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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.5 | ||
Root | \(3.60306 - 3.60306i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.43 |
Dual form | 210.3.l.b.127.5 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||
\(5\) | −4.39814 | − | 2.37832i | −0.879627 | − | 0.475664i | ||||
\(6\) | −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 | ||||||||
\(10\) | 6.77646 | − | 2.01982i | 0.677646 | − | 0.201982i | ||||
\(11\) | −14.7776 | −1.34342 | −0.671710 | − | 0.740814i | \(-0.734440\pi\) | ||||
−0.671710 | + | 0.740814i | \(0.734440\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | −13.2827 | − | 13.2827i | −1.02175 | − | 1.02175i | −0.999758 | − | 0.0219895i | \(-0.993000\pi\) |
−0.0219895 | − | 0.999758i | \(-0.507000\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | −2.47376 | − | 8.29943i | −0.164917 | − | 0.553295i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 1.17963 | − | 1.17963i | 0.0693902 | − | 0.0693902i | −0.671560 | − | 0.740950i | \(-0.734375\pi\) |
0.740950 | + | 0.671560i | \(0.234375\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | − | 15.1298i | − | 0.796307i | −0.917319 | − | 0.398154i | \(-0.869651\pi\) | ||
0.917319 | − | 0.398154i | \(-0.130349\pi\) | |||||||
\(20\) | −4.75664 | + | 8.79627i | −0.237832 | + | 0.439814i | ||||
\(21\) | 4.58258 | 0.218218 | ||||||||
\(22\) | 14.7776 | − | 14.7776i | 0.671710 | − | 0.671710i | ||||
\(23\) | −22.5070 | − | 22.5070i | −0.978567 | − | 0.978567i | 0.0212084 | − | 0.999775i | \(-0.493249\pi\) |
−0.999775 | + | 0.0212084i | \(0.993249\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 13.6872 | + | 20.9203i | 0.547488 | + | 0.836814i | ||||
\(26\) | 26.5654 | 1.02175 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | −3.74166 | − | 3.74166i | −0.133631 | − | 0.133631i | ||||
\(29\) | 3.29748i | 0.113706i | 0.998383 | + | 0.0568530i | \(0.0181066\pi\) | ||||
−0.998383 | + | 0.0568530i | \(0.981893\pi\) | |||||||
\(30\) | 10.7732 | + | 5.82567i | 0.359106 | + | 0.194189i | ||||
\(31\) | 50.0892 | 1.61578 | 0.807890 | − | 0.589334i | \(-0.200610\pi\) | ||||
0.807890 | + | 0.589334i | \(0.200610\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | −18.0988 | − | 18.0988i | −0.548449 | − | 0.548449i | ||||
\(34\) | 2.35927i | 0.0693902i | ||||||||
\(35\) | −12.6776 | + | 3.77873i | −0.362217 | + | 0.107964i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 6.15735 | − | 6.15735i | 0.166415 | − | 0.166415i | −0.618987 | − | 0.785401i | \(-0.712457\pi\) |
0.785401 | + | 0.618987i | \(0.212457\pi\) | |||||||
\(38\) | 15.1298 | + | 15.1298i | 0.398154 | + | 0.398154i | ||||
\(39\) | − | 32.5359i | − | 0.834254i | ||||||
\(40\) | −4.03963 | − | 13.5529i | −0.100991 | − | 0.338823i | ||||
\(41\) | −35.1369 | −0.856998 | −0.428499 | − | 0.903542i | \(-0.640957\pi\) | ||||
−0.428499 | + | 0.903542i | \(0.640957\pi\) | |||||||
\(42\) | −4.58258 | + | 4.58258i | −0.109109 | + | 0.109109i | ||||
\(43\) | −58.9417 | − | 58.9417i | −1.37074 | − | 1.37074i | −0.859350 | − | 0.511388i | \(-0.829131\pi\) |
−0.511388 | − | 0.859350i | \(-0.670869\pi\) | |||||||
\(44\) | 29.5552i | 0.671710i | ||||||||
\(45\) | 7.13496 | − | 13.1944i | 0.158555 | − | 0.293209i | ||||
\(46\) | 45.0141 | 0.978567 | ||||||||
\(47\) | −20.1645 | + | 20.1645i | −0.429032 | + | 0.429032i | −0.888299 | − | 0.459266i | \(-0.848112\pi\) |
0.459266 | + | 0.888299i | \(0.348112\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | −34.6075 | − | 7.23315i | −0.692151 | − | 0.144663i | ||||
\(51\) | 2.88950 | 0.0566569 | ||||||||
\(52\) | −26.5654 | + | 26.5654i | −0.510874 | + | 0.510874i | ||||
\(53\) | 10.9028 | + | 10.9028i | 0.205712 | + | 0.205712i | 0.802442 | − | 0.596730i | \(-0.203534\pi\) |
−0.596730 | + | 0.802442i | \(0.703534\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 64.9939 | + | 35.1459i | 1.18171 | + | 0.639016i | ||||
\(56\) | 7.48331 | 0.133631 | ||||||||
\(57\) | 18.5302 | − | 18.5302i | 0.325091 | − | 0.325091i | ||||
\(58\) | −3.29748 | − | 3.29748i | −0.0568530 | − | 0.0568530i | ||||
\(59\) | 66.6774i | 1.13013i | 0.825048 | + | 0.565063i | \(0.191148\pi\) | ||||
−0.825048 | + | 0.565063i | \(0.808852\pi\) | |||||||
\(60\) | −16.5989 | + | 4.94752i | −0.276648 | + | 0.0824586i | ||||
\(61\) | −4.45593 | −0.0730481 | −0.0365241 | − | 0.999333i | \(-0.511629\pi\) | ||||
−0.0365241 | + | 0.999333i | \(0.511629\pi\) | |||||||
\(62\) | −50.0892 | + | 50.0892i | −0.807890 | + | 0.807890i | ||||
\(63\) | 5.61249 | + | 5.61249i | 0.0890871 | + | 0.0890871i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 26.8286 | + | 90.0098i | 0.412748 | + | 1.38477i | ||||
\(66\) | 36.1976 | 0.548449 | ||||||||
\(67\) | −88.4424 | + | 88.4424i | −1.32004 | + | 1.32004i | −0.406293 | + | 0.913743i | \(0.633179\pi\) |
−0.913743 | + | 0.406293i | \(0.866821\pi\) | |||||||
\(68\) | −2.35927 | − | 2.35927i | −0.0346951 | − | 0.0346951i | ||||
\(69\) | − | 55.1307i | − | 0.798996i | ||||||
\(70\) | 8.89886 | − | 16.4563i | 0.127127 | − | 0.235090i | ||||
\(71\) | 69.3188 | 0.976321 | 0.488161 | − | 0.872754i | \(-0.337668\pi\) | ||||
0.488161 | + | 0.872754i | \(0.337668\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 58.4166 | + | 58.4166i | 0.800227 | + | 0.800227i | 0.983131 | − | 0.182903i | \(-0.0585496\pi\) |
−0.182903 | + | 0.983131i | \(0.558550\pi\) | |||||||
\(74\) | 12.3147i | 0.166415i | ||||||||
\(75\) | −8.85877 | + | 42.3854i | −0.118117 | + | 0.565139i | ||||
\(76\) | −30.2597 | −0.398154 | ||||||||
\(77\) | −27.6464 | + | 27.6464i | −0.359044 | + | 0.359044i | ||||
\(78\) | 32.5359 | + | 32.5359i | 0.417127 | + | 0.417127i | ||||
\(79\) | 52.8307i | 0.668744i | 0.942441 | + | 0.334372i | \(0.108524\pi\) | ||||
−0.942441 | + | 0.334372i | \(0.891476\pi\) | |||||||
\(80\) | 17.5925 | + | 9.51328i | 0.219907 | + | 0.118916i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 35.1369 | − | 35.1369i | 0.428499 | − | 0.428499i | ||||
\(83\) | −53.4286 | − | 53.4286i | −0.643718 | − | 0.643718i | 0.307749 | − | 0.951468i | \(-0.400424\pi\) |
−0.951468 | + | 0.307749i | \(0.900424\pi\) | |||||||
\(84\) | − | 9.16515i | − | 0.109109i | ||||||
\(85\) | −7.99374 | + | 2.38264i | −0.0940440 | + | 0.0280311i | ||||
\(86\) | 117.883 | 1.37074 | ||||||||
\(87\) | −4.03857 | + | 4.03857i | −0.0464203 | + | 0.0464203i | ||||
\(88\) | −29.5552 | − | 29.5552i | −0.335855 | − | 0.335855i | ||||
\(89\) | 21.3553i | 0.239947i | 0.992777 | + | 0.119973i | \(0.0382809\pi\) | ||||
−0.992777 | + | 0.119973i | \(0.961719\pi\) | |||||||
\(90\) | 6.05945 | + | 20.3294i | 0.0673272 | + | 0.225882i | ||||
\(91\) | −49.6994 | −0.546147 | ||||||||
\(92\) | −45.0141 | + | 45.0141i | −0.489283 | + | 0.489283i | ||||
\(93\) | 61.3464 | + | 61.3464i | 0.659639 | + | 0.659639i | ||||
\(94\) | − | 40.3290i | − | 0.429032i | ||||||
\(95\) | −35.9836 | + | 66.5431i | −0.378775 | + | 0.700453i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 90.3562 | − | 90.3562i | 0.931507 | − | 0.931507i | −0.0662929 | − | 0.997800i | \(-0.521117\pi\) |
0.997800 | + | 0.0662929i | \(0.0211172\pi\) | |||||||
\(98\) | 7.00000 | + | 7.00000i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | − | 44.3328i | − | 0.447806i | ||||||
\(100\) | 41.8407 | − | 27.3744i | 0.418407 | − | 0.273744i | ||||
\(101\) | 43.6109 | 0.431791 | 0.215896 | − | 0.976416i | \(-0.430733\pi\) | ||||
0.215896 | + | 0.976416i | \(0.430733\pi\) | |||||||
\(102\) | −2.88950 | + | 2.88950i | −0.0283284 | + | 0.0283284i | ||||
\(103\) | −48.8638 | − | 48.8638i | −0.474405 | − | 0.474405i | 0.428932 | − | 0.903337i | \(-0.358890\pi\) |
−0.903337 | + | 0.428932i | \(0.858890\pi\) | |||||||
\(104\) | − | 53.1309i | − | 0.510874i | ||||||
\(105\) | −20.1548 | − | 10.8988i | −0.191950 | − | 0.103798i | ||||
\(106\) | −21.8055 | −0.205712 | ||||||||
\(107\) | 23.1497 | − | 23.1497i | 0.216352 | − | 0.216352i | −0.590607 | − | 0.806959i | \(-0.701112\pi\) |
0.806959 | + | 0.590607i | \(0.201112\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 141.834i | − | 1.30123i | −0.759409 | − | 0.650613i | \(-0.774512\pi\) | ||
0.759409 | − | 0.650613i | \(-0.225488\pi\) | |||||||
\(110\) | −100.140 | + | 29.8481i | −0.910362 | + | 0.271346i | ||||
\(111\) | 15.0824 | 0.135877 | ||||||||
\(112\) | −7.48331 | + | 7.48331i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | −113.746 | − | 113.746i | −1.00660 | − | 1.00660i | −0.999978 | − | 0.00662298i | \(-0.997892\pi\) |
−0.00662298 | − | 0.999978i | \(-0.502108\pi\) | |||||||
\(114\) | 37.0604i | 0.325091i | ||||||||
\(115\) | 45.4601 | + | 152.518i | 0.395305 | + | 1.32624i | ||||
\(116\) | 6.59495 | 0.0568530 | ||||||||
\(117\) | 39.8482 | − | 39.8482i | 0.340583 | − | 0.340583i | ||||
\(118\) | −66.6774 | − | 66.6774i | −0.565063 | − | 0.565063i | ||||
\(119\) | − | 4.41379i | − | 0.0370906i | ||||||
\(120\) | 11.6513 | − | 21.5464i | 0.0970945 | − | 0.179553i | ||||
\(121\) | 97.3779 | 0.804776 | ||||||||
\(122\) | 4.45593 | − | 4.45593i | 0.0365241 | − | 0.0365241i | ||||
\(123\) | −43.0338 | − | 43.0338i | −0.349868 | − | 0.349868i | ||||
\(124\) | − | 100.178i | − | 0.807890i | ||||||
\(125\) | −10.4429 | − | 124.563i | −0.0835428 | − | 0.996504i | ||||
\(126\) | −11.2250 | −0.0890871 | ||||||||
\(127\) | −172.678 | + | 172.678i | −1.35967 | + | 1.35967i | −0.485341 | + | 0.874325i | \(0.661305\pi\) |
−0.874325 | + | 0.485341i | \(0.838695\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 144.377i | − | 1.11920i | ||||||
\(130\) | −116.838 | − | 63.1811i | −0.898757 | − | 0.486009i | ||||
\(131\) | 147.540 | 1.12626 | 0.563129 | − | 0.826369i | \(-0.309597\pi\) | ||||
0.563129 | + | 0.826369i | \(0.309597\pi\) | |||||||
\(132\) | −36.1976 | + | 36.1976i | −0.274224 | + | 0.274224i | ||||
\(133\) | −28.3053 | − | 28.3053i | −0.212822 | − | 0.212822i | ||||
\(134\) | − | 176.885i | − | 1.32004i | ||||||
\(135\) | 24.8983 | − | 7.42128i | 0.184432 | − | 0.0549724i | ||||
\(136\) | 4.71854 | 0.0346951 | ||||||||
\(137\) | 96.5907 | − | 96.5907i | 0.705042 | − | 0.705042i | −0.260447 | − | 0.965488i | \(-0.583870\pi\) |
0.965488 | + | 0.260447i | \(0.0838698\pi\) | |||||||
\(138\) | 55.1307 | + | 55.1307i | 0.399498 | + | 0.399498i | ||||
\(139\) | 184.197i | 1.32516i | 0.748993 | + | 0.662578i | \(0.230538\pi\) | ||||
−0.748993 | + | 0.662578i | \(0.769462\pi\) | |||||||
\(140\) | 7.55746 | + | 25.3552i | 0.0539818 | + | 0.181108i | ||||
\(141\) | −49.3928 | −0.350303 | ||||||||
\(142\) | −69.3188 | + | 69.3188i | −0.488161 | + | 0.488161i | ||||
\(143\) | 196.287 | + | 196.287i | 1.37264 | + | 1.37264i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 7.84245 | − | 14.5027i | 0.0540859 | − | 0.100019i | ||||
\(146\) | −116.833 | −0.800227 | ||||||||
\(147\) | 8.57321 | − | 8.57321i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | −12.3147 | − | 12.3147i | −0.0832074 | − | 0.0832074i | ||||
\(149\) | − | 206.358i | − | 1.38495i | −0.721442 | − | 0.692475i | \(-0.756520\pi\) | ||
0.721442 | − | 0.692475i | \(-0.243480\pi\) | |||||||
\(150\) | −33.5266 | − | 51.2442i | −0.223511 | − | 0.341628i | ||||
\(151\) | 51.4825 | 0.340944 | 0.170472 | − | 0.985363i | \(-0.445471\pi\) | ||||
0.170472 | + | 0.985363i | \(0.445471\pi\) | |||||||
\(152\) | 30.2597 | − | 30.2597i | 0.199077 | − | 0.199077i | ||||
\(153\) | 3.53890 | + | 3.53890i | 0.0231301 | + | 0.0231301i | ||||
\(154\) | − | 55.2928i | − | 0.359044i | ||||||
\(155\) | −220.299 | − | 119.128i | −1.42128 | − | 0.768568i | ||||
\(156\) | −65.0718 | −0.417127 | ||||||||
\(157\) | 91.7859 | − | 91.7859i | 0.584624 | − | 0.584624i | −0.351547 | − | 0.936170i | \(-0.614344\pi\) |
0.936170 | + | 0.351547i | \(0.114344\pi\) | |||||||
\(158\) | −52.8307 | − | 52.8307i | −0.334372 | − | 0.334372i | ||||
\(159\) | 26.7062i | 0.167963i | ||||||||
\(160\) | −27.1058 | + | 8.07926i | −0.169411 | + | 0.0504954i | ||||
\(161\) | −84.2136 | −0.523066 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −11.1451 | − | 11.1451i | −0.0683748 | − | 0.0683748i | 0.672092 | − | 0.740467i | \(-0.265396\pi\) |
−0.740467 | + | 0.672092i | \(0.765396\pi\) | |||||||
\(164\) | 70.2739i | 0.428499i | ||||||||
\(165\) | 36.5563 | + | 122.646i | 0.221553 | + | 0.743308i | ||||
\(166\) | 106.857 | 0.643718 | ||||||||
\(167\) | 224.811 | − | 224.811i | 1.34617 | − | 1.34617i | 0.456397 | − | 0.889776i | \(-0.349140\pi\) |
0.889776 | − | 0.456397i | \(-0.150860\pi\) | |||||||
\(168\) | 9.16515 | + | 9.16515i | 0.0545545 | + | 0.0545545i | ||||
\(169\) | 183.861i | 1.08794i | ||||||||
\(170\) | 5.61109 | − | 10.3764i | 0.0330064 | − | 0.0610375i | ||||
\(171\) | 45.3895 | 0.265436 | ||||||||
\(172\) | −117.883 | + | 117.883i | −0.685369 | + | 0.685369i | ||||
\(173\) | 43.4546 | + | 43.4546i | 0.251183 | + | 0.251183i | 0.821455 | − | 0.570273i | \(-0.193162\pi\) |
−0.570273 | + | 0.821455i | \(0.693162\pi\) | |||||||
\(174\) | − | 8.07713i | − | 0.0464203i | ||||||
\(175\) | 64.7448 | + | 13.5320i | 0.369970 | + | 0.0773257i | ||||
\(176\) | 59.1105 | 0.335855 | ||||||||
\(177\) | −81.6628 | + | 81.6628i | −0.461372 | + | 0.461372i | ||||
\(178\) | −21.3553 | − | 21.3553i | −0.119973 | − | 0.119973i | ||||
\(179\) | − | 167.373i | − | 0.935046i | −0.883981 | − | 0.467523i | \(-0.845146\pi\) | ||
0.883981 | − | 0.467523i | \(-0.154854\pi\) | |||||||
\(180\) | −26.3888 | − | 14.2699i | −0.146605 | − | 0.0792773i | ||||
\(181\) | 225.762 | 1.24730 | 0.623652 | − | 0.781702i | \(-0.285648\pi\) | ||||
0.623652 | + | 0.781702i | \(0.285648\pi\) | |||||||
\(182\) | 49.6994 | − | 49.6994i | 0.273074 | − | 0.273074i | ||||
\(183\) | −5.45738 | − | 5.45738i | −0.0298218 | − | 0.0298218i | ||||
\(184\) | − | 90.0281i | − | 0.489283i | ||||||
\(185\) | −41.7250 | + | 12.4367i | −0.225540 | + | 0.0672254i | ||||
\(186\) | −122.693 | −0.659639 | ||||||||
\(187\) | −17.4322 | + | 17.4322i | −0.0932202 | + | 0.0932202i | ||||
\(188\) | 40.3290 | + | 40.3290i | 0.214516 | + | 0.214516i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | −30.5595 | − | 102.527i | −0.160839 | − | 0.539614i | ||||
\(191\) | −148.626 | −0.778145 | −0.389073 | − | 0.921207i | \(-0.627204\pi\) | ||||
−0.389073 | + | 0.921207i | \(0.627204\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −158.063 | − | 158.063i | −0.818979 | − | 0.818979i | 0.166982 | − | 0.985960i | \(-0.446598\pi\) |
−0.985960 | + | 0.166982i | \(0.946598\pi\) | |||||||
\(194\) | 180.712i | 0.931507i | ||||||||
\(195\) | −77.3807 | + | 143.097i | −0.396824 | + | 0.733832i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 26.7707 | − | 26.7707i | 0.135892 | − | 0.135892i | −0.635889 | − | 0.771781i | \(-0.719366\pi\) |
0.771781 | + | 0.635889i | \(0.219366\pi\) | |||||||
\(198\) | 44.3328 | + | 44.3328i | 0.223903 | + | 0.223903i | ||||
\(199\) | 171.790i | 0.863269i | 0.902049 | + | 0.431634i | \(0.142063\pi\) | ||||
−0.902049 | + | 0.431634i | \(0.857937\pi\) | |||||||
\(200\) | −14.4663 | + | 69.2151i | −0.0723315 | + | 0.346075i | ||||
\(201\) | −216.639 | −1.07780 | ||||||||
\(202\) | −43.6109 | + | 43.6109i | −0.215896 | + | 0.215896i | ||||
\(203\) | 6.16901 | + | 6.16901i | 0.0303892 | + | 0.0303892i | ||||
\(204\) | − | 5.77900i | − | 0.0283284i | ||||||
\(205\) | 154.537 | + | 83.5668i | 0.753839 | + | 0.407643i | ||||
\(206\) | 97.7275 | 0.474405 | ||||||||
\(207\) | 67.5211 | − | 67.5211i | 0.326189 | − | 0.326189i | ||||
\(208\) | 53.1309 | + | 53.1309i | 0.255437 | + | 0.255437i | ||||
\(209\) | 223.583i | 1.06977i | ||||||||
\(210\) | 31.0536 | − | 9.25596i | 0.147874 | − | 0.0440760i | ||||
\(211\) | −302.432 | −1.43333 | −0.716664 | − | 0.697419i | \(-0.754332\pi\) | ||||
−0.716664 | + | 0.697419i | \(0.754332\pi\) | |||||||
\(212\) | 21.8055 | − | 21.8055i | 0.102856 | − | 0.102856i | ||||
\(213\) | 84.8978 | + | 84.8978i | 0.398581 | + | 0.398581i | ||||
\(214\) | 46.2994i | 0.216352i | ||||||||
\(215\) | 119.051 | + | 399.416i | 0.553728 | + | 1.85775i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 93.7082 | − | 93.7082i | 0.431835 | − | 0.431835i | ||||
\(218\) | 141.834 | + | 141.834i | 0.650613 | + | 0.650613i | ||||
\(219\) | 143.091i | 0.653383i | ||||||||
\(220\) | 70.2918 | − | 129.988i | 0.319508 | − | 0.590854i | ||||
\(221\) | −31.3375 | −0.141799 | ||||||||
\(222\) | −15.0824 | + | 15.0824i | −0.0679385 | + | 0.0679385i | ||||
\(223\) | −170.784 | − | 170.784i | −0.765850 | − | 0.765850i | 0.211523 | − | 0.977373i | \(-0.432158\pi\) |
−0.977373 | + | 0.211523i | \(0.932158\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | −62.7610 | + | 41.0616i | −0.278938 | + | 0.182496i | ||||
\(226\) | 227.492 | 1.00660 | ||||||||
\(227\) | 154.323 | − | 154.323i | 0.679838 | − | 0.679838i | −0.280125 | − | 0.959963i | \(-0.590376\pi\) |
0.959963 | + | 0.280125i | \(0.0903760\pi\) | |||||||
\(228\) | −37.0604 | − | 37.0604i | −0.162546 | − | 0.162546i | ||||
\(229\) | 33.7243i | 0.147267i | 0.997285 | + | 0.0736337i | \(0.0234596\pi\) | ||||
−0.997285 | + | 0.0736337i | \(0.976540\pi\) | |||||||
\(230\) | −197.978 | − | 107.058i | −0.860774 | − | 0.465469i | ||||
\(231\) | −67.7195 | −0.293158 | ||||||||
\(232\) | −6.59495 | + | 6.59495i | −0.0284265 | + | 0.0284265i | ||||
\(233\) | −207.998 | − | 207.998i | −0.892697 | − | 0.892697i | 0.102079 | − | 0.994776i | \(-0.467450\pi\) |
−0.994776 | + | 0.102079i | \(0.967450\pi\) | |||||||
\(234\) | 79.6963i | 0.340583i | ||||||||
\(235\) | 136.644 | − | 40.7286i | 0.581464 | − | 0.173313i | ||||
\(236\) | 133.355 | 0.565063 | ||||||||
\(237\) | −64.7042 | + | 64.7042i | −0.273013 | + | 0.273013i | ||||
\(238\) | 4.41379 | + | 4.41379i | 0.0185453 | + | 0.0185453i | ||||
\(239\) | − | 49.7163i | − | 0.208018i | −0.994576 | − | 0.104009i | \(-0.966833\pi\) | ||
0.994576 | − | 0.104009i | \(-0.0331670\pi\) | |||||||
\(240\) | 9.89504 | + | 33.1977i | 0.0412293 | + | 0.138324i | ||||
\(241\) | −49.9716 | −0.207351 | −0.103676 | − | 0.994611i | \(-0.533060\pi\) | ||||
−0.103676 | + | 0.994611i | \(0.533060\pi\) | |||||||
\(242\) | −97.3779 | + | 97.3779i | −0.402388 | + | 0.402388i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 8.91187i | 0.0365241i | ||||||||
\(245\) | −16.6482 | + | 30.7869i | −0.0679520 | + | 0.125661i | ||||
\(246\) | 86.0675 | 0.349868 | ||||||||
\(247\) | −200.965 | + | 200.965i | −0.813625 | + | 0.813625i | ||||
\(248\) | 100.178 | + | 100.178i | 0.403945 | + | 0.403945i | ||||
\(249\) | − | 130.873i | − | 0.525594i | ||||||
\(250\) | 135.006 | + | 114.120i | 0.540023 | + | 0.456481i | ||||
\(251\) | −315.486 | −1.25692 | −0.628459 | − | 0.777843i | \(-0.716314\pi\) | ||||
−0.628459 | + | 0.777843i | \(0.716314\pi\) | |||||||
\(252\) | 11.2250 | − | 11.2250i | 0.0445435 | − | 0.0445435i | ||||
\(253\) | 332.600 | + | 332.600i | 1.31463 | + | 1.31463i | ||||
\(254\) | − | 345.355i | − | 1.35967i | ||||||
\(255\) | −12.7084 | − | 6.87216i | −0.0498369 | − | 0.0269496i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 275.744 | − | 275.744i | 1.07293 | − | 1.07293i | 0.0758107 | − | 0.997122i | \(-0.475846\pi\) |
0.997122 | − | 0.0758107i | \(-0.0241545\pi\) | |||||||
\(258\) | 144.377 | + | 144.377i | 0.559601 | + | 0.559601i | ||||
\(259\) | − | 23.0387i | − | 0.0889524i | ||||||
\(260\) | 180.020 | − | 53.6573i | 0.692383 | − | 0.206374i | ||||
\(261\) | −9.89243 | −0.0379020 | ||||||||
\(262\) | −147.540 | + | 147.540i | −0.563129 | + | 0.563129i | ||||
\(263\) | 122.744 | + | 122.744i | 0.466708 | + | 0.466708i | 0.900846 | − | 0.434138i | \(-0.142947\pi\) |
−0.434138 | + | 0.900846i | \(0.642947\pi\) | |||||||
\(264\) | − | 72.3952i | − | 0.274224i | ||||||
\(265\) | −22.0216 | − | 73.8820i | −0.0831002 | − | 0.278800i | ||||
\(266\) | 56.6107 | 0.212822 | ||||||||
\(267\) | −26.1547 | + | 26.1547i | −0.0979578 | + | 0.0979578i | ||||
\(268\) | 176.885 | + | 176.885i | 0.660018 | + | 0.660018i | ||||
\(269\) | − | 62.3232i | − | 0.231685i | −0.993268 | − | 0.115842i | \(-0.963043\pi\) | ||
0.993268 | − | 0.115842i | \(-0.0369567\pi\) | |||||||
\(270\) | −17.4770 | + | 32.3196i | −0.0647297 | + | 0.119702i | ||||
\(271\) | 127.663 | 0.471081 | 0.235541 | − | 0.971864i | \(-0.424314\pi\) | ||||
0.235541 | + | 0.971864i | \(0.424314\pi\) | |||||||
\(272\) | −4.71854 | + | 4.71854i | −0.0173476 | + | 0.0173476i | ||||
\(273\) | −60.8691 | − | 60.8691i | −0.222964 | − | 0.222964i | ||||
\(274\) | 193.181i | 0.705042i | ||||||||
\(275\) | −202.264 | − | 309.153i | −0.735506 | − | 1.12419i | ||||
\(276\) | −110.261 | −0.399498 | ||||||||
\(277\) | −57.6863 | + | 57.6863i | −0.208254 | + | 0.208254i | −0.803525 | − | 0.595271i | \(-0.797045\pi\) |
0.595271 | + | 0.803525i | \(0.297045\pi\) | |||||||
\(278\) | −184.197 | − | 184.197i | −0.662578 | − | 0.662578i | ||||
\(279\) | 150.267i | 0.538593i | ||||||||
\(280\) | −32.9126 | − | 17.7977i | −0.117545 | − | 0.0635633i | ||||
\(281\) | 119.372 | 0.424812 | 0.212406 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212406 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(282\) | 49.3928 | − | 49.3928i | 0.175152 | − | 0.175152i | ||||
\(283\) | −175.257 | − | 175.257i | −0.619282 | − | 0.619282i | 0.326065 | − | 0.945347i | \(-0.394277\pi\) |
−0.945347 | + | 0.326065i | \(0.894277\pi\) | |||||||
\(284\) | − | 138.638i | − | 0.488161i | ||||||
\(285\) | −125.569 | + | 37.4276i | −0.440593 | + | 0.131325i | ||||
\(286\) | −392.574 | −1.37264 | ||||||||
\(287\) | −65.7352 | + | 65.7352i | −0.229042 | + | 0.229042i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 286.217i | 0.990370i | ||||||||
\(290\) | 6.66029 | + | 22.3452i | 0.0229665 | + | 0.0770524i | ||||
\(291\) | 221.327 | 0.760572 | ||||||||
\(292\) | 116.833 | − | 116.833i | 0.400114 | − | 0.400114i | ||||
\(293\) | 224.254 | + | 224.254i | 0.765372 | + | 0.765372i | 0.977288 | − | 0.211916i | \(-0.0679703\pi\) |
−0.211916 | + | 0.977288i | \(0.567970\pi\) | |||||||
\(294\) | 17.1464i | 0.0583212i | ||||||||
\(295\) | 158.580 | − | 293.256i | 0.537560 | − | 0.994089i | ||||
\(296\) | 24.6294 | 0.0832074 | ||||||||
\(297\) | 54.2964 | − | 54.2964i | 0.182816 | − | 0.182816i | ||||
\(298\) | 206.358 | + | 206.358i | 0.692475 | + | 0.692475i | ||||
\(299\) | 597.909i | 1.99970i | ||||||||
\(300\) | 84.7708 | + | 17.7175i | 0.282569 | + | 0.0590585i | ||||
\(301\) | −220.540 | −0.732690 | ||||||||
\(302\) | −51.4825 | + | 51.4825i | −0.170472 | + | 0.170472i | ||||
\(303\) | 53.4123 | + | 53.4123i | 0.176278 | + | 0.176278i | ||||
\(304\) | 60.5194i | 0.199077i | ||||||||
\(305\) | 19.5978 | + | 10.5976i | 0.0642551 | + | 0.0347464i | ||||
\(306\) | −7.07780 | −0.0231301 | ||||||||
\(307\) | 202.366 | − | 202.366i | 0.659172 | − | 0.659172i | −0.296012 | − | 0.955184i | \(-0.595657\pi\) |
0.955184 | + | 0.296012i | \(0.0956569\pi\) | |||||||
\(308\) | 55.2928 | + | 55.2928i | 0.179522 | + | 0.179522i | ||||
\(309\) | − | 119.691i | − | 0.387350i | ||||||
\(310\) | 339.427 | − | 101.171i | 1.09493 | − | 0.326358i | ||||
\(311\) | −382.114 | −1.22866 | −0.614331 | − | 0.789049i | \(-0.710574\pi\) | ||||
−0.614331 | + | 0.789049i | \(0.710574\pi\) | |||||||
\(312\) | 65.0718 | − | 65.0718i | 0.208563 | − | 0.208563i | ||||
\(313\) | −235.445 | − | 235.445i | −0.752220 | − | 0.752220i | 0.222674 | − | 0.974893i | \(-0.428522\pi\) |
−0.974893 | + | 0.222674i | \(0.928522\pi\) | |||||||
\(314\) | 183.572i | 0.584624i | ||||||||
\(315\) | −11.3362 | − | 38.0328i | −0.0359879 | − | 0.120739i | ||||
\(316\) | 105.661 | 0.334372 | ||||||||
\(317\) | 297.704 | − | 297.704i | 0.939129 | − | 0.939129i | −0.0591213 | − | 0.998251i | \(-0.518830\pi\) |
0.998251 | + | 0.0591213i | \(0.0188299\pi\) | |||||||
\(318\) | −26.7062 | − | 26.7062i | −0.0839817 | − | 0.0839817i | ||||
\(319\) | − | 48.7288i | − | 0.152755i | ||||||
\(320\) | 19.0266 | − | 35.1851i | 0.0594580 | − | 0.109953i | ||||
\(321\) | 56.7049 | 0.176651 | ||||||||
\(322\) | 84.2136 | − | 84.2136i | 0.261533 | − | 0.261533i | ||||
\(323\) | −17.8477 | − | 17.8477i | −0.0552559 | − | 0.0552559i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 96.0760 | − | 459.682i | 0.295618 | − | 1.41441i | ||||
\(326\) | 22.2902 | 0.0683748 | ||||||||
\(327\) | 173.710 | − | 173.710i | 0.531223 | − | 0.531223i | ||||
\(328\) | −70.2739 | − | 70.2739i | −0.214250 | − | 0.214250i | ||||
\(329\) | 75.4487i | 0.229327i | ||||||||
\(330\) | −159.202 | − | 86.0895i | −0.482430 | − | 0.260877i | ||||
\(331\) | −197.349 | −0.596221 | −0.298110 | − | 0.954531i | \(-0.596356\pi\) | ||||
−0.298110 | + | 0.954531i | \(0.596356\pi\) | |||||||
\(332\) | −106.857 | + | 106.857i | −0.321859 | + | 0.321859i | ||||
\(333\) | 18.4720 | + | 18.4720i | 0.0554716 | + | 0.0554716i | ||||
\(334\) | 449.622i | 1.34617i | ||||||||
\(335\) | 599.326 | − | 178.637i | 1.78903 | − | 0.533246i | ||||
\(336\) | −18.3303 | −0.0545545 | ||||||||
\(337\) | −259.060 | + | 259.060i | −0.768723 | + | 0.768723i | −0.977882 | − | 0.209159i | \(-0.932927\pi\) |
0.209159 | + | 0.977882i | \(0.432927\pi\) | |||||||
\(338\) | −183.861 | − | 183.861i | −0.543968 | − | 0.543968i | ||||
\(339\) | − | 278.619i | − | 0.821886i | ||||||
\(340\) | 4.76529 | + | 15.9875i | 0.0140155 | + | 0.0470220i | ||||
\(341\) | −740.198 | −2.17067 | ||||||||
\(342\) | −45.3895 | + | 45.3895i | −0.132718 | + | 0.132718i | ||||
\(343\) | −13.0958 | − | 13.0958i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 235.767i | − | 0.685369i | ||||||
\(345\) | −131.119 | + | 242.472i | −0.380054 | + | 0.702819i | ||||
\(346\) | −86.9092 | −0.251183 | ||||||||
\(347\) | −316.016 | + | 316.016i | −0.910710 | + | 0.910710i | −0.996328 | − | 0.0856183i | \(-0.972713\pi\) |
0.0856183 | + | 0.996328i | \(0.472713\pi\) | |||||||
\(348\) | 8.07713 | + | 8.07713i | 0.0232102 | + | 0.0232102i | ||||
\(349\) | 64.9155i | 0.186004i | 0.995666 | + | 0.0930022i | \(0.0296464\pi\) | ||||
−0.995666 | + | 0.0930022i | \(0.970354\pi\) | |||||||
\(350\) | −78.2768 | + | 51.2128i | −0.223648 | + | 0.146322i | ||||
\(351\) | 97.6077 | 0.278085 | ||||||||
\(352\) | −59.1105 | + | 59.1105i | −0.167927 | + | 0.167927i | ||||
\(353\) | 328.571 | + | 328.571i | 0.930796 | + | 0.930796i | 0.997756 | − | 0.0669597i | \(-0.0213299\pi\) |
−0.0669597 | + | 0.997756i | \(0.521330\pi\) | |||||||
\(354\) | − | 163.326i | − | 0.461372i | ||||||
\(355\) | −304.873 | − | 164.862i | −0.858798 | − | 0.464401i | ||||
\(356\) | 42.7105 | 0.119973 | ||||||||
\(357\) | 5.40576 | − | 5.40576i | 0.0151422 | − | 0.0151422i | ||||
\(358\) | 167.373 | + | 167.373i | 0.467523 | + | 0.467523i | ||||
\(359\) | 110.889i | 0.308883i | 0.988002 | + | 0.154442i | \(0.0493579\pi\) | ||||
−0.988002 | + | 0.154442i | \(0.950642\pi\) | |||||||
\(360\) | 40.6587 | − | 12.1189i | 0.112941 | − | 0.0336636i | ||||
\(361\) | 132.088 | 0.365895 | ||||||||
\(362\) | −225.762 | + | 225.762i | −0.623652 | + | 0.623652i | ||||
\(363\) | 119.263 | + | 119.263i | 0.328548 | + | 0.328548i | ||||
\(364\) | 99.3988i | 0.273074i | ||||||||
\(365\) | −117.991 | − | 395.857i | −0.323262 | − | 1.08454i | ||||
\(366\) | 10.9148 | 0.0298218 | ||||||||
\(367\) | −347.342 | + | 347.342i | −0.946436 | + | 0.946436i | −0.998637 | − | 0.0522011i | \(-0.983376\pi\) |
0.0522011 | + | 0.998637i | \(0.483376\pi\) | |||||||
\(368\) | 90.0281 | + | 90.0281i | 0.244642 | + | 0.244642i | ||||
\(369\) | − | 105.411i | − | 0.285666i | ||||||
\(370\) | 29.2883 | − | 54.1617i | 0.0791575 | − | 0.146383i | ||||
\(371\) | 40.7944 | 0.109958 | ||||||||
\(372\) | 122.693 | − | 122.693i | 0.329820 | − | 0.329820i | ||||
\(373\) | −433.660 | − | 433.660i | −1.16263 | − | 1.16263i | −0.983899 | − | 0.178728i | \(-0.942802\pi\) |
−0.178728 | − | 0.983899i | \(-0.557198\pi\) | |||||||
\(374\) | − | 34.8644i | − | 0.0932202i | ||||||
\(375\) | 139.768 | − | 165.348i | 0.372715 | − | 0.440927i | ||||
\(376\) | −80.6581 | −0.214516 | ||||||||
\(377\) | 43.7995 | − | 43.7995i | 0.116179 | − | 0.116179i | ||||
\(378\) | −13.7477 | − | 13.7477i | −0.0363696 | − | 0.0363696i | ||||
\(379\) | − | 5.82662i | − | 0.0153737i | −0.999970 | − | 0.00768684i | \(-0.997553\pi\) | ||
0.999970 | − | 0.00768684i | \(-0.00244682\pi\) | |||||||
\(380\) | 133.086 | + | 71.9672i | 0.350227 | + | 0.189387i | ||||
\(381\) | −422.972 | −1.11016 | ||||||||
\(382\) | 148.626 | − | 148.626i | 0.389073 | − | 0.389073i | ||||
\(383\) | −84.7856 | − | 84.7856i | −0.221372 | − | 0.221372i | 0.587704 | − | 0.809076i | \(-0.300032\pi\) |
−0.809076 | + | 0.587704i | \(0.800032\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 187.344 | − | 55.8406i | 0.486609 | − | 0.145041i | ||||
\(386\) | 316.126 | 0.818979 | ||||||||
\(387\) | 176.825 | − | 176.825i | 0.456913 | − | 0.456913i | ||||
\(388\) | −180.712 | − | 180.712i | −0.465754 | − | 0.465754i | ||||
\(389\) | 287.140i | 0.738150i | 0.929400 | + | 0.369075i | \(0.120325\pi\) | ||||
−0.929400 | + | 0.369075i | \(0.879675\pi\) | |||||||
\(390\) | −65.7165 | − | 220.478i | −0.168504 | − | 0.565328i | ||||
\(391\) | −53.1001 | −0.135806 | ||||||||
\(392\) | 14.0000 | − | 14.0000i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | 180.699 | + | 180.699i | 0.459793 | + | 0.459793i | ||||
\(394\) | 53.5413i | 0.135892i | ||||||||
\(395\) | 125.648 | − | 232.357i | 0.318097 | − | 0.588245i | ||||
\(396\) | −88.6657 | −0.223903 | ||||||||
\(397\) | 89.5514 | − | 89.5514i | 0.225570 | − | 0.225570i | −0.585269 | − | 0.810839i | \(-0.699011\pi\) |
0.810839 | + | 0.585269i | \(0.199011\pi\) | |||||||
\(398\) | −171.790 | − | 171.790i | −0.431634 | − | 0.431634i | ||||
\(399\) | − | 69.3336i | − | 0.173768i | ||||||
\(400\) | −54.7488 | − | 83.6814i | −0.136872 | − | 0.209203i | ||||
\(401\) | −649.944 | −1.62081 | −0.810405 | − | 0.585871i | \(-0.800753\pi\) | ||||
−0.810405 | + | 0.585871i | \(0.800753\pi\) | |||||||
\(402\) | 216.639 | − | 216.639i | 0.538902 | − | 0.538902i | ||||
\(403\) | −665.320 | − | 665.320i | −1.65092 | − | 1.65092i | ||||
\(404\) | − | 87.2218i | − | 0.215896i | ||||||
\(405\) | 39.5832 | + | 21.4049i | 0.0977363 | + | 0.0528515i | ||||
\(406\) | −12.3380 | −0.0303892 | ||||||||
\(407\) | −90.9909 | + | 90.9909i | −0.223565 | + | 0.223565i | ||||
\(408\) | 5.77900 | + | 5.77900i | 0.0141642 | + | 0.0141642i | ||||
\(409\) | − | 717.337i | − | 1.75388i | −0.480600 | − | 0.876940i | \(-0.659581\pi\) | ||
0.480600 | − | 0.876940i | \(-0.340419\pi\) | |||||||
\(410\) | −238.104 | + | 70.9701i | −0.580741 | + | 0.173098i | ||||
\(411\) | 236.598 | 0.575664 | ||||||||
\(412\) | −97.7275 | + | 97.7275i | −0.237203 | + | 0.237203i | ||||
\(413\) | 124.742 | + | 124.742i | 0.302039 | + | 0.302039i | ||||
\(414\) | 135.042i | 0.326189i | ||||||||
\(415\) | 107.916 | + | 362.057i | 0.260038 | + | 0.872426i | ||||
\(416\) | −106.262 | −0.255437 | ||||||||
\(417\) | −225.594 | + | 225.594i | −0.540992 | + | 0.540992i | ||||
\(418\) | −223.583 | − | 223.583i | −0.534887 | − | 0.534887i | ||||
\(419\) | − | 680.885i | − | 1.62502i | −0.582945 | − | 0.812511i | \(-0.698100\pi\) | ||
0.582945 | − | 0.812511i | \(-0.301900\pi\) | |||||||
\(420\) | −21.7977 | + | 40.3096i | −0.0518992 | + | 0.0959752i | ||||
\(421\) | 710.333 | 1.68725 | 0.843626 | − | 0.536931i | \(-0.180416\pi\) | ||||
0.843626 | + | 0.536931i | \(0.180416\pi\) | |||||||
\(422\) | 302.432 | − | 302.432i | 0.716664 | − | 0.716664i | ||||
\(423\) | −60.4936 | − | 60.4936i | −0.143011 | − | 0.143011i | ||||
\(424\) | 43.6110i | 0.102856i | ||||||||
\(425\) | 40.8242 | + | 8.53247i | 0.0960570 | + | 0.0200764i | ||||
\(426\) | −169.796 | −0.398581 | ||||||||
\(427\) | −8.33629 | + | 8.33629i | −0.0195229 | + | 0.0195229i | ||||
\(428\) | −46.2994 | − | 46.2994i | −0.108176 | − | 0.108176i | ||||
\(429\) | 480.803i | 1.12075i | ||||||||
\(430\) | −518.467 | − | 280.365i | −1.20574 | − | 0.652011i | ||||
\(431\) | 785.543 | 1.82261 | 0.911303 | − | 0.411737i | \(-0.135078\pi\) | ||||
0.911303 | + | 0.411737i | \(0.135078\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 484.429 | + | 484.429i | 1.11877 | + | 1.11877i | 0.991922 | + | 0.126852i | \(0.0404874\pi\) |
0.126852 | + | 0.991922i | \(0.459513\pi\) | |||||||
\(434\) | 187.416i | 0.431835i | ||||||||
\(435\) | 27.3672 | − | 8.15716i | 0.0629130 | − | 0.0187521i | ||||
\(436\) | −283.667 | −0.650613 | ||||||||
\(437\) | −340.528 | + | 340.528i | −0.779240 | + | 0.779240i | ||||
\(438\) | −143.091 | − | 143.091i | −0.326691 | − | 0.326691i | ||||
\(439\) | − | 558.366i | − | 1.27190i | −0.771728 | − | 0.635952i | \(-0.780608\pi\) | ||
0.771728 | − | 0.635952i | \(-0.219392\pi\) | |||||||
\(440\) | 59.6961 | + | 200.280i | 0.135673 | + | 0.455181i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | 31.3375 | − | 31.3375i | 0.0708993 | − | 0.0708993i | ||||
\(443\) | 94.3596 | + | 94.3596i | 0.213001 | + | 0.213001i | 0.805541 | − | 0.592540i | \(-0.201875\pi\) |
−0.592540 | + | 0.805541i | \(0.701875\pi\) | |||||||
\(444\) | − | 30.1647i | − | 0.0679385i | ||||||
\(445\) | 50.7896 | − | 93.9233i | 0.114134 | − | 0.211064i | ||||
\(446\) | 341.569 | 0.765850 | ||||||||
\(447\) | 252.735 | − | 252.735i | 0.565404 | − | 0.565404i | ||||
\(448\) | 14.9666 | + | 14.9666i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | 642.007i | 1.42986i | 0.699197 | + | 0.714929i | \(0.253541\pi\) | ||||
−0.699197 | + | 0.714929i | \(0.746459\pi\) | |||||||
\(450\) | 21.6995 | − | 103.823i | 0.0482210 | − | 0.230717i | ||||
\(451\) | 519.240 | 1.15131 | ||||||||
\(452\) | −227.492 | + | 227.492i | −0.503301 | + | 0.503301i | ||||
\(453\) | 63.0529 | + | 63.0529i | 0.139190 | + | 0.139190i | ||||
\(454\) | 308.647i | 0.679838i | ||||||||
\(455\) | 218.585 | + | 118.201i | 0.480406 | + | 0.259782i | ||||
\(456\) | 74.1208 | 0.162546 | ||||||||
\(457\) | 320.594 | − | 320.594i | 0.701519 | − | 0.701519i | −0.263218 | − | 0.964736i | \(-0.584784\pi\) |
0.964736 | + | 0.263218i | \(0.0847838\pi\) | |||||||
\(458\) | −33.7243 | − | 33.7243i | −0.0736337 | − | 0.0736337i | ||||
\(459\) | 8.66850i | 0.0188856i | ||||||||
\(460\) | 305.036 | − | 90.9201i | 0.663121 | − | 0.197652i | ||||
\(461\) | −300.193 | −0.651177 | −0.325589 | − | 0.945512i | \(-0.605562\pi\) | ||||
−0.325589 | + | 0.945512i | \(0.605562\pi\) | |||||||
\(462\) | 67.7195 | − | 67.7195i | 0.146579 | − | 0.146579i | ||||
\(463\) | 58.9154 | + | 58.9154i | 0.127247 | + | 0.127247i | 0.767862 | − | 0.640615i | \(-0.221321\pi\) |
−0.640615 | + | 0.767862i | \(0.721321\pi\) | |||||||
\(464\) | − | 13.1899i | − | 0.0284265i | ||||||
\(465\) | −123.908 | − | 415.711i | −0.266470 | − | 0.894003i | ||||
\(466\) | 415.997 | 0.892697 | ||||||||
\(467\) | −362.497 | + | 362.497i | −0.776226 | + | 0.776226i | −0.979187 | − | 0.202961i | \(-0.934943\pi\) |
0.202961 | + | 0.979187i | \(0.434943\pi\) | |||||||
\(468\) | −79.6963 | − | 79.6963i | −0.170291 | − | 0.170291i | ||||
\(469\) | 330.921i | 0.705589i | ||||||||
\(470\) | −95.9153 | + | 177.373i | −0.204075 | + | 0.377388i | ||||
\(471\) | 224.829 | 0.477343 | ||||||||
\(472\) | −133.355 | + | 133.355i | −0.282531 | + | 0.282531i | ||||
\(473\) | 871.018 | + | 871.018i | 1.84148 | + | 1.84148i | ||||
\(474\) | − | 129.408i | − | 0.273013i | ||||||
\(475\) | 316.521 | − | 207.085i | 0.666361 | − | 0.435968i | ||||
\(476\) | −8.82757 | −0.0185453 | ||||||||
\(477\) | −32.7083 | + | 32.7083i | −0.0685708 | + | 0.0685708i | ||||
\(478\) | 49.7163 | + | 49.7163i | 0.104009 | + | 0.104009i | ||||
\(479\) | 233.704i | 0.487900i | 0.969788 | + | 0.243950i | \(0.0784433\pi\) | ||||
−0.969788 | + | 0.243950i | \(0.921557\pi\) | |||||||
\(480\) | −43.0928 | − | 23.3027i | −0.0897766 | − | 0.0485472i | ||||
\(481\) | −163.573 | −0.340068 | ||||||||
\(482\) | 49.9716 | − | 49.9716i | 0.103676 | − | 0.103676i | ||||
\(483\) | −103.140 | − | 103.140i | −0.213541 | − | 0.213541i | ||||
\(484\) | − | 194.756i | − | 0.402388i | ||||||
\(485\) | −612.295 | + | 182.503i | −1.26246 | + | 0.376295i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 234.027 | − | 234.027i | 0.480549 | − | 0.480549i | −0.424758 | − | 0.905307i | \(-0.639641\pi\) |
0.905307 | + | 0.424758i | \(0.139641\pi\) | |||||||
\(488\) | −8.91187 | − | 8.91187i | −0.0182620 | − | 0.0182620i | ||||
\(489\) | − | 27.2998i | − | 0.0558278i | ||||||
\(490\) | −14.1387 | − | 47.4352i | −0.0288545 | − | 0.0968065i | ||||
\(491\) | 29.6268 | 0.0603398 | 0.0301699 | − | 0.999545i | \(-0.490395\pi\) | ||||
0.0301699 | + | 0.999545i | \(0.490395\pi\) | |||||||
\(492\) | −86.0675 | + | 86.0675i | −0.174934 | + | 0.174934i | ||||
\(493\) | 3.88981 | + | 3.88981i | 0.00789009 | + | 0.00789009i | ||||
\(494\) | − | 401.931i | − | 0.813625i | ||||||
\(495\) | −105.438 | + | 194.982i | −0.213005 | + | 0.393903i | ||||
\(496\) | −200.357 | −0.403945 | ||||||||
\(497\) | 129.684 | − | 129.684i | 0.260933 | − | 0.260933i | ||||
\(498\) | 130.873 | + | 130.873i | 0.262797 | + | 0.262797i | ||||
\(499\) | 322.566i | 0.646426i | 0.946326 | + | 0.323213i | \(0.104763\pi\) | ||||
−0.946326 | + | 0.323213i | \(0.895237\pi\) | |||||||
\(500\) | −249.126 | + | 20.8857i | −0.498252 | + | 0.0417714i | ||||
\(501\) | 550.672 | 1.09915 | ||||||||
\(502\) | 315.486 | − | 315.486i | 0.628459 | − | 0.628459i | ||||
\(503\) | −350.402 | − | 350.402i | −0.696625 | − | 0.696625i | 0.267056 | − | 0.963681i | \(-0.413949\pi\) |
−0.963681 | + | 0.267056i | \(0.913949\pi\) | |||||||
\(504\) | 22.4499i | 0.0445435i | ||||||||
\(505\) | −191.807 | − | 103.721i | −0.379815 | − | 0.205388i | ||||
\(506\) | −665.200 | −1.31463 | ||||||||
\(507\) | −225.183 | + | 225.183i | −0.444148 | + | 0.444148i | ||||
\(508\) | 345.355 | + | 345.355i | 0.679833 | + | 0.679833i | ||||
\(509\) | − | 66.4967i | − | 0.130642i | −0.997864 | − | 0.0653210i | \(-0.979193\pi\) | ||
0.997864 | − | 0.0653210i | \(-0.0208071\pi\) | |||||||
\(510\) | 19.5806 | − | 5.83626i | 0.0383933 | − | 0.0114436i | ||||
\(511\) | 218.575 | 0.427740 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 55.5906 | + | 55.5906i | 0.108364 | + | 0.108364i | ||||
\(514\) | 551.488i | 1.07293i | ||||||||
\(515\) | 98.6958 | + | 331.123i | 0.191642 | + | 0.642957i | ||||
\(516\) | −288.754 | −0.559601 | ||||||||
\(517\) | 297.983 | − | 297.983i | 0.576370 | − | 0.576370i | ||||
\(518\) | 23.0387 | + | 23.0387i | 0.0444762 | + | 0.0444762i | ||||
\(519\) | 106.442i | 0.205090i | ||||||||
\(520\) | −126.362 | + | 233.677i | −0.243004 | + | 0.449378i | ||||
\(521\) | −603.618 | −1.15858 | −0.579288 | − | 0.815123i | \(-0.696669\pi\) | ||||
−0.579288 | + | 0.815123i | \(0.696669\pi\) | |||||||
\(522\) | 9.89243 | − | 9.89243i | 0.0189510 | − | 0.0189510i | ||||
\(523\) | −294.450 | − | 294.450i | −0.563002 | − | 0.563002i | 0.367157 | − | 0.930159i | \(-0.380331\pi\) |
−0.930159 | + | 0.367157i | \(0.880331\pi\) | |||||||
\(524\) | − | 295.080i | − | 0.563129i | ||||||
\(525\) | 62.7226 | + | 95.8691i | 0.119472 | + | 0.182608i | ||||
\(526\) | −245.488 | −0.466708 | ||||||||
\(527\) | 59.0869 | − | 59.0869i | 0.112119 | − | 0.112119i | ||||
\(528\) | 72.3952 | + | 72.3952i | 0.137112 | + | 0.137112i | ||||
\(529\) | 484.133i | 0.915185i | ||||||||
\(530\) | 95.9036 | + | 51.8605i | 0.180950 | + | 0.0978499i | ||||
\(531\) | −200.032 | −0.376709 | ||||||||
\(532\) | −56.6107 | + | 56.6107i | −0.106411 | + | 0.106411i | ||||
\(533\) | 466.714 | + | 466.714i | 0.875636 | + | 0.875636i | ||||
\(534\) | − | 52.3095i | − | 0.0979578i | ||||||
\(535\) | −156.873 | + | 46.7581i | −0.293220 | + | 0.0873983i | ||||
\(536\) | −353.770 | −0.660018 | ||||||||
\(537\) | 204.990 | − | 204.990i | 0.381731 | − | 0.381731i | ||||
\(538\) | 62.3232 | + | 62.3232i | 0.115842 | + | 0.115842i | ||||
\(539\) | 103.443i | 0.191917i | ||||||||
\(540\) | −14.8426 | − | 49.7966i | −0.0274862 | − | 0.0922159i | ||||
\(541\) | −248.513 | −0.459358 | −0.229679 | − | 0.973266i | \(-0.573768\pi\) | ||||
−0.229679 | + | 0.973266i | \(0.573768\pi\) | |||||||
\(542\) | −127.663 | + | 127.663i | −0.235541 | + | 0.235541i | ||||
\(543\) | 276.501 | + | 276.501i | 0.509209 | + | 0.509209i | ||||
\(544\) | − | 9.43707i | − | 0.0173476i | ||||||
\(545\) | −337.326 | + | 623.804i | −0.618946 | + | 1.14459i | ||||
\(546\) | 121.738 | 0.222964 | ||||||||
\(547\) | −246.861 | + | 246.861i | −0.451299 | + | 0.451299i | −0.895786 | − | 0.444487i | \(-0.853386\pi\) |
0.444487 | + | 0.895786i | \(0.353386\pi\) | |||||||
\(548\) | −193.181 | − | 193.181i | −0.352521 | − | 0.352521i | ||||
\(549\) | − | 13.3678i | − | 0.0243494i | ||||||
\(550\) | 511.417 | + | 106.889i | 0.929849 | + | 0.194343i | ||||
\(551\) | 49.8903 | 0.0905450 | ||||||||
\(552\) | 110.261 | − | 110.261i | 0.199749 | − | 0.199749i | ||||
\(553\) | 98.8373 | + | 98.8373i | 0.178729 | + | 0.178729i | ||||
\(554\) | − | 115.373i | − | 0.208254i | ||||||
\(555\) | −66.3343 | − | 35.8707i | −0.119521 | − | 0.0646318i | ||||
\(556\) | 368.393 | 0.662578 | ||||||||
\(557\) | −333.317 | + | 333.317i | −0.598416 | + | 0.598416i | −0.939891 | − | 0.341475i | \(-0.889073\pi\) |
0.341475 | + | 0.939891i | \(0.389073\pi\) | |||||||
\(558\) | −150.267 | − | 150.267i | −0.269297 | − | 0.269297i | ||||
\(559\) | 1565.81i | 2.80110i | ||||||||
\(560\) | 50.7103 | − | 15.1149i | 0.0905542 | − | 0.0269909i | ||||
\(561\) | −42.6999 | −0.0761140 | ||||||||
\(562\) | −119.372 | + | 119.372i | −0.212406 | + | 0.212406i | ||||
\(563\) | 499.267 | + | 499.267i | 0.886798 | + | 0.886798i | 0.994214 | − | 0.107416i | \(-0.0342577\pi\) |
−0.107416 | + | 0.994214i | \(0.534258\pi\) | |||||||
\(564\) | 98.7856i | 0.175152i | ||||||||
\(565\) | 229.746 | + | 770.794i | 0.406630 | + | 1.36424i | ||||
\(566\) | 350.514 | 0.619282 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.0296957 | + | 0.0296957i | ||||
\(568\) | 138.638 | + | 138.638i | 0.244080 | + | 0.244080i | ||||
\(569\) | − | 990.818i | − | 1.74133i | −0.491874 | − | 0.870666i | \(-0.663688\pi\) | ||
0.491874 | − | 0.870666i | \(-0.336312\pi\) | |||||||
\(570\) | 88.1414 | − | 162.997i | 0.154634 | − | 0.285959i | ||||
\(571\) | −172.474 | −0.302057 | −0.151028 | − | 0.988529i | \(-0.548258\pi\) | ||||
−0.151028 | + | 0.988529i | \(0.548258\pi\) | |||||||
\(572\) | 392.574 | − | 392.574i | 0.686318 | − | 0.686318i | ||||
\(573\) | −182.029 | − | 182.029i | −0.317676 | − | 0.317676i | ||||
\(574\) | − | 131.470i | − | 0.229042i | ||||||
\(575\) | 162.797 | − | 778.913i | 0.283125 | − | 1.35463i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −75.2134 | + | 75.2134i | −0.130352 | + | 0.130352i | −0.769273 | − | 0.638920i | \(-0.779381\pi\) |
0.638920 | + | 0.769273i | \(0.279381\pi\) | |||||||
\(578\) | −286.217 | − | 286.217i | −0.495185 | − | 0.495185i | ||||
\(579\) | − | 387.173i | − | 0.668693i | ||||||
\(580\) | −29.0055 | − | 15.6849i | −0.0500095 | − | 0.0270429i | ||||
\(581\) | −199.912 | −0.344082 | ||||||||
\(582\) | −221.327 | + | 221.327i | −0.380286 | + | 0.380286i | ||||
\(583\) | −161.117 | − | 161.117i | −0.276358 | − | 0.276358i | ||||
\(584\) | 233.666i | 0.400114i | ||||||||
\(585\) | −270.029 | + | 80.4859i | −0.461588 | + | 0.137583i | ||||
\(586\) | −448.508 | −0.765372 | ||||||||
\(587\) | 371.013 | − | 371.013i | 0.632050 | − | 0.632050i | −0.316532 | − | 0.948582i | \(-0.602519\pi\) |
0.948582 | + | 0.316532i | \(0.102519\pi\) | |||||||
\(588\) | −17.1464 | − | 17.1464i | −0.0291606 | − | 0.0291606i | ||||
\(589\) | − | 757.841i | − | 1.28666i | ||||||
\(590\) | 134.676 | + | 451.836i | 0.228265 | + | 0.765824i | ||||
\(591\) | 65.5745 | 0.110955 | ||||||||
\(592\) | −24.6294 | + | 24.6294i | −0.0416037 | + | 0.0416037i | ||||
\(593\) | 106.940 | + | 106.940i | 0.180337 | + | 0.180337i | 0.791503 | − | 0.611166i | \(-0.209299\pi\) |
−0.611166 | + | 0.791503i | \(0.709299\pi\) | |||||||
\(594\) | 108.593i | 0.182816i | ||||||||
\(595\) | −10.4974 | + | 19.4124i | −0.0176427 | + | 0.0326259i | ||||
\(596\) | −412.715 | −0.692475 | ||||||||
\(597\) | −210.399 | + | 210.399i | −0.352428 | + | 0.352428i | ||||
\(598\) | −597.909 | − | 597.909i | −0.999848 | − | 0.999848i | ||||
\(599\) | − | 382.077i | − | 0.637859i | −0.947778 | − | 0.318929i | \(-0.896677\pi\) | ||
0.947778 | − | 0.318929i | \(-0.103323\pi\) | |||||||
\(600\) | −102.488 | + | 67.0533i | −0.170814 | + | 0.111755i | ||||
\(601\) | 618.446 | 1.02903 | 0.514514 | − | 0.857482i | \(-0.327972\pi\) | ||||
0.514514 | + | 0.857482i | \(0.327972\pi\) | |||||||
\(602\) | 220.540 | − | 220.540i | 0.366345 | − | 0.366345i | ||||
\(603\) | −265.327 | − | 265.327i | −0.440012 | − | 0.440012i | ||||
\(604\) | − | 102.965i | − | 0.170472i | ||||||
\(605\) | −428.281 | − | 231.596i | −0.707903 | − | 0.382803i | ||||
\(606\) | −106.825 | −0.176278 | ||||||||
\(607\) | 222.670 | − | 222.670i | 0.366837 | − | 0.366837i | −0.499485 | − | 0.866322i | \(-0.666477\pi\) |
0.866322 | + | 0.499485i | \(0.166477\pi\) | |||||||
\(608\) | −60.5194 | − | 60.5194i | −0.0995384 | − | 0.0995384i | ||||
\(609\) | 15.1109i | 0.0248127i | ||||||||
\(610\) | −30.1954 | + | 9.00017i | −0.0495007 | + | 0.0147544i | ||||
\(611\) | 535.679 | 0.876725 | ||||||||
\(612\) | 7.07780 | − | 7.07780i | 0.0115650 | − | 0.0115650i | ||||
\(613\) | 422.055 | + | 422.055i | 0.688508 | + | 0.688508i | 0.961902 | − | 0.273394i | \(-0.0881464\pi\) |
−0.273394 | + | 0.961902i | \(0.588146\pi\) | |||||||
\(614\) | 404.731i | 0.659172i | ||||||||
\(615\) | 86.9203 | + | 291.616i | 0.141334 | + | 0.474173i | ||||
\(616\) | −110.586 | −0.179522 | ||||||||
\(617\) | −651.882 | + | 651.882i | −1.05653 | + | 1.05653i | −0.0582314 | + | 0.998303i | \(0.518546\pi\) |
−0.998303 | + | 0.0582314i | \(0.981454\pi\) | |||||||
\(618\) | 119.691 | + | 119.691i | 0.193675 | + | 0.193675i | ||||
\(619\) | − | 687.434i | − | 1.11056i | −0.831665 | − | 0.555278i | \(-0.812612\pi\) | ||
0.831665 | − | 0.555278i | \(-0.187388\pi\) | |||||||
\(620\) | −238.256 | + | 440.598i | −0.384284 | + | 0.710642i | ||||
\(621\) | 165.392 | 0.266332 | ||||||||
\(622\) | 382.114 | − | 382.114i | 0.614331 | − | 0.614331i | ||||
\(623\) | 39.9520 | + | 39.9520i | 0.0641284 | + | 0.0641284i | ||||
\(624\) | 130.144i | 0.208563i | ||||||||
\(625\) | −250.322 | + | 572.681i | −0.400515 | + | 0.916290i | ||||
\(626\) | 470.889 | 0.752220 | ||||||||
\(627\) | −273.832 | + | 273.832i | −0.436734 | + | 0.436734i | ||||
\(628\) | −183.572 | − | 183.572i | −0.292312 | − | 0.292312i | ||||
\(629\) | − | 14.5268i | − | 0.0230951i | ||||||
\(630\) | 49.3689 | + | 26.6966i | 0.0783634 | + | 0.0423755i | ||||
\(631\) | 589.381 | 0.934043 | 0.467021 | − | 0.884246i | \(-0.345327\pi\) | ||||
0.467021 | + | 0.884246i | \(0.345327\pi\) | |||||||
\(632\) | −105.661 | + | 105.661i | −0.167186 | + | 0.167186i | ||||
\(633\) | −370.402 | − | 370.402i | −0.585154 | − | 0.585154i | ||||
\(634\) | 595.408i | 0.939129i | ||||||||
\(635\) | 1170.14 | − | 348.777i | 1.84274 | − | 0.549255i | ||||
\(636\) | 53.4124 | 0.0839817 | ||||||||
\(637\) | −92.9790 | + | 92.9790i | −0.145964 | + | 0.145964i | ||||
\(638\) | 48.7288 | + | 48.7288i | 0.0763775 | + | 0.0763775i | ||||
\(639\) | 207.956i | 0.325440i | ||||||||
\(640\) | 16.1585 | + | 54.2116i | 0.0252477 | + | 0.0847057i | ||||
\(641\) | 410.799 | 0.640872 | 0.320436 | − | 0.947270i | \(-0.396171\pi\) | ||||
0.320436 | + | 0.947270i | \(0.396171\pi\) | |||||||
\(642\) | −56.7049 | + | 56.7049i | −0.0883254 | + | 0.0883254i | ||||
\(643\) | 216.800 | + | 216.800i | 0.337169 | + | 0.337169i | 0.855301 | − | 0.518132i | \(-0.173372\pi\) |
−0.518132 | + | 0.855301i | \(0.673372\pi\) | |||||||
\(644\) | 168.427i | 0.261533i | ||||||||
\(645\) | −343.375 | + | 634.990i | −0.532364 | + | 0.984481i | ||||
\(646\) | 35.6953 | 0.0552559 | ||||||||
\(647\) | −411.008 | + | 411.008i | −0.635252 | + | 0.635252i | −0.949380 | − | 0.314129i | \(-0.898288\pi\) |
0.314129 | + | 0.949380i | \(0.398288\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 985.333i | − | 1.51823i | ||||||
\(650\) | 363.606 | + | 555.758i | 0.559394 | + | 0.855013i | ||||
\(651\) | 229.537 | 0.352592 | ||||||||
\(652\) | −22.2902 | + | 22.2902i | −0.0341874 | + | 0.0341874i | ||||
\(653\) | −46.1020 | − | 46.1020i | −0.0706003 | − | 0.0706003i | 0.670925 | − | 0.741525i | \(-0.265897\pi\) |
−0.741525 | + | 0.670925i | \(0.765897\pi\) | |||||||
\(654\) | 347.420i | 0.531223i | ||||||||
\(655\) | −648.900 | − | 350.897i | −0.990687 | − | 0.535720i | ||||
\(656\) | 140.548 | 0.214250 | ||||||||
\(657\) | −175.250 | + | 175.250i | −0.266742 | + | 0.266742i | ||||
\(658\) | −75.4487 | − | 75.4487i | −0.114664 | − | 0.114664i | ||||
\(659\) | − | 911.116i | − | 1.38257i | −0.722580 | − | 0.691287i | \(-0.757044\pi\) | ||
0.722580 | − | 0.691287i | \(-0.242956\pi\) | |||||||
\(660\) | 245.292 | − | 73.1125i | 0.371654 | − | 0.110777i | ||||
\(661\) | 24.2084 | 0.0366239 | 0.0183120 | − | 0.999832i | \(-0.494171\pi\) | ||||
0.0183120 | + | 0.999832i | \(0.494171\pi\) | |||||||
\(662\) | 197.349 | − | 197.349i | 0.298110 | − | 0.298110i | ||||
\(663\) | −38.3804 | − | 38.3804i | −0.0578890 | − | 0.0578890i | ||||
\(664\) | − | 213.714i | − | 0.321859i | ||||||
\(665\) | 57.1716 | + | 191.810i | 0.0859723 | + | 0.288436i | ||||
\(666\) | −36.9441 | −0.0554716 | ||||||||
\(667\) | 74.2164 | − | 74.2164i | 0.111269 | − | 0.111269i | ||||
\(668\) | −449.622 | − | 449.622i | −0.673087 | − | 0.673087i | ||||
\(669\) | − | 418.335i | − | 0.625314i | ||||||
\(670\) | −420.689 | + | 777.963i | −0.627894 | + | 1.16114i | ||||
\(671\) | 65.8481 | 0.0981343 | ||||||||
\(672\) | 18.3303 | − | 18.3303i | 0.0272772 | − | 0.0272772i | ||||
\(673\) | 522.406 | + | 522.406i | 0.776235 | + | 0.776235i | 0.979188 | − | 0.202954i | \(-0.0650541\pi\) |
−0.202954 | + | 0.979188i | \(0.565054\pi\) | |||||||
\(674\) | − | 518.119i | − | 0.768723i | ||||||
\(675\) | −127.156 | − | 26.5763i | −0.188380 | − | 0.0393723i | ||||
\(676\) | 367.723 | 0.543968 | ||||||||
\(677\) | −283.980 | + | 283.980i | −0.419468 | + | 0.419468i | −0.885020 | − | 0.465552i | \(-0.845856\pi\) |
0.465552 | + | 0.885020i | \(0.345856\pi\) | |||||||
\(678\) | 278.619 | + | 278.619i | 0.410943 | + | 0.410943i | ||||
\(679\) | − | 338.082i | − | 0.497912i | ||||||
\(680\) | −20.7528 | − | 11.2222i | −0.0305188 | − | 0.0165032i | ||||
\(681\) | 378.013 | 0.555086 | ||||||||
\(682\) | 740.198 | − | 740.198i | 1.08533 | − | 1.08533i | ||||
\(683\) | −549.911 | − | 549.911i | −0.805141 | − | 0.805141i | 0.178753 | − | 0.983894i | \(-0.442794\pi\) |
−0.983894 | + | 0.178753i | \(0.942794\pi\) | |||||||
\(684\) | − | 90.7790i | − | 0.132718i | ||||||
\(685\) | −654.542 | + | 195.095i | −0.955536 | + | 0.284811i | ||||
\(686\) | 26.1916 | 0.0381802 | ||||||||
\(687\) | −41.3036 | + | 41.3036i | −0.0601217 | + | 0.0601217i | ||||
\(688\) | 235.767 | + | 235.767i | 0.342685 | + | 0.342685i | ||||
\(689\) | − | 289.636i | − | 0.420372i | ||||||
\(690\) | −111.354 | − | 373.591i | −0.161383 | − | 0.541436i | ||||
\(691\) | −1119.58 | −1.62023 | −0.810117 | − | 0.586268i | \(-0.800597\pi\) | ||||
−0.810117 | + | 0.586268i | \(0.800597\pi\) | |||||||
\(692\) | 86.9092 | − | 86.9092i | 0.125591 | − | 0.125591i | ||||
\(693\) | −82.9392 | − | 82.9392i | −0.119681 | − | 0.119681i | ||||
\(694\) | − | 632.033i | − | 0.910710i | ||||||
\(695\) | 438.078 | − | 810.122i | 0.630329 | − | 1.16564i | ||||
\(696\) | −16.1543 | −0.0232102 | ||||||||
\(697\) | −41.4487 | + | 41.4487i | −0.0594673 | + | 0.0594673i | ||||
\(698\) | −64.9155 | − | 64.9155i | −0.0930022 | − | 0.0930022i | ||||
\(699\) | − | 509.490i | − | 0.728884i | ||||||
\(700\) | 27.0640 | − | 129.490i | 0.0386628 | − | 0.184985i | ||||
\(701\) | 693.405 | 0.989166 | 0.494583 | − | 0.869130i | \(-0.335321\pi\) | ||||
0.494583 | + | 0.869130i | \(0.335321\pi\) | |||||||
\(702\) | −97.6077 | + | 97.6077i | −0.139042 | + | 0.139042i | ||||
\(703\) | −93.1597 | − | 93.1597i | −0.132517 | − | 0.132517i | ||||
\(704\) | − | 118.221i | − | 0.167927i | ||||||
\(705\) | 217.236 | + | 117.472i | 0.308136 | + | 0.166627i | ||||
\(706\) | −657.142 | −0.930796 | ||||||||
\(707\) | 81.5886 | − | 81.5886i | 0.115401 | − | 0.115401i | ||||
\(708\) | 163.326 | + | 163.326i | 0.230686 | + | 0.230686i | ||||
\(709\) | − | 774.547i | − | 1.09245i | −0.837638 | − | 0.546225i | \(-0.816064\pi\) | ||
0.837638 | − | 0.546225i | \(-0.183936\pi\) | |||||||
\(710\) | 469.736 | − | 140.011i | 0.661600 | − | 0.197199i | ||||
\(711\) | −158.492 | −0.222915 | ||||||||
\(712\) | −42.7105 | + | 42.7105i | −0.0599867 | + | 0.0599867i | ||||
\(713\) | −1127.36 | − | 1127.36i | −1.58115 | − | 1.58115i | ||||
\(714\) | 10.8115i | 0.0151422i | ||||||||
\(715\) | −396.463 | − | 1330.13i | −0.554494 | − | 1.86032i | ||||
\(716\) | −334.747 | −0.467523 | ||||||||
\(717\) | 60.8897 | − | 60.8897i | 0.0849229 | − | 0.0849229i | ||||
\(718\) | −110.889 | − | 110.889i | −0.154442 | − | 0.154442i | ||||
\(719\) | 8.61314i | 0.0119793i | 0.999982 | + | 0.00598966i | \(0.00190658\pi\) | ||||
−0.999982 | + | 0.00598966i | \(0.998093\pi\) | |||||||
\(720\) | −28.5398 | + | 52.7776i | −0.0396387 | + | 0.0733023i | ||||
\(721\) | −182.831 | −0.253580 | ||||||||
\(722\) | −132.088 | + | 132.088i | −0.182947 | + | 0.182947i | ||||
\(723\) | −61.2025 | − | 61.2025i | −0.0846507 | − | 0.0846507i | ||||
\(724\) | − | 451.524i | − | 0.623652i | ||||||
\(725\) | −68.9843 | + | 45.1332i | −0.0951508 | + | 0.0622527i | ||||
\(726\) | −238.526 | −0.328548 | ||||||||
\(727\) | −305.108 | + | 305.108i | −0.419681 | + | 0.419681i | −0.885094 | − | 0.465413i | \(-0.845906\pi\) |
0.465413 | + | 0.885094i | \(0.345906\pi\) | |||||||
\(728\) | −99.3988 | − | 99.3988i | −0.136537 | − | 0.136537i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 513.848 | + | 277.867i | 0.703902 | + | 0.380639i | ||||
\(731\) | −139.059 | −0.190232 | ||||||||
\(732\) | −10.9148 | + | 10.9148i | −0.0149109 | + | 0.0149109i | ||||
\(733\) | −73.0619 | − | 73.0619i | −0.0996751 | − | 0.0996751i | 0.655511 | − | 0.755186i | \(-0.272453\pi\) |
−0.755186 | + | 0.655511i | \(0.772453\pi\) | |||||||
\(734\) | − | 694.684i | − | 0.946436i | ||||||
\(735\) | −58.0960 | + | 17.3163i | −0.0790422 | + | 0.0235596i | ||||
\(736\) | −180.056 | −0.244642 | ||||||||
\(737\) | 1306.97 | − | 1306.97i | 1.77336 | − | 1.77336i | ||||
\(738\) | 105.411 | + | 105.411i | 0.142833 | + | 0.142833i | ||||
\(739\) | − | 81.9526i | − | 0.110897i | −0.998462 | − | 0.0554483i | \(-0.982341\pi\) | ||
0.998462 | − | 0.0554483i | \(-0.0176588\pi\) | |||||||
\(740\) | 24.8734 | + | 83.4500i | 0.0336127 | + | 0.112770i | ||||
\(741\) | −492.263 | −0.664322 | ||||||||
\(742\) | −40.7944 | + | 40.7944i | −0.0549789 | + | 0.0549789i | ||||
\(743\) | 225.872 | + | 225.872i | 0.304000 | + | 0.304000i | 0.842577 | − | 0.538577i | \(-0.181038\pi\) |
−0.538577 | + | 0.842577i | \(0.681038\pi\) | |||||||
\(744\) | 245.386i | 0.329820i | ||||||||
\(745\) | −490.784 | + | 907.589i | −0.658771 | + | 1.21824i | ||||
\(746\) | 867.319 | 1.16263 | ||||||||
\(747\) | 160.286 | − | 160.286i | 0.214573 | − | 0.214573i | ||||
\(748\) | 34.8644 | + | 34.8644i | 0.0466101 | + | 0.0466101i | ||||
\(749\) | − | 86.6182i | − | 0.115645i | ||||||
\(750\) | 25.5797 | + | 305.116i | 0.0341062 | + | 0.406821i | ||||
\(751\) | 795.157 | 1.05880 | 0.529399 | − | 0.848373i | \(-0.322417\pi\) | ||||
0.529399 | + | 0.848373i | \(0.322417\pi\) | |||||||
\(752\) | 80.6581 | − | 80.6581i | 0.107258 | − | 0.107258i | ||||
\(753\) | −386.390 | − | 386.390i | −0.513134 | − | 0.513134i | ||||
\(754\) | 87.5989i | 0.116179i | ||||||||
\(755\) | −226.427 | − | 122.442i | −0.299903 | − | 0.162175i | ||||
\(756\) | 27.4955 | 0.0363696 | ||||||||
\(757\) | −43.3607 | + | 43.3607i | −0.0572796 | + | 0.0572796i | −0.735166 | − | 0.677887i | \(-0.762896\pi\) |
0.677887 | + | 0.735166i | \(0.262896\pi\) | |||||||
\(758\) | 5.82662 | + | 5.82662i | 0.00768684 | + | 0.00768684i | ||||
\(759\) | 814.701i | 1.07339i | ||||||||
\(760\) | −205.053 | + | 61.1190i | −0.269807 | + | 0.0804197i | ||||
\(761\) | 448.207 | 0.588972 | 0.294486 | − | 0.955656i | \(-0.404852\pi\) | ||||
0.294486 | + | 0.955656i | \(0.404852\pi\) | |||||||
\(762\) | 422.972 | − | 422.972i | 0.555081 | − | 0.555081i | ||||
\(763\) | −265.346 | − | 265.346i | −0.347767 | − | 0.347767i | ||||
\(764\) | 297.251i | 0.389073i | ||||||||
\(765\) | −7.14793 | − | 23.9812i | −0.00934370 | − | 0.0313480i | ||||
\(766\) | 169.571 | 0.221372 | ||||||||
\(767\) | 885.657 | − | 885.657i | 1.15470 | − | 1.15470i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 126.308i | − | 0.164249i | −0.996622 | − | 0.0821245i | \(-0.973829\pi\) | ||
0.996622 | − | 0.0821245i | \(-0.0261705\pi\) | |||||||
\(770\) | −131.504 | + | 243.185i | −0.170784 | + | 0.315825i | ||||
\(771\) | 675.432 | 0.876046 | ||||||||
\(772\) | −316.126 | + | 316.126i | −0.409489 | + | 0.409489i | ||||
\(773\) | −534.661 | − | 534.661i | −0.691670 | − | 0.691670i | 0.270929 | − | 0.962599i | \(-0.412669\pi\) |
−0.962599 | + | 0.270929i | \(0.912669\pi\) | |||||||
\(774\) | 353.650i | 0.456913i | ||||||||
\(775\) | 685.580 | + | 1047.88i | 0.884619 | + | 1.35211i | ||||
\(776\) | 361.425 | 0.465754 | ||||||||
\(777\) | 28.2165 | − | 28.2165i | 0.0363147 | − | 0.0363147i | ||||
\(778\) | −287.140 | − | 287.140i | −0.369075 | − | 0.369075i | ||||
\(779\) | 531.616i | 0.682434i | ||||||||
\(780\) | 286.194 | + | 154.761i | 0.366916 | + | 0.198412i | ||||
\(781\) | −1024.37 | −1.31161 | ||||||||
\(782\) | 53.1001 | − | 53.1001i | 0.0679030 | − | 0.0679030i | ||||
\(783\) | −12.1157 | − | 12.1157i | −0.0154734 | − | 0.0154734i | ||||
\(784\) | 28.0000i | 0.0357143i | ||||||||
\(785\) | −621.983 | + | 185.391i | −0.792335 | + | 0.236166i | ||||
\(786\) | −361.397 | −0.459793 | ||||||||
\(787\) | −1038.23 | + | 1038.23i | −1.31922 | + | 1.31922i | −0.404825 | + | 0.914394i | \(0.632668\pi\) |
−0.914394 | + | 0.404825i | \(0.867332\pi\) | |||||||
\(788\) | −53.5413 | − | 53.5413i | −0.0679458 | − | 0.0679458i | ||||
\(789\) | 300.661i | 0.381065i | ||||||||
\(790\) | 106.708 | + | 358.005i | 0.135074 | + | 0.453171i | ||||
\(791\) | −425.598 | −0.538051 | ||||||||
\(792\) | 88.6657 | − | 88.6657i | 0.111952 | − | 0.111952i | ||||
\(793\) | 59.1869 | + | 59.1869i | 0.0746367 | + | 0.0746367i | ||||
\(794\) | 179.103i | 0.225570i | ||||||||
\(795\) | 63.5158 | − | 117.457i | 0.0798941 | − | 0.147745i | ||||
\(796\) | 343.581 | 0.431634 | ||||||||
\(797\) | −294.158 | + | 294.158i | −0.369081 | + | 0.369081i | −0.867142 | − | 0.498061i | \(-0.834046\pi\) |
0.498061 | + | 0.867142i | \(0.334046\pi\) | |||||||
\(798\) | 69.3336 | + | 69.3336i | 0.0868842 | + | 0.0868842i | ||||
\(799\) | 47.5735i | 0.0595413i | ||||||||
\(800\) | 138.430 | + | 28.9326i | 0.173038 | + | 0.0361658i | ||||
\(801\) | −64.0658 | −0.0799822 | ||||||||
\(802\) | 649.944 | − | 649.944i | 0.810405 | − | 0.810405i | ||||
\(803\) | −863.258 | − | 863.258i | −1.07504 | − | 1.07504i | ||||
\(804\) | 433.278i | 0.538902i | ||||||||
\(805\) | 370.383 | + | 200.287i | 0.460103 | + | 0.248804i | ||||
\(806\) | 1330.64 | 1.65092 | ||||||||
\(807\) | 76.3300 | − | 76.3300i | 0.0945849 | − | 0.0945849i | ||||
\(808\) | 87.2218 | + | 87.2218i | 0.107948 | + | 0.107948i | ||||
\(809\) | 22.0860i | 0.0273004i | 0.999907 | + | 0.0136502i | \(0.00434513\pi\) | ||||
−0.999907 | + | 0.0136502i | \(0.995655\pi\) | |||||||
\(810\) | −60.9881 | + | 18.1783i | −0.0752939 | + | 0.0224424i | ||||
\(811\) | −242.865 | −0.299464 | −0.149732 | − | 0.988727i | \(-0.547841\pi\) | ||||
−0.149732 | + | 0.988727i | \(0.547841\pi\) | |||||||
\(812\) | 12.3380 | − | 12.3380i | 0.0151946 | − | 0.0151946i | ||||
\(813\) | 156.355 | + | 156.355i | 0.192318 | + | 0.192318i | ||||
\(814\) | − | 181.982i | − | 0.223565i | ||||||
\(815\) | 22.5110 | + | 75.5242i | 0.0276209 | + | 0.0926677i | ||||
\(816\) | −11.5580 | −0.0141642 | ||||||||
\(817\) | −891.779 | + | 891.779i | −1.09153 | + | 1.09153i | ||||
\(818\) | 717.337 | + | 717.337i | 0.876940 | + | 0.876940i | ||||
\(819\) | − | 149.098i | − | 0.182049i | ||||||
\(820\) | 167.134 | − | 309.074i | 0.203822 | − | 0.376919i | ||||
\(821\) | 228.561 | 0.278394 | 0.139197 | − | 0.990265i | \(-0.455548\pi\) | ||||
0.139197 | + | 0.990265i | \(0.455548\pi\) | |||||||
\(822\) | −236.598 | + | 236.598i | −0.287832 | + | 0.287832i | ||||
\(823\) | −641.691 | − | 641.691i | −0.779698 | − | 0.779698i | 0.200081 | − | 0.979779i | \(-0.435879\pi\) |
−0.979779 | + | 0.200081i | \(0.935879\pi\) | |||||||
\(824\) | − | 195.455i | − | 0.237203i | ||||||
\(825\) | 130.911 | − | 626.355i | 0.158681 | − | 0.759218i | ||||
\(826\) | −249.484 | −0.302039 | ||||||||
\(827\) | −1075.03 | + | 1075.03i | −1.29992 | + | 1.29992i | −0.371479 | + | 0.928441i | \(0.621149\pi\) |
−0.928441 | + | 0.371479i | \(0.878851\pi\) | |||||||
\(828\) | −135.042 | − | 135.042i | −0.163094 | − | 0.163094i | ||||
\(829\) | − | 530.478i | − | 0.639901i | −0.947434 | − | 0.319950i | \(-0.896334\pi\) | ||
0.947434 | − | 0.319950i | \(-0.103666\pi\) | |||||||
\(830\) | −469.973 | − | 254.141i | −0.566232 | − | 0.306194i | ||||
\(831\) | −141.302 | −0.170039 | ||||||||
\(832\) | 106.262 | − | 106.262i | 0.127718 | − | 0.127718i | ||||
\(833\) | −8.25744 | − | 8.25744i | −0.00991289 | − | 0.00991289i | ||||
\(834\) | − | 451.188i | − | 0.540992i | ||||||
\(835\) | −1523.42 | + | 454.077i | −1.82446 | + | 0.543804i | ||||
\(836\) | 447.166 | 0.534887 | ||||||||
\(837\) | −184.039 | + | 184.039i | −0.219880 | + | 0.219880i | ||||
\(838\) | 680.885 | + | 680.885i | 0.812511 | + | 0.812511i | ||||
\(839\) | 618.719i | 0.737448i | 0.929539 | + | 0.368724i | \(0.120205\pi\) | ||||
−0.929539 | + | 0.368724i | \(0.879795\pi\) | |||||||
\(840\) | −18.5119 | − | 62.1072i | −0.0220380 | − | 0.0739372i | ||||
\(841\) | 830.127 | 0.987071 | ||||||||
\(842\) | −710.333 | + | 710.333i | −0.843626 | + | 0.843626i | ||||
\(843\) | 146.200 | + | 146.200i | 0.173429 | + | 0.173429i | ||||
\(844\) | 604.864i | 0.716664i | ||||||||
\(845\) | 437.281 | − | 808.647i | 0.517492 | − | 0.956979i | ||||
\(846\) | 120.987 | 0.143011 | ||||||||
\(847\) | 182.177 | − | 182.177i | 0.215085 | − | 0.215085i | ||||
\(848\) | −43.6110 | − | 43.6110i | −0.0514281 | − | 0.0514281i | ||||
\(849\) | − | 429.290i | − | 0.505642i | ||||||
\(850\) | −49.3567 | + | 32.2918i | −0.0580667 | + | 0.0379903i | ||||
\(851\) | −277.167 | −0.325696 | ||||||||
\(852\) | 169.796 | − | 169.796i | 0.199291 | − | 0.199291i | ||||
\(853\) | 164.001 | + | 164.001i | 0.192264 | + | 0.192264i | 0.796674 | − | 0.604410i | \(-0.206591\pi\) |
−0.604410 | + | 0.796674i | \(0.706591\pi\) | |||||||
\(854\) | − | 16.6726i | − | 0.0195229i | ||||||
\(855\) | −199.629 | − | 107.951i | −0.233484 | − | 0.126258i | ||||
\(856\) | 92.5987 | 0.108176 | ||||||||
\(857\) | 889.068 | − | 889.068i | 1.03742 | − | 1.03742i | 0.0381473 | − | 0.999272i | \(-0.487854\pi\) |
0.999272 | − | 0.0381473i | \(-0.0121456\pi\) | |||||||
\(858\) | −480.803 | − | 480.803i | −0.560376 | − | 0.560376i | ||||
\(859\) | 1203.95i | 1.40157i | 0.713374 | + | 0.700783i | \(0.247166\pi\) | ||||
−0.713374 | + | 0.700783i | \(0.752834\pi\) | |||||||
\(860\) | 798.832 | − | 238.103i | 0.928875 | − | 0.276864i | ||||
\(861\) | −161.018 | −0.187012 | ||||||||
\(862\) | −785.543 | + | 785.543i | −0.911303 | + | 0.911303i | ||||
\(863\) | 813.145 | + | 813.145i | 0.942230 | + | 0.942230i | 0.998420 | − | 0.0561900i | \(-0.0178953\pi\) |
−0.0561900 | + | 0.998420i | \(0.517895\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −87.7703 | − | 294.468i | −0.101469 | − | 0.340426i | ||||
\(866\) | −968.858 | −1.11877 | ||||||||
\(867\) | −350.543 | + | 350.543i | −0.404317 | + | 0.404317i | ||||
\(868\) | −187.416 | − | 187.416i | −0.215918 | − | 0.215918i | ||||
\(869\) | − | 780.712i | − | 0.898403i | ||||||
\(870\) | −19.2100 | + | 35.5243i | −0.0220805 | + | 0.0408326i | ||||
\(871\) | 2349.51 | 2.69749 | ||||||||
\(872\) | 283.667 | − | 283.667i | 0.325307 | − | 0.325307i | ||||
\(873\) | 271.069 | + | 271.069i | 0.310502 | + | 0.310502i | ||||
\(874\) | − | 681.056i | − | 0.779240i | ||||||
\(875\) | −252.573 | − | 213.499i | −0.288655 | − | 0.243999i | ||||
\(876\) | 286.182 | 0.326691 | ||||||||
\(877\) | −233.930 | + | 233.930i | −0.266739 | + | 0.266739i | −0.827785 | − | 0.561046i | \(-0.810399\pi\) |
0.561046 | + | 0.827785i | \(0.310399\pi\) | |||||||
\(878\) | 558.366 | + | 558.366i | 0.635952 | + | 0.635952i | ||||
\(879\) | 549.308i | 0.624923i | ||||||||
\(880\) | −259.976 | − | 140.584i | −0.295427 | − | 0.159754i | ||||
\(881\) | 34.2672 | 0.0388957 | 0.0194479 | − | 0.999811i | \(-0.493809\pi\) | ||||
0.0194479 | + | 0.999811i | \(0.493809\pi\) | |||||||
\(882\) | −21.0000 | + | 21.0000i | −0.0238095 | + | 0.0238095i | ||||
\(883\) | 1030.29 | + | 1030.29i | 1.16680 | + | 1.16680i | 0.982955 | + | 0.183846i | \(0.0588547\pi\) |
0.183846 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(884\) | 62.6750i | 0.0708993i | ||||||||
\(885\) | 553.384 | − | 164.944i | 0.625293 | − | 0.186377i | ||||
\(886\) | −188.719 | −0.213001 | ||||||||
\(887\) | −129.771 | + | 129.771i | −0.146303 | + | 0.146303i | −0.776464 | − | 0.630161i | \(-0.782989\pi\) |
0.630161 | + | 0.776464i | \(0.282989\pi\) | |||||||
\(888\) | 30.1647 | + | 30.1647i | 0.0339693 | + | 0.0339693i | ||||
\(889\) | 646.100i | 0.726772i | ||||||||
\(890\) | 43.1337 | + | 144.713i | 0.0484648 | + | 0.162599i | ||||
\(891\) | 132.999 | 0.149269 | ||||||||
\(892\) | −341.569 | + | 341.569i | −0.382925 | + | 0.382925i | ||||
\(893\) | 305.086 | + | 305.086i | 0.341642 | + | 0.341642i | ||||
\(894\) | 505.471i | 0.565404i | ||||||||
\(895\) | −398.067 | + | 736.130i | −0.444768 | + | 0.822492i | ||||
\(896\) | −29.9333 | −0.0334077 | ||||||||
\(897\) | −732.286 | + | 732.286i | −0.816373 | + | 0.816373i | ||||
\(898\) | −642.007 | − | 642.007i | −0.714929 | − | 0.714929i | ||||
\(899\) | 165.168i | 0.183724i | ||||||||
\(900\) | 82.1231 | + | 125.522i | 0.0912479 | + | 0.139469i | ||||
\(901\) | 25.7225 | 0.0285489 | ||||||||
\(902\) | −519.240 | + | 519.240i | −0.575654 | + | 0.575654i | ||||
\(903\) | −270.105 | − | 270.105i | −0.299120 | − | 0.299120i | ||||
\(904\) | − | 454.984i | − | 0.503301i | ||||||
\(905\) | −992.931 | − | 536.934i | −1.09716 | − | 0.593297i | ||||
\(906\) | −126.106 | −0.139190 | ||||||||
\(907\) | −914.642 | + | 914.642i | −1.00843 | + | 1.00843i | −0.00846121 | + | 0.999964i | \(0.502693\pi\) |
−0.999964 | + | 0.00846121i | \(0.997307\pi\) | |||||||
\(908\) | −308.647 | − | 308.647i | −0.339919 | − | 0.339919i | ||||
\(909\) | 130.833i | 0.143930i | ||||||||
\(910\) | −336.786 | + | 100.384i | −0.370094 | + | 0.110312i | ||||
\(911\) | 75.4264 | 0.0827952 | 0.0413976 | − | 0.999143i | \(-0.486819\pi\) | ||||
0.0413976 | + | 0.999143i | \(0.486819\pi\) | |||||||
\(912\) | −74.1208 | + | 74.1208i | −0.0812728 | + | 0.0812728i | ||||
\(913\) | 789.548 | + | 789.548i | 0.864784 | + | 0.864784i | ||||
\(914\) | 641.188i | 0.701519i | ||||||||
\(915\) | 11.0229 | + | 36.9817i | 0.0120469 | + | 0.0404172i | ||||
\(916\) | 67.4485 | 0.0736337 | ||||||||
\(917\) | 276.022 | − | 276.022i | 0.301005 | − | 0.301005i | ||||
\(918\) | −8.66850 | − | 8.66850i | −0.00944281 | − | 0.00944281i | ||||
\(919\) | 1008.57i | 1.09747i | 0.835998 | + | 0.548733i | \(0.184889\pi\) | ||||
−0.835998 | + | 0.548733i | \(0.815111\pi\) | |||||||
\(920\) | −214.116 | + | 395.956i | −0.232734 | + | 0.430387i | ||||
\(921\) | 495.693 | 0.538212 | ||||||||
\(922\) | 300.193 | − | 300.193i | 0.325589 | − | 0.325589i | ||||
\(923\) | −920.742 | − | 920.742i | −0.997554 | − | 0.997554i | ||||
\(924\) | 135.439i | 0.146579i | ||||||||
\(925\) | 213.091 | + | 44.5370i | 0.230368 | + | 0.0481481i | ||||
\(926\) | −117.831 | −0.127247 | ||||||||
\(927\) | 146.591 | − | 146.591i | 0.158135 | − | 0.158135i | ||||
\(928\) | 13.1899 | + | 13.1899i | 0.0142133 | + | 0.0142133i | ||||
\(929\) | 1240.03i | 1.33480i | 0.744699 | + | 0.667400i | \(0.232593\pi\) | ||||
−0.744699 | + | 0.667400i | \(0.767407\pi\) | |||||||
\(930\) | 539.620 | + | 291.803i | 0.580236 | + | 0.313767i | ||||
\(931\) | −105.909 | −0.113758 | ||||||||
\(932\) | −415.997 | + | 415.997i | −0.446348 | + | 0.446348i | ||||
\(933\) | −467.992 | − | 467.992i | −0.501599 | − | 0.501599i | ||||
\(934\) | − | 724.995i | − | 0.776226i | ||||||
\(935\) | 118.128 | − | 35.2098i | 0.126340 | − | 0.0376575i | ||||
\(936\) | 159.393 | 0.170291 | ||||||||
\(937\) | 239.199 | − | 239.199i | 0.255282 | − | 0.255282i | −0.567850 | − | 0.823132i | \(-0.692225\pi\) |
0.823132 | + | 0.567850i | \(0.192225\pi\) | |||||||
\(938\) | −330.921 | − | 330.921i | −0.352794 | − | 0.352794i | ||||
\(939\) | − | 576.719i | − | 0.614185i | ||||||
\(940\) | −81.4572 | − | 273.288i | −0.0866566 | − | 0.290732i | ||||
\(941\) | 1412.22 | 1.50077 | 0.750384 | − | 0.661003i | \(-0.229869\pi\) | ||||
0.750384 | + | 0.661003i | \(0.229869\pi\) | |||||||
\(942\) | −224.829 | + | 224.829i | −0.238672 | + | 0.238672i | ||||
\(943\) | 790.828 | + | 790.828i | 0.838630 | + | 0.838630i | ||||
\(944\) | − | 266.710i | − | 0.282531i | ||||||
\(945\) | 32.6965 | − | 60.4644i | 0.0345995 | − | 0.0639835i | ||||
\(946\) | −1742.04 | −1.84148 | ||||||||
\(947\) | 13.0937 | − | 13.0937i | 0.0138265 | − | 0.0138265i | −0.700160 | − | 0.713986i | \(-0.746888\pi\) |
0.713986 | + | 0.700160i | \(0.246888\pi\) | |||||||
\(948\) | 129.408 | + | 129.408i | 0.136507 | + | 0.136507i | ||||
\(949\) | − | 1551.86i | − | 1.63526i | ||||||
\(950\) | −109.436 | + | 523.606i | −0.115196 | + | 0.551165i | ||||
\(951\) | 729.223 | 0.766796 | ||||||||
\(952\) | 8.82757 | − | 8.82757i | 0.00927266 | − | 0.00927266i | ||||
\(953\) | −1186.29 | − | 1186.29i | −1.24480 | − | 1.24480i | −0.957988 | − | 0.286809i | \(-0.907406\pi\) |
−0.286809 | − | 0.957988i | \(-0.592594\pi\) | |||||||
\(954\) | − | 65.4165i | − | 0.0685708i | ||||||
\(955\) | 653.676 | + | 353.479i | 0.684477 | + | 0.370136i | ||||
\(956\) | −99.4325 | −0.104009 | ||||||||
\(957\) | 59.6804 | − | 59.6804i | 0.0623619 | − | 0.0623619i | ||||
\(958\) | −233.704 | − | 233.704i | −0.243950 | − | 0.243950i | ||||
\(959\) | − | 361.409i | − | 0.376861i | ||||||
\(960\) | 66.3954 | − | 19.7901i | 0.0691619 | − | 0.0206147i | ||||
\(961\) | 1547.92 | 1.61074 | ||||||||
\(962\) | 163.573 | − | 163.573i | 0.170034 | − | 0.170034i | ||||
\(963\) | 69.4491 | + | 69.4491i | 0.0721174 | + | 0.0721174i | ||||
\(964\) | 99.9432i | 0.103676i | ||||||||
\(965\) | 319.258 | + | 1071.11i | 0.330837 | + | 1.10995i | ||||
\(966\) | 206.280 | 0.213541 | ||||||||
\(967\) | 989.527 | − | 989.527i | 1.02330 | − | 1.02330i | 0.0235735 | − | 0.999722i | \(-0.492496\pi\) |
0.999722 | − | 0.0235735i | \(-0.00750437\pi\) | |||||||
\(968\) | 194.756 | + | 194.756i | 0.201194 | + | 0.201194i | ||||
\(969\) | − | 43.7177i | − | 0.0451163i | ||||||
\(970\) | 429.792 | − | 794.798i | 0.443084 | − | 0.819379i | ||||
\(971\) | 104.077 | 0.107185 | 0.0535927 | − | 0.998563i | \(-0.482933\pi\) | ||||
0.0535927 | + | 0.998563i | \(0.482933\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 344.600 | + | 344.600i | 0.354163 | + | 0.354163i | ||||
\(974\) | 468.055i | 0.480549i | ||||||||
\(975\) | 680.662 | − | 445.325i | 0.698115 | − | 0.456743i | ||||
\(976\) | 17.8237 | 0.0182620 | ||||||||
\(977\) | −635.859 | + | 635.859i | −0.650828 | + | 0.650828i | −0.953192 | − | 0.302364i | \(-0.902224\pi\) |
0.302364 | + | 0.953192i | \(0.402224\pi\) | |||||||
\(978\) | 27.2998 | + | 27.2998i | 0.0279139 | + | 0.0279139i | ||||
\(979\) | − | 315.580i | − | 0.322349i | ||||||
\(980\) | 61.5739 | + | 33.2965i | 0.0628305 | + | 0.0339760i | ||||
\(981\) | 425.501 | 0.433742 | ||||||||
\(982\) | −29.6268 | + | 29.6268i | −0.0301699 | + | 0.0301699i | ||||
\(983\) | 1166.39 | + | 1166.39i | 1.18656 | + | 1.18656i | 0.978011 | + | 0.208553i | \(0.0668752\pi\) |
0.208553 | + | 0.978011i | \(0.433125\pi\) | |||||||
\(984\) | − | 172.135i | − | 0.174934i | ||||||
\(985\) | −181.410 | + | 54.0718i | −0.184173 | + | 0.0548952i | ||||
\(986\) | −7.77963 | −0.00789009 | ||||||||
\(987\) | −92.4054 | + | 92.4054i | −0.0936225 | + | 0.0936225i | ||||
\(988\) | 401.931 | + | 401.931i | 0.406813 | + | 0.406813i | ||||
\(989\) | 2653.21i | 2.68272i | ||||||||
\(990\) | −89.5442 | − | 300.420i | −0.0904487 | − | 0.303454i | ||||
\(991\) | −978.880 | −0.987770 | −0.493885 | − | 0.869527i | \(-0.664424\pi\) | ||||
−0.493885 | + | 0.869527i | \(0.664424\pi\) | |||||||
\(992\) | 200.357 | − | 200.357i | 0.201972 | − | 0.201972i | ||||
\(993\) | −241.702 | − | 241.702i | −0.243406 | − | 0.243406i | ||||
\(994\) | 259.367i | 0.260933i | ||||||||
\(995\) | 408.573 | − | 755.558i | 0.410626 | − | 0.759354i | ||||
\(996\) | −261.746 | −0.262797 | ||||||||
\(997\) | 646.604 | − | 646.604i | 0.648550 | − | 0.648550i | −0.304093 | − | 0.952642i | \(-0.598353\pi\) |
0.952642 | + | 0.304093i | \(0.0983532\pi\) | |||||||
\(998\) | −322.566 | − | 322.566i | −0.323213 | − | 0.323213i | ||||
\(999\) | 45.2471i | 0.0452924i |
(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.b.43.5 | ✓ | 16 | |
3.2 | odd | 2 | 630.3.o.f.253.7 | 16 | |||
5.2 | odd | 4 | inner | 210.3.l.b.127.5 | yes | 16 | |
5.3 | odd | 4 | 1050.3.l.h.757.1 | 16 | |||
5.4 | even | 2 | 1050.3.l.h.43.1 | 16 | |||
15.2 | even | 4 | 630.3.o.f.127.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.b.43.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
210.3.l.b.127.5 | yes | 16 | 5.2 | odd | 4 | inner | |
630.3.o.f.127.7 | 16 | 15.2 | even | 4 | |||
630.3.o.f.253.7 | 16 | 3.2 | odd | 2 | |||
1050.3.l.h.43.1 | 16 | 5.4 | even | 2 | |||
1050.3.l.h.757.1 | 16 | 5.3 | odd | 4 |