Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,2,Mod(16,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.g (of order \(5\), degree \(4\), 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: | \(0.598878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.61 |
Dual form | 75.2.g.a.16.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | −0.835853 | − | 0.548953i | \(-0.815027\pi\) |
0.263792 | + | 0.964580i | \(0.415027\pi\) | |||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | −0.309017 | + | 0.951057i | −0.154508 | + | 0.475528i | ||||
\(5\) | 0.690983 | + | 2.12663i | 0.309017 | + | 0.951057i | ||||
\(6\) | 0.309017 | + | 0.951057i | 0.126156 | + | 0.388267i | ||||
\(7\) | 4.47214 | 1.69031 | 0.845154 | − | 0.534522i | \(-0.179509\pi\) | ||||
0.845154 | + | 0.534522i | \(0.179509\pi\) | |||||||
\(8\) | −0.927051 | − | 2.85317i | −0.327762 | − | 1.00875i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | −1.80902 | − | 1.31433i | −0.572061 | − | 0.415627i | ||||
\(11\) | −2.61803 | + | 1.90211i | −0.789367 | + | 0.573509i | −0.907776 | − | 0.419456i | \(-0.862221\pi\) |
0.118409 | + | 0.992965i | \(0.462221\pi\) | |||||||
\(12\) | 0.809017 | + | 0.587785i | 0.233543 | + | 0.169679i | ||||
\(13\) | −2.73607 | − | 1.98787i | −0.758849 | − | 0.551336i | 0.139708 | − | 0.990193i | \(-0.455384\pi\) |
−0.898557 | + | 0.438857i | \(0.855384\pi\) | |||||||
\(14\) | −3.61803 | + | 2.62866i | −0.966960 | + | 0.702538i | ||||
\(15\) | 2.23607 | 0.577350 | ||||||||
\(16\) | 0.809017 | + | 0.587785i | 0.202254 | + | 0.146946i | ||||
\(17\) | −0.881966 | − | 2.71441i | −0.213908 | − | 0.658342i | −0.999229 | − | 0.0392530i | \(-0.987502\pi\) |
0.785321 | − | 0.619089i | \(-0.212498\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | − | 3.07768i | −0.229416 | − | 0.706069i | −0.997813 | − | 0.0660962i | \(-0.978946\pi\) |
0.768398 | − | 0.639973i | \(-0.221054\pi\) | |||||||
\(20\) | −2.23607 | −0.500000 | ||||||||
\(21\) | 1.38197 | − | 4.25325i | 0.301570 | − | 0.928136i | ||||
\(22\) | 1.00000 | − | 3.07768i | 0.213201 | − | 0.656164i | ||||
\(23\) | 3.61803 | − | 2.62866i | 0.754412 | − | 0.548113i | −0.142779 | − | 0.989755i | \(-0.545604\pi\) |
0.897191 | + | 0.441642i | \(0.145604\pi\) | |||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | −4.04508 | + | 2.93893i | −0.809017 | + | 0.587785i | ||||
\(26\) | 3.38197 | 0.663258 | ||||||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | −1.38197 | + | 4.25325i | −0.261167 | + | 0.803789i | ||||
\(29\) | 1.35410 | − | 4.16750i | 0.251450 | − | 0.773885i | −0.743058 | − | 0.669227i | \(-0.766625\pi\) |
0.994508 | − | 0.104658i | \(-0.0333747\pi\) | |||||||
\(30\) | −1.80902 | + | 1.31433i | −0.330280 | + | 0.239962i | ||||
\(31\) | 2.23607 | + | 6.88191i | 0.401610 | + | 1.23603i | 0.923693 | + | 0.383133i | \(0.125155\pi\) |
−0.522083 | + | 0.852894i | \(0.674845\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 1.00000 | + | 3.07768i | 0.174078 | + | 0.535756i | ||||
\(34\) | 2.30902 | + | 1.67760i | 0.395993 | + | 0.287706i | ||||
\(35\) | 3.09017 | + | 9.51057i | 0.522334 | + | 1.60758i | ||||
\(36\) | 0.809017 | − | 0.587785i | 0.134836 | − | 0.0979642i | ||||
\(37\) | −6.54508 | − | 4.75528i | −1.07601 | − | 0.781764i | −0.0990233 | − | 0.995085i | \(-0.531572\pi\) |
−0.976982 | + | 0.213321i | \(0.931572\pi\) | |||||||
\(38\) | 2.61803 | + | 1.90211i | 0.424701 | + | 0.308563i | ||||
\(39\) | −2.73607 | + | 1.98787i | −0.438122 | + | 0.318314i | ||||
\(40\) | 5.42705 | − | 3.94298i | 0.858092 | − | 0.623440i | ||||
\(41\) | 1.11803 | + | 0.812299i | 0.174608 | + | 0.126860i | 0.671657 | − | 0.740863i | \(-0.265583\pi\) |
−0.497049 | + | 0.867722i | \(0.665583\pi\) | |||||||
\(42\) | 1.38197 | + | 4.25325i | 0.213242 | + | 0.656291i | ||||
\(43\) | −5.70820 | −0.870493 | −0.435246 | − | 0.900311i | \(-0.643339\pi\) | ||||
−0.435246 | + | 0.900311i | \(0.643339\pi\) | |||||||
\(44\) | −1.00000 | − | 3.07768i | −0.150756 | − | 0.463978i | ||||
\(45\) | 0.690983 | − | 2.12663i | 0.103006 | − | 0.317019i | ||||
\(46\) | −1.38197 | + | 4.25325i | −0.203760 | + | 0.627108i | ||||
\(47\) | −1.61803 | + | 4.97980i | −0.236015 | + | 0.726378i | 0.760971 | + | 0.648786i | \(0.224723\pi\) |
−0.996985 | + | 0.0775917i | \(0.975277\pi\) | |||||||
\(48\) | 0.809017 | − | 0.587785i | 0.116772 | − | 0.0848395i | ||||
\(49\) | 13.0000 | 1.85714 | ||||||||
\(50\) | 1.54508 | − | 4.75528i | 0.218508 | − | 0.672499i | ||||
\(51\) | −2.85410 | −0.399654 | ||||||||
\(52\) | 2.73607 | − | 1.98787i | 0.379424 | − | 0.275668i | ||||
\(53\) | 0.427051 | − | 1.31433i | 0.0586600 | − | 0.180537i | −0.917433 | − | 0.397890i | \(-0.869742\pi\) |
0.976093 | + | 0.217354i | \(0.0697424\pi\) | |||||||
\(54\) | 0.309017 | − | 0.951057i | 0.0420519 | − | 0.129422i | ||||
\(55\) | −5.85410 | − | 4.25325i | −0.789367 | − | 0.573509i | ||||
\(56\) | −4.14590 | − | 12.7598i | −0.554019 | − | 1.70509i | ||||
\(57\) | −3.23607 | −0.428628 | ||||||||
\(58\) | 1.35410 | + | 4.16750i | 0.177802 | + | 0.547219i | ||||
\(59\) | 3.23607 | + | 2.35114i | 0.421300 | + | 0.306092i | 0.778161 | − | 0.628065i | \(-0.216153\pi\) |
−0.356861 | + | 0.934158i | \(0.616153\pi\) | |||||||
\(60\) | −0.690983 | + | 2.12663i | −0.0892055 | + | 0.274546i | ||||
\(61\) | 0.500000 | − | 0.363271i | 0.0640184 | − | 0.0465121i | −0.555316 | − | 0.831640i | \(-0.687403\pi\) |
0.619334 | + | 0.785127i | \(0.287403\pi\) | |||||||
\(62\) | −5.85410 | − | 4.25325i | −0.743472 | − | 0.540164i | ||||
\(63\) | −3.61803 | − | 2.62866i | −0.455829 | − | 0.331179i | ||||
\(64\) | −5.66312 | + | 4.11450i | −0.707890 | + | 0.514312i | ||||
\(65\) | 2.33688 | − | 7.19218i | 0.289854 | − | 0.892080i | ||||
\(66\) | −2.61803 | − | 1.90211i | −0.322258 | − | 0.234134i | ||||
\(67\) | 1.61803 | + | 4.97980i | 0.197674 | + | 0.608379i | 0.999935 | + | 0.0114051i | \(0.00363042\pi\) |
−0.802261 | + | 0.596974i | \(0.796370\pi\) | |||||||
\(68\) | 2.85410 | 0.346111 | ||||||||
\(69\) | −1.38197 | − | 4.25325i | −0.166369 | − | 0.512032i | ||||
\(70\) | −8.09017 | − | 5.87785i | −0.966960 | − | 0.702538i | ||||
\(71\) | −0.236068 | + | 0.726543i | −0.0280161 | + | 0.0862247i | −0.964087 | − | 0.265587i | \(-0.914434\pi\) |
0.936071 | + | 0.351812i | \(0.114434\pi\) | |||||||
\(72\) | −0.927051 | + | 2.85317i | −0.109254 | + | 0.336249i | ||||
\(73\) | −2.50000 | + | 1.81636i | −0.292603 | + | 0.212588i | −0.724396 | − | 0.689384i | \(-0.757881\pi\) |
0.431793 | + | 0.901973i | \(0.357881\pi\) | |||||||
\(74\) | 8.09017 | 0.940463 | ||||||||
\(75\) | 1.54508 | + | 4.75528i | 0.178411 | + | 0.549093i | ||||
\(76\) | 3.23607 | 0.371202 | ||||||||
\(77\) | −11.7082 | + | 8.50651i | −1.33427 | + | 0.969407i | ||||
\(78\) | 1.04508 | − | 3.21644i | 0.118333 | − | 0.364190i | ||||
\(79\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(80\) | −0.690983 | + | 2.12663i | −0.0772542 | + | 0.237764i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −1.38197 | −0.152613 | ||||||||
\(83\) | 1.09017 | + | 3.35520i | 0.119662 | + | 0.368281i | 0.992891 | − | 0.119029i | \(-0.0379782\pi\) |
−0.873229 | + | 0.487310i | \(0.837978\pi\) | |||||||
\(84\) | 3.61803 | + | 2.62866i | 0.394760 | + | 0.286810i | ||||
\(85\) | 5.16312 | − | 3.75123i | 0.560019 | − | 0.406878i | ||||
\(86\) | 4.61803 | − | 3.35520i | 0.497975 | − | 0.361800i | ||||
\(87\) | −3.54508 | − | 2.57565i | −0.380073 | − | 0.276139i | ||||
\(88\) | 7.85410 | + | 5.70634i | 0.837250 | + | 0.608298i | ||||
\(89\) | −6.16312 | + | 4.47777i | −0.653289 | + | 0.474642i | −0.864390 | − | 0.502822i | \(-0.832295\pi\) |
0.211101 | + | 0.977464i | \(0.432295\pi\) | |||||||
\(90\) | 0.690983 | + | 2.12663i | 0.0728360 | + | 0.224166i | ||||
\(91\) | −12.2361 | − | 8.89002i | −1.28269 | − | 0.931928i | ||||
\(92\) | 1.38197 | + | 4.25325i | 0.144080 | + | 0.443432i | ||||
\(93\) | 7.23607 | 0.750345 | ||||||||
\(94\) | −1.61803 | − | 4.97980i | −0.166887 | − | 0.513627i | ||||
\(95\) | 5.85410 | − | 4.25325i | 0.600618 | − | 0.436375i | ||||
\(96\) | 1.54508 | − | 4.75528i | 0.157695 | − | 0.485334i | ||||
\(97\) | 2.73607 | − | 8.42075i | 0.277806 | − | 0.854998i | −0.710658 | − | 0.703538i | \(-0.751603\pi\) |
0.988463 | − | 0.151460i | \(-0.0483974\pi\) | |||||||
\(98\) | −10.5172 | + | 7.64121i | −1.06240 | + | 0.771879i | ||||
\(99\) | 3.23607 | 0.325237 | ||||||||
\(100\) | −1.54508 | − | 4.75528i | −0.154508 | − | 0.475528i | ||||
\(101\) | −16.5623 | −1.64801 | −0.824006 | − | 0.566582i | \(-0.808266\pi\) | ||||
−0.824006 | + | 0.566582i | \(0.808266\pi\) | |||||||
\(102\) | 2.30902 | − | 1.67760i | 0.228627 | − | 0.166107i | ||||
\(103\) | −0.381966 | + | 1.17557i | −0.0376362 | + | 0.115832i | −0.968110 | − | 0.250527i | \(-0.919396\pi\) |
0.930473 | + | 0.366360i | \(0.119396\pi\) | |||||||
\(104\) | −3.13525 | + | 9.64932i | −0.307437 | + | 0.946194i | ||||
\(105\) | 10.0000 | 0.975900 | ||||||||
\(106\) | 0.427051 | + | 1.31433i | 0.0414789 | + | 0.127659i | ||||
\(107\) | 16.4721 | 1.59242 | 0.796211 | − | 0.605019i | \(-0.206835\pi\) | ||||
0.796211 | + | 0.605019i | \(0.206835\pi\) | |||||||
\(108\) | −0.309017 | − | 0.951057i | −0.0297352 | − | 0.0915155i | ||||
\(109\) | 15.4443 | + | 11.2209i | 1.47929 | + | 1.07477i | 0.977784 | + | 0.209617i | \(0.0672217\pi\) |
0.501509 | + | 0.865152i | \(0.332778\pi\) | |||||||
\(110\) | 7.23607 | 0.689932 | ||||||||
\(111\) | −6.54508 | + | 4.75528i | −0.621232 | + | 0.451351i | ||||
\(112\) | 3.61803 | + | 2.62866i | 0.341872 | + | 0.248385i | ||||
\(113\) | −2.16312 | − | 1.57160i | −0.203489 | − | 0.147843i | 0.481374 | − | 0.876515i | \(-0.340138\pi\) |
−0.684863 | + | 0.728672i | \(0.740138\pi\) | |||||||
\(114\) | 2.61803 | − | 1.90211i | 0.245201 | − | 0.178149i | ||||
\(115\) | 8.09017 | + | 5.87785i | 0.754412 | + | 0.548113i | ||||
\(116\) | 3.54508 | + | 2.57565i | 0.329153 | + | 0.239144i | ||||
\(117\) | 1.04508 | + | 3.21644i | 0.0966181 | + | 0.297360i | ||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | −3.94427 | − | 12.1392i | −0.361571 | − | 1.11280i | ||||
\(120\) | −2.07295 | − | 6.37988i | −0.189233 | − | 0.582401i | ||||
\(121\) | −0.163119 | + | 0.502029i | −0.0148290 | + | 0.0456390i | ||||
\(122\) | −0.190983 | + | 0.587785i | −0.0172908 | + | 0.0532156i | ||||
\(123\) | 1.11803 | − | 0.812299i | 0.100810 | − | 0.0732426i | ||||
\(124\) | −7.23607 | −0.649818 | ||||||||
\(125\) | −9.04508 | − | 6.57164i | −0.809017 | − | 0.587785i | ||||
\(126\) | 4.47214 | 0.398410 | ||||||||
\(127\) | −7.85410 | + | 5.70634i | −0.696939 | + | 0.506356i | −0.878934 | − | 0.476944i | \(-0.841745\pi\) |
0.181995 | + | 0.983299i | \(0.441745\pi\) | |||||||
\(128\) | −0.927051 | + | 2.85317i | −0.0819405 | + | 0.252187i | ||||
\(129\) | −1.76393 | + | 5.42882i | −0.155306 | + | 0.477981i | ||||
\(130\) | 2.33688 | + | 7.19218i | 0.204958 | + | 0.630796i | ||||
\(131\) | 4.38197 | + | 13.4863i | 0.382854 | + | 1.17830i | 0.938025 | + | 0.346568i | \(0.112653\pi\) |
−0.555171 | + | 0.831736i | \(0.687347\pi\) | |||||||
\(132\) | −3.23607 | −0.281664 | ||||||||
\(133\) | −4.47214 | − | 13.7638i | −0.387783 | − | 1.19347i | ||||
\(134\) | −4.23607 | − | 3.07768i | −0.365941 | − | 0.265871i | ||||
\(135\) | −1.80902 | − | 1.31433i | −0.155695 | − | 0.113119i | ||||
\(136\) | −6.92705 | + | 5.03280i | −0.593990 | + | 0.431559i | ||||
\(137\) | 4.35410 | + | 3.16344i | 0.371996 | + | 0.270271i | 0.758038 | − | 0.652210i | \(-0.226158\pi\) |
−0.386042 | + | 0.922481i | \(0.626158\pi\) | |||||||
\(138\) | 3.61803 | + | 2.62866i | 0.307988 | + | 0.223766i | ||||
\(139\) | 4.09017 | − | 2.97168i | 0.346924 | − | 0.252055i | −0.400654 | − | 0.916230i | \(-0.631217\pi\) |
0.747577 | + | 0.664175i | \(0.231217\pi\) | |||||||
\(140\) | −10.0000 | −0.845154 | ||||||||
\(141\) | 4.23607 | + | 3.07768i | 0.356741 | + | 0.259188i | ||||
\(142\) | −0.236068 | − | 0.726543i | −0.0198104 | − | 0.0609701i | ||||
\(143\) | 10.9443 | 0.915206 | ||||||||
\(144\) | −0.309017 | − | 0.951057i | −0.0257514 | − | 0.0792547i | ||||
\(145\) | 9.79837 | 0.813711 | ||||||||
\(146\) | 0.954915 | − | 2.93893i | 0.0790293 | − | 0.243227i | ||||
\(147\) | 4.01722 | − | 12.3637i | 0.331335 | − | 1.01974i | ||||
\(148\) | 6.54508 | − | 4.75528i | 0.538003 | − | 0.390882i | ||||
\(149\) | −12.1459 | −0.995031 | −0.497515 | − | 0.867455i | \(-0.665754\pi\) | ||||
−0.497515 | + | 0.867455i | \(0.665754\pi\) | |||||||
\(150\) | −4.04508 | − | 2.93893i | −0.330280 | − | 0.239962i | ||||
\(151\) | 16.4721 | 1.34048 | 0.670242 | − | 0.742143i | \(-0.266190\pi\) | ||||
0.670242 | + | 0.742143i | \(0.266190\pi\) | |||||||
\(152\) | −7.85410 | + | 5.70634i | −0.637052 | + | 0.462845i | ||||
\(153\) | −0.881966 | + | 2.71441i | −0.0713027 | + | 0.219447i | ||||
\(154\) | 4.47214 | − | 13.7638i | 0.360375 | − | 1.10912i | ||||
\(155\) | −13.0902 | + | 9.51057i | −1.05143 | + | 0.763907i | ||||
\(156\) | −1.04508 | − | 3.21644i | −0.0836738 | − | 0.257521i | ||||
\(157\) | −13.7984 | −1.10123 | −0.550615 | − | 0.834759i | \(-0.685607\pi\) | ||||
−0.550615 | + | 0.834759i | \(0.685607\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.11803 | − | 0.812299i | −0.0886659 | − | 0.0644195i | ||||
\(160\) | 3.45492 | + | 10.6331i | 0.273135 | + | 0.840623i | ||||
\(161\) | 16.1803 | − | 11.7557i | 1.27519 | − | 0.926479i | ||||
\(162\) | −0.809017 | − | 0.587785i | −0.0635624 | − | 0.0461808i | ||||
\(163\) | −2.38197 | − | 1.73060i | −0.186570 | − | 0.135551i | 0.490580 | − | 0.871396i | \(-0.336785\pi\) |
−0.677150 | + | 0.735845i | \(0.736785\pi\) | |||||||
\(164\) | −1.11803 | + | 0.812299i | −0.0873038 | + | 0.0634299i | ||||
\(165\) | −5.85410 | + | 4.25325i | −0.455741 | + | 0.331115i | ||||
\(166\) | −2.85410 | − | 2.07363i | −0.221521 | − | 0.160945i | ||||
\(167\) | −7.23607 | − | 22.2703i | −0.559944 | − | 1.72333i | −0.682517 | − | 0.730870i | \(-0.739114\pi\) |
0.122573 | − | 0.992460i | \(-0.460886\pi\) | |||||||
\(168\) | −13.4164 | −1.03510 | ||||||||
\(169\) | −0.482779 | − | 1.48584i | −0.0371369 | − | 0.114295i | ||||
\(170\) | −1.97214 | + | 6.06961i | −0.151256 | + | 0.465518i | ||||
\(171\) | −1.00000 | + | 3.07768i | −0.0764719 | + | 0.235356i | ||||
\(172\) | 1.76393 | − | 5.42882i | 0.134499 | − | 0.413944i | ||||
\(173\) | −8.01722 | + | 5.82485i | −0.609538 | + | 0.442855i | −0.849252 | − | 0.527988i | \(-0.822946\pi\) |
0.239714 | + | 0.970844i | \(0.422946\pi\) | |||||||
\(174\) | 4.38197 | 0.332196 | ||||||||
\(175\) | −18.0902 | + | 13.1433i | −1.36749 | + | 0.993538i | ||||
\(176\) | −3.23607 | −0.243928 | ||||||||
\(177\) | 3.23607 | − | 2.35114i | 0.243238 | − | 0.176723i | ||||
\(178\) | 2.35410 | − | 7.24518i | 0.176447 | − | 0.543049i | ||||
\(179\) | 1.90983 | − | 5.87785i | 0.142747 | − | 0.439331i | −0.853967 | − | 0.520327i | \(-0.825810\pi\) |
0.996714 | + | 0.0809958i | \(0.0258100\pi\) | |||||||
\(180\) | 1.80902 | + | 1.31433i | 0.134836 | + | 0.0979642i | ||||
\(181\) | −3.02786 | − | 9.31881i | −0.225059 | − | 0.692661i | −0.998286 | − | 0.0585312i | \(-0.981358\pi\) |
0.773226 | − | 0.634130i | \(-0.218642\pi\) | |||||||
\(182\) | 15.1246 | 1.12111 | ||||||||
\(183\) | −0.190983 | − | 0.587785i | −0.0141179 | − | 0.0434503i | ||||
\(184\) | −10.8541 | − | 7.88597i | −0.800175 | − | 0.581361i | ||||
\(185\) | 5.59017 | − | 17.2048i | 0.410997 | − | 1.26492i | ||||
\(186\) | −5.85410 | + | 4.25325i | −0.429244 | + | 0.311864i | ||||
\(187\) | 7.47214 | + | 5.42882i | 0.546417 | + | 0.396995i | ||||
\(188\) | −4.23607 | − | 3.07768i | −0.308947 | − | 0.224463i | ||||
\(189\) | −3.61803 | + | 2.62866i | −0.263173 | + | 0.191207i | ||||
\(190\) | −2.23607 | + | 6.88191i | −0.162221 | + | 0.499266i | ||||
\(191\) | 19.9443 | + | 14.4904i | 1.44312 | + | 1.04849i | 0.987380 | + | 0.158371i | \(0.0506243\pi\) |
0.455737 | + | 0.890114i | \(0.349376\pi\) | |||||||
\(192\) | 2.16312 | + | 6.65740i | 0.156110 | + | 0.480456i | ||||
\(193\) | 7.67376 | 0.552369 | 0.276185 | − | 0.961105i | \(-0.410930\pi\) | ||||
0.276185 | + | 0.961105i | \(0.410930\pi\) | |||||||
\(194\) | 2.73607 | + | 8.42075i | 0.196438 | + | 0.604575i | ||||
\(195\) | −6.11803 | − | 4.44501i | −0.438122 | − | 0.318314i | ||||
\(196\) | −4.01722 | + | 12.3637i | −0.286944 | + | 0.883124i | ||||
\(197\) | 1.66312 | − | 5.11855i | 0.118492 | − | 0.364682i | −0.874167 | − | 0.485625i | \(-0.838592\pi\) |
0.992659 | + | 0.120943i | \(0.0385920\pi\) | |||||||
\(198\) | −2.61803 | + | 1.90211i | −0.186056 | + | 0.135177i | ||||
\(199\) | −18.6525 | −1.32224 | −0.661119 | − | 0.750281i | \(-0.729918\pi\) | ||||
−0.661119 | + | 0.750281i | \(0.729918\pi\) | |||||||
\(200\) | 12.1353 | + | 8.81678i | 0.858092 | + | 0.623440i | ||||
\(201\) | 5.23607 | 0.369324 | ||||||||
\(202\) | 13.3992 | − | 9.73508i | 0.942764 | − | 0.684958i | ||||
\(203\) | 6.05573 | − | 18.6376i | 0.425029 | − | 1.30810i | ||||
\(204\) | 0.881966 | − | 2.71441i | 0.0617500 | − | 0.190047i | ||||
\(205\) | −0.954915 | + | 2.93893i | −0.0666942 | + | 0.205264i | ||||
\(206\) | −0.381966 | − | 1.17557i | −0.0266128 | − | 0.0819059i | ||||
\(207\) | −4.47214 | −0.310835 | ||||||||
\(208\) | −1.04508 | − | 3.21644i | −0.0724636 | − | 0.223020i | ||||
\(209\) | 8.47214 | + | 6.15537i | 0.586030 | + | 0.425776i | ||||
\(210\) | −8.09017 | + | 5.87785i | −0.558275 | + | 0.405610i | ||||
\(211\) | 14.4721 | − | 10.5146i | 0.996303 | − | 0.723856i | 0.0350106 | − | 0.999387i | \(-0.488854\pi\) |
0.961292 | + | 0.275530i | \(0.0888535\pi\) | |||||||
\(212\) | 1.11803 | + | 0.812299i | 0.0767869 | + | 0.0557889i | ||||
\(213\) | 0.618034 | + | 0.449028i | 0.0423470 | + | 0.0307669i | ||||
\(214\) | −13.3262 | + | 9.68208i | −0.910963 | + | 0.661853i | ||||
\(215\) | −3.94427 | − | 12.1392i | −0.268997 | − | 0.827888i | ||||
\(216\) | 2.42705 | + | 1.76336i | 0.165140 | + | 0.119981i | ||||
\(217\) | 10.0000 | + | 30.7768i | 0.678844 | + | 2.08927i | ||||
\(218\) | −19.0902 | −1.29295 | ||||||||
\(219\) | 0.954915 | + | 2.93893i | 0.0645272 | + | 0.198594i | ||||
\(220\) | 5.85410 | − | 4.25325i | 0.394683 | − | 0.286754i | ||||
\(221\) | −2.98278 | + | 9.18005i | −0.200643 | + | 0.617517i | ||||
\(222\) | 2.50000 | − | 7.69421i | 0.167789 | − | 0.516401i | ||||
\(223\) | 11.4721 | − | 8.33499i | 0.768231 | − | 0.558153i | −0.133193 | − | 0.991090i | \(-0.542523\pi\) |
0.901424 | + | 0.432938i | \(0.142523\pi\) | |||||||
\(224\) | 22.3607 | 1.49404 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 2.67376 | 0.177856 | ||||||||
\(227\) | 16.1803 | − | 11.7557i | 1.07393 | − | 0.780254i | 0.0973129 | − | 0.995254i | \(-0.468975\pi\) |
0.976614 | + | 0.215000i | \(0.0689752\pi\) | |||||||
\(228\) | 1.00000 | − | 3.07768i | 0.0662266 | − | 0.203825i | ||||
\(229\) | −7.71885 | + | 23.7562i | −0.510076 | + | 1.56985i | 0.281991 | + | 0.959417i | \(0.409005\pi\) |
−0.792067 | + | 0.610435i | \(0.790995\pi\) | |||||||
\(230\) | −10.0000 | −0.659380 | ||||||||
\(231\) | 4.47214 | + | 13.7638i | 0.294245 | + | 0.905593i | ||||
\(232\) | −13.1459 | −0.863070 | ||||||||
\(233\) | 4.51722 | + | 13.9026i | 0.295933 | + | 0.910788i | 0.982906 | + | 0.184106i | \(0.0589388\pi\) |
−0.686973 | + | 0.726682i | \(0.741061\pi\) | |||||||
\(234\) | −2.73607 | − | 1.98787i | −0.178862 | − | 0.129951i | ||||
\(235\) | −11.7082 | −0.763759 | ||||||||
\(236\) | −3.23607 | + | 2.35114i | −0.210650 | + | 0.153046i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.3262 | + | 7.50245i | 0.669351 | + | 0.486312i | ||||
\(239\) | 5.70820 | − | 4.14725i | 0.369233 | − | 0.268263i | −0.387660 | − | 0.921803i | \(-0.626716\pi\) |
0.756893 | + | 0.653539i | \(0.226716\pi\) | |||||||
\(240\) | 1.80902 | + | 1.31433i | 0.116772 | + | 0.0848395i | ||||
\(241\) | 0.836881 | + | 0.608030i | 0.0539082 | + | 0.0391666i | 0.614413 | − | 0.788985i | \(-0.289393\pi\) |
−0.560505 | + | 0.828151i | \(0.689393\pi\) | |||||||
\(242\) | −0.163119 | − | 0.502029i | −0.0104857 | − | 0.0322716i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.190983 | + | 0.587785i | 0.0122264 | + | 0.0376291i | ||||
\(245\) | 8.98278 | + | 27.6462i | 0.573889 | + | 1.76625i | ||||
\(246\) | −0.427051 | + | 1.31433i | −0.0272278 | + | 0.0837985i | ||||
\(247\) | −3.38197 | + | 10.4086i | −0.215189 | + | 0.662285i | ||||
\(248\) | 17.5623 | − | 12.7598i | 1.11521 | − | 0.810246i | ||||
\(249\) | 3.52786 | 0.223569 | ||||||||
\(250\) | 11.1803 | 0.707107 | ||||||||
\(251\) | −26.9443 | −1.70071 | −0.850354 | − | 0.526212i | \(-0.823612\pi\) | ||||
−0.850354 | + | 0.526212i | \(0.823612\pi\) | |||||||
\(252\) | 3.61803 | − | 2.62866i | 0.227915 | − | 0.165590i | ||||
\(253\) | −4.47214 | + | 13.7638i | −0.281161 | + | 0.865324i | ||||
\(254\) | 3.00000 | − | 9.23305i | 0.188237 | − | 0.579333i | ||||
\(255\) | −1.97214 | − | 6.06961i | −0.123500 | − | 0.380094i | ||||
\(256\) | −5.25329 | − | 16.1680i | −0.328331 | − | 1.01050i | ||||
\(257\) | −12.7984 | −0.798341 | −0.399170 | − | 0.916877i | \(-0.630702\pi\) | ||||
−0.399170 | + | 0.916877i | \(0.630702\pi\) | |||||||
\(258\) | −1.76393 | − | 5.42882i | −0.109818 | − | 0.337984i | ||||
\(259\) | −29.2705 | − | 21.2663i | −1.81878 | − | 1.32142i | ||||
\(260\) | 6.11803 | + | 4.44501i | 0.379424 | + | 0.275668i | ||||
\(261\) | −3.54508 | + | 2.57565i | −0.219435 | + | 0.159429i | ||||
\(262\) | −11.4721 | − | 8.33499i | −0.708751 | − | 0.514938i | ||||
\(263\) | −9.61803 | − | 6.98791i | −0.593073 | − | 0.430893i | 0.250340 | − | 0.968158i | \(-0.419458\pi\) |
−0.843414 | + | 0.537265i | \(0.819458\pi\) | |||||||
\(264\) | 7.85410 | − | 5.70634i | 0.483387 | − | 0.351201i | ||||
\(265\) | 3.09017 | 0.189828 | ||||||||
\(266\) | 11.7082 | + | 8.50651i | 0.717876 | + | 0.521567i | ||||
\(267\) | 2.35410 | + | 7.24518i | 0.144069 | + | 0.443398i | ||||
\(268\) | −5.23607 | −0.319844 | ||||||||
\(269\) | −0.0450850 | − | 0.138757i | −0.00274888 | − | 0.00846018i | 0.949673 | − | 0.313244i | \(-0.101416\pi\) |
−0.952422 | + | 0.304784i | \(0.901416\pi\) | |||||||
\(270\) | 2.23607 | 0.136083 | ||||||||
\(271\) | 6.85410 | − | 21.0948i | 0.416357 | − | 1.28142i | −0.494674 | − | 0.869078i | \(-0.664713\pi\) |
0.911031 | − | 0.412337i | \(-0.135287\pi\) | |||||||
\(272\) | 0.881966 | − | 2.71441i | 0.0534770 | − | 0.164585i | ||||
\(273\) | −12.2361 | + | 8.89002i | −0.740561 | + | 0.538049i | ||||
\(274\) | −5.38197 | −0.325136 | ||||||||
\(275\) | 5.00000 | − | 15.3884i | 0.301511 | − | 0.927957i | ||||
\(276\) | 4.47214 | 0.269191 | ||||||||
\(277\) | 4.69098 | − | 3.40820i | 0.281854 | − | 0.204779i | −0.437872 | − | 0.899037i | \(-0.644268\pi\) |
0.719726 | + | 0.694259i | \(0.244268\pi\) | |||||||
\(278\) | −1.56231 | + | 4.80828i | −0.0937009 | + | 0.288382i | ||||
\(279\) | 2.23607 | − | 6.88191i | 0.133870 | − | 0.412009i | ||||
\(280\) | 24.2705 | − | 17.6336i | 1.45044 | − | 1.05381i | ||||
\(281\) | −5.37132 | − | 16.5312i | −0.320426 | − | 0.986171i | −0.973463 | − | 0.228844i | \(-0.926505\pi\) |
0.653037 | − | 0.757326i | \(-0.273495\pi\) | |||||||
\(282\) | −5.23607 | −0.311803 | ||||||||
\(283\) | 0.0901699 | + | 0.277515i | 0.00536005 | + | 0.0164965i | 0.953701 | − | 0.300757i | \(-0.0972393\pi\) |
−0.948341 | + | 0.317254i | \(0.897239\pi\) | |||||||
\(284\) | −0.618034 | − | 0.449028i | −0.0366736 | − | 0.0266449i | ||||
\(285\) | −2.23607 | − | 6.88191i | −0.132453 | − | 0.407649i | ||||
\(286\) | −8.85410 | + | 6.43288i | −0.523554 | + | 0.380384i | ||||
\(287\) | 5.00000 | + | 3.63271i | 0.295141 | + | 0.214432i | ||||
\(288\) | −4.04508 | − | 2.93893i | −0.238359 | − | 0.173178i | ||||
\(289\) | 7.16312 | − | 5.20431i | 0.421360 | − | 0.306136i | ||||
\(290\) | −7.92705 | + | 5.75934i | −0.465492 | + | 0.338200i | ||||
\(291\) | −7.16312 | − | 5.20431i | −0.419909 | − | 0.305082i | ||||
\(292\) | −0.954915 | − | 2.93893i | −0.0558822 | − | 0.171988i | ||||
\(293\) | 3.79837 | 0.221903 | 0.110952 | − | 0.993826i | \(-0.464610\pi\) | ||||
0.110952 | + | 0.993826i | \(0.464610\pi\) | |||||||
\(294\) | 4.01722 | + | 12.3637i | 0.234289 | + | 0.721068i | ||||
\(295\) | −2.76393 | + | 8.50651i | −0.160922 | + | 0.495268i | ||||
\(296\) | −7.50000 | + | 23.0826i | −0.435929 | + | 1.34165i | ||||
\(297\) | 1.00000 | − | 3.07768i | 0.0580259 | − | 0.178585i | ||||
\(298\) | 9.82624 | − | 7.13918i | 0.569219 | − | 0.413562i | ||||
\(299\) | −15.1246 | −0.874679 | ||||||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | −25.5279 | −1.47140 | ||||||||
\(302\) | −13.3262 | + | 9.68208i | −0.766839 | + | 0.557141i | ||||
\(303\) | −5.11803 | + | 15.7517i | −0.294023 | + | 0.904911i | ||||
\(304\) | 1.00000 | − | 3.07768i | 0.0573539 | − | 0.176517i | ||||
\(305\) | 1.11803 | + | 0.812299i | 0.0640184 | + | 0.0465121i | ||||
\(306\) | −0.881966 | − | 2.71441i | −0.0504186 | − | 0.155173i | ||||
\(307\) | 1.34752 | 0.0769073 | 0.0384536 | − | 0.999260i | \(-0.487757\pi\) | ||||
0.0384536 | + | 0.999260i | \(0.487757\pi\) | |||||||
\(308\) | −4.47214 | − | 13.7638i | −0.254824 | − | 0.784266i | ||||
\(309\) | 1.00000 | + | 0.726543i | 0.0568880 | + | 0.0413316i | ||||
\(310\) | 5.00000 | − | 15.3884i | 0.283981 | − | 0.874003i | ||||
\(311\) | −3.47214 | + | 2.52265i | −0.196887 | + | 0.143047i | −0.681861 | − | 0.731482i | \(-0.738829\pi\) |
0.484974 | + | 0.874529i | \(0.338829\pi\) | |||||||
\(312\) | 8.20820 | + | 5.96361i | 0.464698 | + | 0.337623i | ||||
\(313\) | −6.85410 | − | 4.97980i | −0.387417 | − | 0.281475i | 0.376979 | − | 0.926222i | \(-0.376963\pi\) |
−0.764396 | + | 0.644747i | \(0.776963\pi\) | |||||||
\(314\) | 11.1631 | − | 8.11048i | 0.629971 | − | 0.457701i | ||||
\(315\) | 3.09017 | − | 9.51057i | 0.174111 | − | 0.535860i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.67376 | − | 23.6174i | −0.431001 | − | 1.32649i | −0.897129 | − | 0.441768i | \(-0.854351\pi\) |
0.466128 | − | 0.884717i | \(-0.345649\pi\) | |||||||
\(318\) | 1.38197 | 0.0774968 | ||||||||
\(319\) | 4.38197 | + | 13.4863i | 0.245343 | + | 0.755088i | ||||
\(320\) | −12.6631 | − | 9.20029i | −0.707890 | − | 0.514312i | ||||
\(321\) | 5.09017 | − | 15.6659i | 0.284106 | − | 0.874387i | ||||
\(322\) | −6.18034 | + | 19.0211i | −0.344417 | + | 1.06001i | ||||
\(323\) | −7.47214 | + | 5.42882i | −0.415761 | + | 0.302068i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 16.9098 | 0.937989 | ||||||||
\(326\) | 2.94427 | 0.163068 | ||||||||
\(327\) | 15.4443 | − | 11.2209i | 0.854070 | − | 0.620518i | ||||
\(328\) | 1.28115 | − | 3.94298i | 0.0707398 | − | 0.217715i | ||||
\(329\) | −7.23607 | + | 22.2703i | −0.398937 | + | 1.22780i | ||||
\(330\) | 2.23607 | − | 6.88191i | 0.123091 | − | 0.378837i | ||||
\(331\) | 3.38197 | + | 10.4086i | 0.185890 | + | 0.572110i | 0.999963 | − | 0.00865315i | \(-0.00275442\pi\) |
−0.814073 | + | 0.580763i | \(0.802754\pi\) | |||||||
\(332\) | −3.52786 | −0.193617 | ||||||||
\(333\) | 2.50000 | + | 7.69421i | 0.136999 | + | 0.421640i | ||||
\(334\) | 18.9443 | + | 13.7638i | 1.03658 | + | 0.753123i | ||||
\(335\) | −9.47214 | + | 6.88191i | −0.517518 | + | 0.375999i | ||||
\(336\) | 3.61803 | − | 2.62866i | 0.197380 | − | 0.143405i | ||||
\(337\) | 12.0902 | + | 8.78402i | 0.658594 | + | 0.478496i | 0.866188 | − | 0.499719i | \(-0.166563\pi\) |
−0.207594 | + | 0.978215i | \(0.566563\pi\) | |||||||
\(338\) | 1.26393 | + | 0.918300i | 0.0687488 | + | 0.0499490i | ||||
\(339\) | −2.16312 | + | 1.57160i | −0.117484 | + | 0.0853575i | ||||
\(340\) | 1.97214 | + | 6.06961i | 0.106954 | + | 0.329171i | ||||
\(341\) | −18.9443 | − | 13.7638i | −1.02589 | − | 0.745353i | ||||
\(342\) | −1.00000 | − | 3.07768i | −0.0540738 | − | 0.166422i | ||||
\(343\) | 26.8328 | 1.44884 | ||||||||
\(344\) | 5.29180 | + | 16.2865i | 0.285315 | + | 0.878108i | ||||
\(345\) | 8.09017 | − | 5.87785i | 0.435560 | − | 0.316453i | ||||
\(346\) | 3.06231 | − | 9.42481i | 0.164631 | − | 0.506681i | ||||
\(347\) | −10.4164 | + | 32.0584i | −0.559182 | + | 1.72099i | 0.125453 | + | 0.992100i | \(0.459962\pi\) |
−0.684635 | + | 0.728886i | \(0.740038\pi\) | |||||||
\(348\) | 3.54508 | − | 2.57565i | 0.190037 | − | 0.138070i | ||||
\(349\) | 25.0344 | 1.34006 | 0.670031 | − | 0.742333i | \(-0.266281\pi\) | ||||
0.670031 | + | 0.742333i | \(0.266281\pi\) | |||||||
\(350\) | 6.90983 | − | 21.2663i | 0.369346 | − | 1.13673i | ||||
\(351\) | 3.38197 | 0.180516 | ||||||||
\(352\) | −13.0902 | + | 9.51057i | −0.697708 | + | 0.506915i | ||||
\(353\) | −9.38197 | + | 28.8747i | −0.499352 | + | 1.53685i | 0.310712 | + | 0.950504i | \(0.399433\pi\) |
−0.810063 | + | 0.586342i | \(0.800567\pi\) | |||||||
\(354\) | −1.23607 | + | 3.80423i | −0.0656963 | + | 0.202192i | ||||
\(355\) | −1.70820 | −0.0906621 | ||||||||
\(356\) | −2.35410 | − | 7.24518i | −0.124767 | − | 0.383994i | ||||
\(357\) | −12.7639 | −0.675539 | ||||||||
\(358\) | 1.90983 | + | 5.87785i | 0.100938 | + | 0.310654i | ||||
\(359\) | 8.56231 | + | 6.22088i | 0.451901 | + | 0.328325i | 0.790346 | − | 0.612661i | \(-0.209901\pi\) |
−0.338445 | + | 0.940986i | \(0.609901\pi\) | |||||||
\(360\) | −6.70820 | −0.353553 | ||||||||
\(361\) | 6.89919 | − | 5.01255i | 0.363115 | − | 0.263819i | ||||
\(362\) | 7.92705 | + | 5.75934i | 0.416637 | + | 0.302704i | ||||
\(363\) | 0.427051 | + | 0.310271i | 0.0224144 | + | 0.0162850i | ||||
\(364\) | 12.2361 | − | 8.89002i | 0.641344 | − | 0.465964i | ||||
\(365\) | −5.59017 | − | 4.06150i | −0.292603 | − | 0.212588i | ||||
\(366\) | 0.500000 | + | 0.363271i | 0.0261354 | + | 0.0189885i | ||||
\(367\) | −1.85410 | − | 5.70634i | −0.0967833 | − | 0.297868i | 0.890931 | − | 0.454139i | \(-0.150053\pi\) |
−0.987714 | + | 0.156270i | \(0.950053\pi\) | |||||||
\(368\) | 4.47214 | 0.233126 | ||||||||
\(369\) | −0.427051 | − | 1.31433i | −0.0222314 | − | 0.0684212i | ||||
\(370\) | 5.59017 | + | 17.2048i | 0.290619 | + | 0.894434i | ||||
\(371\) | 1.90983 | − | 5.87785i | 0.0991534 | − | 0.305163i | ||||
\(372\) | −2.23607 | + | 6.88191i | −0.115935 | + | 0.356810i | ||||
\(373\) | −23.7984 | + | 17.2905i | −1.23223 | + | 0.895270i | −0.997056 | − | 0.0766827i | \(-0.975567\pi\) |
−0.235178 | + | 0.971952i | \(0.575567\pi\) | |||||||
\(374\) | −9.23607 | −0.477586 | ||||||||
\(375\) | −9.04508 | + | 6.57164i | −0.467086 | + | 0.339358i | ||||
\(376\) | 15.7082 | 0.810089 | ||||||||
\(377\) | −11.9894 | + | 8.71078i | −0.617483 | + | 0.448628i | ||||
\(378\) | 1.38197 | − | 4.25325i | 0.0710807 | − | 0.218764i | ||||
\(379\) | 7.23607 | − | 22.2703i | 0.371692 | − | 1.14395i | −0.573992 | − | 0.818861i | \(-0.694606\pi\) |
0.945684 | − | 0.325089i | \(-0.105394\pi\) | |||||||
\(380\) | 2.23607 | + | 6.88191i | 0.114708 | + | 0.353035i | ||||
\(381\) | 3.00000 | + | 9.23305i | 0.153695 | + | 0.473024i | ||||
\(382\) | −24.6525 | −1.26133 | ||||||||
\(383\) | 6.43769 | + | 19.8132i | 0.328951 | + | 1.01241i | 0.969626 | + | 0.244594i | \(0.0786547\pi\) |
−0.640675 | + | 0.767812i | \(0.721345\pi\) | |||||||
\(384\) | 2.42705 | + | 1.76336i | 0.123855 | + | 0.0899859i | ||||
\(385\) | −26.1803 | − | 19.0211i | −1.33427 | − | 0.969407i | ||||
\(386\) | −6.20820 | + | 4.51052i | −0.315989 | + | 0.229580i | ||||
\(387\) | 4.61803 | + | 3.35520i | 0.234748 | + | 0.170554i | ||||
\(388\) | 7.16312 | + | 5.20431i | 0.363652 | + | 0.264209i | ||||
\(389\) | 30.0066 | − | 21.8011i | 1.52139 | − | 1.10536i | 0.560603 | − | 0.828085i | \(-0.310570\pi\) |
0.960791 | − | 0.277272i | \(-0.0894304\pi\) | |||||||
\(390\) | 7.56231 | 0.382932 | ||||||||
\(391\) | −10.3262 | − | 7.50245i | −0.522220 | − | 0.379415i | ||||
\(392\) | −12.0517 | − | 37.0912i | −0.608701 | − | 1.87339i | ||||
\(393\) | 14.1803 | 0.715304 | ||||||||
\(394\) | 1.66312 | + | 5.11855i | 0.0837867 | + | 0.257869i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | + | 3.07768i | −0.0502519 | + | 0.154659i | ||||
\(397\) | 3.38197 | − | 10.4086i | 0.169736 | − | 0.522394i | −0.829618 | − | 0.558331i | \(-0.811442\pi\) |
0.999354 | + | 0.0359377i | \(0.0114418\pi\) | |||||||
\(398\) | 15.0902 | − | 10.9637i | 0.756402 | − | 0.549558i | ||||
\(399\) | −14.4721 | −0.724513 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 33.4508 | 1.67046 | 0.835228 | − | 0.549904i | \(-0.185336\pi\) | ||||
0.835228 | + | 0.549904i | \(0.185336\pi\) | |||||||
\(402\) | −4.23607 | + | 3.07768i | −0.211276 | + | 0.153501i | ||||
\(403\) | 7.56231 | − | 23.2744i | 0.376705 | − | 1.15938i | ||||
\(404\) | 5.11803 | − | 15.7517i | 0.254632 | − | 0.783676i | ||||
\(405\) | −1.80902 | + | 1.31433i | −0.0898908 | + | 0.0653095i | ||||
\(406\) | 6.05573 | + | 18.6376i | 0.300541 | + | 0.924969i | ||||
\(407\) | 26.1803 | 1.29771 | ||||||||
\(408\) | 2.64590 | + | 8.14324i | 0.130991 | + | 0.403150i | ||||
\(409\) | −20.8713 | − | 15.1639i | −1.03202 | − | 0.749807i | −0.0633084 | − | 0.997994i | \(-0.520165\pi\) |
−0.968712 | + | 0.248187i | \(0.920165\pi\) | |||||||
\(410\) | −0.954915 | − | 2.93893i | −0.0471599 | − | 0.145143i | ||||
\(411\) | 4.35410 | − | 3.16344i | 0.214772 | − | 0.156041i | ||||
\(412\) | −1.00000 | − | 0.726543i | −0.0492665 | − | 0.0357942i | ||||
\(413\) | 14.4721 | + | 10.5146i | 0.712127 | + | 0.517391i | ||||
\(414\) | 3.61803 | − | 2.62866i | 0.177817 | − | 0.129191i | ||||
\(415\) | −6.38197 | + | 4.63677i | −0.313278 | + | 0.227610i | ||||
\(416\) | −13.6803 | − | 9.93935i | −0.670734 | − | 0.487317i | ||||
\(417\) | −1.56231 | − | 4.80828i | −0.0765064 | − | 0.235463i | ||||
\(418\) | −10.4721 | −0.512209 | ||||||||
\(419\) | 10.1803 | + | 31.3319i | 0.497342 | + | 1.53066i | 0.813275 | + | 0.581880i | \(0.197683\pi\) |
−0.315932 | + | 0.948782i | \(0.602317\pi\) | |||||||
\(420\) | −3.09017 | + | 9.51057i | −0.150785 | + | 0.464068i | ||||
\(421\) | 7.15248 | − | 22.0131i | 0.348590 | − | 1.07285i | −0.611043 | − | 0.791597i | \(-0.709250\pi\) |
0.959634 | − | 0.281253i | \(-0.0907502\pi\) | |||||||
\(422\) | −5.52786 | + | 17.0130i | −0.269092 | + | 0.828181i | ||||
\(423\) | 4.23607 | − | 3.07768i | 0.205965 | − | 0.149642i | ||||
\(424\) | −4.14590 | −0.201343 | ||||||||
\(425\) | 11.5451 | + | 8.38800i | 0.560019 | + | 0.406878i | ||||
\(426\) | −0.763932 | −0.0370126 | ||||||||
\(427\) | 2.23607 | − | 1.62460i | 0.108211 | − | 0.0786198i | ||||
\(428\) | −5.09017 | + | 15.6659i | −0.246043 | + | 0.757241i | ||||
\(429\) | 3.38197 | − | 10.4086i | 0.163283 | − | 0.502533i | ||||
\(430\) | 10.3262 | + | 7.50245i | 0.497975 | + | 0.361800i | ||||
\(431\) | −3.29180 | − | 10.1311i | −0.158560 | − | 0.487998i | 0.839944 | − | 0.542673i | \(-0.182588\pi\) |
−0.998504 | + | 0.0546749i | \(0.982588\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 7.71885 | + | 23.7562i | 0.370944 | + | 1.14165i | 0.946174 | + | 0.323657i | \(0.104912\pi\) |
−0.575230 | + | 0.817991i | \(0.695088\pi\) | |||||||
\(434\) | −26.1803 | − | 19.0211i | −1.25670 | − | 0.913043i | ||||
\(435\) | 3.02786 | − | 9.31881i | 0.145175 | − | 0.446803i | ||||
\(436\) | −15.4443 | + | 11.2209i | −0.739646 | + | 0.537385i | ||||
\(437\) | −11.7082 | − | 8.50651i | −0.560079 | − | 0.406921i | ||||
\(438\) | −2.50000 | − | 1.81636i | −0.119455 | − | 0.0867889i | ||||
\(439\) | 5.00000 | − | 3.63271i | 0.238637 | − | 0.173380i | −0.462039 | − | 0.886860i | \(-0.652882\pi\) |
0.700676 | + | 0.713480i | \(0.252882\pi\) | |||||||
\(440\) | −6.70820 | + | 20.6457i | −0.319801 | + | 0.984247i | ||||
\(441\) | −10.5172 | − | 7.64121i | −0.500820 | − | 0.363867i | ||||
\(442\) | −2.98278 | − | 9.18005i | −0.141876 | − | 0.436650i | ||||
\(443\) | −30.7639 | −1.46164 | −0.730819 | − | 0.682571i | \(-0.760862\pi\) | ||||
−0.730819 | + | 0.682571i | \(0.760862\pi\) | |||||||
\(444\) | −2.50000 | − | 7.69421i | −0.118645 | − | 0.365151i | ||||
\(445\) | −13.7812 | − | 10.0126i | −0.653289 | − | 0.474642i | ||||
\(446\) | −4.38197 | + | 13.4863i | −0.207492 | + | 0.638595i | ||||
\(447\) | −3.75329 | + | 11.5514i | −0.177524 | + | 0.546364i | ||||
\(448\) | −25.3262 | + | 18.4006i | −1.19655 | + | 0.869346i | ||||
\(449\) | −7.79837 | −0.368028 | −0.184014 | − | 0.982924i | \(-0.558909\pi\) | ||||
−0.184014 | + | 0.982924i | \(0.558909\pi\) | |||||||
\(450\) | −4.04508 | + | 2.93893i | −0.190687 | + | 0.138542i | ||||
\(451\) | −4.47214 | −0.210585 | ||||||||
\(452\) | 2.16312 | − | 1.57160i | 0.101745 | − | 0.0739217i | ||||
\(453\) | 5.09017 | − | 15.6659i | 0.239157 | − | 0.736050i | ||||
\(454\) | −6.18034 | + | 19.0211i | −0.290058 | + | 0.892706i | ||||
\(455\) | 10.4508 | − | 32.1644i | 0.489943 | − | 1.50789i | ||||
\(456\) | 3.00000 | + | 9.23305i | 0.140488 | + | 0.432377i | ||||
\(457\) | 22.3607 | 1.04599 | 0.522994 | − | 0.852336i | \(-0.324815\pi\) | ||||
0.522994 | + | 0.852336i | \(0.324815\pi\) | |||||||
\(458\) | −7.71885 | − | 23.7562i | −0.360678 | − | 1.11005i | ||||
\(459\) | 2.30902 | + | 1.67760i | 0.107776 | + | 0.0783036i | ||||
\(460\) | −8.09017 | + | 5.87785i | −0.377206 | + | 0.274056i | ||||
\(461\) | 6.63525 | − | 4.82079i | 0.309035 | − | 0.224527i | −0.422448 | − | 0.906387i | \(-0.638829\pi\) |
0.731482 | + | 0.681861i | \(0.238829\pi\) | |||||||
\(462\) | −11.7082 | − | 8.50651i | −0.544715 | − | 0.395759i | ||||
\(463\) | −18.7984 | − | 13.6578i | −0.873635 | − | 0.634733i | 0.0579252 | − | 0.998321i | \(-0.481552\pi\) |
−0.931560 | + | 0.363588i | \(0.881552\pi\) | |||||||
\(464\) | 3.54508 | − | 2.57565i | 0.164576 | − | 0.119572i | ||||
\(465\) | 5.00000 | + | 15.3884i | 0.231869 | + | 0.713621i | ||||
\(466\) | −11.8262 | − | 8.59226i | −0.547840 | − | 0.398029i | ||||
\(467\) | 1.79837 | + | 5.53483i | 0.0832188 | + | 0.256121i | 0.984005 | − | 0.178142i | \(-0.0570087\pi\) |
−0.900786 | + | 0.434263i | \(0.857009\pi\) | |||||||
\(468\) | −3.38197 | −0.156331 | ||||||||
\(469\) | 7.23607 | + | 22.2703i | 0.334131 | + | 1.02835i | ||||
\(470\) | 9.47214 | − | 6.88191i | 0.436917 | − | 0.317439i | ||||
\(471\) | −4.26393 | + | 13.1230i | −0.196472 | + | 0.604677i | ||||
\(472\) | 3.70820 | − | 11.4127i | 0.170684 | − | 0.525311i | ||||
\(473\) | 14.9443 | − | 10.8576i | 0.687138 | − | 0.499235i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.0902 | + | 9.51057i | 0.600618 | + | 0.436375i | ||||
\(476\) | 12.7639 | 0.585034 | ||||||||
\(477\) | −1.11803 | + | 0.812299i | −0.0511913 | + | 0.0371926i | ||||
\(478\) | −2.18034 | + | 6.71040i | −0.0997264 | + | 0.306926i | ||||
\(479\) | 0.326238 | − | 1.00406i | 0.0149062 | − | 0.0458765i | −0.943327 | − | 0.331865i | \(-0.892322\pi\) |
0.958233 | + | 0.285989i | \(0.0923220\pi\) | |||||||
\(480\) | 11.1803 | 0.510310 | ||||||||
\(481\) | 8.45492 | + | 26.0216i | 0.385511 | + | 1.18648i | ||||
\(482\) | −1.03444 | −0.0471175 | ||||||||
\(483\) | −6.18034 | − | 19.0211i | −0.281215 | − | 0.865491i | ||||
\(484\) | −0.427051 | − | 0.310271i | −0.0194114 | − | 0.0141032i | ||||
\(485\) | 19.7984 | 0.898998 | ||||||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | 3.00000 | + | 2.17963i | 0.135943 | + | 0.0987684i | 0.653679 | − | 0.756772i | \(-0.273225\pi\) |
−0.517736 | + | 0.855541i | \(0.673225\pi\) | |||||||
\(488\) | −1.50000 | − | 1.08981i | −0.0679018 | − | 0.0493336i | ||||
\(489\) | −2.38197 | + | 1.73060i | −0.107716 | + | 0.0782604i | ||||
\(490\) | −23.5172 | − | 17.0863i | −1.06240 | − | 0.771879i | ||||
\(491\) | 24.1803 | + | 17.5680i | 1.09124 | + | 0.792835i | 0.979609 | − | 0.200915i | \(-0.0643914\pi\) |
0.111635 | + | 0.993749i | \(0.464391\pi\) | |||||||
\(492\) | 0.427051 | + | 1.31433i | 0.0192529 | + | 0.0592545i | ||||
\(493\) | −12.5066 | −0.563268 | ||||||||
\(494\) | −3.38197 | − | 10.4086i | −0.152162 | − | 0.468306i | ||||
\(495\) | 2.23607 | + | 6.88191i | 0.100504 | + | 0.309319i | ||||
\(496\) | −2.23607 | + | 6.88191i | −0.100402 | + | 0.309007i | ||||
\(497\) | −1.05573 | + | 3.24920i | −0.0473559 | + | 0.145746i | ||||
\(498\) | −2.85410 | + | 2.07363i | −0.127895 | + | 0.0929214i | ||||
\(499\) | −6.00000 | −0.268597 | −0.134298 | − | 0.990941i | \(-0.542878\pi\) | ||||
−0.134298 | + | 0.990941i | \(0.542878\pi\) | |||||||
\(500\) | 9.04508 | − | 6.57164i | 0.404508 | − | 0.293893i | ||||
\(501\) | −23.4164 | −1.04617 | ||||||||
\(502\) | 21.7984 | − | 15.8374i | 0.972909 | − | 0.706860i | ||||
\(503\) | 10.9443 | − | 33.6830i | 0.487981 | − | 1.50185i | −0.339636 | − | 0.940557i | \(-0.610304\pi\) |
0.827617 | − | 0.561294i | \(-0.189696\pi\) | |||||||
\(504\) | −4.14590 | + | 12.7598i | −0.184673 | + | 0.568365i | ||||
\(505\) | −11.4443 | − | 35.2218i | −0.509263 | − | 1.56735i | ||||
\(506\) | −4.47214 | − | 13.7638i | −0.198811 | − | 0.611876i | ||||
\(507\) | −1.56231 | −0.0693844 | ||||||||
\(508\) | −3.00000 | − | 9.23305i | −0.133103 | − | 0.409650i | ||||
\(509\) | −21.7254 | − | 15.7844i | −0.962963 | − | 0.699633i | −0.00912564 | − | 0.999958i | \(-0.502905\pi\) |
−0.953837 | + | 0.300325i | \(0.902905\pi\) | |||||||
\(510\) | 5.16312 | + | 3.75123i | 0.228627 | + | 0.166107i | ||||
\(511\) | −11.1803 | + | 8.12299i | −0.494589 | + | 0.359340i | ||||
\(512\) | 8.89919 | + | 6.46564i | 0.393292 | + | 0.285744i | ||||
\(513\) | 2.61803 | + | 1.90211i | 0.115589 | + | 0.0839803i | ||||
\(514\) | 10.3541 | − | 7.52270i | 0.456700 | − | 0.331812i | ||||
\(515\) | −2.76393 | −0.121793 | ||||||||
\(516\) | −4.61803 | − | 3.35520i | −0.203298 | − | 0.147704i | ||||
\(517\) | −5.23607 | − | 16.1150i | −0.230282 | − | 0.708735i | ||||
\(518\) | 36.1803 | 1.58967 | ||||||||
\(519\) | 3.06231 | + | 9.42481i | 0.134420 | + | 0.413703i | ||||
\(520\) | −22.6869 | −0.994887 | ||||||||
\(521\) | 0.628677 | − | 1.93487i | 0.0275428 | − | 0.0847682i | −0.936340 | − | 0.351094i | \(-0.885810\pi\) |
0.963883 | + | 0.266326i | \(0.0858097\pi\) | |||||||
\(522\) | 1.35410 | − | 4.16750i | 0.0592674 | − | 0.182406i | ||||
\(523\) | 9.94427 | − | 7.22494i | 0.434833 | − | 0.315924i | −0.348746 | − | 0.937217i | \(-0.613392\pi\) |
0.783578 | + | 0.621293i | \(0.213392\pi\) | |||||||
\(524\) | −14.1803 | −0.619471 | ||||||||
\(525\) | 6.90983 | + | 21.2663i | 0.301570 | + | 0.928136i | ||||
\(526\) | 11.8885 | 0.518365 | ||||||||
\(527\) | 16.7082 | − | 12.1392i | 0.727821 | − | 0.528793i | ||||
\(528\) | −1.00000 | + | 3.07768i | −0.0435194 | + | 0.133939i | ||||
\(529\) | −0.927051 | + | 2.85317i | −0.0403066 | + | 0.124051i | ||||
\(530\) | −2.50000 | + | 1.81636i | −0.108593 | + | 0.0788975i | ||||
\(531\) | −1.23607 | − | 3.80423i | −0.0536408 | − | 0.165089i | ||||
\(532\) | 14.4721 | 0.627447 | ||||||||
\(533\) | −1.44427 | − | 4.44501i | −0.0625584 | − | 0.192535i | ||||
\(534\) | −6.16312 | − | 4.47777i | −0.266704 | − | 0.193772i | ||||
\(535\) | 11.3820 | + | 35.0301i | 0.492085 | + | 1.51448i | ||||
\(536\) | 12.7082 | − | 9.23305i | 0.548911 | − | 0.398807i | ||||
\(537\) | −5.00000 | − | 3.63271i | −0.215766 | − | 0.156763i | ||||
\(538\) | 0.118034 | + | 0.0857567i | 0.00508881 | + | 0.00369723i | ||||
\(539\) | −34.0344 | + | 24.7275i | −1.46597 | + | 1.06509i | ||||
\(540\) | 1.80902 | − | 1.31433i | 0.0778477 | − | 0.0565597i | ||||
\(541\) | 28.5795 | + | 20.7642i | 1.22873 | + | 0.892724i | 0.996794 | − | 0.0800067i | \(-0.0254942\pi\) |
0.231936 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(542\) | 6.85410 | + | 21.0948i | 0.294409 | + | 0.906097i | ||||
\(543\) | −9.79837 | −0.420488 | ||||||||
\(544\) | −4.40983 | − | 13.5721i | −0.189070 | − | 0.581897i | ||||
\(545\) | −13.1910 | + | 40.5977i | −0.565040 | + | 1.73901i | ||||
\(546\) | 4.67376 | − | 14.3844i | 0.200019 | − | 0.615594i | ||||
\(547\) | −0.729490 | + | 2.24514i | −0.0311907 | + | 0.0959952i | −0.965440 | − | 0.260626i | \(-0.916071\pi\) |
0.934249 | + | 0.356621i | \(0.116071\pi\) | |||||||
\(548\) | −4.35410 | + | 3.16344i | −0.185998 | + | 0.135135i | ||||
\(549\) | −0.618034 | −0.0263770 | ||||||||
\(550\) | 5.00000 | + | 15.3884i | 0.213201 | + | 0.656164i | ||||
\(551\) | −14.1803 | −0.604103 | ||||||||
\(552\) | −10.8541 | + | 7.88597i | −0.461981 | + | 0.335649i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.79180 | + | 5.51458i | −0.0761261 | + | 0.234292i | ||||
\(555\) | −14.6353 | − | 10.6331i | −0.621232 | − | 0.451351i | ||||
\(556\) | 1.56231 | + | 4.80828i | 0.0662565 | + | 0.203917i | ||||
\(557\) | 22.2705 | 0.943632 | 0.471816 | − | 0.881697i | \(-0.343599\pi\) | ||||
0.471816 | + | 0.881697i | \(0.343599\pi\) | |||||||
\(558\) | 2.23607 | + | 6.88191i | 0.0946603 | + | 0.291334i | ||||
\(559\) | 15.6180 | + | 11.3472i | 0.660572 | + | 0.479934i | ||||
\(560\) | −3.09017 | + | 9.51057i | −0.130584 | + | 0.401895i | ||||
\(561\) | 7.47214 | − | 5.42882i | 0.315474 | − | 0.229205i | ||||
\(562\) | 14.0623 | + | 10.2169i | 0.593183 | + | 0.430972i | ||||
\(563\) | 14.1803 | + | 10.3026i | 0.597630 | + | 0.434204i | 0.845037 | − | 0.534708i | \(-0.179578\pi\) |
−0.247407 | + | 0.968912i | \(0.579578\pi\) | |||||||
\(564\) | −4.23607 | + | 3.07768i | −0.178371 | + | 0.129594i | ||||
\(565\) | 1.84752 | − | 5.68609i | 0.0777259 | − | 0.239216i | ||||
\(566\) | −0.236068 | − | 0.171513i | −0.00992268 | − | 0.00720925i | ||||
\(567\) | 1.38197 | + | 4.25325i | 0.0580371 | + | 0.178620i | ||||
\(568\) | 2.29180 | 0.0961616 | ||||||||
\(569\) | −9.35410 | − | 28.7890i | −0.392144 | − | 1.20690i | −0.931163 | − | 0.364603i | \(-0.881205\pi\) |
0.539019 | − | 0.842294i | \(-0.318795\pi\) | |||||||
\(570\) | 5.85410 | + | 4.25325i | 0.245201 | + | 0.178149i | ||||
\(571\) | −6.56231 | + | 20.1967i | −0.274624 | + | 0.845206i | 0.714695 | + | 0.699437i | \(0.246566\pi\) |
−0.989319 | + | 0.145769i | \(0.953434\pi\) | |||||||
\(572\) | −3.38197 | + | 10.4086i | −0.141407 | + | 0.435206i | ||||
\(573\) | 19.9443 | − | 14.4904i | 0.833184 | − | 0.605344i | ||||
\(574\) | −6.18034 | −0.257962 | ||||||||
\(575\) | −6.90983 | + | 21.2663i | −0.288160 | + | 0.886865i | ||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | 25.0344 | − | 18.1886i | 1.04220 | − | 0.757201i | 0.0714842 | − | 0.997442i | \(-0.477226\pi\) |
0.970713 | + | 0.240241i | \(0.0772265\pi\) | |||||||
\(578\) | −2.73607 | + | 8.42075i | −0.113805 | + | 0.350257i | ||||
\(579\) | 2.37132 | − | 7.29818i | 0.0985488 | − | 0.303302i | ||||
\(580\) | −3.02786 | + | 9.31881i | −0.125725 | + | 0.386942i | ||||
\(581\) | 4.87539 | + | 15.0049i | 0.202265 | + | 0.622508i | ||||
\(582\) | 8.85410 | 0.367014 | ||||||||
\(583\) | 1.38197 | + | 4.25325i | 0.0572352 | + | 0.176152i | ||||
\(584\) | 7.50000 | + | 5.44907i | 0.310352 | + | 0.225484i | ||||
\(585\) | −6.11803 | + | 4.44501i | −0.252950 | + | 0.183779i | ||||
\(586\) | −3.07295 | + | 2.23263i | −0.126942 | + | 0.0922290i | ||||
\(587\) | 11.7984 | + | 8.57202i | 0.486971 | + | 0.353805i | 0.804018 | − | 0.594605i | \(-0.202691\pi\) |
−0.317047 | + | 0.948410i | \(0.602691\pi\) | |||||||
\(588\) | 10.5172 | + | 7.64121i | 0.433723 | + | 0.315118i | ||||
\(589\) | 18.9443 | − | 13.7638i | 0.780585 | − | 0.567128i | ||||
\(590\) | −2.76393 | − | 8.50651i | −0.113789 | − | 0.350207i | ||||
\(591\) | −4.35410 | − | 3.16344i | −0.179104 | − | 0.130127i | ||||
\(592\) | −2.50000 | − | 7.69421i | −0.102749 | − | 0.316230i | ||||
\(593\) | −32.7426 | −1.34458 | −0.672290 | − | 0.740288i | \(-0.734689\pi\) | ||||
−0.672290 | + | 0.740288i | \(0.734689\pi\) | |||||||
\(594\) | 1.00000 | + | 3.07768i | 0.0410305 | + | 0.126279i | ||||
\(595\) | 23.0902 | − | 16.7760i | 0.946605 | − | 0.687749i | ||||
\(596\) | 3.75329 | − | 11.5514i | 0.153741 | − | 0.473165i | ||||
\(597\) | −5.76393 | + | 17.7396i | −0.235902 | + | 0.726032i | ||||
\(598\) | 12.2361 | − | 8.89002i | 0.500370 | − | 0.363540i | ||||
\(599\) | −12.4721 | −0.509598 | −0.254799 | − | 0.966994i | \(-0.582009\pi\) | ||||
−0.254799 | + | 0.966994i | \(0.582009\pi\) | |||||||
\(600\) | 12.1353 | − | 8.81678i | 0.495420 | − | 0.359943i | ||||
\(601\) | −24.3262 | −0.992288 | −0.496144 | − | 0.868240i | \(-0.665251\pi\) | ||||
−0.496144 | + | 0.868240i | \(0.665251\pi\) | |||||||
\(602\) | 20.6525 | − | 15.0049i | 0.841732 | − | 0.611554i | ||||
\(603\) | 1.61803 | − | 4.97980i | 0.0658914 | − | 0.202793i | ||||
\(604\) | −5.09017 | + | 15.6659i | −0.207116 | + | 0.637438i | ||||
\(605\) | −1.18034 | −0.0479876 | ||||||||
\(606\) | −5.11803 | − | 15.7517i | −0.207906 | − | 0.639869i | ||||
\(607\) | −39.2361 | −1.59254 | −0.796271 | − | 0.604940i | \(-0.793197\pi\) | ||||
−0.796271 | + | 0.604940i | \(0.793197\pi\) | |||||||
\(608\) | −5.00000 | − | 15.3884i | −0.202777 | − | 0.624083i | ||||
\(609\) | −15.8541 | − | 11.5187i | −0.642441 | − | 0.466760i | ||||
\(610\) | −1.38197 | −0.0559542 | ||||||||
\(611\) | 14.3262 | − | 10.4086i | 0.579578 | − | 0.421088i | ||||
\(612\) | −2.30902 | − | 1.67760i | −0.0933365 | − | 0.0678129i | ||||
\(613\) | −31.9615 | − | 23.2214i | −1.29091 | − | 0.937903i | −0.291089 | − | 0.956696i | \(-0.594018\pi\) |
−0.999823 | + | 0.0187931i | \(0.994018\pi\) | |||||||
\(614\) | −1.09017 | + | 0.792055i | −0.0439957 | + | 0.0319647i | ||||
\(615\) | 2.50000 | + | 1.81636i | 0.100810 | + | 0.0732426i | ||||
\(616\) | 35.1246 | + | 25.5195i | 1.41521 | + | 1.02821i | ||||
\(617\) | 8.33688 | + | 25.6583i | 0.335630 | + | 1.03296i | 0.966411 | + | 0.257002i | \(0.0827348\pi\) |
−0.630781 | + | 0.775961i | \(0.717265\pi\) | |||||||
\(618\) | −1.23607 | −0.0497219 | ||||||||
\(619\) | 8.76393 | + | 26.9726i | 0.352252 | + | 1.08412i | 0.957586 | + | 0.288149i | \(0.0930398\pi\) |
−0.605333 | + | 0.795972i | \(0.706960\pi\) | |||||||
\(620\) | −5.00000 | − | 15.3884i | −0.200805 | − | 0.618014i | ||||
\(621\) | −1.38197 | + | 4.25325i | −0.0554564 | + | 0.170677i | ||||
\(622\) | 1.32624 | − | 4.08174i | 0.0531773 | − | 0.163663i | ||||
\(623\) | −27.5623 | + | 20.0252i | −1.10426 | + | 0.802292i | ||||
\(624\) | −3.38197 | −0.135387 | ||||||||
\(625\) | 7.72542 | − | 23.7764i | 0.309017 | − | 0.951057i | ||||
\(626\) | 8.47214 | 0.338615 | ||||||||
\(627\) | 8.47214 | − | 6.15537i | 0.338345 | − | 0.245822i | ||||
\(628\) | 4.26393 | − | 13.1230i | 0.170149 | − | 0.523666i | ||||
\(629\) | −7.13525 | + | 21.9601i | −0.284501 | + | 0.875605i | ||||
\(630\) | 3.09017 | + | 9.51057i | 0.123115 | + | 0.378910i | ||||
\(631\) | 3.18034 | + | 9.78808i | 0.126607 | + | 0.389657i | 0.994190 | − | 0.107635i | \(-0.0343277\pi\) |
−0.867583 | + | 0.497292i | \(0.834328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.52786 | − | 17.0130i | −0.219713 | − | 0.676207i | ||||
\(634\) | 20.0902 | + | 14.5964i | 0.797883 | + | 0.579696i | ||||
\(635\) | −17.5623 | − | 12.7598i | −0.696939 | − | 0.506356i | ||||
\(636\) | 1.11803 | − | 0.812299i | 0.0443329 | − | 0.0322098i | ||||
\(637\) | −35.5689 | − | 25.8423i | −1.40929 | − | 1.02391i | ||||
\(638\) | −11.4721 | − | 8.33499i | −0.454186 | − | 0.329986i | ||||
\(639\) | 0.618034 | − | 0.449028i | 0.0244490 | − | 0.0177633i | ||||
\(640\) | −6.70820 | −0.265165 | ||||||||
\(641\) | −31.5066 | − | 22.8909i | −1.24444 | − | 0.904135i | −0.246549 | − | 0.969130i | \(-0.579297\pi\) |
−0.997886 | + | 0.0649953i | \(0.979297\pi\) | |||||||
\(642\) | 5.09017 | + | 15.6659i | 0.200893 | + | 0.618285i | ||||
\(643\) | 13.8885 | 0.547711 | 0.273855 | − | 0.961771i | \(-0.411701\pi\) | ||||
0.273855 | + | 0.961771i | \(0.411701\pi\) | |||||||
\(644\) | 6.18034 | + | 19.0211i | 0.243540 | + | 0.749538i | ||||
\(645\) | −12.7639 | −0.502579 | ||||||||
\(646\) | 2.85410 | − | 8.78402i | 0.112293 | − | 0.345603i | ||||
\(647\) | 3.20163 | − | 9.85359i | 0.125869 | − | 0.387385i | −0.868189 | − | 0.496233i | \(-0.834716\pi\) |
0.994058 | + | 0.108848i | \(0.0347162\pi\) | |||||||
\(648\) | 2.42705 | − | 1.76336i | 0.0953436 | − | 0.0692712i | ||||
\(649\) | −12.9443 | −0.508107 | ||||||||
\(650\) | −13.6803 | + | 9.93935i | −0.536587 | + | 0.389853i | ||||
\(651\) | 32.3607 | 1.26832 | ||||||||
\(652\) | 2.38197 | − | 1.73060i | 0.0932850 | − | 0.0677755i | ||||
\(653\) | 13.9377 | − | 42.8958i | 0.545424 | − | 1.67864i | −0.174555 | − | 0.984647i | \(-0.555849\pi\) |
0.719979 | − | 0.693995i | \(-0.244151\pi\) | |||||||
\(654\) | −5.89919 | + | 18.1558i | −0.230676 | + | 0.709949i | ||||
\(655\) | −25.6525 | + | 18.6376i | −1.00233 | + | 0.728232i | ||||
\(656\) | 0.427051 | + | 1.31433i | 0.0166735 | + | 0.0513159i | ||||
\(657\) | 3.09017 | 0.120559 | ||||||||
\(658\) | −7.23607 | − | 22.2703i | −0.282091 | − | 0.868188i | ||||
\(659\) | 5.32624 | + | 3.86974i | 0.207481 | + | 0.150744i | 0.686673 | − | 0.726966i | \(-0.259070\pi\) |
−0.479192 | + | 0.877710i | \(0.659070\pi\) | |||||||
\(660\) | −2.23607 | − | 6.88191i | −0.0870388 | − | 0.267878i | ||||
\(661\) | −20.5623 | + | 14.9394i | −0.799781 | + | 0.581075i | −0.910850 | − | 0.412738i | \(-0.864573\pi\) |
0.111069 | + | 0.993813i | \(0.464573\pi\) | |||||||
\(662\) | −8.85410 | − | 6.43288i | −0.344124 | − | 0.250021i | ||||
\(663\) | 7.80902 | + | 5.67358i | 0.303277 | + | 0.220344i | ||||
\(664\) | 8.56231 | − | 6.22088i | 0.332282 | − | 0.241417i | ||||
\(665\) | 26.1803 | − | 19.0211i | 1.01523 | − | 0.737608i | ||||
\(666\) | −6.54508 | − | 4.75528i | −0.253617 | − | 0.184263i | ||||
\(667\) | −6.05573 | − | 18.6376i | −0.234479 | − | 0.721651i | ||||
\(668\) | 23.4164 | 0.906008 | ||||||||
\(669\) | −4.38197 | − | 13.4863i | −0.169417 | − | 0.521411i | ||||
\(670\) | 3.61803 | − | 11.1352i | 0.139777 | − | 0.430189i | ||||
\(671\) | −0.618034 | + | 1.90211i | −0.0238589 | + | 0.0734303i | ||||
\(672\) | 6.90983 | − | 21.2663i | 0.266552 | − | 0.820364i | ||||
\(673\) | −24.1074 | + | 17.5150i | −0.929272 | + | 0.675155i | −0.945814 | − | 0.324708i | \(-0.894734\pi\) |
0.0165428 | + | 0.999863i | \(0.494734\pi\) | |||||||
\(674\) | −14.9443 | −0.575632 | ||||||||
\(675\) | 1.54508 | − | 4.75528i | 0.0594703 | − | 0.183031i | ||||
\(676\) | 1.56231 | 0.0600887 | ||||||||
\(677\) | −30.2705 | + | 21.9928i | −1.16339 | + | 0.845252i | −0.990203 | − | 0.139636i | \(-0.955407\pi\) |
−0.173187 | + | 0.984889i | \(0.555407\pi\) | |||||||
\(678\) | 0.826238 | − | 2.54290i | 0.0317315 | − | 0.0976594i | ||||
\(679\) | 12.2361 | − | 37.6587i | 0.469577 | − | 1.44521i | ||||
\(680\) | −15.4894 | − | 11.2537i | −0.593990 | − | 0.431559i | ||||
\(681\) | −6.18034 | − | 19.0211i | −0.236831 | − | 0.728891i | ||||
\(682\) | 23.4164 | 0.896661 | ||||||||
\(683\) | 2.29180 | + | 7.05342i | 0.0876931 | + | 0.269892i | 0.985281 | − | 0.170945i | \(-0.0546819\pi\) |
−0.897588 | + | 0.440836i | \(0.854682\pi\) | |||||||
\(684\) | −2.61803 | − | 1.90211i | −0.100103 | − | 0.0727291i | ||||
\(685\) | −3.71885 | + | 11.4454i | −0.142090 | + | 0.437308i | ||||
\(686\) | −21.7082 | + | 15.7719i | −0.828823 | + | 0.602175i | ||||
\(687\) | 20.2082 | + | 14.6821i | 0.770991 | + | 0.560158i | ||||
\(688\) | −4.61803 | − | 3.35520i | −0.176061 | − | 0.127916i | ||||
\(689\) | −3.78115 | + | 2.74717i | −0.144050 | + | 0.104659i | ||||
\(690\) | −3.09017 | + | 9.51057i | −0.117641 | + | 0.362061i | ||||
\(691\) | 17.1803 | + | 12.4822i | 0.653571 | + | 0.474847i | 0.864486 | − | 0.502657i | \(-0.167644\pi\) |
−0.210915 | + | 0.977504i | \(0.567644\pi\) | |||||||
\(692\) | −3.06231 | − | 9.42481i | −0.116411 | − | 0.358277i | ||||
\(693\) | 14.4721 | 0.549751 | ||||||||
\(694\) | −10.4164 | − | 32.0584i | −0.395401 | − | 1.21692i | ||||
\(695\) | 9.14590 | + | 6.64488i | 0.346924 | + | 0.252055i | ||||
\(696\) | −4.06231 | + | 12.5025i | −0.153981 | + | 0.473906i | ||||
\(697\) | 1.21885 | − | 3.75123i | 0.0461671 | − | 0.142088i | ||||
\(698\) | −20.2533 | + | 14.7149i | −0.766598 | + | 0.556966i | ||||
\(699\) | 14.6180 | 0.552905 | ||||||||
\(700\) | −6.90983 | − | 21.2663i | −0.261167 | − | 0.803789i | ||||
\(701\) | 0.437694 | 0.0165315 | 0.00826574 | − | 0.999966i | \(-0.497369\pi\) | ||||
0.00826574 | + | 0.999966i | \(0.497369\pi\) | |||||||
\(702\) | −2.73607 | + | 1.98787i | −0.103266 | + | 0.0750273i | ||||
\(703\) | −8.09017 | + | 24.8990i | −0.305127 | + | 0.939083i | ||||
\(704\) | 7.00000 | − | 21.5438i | 0.263822 | − | 0.811962i | ||||
\(705\) | −3.61803 | + | 11.1352i | −0.136263 | + | 0.419375i | ||||
\(706\) | −9.38197 | − | 28.8747i | −0.353095 | − | 1.08671i | ||||
\(707\) | −74.0689 | −2.78565 | ||||||||
\(708\) | 1.23607 | + | 3.80423i | 0.0464543 | + | 0.142972i | ||||
\(709\) | 5.44427 | + | 3.95550i | 0.204464 | + | 0.148552i | 0.685305 | − | 0.728256i | \(-0.259669\pi\) |
−0.480841 | + | 0.876808i | \(0.659669\pi\) | |||||||
\(710\) | 1.38197 | − | 1.00406i | 0.0518643 | − | 0.0376816i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.4894 | + | 13.4333i | 0.692918 | + | 0.503434i | ||||
\(713\) | 26.1803 | + | 19.0211i | 0.980461 | + | 0.712347i | ||||
\(714\) | 10.3262 | − | 7.50245i | 0.386450 | − | 0.280772i | ||||
\(715\) | 7.56231 | + | 23.2744i | 0.282814 | + | 0.870413i | ||||
\(716\) | 5.00000 | + | 3.63271i | 0.186859 | + | 0.135761i | ||||
\(717\) | −2.18034 | − | 6.71040i | −0.0814263 | − | 0.250604i | ||||
\(718\) | −10.5836 | −0.394976 | ||||||||
\(719\) | −11.0902 | − | 34.1320i | −0.413594 | − | 1.27291i | −0.913503 | − | 0.406832i | \(-0.866633\pi\) |
0.499909 | − | 0.866078i | \(-0.333367\pi\) | |||||||
\(720\) | 1.80902 | − | 1.31433i | 0.0674181 | − | 0.0489821i | ||||
\(721\) | −1.70820 | + | 5.25731i | −0.0636168 | + | 0.195792i | ||||
\(722\) | −2.63525 | + | 8.11048i | −0.0980740 | + | 0.301841i | ||||
\(723\) | 0.836881 | − | 0.608030i | 0.0311239 | − | 0.0226129i | ||||
\(724\) | 9.79837 | 0.364154 | ||||||||
\(725\) | 6.77051 | + | 20.8375i | 0.251450 | + | 0.773885i | ||||
\(726\) | −0.527864 | −0.0195909 | ||||||||
\(727\) | −12.4164 | + | 9.02105i | −0.460499 | + | 0.334572i | −0.793727 | − | 0.608274i | \(-0.791862\pi\) |
0.333228 | + | 0.942846i | \(0.391862\pi\) | |||||||
\(728\) | −14.0213 | + | 43.1531i | −0.519663 | + | 1.59936i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 6.90983 | 0.255744 | ||||||||
\(731\) | 5.03444 | + | 15.4944i | 0.186206 | + | 0.573082i | ||||
\(732\) | 0.618034 | 0.0228432 | ||||||||
\(733\) | 0.798374 | + | 2.45714i | 0.0294886 | + | 0.0907566i | 0.964718 | − | 0.263287i | \(-0.0848065\pi\) |
−0.935229 | + | 0.354043i | \(0.884807\pi\) | |||||||
\(734\) | 4.85410 | + | 3.52671i | 0.179168 | + | 0.130173i | ||||
\(735\) | 29.0689 | 1.07222 | ||||||||
\(736\) | 18.0902 | − | 13.1433i | 0.666813 | − | 0.484468i | ||||
\(737\) | −13.7082 | − | 9.95959i | −0.504948 | − | 0.366866i | ||||
\(738\) | 1.11803 | + | 0.812299i | 0.0411554 | + | 0.0299011i | ||||
\(739\) | −14.3262 | + | 10.4086i | −0.526999 | + | 0.382887i | −0.819234 | − | 0.573459i | \(-0.805601\pi\) |
0.292235 | + | 0.956347i | \(0.405601\pi\) | |||||||
\(740\) | 14.6353 | + | 10.6331i | 0.538003 | + | 0.390882i | ||||
\(741\) | 8.85410 | + | 6.43288i | 0.325264 | + | 0.236318i | ||||
\(742\) | 1.90983 | + | 5.87785i | 0.0701121 | + | 0.215783i | ||||
\(743\) | 0.875388 | 0.0321149 | 0.0160574 | − | 0.999871i | \(-0.494889\pi\) | ||||
0.0160574 | + | 0.999871i | \(0.494889\pi\) | |||||||
\(744\) | −6.70820 | − | 20.6457i | −0.245935 | − | 0.756909i | ||||
\(745\) | −8.39261 | − | 25.8298i | −0.307481 | − | 0.946330i | ||||
\(746\) | 9.09017 | − | 27.9767i | 0.332815 | − | 1.02430i | ||||
\(747\) | 1.09017 | − | 3.35520i | 0.0398872 | − | 0.122760i | ||||
\(748\) | −7.47214 | + | 5.42882i | −0.273208 | + | 0.198497i | ||||
\(749\) | 73.6656 | 2.69168 | ||||||||
\(750\) | 3.45492 | − | 10.6331i | 0.126156 | − | 0.388267i | ||||
\(751\) | 5.34752 | 0.195134 | 0.0975670 | − | 0.995229i | \(-0.468894\pi\) | ||||
0.0975670 | + | 0.995229i | \(0.468894\pi\) | |||||||
\(752\) | −4.23607 | + | 3.07768i | −0.154474 | + | 0.112232i | ||||
\(753\) | −8.32624 | + | 25.6255i | −0.303425 | + | 0.933846i | ||||
\(754\) | 4.57953 | − | 14.0943i | 0.166777 | − | 0.513285i | ||||
\(755\) | 11.3820 | + | 35.0301i | 0.414232 | + | 1.27488i | ||||
\(756\) | −1.38197 | − | 4.25325i | −0.0502616 | − | 0.154689i | ||||
\(757\) | 27.3820 | 0.995214 | 0.497607 | − | 0.867402i | \(-0.334212\pi\) | ||||
0.497607 | + | 0.867402i | \(0.334212\pi\) | |||||||
\(758\) | 7.23607 | + | 22.2703i | 0.262826 | + | 0.808895i | ||||
\(759\) | 11.7082 | + | 8.50651i | 0.424981 | + | 0.308767i | ||||
\(760\) | −17.5623 | − | 12.7598i | −0.637052 | − | 0.462845i | ||||
\(761\) | 7.88197 | − | 5.72658i | 0.285721 | − | 0.207588i | −0.435688 | − | 0.900098i | \(-0.643495\pi\) |
0.721409 | + | 0.692509i | \(0.243495\pi\) | |||||||
\(762\) | −7.85410 | − | 5.70634i | −0.284524 | − | 0.206719i | ||||
\(763\) | 69.0689 | + | 50.1815i | 2.50046 | + | 1.81669i | ||||
\(764\) | −19.9443 | + | 14.4904i | −0.721558 | + | 0.524243i | ||||
\(765\) | −6.38197 | −0.230740 | ||||||||
\(766\) | −16.8541 | − | 12.2452i | −0.608963 | − | 0.442438i | ||||
\(767\) | −4.18034 | − | 12.8658i | −0.150943 | − | 0.464556i | ||||
\(768\) | −17.0000 | −0.613435 | ||||||||
\(769\) | −1.74265 | − | 5.36331i | −0.0628414 | − | 0.193406i | 0.914707 | − | 0.404118i | \(-0.132422\pi\) |
−0.977548 | + | 0.210712i | \(0.932422\pi\) | |||||||
\(770\) | 32.3607 | 1.16620 | ||||||||
\(771\) | −3.95492 | + | 12.1720i | −0.142433 | + | 0.438363i | ||||
\(772\) | −2.37132 | + | 7.29818i | −0.0853458 | + | 0.262667i | ||||
\(773\) | 29.0623 | − | 21.1150i | 1.04530 | − | 0.759454i | 0.0739857 | − | 0.997259i | \(-0.476428\pi\) |
0.971313 | + | 0.237805i | \(0.0764281\pi\) | |||||||
\(774\) | −5.70820 | −0.205177 | ||||||||
\(775\) | −29.2705 | − | 21.2663i | −1.05143 | − | 0.763907i | ||||
\(776\) | −26.5623 | −0.953531 | ||||||||
\(777\) | −29.2705 | + | 21.2663i | −1.05007 | + | 0.762923i | ||||
\(778\) | −11.4615 | + | 35.2748i | −0.410914 | + | 1.26466i | ||||
\(779\) | 1.38197 | − | 4.25325i | 0.0495141 | − | 0.152389i | ||||
\(780\) | 6.11803 | − | 4.44501i | 0.219061 | − | 0.159157i | ||||
\(781\) | −0.763932 | − | 2.35114i | −0.0273356 | − | 0.0841304i | ||||
\(782\) | 12.7639 | 0.456437 | ||||||||
\(783\) | 1.35410 | + | 4.16750i | 0.0483917 | + | 0.148934i | ||||
\(784\) | 10.5172 | + | 7.64121i | 0.375615 | + | 0.272900i | ||||
\(785\) | −9.53444 | − | 29.3440i | −0.340299 | − | 1.04733i | ||||
\(786\) | −11.4721 | + | 8.33499i | −0.409198 | + | 0.297299i | ||||
\(787\) | −6.61803 | − | 4.80828i | −0.235907 | − | 0.171397i | 0.463551 | − | 0.886070i | \(-0.346575\pi\) |
−0.699458 | + | 0.714674i | \(0.746575\pi\) | |||||||
\(788\) | 4.35410 | + | 3.16344i | 0.155108 | + | 0.112693i | ||||
\(789\) | −9.61803 | + | 6.98791i | −0.342411 | + | 0.248776i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.67376 | − | 7.02840i | −0.343959 | − | 0.249901i | ||||
\(792\) | −3.00000 | − | 9.23305i | −0.106600 | − | 0.328082i | ||||
\(793\) | −2.09017 | −0.0742241 | ||||||||
\(794\) | 3.38197 | + | 10.4086i | 0.120021 | + | 0.369388i | ||||
\(795\) | 0.954915 | − | 2.93893i | 0.0338673 | − | 0.104233i | ||||
\(796\) | 5.76393 | − | 17.7396i | 0.204297 | − | 0.628762i | ||||
\(797\) | 11.7746 | − | 36.2384i | 0.417077 | − | 1.28363i | −0.493303 | − | 0.869857i | \(-0.664211\pi\) |
0.910380 | − | 0.413773i | \(-0.135789\pi\) | |||||||
\(798\) | 11.7082 | − | 8.50651i | 0.414466 | − | 0.301127i | ||||
\(799\) | 14.9443 | 0.528690 | ||||||||
\(800\) | −20.2254 | + | 14.6946i | −0.715077 | + | 0.519534i | ||||
\(801\) | 7.61803 | 0.269170 | ||||||||
\(802\) | −27.0623 | + | 19.6619i | −0.955603 | + | 0.694286i | ||||
\(803\) | 3.09017 | − | 9.51057i | 0.109050 | − | 0.335621i | ||||
\(804\) | −1.61803 | + | 4.97980i | −0.0570637 | + | 0.175624i | ||||
\(805\) | 36.1803 | + | 26.2866i | 1.27519 | + | 0.926479i | ||||
\(806\) | 7.56231 | + | 23.2744i | 0.266371 | + | 0.819805i | ||||
\(807\) | −0.145898 | −0.00513585 | ||||||||
\(808\) | 15.3541 | + | 47.2551i | 0.540155 | + | 1.66243i | ||||
\(809\) | 18.7812 | + | 13.6453i | 0.660310 | + | 0.479743i | 0.866768 | − | 0.498712i | \(-0.166194\pi\) |
−0.206457 | + | 0.978456i | \(0.566194\pi\) | |||||||
\(810\) | 0.690983 | − | 2.12663i | 0.0242787 | − | 0.0747221i | ||||
\(811\) | −7.47214 | + | 5.42882i | −0.262382 | + | 0.190632i | −0.711197 | − | 0.702993i | \(-0.751846\pi\) |
0.448814 | + | 0.893625i | \(0.351846\pi\) | |||||||
\(812\) | 15.8541 | + | 11.5187i | 0.556370 | + | 0.404226i | ||||
\(813\) | −17.9443 | − | 13.0373i | −0.629333 | − | 0.457237i | ||||
\(814\) | −21.1803 | + | 15.3884i | −0.742371 | + | 0.539364i | ||||
\(815\) | 2.03444 | − | 6.26137i | 0.0712634 | − | 0.219326i | ||||
\(816\) | −2.30902 | − | 1.67760i | −0.0808318 | − | 0.0587277i | ||||
\(817\) | 5.70820 | + | 17.5680i | 0.199705 | + | 0.614628i | ||||
\(818\) | 25.7984 | 0.902019 | ||||||||
\(819\) | 4.67376 | + | 14.3844i | 0.163314 | + | 0.502630i | ||||
\(820\) | −2.50000 | − | 1.81636i | −0.0873038 | − | 0.0634299i | ||||
\(821\) | 1.56231 | − | 4.80828i | 0.0545249 | − | 0.167810i | −0.920086 | − | 0.391717i | \(-0.871881\pi\) |
0.974611 | + | 0.223907i | \(0.0718812\pi\) | |||||||
\(822\) | −1.66312 | + | 5.11855i | −0.0580079 | + | 0.178530i | ||||
\(823\) | 11.9443 | − | 8.67802i | 0.416351 | − | 0.302497i | −0.359817 | − | 0.933023i | \(-0.617161\pi\) |
0.776168 | + | 0.630526i | \(0.217161\pi\) | |||||||
\(824\) | 3.70820 | 0.129181 | ||||||||
\(825\) | −13.0902 | − | 9.51057i | −0.455741 | − | 0.331115i | ||||
\(826\) | −17.8885 | −0.622422 | ||||||||
\(827\) | −17.8541 | + | 12.9718i | −0.620848 | + | 0.451072i | −0.853218 | − | 0.521555i | \(-0.825352\pi\) |
0.232370 | + | 0.972628i | \(0.425352\pi\) | |||||||
\(828\) | 1.38197 | − | 4.25325i | 0.0480266 | − | 0.147811i | ||||
\(829\) | −8.19098 | + | 25.2093i | −0.284485 | + | 0.875554i | 0.702068 | + | 0.712110i | \(0.252260\pi\) |
−0.986553 | + | 0.163444i | \(0.947740\pi\) | |||||||
\(830\) | 2.43769 | − | 7.50245i | 0.0846136 | − | 0.260414i | ||||
\(831\) | −1.79180 | − | 5.51458i | −0.0621567 | − | 0.191299i | ||||
\(832\) | 23.6738 | 0.820740 | ||||||||
\(833\) | −11.4656 | − | 35.2874i | −0.397258 | − | 1.22263i | ||||
\(834\) | 4.09017 | + | 2.97168i | 0.141631 | + | 0.102901i | ||||
\(835\) | 42.3607 | − | 30.7768i | 1.46595 | − | 1.06508i | ||||
\(836\) | −8.47214 | + | 6.15537i | −0.293015 | + | 0.212888i | ||||
\(837\) | −5.85410 | − | 4.25325i | −0.202347 | − | 0.147014i | ||||
\(838\) | −26.6525 | − | 19.3642i | −0.920695 | − | 0.668924i | ||||
\(839\) | 35.6525 | − | 25.9030i | 1.23086 | − | 0.894272i | 0.233906 | − | 0.972259i | \(-0.424849\pi\) |
0.996954 | + | 0.0779870i | \(0.0248493\pi\) | |||||||
\(840\) | −9.27051 | − | 28.5317i | −0.319863 | − | 0.984437i | ||||
\(841\) | 7.92705 | + | 5.75934i | 0.273347 | + | 0.198598i | ||||
\(842\) | 7.15248 | + | 22.0131i | 0.246491 | + | 0.758620i | ||||
\(843\) | −17.3820 | −0.598667 | ||||||||
\(844\) | 5.52786 | + | 17.0130i | 0.190277 | + | 0.585612i | ||||
\(845\) | 2.82624 | − | 2.05338i | 0.0972255 | − | 0.0706385i | ||||
\(846\) | −1.61803 | + | 4.97980i | −0.0556292 | + | 0.171209i | ||||
\(847\) | −0.729490 | + | 2.24514i | −0.0250656 | + | 0.0771439i | ||||
\(848\) | 1.11803 | − | 0.812299i | 0.0383934 | − | 0.0278945i | ||||
\(849\) | 0.291796 | 0.0100144 | ||||||||
\(850\) | −14.2705 | −0.489474 | ||||||||
\(851\) | −36.1803 | −1.24025 | ||||||||
\(852\) | −0.618034 | + | 0.449028i | −0.0211735 | + | 0.0153834i | ||||
\(853\) | 9.22542 | − | 28.3929i | 0.315873 | − | 0.972156i | −0.659521 | − | 0.751686i | \(-0.729241\pi\) |
0.975394 | − | 0.220470i | \(-0.0707590\pi\) | |||||||
\(854\) | −0.854102 | + | 2.62866i | −0.0292268 | + | 0.0899507i | ||||
\(855\) | −7.23607 | −0.247468 | ||||||||
\(856\) | −15.2705 | − | 46.9978i | −0.521935 | − | 1.60635i | ||||
\(857\) | −3.52786 | −0.120510 | −0.0602548 | − | 0.998183i | \(-0.519191\pi\) | ||||
−0.0602548 | + | 0.998183i | \(0.519191\pi\) | |||||||
\(858\) | 3.38197 | + | 10.4086i | 0.115458 | + | 0.355344i | ||||
\(859\) | −2.76393 | − | 2.00811i | −0.0943041 | − | 0.0685160i | 0.539634 | − | 0.841900i | \(-0.318563\pi\) |
−0.633938 | + | 0.773384i | \(0.718563\pi\) | |||||||
\(860\) | 12.7639 | 0.435246 | ||||||||
\(861\) | 5.00000 | − | 3.63271i | 0.170400 | − | 0.123803i | ||||
\(862\) | 8.61803 | + | 6.26137i | 0.293531 | + | 0.213263i | ||||
\(863\) | −41.3607 | − | 30.0503i | −1.40793 | − | 1.02292i | −0.993619 | − | 0.112790i | \(-0.964021\pi\) |
−0.414315 | − | 0.910134i | \(-0.635979\pi\) | |||||||
\(864\) | −4.04508 | + | 2.93893i | −0.137617 | + | 0.0999843i | ||||
\(865\) | −17.9271 | − | 13.0248i | −0.609538 | − | 0.442855i | ||||
\(866\) | −20.2082 | − | 14.6821i | −0.686703 | − | 0.498919i | ||||
\(867\) | −2.73607 | − | 8.42075i | −0.0929217 | − | 0.285984i | ||||
\(868\) | −32.3607 | −1.09839 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.02786 | + | 9.31881i | 0.102654 | + | 0.315937i | ||||
\(871\) | 5.47214 | − | 16.8415i | 0.185416 | − | 0.570653i | ||||
\(872\) | 17.6976 | − | 54.4675i | 0.599315 | − | 1.84450i | ||||
\(873\) | −7.16312 | + | 5.20431i | −0.242435 | + | 0.176139i | ||||
\(874\) | 14.4721 | 0.489527 | ||||||||
\(875\) | −40.4508 | − | 29.3893i | −1.36749 | − | 0.993538i | ||||
\(876\) | −3.09017 | −0.104407 | ||||||||
\(877\) | −14.7361 | + | 10.7064i | −0.497602 | + | 0.361529i | −0.808100 | − | 0.589045i | \(-0.799504\pi\) |
0.310499 | + | 0.950574i | \(0.399504\pi\) | |||||||
\(878\) | −1.90983 | + | 5.87785i | −0.0644536 | + | 0.198368i | ||||
\(879\) | 1.17376 | − | 3.61247i | 0.0395900 | − | 0.121846i | ||||
\(880\) | −2.23607 | − | 6.88191i | −0.0753778 | − | 0.231989i | ||||
\(881\) | 7.74265 | + | 23.8294i | 0.260856 | + | 0.802833i | 0.992619 | + | 0.121274i | \(0.0386979\pi\) |
−0.731763 | + | 0.681559i | \(0.761302\pi\) | |||||||
\(882\) | 13.0000 | 0.437733 | ||||||||
\(883\) | −0.0557281 | − | 0.171513i | −0.00187540 | − | 0.00577189i | 0.950114 | − | 0.311902i | \(-0.100966\pi\) |
−0.951990 | + | 0.306130i | \(0.900966\pi\) | |||||||
\(884\) | −7.80902 | − | 5.67358i | −0.262646 | − | 0.190823i | ||||
\(885\) | 7.23607 | + | 5.25731i | 0.243238 | + | 0.176723i | ||||
\(886\) | 24.8885 | − | 18.0826i | 0.836147 | − | 0.607496i | ||||
\(887\) | −13.8541 | − | 10.0656i | −0.465175 | − | 0.337970i | 0.330383 | − | 0.943847i | \(-0.392822\pi\) |
−0.795558 | + | 0.605877i | \(0.792822\pi\) | |||||||
\(888\) | 19.6353 | + | 14.2658i | 0.658916 | + | 0.478731i | ||||
\(889\) | −35.1246 | + | 25.5195i | −1.17804 | + | 0.855897i | ||||
\(890\) | 17.0344 | 0.570996 | ||||||||
\(891\) | −2.61803 | − | 1.90211i | −0.0877074 | − | 0.0637232i | ||||
\(892\) | 4.38197 | + | 13.4863i | 0.146719 | + | 0.451555i | ||||
\(893\) | 16.9443 | 0.567018 | ||||||||
\(894\) | −3.75329 | − | 11.5514i | −0.125529 | − | 0.386338i | ||||
\(895\) | 13.8197 | 0.461940 | ||||||||
\(896\) | −4.14590 | + | 12.7598i | −0.138505 | + | 0.426274i | ||||
\(897\) | −4.67376 | + | 14.3844i | −0.156052 | + | 0.480280i | ||||
\(898\) | 6.30902 | − | 4.58377i | 0.210535 | − | 0.152962i | ||||
\(899\) | 31.7082 | 1.05753 | ||||||||
\(900\) | −1.54508 | + | 4.75528i | −0.0515028 | + | 0.158509i | ||||
\(901\) | −3.94427 | −0.131403 | ||||||||
\(902\) | 3.61803 | − | 2.62866i | 0.120467 | − | 0.0875247i | ||||
\(903\) | −7.88854 | + | 24.2784i | −0.262514 | + | 0.807936i | ||||
\(904\) | −2.47871 | + | 7.62870i | −0.0824408 | + | 0.253727i | ||||
\(905\) | 17.7254 | − | 12.8783i | 0.589213 | − | 0.428088i | ||||
\(906\) | 5.09017 | + | 15.6659i | 0.169110 | + | 0.520466i | ||||
\(907\) | −33.1246 | −1.09988 | −0.549942 | − | 0.835203i | \(-0.685350\pi\) | ||||
−0.549942 | + | 0.835203i | \(0.685350\pi\) | |||||||
\(908\) | 6.18034 | + | 19.0211i | 0.205102 | + | 0.631238i | ||||
\(909\) | 13.3992 | + | 9.73508i | 0.444423 | + | 0.322892i | ||||
\(910\) | 10.4508 | + | 32.1644i | 0.346442 | + | 1.06624i | ||||
\(911\) | 3.38197 | − | 2.45714i | 0.112050 | − | 0.0814088i | −0.530349 | − | 0.847779i | \(-0.677939\pi\) |
0.642399 | + | 0.766370i | \(0.277939\pi\) | |||||||
\(912\) | −2.61803 | − | 1.90211i | −0.0866918 | − | 0.0629853i | ||||
\(913\) | −9.23607 | − | 6.71040i | −0.305669 | − | 0.222082i | ||||
\(914\) | −18.0902 | + | 13.1433i | −0.598370 | + | 0.434741i | ||||
\(915\) | 1.11803 | − | 0.812299i | 0.0369611 | − | 0.0268538i | ||||
\(916\) | −20.2082 | − | 14.6821i | −0.667698 | − | 0.485111i | ||||
\(917\) | 19.5967 | + | 60.3126i | 0.647142 | + | 1.99170i | ||||
\(918\) | −2.85410 | −0.0941994 | ||||||||
\(919\) | −15.2016 | − | 46.7858i | −0.501455 | − | 1.54332i | −0.806649 | − | 0.591031i | \(-0.798721\pi\) |
0.305194 | − | 0.952290i | \(-0.401279\pi\) | |||||||
\(920\) | 9.27051 | − | 28.5317i | 0.305640 | − | 0.940662i | ||||
\(921\) | 0.416408 | − | 1.28157i | 0.0137211 | − | 0.0422292i | ||||
\(922\) | −2.53444 | + | 7.80021i | −0.0834674 | + | 0.256886i | ||||
\(923\) | 2.09017 | − | 1.51860i | 0.0687988 | − | 0.0499852i | ||||
\(924\) | −14.4721 | −0.476098 | ||||||||
\(925\) | 40.4508 | 1.33002 | ||||||||
\(926\) | 23.2361 | 0.763585 | ||||||||
\(927\) | 1.00000 | − | 0.726543i | 0.0328443 | − | 0.0238628i | ||||
\(928\) | 6.77051 | − | 20.8375i | 0.222253 | − | 0.684024i | ||||
\(929\) | 0.645898 | − | 1.98787i | 0.0211912 | − | 0.0652199i | −0.939902 | − | 0.341445i | \(-0.889084\pi\) |
0.961093 | + | 0.276225i | \(0.0890836\pi\) | |||||||
\(930\) | −13.0902 | − | 9.51057i | −0.429244 | − | 0.311864i | ||||
\(931\) | −13.0000 | − | 40.0099i | −0.426058 | − | 1.31127i | ||||
\(932\) | −14.6180 | −0.478830 | ||||||||
\(933\) | 1.32624 | + | 4.08174i | 0.0434191 | + | 0.133630i | ||||
\(934\) | −4.70820 | − | 3.42071i | −0.154057 | − | 0.111929i | ||||
\(935\) | −6.38197 | + | 19.6417i | −0.208713 | + | 0.642351i | ||||
\(936\) | 8.20820 | − | 5.96361i | 0.268294 | − | 0.194927i | ||||
\(937\) | −9.45492 | − | 6.86940i | −0.308879 | − | 0.224413i | 0.422537 | − | 0.906346i | \(-0.361140\pi\) |
−0.731415 | + | 0.681932i | \(0.761140\pi\) | |||||||
\(938\) | −18.9443 | − | 13.7638i | −0.618552 | − | 0.449405i | ||||
\(939\) | −6.85410 | + | 4.97980i | −0.223675 | + | 0.162510i | ||||
\(940\) | 3.61803 | − | 11.1352i | 0.118007 | − | 0.363189i | ||||
\(941\) | −4.30902 | − | 3.13068i | −0.140470 | − | 0.102057i | 0.515331 | − | 0.856991i | \(-0.327669\pi\) |
−0.655801 | + | 0.754934i | \(0.727669\pi\) | |||||||
\(942\) | −4.26393 | − | 13.1230i | −0.138926 | − | 0.427572i | ||||
\(943\) | 6.18034 | 0.201260 | ||||||||
\(944\) | 1.23607 | + | 3.80423i | 0.0402306 | + | 0.123817i | ||||
\(945\) | −8.09017 | − | 5.87785i | −0.263173 | − | 0.191207i | ||||
\(946\) | −5.70820 | + | 17.5680i | −0.185590 | + | 0.571186i | ||||
\(947\) | 9.09017 | − | 27.9767i | 0.295391 | − | 0.909120i | −0.687699 | − | 0.725996i | \(-0.741379\pi\) |
0.983090 | − | 0.183124i | \(-0.0586209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4508 | 0.339249 | ||||||||
\(950\) | −16.1803 | −0.524960 | ||||||||
\(951\) | −24.8328 | −0.805259 | ||||||||
\(952\) | −30.9787 | + | 22.5074i | −1.00403 | + | 0.729468i | ||||
\(953\) | 3.11803 | − | 9.59632i | 0.101003 | − | 0.310855i | −0.887769 | − | 0.460290i | \(-0.847745\pi\) |
0.988772 | + | 0.149435i | \(0.0477454\pi\) | |||||||
\(954\) | 0.427051 | − | 1.31433i | 0.0138263 | − | 0.0425529i | ||||
\(955\) | −17.0344 | + | 52.4266i | −0.551222 | + | 1.69649i | ||||
\(956\) | 2.18034 | + | 6.71040i | 0.0705172 | + | 0.217030i | ||||
\(957\) | 14.1803 | 0.458385 | ||||||||
\(958\) | 0.326238 | + | 1.00406i | 0.0105403 | + | 0.0324396i | ||||
\(959\) | 19.4721 | + | 14.1473i | 0.628788 | + | 0.456841i | ||||
\(960\) | −12.6631 | + | 9.20029i | −0.408700 | + | 0.296938i | ||||
\(961\) | −17.2812 | + | 12.5555i | −0.557457 | + | 0.405016i | ||||
\(962\) | −22.1353 | − | 16.0822i | −0.713669 | − | 0.518511i | ||||
\(963\) | −13.3262 | − | 9.68208i | −0.429432 | − | 0.312001i | ||||
\(964\) | −0.836881 | + | 0.608030i | −0.0269541 | + | 0.0195833i | ||||
\(965\) | 5.30244 | + | 16.3192i | 0.170692 | + | 0.525335i | ||||
\(966\) | 16.1803 | + | 11.7557i | 0.520594 | + | 0.378234i | ||||
\(967\) | 10.7639 | + | 33.1280i | 0.346145 | + | 1.06532i | 0.960968 | + | 0.276659i | \(0.0892273\pi\) |
−0.614823 | + | 0.788665i | \(0.710773\pi\) | |||||||
\(968\) | 1.58359 | 0.0508986 | ||||||||
\(969\) | 2.85410 | + | 8.78402i | 0.0916870 | + | 0.282183i | ||||
\(970\) | −16.0172 | + | 11.6372i | −0.514282 | + | 0.373648i | ||||
\(971\) | −2.03444 | + | 6.26137i | −0.0652883 | + | 0.200937i | −0.978379 | − | 0.206819i | \(-0.933689\pi\) |
0.913091 | + | 0.407756i | \(0.133689\pi\) | |||||||
\(972\) | −0.309017 | + | 0.951057i | −0.00991172 | + | 0.0305052i | ||||
\(973\) | 18.2918 | − | 13.2898i | 0.586408 | − | 0.426050i | ||||
\(974\) | −3.70820 | −0.118819 | ||||||||
\(975\) | 5.22542 | − | 16.0822i | 0.167348 | − | 0.515043i | ||||
\(976\) | 0.618034 | 0.0197828 | ||||||||
\(977\) | 37.0066 | − | 26.8869i | 1.18395 | − | 0.860187i | 0.191334 | − | 0.981525i | \(-0.438719\pi\) |
0.992611 | + | 0.121338i | \(0.0387186\pi\) | |||||||
\(978\) | 0.909830 | − | 2.80017i | 0.0290932 | − | 0.0895395i | ||||
\(979\) | 7.61803 | − | 23.4459i | 0.243473 | − | 0.749334i | ||||
\(980\) | −29.0689 | −0.928571 | ||||||||
\(981\) | −5.89919 | − | 18.1558i | −0.188347 | − | 0.579671i | ||||
\(982\) | −29.8885 | −0.953782 | ||||||||
\(983\) | 6.70820 | + | 20.6457i | 0.213958 | + | 0.658496i | 0.999226 | + | 0.0393397i | \(0.0125255\pi\) |
−0.785267 | + | 0.619157i | \(0.787475\pi\) | |||||||
\(984\) | −3.35410 | − | 2.43690i | −0.106925 | − | 0.0776855i | ||||
\(985\) | 12.0344 | 0.383449 | ||||||||
\(986\) | 10.1180 | − | 7.35118i | 0.322224 | − | 0.234109i | ||||
\(987\) | 18.9443 | + | 13.7638i | 0.603003 | + | 0.438107i | ||||
\(988\) | −8.85410 | − | 6.43288i | −0.281687 | − | 0.204657i | ||||
\(989\) | −20.6525 | + | 15.0049i | −0.656711 | + | 0.477128i | ||||
\(990\) | −5.85410 | − | 4.25325i | −0.186056 | − | 0.135177i | ||||
\(991\) | 2.52786 | + | 1.83660i | 0.0803002 | + | 0.0583415i | 0.627211 | − | 0.778849i | \(-0.284196\pi\) |
−0.546911 | + | 0.837191i | \(0.684196\pi\) | |||||||
\(992\) | 11.1803 | + | 34.4095i | 0.354976 | + | 1.09250i | ||||
\(993\) | 10.9443 | 0.347306 | ||||||||
\(994\) | −1.05573 | − | 3.24920i | −0.0334857 | − | 0.103058i | ||||
\(995\) | −12.8885 | − | 39.6669i | −0.408594 | − | 1.25752i | ||||
\(996\) | −1.09017 | + | 3.35520i | −0.0345434 | + | 0.106314i | ||||
\(997\) | 2.90983 | − | 8.95554i | 0.0921552 | − | 0.283625i | −0.894347 | − | 0.447375i | \(-0.852359\pi\) |
0.986502 | + | 0.163750i | \(0.0523590\pi\) | |||||||
\(998\) | 4.85410 | − | 3.52671i | 0.153654 | − | 0.111636i | ||||
\(999\) | 8.09017 | 0.255962 |
(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 | 75.2.g.a.61.1 | yes | 4 | |
3.2 | odd | 2 | 225.2.h.a.136.1 | 4 | |||
5.2 | odd | 4 | 375.2.i.a.199.1 | 8 | |||
5.3 | odd | 4 | 375.2.i.a.199.2 | 8 | |||
5.4 | even | 2 | 375.2.g.a.301.1 | 4 | |||
25.3 | odd | 20 | 1875.2.b.b.1249.1 | 4 | |||
25.4 | even | 10 | 1875.2.a.a.1.1 | 2 | |||
25.9 | even | 10 | 375.2.g.a.76.1 | 4 | |||
25.12 | odd | 20 | 375.2.i.a.49.2 | 8 | |||
25.13 | odd | 20 | 375.2.i.a.49.1 | 8 | |||
25.16 | even | 5 | inner | 75.2.g.a.16.1 | ✓ | 4 | |
25.21 | even | 5 | 1875.2.a.d.1.2 | 2 | |||
25.22 | odd | 20 | 1875.2.b.b.1249.4 | 4 | |||
75.29 | odd | 10 | 5625.2.a.h.1.1 | 2 | |||
75.41 | odd | 10 | 225.2.h.a.91.1 | 4 | |||
75.71 | odd | 10 | 5625.2.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.a.16.1 | ✓ | 4 | 25.16 | even | 5 | inner | |
75.2.g.a.61.1 | yes | 4 | 1.1 | even | 1 | trivial | |
225.2.h.a.91.1 | 4 | 75.41 | odd | 10 | |||
225.2.h.a.136.1 | 4 | 3.2 | odd | 2 | |||
375.2.g.a.76.1 | 4 | 25.9 | even | 10 | |||
375.2.g.a.301.1 | 4 | 5.4 | even | 2 | |||
375.2.i.a.49.1 | 8 | 25.13 | odd | 20 | |||
375.2.i.a.49.2 | 8 | 25.12 | odd | 20 | |||
375.2.i.a.199.1 | 8 | 5.2 | odd | 4 | |||
375.2.i.a.199.2 | 8 | 5.3 | odd | 4 | |||
1875.2.a.a.1.1 | 2 | 25.4 | even | 10 | |||
1875.2.a.d.1.2 | 2 | 25.21 | even | 5 | |||
1875.2.b.b.1249.1 | 4 | 25.3 | odd | 20 | |||
1875.2.b.b.1249.4 | 4 | 25.22 | odd | 20 | |||
5625.2.a.a.1.2 | 2 | 75.71 | odd | 10 | |||
5625.2.a.h.1.1 | 2 | 75.29 | odd | 10 |