Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(391,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.391");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.c (of order \(2\), degree \(1\), 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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.10 | ||
Root | \(0.309204 + 1.38000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.391 |
Dual form | 420.2.c.b.391.9 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309204 | + | 1.38000i | 0.218640 | + | 0.975806i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.80879 | + | 0.853401i | −0.904393 | + | 0.426701i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0.309204 | + | 1.38000i | 0.126232 | + | 0.563382i | ||||
\(7\) | 2.64459 | + | 0.0785232i | 0.999559 | + | 0.0296790i | ||||
\(8\) | −1.73698 | − | 2.23224i | −0.614114 | − | 0.789218i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.38000 | + | 0.309204i | −0.436394 | + | 0.0977789i | ||||
\(11\) | 0.987080i | 0.297616i | 0.988866 | + | 0.148808i | \(0.0475436\pi\) | ||||
−0.988866 | + | 0.148808i | \(0.952456\pi\) | |||||||
\(12\) | −1.80879 | + | 0.853401i | −0.522151 | + | 0.246356i | ||||
\(13\) | 4.69157i | 1.30121i | 0.759417 | + | 0.650604i | \(0.225484\pi\) | ||||
−0.759417 | + | 0.650604i | \(0.774516\pi\) | |||||||
\(14\) | 0.709355 | + | 3.67380i | 0.189583 | + | 0.981865i | ||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 2.54341 | − | 3.08724i | 0.635853 | − | 0.771810i | ||||
\(17\) | 3.93531i | 0.954453i | 0.878780 | + | 0.477227i | \(0.158358\pi\) | ||||
−0.878780 | + | 0.477227i | \(0.841642\pi\) | |||||||
\(18\) | 0.309204 | + | 1.38000i | 0.0728801 | + | 0.325269i | ||||
\(19\) | −0.223896 | −0.0513653 | −0.0256826 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256826 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(20\) | −0.853401 | − | 1.80879i | −0.190826 | − | 0.404457i | ||||
\(21\) | 2.64459 | + | 0.0785232i | 0.577096 | + | 0.0171352i | ||||
\(22\) | −1.36217 | + | 0.305209i | −0.290415 | + | 0.0650708i | ||||
\(23\) | − | 5.88128i | − | 1.22633i | −0.789954 | − | 0.613166i | \(-0.789896\pi\) | ||
0.789954 | − | 0.613166i | \(-0.210104\pi\) | |||||||
\(24\) | −1.73698 | − | 2.23224i | −0.354559 | − | 0.455655i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −6.47436 | + | 1.45065i | −1.26973 | + | 0.284497i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.85050 | + | 2.11486i | −0.916659 | + | 0.399671i | ||||
\(29\) | −10.2502 | −1.90342 | −0.951710 | − | 0.307000i | \(-0.900675\pi\) | ||||
−0.951710 | + | 0.307000i | \(0.900675\pi\) | |||||||
\(30\) | −1.38000 | + | 0.309204i | −0.251952 | + | 0.0564527i | ||||
\(31\) | 2.77439 | 0.498295 | 0.249147 | − | 0.968466i | \(-0.419850\pi\) | ||||
0.249147 | + | 0.968466i | \(0.419850\pi\) | |||||||
\(32\) | 5.04682 | + | 2.55532i | 0.892160 | + | 0.451720i | ||||
\(33\) | 0.987080i | 0.171829i | ||||||||
\(34\) | −5.43072 | + | 1.21681i | −0.931361 | + | 0.208682i | ||||
\(35\) | −0.0785232 | + | 2.64459i | −0.0132728 | + | 0.447017i | ||||
\(36\) | −1.80879 | + | 0.853401i | −0.301464 | + | 0.142234i | ||||
\(37\) | 8.26915 | 1.35944 | 0.679720 | − | 0.733472i | \(-0.262101\pi\) | ||||
0.679720 | + | 0.733472i | \(0.262101\pi\) | |||||||
\(38\) | −0.0692296 | − | 0.308976i | −0.0112305 | − | 0.0501225i | ||||
\(39\) | 4.69157i | 0.751253i | ||||||||
\(40\) | 2.23224 | − | 1.73698i | 0.352949 | − | 0.274640i | ||||
\(41\) | − | 7.34910i | − | 1.14774i | −0.818948 | − | 0.573868i | \(-0.805442\pi\) | ||
0.818948 | − | 0.573868i | \(-0.194558\pi\) | |||||||
\(42\) | 0.709355 | + | 3.67380i | 0.109456 | + | 0.566880i | ||||
\(43\) | − | 4.32318i | − | 0.659278i | −0.944107 | − | 0.329639i | \(-0.893073\pi\) | ||
0.944107 | − | 0.329639i | \(-0.106927\pi\) | |||||||
\(44\) | −0.842376 | − | 1.78542i | −0.126993 | − | 0.269162i | ||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 8.11616 | − | 1.81852i | 1.19666 | − | 0.268126i | ||||
\(47\) | 2.40779 | 0.351212 | 0.175606 | − | 0.984461i | \(-0.443812\pi\) | ||||
0.175606 | + | 0.984461i | \(0.443812\pi\) | |||||||
\(48\) | 2.54341 | − | 3.08724i | 0.367110 | − | 0.445605i | ||||
\(49\) | 6.98767 | + | 0.415323i | 0.998238 | + | 0.0593318i | ||||
\(50\) | −0.309204 | − | 1.38000i | −0.0437280 | − | 0.195161i | ||||
\(51\) | 3.93531i | 0.551054i | ||||||||
\(52\) | −4.00380 | − | 8.48605i | −0.555227 | − | 1.17680i | ||||
\(53\) | −8.35002 | −1.14696 | −0.573482 | − | 0.819218i | \(-0.694408\pi\) | ||||
−0.573482 | + | 0.819218i | \(0.694408\pi\) | |||||||
\(54\) | 0.309204 | + | 1.38000i | 0.0420773 | + | 0.187794i | ||||
\(55\) | −0.987080 | −0.133098 | ||||||||
\(56\) | −4.41830 | − | 6.03976i | −0.590420 | − | 0.807096i | ||||
\(57\) | −0.223896 | −0.0296558 | ||||||||
\(58\) | −3.16941 | − | 14.1453i | −0.416164 | − | 1.85737i | ||||
\(59\) | 13.9829 | 1.82042 | 0.910210 | − | 0.414147i | \(-0.135920\pi\) | ||||
0.910210 | + | 0.414147i | \(0.135920\pi\) | |||||||
\(60\) | −0.853401 | − | 1.80879i | −0.110174 | − | 0.233513i | ||||
\(61\) | 4.93374i | 0.631700i | 0.948809 | + | 0.315850i | \(0.102290\pi\) | ||||
−0.948809 | + | 0.315850i | \(0.897710\pi\) | |||||||
\(62\) | 0.857851 | + | 3.82865i | 0.108947 | + | 0.486239i | ||||
\(63\) | 2.64459 | + | 0.0785232i | 0.333186 | + | 0.00989300i | ||||
\(64\) | −1.96583 | + | 7.75471i | −0.245729 | + | 0.969339i | ||||
\(65\) | −4.69157 | −0.581918 | ||||||||
\(66\) | −1.36217 | + | 0.305209i | −0.167671 | + | 0.0375686i | ||||
\(67\) | − | 7.84723i | − | 0.958692i | −0.877626 | − | 0.479346i | \(-0.840874\pi\) | ||
0.877626 | − | 0.479346i | \(-0.159126\pi\) | |||||||
\(68\) | −3.35840 | − | 7.11814i | −0.407266 | − | 0.863201i | ||||
\(69\) | − | 5.88128i | − | 0.708023i | ||||||
\(70\) | −3.67380 | + | 0.709355i | −0.439103 | + | 0.0847841i | ||||
\(71\) | 8.49881i | 1.00862i | 0.863522 | + | 0.504311i | \(0.168254\pi\) | ||||
−0.863522 | + | 0.504311i | \(0.831746\pi\) | |||||||
\(72\) | −1.73698 | − | 2.23224i | −0.204705 | − | 0.263073i | ||||
\(73\) | − | 14.4665i | − | 1.69318i | −0.532244 | − | 0.846591i | \(-0.678651\pi\) | ||
0.532244 | − | 0.846591i | \(-0.321349\pi\) | |||||||
\(74\) | 2.55685 | + | 11.4114i | 0.297228 | + | 1.32655i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0.404980 | − | 0.191073i | 0.0464544 | − | 0.0219176i | ||||
\(77\) | −0.0775087 | + | 2.61042i | −0.00883294 | + | 0.297485i | ||||
\(78\) | −6.47436 | + | 1.45065i | −0.733077 | + | 0.164254i | ||||
\(79\) | − | 11.5183i | − | 1.29591i | −0.761678 | − | 0.647956i | \(-0.775624\pi\) | ||
0.761678 | − | 0.647956i | \(-0.224376\pi\) | |||||||
\(80\) | 3.08724 | + | 2.54341i | 0.345164 | + | 0.284362i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.1417 | − | 2.27237i | 1.11997 | − | 0.250941i | ||||
\(83\) | −1.67114 | −0.183431 | −0.0917156 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917156 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(84\) | −4.85050 | + | 2.11486i | −0.529233 | + | 0.230750i | ||||
\(85\) | −3.93531 | −0.426845 | ||||||||
\(86\) | 5.96597 | − | 1.33674i | 0.643327 | − | 0.144145i | ||||
\(87\) | −10.2502 | −1.09894 | ||||||||
\(88\) | 2.20340 | − | 1.71453i | 0.234884 | − | 0.182770i | ||||
\(89\) | 0.493375i | 0.0522977i | 0.999658 | + | 0.0261488i | \(0.00832438\pi\) | ||||
−0.999658 | + | 0.0261488i | \(0.991676\pi\) | |||||||
\(90\) | −1.38000 | + | 0.309204i | −0.145465 | + | 0.0325930i | ||||
\(91\) | −0.368398 | + | 12.4073i | −0.0386186 | + | 1.30064i | ||||
\(92\) | 5.01910 | + | 10.6380i | 0.523277 | + | 1.10909i | ||||
\(93\) | 2.77439 | 0.287690 | ||||||||
\(94\) | 0.744498 | + | 3.32274i | 0.0767891 | + | 0.342715i | ||||
\(95\) | − | 0.223896i | − | 0.0229713i | ||||||
\(96\) | 5.04682 | + | 2.55532i | 0.515089 | + | 0.260801i | ||||
\(97\) | − | 4.31036i | − | 0.437650i | −0.975764 | − | 0.218825i | \(-0.929778\pi\) | ||
0.975764 | − | 0.218825i | \(-0.0702224\pi\) | |||||||
\(98\) | 1.58747 | + | 9.77138i | 0.160359 | + | 0.987059i | ||||
\(99\) | 0.987080i | 0.0992053i | ||||||||
\(100\) | 1.80879 | − | 0.853401i | 0.180879 | − | 0.0853401i | ||||
\(101\) | 6.03671i | 0.600675i | 0.953833 | + | 0.300338i | \(0.0970994\pi\) | ||||
−0.953833 | + | 0.300338i | \(0.902901\pi\) | |||||||
\(102\) | −5.43072 | + | 1.21681i | −0.537722 | + | 0.120483i | ||||
\(103\) | 7.83090 | 0.771602 | 0.385801 | − | 0.922582i | \(-0.373925\pi\) | ||||
0.385801 | + | 0.922582i | \(0.373925\pi\) | |||||||
\(104\) | 10.4727 | − | 8.14915i | 1.02694 | − | 0.799090i | ||||
\(105\) | −0.0785232 | + | 2.64459i | −0.00766308 | + | 0.258085i | ||||
\(106\) | −2.58186 | − | 11.5230i | −0.250772 | − | 1.11921i | ||||
\(107\) | − | 13.9860i | − | 1.35208i | −0.736866 | − | 0.676039i | \(-0.763695\pi\) | ||
0.736866 | − | 0.676039i | \(-0.236305\pi\) | |||||||
\(108\) | −1.80879 | + | 0.853401i | −0.174050 | + | 0.0821186i | ||||
\(109\) | 4.06579 | 0.389432 | 0.194716 | − | 0.980860i | \(-0.437621\pi\) | ||||
0.194716 | + | 0.980860i | \(0.437621\pi\) | |||||||
\(110\) | −0.305209 | − | 1.36217i | −0.0291005 | − | 0.129878i | ||||
\(111\) | 8.26915 | 0.784873 | ||||||||
\(112\) | 6.96869 | − | 7.96476i | 0.658479 | − | 0.752599i | ||||
\(113\) | −8.66412 | −0.815052 | −0.407526 | − | 0.913194i | \(-0.633608\pi\) | ||||
−0.407526 | + | 0.913194i | \(0.633608\pi\) | |||||||
\(114\) | −0.0692296 | − | 0.308976i | −0.00648394 | − | 0.0289383i | ||||
\(115\) | 5.88128 | 0.548433 | ||||||||
\(116\) | 18.5405 | − | 8.74756i | 1.72144 | − | 0.812190i | ||||
\(117\) | 4.69157i | 0.433736i | ||||||||
\(118\) | 4.32357 | + | 19.2964i | 0.398017 | + | 1.77638i | ||||
\(119\) | −0.309013 | + | 10.4073i | −0.0283272 | + | 0.954033i | ||||
\(120\) | 2.23224 | − | 1.73698i | 0.203775 | − | 0.158563i | ||||
\(121\) | 10.0257 | 0.911425 | ||||||||
\(122\) | −6.80855 | + | 1.52553i | −0.616417 | + | 0.138115i | ||||
\(123\) | − | 7.34910i | − | 0.662646i | ||||||
\(124\) | −5.01827 | + | 2.36767i | −0.450654 | + | 0.212623i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0.709355 | + | 3.67380i | 0.0631943 | + | 0.327288i | ||||
\(127\) | − | 5.18615i | − | 0.460197i | −0.973167 | − | 0.230098i | \(-0.926095\pi\) | ||
0.973167 | − | 0.230098i | \(-0.0739048\pi\) | |||||||
\(128\) | −11.3093 | − | 0.315057i | −0.999612 | − | 0.0278473i | ||||
\(129\) | − | 4.32318i | − | 0.380635i | ||||||
\(130\) | −1.45065 | − | 6.47436i | −0.127231 | − | 0.567839i | ||||
\(131\) | −11.3617 | −0.992679 | −0.496340 | − | 0.868128i | \(-0.665323\pi\) | ||||
−0.496340 | + | 0.868128i | \(0.665323\pi\) | |||||||
\(132\) | −0.842376 | − | 1.78542i | −0.0733194 | − | 0.155401i | ||||
\(133\) | −0.592112 | − | 0.0175810i | −0.0513427 | − | 0.00152447i | ||||
\(134\) | 10.8292 | − | 2.42640i | 0.935497 | − | 0.209609i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 8.78458 | − | 6.83554i | 0.753272 | − | 0.586143i | ||||
\(137\) | −5.85931 | −0.500595 | −0.250297 | − | 0.968169i | \(-0.580528\pi\) | ||||
−0.250297 | + | 0.968169i | \(0.580528\pi\) | |||||||
\(138\) | 8.11616 | − | 1.81852i | 0.690893 | − | 0.154802i | ||||
\(139\) | −18.1460 | −1.53912 | −0.769562 | − | 0.638572i | \(-0.779525\pi\) | ||||
−0.769562 | + | 0.638572i | \(0.779525\pi\) | |||||||
\(140\) | −2.11486 | − | 4.85050i | −0.178738 | − | 0.409942i | ||||
\(141\) | 2.40779 | 0.202772 | ||||||||
\(142\) | −11.7283 | + | 2.62786i | −0.984220 | + | 0.220525i | ||||
\(143\) | −4.63096 | −0.387260 | ||||||||
\(144\) | 2.54341 | − | 3.08724i | 0.211951 | − | 0.257270i | ||||
\(145\) | − | 10.2502i | − | 0.851235i | ||||||
\(146\) | 19.9638 | − | 4.47311i | 1.65222 | − | 0.370198i | ||||
\(147\) | 6.98767 | + | 0.415323i | 0.576333 | + | 0.0342552i | ||||
\(148\) | −14.9571 | + | 7.05690i | −1.22947 | + | 0.580074i | ||||
\(149\) | 15.4737 | 1.26766 | 0.633829 | − | 0.773473i | \(-0.281482\pi\) | ||||
0.633829 | + | 0.773473i | \(0.281482\pi\) | |||||||
\(150\) | −0.309204 | − | 1.38000i | −0.0252464 | − | 0.112676i | ||||
\(151\) | 11.5322i | 0.938474i | 0.883072 | + | 0.469237i | \(0.155471\pi\) | ||||
−0.883072 | + | 0.469237i | \(0.844529\pi\) | |||||||
\(152\) | 0.388902 | + | 0.499791i | 0.0315441 | + | 0.0405384i | ||||
\(153\) | 3.93531i | 0.318151i | ||||||||
\(154\) | −3.62634 | + | 0.700190i | −0.292219 | + | 0.0564229i | ||||
\(155\) | 2.77439i | 0.222844i | ||||||||
\(156\) | −4.00380 | − | 8.48605i | −0.320560 | − | 0.679428i | ||||
\(157\) | − | 0.806743i | − | 0.0643851i | −0.999482 | − | 0.0321926i | \(-0.989751\pi\) | ||
0.999482 | − | 0.0321926i | \(-0.0102490\pi\) | |||||||
\(158\) | 15.8952 | − | 3.56151i | 1.26456 | − | 0.283338i | ||||
\(159\) | −8.35002 | −0.662200 | ||||||||
\(160\) | −2.55532 | + | 5.04682i | −0.202015 | + | 0.398986i | ||||
\(161\) | 0.461817 | − | 15.5536i | 0.0363963 | − | 1.22579i | ||||
\(162\) | 0.309204 | + | 1.38000i | 0.0242934 | + | 0.108423i | ||||
\(163\) | 6.48272i | 0.507766i | 0.967235 | + | 0.253883i | \(0.0817077\pi\) | ||||
−0.967235 | + | 0.253883i | \(0.918292\pi\) | |||||||
\(164\) | 6.27173 | + | 13.2929i | 0.489740 | + | 1.03800i | ||||
\(165\) | −0.987080 | −0.0768441 | ||||||||
\(166\) | −0.516722 | − | 2.30616i | −0.0401054 | − | 0.178993i | ||||
\(167\) | −7.65678 | −0.592499 | −0.296250 | − | 0.955111i | \(-0.595736\pi\) | ||||
−0.296250 | + | 0.955111i | \(0.595736\pi\) | |||||||
\(168\) | −4.41830 | − | 6.03976i | −0.340879 | − | 0.465977i | ||||
\(169\) | −9.01087 | −0.693144 | ||||||||
\(170\) | −1.21681 | − | 5.43072i | −0.0933254 | − | 0.416517i | ||||
\(171\) | −0.223896 | −0.0171218 | ||||||||
\(172\) | 3.68941 | + | 7.81970i | 0.281315 | + | 0.596247i | ||||
\(173\) | − | 7.12007i | − | 0.541329i | −0.962674 | − | 0.270665i | \(-0.912757\pi\) | ||
0.962674 | − | 0.270665i | \(-0.0872434\pi\) | |||||||
\(174\) | −3.16941 | − | 14.1453i | −0.240272 | − | 1.07235i | ||||
\(175\) | −2.64459 | − | 0.0785232i | −0.199912 | − | 0.00593580i | ||||
\(176\) | 3.04735 | + | 2.51055i | 0.229703 | + | 0.189240i | ||||
\(177\) | 13.9829 | 1.05102 | ||||||||
\(178\) | −0.680856 | + | 0.152554i | −0.0510323 | + | 0.0114344i | ||||
\(179\) | − | 20.8439i | − | 1.55794i | −0.627059 | − | 0.778972i | \(-0.715742\pi\) | ||
0.627059 | − | 0.778972i | \(-0.284258\pi\) | |||||||
\(180\) | −0.853401 | − | 1.80879i | −0.0636088 | − | 0.134819i | ||||
\(181\) | 24.4428i | 1.81682i | 0.418079 | + | 0.908411i | \(0.362703\pi\) | ||||
−0.418079 | + | 0.908411i | \(0.637297\pi\) | |||||||
\(182\) | −17.2359 | + | 3.32799i | −1.27761 | + | 0.246687i | ||||
\(183\) | 4.93374i | 0.364712i | ||||||||
\(184\) | −13.1285 | + | 10.2156i | −0.967843 | + | 0.753107i | ||||
\(185\) | 8.26915i | 0.607960i | ||||||||
\(186\) | 0.857851 | + | 3.82865i | 0.0629007 | + | 0.280730i | ||||
\(187\) | −3.88447 | −0.284061 | ||||||||
\(188\) | −4.35517 | + | 2.05481i | −0.317634 | + | 0.149862i | ||||
\(189\) | 2.64459 | + | 0.0785232i | 0.192365 | + | 0.00571172i | ||||
\(190\) | 0.308976 | − | 0.0692296i | 0.0224155 | − | 0.00502244i | ||||
\(191\) | 19.3047i | 1.39684i | 0.715689 | + | 0.698419i | \(0.246113\pi\) | ||||
−0.715689 | + | 0.698419i | \(0.753887\pi\) | |||||||
\(192\) | −1.96583 | + | 7.75471i | −0.141872 | + | 0.559648i | ||||
\(193\) | −15.2505 | −1.09776 | −0.548879 | − | 0.835902i | \(-0.684945\pi\) | ||||
−0.548879 | + | 0.835902i | \(0.684945\pi\) | |||||||
\(194\) | 5.94828 | − | 1.33278i | 0.427062 | − | 0.0956880i | ||||
\(195\) | −4.69157 | −0.335971 | ||||||||
\(196\) | −12.9936 | + | 5.21206i | −0.928117 | + | 0.372290i | ||||
\(197\) | 3.00729 | 0.214260 | 0.107130 | − | 0.994245i | \(-0.465834\pi\) | ||||
0.107130 | + | 0.994245i | \(0.465834\pi\) | |||||||
\(198\) | −1.36217 | + | 0.305209i | −0.0968051 | + | 0.0216903i | ||||
\(199\) | −22.1587 | −1.57079 | −0.785395 | − | 0.618995i | \(-0.787540\pi\) | ||||
−0.785395 | + | 0.618995i | \(0.787540\pi\) | |||||||
\(200\) | 1.73698 | + | 2.23224i | 0.122823 | + | 0.157844i | ||||
\(201\) | − | 7.84723i | − | 0.553501i | ||||||
\(202\) | −8.33065 | + | 1.86658i | −0.586142 | + | 0.131332i | ||||
\(203\) | −27.1076 | − | 0.804881i | −1.90258 | − | 0.0564916i | ||||
\(204\) | −3.35840 | − | 7.11814i | −0.235135 | − | 0.498369i | ||||
\(205\) | 7.34910 | 0.513283 | ||||||||
\(206\) | 2.42135 | + | 10.8066i | 0.168703 | + | 0.752933i | ||||
\(207\) | − | 5.88128i | − | 0.408778i | ||||||
\(208\) | 14.4840 | + | 11.9326i | 1.00429 | + | 0.827377i | ||||
\(209\) | − | 0.221003i | − | 0.0152871i | ||||||
\(210\) | −3.67380 | + | 0.709355i | −0.253516 | + | 0.0489501i | ||||
\(211\) | 12.6769i | 0.872714i | 0.899774 | + | 0.436357i | \(0.143731\pi\) | ||||
−0.899774 | + | 0.436357i | \(0.856269\pi\) | |||||||
\(212\) | 15.1034 | − | 7.12592i | 1.03731 | − | 0.489410i | ||||
\(213\) | 8.49881i | 0.582329i | ||||||||
\(214\) | 19.3006 | − | 4.32453i | 1.31936 | − | 0.295618i | ||||
\(215\) | 4.32318 | 0.294838 | ||||||||
\(216\) | −1.73698 | − | 2.23224i | −0.118186 | − | 0.151885i | ||||
\(217\) | 7.33710 | + | 0.217854i | 0.498075 | + | 0.0147889i | ||||
\(218\) | 1.25716 | + | 5.61078i | 0.0851455 | + | 0.380010i | ||||
\(219\) | − | 14.4665i | − | 0.977559i | ||||||
\(220\) | 1.78542 | − | 0.842376i | 0.120373 | − | 0.0567930i | ||||
\(221\) | −18.4628 | −1.24194 | ||||||||
\(222\) | 2.55685 | + | 11.4114i | 0.171605 | + | 0.765883i | ||||
\(223\) | −6.45632 | −0.432347 | −0.216173 | − | 0.976355i | \(-0.569358\pi\) | ||||
−0.216173 | + | 0.976355i | \(0.569358\pi\) | |||||||
\(224\) | 13.1461 | + | 7.15404i | 0.878360 | + | 0.478000i | ||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −2.67898 | − | 11.9565i | −0.178203 | − | 0.795332i | ||||
\(227\) | −14.0882 | −0.935066 | −0.467533 | − | 0.883976i | \(-0.654857\pi\) | ||||
−0.467533 | + | 0.883976i | \(0.654857\pi\) | |||||||
\(228\) | 0.404980 | − | 0.191073i | 0.0268205 | − | 0.0126541i | ||||
\(229\) | 9.74932i | 0.644253i | 0.946697 | + | 0.322126i | \(0.104398\pi\) | ||||
−0.946697 | + | 0.322126i | \(0.895602\pi\) | |||||||
\(230\) | 1.81852 | + | 8.11616i | 0.119909 | + | 0.535164i | ||||
\(231\) | −0.0775087 | + | 2.61042i | −0.00509970 | + | 0.171753i | ||||
\(232\) | 17.8044 | + | 22.8810i | 1.16892 | + | 1.50221i | ||||
\(233\) | 1.64231 | 0.107591 | 0.0537955 | − | 0.998552i | \(-0.482868\pi\) | ||||
0.0537955 | + | 0.998552i | \(0.482868\pi\) | |||||||
\(234\) | −6.47436 | + | 1.45065i | −0.423242 | + | 0.0948322i | ||||
\(235\) | 2.40779i | 0.157067i | ||||||||
\(236\) | −25.2921 | + | 11.9330i | −1.64637 | + | 0.776774i | ||||
\(237\) | − | 11.5183i | − | 0.748195i | ||||||
\(238\) | −14.4576 | + | 2.79153i | −0.937144 | + | 0.180948i | ||||
\(239\) | − | 9.77724i | − | 0.632437i | −0.948686 | − | 0.316219i | \(-0.897587\pi\) | ||
0.948686 | − | 0.316219i | \(-0.102413\pi\) | |||||||
\(240\) | 3.08724 | + | 2.54341i | 0.199281 | + | 0.164177i | ||||
\(241\) | 6.84106i | 0.440671i | 0.975424 | + | 0.220336i | \(0.0707152\pi\) | ||||
−0.975424 | + | 0.220336i | \(0.929285\pi\) | |||||||
\(242\) | 3.09998 | + | 13.8354i | 0.199274 | + | 0.889373i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.21046 | − | 8.92408i | −0.269547 | − | 0.571305i | ||||
\(245\) | −0.415323 | + | 6.98767i | −0.0265340 | + | 0.446426i | ||||
\(246\) | 10.1417 | − | 2.27237i | 0.646614 | − | 0.144881i | ||||
\(247\) | − | 1.05043i | − | 0.0668370i | ||||||
\(248\) | −4.81904 | − | 6.19311i | −0.306009 | − | 0.393263i | ||||
\(249\) | −1.67114 | −0.105904 | ||||||||
\(250\) | 1.38000 | − | 0.309204i | 0.0872787 | − | 0.0195558i | ||||
\(251\) | −2.34972 | −0.148313 | −0.0741564 | − | 0.997247i | \(-0.523626\pi\) | ||||
−0.0741564 | + | 0.997247i | \(0.523626\pi\) | |||||||
\(252\) | −4.85050 | + | 2.11486i | −0.305553 | + | 0.133224i | ||||
\(253\) | 5.80530 | 0.364976 | ||||||||
\(254\) | 7.15688 | − | 1.60358i | 0.449063 | − | 0.100618i | ||||
\(255\) | −3.93531 | −0.246439 | ||||||||
\(256\) | −3.06211 | − | 15.7043i | −0.191382 | − | 0.981516i | ||||
\(257\) | − | 6.47150i | − | 0.403681i | −0.979418 | − | 0.201840i | \(-0.935308\pi\) | ||
0.979418 | − | 0.201840i | \(-0.0646922\pi\) | |||||||
\(258\) | 5.96597 | − | 1.33674i | 0.371425 | − | 0.0832220i | ||||
\(259\) | 21.8685 | + | 0.649320i | 1.35884 | + | 0.0403468i | ||||
\(260\) | 8.48605 | − | 4.00380i | 0.526283 | − | 0.248305i | ||||
\(261\) | −10.2502 | −0.634473 | ||||||||
\(262\) | −3.51309 | − | 15.6792i | −0.217040 | − | 0.968662i | ||||
\(263\) | − | 2.38076i | − | 0.146804i | −0.997302 | − | 0.0734018i | \(-0.976614\pi\) | ||
0.997302 | − | 0.0734018i | \(-0.0233856\pi\) | |||||||
\(264\) | 2.20340 | − | 1.71453i | 0.135610 | − | 0.105522i | ||||
\(265\) | − | 8.35002i | − | 0.512938i | ||||||
\(266\) | −0.158822 | − | 0.822550i | −0.00973799 | − | 0.0504338i | ||||
\(267\) | 0.493375i | 0.0301941i | ||||||||
\(268\) | 6.69684 | + | 14.1940i | 0.409075 | + | 0.867034i | ||||
\(269\) | 9.44894i | 0.576112i | 0.957614 | + | 0.288056i | \(0.0930089\pi\) | ||||
−0.957614 | + | 0.288056i | \(0.906991\pi\) | |||||||
\(270\) | −1.38000 | + | 0.309204i | −0.0839840 | + | 0.0188176i | ||||
\(271\) | −22.1827 | −1.34750 | −0.673752 | − | 0.738958i | \(-0.735318\pi\) | ||||
−0.673752 | + | 0.738958i | \(0.735318\pi\) | |||||||
\(272\) | 12.1493 | + | 10.0091i | 0.736657 | + | 0.606892i | ||||
\(273\) | −0.368398 | + | 12.4073i | −0.0222964 | + | 0.750922i | ||||
\(274\) | −1.81172 | − | 8.08583i | −0.109450 | − | 0.488483i | ||||
\(275\) | − | 0.987080i | − | 0.0595232i | ||||||
\(276\) | 5.01910 | + | 10.6380i | 0.302114 | + | 0.640331i | ||||
\(277\) | −26.7718 | −1.60856 | −0.804281 | − | 0.594249i | \(-0.797449\pi\) | ||||
−0.804281 | + | 0.594249i | \(0.797449\pi\) | |||||||
\(278\) | −5.61082 | − | 25.0414i | −0.336514 | − | 1.50189i | ||||
\(279\) | 2.77439 | 0.166098 | ||||||||
\(280\) | 6.03976 | − | 4.41830i | 0.360944 | − | 0.264044i | ||||
\(281\) | −8.64183 | −0.515529 | −0.257764 | − | 0.966208i | \(-0.582986\pi\) | ||||
−0.257764 | + | 0.966208i | \(0.582986\pi\) | |||||||
\(282\) | 0.744498 | + | 3.32274i | 0.0443342 | + | 0.197866i | ||||
\(283\) | 5.92047 | 0.351935 | 0.175968 | − | 0.984396i | \(-0.443695\pi\) | ||||
0.175968 | + | 0.984396i | \(0.443695\pi\) | |||||||
\(284\) | −7.25289 | − | 15.3725i | −0.430380 | − | 0.912191i | ||||
\(285\) | − | 0.223896i | − | 0.0132625i | ||||||
\(286\) | −1.43191 | − | 6.39071i | −0.0846707 | − | 0.377891i | ||||
\(287\) | 0.577075 | − | 19.4353i | 0.0340637 | − | 1.14723i | ||||
\(288\) | 5.04682 | + | 2.55532i | 0.297387 | + | 0.150573i | ||||
\(289\) | 1.51332 | 0.0890186 | ||||||||
\(290\) | 14.1453 | − | 3.16941i | 0.830640 | − | 0.186114i | ||||
\(291\) | − | 4.31036i | − | 0.252678i | ||||||
\(292\) | 12.3458 | + | 26.1669i | 0.722482 | + | 1.53130i | ||||
\(293\) | 26.2654i | 1.53444i | 0.641382 | + | 0.767221i | \(0.278361\pi\) | ||||
−0.641382 | + | 0.767221i | \(0.721639\pi\) | |||||||
\(294\) | 1.58747 | + | 9.77138i | 0.0925832 | + | 0.569879i | ||||
\(295\) | 13.9829i | 0.814116i | ||||||||
\(296\) | −14.3633 | − | 18.4588i | −0.834850 | − | 1.07289i | ||||
\(297\) | 0.987080i | 0.0572762i | ||||||||
\(298\) | 4.78454 | + | 21.3537i | 0.277161 | + | 1.23699i | ||||
\(299\) | 27.5925 | 1.59571 | ||||||||
\(300\) | 1.80879 | − | 0.853401i | 0.104430 | − | 0.0492712i | ||||
\(301\) | 0.339470 | − | 11.4330i | 0.0195667 | − | 0.658988i | ||||
\(302\) | −15.9144 | + | 3.56579i | −0.915768 | + | 0.205188i | ||||
\(303\) | 6.03671i | 0.346800i | ||||||||
\(304\) | −0.569460 | + | 0.691221i | −0.0326608 | + | 0.0396443i | ||||
\(305\) | −4.93374 | −0.282505 | ||||||||
\(306\) | −5.43072 | + | 1.21681i | −0.310454 | + | 0.0695606i | ||||
\(307\) | 18.5432 | 1.05832 | 0.529158 | − | 0.848524i | \(-0.322508\pi\) | ||||
0.529158 | + | 0.848524i | \(0.322508\pi\) | |||||||
\(308\) | −2.08754 | − | 4.78783i | −0.118949 | − | 0.272812i | ||||
\(309\) | 7.83090 | 0.445485 | ||||||||
\(310\) | −3.82865 | + | 0.857851i | −0.217453 | + | 0.0487227i | ||||
\(311\) | 30.8370 | 1.74861 | 0.874304 | − | 0.485379i | \(-0.161318\pi\) | ||||
0.874304 | + | 0.485379i | \(0.161318\pi\) | |||||||
\(312\) | 10.4727 | − | 8.14915i | 0.592902 | − | 0.461355i | ||||
\(313\) | − | 20.8250i | − | 1.17710i | −0.808461 | − | 0.588550i | \(-0.799699\pi\) | ||
0.808461 | − | 0.588550i | \(-0.200301\pi\) | |||||||
\(314\) | 1.11330 | − | 0.249448i | 0.0628274 | − | 0.0140772i | ||||
\(315\) | −0.0785232 | + | 2.64459i | −0.00442428 | + | 0.149006i | ||||
\(316\) | 9.82975 | + | 20.8342i | 0.552967 | + | 1.17201i | ||||
\(317\) | 5.41152 | 0.303941 | 0.151971 | − | 0.988385i | \(-0.451438\pi\) | ||||
0.151971 | + | 0.988385i | \(0.451438\pi\) | |||||||
\(318\) | −2.58186 | − | 11.5230i | −0.144784 | − | 0.646178i | ||||
\(319\) | − | 10.1178i | − | 0.566488i | ||||||
\(320\) | −7.75471 | − | 1.96583i | −0.433501 | − | 0.109893i | ||||
\(321\) | − | 13.9860i | − | 0.780622i | ||||||
\(322\) | 21.6067 | − | 4.17192i | 1.20409 | − | 0.232492i | ||||
\(323\) | − | 0.881101i | − | 0.0490258i | ||||||
\(324\) | −1.80879 | + | 0.853401i | −0.100488 | + | 0.0474112i | ||||
\(325\) | − | 4.69157i | − | 0.260242i | ||||||
\(326\) | −8.94613 | + | 2.00448i | −0.495480 | + | 0.111018i | ||||
\(327\) | 4.06579 | 0.224839 | ||||||||
\(328\) | −16.4050 | + | 12.7652i | −0.905814 | + | 0.704841i | ||||
\(329\) | 6.36760 | + | 0.189067i | 0.351057 | + | 0.0104236i | ||||
\(330\) | −0.305209 | − | 1.36217i | −0.0168012 | − | 0.0749849i | ||||
\(331\) | − | 1.77494i | − | 0.0975597i | −0.998810 | − | 0.0487799i | \(-0.984467\pi\) | ||
0.998810 | − | 0.0487799i | \(-0.0155333\pi\) | |||||||
\(332\) | 3.02273 | − | 1.42615i | 0.165894 | − | 0.0782702i | ||||
\(333\) | 8.26915 | 0.453147 | ||||||||
\(334\) | −2.36751 | − | 10.5663i | −0.129544 | − | 0.578164i | ||||
\(335\) | 7.84723 | 0.428740 | ||||||||
\(336\) | 6.96869 | − | 7.96476i | 0.380173 | − | 0.434513i | ||||
\(337\) | 22.3668 | 1.21839 | 0.609197 | − | 0.793019i | \(-0.291492\pi\) | ||||
0.609197 | + | 0.793019i | \(0.291492\pi\) | |||||||
\(338\) | −2.78620 | − | 12.4350i | −0.151549 | − | 0.676374i | ||||
\(339\) | −8.66412 | −0.470570 | ||||||||
\(340\) | 7.11814 | − | 3.35840i | 0.386035 | − | 0.182135i | ||||
\(341\) | 2.73854i | 0.148300i | ||||||||
\(342\) | −0.0692296 | − | 0.308976i | −0.00374351 | − | 0.0167075i | ||||
\(343\) | 18.4469 | + | 1.64705i | 0.996038 | + | 0.0889324i | ||||
\(344\) | −9.65039 | + | 7.50925i | −0.520314 | + | 0.404872i | ||||
\(345\) | 5.88128 | 0.316638 | ||||||||
\(346\) | 9.82569 | − | 2.20156i | 0.528232 | − | 0.118356i | ||||
\(347\) | 0.606084i | 0.0325363i | 0.999868 | + | 0.0162681i | \(0.00517854\pi\) | ||||
−0.999868 | + | 0.0162681i | \(0.994821\pi\) | |||||||
\(348\) | 18.5405 | − | 8.74756i | 0.993873 | − | 0.468918i | ||||
\(349\) | 31.6682i | 1.69516i | 0.530668 | + | 0.847580i | \(0.321941\pi\) | ||||
−0.530668 | + | 0.847580i | \(0.678059\pi\) | |||||||
\(350\) | −0.709355 | − | 3.67380i | −0.0379166 | − | 0.196373i | ||||
\(351\) | 4.69157i | 0.250418i | ||||||||
\(352\) | −2.52230 | + | 4.98161i | −0.134439 | + | 0.265521i | ||||
\(353\) | − | 4.06901i | − | 0.216572i | −0.994120 | − | 0.108286i | \(-0.965464\pi\) | ||
0.994120 | − | 0.108286i | \(-0.0345362\pi\) | |||||||
\(354\) | 4.32357 | + | 19.2964i | 0.229795 | + | 1.02559i | ||||
\(355\) | −8.49881 | −0.451070 | ||||||||
\(356\) | −0.421047 | − | 0.892410i | −0.0223154 | − | 0.0472976i | ||||
\(357\) | −0.309013 | + | 10.4073i | −0.0163547 | + | 0.550811i | ||||
\(358\) | 28.7645 | − | 6.44500i | 1.52025 | − | 0.340629i | ||||
\(359\) | − | 11.0427i | − | 0.582809i | −0.956600 | − | 0.291405i | \(-0.905877\pi\) | ||
0.956600 | − | 0.291405i | \(-0.0941226\pi\) | |||||||
\(360\) | 2.23224 | − | 1.73698i | 0.117650 | − | 0.0915466i | ||||
\(361\) | −18.9499 | −0.997362 | ||||||||
\(362\) | −33.7310 | + | 7.55782i | −1.77286 | + | 0.397230i | ||||
\(363\) | 10.0257 | 0.526211 | ||||||||
\(364\) | −9.92203 | − | 22.7565i | −0.520056 | − | 1.19276i | ||||
\(365\) | 14.4665 | 0.757214 | ||||||||
\(366\) | −6.80855 | + | 1.52553i | −0.355888 | + | 0.0797408i | ||||
\(367\) | −0.0725720 | −0.00378823 | −0.00189411 | − | 0.999998i | \(-0.500603\pi\) | ||||
−0.00189411 | + | 0.999998i | \(0.500603\pi\) | |||||||
\(368\) | −18.1569 | − | 14.9585i | −0.946496 | − | 0.779767i | ||||
\(369\) | − | 7.34910i | − | 0.382579i | ||||||
\(370\) | −11.4114 | + | 2.55685i | −0.593251 | + | 0.132924i | ||||
\(371\) | −22.0824 | − | 0.655671i | −1.14646 | − | 0.0340407i | ||||
\(372\) | −5.01827 | + | 2.36767i | −0.260185 | + | 0.122758i | ||||
\(373\) | 22.4132 | 1.16051 | 0.580257 | − | 0.814433i | \(-0.302952\pi\) | ||||
0.580257 | + | 0.814433i | \(0.302952\pi\) | |||||||
\(374\) | −1.20109 | − | 5.36056i | −0.0621071 | − | 0.277188i | ||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | −4.18227 | − | 5.37477i | −0.215684 | − | 0.277183i | ||||
\(377\) | − | 48.0897i | − | 2.47675i | ||||||
\(378\) | 0.709355 | + | 3.67380i | 0.0364853 | + | 0.188960i | ||||
\(379\) | 26.9969i | 1.38674i | 0.720584 | + | 0.693368i | \(0.243874\pi\) | ||||
−0.720584 | + | 0.693368i | \(0.756126\pi\) | |||||||
\(380\) | 0.191073 | + | 0.404980i | 0.00980185 | + | 0.0207750i | ||||
\(381\) | − | 5.18615i | − | 0.265695i | ||||||
\(382\) | −26.6404 | + | 5.96909i | −1.36304 | + | 0.305405i | ||||
\(383\) | 19.7866 | 1.01105 | 0.505523 | − | 0.862813i | \(-0.331299\pi\) | ||||
0.505523 | + | 0.862813i | \(0.331299\pi\) | |||||||
\(384\) | −11.3093 | − | 0.315057i | −0.577126 | − | 0.0160777i | ||||
\(385\) | −2.61042 | − | 0.0775087i | −0.133039 | − | 0.00395021i | ||||
\(386\) | −4.71553 | − | 21.0457i | −0.240014 | − | 1.07120i | ||||
\(387\) | − | 4.32318i | − | 0.219759i | ||||||
\(388\) | 3.67846 | + | 7.79651i | 0.186746 | + | 0.395808i | ||||
\(389\) | −29.6119 | −1.50138 | −0.750690 | − | 0.660654i | \(-0.770279\pi\) | ||||
−0.750690 | + | 0.660654i | \(0.770279\pi\) | |||||||
\(390\) | −1.45065 | − | 6.47436i | −0.0734567 | − | 0.327842i | ||||
\(391\) | 23.1447 | 1.17048 | ||||||||
\(392\) | −11.2103 | − | 16.3196i | −0.566206 | − | 0.824264i | ||||
\(393\) | −11.3617 | −0.573124 | ||||||||
\(394\) | 0.929865 | + | 4.15005i | 0.0468459 | + | 0.209076i | ||||
\(395\) | 11.5183 | 0.579549 | ||||||||
\(396\) | −0.842376 | − | 1.78542i | −0.0423310 | − | 0.0897206i | ||||
\(397\) | 21.2555i | 1.06678i | 0.845868 | + | 0.533392i | \(0.179083\pi\) | ||||
−0.845868 | + | 0.533392i | \(0.820917\pi\) | |||||||
\(398\) | −6.85156 | − | 30.5790i | −0.343438 | − | 1.53279i | ||||
\(399\) | −0.592112 | − | 0.0175810i | −0.0296427 | − | 0.000880153i | ||||
\(400\) | −2.54341 | + | 3.08724i | −0.127171 | + | 0.154362i | ||||
\(401\) | 24.5750 | 1.22722 | 0.613608 | − | 0.789610i | \(-0.289717\pi\) | ||||
0.613608 | + | 0.789610i | \(0.289717\pi\) | |||||||
\(402\) | 10.8292 | − | 2.42640i | 0.540110 | − | 0.121018i | ||||
\(403\) | 13.0162i | 0.648385i | ||||||||
\(404\) | −5.15174 | − | 10.9191i | −0.256309 | − | 0.543246i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −7.27104 | − | 37.6573i | −0.360856 | − | 1.86890i | ||||
\(407\) | 8.16231i | 0.404591i | ||||||||
\(408\) | 8.78458 | − | 6.83554i | 0.434902 | − | 0.338410i | ||||
\(409\) | − | 34.9158i | − | 1.72648i | −0.504797 | − | 0.863238i | \(-0.668433\pi\) | ||
0.504797 | − | 0.863238i | \(-0.331567\pi\) | |||||||
\(410\) | 2.27237 | + | 10.1417i | 0.112224 | + | 0.500865i | ||||
\(411\) | −5.85931 | −0.289018 | ||||||||
\(412\) | −14.1644 | + | 6.68290i | −0.697831 | + | 0.329243i | ||||
\(413\) | 36.9790 | + | 1.09798i | 1.81962 | + | 0.0540282i | ||||
\(414\) | 8.11616 | − | 1.81852i | 0.398887 | − | 0.0893752i | ||||
\(415\) | − | 1.67114i | − | 0.0820329i | ||||||
\(416\) | −11.9885 | + | 23.6775i | −0.587782 | + | 1.16089i | ||||
\(417\) | −18.1460 | −0.888614 | ||||||||
\(418\) | 0.304984 | − | 0.0683351i | 0.0149173 | − | 0.00334238i | ||||
\(419\) | 2.32360 | 0.113515 | 0.0567577 | − | 0.998388i | \(-0.481924\pi\) | ||||
0.0567577 | + | 0.998388i | \(0.481924\pi\) | |||||||
\(420\) | −2.11486 | − | 4.85050i | −0.103195 | − | 0.236680i | ||||
\(421\) | −22.9539 | −1.11870 | −0.559352 | − | 0.828930i | \(-0.688950\pi\) | ||||
−0.559352 | + | 0.828930i | \(0.688950\pi\) | |||||||
\(422\) | −17.4941 | + | 3.91975i | −0.851599 | + | 0.190810i | ||||
\(423\) | 2.40779 | 0.117071 | ||||||||
\(424\) | 14.5038 | + | 18.6393i | 0.704366 | + | 0.905204i | ||||
\(425\) | − | 3.93531i | − | 0.190891i | ||||||
\(426\) | −11.7283 | + | 2.62786i | −0.568239 | + | 0.127320i | ||||
\(427\) | −0.387413 | + | 13.0477i | −0.0187482 | + | 0.631422i | ||||
\(428\) | 11.9357 | + | 25.2977i | 0.576932 | + | 1.22281i | ||||
\(429\) | −4.63096 | −0.223585 | ||||||||
\(430\) | 1.33674 | + | 5.96597i | 0.0644635 | + | 0.287705i | ||||
\(431\) | − | 0.0761033i | − | 0.00366577i | −0.999998 | − | 0.00183288i | \(-0.999417\pi\) | ||
0.999998 | − | 0.00183288i | \(-0.000583425\pi\) | |||||||
\(432\) | 2.54341 | − | 3.08724i | 0.122370 | − | 0.148535i | ||||
\(433\) | 9.43899i | 0.453609i | 0.973940 | + | 0.226805i | \(0.0728278\pi\) | ||||
−0.973940 | + | 0.226805i | \(0.927172\pi\) | |||||||
\(434\) | 1.96802 | + | 10.1925i | 0.0944682 | + | 0.489258i | ||||
\(435\) | − | 10.2502i | − | 0.491461i | ||||||
\(436\) | −7.35414 | + | 3.46975i | −0.352199 | + | 0.166171i | ||||
\(437\) | 1.31680i | 0.0629909i | ||||||||
\(438\) | 19.9638 | − | 4.47311i | 0.953907 | − | 0.213734i | ||||
\(439\) | −4.35512 | −0.207858 | −0.103929 | − | 0.994585i | \(-0.533142\pi\) | ||||
−0.103929 | + | 0.994585i | \(0.533142\pi\) | |||||||
\(440\) | 1.71453 | + | 2.20340i | 0.0817372 | + | 0.105043i | ||||
\(441\) | 6.98767 | + | 0.415323i | 0.332746 | + | 0.0197773i | ||||
\(442\) | −5.70878 | − | 25.4786i | −0.271539 | − | 1.21190i | ||||
\(443\) | 35.6619i | 1.69435i | 0.531315 | + | 0.847174i | \(0.321698\pi\) | ||||
−0.531315 | + | 0.847174i | \(0.678302\pi\) | |||||||
\(444\) | −14.9571 | + | 7.05690i | −0.709833 | + | 0.334906i | ||||
\(445\) | −0.493375 | −0.0233882 | ||||||||
\(446\) | −1.99632 | − | 8.90970i | −0.0945284 | − | 0.421886i | ||||
\(447\) | 15.4737 | 0.731883 | ||||||||
\(448\) | −5.80774 | + | 20.3536i | −0.274390 | + | 0.961619i | ||||
\(449\) | 15.1046 | 0.712832 | 0.356416 | − | 0.934327i | \(-0.383999\pi\) | ||||
0.356416 | + | 0.934327i | \(0.383999\pi\) | |||||||
\(450\) | −0.309204 | − | 1.38000i | −0.0145760 | − | 0.0650537i | ||||
\(451\) | 7.25415 | 0.341585 | ||||||||
\(452\) | 15.6715 | − | 7.39397i | 0.737127 | − | 0.347783i | ||||
\(453\) | 11.5322i | 0.541828i | ||||||||
\(454\) | −4.35613 | − | 19.4417i | −0.204443 | − | 0.912443i | ||||
\(455\) | −12.4073 | − | 0.368398i | −0.581662 | − | 0.0172707i | ||||
\(456\) | 0.388902 | + | 0.499791i | 0.0182120 | + | 0.0234049i | ||||
\(457\) | −23.3917 | −1.09422 | −0.547109 | − | 0.837061i | \(-0.684272\pi\) | ||||
−0.547109 | + | 0.837061i | \(0.684272\pi\) | |||||||
\(458\) | −13.4540 | + | 3.01453i | −0.628666 | + | 0.140860i | ||||
\(459\) | 3.93531i | 0.183685i | ||||||||
\(460\) | −10.6380 | + | 5.01910i | −0.495999 | + | 0.234017i | ||||
\(461\) | − | 22.6568i | − | 1.05523i | −0.849482 | − | 0.527617i | \(-0.823086\pi\) | ||
0.849482 | − | 0.527617i | \(-0.176914\pi\) | |||||||
\(462\) | −3.62634 | + | 0.700190i | −0.168712 | + | 0.0325758i | ||||
\(463\) | − | 31.9975i | − | 1.48705i | −0.668707 | − | 0.743526i | \(-0.733152\pi\) | ||
0.668707 | − | 0.743526i | \(-0.266848\pi\) | |||||||
\(464\) | −26.0705 | + | 31.6449i | −1.21029 | + | 1.46908i | ||||
\(465\) | 2.77439i | 0.128659i | ||||||||
\(466\) | 0.507807 | + | 2.26638i | 0.0235237 | + | 0.104988i | ||||
\(467\) | 42.6816 | 1.97507 | 0.987533 | − | 0.157409i | \(-0.0503142\pi\) | ||||
0.987533 | + | 0.157409i | \(0.0503142\pi\) | |||||||
\(468\) | −4.00380 | − | 8.48605i | −0.185076 | − | 0.392268i | ||||
\(469\) | 0.616190 | − | 20.7527i | 0.0284530 | − | 0.958270i | ||||
\(470\) | −3.32274 | + | 0.744498i | −0.153267 | + | 0.0343411i | ||||
\(471\) | − | 0.806743i | − | 0.0371728i | ||||||
\(472\) | −24.2880 | − | 31.2133i | −1.11794 | − | 1.43671i | ||||
\(473\) | 4.26732 | 0.196212 | ||||||||
\(474\) | 15.8952 | − | 3.56151i | 0.730093 | − | 0.163586i | ||||
\(475\) | 0.223896 | 0.0102731 | ||||||||
\(476\) | −8.32264 | − | 19.0882i | −0.381468 | − | 0.874908i | ||||
\(477\) | −8.35002 | −0.382321 | ||||||||
\(478\) | 13.4926 | − | 3.02316i | 0.617136 | − | 0.138276i | ||||
\(479\) | −0.259729 | −0.0118673 | −0.00593366 | − | 0.999982i | \(-0.501889\pi\) | ||||
−0.00593366 | + | 0.999982i | \(0.501889\pi\) | |||||||
\(480\) | −2.55532 | + | 5.04682i | −0.116634 | + | 0.230355i | ||||
\(481\) | 38.7953i | 1.76891i | ||||||||
\(482\) | −9.44064 | + | 2.11528i | −0.430009 | + | 0.0963484i | ||||
\(483\) | 0.461817 | − | 15.5536i | 0.0210134 | − | 0.707712i | ||||
\(484\) | −18.1343 | + | 8.55592i | −0.824286 | + | 0.388906i | ||||
\(485\) | 4.31036 | 0.195723 | ||||||||
\(486\) | 0.309204 | + | 1.38000i | 0.0140258 | + | 0.0625980i | ||||
\(487\) | − | 29.8196i | − | 1.35126i | −0.737242 | − | 0.675628i | \(-0.763872\pi\) | ||
0.737242 | − | 0.675628i | \(-0.236128\pi\) | |||||||
\(488\) | 11.0133 | − | 8.56978i | 0.498549 | − | 0.387936i | ||||
\(489\) | 6.48272i | 0.293159i | ||||||||
\(490\) | −9.77138 | + | 1.58747i | −0.441426 | + | 0.0717146i | ||||
\(491\) | − | 25.9448i | − | 1.17087i | −0.810718 | − | 0.585437i | \(-0.800923\pi\) | ||
0.810718 | − | 0.585437i | \(-0.199077\pi\) | |||||||
\(492\) | 6.27173 | + | 13.2929i | 0.282751 | + | 0.599292i | ||||
\(493\) | − | 40.3378i | − | 1.81672i | ||||||
\(494\) | 1.44958 | − | 0.324796i | 0.0652199 | − | 0.0146132i | ||||
\(495\) | −0.987080 | −0.0443660 | ||||||||
\(496\) | 7.05641 | − | 8.56520i | 0.316842 | − | 0.384589i | ||||
\(497\) | −0.667354 | + | 22.4758i | −0.0299349 | + | 1.00818i | ||||
\(498\) | −0.516722 | − | 2.30616i | −0.0231549 | − | 0.103342i | ||||
\(499\) | 22.9135i | 1.02575i | 0.858464 | + | 0.512874i | \(0.171419\pi\) | ||||
−0.858464 | + | 0.512874i | \(0.828581\pi\) | |||||||
\(500\) | 0.853401 | + | 1.80879i | 0.0381653 | + | 0.0808914i | ||||
\(501\) | −7.65678 | −0.342080 | ||||||||
\(502\) | −0.726541 | − | 3.24260i | −0.0324271 | − | 0.144724i | ||||
\(503\) | −29.7060 | −1.32453 | −0.662263 | − | 0.749271i | \(-0.730404\pi\) | ||||
−0.662263 | + | 0.749271i | \(0.730404\pi\) | |||||||
\(504\) | −4.41830 | − | 6.03976i | −0.196807 | − | 0.269032i | ||||
\(505\) | −6.03671 | −0.268630 | ||||||||
\(506\) | 1.79502 | + | 8.01130i | 0.0797984 | + | 0.356146i | ||||
\(507\) | −9.01087 | −0.400187 | ||||||||
\(508\) | 4.42587 | + | 9.38064i | 0.196366 | + | 0.416199i | ||||
\(509\) | 15.8710i | 0.703470i | 0.936100 | + | 0.351735i | \(0.114408\pi\) | ||||
−0.936100 | + | 0.351735i | \(0.885592\pi\) | |||||||
\(510\) | −1.21681 | − | 5.43072i | −0.0538814 | − | 0.240476i | ||||
\(511\) | 1.13596 | − | 38.2580i | 0.0502519 | − | 1.69244i | ||||
\(512\) | 20.7250 | − | 9.08152i | 0.915925 | − | 0.401350i | ||||
\(513\) | −0.223896 | −0.00988525 | ||||||||
\(514\) | 8.93065 | − | 2.00101i | 0.393914 | − | 0.0882609i | ||||
\(515\) | 7.83090i | 0.345071i | ||||||||
\(516\) | 3.68941 | + | 7.81970i | 0.162417 | + | 0.344243i | ||||
\(517\) | 2.37668i | 0.104526i | ||||||||
\(518\) | 5.86576 | + | 30.3792i | 0.257727 | + | 1.33479i | ||||
\(519\) | − | 7.12007i | − | 0.312537i | ||||||
\(520\) | 8.14915 | + | 10.4727i | 0.357364 | + | 0.459260i | ||||
\(521\) | 10.0748i | 0.441387i | 0.975343 | + | 0.220693i | \(0.0708320\pi\) | ||||
−0.975343 | + | 0.220693i | \(0.929168\pi\) | |||||||
\(522\) | −3.16941 | − | 14.1453i | −0.138721 | − | 0.619122i | ||||
\(523\) | 15.4083 | 0.673759 | 0.336880 | − | 0.941548i | \(-0.390628\pi\) | ||||
0.336880 | + | 0.941548i | \(0.390628\pi\) | |||||||
\(524\) | 20.5509 | − | 9.69612i | 0.897772 | − | 0.423577i | ||||
\(525\) | −2.64459 | − | 0.0785232i | −0.115419 | − | 0.00342703i | ||||
\(526\) | 3.28544 | − | 0.736139i | 0.143252 | − | 0.0320972i | ||||
\(527\) | 10.9181i | 0.475599i | ||||||||
\(528\) | 3.04735 | + | 2.51055i | 0.132619 | + | 0.109258i | ||||
\(529\) | −11.5895 | −0.503891 | ||||||||
\(530\) | 11.5230 | − | 2.58186i | 0.500528 | − | 0.112149i | ||||
\(531\) | 13.9829 | 0.606807 | ||||||||
\(532\) | 1.08601 | − | 0.473509i | 0.0470844 | − | 0.0205292i | ||||
\(533\) | 34.4788 | 1.49344 | ||||||||
\(534\) | −0.680856 | + | 0.152554i | −0.0294635 | + | 0.00660164i | ||||
\(535\) | 13.9860 | 0.604667 | ||||||||
\(536\) | −17.5169 | + | 13.6305i | −0.756617 | + | 0.588746i | ||||
\(537\) | − | 20.8439i | − | 0.899479i | ||||||
\(538\) | −13.0395 | + | 2.92165i | −0.562173 | + | 0.125961i | ||||
\(539\) | −0.409957 | + | 6.89739i | −0.0176581 | + | 0.297092i | ||||
\(540\) | −0.853401 | − | 1.80879i | −0.0367245 | − | 0.0778377i | ||||
\(541\) | −11.4549 | −0.492486 | −0.246243 | − | 0.969208i | \(-0.579196\pi\) | ||||
−0.246243 | + | 0.969208i | \(0.579196\pi\) | |||||||
\(542\) | −6.85898 | − | 30.6121i | −0.294619 | − | 1.31490i | ||||
\(543\) | 24.4428i | 1.04894i | ||||||||
\(544\) | −10.0560 | + | 19.8608i | −0.431146 | + | 0.851525i | ||||
\(545\) | 4.06579i | 0.174159i | ||||||||
\(546\) | −17.2359 | + | 3.32799i | −0.737629 | + | 0.142425i | ||||
\(547\) | − | 25.1553i | − | 1.07556i | −0.843085 | − | 0.537781i | \(-0.819263\pi\) | ||
0.843085 | − | 0.537781i | \(-0.180737\pi\) | |||||||
\(548\) | 10.5982 | − | 5.00034i | 0.452734 | − | 0.213604i | ||||
\(549\) | 4.93374i | 0.210567i | ||||||||
\(550\) | 1.36217 | − | 0.305209i | 0.0580830 | − | 0.0130142i | ||||
\(551\) | 2.29499 | 0.0977697 | ||||||||
\(552\) | −13.1285 | + | 10.2156i | −0.558785 | + | 0.434807i | ||||
\(553\) | 0.904455 | − | 30.4612i | 0.0384614 | − | 1.29534i | ||||
\(554\) | −8.27795 | − | 36.9450i | −0.351696 | − | 1.56964i | ||||
\(555\) | 8.26915i | 0.351006i | ||||||||
\(556\) | 32.8222 | − | 15.4858i | 1.39197 | − | 0.656745i | ||||
\(557\) | 26.6942 | 1.13107 | 0.565534 | − | 0.824725i | \(-0.308670\pi\) | ||||
0.565534 | + | 0.824725i | \(0.308670\pi\) | |||||||
\(558\) | 0.857851 | + | 3.82865i | 0.0363157 | + | 0.162080i | ||||
\(559\) | 20.2825 | 0.857859 | ||||||||
\(560\) | 7.96476 | + | 6.96869i | 0.336572 | + | 0.294481i | ||||
\(561\) | −3.88447 | −0.164002 | ||||||||
\(562\) | −2.67209 | − | 11.9257i | −0.112715 | − | 0.503056i | ||||
\(563\) | −10.8180 | −0.455923 | −0.227962 | − | 0.973670i | \(-0.573206\pi\) | ||||
−0.227962 | + | 0.973670i | \(0.573206\pi\) | |||||||
\(564\) | −4.35517 | + | 2.05481i | −0.183386 | + | 0.0865231i | ||||
\(565\) | − | 8.66412i | − | 0.364502i | ||||||
\(566\) | 1.83063 | + | 8.17023i | 0.0769472 | + | 0.343420i | ||||
\(567\) | 2.64459 | + | 0.0785232i | 0.111062 | + | 0.00329767i | ||||
\(568\) | 18.9714 | − | 14.7622i | 0.796023 | − | 0.619409i | ||||
\(569\) | 15.0833 | 0.632323 | 0.316162 | − | 0.948705i | \(-0.397606\pi\) | ||||
0.316162 | + | 0.948705i | \(0.397606\pi\) | |||||||
\(570\) | 0.308976 | − | 0.0692296i | 0.0129416 | − | 0.00289971i | ||||
\(571\) | 11.4509i | 0.479206i | 0.970871 | + | 0.239603i | \(0.0770174\pi\) | ||||
−0.970871 | + | 0.239603i | \(0.922983\pi\) | |||||||
\(572\) | 8.37642 | − | 3.95207i | 0.350236 | − | 0.165244i | ||||
\(573\) | 19.3047i | 0.806465i | ||||||||
\(574\) | 26.9991 | − | 5.21312i | 1.12692 | − | 0.217591i | ||||
\(575\) | 5.88128i | 0.245267i | ||||||||
\(576\) | −1.96583 | + | 7.75471i | −0.0819097 | + | 0.323113i | ||||
\(577\) | 27.7622i | 1.15576i | 0.816123 | + | 0.577878i | \(0.196119\pi\) | ||||
−0.816123 | + | 0.577878i | \(0.803881\pi\) | |||||||
\(578\) | 0.467923 | + | 2.08837i | 0.0194630 | + | 0.0868648i | ||||
\(579\) | −15.2505 | −0.633791 | ||||||||
\(580\) | 8.74756 | + | 18.5405i | 0.363223 | + | 0.769851i | ||||
\(581\) | −4.41946 | − | 0.131223i | −0.183350 | − | 0.00544405i | ||||
\(582\) | 5.94828 | − | 1.33278i | 0.246564 | − | 0.0552455i | ||||
\(583\) | − | 8.24214i | − | 0.341355i | ||||||
\(584\) | −32.2929 | + | 25.1280i | −1.33629 | + | 1.03981i | ||||
\(585\) | −4.69157 | −0.193973 | ||||||||
\(586\) | −36.2462 | + | 8.12137i | −1.49732 | + | 0.335491i | ||||
\(587\) | −4.20086 | −0.173388 | −0.0866941 | − | 0.996235i | \(-0.527630\pi\) | ||||
−0.0866941 | + | 0.996235i | \(0.527630\pi\) | |||||||
\(588\) | −12.9936 | + | 5.21206i | −0.535848 | + | 0.214942i | ||||
\(589\) | −0.621174 | −0.0255950 | ||||||||
\(590\) | −19.2964 | + | 4.32357i | −0.794419 | + | 0.177999i | ||||
\(591\) | 3.00729 | 0.123703 | ||||||||
\(592\) | 21.0319 | − | 25.5289i | 0.864404 | − | 1.04923i | ||||
\(593\) | 12.2323i | 0.502321i | 0.967945 | + | 0.251161i | \(0.0808123\pi\) | ||||
−0.967945 | + | 0.251161i | \(0.919188\pi\) | |||||||
\(594\) | −1.36217 | + | 0.305209i | −0.0558904 | + | 0.0125229i | ||||
\(595\) | −10.4073 | − | 0.309013i | −0.426657 | − | 0.0126683i | ||||
\(596\) | −27.9887 | + | 13.2053i | −1.14646 | + | 0.540911i | ||||
\(597\) | −22.1587 | −0.906896 | ||||||||
\(598\) | 8.53171 | + | 38.0776i | 0.348887 | + | 1.55711i | ||||
\(599\) | 43.8944i | 1.79348i | 0.442562 | + | 0.896738i | \(0.354070\pi\) | ||||
−0.442562 | + | 0.896738i | \(0.645930\pi\) | |||||||
\(600\) | 1.73698 | + | 2.23224i | 0.0709117 | + | 0.0911310i | ||||
\(601\) | 5.44570i | 0.222135i | 0.993813 | + | 0.111067i | \(0.0354269\pi\) | ||||
−0.993813 | + | 0.111067i | \(0.964573\pi\) | |||||||
\(602\) | 15.8825 | − | 3.06667i | 0.647322 | − | 0.124988i | ||||
\(603\) | − | 7.84723i | − | 0.319564i | ||||||
\(604\) | −9.84156 | − | 20.8592i | −0.400447 | − | 0.848749i | ||||
\(605\) | 10.0257i | 0.407602i | ||||||||
\(606\) | −8.33065 | + | 1.86658i | −0.338409 | + | 0.0758244i | ||||
\(607\) | −29.7406 | −1.20713 | −0.603567 | − | 0.797312i | \(-0.706255\pi\) | ||||
−0.603567 | + | 0.797312i | \(0.706255\pi\) | |||||||
\(608\) | −1.12996 | − | 0.572125i | −0.0458260 | − | 0.0232027i | ||||
\(609\) | −27.1076 | − | 0.804881i | −1.09846 | − | 0.0326154i | ||||
\(610\) | −1.52553 | − | 6.80855i | −0.0617670 | − | 0.275670i | ||||
\(611\) | 11.2963i | 0.457000i | ||||||||
\(612\) | −3.35840 | − | 7.11814i | −0.135755 | − | 0.287734i | ||||
\(613\) | 26.7046 | 1.07859 | 0.539295 | − | 0.842117i | \(-0.318691\pi\) | ||||
0.539295 | + | 0.842117i | \(0.318691\pi\) | |||||||
\(614\) | 5.73363 | + | 25.5895i | 0.231390 | + | 1.03271i | ||||
\(615\) | 7.34910 | 0.296344 | ||||||||
\(616\) | 5.96172 | − | 4.36121i | 0.240205 | − | 0.175718i | ||||
\(617\) | −18.7712 | −0.755701 | −0.377851 | − | 0.925867i | \(-0.623337\pi\) | ||||
−0.377851 | + | 0.925867i | \(0.623337\pi\) | |||||||
\(618\) | 2.42135 | + | 10.8066i | 0.0974008 | + | 0.434706i | ||||
\(619\) | −6.00143 | −0.241218 | −0.120609 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120609 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(620\) | −2.36767 | − | 5.01827i | −0.0950877 | − | 0.201539i | ||||
\(621\) | − | 5.88128i | − | 0.236008i | ||||||
\(622\) | 9.53493 | + | 42.5550i | 0.382316 | + | 1.70630i | ||||
\(623\) | −0.0387414 | + | 1.30477i | −0.00155214 | + | 0.0522746i | ||||
\(624\) | 14.4840 | + | 11.9326i | 0.579825 | + | 0.477687i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 28.7385 | − | 6.43918i | 1.14862 | − | 0.257361i | ||||
\(627\) | − | 0.221003i | − | 0.00882603i | ||||||
\(628\) | 0.688476 | + | 1.45923i | 0.0274732 | + | 0.0582294i | ||||
\(629\) | 32.5417i | 1.29752i | ||||||||
\(630\) | −3.67380 | + | 0.709355i | −0.146368 | + | 0.0282614i | ||||
\(631\) | − | 42.7851i | − | 1.70325i | −0.524154 | − | 0.851623i | \(-0.675619\pi\) | ||
0.524154 | − | 0.851623i | \(-0.324381\pi\) | |||||||
\(632\) | −25.7117 | + | 20.0070i | −1.02276 | + | 0.795837i | ||||
\(633\) | 12.6769i | 0.503862i | ||||||||
\(634\) | 1.67326 | + | 7.46788i | 0.0664538 | + | 0.296587i | ||||
\(635\) | 5.18615 | 0.205806 | ||||||||
\(636\) | 15.1034 | − | 7.12592i | 0.598889 | − | 0.282561i | ||||
\(637\) | −1.94852 | + | 32.7832i | −0.0772031 | + | 1.29892i | ||||
\(638\) | 13.9625 | − | 3.12846i | 0.552782 | − | 0.123857i | ||||
\(639\) | 8.49881i | 0.336208i | ||||||||
\(640\) | 0.315057 | − | 11.3093i | 0.0124537 | − | 0.447040i | ||||
\(641\) | 32.5398 | 1.28525 | 0.642623 | − | 0.766182i | \(-0.277846\pi\) | ||||
0.642623 | + | 0.766182i | \(0.277846\pi\) | |||||||
\(642\) | 19.3006 | − | 4.32453i | 0.761735 | − | 0.170675i | ||||
\(643\) | 10.1954 | 0.402068 | 0.201034 | − | 0.979584i | \(-0.435570\pi\) | ||||
0.201034 | + | 0.979584i | \(0.435570\pi\) | |||||||
\(644\) | 12.4381 | + | 28.5272i | 0.490130 | + | 1.12413i | ||||
\(645\) | 4.32318 | 0.170225 | ||||||||
\(646\) | 1.21592 | − | 0.272440i | 0.0478396 | − | 0.0107190i | ||||
\(647\) | −32.1295 | −1.26314 | −0.631571 | − | 0.775318i | \(-0.717590\pi\) | ||||
−0.631571 | + | 0.775318i | \(0.717590\pi\) | |||||||
\(648\) | −1.73698 | − | 2.23224i | −0.0682348 | − | 0.0876909i | ||||
\(649\) | 13.8023i | 0.541786i | ||||||||
\(650\) | 6.47436 | − | 1.45065i | 0.253945 | − | 0.0568993i | ||||
\(651\) | 7.33710 | + | 0.217854i | 0.287564 | + | 0.00853836i | ||||
\(652\) | −5.53236 | − | 11.7258i | −0.216664 | − | 0.459220i | ||||
\(653\) | −25.0805 | −0.981476 | −0.490738 | − | 0.871307i | \(-0.663273\pi\) | ||||
−0.490738 | + | 0.871307i | \(0.663273\pi\) | |||||||
\(654\) | 1.25716 | + | 5.61078i | 0.0491588 | + | 0.219399i | ||||
\(655\) | − | 11.3617i | − | 0.443940i | ||||||
\(656\) | −22.6884 | − | 18.6918i | −0.885835 | − | 0.729792i | ||||
\(657\) | − | 14.4665i | − | 0.564394i | ||||||
\(658\) | 1.70798 | + | 8.84574i | 0.0665838 | + | 0.344843i | ||||
\(659\) | 8.80669i | 0.343060i | 0.985179 | + | 0.171530i | \(0.0548710\pi\) | ||||
−0.985179 | + | 0.171530i | \(0.945129\pi\) | |||||||
\(660\) | 1.78542 | − | 0.842376i | 0.0694972 | − | 0.0327894i | ||||
\(661\) | 43.1173i | 1.67707i | 0.544849 | + | 0.838534i | \(0.316587\pi\) | ||||
−0.544849 | + | 0.838534i | \(0.683413\pi\) | |||||||
\(662\) | 2.44942 | − | 0.548820i | 0.0951993 | − | 0.0213305i | ||||
\(663\) | −18.4628 | −0.717036 | ||||||||
\(664\) | 2.90272 | + | 3.73039i | 0.112648 | + | 0.144767i | ||||
\(665\) | 0.0175810 | − | 0.592112i | 0.000681764 | − | 0.0229611i | ||||
\(666\) | 2.55685 | + | 11.4114i | 0.0990761 | + | 0.442183i | ||||
\(667\) | 60.2845i | 2.33422i | ||||||||
\(668\) | 13.8495 | − | 6.53430i | 0.535852 | − | 0.252820i | ||||
\(669\) | −6.45632 | −0.249616 | ||||||||
\(670\) | 2.42640 | + | 10.8292i | 0.0937399 | + | 0.418367i | ||||
\(671\) | −4.87000 | −0.188004 | ||||||||
\(672\) | 13.1461 | + | 7.15404i | 0.507121 | + | 0.275973i | ||||
\(673\) | −12.2583 | −0.472524 | −0.236262 | − | 0.971689i | \(-0.575922\pi\) | ||||
−0.236262 | + | 0.971689i | \(0.575922\pi\) | |||||||
\(674\) | 6.91589 | + | 30.8661i | 0.266390 | + | 1.18892i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 16.2987 | − | 7.68989i | 0.626875 | − | 0.295765i | ||||
\(677\) | 29.7024i | 1.14155i | 0.821105 | + | 0.570777i | \(0.193358\pi\) | ||||
−0.821105 | + | 0.570777i | \(0.806642\pi\) | |||||||
\(678\) | −2.67898 | − | 11.9565i | −0.102886 | − | 0.459185i | ||||
\(679\) | 0.338463 | − | 11.3991i | 0.0129890 | − | 0.437458i | ||||
\(680\) | 6.83554 | + | 8.78458i | 0.262131 | + | 0.336873i | ||||
\(681\) | −14.0882 | −0.539861 | ||||||||
\(682\) | −3.77918 | + | 0.846768i | −0.144712 | + | 0.0324244i | ||||
\(683\) | − | 35.1749i | − | 1.34593i | −0.739674 | − | 0.672965i | \(-0.765020\pi\) | ||
0.739674 | − | 0.672965i | \(-0.234980\pi\) | |||||||
\(684\) | 0.404980 | − | 0.191073i | 0.0154848 | − | 0.00730587i | ||||
\(685\) | − | 5.85931i | − | 0.223873i | ||||||
\(686\) | 3.43092 | + | 25.9659i | 0.130993 | + | 0.991383i | ||||
\(687\) | 9.74932i | 0.371960i | ||||||||
\(688\) | −13.3467 | − | 10.9956i | −0.508838 | − | 0.419204i | ||||
\(689\) | − | 39.1748i | − | 1.49244i | ||||||
\(690\) | 1.81852 | + | 8.11616i | 0.0692297 | + | 0.308977i | ||||
\(691\) | −42.9454 | −1.63372 | −0.816860 | − | 0.576836i | \(-0.804287\pi\) | ||||
−0.816860 | + | 0.576836i | \(0.804287\pi\) | |||||||
\(692\) | 6.07628 | + | 12.8787i | 0.230986 | + | 0.489574i | ||||
\(693\) | −0.0775087 | + | 2.61042i | −0.00294431 | + | 0.0991616i | ||||
\(694\) | −0.836394 | + | 0.187403i | −0.0317491 | + | 0.00711374i | ||||
\(695\) | − | 18.1460i | − | 0.688317i | ||||||
\(696\) | 17.8044 | + | 22.8810i | 0.674874 | + | 0.867302i | ||||
\(697\) | 28.9210 | 1.09546 | ||||||||
\(698\) | −43.7020 | + | 9.79193i | −1.65415 | + | 0.370630i | ||||
\(699\) | 1.64231 | 0.0621177 | ||||||||
\(700\) | 4.85050 | − | 2.11486i | 0.183332 | − | 0.0799343i | ||||
\(701\) | −9.37675 | −0.354155 | −0.177077 | − | 0.984197i | \(-0.556664\pi\) | ||||
−0.177077 | + | 0.984197i | \(0.556664\pi\) | |||||||
\(702\) | −6.47436 | + | 1.45065i | −0.244359 | + | 0.0547514i | ||||
\(703\) | −1.85143 | −0.0698280 | ||||||||
\(704\) | −7.65452 | − | 1.94043i | −0.288491 | − | 0.0731329i | ||||
\(705\) | 2.40779i | 0.0906826i | ||||||||
\(706\) | 5.61523 | − | 1.25815i | 0.211332 | − | 0.0473513i | ||||
\(707\) | −0.474022 | + | 15.9646i | −0.0178274 | + | 0.600411i | ||||
\(708\) | −25.2921 | + | 11.9330i | −0.950535 | + | 0.448471i | ||||
\(709\) | −27.6729 | −1.03928 | −0.519638 | − | 0.854386i | \(-0.673933\pi\) | ||||
−0.519638 | + | 0.854386i | \(0.673933\pi\) | |||||||
\(710\) | −2.62786 | − | 11.7283i | −0.0986220 | − | 0.440156i | ||||
\(711\) | − | 11.5183i | − | 0.431971i | ||||||
\(712\) | 1.10133 | − | 0.856980i | 0.0412742 | − | 0.0321167i | ||||
\(713\) | − | 16.3170i | − | 0.611075i | ||||||
\(714\) | −14.4576 | + | 2.79153i | −0.541060 | + | 0.104470i | ||||
\(715\) | − | 4.63096i | − | 0.173188i | ||||||
\(716\) | 17.7882 | + | 37.7021i | 0.664776 | + | 1.40899i | ||||
\(717\) | − | 9.77724i | − | 0.365138i | ||||||
\(718\) | 15.2388 | − | 3.41443i | 0.568708 | − | 0.127426i | ||||
\(719\) | 9.24786 | 0.344887 | 0.172444 | − | 0.985019i | \(-0.444834\pi\) | ||||
0.172444 | + | 0.985019i | \(0.444834\pi\) | |||||||
\(720\) | 3.08724 | + | 2.54341i | 0.115055 | + | 0.0947874i | ||||
\(721\) | 20.7095 | + | 0.614908i | 0.771262 | + | 0.0229004i | ||||
\(722\) | −5.85938 | − | 26.1508i | −0.218063 | − | 0.973231i | ||||
\(723\) | 6.84106i | 0.254422i | ||||||||
\(724\) | −20.8595 | − | 44.2118i | −0.775239 | − | 1.64312i | ||||
\(725\) | 10.2502 | 0.380684 | ||||||||
\(726\) | 3.09998 | + | 13.8354i | 0.115051 | + | 0.513480i | ||||
\(727\) | −34.7371 | −1.28833 | −0.644163 | − | 0.764888i | \(-0.722794\pi\) | ||||
−0.644163 | + | 0.764888i | \(0.722794\pi\) | |||||||
\(728\) | 28.3360 | − | 20.7288i | 1.05020 | − | 0.768259i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.47311 | + | 19.9638i | 0.165557 | + | 0.738893i | ||||
\(731\) | 17.0131 | 0.629250 | ||||||||
\(732\) | −4.21046 | − | 8.92408i | −0.155623 | − | 0.329843i | ||||
\(733\) | − | 38.6871i | − | 1.42894i | −0.699666 | − | 0.714470i | \(-0.746668\pi\) | ||
0.699666 | − | 0.714470i | \(-0.253332\pi\) | |||||||
\(734\) | −0.0224396 | − | 0.100149i | −0.000828259 | − | 0.00369657i | ||||
\(735\) | −0.415323 | + | 6.98767i | −0.0153194 | + | 0.257744i | ||||
\(736\) | 15.0285 | − | 29.6818i | 0.553959 | − | 1.09408i | ||||
\(737\) | 7.74585 | 0.285322 | ||||||||
\(738\) | 10.1417 | − | 2.27237i | 0.373323 | − | 0.0836471i | ||||
\(739\) | − | 40.4228i | − | 1.48698i | −0.668748 | − | 0.743489i | \(-0.733170\pi\) | ||
0.668748 | − | 0.743489i | \(-0.266830\pi\) | |||||||
\(740\) | −7.05690 | − | 14.9571i | −0.259417 | − | 0.549835i | ||||
\(741\) | − | 1.05043i | − | 0.0385883i | ||||||
\(742\) | −5.92313 | − | 30.6763i | −0.217445 | − | 1.12616i | ||||
\(743\) | 25.5119i | 0.935941i | 0.883744 | + | 0.467970i | \(0.155015\pi\) | ||||
−0.883744 | + | 0.467970i | \(0.844985\pi\) | |||||||
\(744\) | −4.81904 | − | 6.19311i | −0.176675 | − | 0.227050i | ||||
\(745\) | 15.4737i | 0.566914i | ||||||||
\(746\) | 6.93026 | + | 30.9302i | 0.253735 | + | 1.13244i | ||||
\(747\) | −1.67114 | −0.0611437 | ||||||||
\(748\) | 7.02617 | − | 3.31501i | 0.256902 | − | 0.121209i | ||||
\(749\) | 1.09823 | − | 36.9872i | 0.0401283 | − | 1.35148i | ||||
\(750\) | 1.38000 | − | 0.309204i | 0.0503904 | − | 0.0112905i | ||||
\(751\) | − | 31.4000i | − | 1.14580i | −0.819625 | − | 0.572901i | \(-0.805818\pi\) | ||
0.819625 | − | 0.572901i | \(-0.194182\pi\) | |||||||
\(752\) | 6.12400 | − | 7.43342i | 0.223319 | − | 0.271069i | ||||
\(753\) | −2.34972 | −0.0856284 | ||||||||
\(754\) | 66.3637 | − | 14.8695i | 2.41682 | − | 0.541516i | ||||
\(755\) | −11.5322 | −0.419698 | ||||||||
\(756\) | −4.85050 | + | 2.11486i | −0.176411 | + | 0.0769168i | ||||
\(757\) | −32.9674 | −1.19822 | −0.599111 | − | 0.800666i | \(-0.704479\pi\) | ||||
−0.599111 | + | 0.800666i | \(0.704479\pi\) | |||||||
\(758\) | −37.2556 | + | 8.34754i | −1.35318 | + | 0.303196i | ||||
\(759\) | 5.80530 | 0.210719 | ||||||||
\(760\) | −0.499791 | + | 0.388902i | −0.0181293 | + | 0.0141070i | ||||
\(761\) | − | 45.0372i | − | 1.63260i | −0.577631 | − | 0.816298i | \(-0.696023\pi\) | ||
0.577631 | − | 0.816298i | \(-0.303977\pi\) | |||||||
\(762\) | 7.15688 | − | 1.60358i | 0.259266 | − | 0.0580916i | ||||
\(763\) | 10.7523 | + | 0.319259i | 0.389260 | + | 0.0115579i | ||||
\(764\) | −16.4747 | − | 34.9181i | −0.596032 | − | 1.26329i | ||||
\(765\) | −3.93531 | −0.142282 | ||||||||
\(766\) | 6.11809 | + | 27.3054i | 0.221056 | + | 0.986585i | ||||
\(767\) | 65.6019i | 2.36875i | ||||||||
\(768\) | −3.06211 | − | 15.7043i | −0.110494 | − | 0.566678i | ||||
\(769\) | 16.6023i | 0.598694i | 0.954144 | + | 0.299347i | \(0.0967688\pi\) | ||||
−0.954144 | + | 0.299347i | \(0.903231\pi\) | |||||||
\(770\) | −0.700190 | − | 3.62634i | −0.0252331 | − | 0.130684i | ||||
\(771\) | − | 6.47150i | − | 0.233065i | ||||||
\(772\) | 27.5850 | − | 13.0148i | 0.992804 | − | 0.468414i | ||||
\(773\) | 23.1862i | 0.833951i | 0.908918 | + | 0.416975i | \(0.136910\pi\) | ||||
−0.908918 | + | 0.416975i | \(0.863090\pi\) | |||||||
\(774\) | 5.96597 | − | 1.33674i | 0.214442 | − | 0.0480483i | ||||
\(775\) | −2.77439 | −0.0996589 | ||||||||
\(776\) | −9.62177 | + | 7.48698i | −0.345401 | + | 0.268767i | ||||
\(777\) | 21.8685 | + | 0.649320i | 0.784527 | + | 0.0232942i | ||||
\(778\) | −9.15610 | − | 40.8643i | −0.328262 | − | 1.46506i | ||||
\(779\) | 1.64543i | 0.0589538i | ||||||||
\(780\) | 8.48605 | − | 4.00380i | 0.303849 | − | 0.143359i | ||||
\(781\) | −8.38900 | −0.300182 | ||||||||
\(782\) | 7.15643 | + | 31.9396i | 0.255913 | + | 1.14216i | ||||
\(783\) | −10.2502 | −0.366313 | ||||||||
\(784\) | 19.0547 | − | 20.5163i | 0.680526 | − | 0.732724i | ||||
\(785\) | 0.806743 | 0.0287939 | ||||||||
\(786\) | −3.51309 | − | 15.6792i | −0.125308 | − | 0.559257i | ||||
\(787\) | −45.5418 | −1.62339 | −0.811695 | − | 0.584081i | \(-0.801455\pi\) | ||||
−0.811695 | + | 0.584081i | \(0.801455\pi\) | |||||||
\(788\) | −5.43954 | + | 2.56642i | −0.193775 | + | 0.0914250i | ||||
\(789\) | − | 2.38076i | − | 0.0847571i | ||||||
\(790\) | 3.56151 | + | 15.8952i | 0.126713 | + | 0.565528i | ||||
\(791\) | −22.9130 | − | 0.680334i | −0.814692 | − | 0.0241899i | ||||
\(792\) | 2.20340 | − | 1.71453i | 0.0782946 | − | 0.0609233i | ||||
\(793\) | −23.1470 | −0.821974 | ||||||||
\(794\) | −29.3326 | + | 6.57229i | −1.04097 | + | 0.233242i | ||||
\(795\) | − | 8.35002i | − | 0.296145i | ||||||
\(796\) | 40.0804 | − | 18.9103i | 1.42061 | − | 0.670257i | ||||
\(797\) | − | 53.9376i | − | 1.91057i | −0.295688 | − | 0.955284i | \(-0.595549\pi\) | ||
0.295688 | − | 0.955284i | \(-0.404451\pi\) | |||||||
\(798\) | −0.158822 | − | 0.822550i | −0.00562223 | − | 0.0291179i | ||||
\(799\) | 9.47540i | 0.335216i | ||||||||
\(800\) | −5.04682 | − | 2.55532i | −0.178432 | − | 0.0903440i | ||||
\(801\) | 0.493375i | 0.0174326i | ||||||||
\(802\) | 7.59869 | + | 33.9134i | 0.268319 | + | 1.19752i | ||||
\(803\) | 14.2796 | 0.503918 | ||||||||
\(804\) | 6.69684 | + | 14.1940i | 0.236179 | + | 0.500583i | ||||
\(805\) | 15.5536 | + | 0.461817i | 0.548191 | + | 0.0162769i | ||||
\(806\) | −17.9624 | + | 4.02467i | −0.632698 | + | 0.141763i | ||||
\(807\) | 9.44894i | 0.332618i | ||||||||
\(808\) | 13.4754 | − | 10.4856i | 0.474064 | − | 0.368883i | ||||
\(809\) | 14.1973 | 0.499151 | 0.249576 | − | 0.968355i | \(-0.419709\pi\) | ||||
0.249576 | + | 0.968355i | \(0.419709\pi\) | |||||||
\(810\) | −1.38000 | + | 0.309204i | −0.0484882 | + | 0.0108643i | ||||
\(811\) | −23.5815 | −0.828059 | −0.414029 | − | 0.910264i | \(-0.635879\pi\) | ||||
−0.414029 | + | 0.910264i | \(0.635879\pi\) | |||||||
\(812\) | 49.7187 | − | 21.6778i | 1.74479 | − | 0.760742i | ||||
\(813\) | −22.1827 | −0.777982 | ||||||||
\(814\) | −11.2640 | + | 2.52382i | −0.394802 | + | 0.0884598i | ||||
\(815\) | −6.48272 | −0.227080 | ||||||||
\(816\) | 12.1493 | + | 10.0091i | 0.425309 | + | 0.350389i | ||||
\(817\) | 0.967942i | 0.0338640i | ||||||||
\(818\) | 48.1837 | − | 10.7961i | 1.68471 | − | 0.377477i | ||||
\(819\) | −0.368398 | + | 12.4073i | −0.0128729 | + | 0.433545i | ||||
\(820\) | −13.2929 | + | 6.27173i | −0.464210 | + | 0.219018i | ||||
\(821\) | −8.67229 | −0.302665 | −0.151332 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151332 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(822\) | −1.81172 | − | 8.08583i | −0.0631911 | − | 0.282026i | ||||
\(823\) | 28.4926i | 0.993191i | 0.867982 | + | 0.496595i | \(0.165417\pi\) | ||||
−0.867982 | + | 0.496595i | \(0.834583\pi\) | |||||||
\(824\) | −13.6021 | − | 17.4805i | −0.473851 | − | 0.608962i | ||||
\(825\) | − | 0.987080i | − | 0.0343657i | ||||||
\(826\) | 9.91884 | + | 51.3704i | 0.345121 | + | 1.78741i | ||||
\(827\) | − | 26.7340i | − | 0.929634i | −0.885407 | − | 0.464817i | \(-0.846120\pi\) | ||
0.885407 | − | 0.464817i | \(-0.153880\pi\) | |||||||
\(828\) | 5.01910 | + | 10.6380i | 0.174426 | + | 0.369695i | ||||
\(829\) | − | 50.3223i | − | 1.74777i | −0.486137 | − | 0.873883i | \(-0.661594\pi\) | ||
0.486137 | − | 0.873883i | \(-0.338406\pi\) | |||||||
\(830\) | 2.30616 | − | 0.516722i | 0.0800481 | − | 0.0179357i | ||||
\(831\) | −26.7718 | −0.928704 | ||||||||
\(832\) | −36.3818 | − | 9.22285i | −1.26131 | − | 0.319745i | ||||
\(833\) | −1.63443 | + | 27.4987i | −0.0566295 | + | 0.952772i | ||||
\(834\) | −5.61082 | − | 25.0414i | −0.194287 | − | 0.867114i | ||||
\(835\) | − | 7.65678i | − | 0.264974i | ||||||
\(836\) | 0.188605 | + | 0.399748i | 0.00652303 | + | 0.0138256i | ||||
\(837\) | 2.77439 | 0.0958968 | ||||||||
\(838\) | 0.718467 | + | 3.20656i | 0.0248190 | + | 0.110769i | ||||
\(839\) | −37.9994 | −1.31188 | −0.655942 | − | 0.754811i | \(-0.727729\pi\) | ||||
−0.655942 | + | 0.754811i | \(0.727729\pi\) | |||||||
\(840\) | 6.03976 | − | 4.41830i | 0.208391 | − | 0.152446i | ||||
\(841\) | 76.0671 | 2.62300 | ||||||||
\(842\) | −7.09743 | − | 31.6763i | −0.244594 | − | 1.09164i | ||||
\(843\) | −8.64183 | −0.297641 | ||||||||
\(844\) | −10.8185 | − | 22.9298i | −0.372388 | − | 0.789276i | ||||
\(845\) | − | 9.01087i | − | 0.309983i | ||||||
\(846\) | 0.744498 | + | 3.32274i | 0.0255964 | + | 0.114238i | ||||
\(847\) | 26.5138 | + | 0.787248i | 0.911023 | + | 0.0270502i | ||||
\(848\) | −21.2376 | + | 25.7785i | −0.729300 | + | 0.885238i | ||||
\(849\) | 5.92047 | 0.203190 | ||||||||
\(850\) | 5.43072 | − | 1.21681i | 0.186272 | − | 0.0417364i | ||||
\(851\) | − | 48.6332i | − | 1.66713i | ||||||
\(852\) | −7.25289 | − | 15.3725i | −0.248480 | − | 0.526654i | ||||
\(853\) | − | 19.8625i | − | 0.680078i | −0.940411 | − | 0.340039i | \(-0.889560\pi\) | ||
0.940411 | − | 0.340039i | \(-0.110440\pi\) | |||||||
\(854\) | −18.1256 | + | 3.49977i | −0.620244 | + | 0.119760i | ||||
\(855\) | − | 0.223896i | − | 0.00765709i | ||||||
\(856\) | −31.2202 | + | 24.2933i | −1.06708 | + | 0.830329i | ||||
\(857\) | 21.4344i | 0.732187i | 0.930578 | + | 0.366093i | \(0.119305\pi\) | ||||
−0.930578 | + | 0.366093i | \(0.880695\pi\) | |||||||
\(858\) | −1.43191 | − | 6.39071i | −0.0488846 | − | 0.218175i | ||||
\(859\) | −12.6251 | −0.430764 | −0.215382 | − | 0.976530i | \(-0.569100\pi\) | ||||
−0.215382 | + | 0.976530i | \(0.569100\pi\) | |||||||
\(860\) | −7.81970 | + | 3.68941i | −0.266650 | + | 0.125808i | ||||
\(861\) | 0.577075 | − | 19.4353i | 0.0196667 | − | 0.662354i | ||||
\(862\) | 0.105022 | − | 0.0235314i | 0.00357707 | − | 0.000801484i | ||||
\(863\) | − | 17.9610i | − | 0.611400i | −0.952128 | − | 0.305700i | \(-0.901110\pi\) | ||
0.952128 | − | 0.305700i | \(-0.0988904\pi\) | |||||||
\(864\) | 5.04682 | + | 2.55532i | 0.171696 | + | 0.0869336i | ||||
\(865\) | 7.12007 | 0.242090 | ||||||||
\(866\) | −13.0258 | + | 2.91857i | −0.442634 | + | 0.0991772i | ||||
\(867\) | 1.51332 | 0.0513949 | ||||||||
\(868\) | −13.4572 | + | 5.86744i | −0.456766 | + | 0.199154i | ||||
\(869\) | 11.3695 | 0.385684 | ||||||||
\(870\) | 14.1453 | − | 3.16941i | 0.479570 | − | 0.107453i | ||||
\(871\) | 36.8159 | 1.24746 | ||||||||
\(872\) | −7.06218 | − | 9.07584i | −0.239155 | − | 0.307347i | ||||
\(873\) | − | 4.31036i | − | 0.145883i | ||||||
\(874\) | −1.81718 | + | 0.407159i | −0.0614669 | + | 0.0137724i | ||||
\(875\) | 0.0785232 | − | 2.64459i | 0.00265457 | − | 0.0894033i | ||||
\(876\) | 12.3458 | + | 26.1669i | 0.417125 | + | 0.884097i | ||||
\(877\) | 12.0637 | 0.407361 | 0.203681 | − | 0.979037i | \(-0.434710\pi\) | ||||
0.203681 | + | 0.979037i | \(0.434710\pi\) | |||||||
\(878\) | −1.34662 | − | 6.01005i | −0.0454462 | − | 0.202829i | ||||
\(879\) | 26.2654i | 0.885911i | ||||||||
\(880\) | −2.51055 | + | 3.04735i | −0.0846307 | + | 0.102726i | ||||
\(881\) | 18.8245i | 0.634213i | 0.948390 | + | 0.317107i | \(0.102711\pi\) | ||||
−0.948390 | + | 0.317107i | \(0.897289\pi\) | |||||||
\(882\) | 1.58747 | + | 9.77138i | 0.0534529 | + | 0.329020i | ||||
\(883\) | − | 12.8758i | − | 0.433305i | −0.976249 | − | 0.216652i | \(-0.930486\pi\) | ||
0.976249 | − | 0.216652i | \(-0.0695138\pi\) | |||||||
\(884\) | 33.3953 | − | 15.7562i | 1.12320 | − | 0.529938i | ||||
\(885\) | 13.9829i | 0.470030i | ||||||||
\(886\) | −49.2134 | + | 11.0268i | −1.65336 | + | 0.370453i | ||||
\(887\) | 44.5236 | 1.49496 | 0.747478 | − | 0.664286i | \(-0.231264\pi\) | ||||
0.747478 | + | 0.664286i | \(0.231264\pi\) | |||||||
\(888\) | −14.3633 | − | 18.4588i | −0.482001 | − | 0.619436i | ||||
\(889\) | 0.407233 | − | 13.7152i | 0.0136582 | − | 0.459994i | ||||
\(890\) | −0.152554 | − | 0.680856i | −0.00511361 | − | 0.0228224i | ||||
\(891\) | 0.987080i | 0.0330684i | ||||||||
\(892\) | 11.6781 | − | 5.50983i | 0.391011 | − | 0.184483i | ||||
\(893\) | −0.539095 | −0.0180401 | ||||||||
\(894\) | 4.78454 | + | 21.3537i | 0.160019 | + | 0.714176i | ||||
\(895\) | 20.8439 | 0.696733 | ||||||||
\(896\) | −29.8837 | − | 1.72124i | −0.998345 | − | 0.0575026i | ||||
\(897\) | 27.5925 | 0.921286 | ||||||||
\(898\) | 4.67042 | + | 20.8444i | 0.155854 | + | 0.695586i | ||||
\(899\) | −28.4381 | −0.948463 | ||||||||
\(900\) | 1.80879 | − | 0.853401i | 0.0602929 | − | 0.0284467i | ||||
\(901\) | − | 32.8600i | − | 1.09472i | ||||||
\(902\) | 2.24301 | + | 10.0107i | 0.0746841 | + | 0.333320i | ||||
\(903\) | 0.339470 | − | 11.4330i | 0.0112968 | − | 0.380467i | ||||
\(904\) | 15.0494 | + | 19.3404i | 0.500534 | + | 0.643253i | ||||
\(905\) | −24.4428 | −0.812507 | ||||||||
\(906\) | −15.9144 | + | 3.56579i | −0.528719 | + | 0.118465i | ||||
\(907\) | 18.9911i | 0.630589i | 0.948994 | + | 0.315295i | \(0.102103\pi\) | ||||
−0.948994 | + | 0.315295i | \(0.897897\pi\) | |||||||
\(908\) | 25.4825 | − | 12.0229i | 0.845667 | − | 0.398993i | ||||
\(909\) | 6.03671i | 0.200225i | ||||||||
\(910\) | −3.32799 | − | 17.2359i | −0.110322 | − | 0.571365i | ||||
\(911\) | − | 27.0080i | − | 0.894816i | −0.894330 | − | 0.447408i | \(-0.852347\pi\) | ||
0.894330 | − | 0.447408i | \(-0.147653\pi\) | |||||||
\(912\) | −0.569460 | + | 0.691221i | −0.0188567 | + | 0.0228886i | ||||
\(913\) | − | 1.64955i | − | 0.0545920i | ||||||
\(914\) | −7.23281 | − | 32.2805i | −0.239240 | − | 1.06774i | ||||
\(915\) | −4.93374 | −0.163104 | ||||||||
\(916\) | −8.32008 | − | 17.6344i | −0.274903 | − | 0.582658i | ||||
\(917\) | −30.0471 | − | 0.892160i | −0.992242 | − | 0.0294617i | ||||
\(918\) | −5.43072 | + | 1.21681i | −0.179241 | + | 0.0401609i | ||||
\(919\) | − | 13.2985i | − | 0.438677i | −0.975649 | − | 0.219338i | \(-0.929610\pi\) | ||
0.975649 | − | 0.219338i | \(-0.0703898\pi\) | |||||||
\(920\) | −10.2156 | − | 13.1285i | −0.336800 | − | 0.432833i | ||||
\(921\) | 18.5432 | 0.611019 | ||||||||
\(922\) | 31.2664 | − | 7.00559i | 1.02970 | − | 0.230717i | ||||
\(923\) | −39.8728 | −1.31243 | ||||||||
\(924\) | −2.08754 | − | 4.78783i | −0.0686750 | − | 0.157508i | ||||
\(925\) | −8.26915 | −0.271888 | ||||||||
\(926\) | 44.1565 | − | 9.89377i | 1.45107 | − | 0.325129i | ||||
\(927\) | 7.83090 | 0.257201 | ||||||||
\(928\) | −51.7310 | − | 26.1926i | −1.69815 | − | 0.859813i | ||||
\(929\) | 30.1489i | 0.989152i | 0.869134 | + | 0.494576i | \(0.164677\pi\) | ||||
−0.869134 | + | 0.494576i | \(0.835323\pi\) | |||||||
\(930\) | −3.82865 | + | 0.857851i | −0.125546 | + | 0.0281301i | ||||
\(931\) | −1.56451 | − | 0.0929892i | −0.0512748 | − | 0.00304760i | ||||
\(932\) | −2.97058 | + | 1.40155i | −0.0973045 | + | 0.0459092i | ||||
\(933\) | 30.8370 | 1.00956 | ||||||||
\(934\) | 13.1973 | + | 58.9004i | 0.431829 | + | 1.92728i | ||||
\(935\) | − | 3.88447i | − | 0.127036i | ||||||
\(936\) | 10.4727 | − | 8.14915i | 0.342312 | − | 0.266363i | ||||
\(937\) | − | 21.3618i | − | 0.697859i | −0.937149 | − | 0.348929i | \(-0.886545\pi\) | ||
0.937149 | − | 0.348929i | \(-0.113455\pi\) | |||||||
\(938\) | 28.8292 | − | 5.56647i | 0.941306 | − | 0.181752i | ||||
\(939\) | − | 20.8250i | − | 0.679599i | ||||||
\(940\) | −2.05481 | − | 4.35517i | −0.0670205 | − | 0.142050i | ||||
\(941\) | − | 48.5491i | − | 1.58266i | −0.611391 | − | 0.791328i | \(-0.709390\pi\) | ||
0.611391 | − | 0.791328i | \(-0.290610\pi\) | |||||||
\(942\) | 1.11330 | − | 0.249448i | 0.0362734 | − | 0.00812746i | ||||
\(943\) | −43.2221 | −1.40751 | ||||||||
\(944\) | 35.5643 | − | 43.1686i | 1.15752 | − | 1.40502i | ||||
\(945\) | −0.0785232 | + | 2.64459i | −0.00255436 | + | 0.0860284i | ||||
\(946\) | 1.31947 | + | 5.88889i | 0.0428998 | + | 0.191464i | ||||
\(947\) | 5.19386i | 0.168778i | 0.996433 | + | 0.0843888i | \(0.0268938\pi\) | ||||
−0.996433 | + | 0.0843888i | \(0.973106\pi\) | |||||||
\(948\) | 9.82975 | + | 20.8342i | 0.319255 | + | 0.676662i | ||||
\(949\) | 67.8709 | 2.20318 | ||||||||
\(950\) | 0.0692296 | + | 0.308976i | 0.00224610 | + | 0.0100245i | ||||
\(951\) | 5.41152 | 0.175480 | ||||||||
\(952\) | 23.7683 | − | 17.3874i | 0.770336 | − | 0.563528i | ||||
\(953\) | −8.36814 | −0.271071 | −0.135535 | − | 0.990773i | \(-0.543275\pi\) | ||||
−0.135535 | + | 0.990773i | \(0.543275\pi\) | |||||||
\(954\) | −2.58186 | − | 11.5230i | −0.0835908 | − | 0.373071i | ||||
\(955\) | −19.3047 | −0.624685 | ||||||||
\(956\) | 8.34391 | + | 17.6849i | 0.269861 | + | 0.571972i | ||||
\(957\) | − | 10.1178i | − | 0.327062i | ||||||
\(958\) | −0.0803092 | − | 0.358425i | −0.00259467 | − | 0.0115802i | ||||
\(959\) | −15.4954 | − | 0.460092i | −0.500374 | − | 0.0148571i | ||||
\(960\) | −7.75471 | − | 1.96583i | −0.250282 | − | 0.0634470i | ||||
\(961\) | −23.3028 | −0.751703 | ||||||||
\(962\) | −53.5375 | + | 11.9957i | −1.72612 | + | 0.386756i | ||||
\(963\) | − | 13.9860i | − | 0.450692i | ||||||
\(964\) | −5.83817 | − | 12.3740i | −0.188035 | − | 0.398540i | ||||
\(965\) | − | 15.2505i | − | 0.490932i | ||||||
\(966\) | 21.6067 | − | 4.17192i | 0.695183 | − | 0.134229i | ||||
\(967\) | 53.7808i | 1.72947i | 0.502225 | + | 0.864737i | \(0.332515\pi\) | ||||
−0.502225 | + | 0.864737i | \(0.667485\pi\) | |||||||
\(968\) | −17.4143 | − | 22.3798i | −0.559718 | − | 0.719313i | ||||
\(969\) | − | 0.881101i | − | 0.0283050i | ||||||
\(970\) | 1.33278 | + | 5.94828i | 0.0427930 | + | 0.190988i | ||||
\(971\) | 27.9111 | 0.895709 | 0.447855 | − | 0.894106i | \(-0.352188\pi\) | ||||
0.447855 | + | 0.894106i | \(0.352188\pi\) | |||||||
\(972\) | −1.80879 | + | 0.853401i | −0.0580168 | + | 0.0273729i | ||||
\(973\) | −47.9887 | − | 1.42488i | −1.53845 | − | 0.0456796i | ||||
\(974\) | 41.1510 | − | 9.22035i | 1.31856 | − | 0.295439i | ||||
\(975\) | − | 4.69157i | − | 0.150251i | ||||||
\(976\) | 15.2316 | + | 12.5485i | 0.487553 | + | 0.401669i | ||||
\(977\) | 16.8294 | 0.538422 | 0.269211 | − | 0.963081i | \(-0.413237\pi\) | ||||
0.269211 | + | 0.963081i | \(0.413237\pi\) | |||||||
\(978\) | −8.94613 | + | 2.00448i | −0.286066 | + | 0.0640963i | ||||
\(979\) | −0.487001 | −0.0155646 | ||||||||
\(980\) | −5.21206 | − | 12.9936i | −0.166493 | − | 0.415066i | ||||
\(981\) | 4.06579 | 0.129811 | ||||||||
\(982\) | 35.8038 | − | 8.02225i | 1.14255 | − | 0.256000i | ||||
\(983\) | 34.1214 | 1.08830 | 0.544151 | − | 0.838987i | \(-0.316852\pi\) | ||||
0.544151 | + | 0.838987i | \(0.316852\pi\) | |||||||
\(984\) | −16.4050 | + | 12.7652i | −0.522972 | + | 0.406940i | ||||
\(985\) | 3.00729i | 0.0958201i | ||||||||
\(986\) | 55.6661 | − | 12.4726i | 1.77277 | − | 0.397209i | ||||
\(987\) | 6.36760 | + | 0.189067i | 0.202683 | + | 0.00601808i | ||||
\(988\) | 0.896434 | + | 1.89999i | 0.0285194 | + | 0.0604469i | ||||
\(989\) | −25.4258 | −0.808494 | ||||||||
\(990\) | −0.305209 | − | 1.36217i | −0.00970018 | − | 0.0432925i | ||||
\(991\) | 56.2777i | 1.78772i | 0.448346 | + | 0.893860i | \(0.352013\pi\) | ||||
−0.448346 | + | 0.893860i | \(0.647987\pi\) | |||||||
\(992\) | 14.0018 | + | 7.08943i | 0.444558 | + | 0.225090i | ||||
\(993\) | − | 1.77494i | − | 0.0563261i | ||||||
\(994\) | −31.2229 | + | 6.02867i | −0.990331 | + | 0.191218i | ||||
\(995\) | − | 22.1587i | − | 0.702478i | ||||||
\(996\) | 3.02273 | − | 1.42615i | 0.0957788 | − | 0.0451893i | ||||
\(997\) | 20.1636i | 0.638589i | 0.947656 | + | 0.319295i | \(0.103446\pi\) | ||||
−0.947656 | + | 0.319295i | \(0.896554\pi\) | |||||||
\(998\) | −31.6205 | + | 7.08493i | −1.00093 | + | 0.224270i | ||||
\(999\) | 8.26915 | 0.261624 |
(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 | 420.2.c.b.391.10 | yes | 16 | |
3.2 | odd | 2 | 1260.2.c.e.811.7 | 16 | |||
4.3 | odd | 2 | 420.2.c.a.391.9 | ✓ | 16 | ||
7.6 | odd | 2 | 420.2.c.a.391.10 | yes | 16 | ||
12.11 | even | 2 | 1260.2.c.d.811.8 | 16 | |||
21.20 | even | 2 | 1260.2.c.d.811.7 | 16 | |||
28.27 | even | 2 | inner | 420.2.c.b.391.9 | yes | 16 | |
84.83 | odd | 2 | 1260.2.c.e.811.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.c.a.391.9 | ✓ | 16 | 4.3 | odd | 2 | ||
420.2.c.a.391.10 | yes | 16 | 7.6 | odd | 2 | ||
420.2.c.b.391.9 | yes | 16 | 28.27 | even | 2 | inner | |
420.2.c.b.391.10 | yes | 16 | 1.1 | even | 1 | trivial | |
1260.2.c.d.811.7 | 16 | 21.20 | even | 2 | |||
1260.2.c.d.811.8 | 16 | 12.11 | even | 2 | |||
1260.2.c.e.811.7 | 16 | 3.2 | odd | 2 | |||
1260.2.c.e.811.8 | 16 | 84.83 | odd | 2 |