | \(0.332028\pi\) | |||||||
\(998\) | −284.928 | + | 284.928i | −0.285499 | + | 0.285499i | ||||
\(999\) | − | 273.617i | − | 0.273891i |
(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 | 210.3.l.a.127.3 | yes | 8 | |
3.2 | odd | 2 | 630.3.o.b.127.2 | 8 | |||
5.2 | odd | 4 | 1050.3.l.b.43.2 | 8 | |||
5.3 | odd | 4 | inner | 210.3.l.a.43.3 | ✓ | 8 | |
5.4 | even | 2 | 1050.3.l.b.757.2 | 8 | |||
15.8 | even | 4 | 630.3.o.b.253.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.a.43.3 | ✓ | 8 | 5.3 | odd | 4 | inner | |
210.3.l.a.127.3 | yes | 8 | 1.1 | even | 1 | trivial | |
630.3.o.b.127.2 | 8 | 3.2 | odd | 2 | |||
630.3.o.b.253.2 | 8 | 15.8 | even | 4 | |||
1050.3.l.b.43.2 | 8 | 5.2 | odd | 4 | |||
1050.3.l.b.757.2 | 8 | 5.4 | even | 2 |