Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), not 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(0.587785 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.199 |
Dual form | 375.2.i.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.587785 | + | 0.809017i | 0.415627 | + | 0.572061i | 0.964580 | − | 0.263792i | \(-0.0849733\pi\) |
−0.548953 | + | 0.835853i | \(0.684973\pi\) | |||||||
\(3\) | 0.951057 | + | 0.309017i | 0.549093 | + | 0.178411i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.309017 | + | 0.951057i | 0.126156 | + | 0.388267i | ||||
\(7\) | − | 4.47214i | − | 1.69031i | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||
0.534522 | − | 0.845154i | \(-0.320491\pi\) | |||||||
\(8\) | 2.85317 | − | 0.927051i | 1.00875 | − | 0.327762i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.61803 | + | 1.90211i | −0.789367 | + | 0.573509i | −0.907776 | − | 0.419456i | \(-0.862221\pi\) |
0.118409 | + | 0.992965i | \(0.462221\pi\) | |||||||
\(12\) | 0.587785 | − | 0.809017i | 0.169679 | − | 0.233543i | ||||
\(13\) | 1.98787 | − | 2.73607i | 0.551336 | − | 0.758849i | −0.438857 | − | 0.898557i | \(-0.644616\pi\) |
0.990193 | + | 0.139708i | \(0.0446165\pi\) | |||||||
\(14\) | 3.61803 | − | 2.62866i | 0.966960 | − | 0.702538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.809017 | + | 0.587785i | 0.202254 | + | 0.146946i | ||||
\(17\) | −2.71441 | + | 0.881966i | −0.658342 | + | 0.213908i | −0.619089 | − | 0.785321i | \(-0.712498\pi\) |
−0.0392530 | + | 0.999229i | \(0.512498\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.00000 | + | 3.07768i | 0.229416 | + | 0.706069i | 0.997813 | + | 0.0660962i | \(0.0210544\pi\) |
−0.768398 | + | 0.639973i | \(0.778946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.38197 | − | 4.25325i | 0.301570 | − | 0.928136i | ||||
\(22\) | −3.07768 | − | 1.00000i | −0.656164 | − | 0.213201i | ||||
\(23\) | 2.62866 | + | 3.61803i | 0.548113 | + | 0.754412i | 0.989755 | − | 0.142779i | \(-0.0456039\pi\) |
−0.441642 | + | 0.897191i | \(0.645604\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.38197 | 0.663258 | ||||||||
\(27\) | 0.587785 | + | 0.809017i | 0.113119 | + | 0.155695i | ||||
\(28\) | −4.25325 | − | 1.38197i | −0.803789 | − | 0.261167i | ||||
\(29\) | −1.35410 | + | 4.16750i | −0.251450 | + | 0.773885i | 0.743058 | + | 0.669227i | \(0.233375\pi\) |
−0.994508 | + | 0.104658i | \(0.966625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.23607 | + | 6.88191i | 0.401610 | + | 1.23603i | 0.923693 | + | 0.383133i | \(0.125155\pi\) |
−0.522083 | + | 0.852894i | \(0.674845\pi\) | |||||||
\(32\) | − | 5.00000i | − | 0.883883i | ||||||
\(33\) | −3.07768 | + | 1.00000i | −0.535756 | + | 0.174078i | ||||
\(34\) | −2.30902 | − | 1.67760i | −0.395993 | − | 0.287706i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.809017 | − | 0.587785i | 0.134836 | − | 0.0979642i | ||||
\(37\) | −4.75528 | + | 6.54508i | −0.781764 | + | 1.07601i | 0.213321 | + | 0.976982i | \(0.431572\pi\) |
−0.995085 | + | 0.0990233i | \(0.968428\pi\) | |||||||
\(38\) | −1.90211 | + | 2.61803i | −0.308563 | + | 0.424701i | ||||
\(39\) | 2.73607 | − | 1.98787i | 0.438122 | − | 0.318314i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.11803 | + | 0.812299i | 0.174608 | + | 0.126860i | 0.671657 | − | 0.740863i | \(-0.265583\pi\) |
−0.497049 | + | 0.867722i | \(0.665583\pi\) | |||||||
\(42\) | 4.25325 | − | 1.38197i | 0.656291 | − | 0.213242i | ||||
\(43\) | − | 5.70820i | − | 0.870493i | −0.900311 | − | 0.435246i | \(-0.856661\pi\) | ||
0.900311 | − | 0.435246i | \(-0.143339\pi\) | |||||||
\(44\) | 1.00000 | + | 3.07768i | 0.150756 | + | 0.463978i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.38197 | + | 4.25325i | −0.203760 | + | 0.627108i | ||||
\(47\) | 4.97980 | + | 1.61803i | 0.726378 | + | 0.236015i | 0.648786 | − | 0.760971i | \(-0.275277\pi\) |
0.0775917 | + | 0.996985i | \(0.475277\pi\) | |||||||
\(48\) | 0.587785 | + | 0.809017i | 0.0848395 | + | 0.116772i | ||||
\(49\) | −13.0000 | −1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.85410 | −0.399654 | ||||||||
\(52\) | −1.98787 | − | 2.73607i | −0.275668 | − | 0.379424i | ||||
\(53\) | 1.31433 | + | 0.427051i | 0.180537 | + | 0.0586600i | 0.397890 | − | 0.917433i | \(-0.369742\pi\) |
−0.217354 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(54\) | −0.309017 | + | 0.951057i | −0.0420519 | + | 0.129422i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.14590 | − | 12.7598i | −0.554019 | − | 1.70509i | ||||
\(57\) | 3.23607i | 0.428628i | ||||||||
\(58\) | −4.16750 | + | 1.35410i | −0.547219 | + | 0.177802i | ||||
\(59\) | −3.23607 | − | 2.35114i | −0.421300 | − | 0.306092i | 0.356861 | − | 0.934158i | \(-0.383847\pi\) |
−0.778161 | + | 0.628065i | \(0.783847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.363271i | 0.0640184 | − | 0.0465121i | −0.555316 | − | 0.831640i | \(-0.687403\pi\) |
0.619334 | + | 0.785127i | \(0.287403\pi\) | |||||||
\(62\) | −4.25325 | + | 5.85410i | −0.540164 | + | 0.743472i | ||||
\(63\) | 2.62866 | − | 3.61803i | 0.331179 | − | 0.455829i | ||||
\(64\) | 5.66312 | − | 4.11450i | 0.707890 | − | 0.514312i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.61803 | − | 1.90211i | −0.322258 | − | 0.234134i | ||||
\(67\) | 4.97980 | − | 1.61803i | 0.608379 | − | 0.197674i | 0.0114051 | − | 0.999935i | \(-0.496370\pi\) |
0.596974 | + | 0.802261i | \(0.296370\pi\) | |||||||
\(68\) | 2.85410i | 0.346111i | ||||||||
\(69\) | 1.38197 | + | 4.25325i | 0.166369 | + | 0.512032i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.236068 | + | 0.726543i | −0.0280161 | + | 0.0862247i | −0.964087 | − | 0.265587i | \(-0.914434\pi\) |
0.936071 | + | 0.351812i | \(0.114434\pi\) | |||||||
\(72\) | 2.85317 | + | 0.927051i | 0.336249 | + | 0.109254i | ||||
\(73\) | −1.81636 | − | 2.50000i | −0.212588 | − | 0.292603i | 0.689384 | − | 0.724396i | \(-0.257881\pi\) |
−0.901973 | + | 0.431793i | \(0.857881\pi\) | |||||||
\(74\) | −8.09017 | −0.940463 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.23607 | 0.371202 | ||||||||
\(77\) | 8.50651 | + | 11.7082i | 0.969407 | + | 1.33427i | ||||
\(78\) | 3.21644 | + | 1.04508i | 0.364190 | + | 0.118333i | ||||
\(79\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 1.38197i | 0.152613i | ||||||||
\(83\) | −3.35520 | + | 1.09017i | −0.368281 | + | 0.119662i | −0.487310 | − | 0.873229i | \(-0.662022\pi\) |
0.119029 | + | 0.992891i | \(0.462022\pi\) | |||||||
\(84\) | −3.61803 | − | 2.62866i | −0.394760 | − | 0.286810i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.61803 | − | 3.35520i | 0.497975 | − | 0.361800i | ||||
\(87\) | −2.57565 | + | 3.54508i | −0.276139 | + | 0.380073i | ||||
\(88\) | −5.70634 | + | 7.85410i | −0.608298 | + | 0.837250i | ||||
\(89\) | 6.16312 | − | 4.47777i | 0.653289 | − | 0.474642i | −0.211101 | − | 0.977464i | \(-0.567705\pi\) |
0.864390 | + | 0.502822i | \(0.167705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.2361 | − | 8.89002i | −1.28269 | − | 0.931928i | ||||
\(92\) | 4.25325 | − | 1.38197i | 0.443432 | − | 0.144080i | ||||
\(93\) | 7.23607i | 0.750345i | ||||||||
\(94\) | 1.61803 | + | 4.97980i | 0.166887 | + | 0.513627i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.54508 | − | 4.75528i | 0.157695 | − | 0.485334i | ||||
\(97\) | −8.42075 | − | 2.73607i | −0.854998 | − | 0.277806i | −0.151460 | − | 0.988463i | \(-0.548397\pi\) |
−0.703538 | + | 0.710658i | \(0.748397\pi\) | |||||||
\(98\) | −7.64121 | − | 10.5172i | −0.771879 | − | 1.06240i | ||||
\(99\) | −3.23607 | −0.325237 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.5623 | −1.64801 | −0.824006 | − | 0.566582i | \(-0.808266\pi\) | ||||
−0.824006 | + | 0.566582i | \(0.808266\pi\) | |||||||
\(102\) | −1.67760 | − | 2.30902i | −0.166107 | − | 0.228627i | ||||
\(103\) | −1.17557 | − | 0.381966i | −0.115832 | − | 0.0376362i | 0.250527 | − | 0.968110i | \(-0.419396\pi\) |
−0.366360 | + | 0.930473i | \(0.619396\pi\) | |||||||
\(104\) | 3.13525 | − | 9.64932i | 0.307437 | − | 0.946194i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.427051 | + | 1.31433i | 0.0414789 | + | 0.127659i | ||||
\(107\) | − | 16.4721i | − | 1.59242i | −0.605019 | − | 0.796211i | \(-0.706835\pi\) | ||
0.605019 | − | 0.796211i | \(-0.293165\pi\) | |||||||
\(108\) | 0.951057 | − | 0.309017i | 0.0915155 | − | 0.0297352i | ||||
\(109\) | −15.4443 | − | 11.2209i | −1.47929 | − | 1.07477i | −0.977784 | − | 0.209617i | \(-0.932778\pi\) |
−0.501509 | − | 0.865152i | \(-0.667222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.54508 | + | 4.75528i | −0.621232 | + | 0.451351i | ||||
\(112\) | 2.62866 | − | 3.61803i | 0.248385 | − | 0.341872i | ||||
\(113\) | 1.57160 | − | 2.16312i | 0.147843 | − | 0.203489i | −0.728672 | − | 0.684863i | \(-0.759862\pi\) |
0.876515 | + | 0.481374i | \(0.159862\pi\) | |||||||
\(114\) | −2.61803 | + | 1.90211i | −0.245201 | + | 0.178149i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.54508 | + | 2.57565i | 0.329153 | + | 0.239144i | ||||
\(117\) | 3.21644 | − | 1.04508i | 0.297360 | − | 0.0966181i | ||||
\(118\) | − | 4.00000i | − | 0.368230i | ||||||
\(119\) | 3.94427 | + | 12.1392i | 0.361571 | + | 1.11280i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.163119 | + | 0.502029i | −0.0148290 | + | 0.0456390i | ||||
\(122\) | 0.587785 | + | 0.190983i | 0.0532156 | + | 0.0172908i | ||||
\(123\) | 0.812299 | + | 1.11803i | 0.0732426 | + | 0.100810i | ||||
\(124\) | 7.23607 | 0.649818 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.47214 | 0.398410 | ||||||||
\(127\) | 5.70634 | + | 7.85410i | 0.506356 | + | 0.696939i | 0.983299 | − | 0.181995i | \(-0.0582555\pi\) |
−0.476944 | + | 0.878934i | \(0.658255\pi\) | |||||||
\(128\) | −2.85317 | − | 0.927051i | −0.252187 | − | 0.0819405i | ||||
\(129\) | 1.76393 | − | 5.42882i | 0.155306 | − | 0.477981i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.38197 | + | 13.4863i | 0.382854 | + | 1.17830i | 0.938025 | + | 0.346568i | \(0.112653\pi\) |
−0.555171 | + | 0.831736i | \(0.687347\pi\) | |||||||
\(132\) | 3.23607i | 0.281664i | ||||||||
\(133\) | 13.7638 | − | 4.47214i | 1.19347 | − | 0.387783i | ||||
\(134\) | 4.23607 | + | 3.07768i | 0.365941 | + | 0.265871i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.92705 | + | 5.03280i | −0.593990 | + | 0.431559i | ||||
\(137\) | 3.16344 | − | 4.35410i | 0.270271 | − | 0.371996i | −0.652210 | − | 0.758038i | \(-0.726158\pi\) |
0.922481 | + | 0.386042i | \(0.126158\pi\) | |||||||
\(138\) | −2.62866 | + | 3.61803i | −0.223766 | + | 0.307988i | ||||
\(139\) | −4.09017 | + | 2.97168i | −0.346924 | + | 0.252055i | −0.747577 | − | 0.664175i | \(-0.768783\pi\) |
0.400654 | + | 0.916230i | \(0.368783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.23607 | + | 3.07768i | 0.356741 | + | 0.259188i | ||||
\(142\) | −0.726543 | + | 0.236068i | −0.0609701 | + | 0.0198104i | ||||
\(143\) | 10.9443i | 0.915206i | ||||||||
\(144\) | 0.309017 | + | 0.951057i | 0.0257514 | + | 0.0792547i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.954915 | − | 2.93893i | 0.0790293 | − | 0.243227i | ||||
\(147\) | −12.3637 | − | 4.01722i | −1.01974 | − | 0.331335i | ||||
\(148\) | 4.75528 | + | 6.54508i | 0.390882 | + | 0.538003i | ||||
\(149\) | 12.1459 | 0.995031 | 0.497515 | − | 0.867455i | \(-0.334246\pi\) | ||||
0.497515 | + | 0.867455i | \(0.334246\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4721 | 1.34048 | 0.670242 | − | 0.742143i | \(-0.266190\pi\) | ||||
0.670242 | + | 0.742143i | \(0.266190\pi\) | |||||||
\(152\) | 5.70634 | + | 7.85410i | 0.462845 | + | 0.637052i | ||||
\(153\) | −2.71441 | − | 0.881966i | −0.219447 | − | 0.0713027i | ||||
\(154\) | −4.47214 | + | 13.7638i | −0.360375 | + | 1.10912i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.04508 | − | 3.21644i | −0.0836738 | − | 0.257521i | ||||
\(157\) | 13.7984i | 1.10123i | 0.834759 | + | 0.550615i | \(0.185607\pi\) | ||||
−0.834759 | + | 0.550615i | \(0.814393\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.11803 | + | 0.812299i | 0.0886659 | + | 0.0644195i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.1803 | − | 11.7557i | 1.27519 | − | 0.926479i | ||||
\(162\) | −0.587785 | + | 0.809017i | −0.0461808 | + | 0.0635624i | ||||
\(163\) | 1.73060 | − | 2.38197i | 0.135551 | − | 0.186570i | −0.735845 | − | 0.677150i | \(-0.763215\pi\) |
0.871396 | + | 0.490580i | \(0.163215\pi\) | |||||||
\(164\) | 1.11803 | − | 0.812299i | 0.0873038 | − | 0.0634299i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.85410 | − | 2.07363i | −0.221521 | − | 0.160945i | ||||
\(167\) | −22.2703 | + | 7.23607i | −1.72333 | + | 0.559944i | −0.992460 | − | 0.122573i | \(-0.960886\pi\) |
−0.730870 | + | 0.682517i | \(0.760886\pi\) | |||||||
\(168\) | − | 13.4164i | − | 1.03510i | ||||||
\(169\) | 0.482779 | + | 1.48584i | 0.0371369 | + | 0.114295i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | + | 3.07768i | −0.0764719 | + | 0.235356i | ||||
\(172\) | −5.42882 | − | 1.76393i | −0.413944 | − | 0.134499i | ||||
\(173\) | −5.82485 | − | 8.01722i | −0.442855 | − | 0.609538i | 0.527988 | − | 0.849252i | \(-0.322946\pi\) |
−0.970844 | + | 0.239714i | \(0.922946\pi\) | |||||||
\(174\) | −4.38197 | −0.332196 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.23607 | −0.243928 | ||||||||
\(177\) | −2.35114 | − | 3.23607i | −0.176723 | − | 0.243238i | ||||
\(178\) | 7.24518 | + | 2.35410i | 0.543049 | + | 0.176447i | ||||
\(179\) | −1.90983 | + | 5.87785i | −0.142747 | + | 0.439331i | −0.996714 | − | 0.0809958i | \(-0.974190\pi\) |
0.853967 | + | 0.520327i | \(0.174190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.02786 | − | 9.31881i | −0.225059 | − | 0.692661i | −0.998286 | − | 0.0585312i | \(-0.981358\pi\) |
0.773226 | − | 0.634130i | \(-0.218642\pi\) | |||||||
\(182\) | − | 15.1246i | − | 1.12111i | ||||||
\(183\) | 0.587785 | − | 0.190983i | 0.0434503 | − | 0.0141179i | ||||
\(184\) | 10.8541 | + | 7.88597i | 0.800175 | + | 0.581361i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.85410 | + | 4.25325i | −0.429244 | + | 0.311864i | ||||
\(187\) | 5.42882 | − | 7.47214i | 0.396995 | − | 0.546417i | ||||
\(188\) | 3.07768 | − | 4.23607i | 0.224463 | − | 0.308947i | ||||
\(189\) | 3.61803 | − | 2.62866i | 0.263173 | − | 0.191207i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.9443 | + | 14.4904i | 1.44312 | + | 1.04849i | 0.987380 | + | 0.158371i | \(0.0506243\pi\) |
0.455737 | + | 0.890114i | \(0.349376\pi\) | |||||||
\(192\) | 6.65740 | − | 2.16312i | 0.480456 | − | 0.156110i | ||||
\(193\) | 7.67376i | 0.552369i | 0.961105 | + | 0.276185i | \(0.0890702\pi\) | ||||
−0.961105 | + | 0.276185i | \(0.910930\pi\) | |||||||
\(194\) | −2.73607 | − | 8.42075i | −0.196438 | − | 0.604575i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.01722 | + | 12.3637i | −0.286944 | + | 0.883124i | ||||
\(197\) | −5.11855 | − | 1.66312i | −0.364682 | − | 0.118492i | 0.120943 | − | 0.992659i | \(-0.461408\pi\) |
−0.485625 | + | 0.874167i | \(0.661408\pi\) | |||||||
\(198\) | −1.90211 | − | 2.61803i | −0.135177 | − | 0.186056i | ||||
\(199\) | 18.6525 | 1.32224 | 0.661119 | − | 0.750281i | \(-0.270082\pi\) | ||||
0.661119 | + | 0.750281i | \(0.270082\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.23607 | 0.369324 | ||||||||
\(202\) | −9.73508 | − | 13.3992i | −0.684958 | − | 0.942764i | ||||
\(203\) | 18.6376 | + | 6.05573i | 1.30810 | + | 0.425029i | ||||
\(204\) | −0.881966 | + | 2.71441i | −0.0617500 | + | 0.190047i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.381966 | − | 1.17557i | −0.0266128 | − | 0.0819059i | ||||
\(207\) | 4.47214i | 0.310835i | ||||||||
\(208\) | 3.21644 | − | 1.04508i | 0.223020 | − | 0.0724636i | ||||
\(209\) | −8.47214 | − | 6.15537i | −0.586030 | − | 0.425776i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4721 | − | 10.5146i | 0.996303 | − | 0.723856i | 0.0350106 | − | 0.999387i | \(-0.488854\pi\) |
0.961292 | + | 0.275530i | \(0.0888535\pi\) | |||||||
\(212\) | 0.812299 | − | 1.11803i | 0.0557889 | − | 0.0767869i | ||||
\(213\) | −0.449028 | + | 0.618034i | −0.0307669 | + | 0.0423470i | ||||
\(214\) | 13.3262 | − | 9.68208i | 0.910963 | − | 0.661853i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.42705 | + | 1.76336i | 0.165140 | + | 0.119981i | ||||
\(217\) | 30.7768 | − | 10.0000i | 2.08927 | − | 0.678844i | ||||
\(218\) | − | 19.0902i | − | 1.29295i | ||||||
\(219\) | −0.954915 | − | 2.93893i | −0.0645272 | − | 0.198594i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.98278 | + | 9.18005i | −0.200643 | + | 0.617517i | ||||
\(222\) | −7.69421 | − | 2.50000i | −0.516401 | − | 0.167789i | ||||
\(223\) | 8.33499 | + | 11.4721i | 0.558153 | + | 0.768231i | 0.991090 | − | 0.133193i | \(-0.0425230\pi\) |
−0.432938 | + | 0.901424i | \(0.642523\pi\) | |||||||
\(224\) | −22.3607 | −1.49404 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.67376 | 0.177856 | ||||||||
\(227\) | −11.7557 | − | 16.1803i | −0.780254 | − | 1.07393i | −0.995254 | − | 0.0973129i | \(-0.968975\pi\) |
0.215000 | − | 0.976614i | \(-0.431025\pi\) | |||||||
\(228\) | 3.07768 | + | 1.00000i | 0.203825 | + | 0.0662266i | ||||
\(229\) | 7.71885 | − | 23.7562i | 0.510076 | − | 1.56985i | −0.281991 | − | 0.959417i | \(-0.590995\pi\) |
0.792067 | − | 0.610435i | \(-0.209005\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.47214 | + | 13.7638i | 0.294245 | + | 0.905593i | ||||
\(232\) | 13.1459i | 0.863070i | ||||||||
\(233\) | −13.9026 | + | 4.51722i | −0.910788 | + | 0.295933i | −0.726682 | − | 0.686973i | \(-0.758939\pi\) |
−0.184106 | + | 0.982906i | \(0.558939\pi\) | |||||||
\(234\) | 2.73607 | + | 1.98787i | 0.178862 | + | 0.129951i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.23607 | + | 2.35114i | −0.210650 | + | 0.153046i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.50245 | + | 10.3262i | −0.486312 | + | 0.669351i | ||||
\(239\) | −5.70820 | + | 4.14725i | −0.369233 | + | 0.268263i | −0.756893 | − | 0.653539i | \(-0.773284\pi\) |
0.387660 | + | 0.921803i | \(0.373284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.836881 | + | 0.608030i | 0.0539082 | + | 0.0391666i | 0.614413 | − | 0.788985i | \(-0.289393\pi\) |
−0.560505 | + | 0.828151i | \(0.689393\pi\) | |||||||
\(242\) | −0.502029 | + | 0.163119i | −0.0322716 | + | 0.0104857i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.190983 | − | 0.587785i | −0.0122264 | − | 0.0376291i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.427051 | + | 1.31433i | −0.0272278 | + | 0.0837985i | ||||
\(247\) | 10.4086 | + | 3.38197i | 0.662285 | + | 0.215189i | ||||
\(248\) | 12.7598 | + | 17.5623i | 0.810246 | + | 1.11521i | ||||
\(249\) | −3.52786 | −0.223569 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.9443 | −1.70071 | −0.850354 | − | 0.526212i | \(-0.823612\pi\) | ||||
−0.850354 | + | 0.526212i | \(0.823612\pi\) | |||||||
\(252\) | −2.62866 | − | 3.61803i | −0.165590 | − | 0.227915i | ||||
\(253\) | −13.7638 | − | 4.47214i | −0.865324 | − | 0.281161i | ||||
\(254\) | −3.00000 | + | 9.23305i | −0.188237 | + | 0.579333i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.25329 | − | 16.1680i | −0.328331 | − | 1.01050i | ||||
\(257\) | 12.7984i | 0.798341i | 0.916877 | + | 0.399170i | \(0.130702\pi\) | ||||
−0.916877 | + | 0.399170i | \(0.869298\pi\) | |||||||
\(258\) | 5.42882 | − | 1.76393i | 0.337984 | − | 0.109818i | ||||
\(259\) | 29.2705 | + | 21.2663i | 1.81878 | + | 1.32142i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.54508 | + | 2.57565i | −0.219435 | + | 0.159429i | ||||
\(262\) | −8.33499 | + | 11.4721i | −0.514938 | + | 0.708751i | ||||
\(263\) | 6.98791 | − | 9.61803i | 0.430893 | − | 0.593073i | −0.537265 | − | 0.843414i | \(-0.680542\pi\) |
0.968158 | + | 0.250340i | \(0.0805425\pi\) | |||||||
\(264\) | −7.85410 | + | 5.70634i | −0.483387 | + | 0.351201i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.7082 | + | 8.50651i | 0.717876 | + | 0.521567i | ||||
\(267\) | 7.24518 | − | 2.35410i | 0.443398 | − | 0.144069i | ||||
\(268\) | − | 5.23607i | − | 0.319844i | ||||||
\(269\) | 0.0450850 | + | 0.138757i | 0.00274888 | + | 0.00846018i | 0.952422 | − | 0.304784i | \(-0.0985842\pi\) |
−0.949673 | + | 0.313244i | \(0.898584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.85410 | − | 21.0948i | 0.416357 | − | 1.28142i | −0.494674 | − | 0.869078i | \(-0.664713\pi\) |
0.911031 | − | 0.412337i | \(-0.135287\pi\) | |||||||
\(272\) | −2.71441 | − | 0.881966i | −0.164585 | − | 0.0534770i | ||||
\(273\) | −8.89002 | − | 12.2361i | −0.538049 | − | 0.740561i | ||||
\(274\) | 5.38197 | 0.325136 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.47214 | 0.269191 | ||||||||
\(277\) | −3.40820 | − | 4.69098i | −0.204779 | − | 0.281854i | 0.694259 | − | 0.719726i | \(-0.255732\pi\) |
−0.899037 | + | 0.437872i | \(0.855732\pi\) | |||||||
\(278\) | −4.80828 | − | 1.56231i | −0.288382 | − | 0.0937009i | ||||
\(279\) | −2.23607 | + | 6.88191i | −0.133870 | + | 0.412009i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.37132 | − | 16.5312i | −0.320426 | − | 0.986171i | −0.973463 | − | 0.228844i | \(-0.926505\pi\) |
0.653037 | − | 0.757326i | \(-0.273495\pi\) | |||||||
\(282\) | 5.23607i | 0.311803i | ||||||||
\(283\) | −0.277515 | + | 0.0901699i | −0.0164965 | + | 0.00536005i | −0.317254 | − | 0.948341i | \(-0.602761\pi\) |
0.300757 | + | 0.953701i | \(0.402761\pi\) | |||||||
\(284\) | 0.618034 | + | 0.449028i | 0.0366736 | + | 0.0266449i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.85410 | + | 6.43288i | −0.523554 | + | 0.380384i | ||||
\(287\) | 3.63271 | − | 5.00000i | 0.214432 | − | 0.295141i | ||||
\(288\) | 2.93893 | − | 4.04508i | 0.173178 | − | 0.238359i | ||||
\(289\) | −7.16312 | + | 5.20431i | −0.421360 | + | 0.306136i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.16312 | − | 5.20431i | −0.419909 | − | 0.305082i | ||||
\(292\) | −2.93893 | + | 0.954915i | −0.171988 | + | 0.0558822i | ||||
\(293\) | 3.79837i | 0.221903i | 0.993826 | + | 0.110952i | \(0.0353899\pi\) | ||||
−0.993826 | + | 0.110952i | \(0.964610\pi\) | |||||||
\(294\) | −4.01722 | − | 12.3637i | −0.234289 | − | 0.721068i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.50000 | + | 23.0826i | −0.435929 | + | 1.34165i | ||||
\(297\) | −3.07768 | − | 1.00000i | −0.178585 | − | 0.0580259i | ||||
\(298\) | 7.13918 | + | 9.82624i | 0.413562 | + | 0.569219i | ||||
\(299\) | 15.1246 | 0.874679 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.5279 | −1.47140 | ||||||||
\(302\) | 9.68208 | + | 13.3262i | 0.557141 | + | 0.766839i | ||||
\(303\) | −15.7517 | − | 5.11803i | −0.904911 | − | 0.294023i | ||||
\(304\) | −1.00000 | + | 3.07768i | −0.0573539 | + | 0.176517i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.881966 | − | 2.71441i | −0.0504186 | − | 0.155173i | ||||
\(307\) | − | 1.34752i | − | 0.0769073i | −0.999260 | − | 0.0384536i | \(-0.987757\pi\) | ||
0.999260 | − | 0.0384536i | \(-0.0122432\pi\) | |||||||
\(308\) | 13.7638 | − | 4.47214i | 0.784266 | − | 0.254824i | ||||
\(309\) | −1.00000 | − | 0.726543i | −0.0568880 | − | 0.0413316i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.47214 | + | 2.52265i | −0.196887 | + | 0.143047i | −0.681861 | − | 0.731482i | \(-0.738829\pi\) |
0.484974 | + | 0.874529i | \(0.338829\pi\) | |||||||
\(312\) | 5.96361 | − | 8.20820i | 0.337623 | − | 0.464698i | ||||
\(313\) | 4.97980 | − | 6.85410i | 0.281475 | − | 0.387417i | −0.644747 | − | 0.764396i | \(-0.723037\pi\) |
0.926222 | + | 0.376979i | \(0.123037\pi\) | |||||||
\(314\) | −11.1631 | + | 8.11048i | −0.629971 | + | 0.457701i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.6174 | + | 7.67376i | −1.32649 | + | 0.431001i | −0.884717 | − | 0.466128i | \(-0.845649\pi\) |
−0.441768 | + | 0.897129i | \(0.645649\pi\) | |||||||
\(318\) | 1.38197i | 0.0774968i | ||||||||
\(319\) | −4.38197 | − | 13.4863i | −0.245343 | − | 0.755088i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.09017 | − | 15.6659i | 0.284106 | − | 0.874387i | ||||
\(322\) | 19.0211 | + | 6.18034i | 1.06001 | + | 0.344417i | ||||
\(323\) | −5.42882 | − | 7.47214i | −0.302068 | − | 0.415761i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.94427 | 0.163068 | ||||||||
\(327\) | −11.2209 | − | 15.4443i | −0.620518 | − | 0.854070i | ||||
\(328\) | 3.94298 | + | 1.28115i | 0.217715 | + | 0.0707398i | ||||
\(329\) | 7.23607 | − | 22.2703i | 0.398937 | − | 1.22780i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.38197 | + | 10.4086i | 0.185890 | + | 0.572110i | 0.999963 | − | 0.00865315i | \(-0.00275442\pi\) |
−0.814073 | + | 0.580763i | \(0.802754\pi\) | |||||||
\(332\) | 3.52786i | 0.193617i | ||||||||
\(333\) | −7.69421 | + | 2.50000i | −0.421640 | + | 0.136999i | ||||
\(334\) | −18.9443 | − | 13.7638i | −1.03658 | − | 0.753123i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.61803 | − | 2.62866i | 0.197380 | − | 0.143405i | ||||
\(337\) | 8.78402 | − | 12.0902i | 0.478496 | − | 0.658594i | −0.499719 | − | 0.866188i | \(-0.666563\pi\) |
0.978215 | + | 0.207594i | \(0.0665633\pi\) | |||||||
\(338\) | −0.918300 | + | 1.26393i | −0.0499490 | + | 0.0687488i | ||||
\(339\) | 2.16312 | − | 1.57160i | 0.117484 | − | 0.0853575i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9443 | − | 13.7638i | −1.02589 | − | 0.745353i | ||||
\(342\) | −3.07768 | + | 1.00000i | −0.166422 | + | 0.0540738i | ||||
\(343\) | 26.8328i | 1.44884i | ||||||||
\(344\) | −5.29180 | − | 16.2865i | −0.285315 | − | 0.878108i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.06231 | − | 9.42481i | 0.164631 | − | 0.506681i | ||||
\(347\) | 32.0584 | + | 10.4164i | 1.72099 | + | 0.559182i | 0.992100 | − | 0.125453i | \(-0.0400385\pi\) |
0.728886 | + | 0.684635i | \(0.240038\pi\) | |||||||
\(348\) | 2.57565 | + | 3.54508i | 0.138070 | + | 0.190037i | ||||
\(349\) | −25.0344 | −1.34006 | −0.670031 | − | 0.742333i | \(-0.733719\pi\) | ||||
−0.670031 | + | 0.742333i | \(0.733719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.38197 | 0.180516 | ||||||||
\(352\) | 9.51057 | + | 13.0902i | 0.506915 | + | 0.697708i | ||||
\(353\) | −28.8747 | − | 9.38197i | −1.53685 | − | 0.499352i | −0.586342 | − | 0.810063i | \(-0.699433\pi\) |
−0.950504 | + | 0.310712i | \(0.899433\pi\) | |||||||
\(354\) | 1.23607 | − | 3.80423i | 0.0656963 | − | 0.202192i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.35410 | − | 7.24518i | −0.124767 | − | 0.383994i | ||||
\(357\) | 12.7639i | 0.675539i | ||||||||
\(358\) | −5.87785 | + | 1.90983i | −0.310654 | + | 0.100938i | ||||
\(359\) | −8.56231 | − | 6.22088i | −0.451901 | − | 0.328325i | 0.338445 | − | 0.940986i | \(-0.390099\pi\) |
−0.790346 | + | 0.612661i | \(0.790099\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.89919 | − | 5.01255i | 0.363115 | − | 0.263819i | ||||
\(362\) | 5.75934 | − | 7.92705i | 0.302704 | − | 0.416637i | ||||
\(363\) | −0.310271 | + | 0.427051i | −0.0162850 | + | 0.0224144i | ||||
\(364\) | −12.2361 | + | 8.89002i | −0.641344 | + | 0.465964i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.500000 | + | 0.363271i | 0.0261354 | + | 0.0189885i | ||||
\(367\) | −5.70634 | + | 1.85410i | −0.297868 | + | 0.0967833i | −0.454139 | − | 0.890931i | \(-0.650053\pi\) |
0.156270 | + | 0.987714i | \(0.450053\pi\) | |||||||
\(368\) | 4.47214i | 0.233126i | ||||||||
\(369\) | 0.427051 | + | 1.31433i | 0.0222314 | + | 0.0684212i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.90983 | − | 5.87785i | 0.0991534 | − | 0.305163i | ||||
\(372\) | 6.88191 | + | 2.23607i | 0.356810 | + | 0.115935i | ||||
\(373\) | −17.2905 | − | 23.7984i | −0.895270 | − | 1.23223i | −0.971952 | − | 0.235178i | \(-0.924433\pi\) |
0.0766827 | − | 0.997056i | \(-0.475567\pi\) | |||||||
\(374\) | 9.23607 | 0.477586 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.7082 | 0.810089 | ||||||||
\(377\) | 8.71078 | + | 11.9894i | 0.448628 | + | 0.617483i | ||||
\(378\) | 4.25325 | + | 1.38197i | 0.218764 | + | 0.0710807i | ||||
\(379\) | −7.23607 | + | 22.2703i | −0.371692 | + | 1.14395i | 0.573992 | + | 0.818861i | \(0.305394\pi\) |
−0.945684 | + | 0.325089i | \(0.894606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00000 | + | 9.23305i | 0.153695 | + | 0.473024i | ||||
\(382\) | 24.6525i | 1.26133i | ||||||||
\(383\) | −19.8132 | + | 6.43769i | −1.01241 | + | 0.328951i | −0.767812 | − | 0.640675i | \(-0.778655\pi\) |
−0.244594 | + | 0.969626i | \(0.578655\pi\) | |||||||
\(384\) | −2.42705 | − | 1.76336i | −0.123855 | − | 0.0899859i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.20820 | + | 4.51052i | −0.315989 | + | 0.229580i | ||||
\(387\) | 3.35520 | − | 4.61803i | 0.170554 | − | 0.234748i | ||||
\(388\) | −5.20431 | + | 7.16312i | −0.264209 | + | 0.363652i | ||||
\(389\) | −30.0066 | + | 21.8011i | −1.52139 | + | 1.10536i | −0.560603 | + | 0.828085i | \(0.689430\pi\) |
−0.960791 | + | 0.277272i | \(0.910570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3262 | − | 7.50245i | −0.522220 | − | 0.379415i | ||||
\(392\) | −37.0912 | + | 12.0517i | −1.87339 | + | 0.608701i | ||||
\(393\) | 14.1803i | 0.715304i | ||||||||
\(394\) | −1.66312 | − | 5.11855i | −0.0837867 | − | 0.257869i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | + | 3.07768i | −0.0502519 | + | 0.154659i | ||||
\(397\) | −10.4086 | − | 3.38197i | −0.522394 | − | 0.169736i | 0.0359377 | − | 0.999354i | \(-0.488558\pi\) |
−0.558331 | + | 0.829618i | \(0.688558\pi\) | |||||||
\(398\) | 10.9637 | + | 15.0902i | 0.549558 | + | 0.756402i | ||||
\(399\) | 14.4721 | 0.724513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.4508 | 1.67046 | 0.835228 | − | 0.549904i | \(-0.185336\pi\) | ||||
0.835228 | + | 0.549904i | \(0.185336\pi\) | |||||||
\(402\) | 3.07768 | + | 4.23607i | 0.153501 | + | 0.211276i | ||||
\(403\) | 23.2744 | + | 7.56231i | 1.15938 | + | 0.376705i | ||||
\(404\) | −5.11803 | + | 15.7517i | −0.254632 | + | 0.783676i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.05573 | + | 18.6376i | 0.300541 | + | 0.924969i | ||||
\(407\) | − | 26.1803i | − | 1.29771i | ||||||
\(408\) | −8.14324 | + | 2.64590i | −0.403150 | + | 0.130991i | ||||
\(409\) | 20.8713 | + | 15.1639i | 1.03202 | + | 0.749807i | 0.968712 | − | 0.248187i | \(-0.0798348\pi\) |
0.0633084 | + | 0.997994i | \(0.479835\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.35410 | − | 3.16344i | 0.214772 | − | 0.156041i | ||||
\(412\) | −0.726543 | + | 1.00000i | −0.0357942 | + | 0.0492665i | ||||
\(413\) | −10.5146 | + | 14.4721i | −0.517391 | + | 0.712127i | ||||
\(414\) | −3.61803 | + | 2.62866i | −0.177817 | + | 0.129191i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13.6803 | − | 9.93935i | −0.670734 | − | 0.487317i | ||||
\(417\) | −4.80828 | + | 1.56231i | −0.235463 | + | 0.0765064i | ||||
\(418\) | − | 10.4721i | − | 0.512209i | ||||||
\(419\) | −10.1803 | − | 31.3319i | −0.497342 | − | 1.53066i | −0.813275 | − | 0.581880i | \(-0.802317\pi\) |
0.315932 | − | 0.948782i | \(-0.397683\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.15248 | − | 22.0131i | 0.348590 | − | 1.07285i | −0.611043 | − | 0.791597i | \(-0.709250\pi\) |
0.959634 | − | 0.281253i | \(-0.0907502\pi\) | |||||||
\(422\) | 17.0130 | + | 5.52786i | 0.828181 | + | 0.269092i | ||||
\(423\) | 3.07768 | + | 4.23607i | 0.149642 | + | 0.205965i | ||||
\(424\) | 4.14590 | 0.201343 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.763932 | −0.0370126 | ||||||||
\(427\) | −1.62460 | − | 2.23607i | −0.0786198 | − | 0.108211i | ||||
\(428\) | −15.6659 | − | 5.09017i | −0.757241 | − | 0.246043i | ||||
\(429\) | −3.38197 | + | 10.4086i | −0.163283 | + | 0.502533i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.29180 | − | 10.1311i | −0.158560 | − | 0.487998i | 0.839944 | − | 0.542673i | \(-0.182588\pi\) |
−0.998504 | + | 0.0546749i | \(0.982588\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | −23.7562 | + | 7.71885i | −1.14165 | + | 0.370944i | −0.817991 | − | 0.575230i | \(-0.804912\pi\) |
−0.323657 | + | 0.946174i | \(0.604912\pi\) | |||||||
\(434\) | 26.1803 | + | 19.0211i | 1.25670 | + | 0.913043i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.4443 | + | 11.2209i | −0.739646 | + | 0.537385i | ||||
\(437\) | −8.50651 | + | 11.7082i | −0.406921 | + | 0.560079i | ||||
\(438\) | 1.81636 | − | 2.50000i | 0.0867889 | − | 0.119455i | ||||
\(439\) | −5.00000 | + | 3.63271i | −0.238637 | + | 0.173380i | −0.700676 | − | 0.713480i | \(-0.747118\pi\) |
0.462039 | + | 0.886860i | \(0.347118\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.5172 | − | 7.64121i | −0.500820 | − | 0.363867i | ||||
\(442\) | −9.18005 | + | 2.98278i | −0.436650 | + | 0.141876i | ||||
\(443\) | − | 30.7639i | − | 1.46164i | −0.682571 | − | 0.730819i | \(-0.739138\pi\) | ||
0.682571 | − | 0.730819i | \(-0.260862\pi\) | |||||||
\(444\) | 2.50000 | + | 7.69421i | 0.118645 | + | 0.365151i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.38197 | + | 13.4863i | −0.207492 | + | 0.638595i | ||||
\(447\) | 11.5514 | + | 3.75329i | 0.546364 | + | 0.177524i | ||||
\(448\) | −18.4006 | − | 25.3262i | −0.869346 | − | 1.19655i | ||||
\(449\) | 7.79837 | 0.368028 | 0.184014 | − | 0.982924i | \(-0.441091\pi\) | ||||
0.184014 | + | 0.982924i | \(0.441091\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.47214 | −0.210585 | ||||||||
\(452\) | −1.57160 | − | 2.16312i | −0.0739217 | − | 0.101745i | ||||
\(453\) | 15.6659 | + | 5.09017i | 0.736050 | + | 0.239157i | ||||
\(454\) | 6.18034 | − | 19.0211i | 0.290058 | − | 0.892706i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | + | 9.23305i | 0.140488 | + | 0.432377i | ||||
\(457\) | − | 22.3607i | − | 1.04599i | −0.852336 | − | 0.522994i | \(-0.824815\pi\) | ||
0.852336 | − | 0.522994i | \(-0.175185\pi\) | |||||||
\(458\) | 23.7562 | − | 7.71885i | 1.11005 | − | 0.360678i | ||||
\(459\) | −2.30902 | − | 1.67760i | −0.107776 | − | 0.0783036i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.63525 | − | 4.82079i | 0.309035 | − | 0.224527i | −0.422448 | − | 0.906387i | \(-0.638829\pi\) |
0.731482 | + | 0.681861i | \(0.238829\pi\) | |||||||
\(462\) | −8.50651 | + | 11.7082i | −0.395759 | + | 0.544715i | ||||
\(463\) | 13.6578 | − | 18.7984i | 0.634733 | − | 0.873635i | −0.363588 | − | 0.931560i | \(-0.618448\pi\) |
0.998321 | + | 0.0579252i | \(0.0184485\pi\) | |||||||
\(464\) | −3.54508 | + | 2.57565i | −0.164576 | + | 0.119572i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.8262 | − | 8.59226i | −0.547840 | − | 0.398029i | ||||
\(467\) | 5.53483 | − | 1.79837i | 0.256121 | − | 0.0832188i | −0.178142 | − | 0.984005i | \(-0.557009\pi\) |
0.434263 | + | 0.900786i | \(0.357009\pi\) | |||||||
\(468\) | − | 3.38197i | − | 0.156331i | ||||||
\(469\) | −7.23607 | − | 22.2703i | −0.334131 | − | 1.02835i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.26393 | + | 13.1230i | −0.196472 | + | 0.604677i | ||||
\(472\) | −11.4127 | − | 3.70820i | −0.525311 | − | 0.170684i | ||||
\(473\) | 10.8576 | + | 14.9443i | 0.499235 | + | 0.687138i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.7639 | 0.585034 | ||||||||
\(477\) | 0.812299 | + | 1.11803i | 0.0371926 | + | 0.0511913i | ||||
\(478\) | −6.71040 | − | 2.18034i | −0.306926 | − | 0.0997264i | ||||
\(479\) | −0.326238 | + | 1.00406i | −0.0149062 | + | 0.0458765i | −0.958233 | − | 0.285989i | \(-0.907678\pi\) |
0.943327 | + | 0.331865i | \(0.107678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.45492 | + | 26.0216i | 0.385511 | + | 1.18648i | ||||
\(482\) | 1.03444i | 0.0471175i | ||||||||
\(483\) | 19.0211 | − | 6.18034i | 0.865491 | − | 0.281215i | ||||
\(484\) | 0.427051 | + | 0.310271i | 0.0194114 | + | 0.0141032i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | 2.17963 | − | 3.00000i | 0.0987684 | − | 0.135943i | −0.756772 | − | 0.653679i | \(-0.773225\pi\) |
0.855541 | + | 0.517736i | \(0.173225\pi\) | |||||||
\(488\) | 1.08981 | − | 1.50000i | 0.0493336 | − | 0.0679018i | ||||
\(489\) | 2.38197 | − | 1.73060i | 0.107716 | − | 0.0782604i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.1803 | + | 17.5680i | 1.09124 | + | 0.792835i | 0.979609 | − | 0.200915i | \(-0.0643914\pi\) |
0.111635 | + | 0.993749i | \(0.464391\pi\) | |||||||
\(492\) | 1.31433 | − | 0.427051i | 0.0592545 | − | 0.0192529i | ||||
\(493\) | − | 12.5066i | − | 0.563268i | ||||||
\(494\) | 3.38197 | + | 10.4086i | 0.152162 | + | 0.468306i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.23607 | + | 6.88191i | −0.100402 | + | 0.309007i | ||||
\(497\) | 3.24920 | + | 1.05573i | 0.145746 | + | 0.0473559i | ||||
\(498\) | −2.07363 | − | 2.85410i | −0.0929214 | − | 0.127895i | ||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.4164 | −1.04617 | ||||||||
\(502\) | −15.8374 | − | 21.7984i | −0.706860 | − | 0.972909i | ||||
\(503\) | 33.6830 | + | 10.9443i | 1.50185 | + | 0.487981i | 0.940557 | − | 0.339636i | \(-0.110304\pi\) |
0.561294 | + | 0.827617i | \(0.310304\pi\) | |||||||
\(504\) | 4.14590 | − | 12.7598i | 0.184673 | − | 0.568365i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.47214 | − | 13.7638i | −0.198811 | − | 0.611876i | ||||
\(507\) | 1.56231i | 0.0693844i | ||||||||
\(508\) | 9.23305 | − | 3.00000i | 0.409650 | − | 0.133103i | ||||
\(509\) | 21.7254 | + | 15.7844i | 0.962963 | + | 0.699633i | 0.953837 | − | 0.300325i | \(-0.0970952\pi\) |
0.00912564 | + | 0.999958i | \(0.497095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1803 | + | 8.12299i | −0.494589 | + | 0.359340i | ||||
\(512\) | 6.46564 | − | 8.89919i | 0.285744 | − | 0.393292i | ||||
\(513\) | −1.90211 | + | 2.61803i | −0.0839803 | + | 0.115589i | ||||
\(514\) | −10.3541 | + | 7.52270i | −0.456700 | + | 0.331812i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.61803 | − | 3.35520i | −0.203298 | − | 0.147704i | ||||
\(517\) | −16.1150 | + | 5.23607i | −0.708735 | + | 0.230282i | ||||
\(518\) | 36.1803i | 1.58967i | ||||||||
\(519\) | −3.06231 | − | 9.42481i | −0.134420 | − | 0.413703i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.628677 | − | 1.93487i | 0.0275428 | − | 0.0847682i | −0.936340 | − | 0.351094i | \(-0.885810\pi\) |
0.963883 | + | 0.266326i | \(0.0858097\pi\) | |||||||
\(522\) | −4.16750 | − | 1.35410i | −0.182406 | − | 0.0592674i | ||||
\(523\) | 7.22494 | + | 9.94427i | 0.315924 | + | 0.434833i | 0.937217 | − | 0.348746i | \(-0.113392\pi\) |
−0.621293 | + | 0.783578i | \(0.713392\pi\) | |||||||
\(524\) | 14.1803 | 0.619471 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.8885 | 0.518365 | ||||||||
\(527\) | −12.1392 | − | 16.7082i | −0.528793 | − | 0.727821i | ||||
\(528\) | −3.07768 | − | 1.00000i | −0.133939 | − | 0.0435194i | ||||
\(529\) | 0.927051 | − | 2.85317i | 0.0403066 | − | 0.124051i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.23607 | − | 3.80423i | −0.0536408 | − | 0.165089i | ||||
\(532\) | − | 14.4721i | − | 0.627447i | ||||||
\(533\) | 4.44501 | − | 1.44427i | 0.192535 | − | 0.0625584i | ||||
\(534\) | 6.16312 | + | 4.47777i | 0.266704 | + | 0.193772i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.7082 | − | 9.23305i | 0.548911 | − | 0.398807i | ||||
\(537\) | −3.63271 | + | 5.00000i | −0.156763 | + | 0.215766i | ||||
\(538\) | −0.0857567 | + | 0.118034i | −0.00369723 | + | 0.00508881i | ||||
\(539\) | 34.0344 | − | 24.7275i | 1.46597 | − | 1.06509i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5795 | + | 20.7642i | 1.22873 | + | 0.892724i | 0.996794 | − | 0.0800067i | \(-0.0254942\pi\) |
0.231936 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(542\) | 21.0948 | − | 6.85410i | 0.906097 | − | 0.294409i | ||||
\(543\) | − | 9.79837i | − | 0.420488i | ||||||
\(544\) | 4.40983 | + | 13.5721i | 0.189070 | + | 0.581897i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.67376 | − | 14.3844i | 0.200019 | − | 0.615594i | ||||
\(547\) | 2.24514 | + | 0.729490i | 0.0959952 | + | 0.0311907i | 0.356621 | − | 0.934249i | \(-0.383929\pi\) |
−0.260626 | + | 0.965440i | \(0.583929\pi\) | |||||||
\(548\) | −3.16344 | − | 4.35410i | −0.135135 | − | 0.185998i | ||||
\(549\) | 0.618034 | 0.0263770 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.1803 | −0.604103 | ||||||||
\(552\) | 7.88597 | + | 10.8541i | 0.335649 | + | 0.461981i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.79180 | − | 5.51458i | 0.0761261 | − | 0.234292i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.56231 | + | 4.80828i | 0.0662565 | + | 0.203917i | ||||
\(557\) | − | 22.2705i | − | 0.943632i | −0.881697 | − | 0.471816i | \(-0.843599\pi\) | ||
0.881697 | − | 0.471816i | \(-0.156401\pi\) | |||||||
\(558\) | −6.88191 | + | 2.23607i | −0.291334 | + | 0.0946603i | ||||
\(559\) | −15.6180 | − | 11.3472i | −0.660572 | − | 0.479934i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.47214 | − | 5.42882i | 0.315474 | − | 0.229205i | ||||
\(562\) | 10.2169 | − | 14.0623i | 0.430972 | − | 0.593183i | ||||
\(563\) | −10.3026 | + | 14.1803i | −0.434204 | + | 0.597630i | −0.968912 | − | 0.247407i | \(-0.920422\pi\) |
0.534708 | + | 0.845037i | \(0.320422\pi\) | |||||||
\(564\) | 4.23607 | − | 3.07768i | 0.178371 | − | 0.129594i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.236068 | − | 0.171513i | −0.00992268 | − | 0.00720925i | ||||
\(567\) | 4.25325 | − | 1.38197i | 0.178620 | − | 0.0580371i | ||||
\(568\) | 2.29180i | 0.0961616i | ||||||||
\(569\) | 9.35410 | + | 28.7890i | 0.392144 | + | 1.20690i | 0.931163 | + | 0.364603i | \(0.118795\pi\) |
−0.539019 | + | 0.842294i | \(0.681205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.56231 | + | 20.1967i | −0.274624 | + | 0.845206i | 0.714695 | + | 0.699437i | \(0.246566\pi\) |
−0.989319 | + | 0.145769i | \(0.953434\pi\) | |||||||
\(572\) | 10.4086 | + | 3.38197i | 0.435206 | + | 0.141407i | ||||
\(573\) | 14.4904 | + | 19.9443i | 0.605344 | + | 0.833184i | ||||
\(574\) | 6.18034 | 0.257962 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | −18.1886 | − | 25.0344i | −0.757201 | − | 1.04220i | −0.997442 | − | 0.0714842i | \(-0.977226\pi\) |
0.240241 | − | 0.970713i | \(-0.422774\pi\) | |||||||
\(578\) | −8.42075 | − | 2.73607i | −0.350257 | − | 0.113805i | ||||
\(579\) | −2.37132 | + | 7.29818i | −0.0985488 | + | 0.303302i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.87539 | + | 15.0049i | 0.202265 | + | 0.622508i | ||||
\(582\) | − | 8.85410i | − | 0.367014i | ||||||
\(583\) | −4.25325 | + | 1.38197i | −0.176152 | + | 0.0572352i | ||||
\(584\) | −7.50000 | − | 5.44907i | −0.310352 | − | 0.225484i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.07295 | + | 2.23263i | −0.126942 | + | 0.0922290i | ||||
\(587\) | 8.57202 | − | 11.7984i | 0.353805 | − | 0.486971i | −0.594605 | − | 0.804018i | \(-0.702691\pi\) |
0.948410 | + | 0.317047i | \(0.102691\pi\) | |||||||
\(588\) | −7.64121 | + | 10.5172i | −0.315118 | + | 0.433723i | ||||
\(589\) | −18.9443 | + | 13.7638i | −0.780585 | + | 0.567128i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.35410 | − | 3.16344i | −0.179104 | − | 0.130127i | ||||
\(592\) | −7.69421 | + | 2.50000i | −0.316230 | + | 0.102749i | ||||
\(593\) | − | 32.7426i | − | 1.34458i | −0.740288 | − | 0.672290i | \(-0.765311\pi\) | ||
0.740288 | − | 0.672290i | \(-0.234689\pi\) | |||||||
\(594\) | −1.00000 | − | 3.07768i | −0.0410305 | − | 0.126279i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.75329 | − | 11.5514i | 0.153741 | − | 0.473165i | ||||
\(597\) | 17.7396 | + | 5.76393i | 0.726032 | + | 0.235902i | ||||
\(598\) | 8.89002 | + | 12.2361i | 0.363540 | + | 0.500370i | ||||
\(599\) | 12.4721 | 0.509598 | 0.254799 | − | 0.966994i | \(-0.417991\pi\) | ||||
0.254799 | + | 0.966994i | \(0.417991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3262 | −0.992288 | −0.496144 | − | 0.868240i | \(-0.665251\pi\) | ||||
−0.496144 | + | 0.868240i | \(0.665251\pi\) | |||||||
\(602\) | −15.0049 | − | 20.6525i | −0.611554 | − | 0.841732i | ||||
\(603\) | 4.97980 | + | 1.61803i | 0.202793 | + | 0.0658914i | ||||
\(604\) | 5.09017 | − | 15.6659i | 0.207116 | − | 0.637438i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.11803 | − | 15.7517i | −0.207906 | − | 0.639869i | ||||
\(607\) | 39.2361i | 1.59254i | 0.604940 | + | 0.796271i | \(0.293197\pi\) | ||||
−0.604940 | + | 0.796271i | \(0.706803\pi\) | |||||||
\(608\) | 15.3884 | − | 5.00000i | 0.624083 | − | 0.202777i | ||||
\(609\) | 15.8541 | + | 11.5187i | 0.642441 | + | 0.466760i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3262 | − | 10.4086i | 0.579578 | − | 0.421088i | ||||
\(612\) | −1.67760 | + | 2.30902i | −0.0678129 | + | 0.0933365i | ||||
\(613\) | 23.2214 | − | 31.9615i | 0.937903 | − | 1.29091i | −0.0187931 | − | 0.999823i | \(-0.505982\pi\) |
0.956696 | − | 0.291089i | \(-0.0940176\pi\) | |||||||
\(614\) | 1.09017 | − | 0.792055i | 0.0439957 | − | 0.0319647i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 35.1246 | + | 25.5195i | 1.41521 | + | 1.02821i | ||||
\(617\) | 25.6583 | − | 8.33688i | 1.03296 | − | 0.335630i | 0.257002 | − | 0.966411i | \(-0.417265\pi\) |
0.775961 | + | 0.630781i | \(0.217265\pi\) | |||||||
\(618\) | − | 1.23607i | − | 0.0497219i | ||||||
\(619\) | −8.76393 | − | 26.9726i | −0.352252 | − | 1.08412i | −0.957586 | − | 0.288149i | \(-0.906960\pi\) |
0.605333 | − | 0.795972i | \(-0.293040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38197 | + | 4.25325i | −0.0554564 | + | 0.170677i | ||||
\(622\) | −4.08174 | − | 1.32624i | −0.163663 | − | 0.0531773i | ||||
\(623\) | −20.0252 | − | 27.5623i | −0.802292 | − | 1.10426i | ||||
\(624\) | 3.38197 | 0.135387 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.47214 | 0.338615 | ||||||||
\(627\) | −6.15537 | − | 8.47214i | −0.245822 | − | 0.338345i | ||||
\(628\) | 13.1230 | + | 4.26393i | 0.523666 | + | 0.170149i | ||||
\(629\) | 7.13525 | − | 21.9601i | 0.284501 | − | 0.875605i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||||||
\(633\) | 17.0130 | − | 5.52786i | 0.676207 | − | 0.219713i | ||||
\(634\) | −20.0902 | − | 14.5964i | −0.797883 | − | 0.579696i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.11803 | − | 0.812299i | 0.0443329 | − | 0.0322098i | ||||
\(637\) | −25.8423 | + | 35.5689i | −1.02391 | + | 1.40929i | ||||
\(638\) | 8.33499 | − | 11.4721i | 0.329986 | − | 0.454186i | ||||
\(639\) | −0.618034 | + | 0.449028i | −0.0244490 | + | 0.0177633i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.5066 | − | 22.8909i | −1.24444 | − | 0.904135i | −0.246549 | − | 0.969130i | \(-0.579297\pi\) |
−0.997886 | + | 0.0649953i | \(0.979297\pi\) | |||||||
\(642\) | 15.6659 | − | 5.09017i | 0.618285 | − | 0.200893i | ||||
\(643\) | 13.8885i | 0.547711i | 0.961771 | + | 0.273855i | \(0.0882990\pi\) | ||||
−0.961771 | + | 0.273855i | \(0.911701\pi\) | |||||||
\(644\) | −6.18034 | − | 19.0211i | −0.243540 | − | 0.749538i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.85410 | − | 8.78402i | 0.112293 | − | 0.345603i | ||||
\(647\) | −9.85359 | − | 3.20163i | −0.387385 | − | 0.125869i | 0.108848 | − | 0.994058i | \(-0.465284\pi\) |
−0.496233 | + | 0.868189i | \(0.665284\pi\) | |||||||
\(648\) | 1.76336 | + | 2.42705i | 0.0692712 | + | 0.0953436i | ||||
\(649\) | 12.9443 | 0.508107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.3607 | 1.26832 | ||||||||
\(652\) | −1.73060 | − | 2.38197i | −0.0677755 | − | 0.0932850i | ||||
\(653\) | 42.8958 | + | 13.9377i | 1.67864 | + | 0.545424i | 0.984647 | − | 0.174555i | \(-0.0558488\pi\) |
0.693995 | + | 0.719979i | \(0.255849\pi\) | |||||||
\(654\) | 5.89919 | − | 18.1558i | 0.230676 | − | 0.709949i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.427051 | + | 1.31433i | 0.0166735 | + | 0.0513159i | ||||
\(657\) | − | 3.09017i | − | 0.120559i | ||||||
\(658\) | 22.2703 | − | 7.23607i | 0.868188 | − | 0.282091i | ||||
\(659\) | −5.32624 | − | 3.86974i | −0.207481 | − | 0.150744i | 0.479192 | − | 0.877710i | \(-0.340930\pi\) |
−0.686673 | + | 0.726966i | \(0.740930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5623 | + | 14.9394i | −0.799781 | + | 0.581075i | −0.910850 | − | 0.412738i | \(-0.864573\pi\) |
0.111069 | + | 0.993813i | \(0.464573\pi\) | |||||||
\(662\) | −6.43288 | + | 8.85410i | −0.250021 | + | 0.344124i | ||||
\(663\) | −5.67358 | + | 7.80902i | −0.220344 | + | 0.303277i | ||||
\(664\) | −8.56231 | + | 6.22088i | −0.332282 | + | 0.241417i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.54508 | − | 4.75528i | −0.253617 | − | 0.184263i | ||||
\(667\) | −18.6376 | + | 6.05573i | −0.721651 | + | 0.234479i | ||||
\(668\) | 23.4164i | 0.906008i | ||||||||
\(669\) | 4.38197 | + | 13.4863i | 0.169417 | + | 0.521411i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.618034 | + | 1.90211i | −0.0238589 | + | 0.0734303i | ||||
\(672\) | −21.2663 | − | 6.90983i | −0.820364 | − | 0.266552i | ||||
\(673\) | −17.5150 | − | 24.1074i | −0.675155 | − | 0.929272i | 0.324708 | − | 0.945814i | \(-0.394734\pi\) |
−0.999863 | + | 0.0165428i | \(0.994734\pi\) | |||||||
\(674\) | 14.9443 | 0.575632 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.56231 | 0.0600887 | ||||||||
\(677\) | 21.9928 | + | 30.2705i | 0.845252 | + | 1.16339i | 0.984889 | + | 0.173187i | \(0.0554066\pi\) |
−0.139636 | + | 0.990203i | \(0.544593\pi\) | |||||||
\(678\) | 2.54290 | + | 0.826238i | 0.0976594 | + | 0.0317315i | ||||
\(679\) | −12.2361 | + | 37.6587i | −0.469577 | + | 1.44521i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.18034 | − | 19.0211i | −0.236831 | − | 0.728891i | ||||
\(682\) | − | 23.4164i | − | 0.896661i | ||||||
\(683\) | −7.05342 | + | 2.29180i | −0.269892 | + | 0.0876931i | −0.440836 | − | 0.897588i | \(-0.645318\pi\) |
0.170945 | + | 0.985281i | \(0.445318\pi\) | |||||||
\(684\) | 2.61803 | + | 1.90211i | 0.100103 | + | 0.0727291i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.7082 | + | 15.7719i | −0.828823 | + | 0.602175i | ||||
\(687\) | 14.6821 | − | 20.2082i | 0.560158 | − | 0.770991i | ||||
\(688\) | 3.35520 | − | 4.61803i | 0.127916 | − | 0.176061i | ||||
\(689\) | 3.78115 | − | 2.74717i | 0.144050 | − | 0.104659i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.1803 | + | 12.4822i | 0.653571 | + | 0.474847i | 0.864486 | − | 0.502657i | \(-0.167644\pi\) |
−0.210915 | + | 0.977504i | \(0.567644\pi\) | |||||||
\(692\) | −9.42481 | + | 3.06231i | −0.358277 | + | 0.116411i | ||||
\(693\) | 14.4721i | 0.549751i | ||||||||
\(694\) | 10.4164 | + | 32.0584i | 0.395401 | + | 1.21692i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.06231 | + | 12.5025i | −0.153981 | + | 0.473906i | ||||
\(697\) | −3.75123 | − | 1.21885i | −0.142088 | − | 0.0461671i | ||||
\(698\) | −14.7149 | − | 20.2533i | −0.556966 | − | 0.766598i | ||||
\(699\) | −14.6180 | −0.552905 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.437694 | 0.0165315 | 0.00826574 | − | 0.999966i | \(-0.497369\pi\) | ||||
0.00826574 | + | 0.999966i | \(0.497369\pi\) | |||||||
\(702\) | 1.98787 | + | 2.73607i | 0.0750273 | + | 0.103266i | ||||
\(703\) | −24.8990 | − | 8.09017i | −0.939083 | − | 0.305127i | ||||
\(704\) | −7.00000 | + | 21.5438i | −0.263822 | + | 0.811962i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.38197 | − | 28.8747i | −0.353095 | − | 1.08671i | ||||
\(707\) | 74.0689i | 2.78565i | ||||||||
\(708\) | −3.80423 | + | 1.23607i | −0.142972 | + | 0.0464543i | ||||
\(709\) | −5.44427 | − | 3.95550i | −0.204464 | − | 0.148552i | 0.480841 | − | 0.876808i | \(-0.340331\pi\) |
−0.685305 | + | 0.728256i | \(0.740331\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.4333 | − | 18.4894i | 0.503434 | − | 0.692918i | ||||
\(713\) | −19.0211 | + | 26.1803i | −0.712347 | + | 0.980461i | ||||
\(714\) | −10.3262 | + | 7.50245i | −0.386450 | + | 0.280772i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.00000 | + | 3.63271i | 0.186859 | + | 0.135761i | ||||
\(717\) | −6.71040 | + | 2.18034i | −0.250604 | + | 0.0814263i | ||||
\(718\) | − | 10.5836i | − | 0.394976i | ||||||
\(719\) | 11.0902 | + | 34.1320i | 0.413594 | + | 1.27291i | 0.913503 | + | 0.406832i | \(0.133367\pi\) |
−0.499909 | + | 0.866078i | \(0.666633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.70820 | + | 5.25731i | −0.0636168 | + | 0.195792i | ||||
\(722\) | 8.11048 | + | 2.63525i | 0.301841 | + | 0.0980740i | ||||
\(723\) | 0.608030 | + | 0.836881i | 0.0226129 | + | 0.0311239i | ||||
\(724\) | −9.79837 | −0.364154 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.527864 | −0.0195909 | ||||||||
\(727\) | 9.02105 | + | 12.4164i | 0.334572 | + | 0.460499i | 0.942846 | − | 0.333228i | \(-0.108138\pi\) |
−0.608274 | + | 0.793727i | \(0.708138\pi\) | |||||||
\(728\) | −43.1531 | − | 14.0213i | −1.59936 | − | 0.519663i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.03444 | + | 15.4944i | 0.186206 | + | 0.573082i | ||||
\(732\) | − | 0.618034i | − | 0.0228432i | ||||||
\(733\) | −2.45714 | + | 0.798374i | −0.0907566 | + | 0.0294886i | −0.354043 | − | 0.935229i | \(-0.615193\pi\) |
0.263287 | + | 0.964718i | \(0.415193\pi\) | |||||||
\(734\) | −4.85410 | − | 3.52671i | −0.179168 | − | 0.130173i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.0902 | − | 13.1433i | 0.666813 | − | 0.484468i | ||||
\(737\) | −9.95959 | + | 13.7082i | −0.366866 | + | 0.504948i | ||||
\(738\) | −0.812299 | + | 1.11803i | −0.0299011 | + | 0.0411554i | ||||
\(739\) | 14.3262 | − | 10.4086i | 0.526999 | − | 0.382887i | −0.292235 | − | 0.956347i | \(-0.594399\pi\) |
0.819234 | + | 0.573459i | \(0.194399\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.85410 | + | 6.43288i | 0.325264 | + | 0.236318i | ||||
\(742\) | 5.87785 | − | 1.90983i | 0.215783 | − | 0.0701121i | ||||
\(743\) | 0.875388i | 0.0321149i | 0.999871 | + | 0.0160574i | \(0.00511146\pi\) | ||||
−0.999871 | + | 0.0160574i | \(0.994889\pi\) | |||||||
\(744\) | 6.70820 | + | 20.6457i | 0.245935 | + | 0.756909i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.09017 | − | 27.9767i | 0.332815 | − | 1.02430i | ||||
\(747\) | −3.35520 | − | 1.09017i | −0.122760 | − | 0.0398872i | ||||
\(748\) | −5.42882 | − | 7.47214i | −0.198497 | − | 0.273208i | ||||
\(749\) | −73.6656 | −2.69168 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.34752 | 0.195134 | 0.0975670 | − | 0.995229i | \(-0.468894\pi\) | ||||
0.0975670 | + | 0.995229i | \(0.468894\pi\) | |||||||
\(752\) | 3.07768 | + | 4.23607i | 0.112232 | + | 0.154474i | ||||
\(753\) | −25.6255 | − | 8.32624i | −0.933846 | − | 0.303425i | ||||
\(754\) | −4.57953 | + | 14.0943i | −0.166777 | + | 0.513285i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.38197 | − | 4.25325i | −0.0502616 | − | 0.154689i | ||||
\(757\) | − | 27.3820i | − | 0.995214i | −0.867402 | − | 0.497607i | \(-0.834212\pi\) | ||
0.867402 | − | 0.497607i | \(-0.165788\pi\) | |||||||
\(758\) | −22.2703 | + | 7.23607i | −0.808895 | + | 0.262826i | ||||
\(759\) | −11.7082 | − | 8.50651i | −0.424981 | − | 0.308767i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.88197 | − | 5.72658i | 0.285721 | − | 0.207588i | −0.435688 | − | 0.900098i | \(-0.643495\pi\) |
0.721409 | + | 0.692509i | \(0.243495\pi\) | |||||||
\(762\) | −5.70634 | + | 7.85410i | −0.206719 | + | 0.284524i | ||||
\(763\) | −50.1815 | + | 69.0689i | −1.81669 | + | 2.50046i | ||||
\(764\) | 19.9443 | − | 14.4904i | 0.721558 | − | 0.524243i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.8541 | − | 12.2452i | −0.608963 | − | 0.442438i | ||||
\(767\) | −12.8658 | + | 4.18034i | −0.464556 | + | 0.150943i | ||||
\(768\) | − | 17.0000i | − | 0.613435i | ||||||
\(769\) | 1.74265 | + | 5.36331i | 0.0628414 | + | 0.193406i | 0.977548 | − | 0.210712i | \(-0.0675784\pi\) |
−0.914707 | + | 0.404118i | \(0.867578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.95492 | + | 12.1720i | −0.142433 | + | 0.438363i | ||||
\(772\) | 7.29818 | + | 2.37132i | 0.262667 | + | 0.0853458i | ||||
\(773\) | 21.1150 | + | 29.0623i | 0.759454 | + | 1.04530i | 0.997259 | + | 0.0739857i | \(0.0235719\pi\) |
−0.237805 | + | 0.971313i | \(0.576428\pi\) | |||||||
\(774\) | 5.70820 | 0.205177 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26.5623 | −0.953531 | ||||||||
\(777\) | 21.2663 | + | 29.2705i | 0.762923 | + | 1.05007i | ||||
\(778\) | −35.2748 | − | 11.4615i | −1.26466 | − | 0.410914i | ||||
\(779\) | −1.38197 | + | 4.25325i | −0.0495141 | + | 0.152389i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.763932 | − | 2.35114i | −0.0273356 | − | 0.0841304i | ||||
\(782\) | − | 12.7639i | − | 0.456437i | ||||||
\(783\) | −4.16750 | + | 1.35410i | −0.148934 | + | 0.0483917i | ||||
\(784\) | −10.5172 | − | 7.64121i | −0.375615 | − | 0.272900i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.4721 | + | 8.33499i | −0.409198 | + | 0.297299i | ||||
\(787\) | −4.80828 | + | 6.61803i | −0.171397 | + | 0.235907i | −0.886070 | − | 0.463551i | \(-0.846575\pi\) |
0.714674 | + | 0.699458i | \(0.246575\pi\) | |||||||
\(788\) | −3.16344 | + | 4.35410i | −0.112693 | + | 0.155108i | ||||
\(789\) | 9.61803 | − | 6.98791i | 0.342411 | − | 0.248776i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.67376 | − | 7.02840i | −0.343959 | − | 0.249901i | ||||
\(792\) | −9.23305 | + | 3.00000i | −0.328082 | + | 0.106600i | ||||
\(793\) | − | 2.09017i | − | 0.0742241i | ||||||
\(794\) | −3.38197 | − | 10.4086i | −0.120021 | − | 0.369388i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.76393 | − | 17.7396i | 0.204297 | − | 0.628762i | ||||
\(797\) | −36.2384 | − | 11.7746i | −1.28363 | − | 0.417077i | −0.413773 | − | 0.910380i | \(-0.635789\pi\) |
−0.869857 | + | 0.493303i | \(0.835789\pi\) | |||||||
\(798\) | 8.50651 | + | 11.7082i | 0.301127 | + | 0.414466i | ||||
\(799\) | −14.9443 | −0.528690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.61803 | 0.269170 | ||||||||
\(802\) | 19.6619 | + | 27.0623i | 0.694286 | + | 0.955603i | ||||
\(803\) | 9.51057 | + | 3.09017i | 0.335621 | + | 0.109050i | ||||
\(804\) | 1.61803 | − | 4.97980i | 0.0570637 | − | 0.175624i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.56231 | + | 23.2744i | 0.266371 | + | 0.819805i | ||||
\(807\) | 0.145898i | 0.00513585i | ||||||||
\(808\) | −47.2551 | + | 15.3541i | −1.66243 | + | 0.540155i | ||||
\(809\) | −18.7812 | − | 13.6453i | −0.660310 | − | 0.479743i | 0.206457 | − | 0.978456i | \(-0.433806\pi\) |
−0.866768 | + | 0.498712i | \(0.833806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.47214 | + | 5.42882i | −0.262382 | + | 0.190632i | −0.711197 | − | 0.702993i | \(-0.751846\pi\) |
0.448814 | + | 0.893625i | \(0.351846\pi\) | |||||||
\(812\) | 11.5187 | − | 15.8541i | 0.404226 | − | 0.556370i | ||||
\(813\) | 13.0373 | − | 17.9443i | 0.457237 | − | 0.629333i | ||||
\(814\) | 21.1803 | − | 15.3884i | 0.742371 | − | 0.539364i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.30902 | − | 1.67760i | −0.0808318 | − | 0.0587277i | ||||
\(817\) | 17.5680 | − | 5.70820i | 0.614628 | − | 0.199705i | ||||
\(818\) | 25.7984i | 0.902019i | ||||||||
\(819\) | −4.67376 | − | 14.3844i | −0.163314 | − | 0.502630i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.56231 | − | 4.80828i | 0.0545249 | − | 0.167810i | −0.920086 | − | 0.391717i | \(-0.871881\pi\) |
0.974611 | + | 0.223907i | \(0.0718812\pi\) | |||||||
\(822\) | 5.11855 | + | 1.66312i | 0.178530 | + | 0.0580079i | ||||
\(823\) | 8.67802 | + | 11.9443i | 0.302497 | + | 0.416351i | 0.933023 | − | 0.359817i | \(-0.117161\pi\) |
−0.630526 | + | 0.776168i | \(0.717161\pi\) | |||||||
\(824\) | −3.70820 | −0.129181 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.8885 | −0.622422 | ||||||||
\(827\) | 12.9718 | + | 17.8541i | 0.451072 | + | 0.620848i | 0.972628 | − | 0.232370i | \(-0.0746479\pi\) |
−0.521555 | + | 0.853218i | \(0.674648\pi\) | |||||||
\(828\) | 4.25325 | + | 1.38197i | 0.147811 | + | 0.0480266i | ||||
\(829\) | 8.19098 | − | 25.2093i | 0.284485 | − | 0.875554i | −0.702068 | − | 0.712110i | \(-0.747740\pi\) |
0.986553 | − | 0.163444i | \(-0.0522602\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.79180 | − | 5.51458i | −0.0621567 | − | 0.191299i | ||||
\(832\) | − | 23.6738i | − | 0.820740i | ||||||
\(833\) | 35.2874 | − | 11.4656i | 1.22263 | − | 0.397258i | ||||
\(834\) | −4.09017 | − | 2.97168i | −0.141631 | − | 0.102901i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.47214 | + | 6.15537i | −0.293015 | + | 0.212888i | ||||
\(837\) | −4.25325 | + | 5.85410i | −0.147014 | + | 0.202347i | ||||
\(838\) | 19.3642 | − | 26.6525i | 0.668924 | − | 0.920695i | ||||
\(839\) | −35.6525 | + | 25.9030i | −1.23086 | + | 0.894272i | −0.996954 | − | 0.0779870i | \(-0.975151\pi\) |
−0.233906 | + | 0.972259i | \(0.575151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.92705 | + | 5.75934i | 0.273347 | + | 0.198598i | ||||
\(842\) | 22.0131 | − | 7.15248i | 0.758620 | − | 0.246491i | ||||
\(843\) | − | 17.3820i | − | 0.598667i | ||||||
\(844\) | −5.52786 | − | 17.0130i | −0.190277 | − | 0.585612i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.61803 | + | 4.97980i | −0.0556292 | + | 0.171209i | ||||
\(847\) | 2.24514 | + | 0.729490i | 0.0771439 | + | 0.0250656i | ||||
\(848\) | 0.812299 | + | 1.11803i | 0.0278945 | + | 0.0383934i | ||||
\(849\) | −0.291796 | −0.0100144 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.1803 | −1.24025 | ||||||||
\(852\) | 0.449028 | + | 0.618034i | 0.0153834 | + | 0.0211735i | ||||
\(853\) | 28.3929 | + | 9.22542i | 0.972156 | + | 0.315873i | 0.751686 | − | 0.659521i | \(-0.229241\pi\) |
0.220470 | + | 0.975394i | \(0.429241\pi\) | |||||||
\(854\) | 0.854102 | − | 2.62866i | 0.0292268 | − | 0.0899507i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.2705 | − | 46.9978i | −0.521935 | − | 1.60635i | ||||
\(857\) | 3.52786i | 0.120510i | 0.998183 | + | 0.0602548i | \(0.0191913\pi\) | ||||
−0.998183 | + | 0.0602548i | \(0.980809\pi\) | |||||||
\(858\) | −10.4086 | + | 3.38197i | −0.355344 | + | 0.115458i | ||||
\(859\) | 2.76393 | + | 2.00811i | 0.0943041 | + | 0.0685160i | 0.633938 | − | 0.773384i | \(-0.281437\pi\) |
−0.539634 | + | 0.841900i | \(0.681437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.00000 | − | 3.63271i | 0.170400 | − | 0.123803i | ||||
\(862\) | 6.26137 | − | 8.61803i | 0.213263 | − | 0.293531i | ||||
\(863\) | 30.0503 | − | 41.3607i | 1.02292 | − | 1.40793i | 0.112790 | − | 0.993619i | \(-0.464021\pi\) |
0.910134 | − | 0.414315i | \(-0.135979\pi\) | |||||||
\(864\) | 4.04508 | − | 2.93893i | 0.137617 | − | 0.0999843i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.2082 | − | 14.6821i | −0.686703 | − | 0.498919i | ||||
\(867\) | −8.42075 | + | 2.73607i | −0.285984 | + | 0.0929217i | ||||
\(868\) | − | 32.3607i | − | 1.09839i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.47214 | − | 16.8415i | 0.185416 | − | 0.570653i | ||||
\(872\) | −54.4675 | − | 17.6976i | −1.84450 | − | 0.599315i | ||||
\(873\) | −5.20431 | − | 7.16312i | −0.176139 | − | 0.242435i | ||||
\(874\) | −14.4721 | −0.489527 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.09017 | −0.104407 | ||||||||
\(877\) | 10.7064 | + | 14.7361i | 0.361529 | + | 0.497602i | 0.950574 | − | 0.310499i | \(-0.100496\pi\) |
−0.589045 | + | 0.808100i | \(0.700496\pi\) | |||||||
\(878\) | −5.87785 | − | 1.90983i | −0.198368 | − | 0.0644536i | ||||
\(879\) | −1.17376 | + | 3.61247i | −0.0395900 | + | 0.121846i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.74265 | + | 23.8294i | 0.260856 | + | 0.802833i | 0.992619 | + | 0.121274i | \(0.0386979\pi\) |
−0.731763 | + | 0.681559i | \(0.761302\pi\) | |||||||
\(882\) | − | 13.0000i | − | 0.437733i | ||||||
\(883\) | 0.171513 | − | 0.0557281i | 0.00577189 | − | 0.00187540i | −0.306130 | − | 0.951990i | \(-0.599034\pi\) |
0.311902 | + | 0.950114i | \(0.399034\pi\) | |||||||
\(884\) | 7.80902 | + | 5.67358i | 0.262646 | + | 0.190823i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.8885 | − | 18.0826i | 0.836147 | − | 0.607496i | ||||
\(887\) | −10.0656 | + | 13.8541i | −0.337970 | + | 0.465175i | −0.943847 | − | 0.330383i | \(-0.892822\pi\) |
0.605877 | + | 0.795558i | \(0.292822\pi\) | |||||||
\(888\) | −14.2658 | + | 19.6353i | −0.478731 | + | 0.658916i | ||||
\(889\) | 35.1246 | − | 25.5195i | 1.17804 | − | 0.855897i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.61803 | − | 1.90211i | −0.0877074 | − | 0.0637232i | ||||
\(892\) | 13.4863 | − | 4.38197i | 0.451555 | − | 0.146719i | ||||
\(893\) | 16.9443i | 0.567018i | ||||||||
\(894\) | 3.75329 | + | 11.5514i | 0.125529 | + | 0.386338i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.14590 | + | 12.7598i | −0.138505 | + | 0.426274i | ||||
\(897\) | 14.3844 | + | 4.67376i | 0.480280 | + | 0.156052i | ||||
\(898\) | 4.58377 | + | 6.30902i | 0.152962 | + | 0.210535i | ||||
\(899\) | −31.7082 | −1.05753 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.94427 | −0.131403 | ||||||||
\(902\) | −2.62866 | − | 3.61803i | −0.0875247 | − | 0.120467i | ||||
\(903\) | −24.2784 | − | 7.88854i | −0.807936 | − | 0.262514i | ||||
\(904\) | 2.47871 | − | 7.62870i | 0.0824408 | − | 0.253727i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.09017 | + | 15.6659i | 0.169110 | + | 0.520466i | ||||
\(907\) | 33.1246i | 1.09988i | 0.835203 | + | 0.549942i | \(0.185350\pi\) | ||||
−0.835203 | + | 0.549942i | \(0.814650\pi\) | |||||||
\(908\) | −19.0211 | + | 6.18034i | −0.631238 | + | 0.205102i | ||||
\(909\) | −13.3992 | − | 9.73508i | −0.444423 | − | 0.322892i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.38197 | − | 2.45714i | 0.112050 | − | 0.0814088i | −0.530349 | − | 0.847779i | \(-0.677939\pi\) |
0.642399 | + | 0.766370i | \(0.277939\pi\) | |||||||
\(912\) | −1.90211 | + | 2.61803i | −0.0629853 | + | 0.0866918i | ||||
\(913\) | 6.71040 | − | 9.23607i | 0.222082 | − | 0.305669i | ||||
\(914\) | 18.0902 | − | 13.1433i | 0.598370 | − | 0.434741i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.2082 | − | 14.6821i | −0.667698 | − | 0.485111i | ||||
\(917\) | 60.3126 | − | 19.5967i | 1.99170 | − | 0.647142i | ||||
\(918\) | − | 2.85410i | − | 0.0941994i | ||||||
\(919\) | 15.2016 | + | 46.7858i | 0.501455 | + | 1.54332i | 0.806649 | + | 0.591031i | \(0.201279\pi\) |
−0.305194 | + | 0.952290i | \(0.598721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.416408 | − | 1.28157i | 0.0137211 | − | 0.0422292i | ||||
\(922\) | 7.80021 | + | 2.53444i | 0.256886 | + | 0.0834674i | ||||
\(923\) | 1.51860 | + | 2.09017i | 0.0499852 | + | 0.0687988i | ||||
\(924\) | 14.4721 | 0.476098 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.2361 | 0.763585 | ||||||||
\(927\) | −0.726543 | − | 1.00000i | −0.0238628 | − | 0.0328443i | ||||
\(928\) | 20.8375 | + | 6.77051i | 0.684024 | + | 0.222253i | ||||
\(929\) | −0.645898 | + | 1.98787i | −0.0211912 | + | 0.0652199i | −0.961093 | − | 0.276225i | \(-0.910916\pi\) |
0.939902 | + | 0.341445i | \(0.110916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.0000 | − | 40.0099i | −0.426058 | − | 1.31127i | ||||
\(932\) | 14.6180i | 0.478830i | ||||||||
\(933\) | −4.08174 | + | 1.32624i | −0.133630 | + | 0.0434191i | ||||
\(934\) | 4.70820 | + | 3.42071i | 0.154057 | + | 0.111929i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.20820 | − | 5.96361i | 0.268294 | − | 0.194927i | ||||
\(937\) | −6.86940 | + | 9.45492i | −0.224413 | + | 0.308879i | −0.906346 | − | 0.422537i | \(-0.861140\pi\) |
0.681932 | + | 0.731415i | \(0.261140\pi\) | |||||||
\(938\) | 13.7638 | − | 18.9443i | 0.449405 | − | 0.618552i | ||||
\(939\) | 6.85410 | − | 4.97980i | 0.223675 | − | 0.162510i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.30902 | − | 3.13068i | −0.140470 | − | 0.102057i | 0.515331 | − | 0.856991i | \(-0.327669\pi\) |
−0.655801 | + | 0.754934i | \(0.727669\pi\) | |||||||
\(942\) | −13.1230 | + | 4.26393i | −0.427572 | + | 0.138926i | ||||
\(943\) | 6.18034i | 0.201260i | ||||||||
\(944\) | −1.23607 | − | 3.80423i | −0.0402306 | − | 0.123817i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.70820 | + | 17.5680i | −0.185590 | + | 0.571186i | ||||
\(947\) | −27.9767 | − | 9.09017i | −0.909120 | − | 0.295391i | −0.183124 | − | 0.983090i | \(-0.558621\pi\) |
−0.725996 | + | 0.687699i | \(0.758621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4508 | −0.339249 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.8328 | −0.805259 | ||||||||
\(952\) | 22.5074 | + | 30.9787i | 0.729468 | + | 1.00403i | ||||
\(953\) | 9.59632 | + | 3.11803i | 0.310855 | + | 0.101003i | 0.460290 | − | 0.887769i | \(-0.347745\pi\) |
−0.149435 | + | 0.988772i | \(0.547745\pi\) | |||||||
\(954\) | −0.427051 | + | 1.31433i | −0.0138263 | + | 0.0425529i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.18034 | + | 6.71040i | 0.0705172 | + | 0.217030i | ||||
\(957\) | − | 14.1803i | − | 0.458385i | ||||||
\(958\) | −1.00406 | + | 0.326238i | −0.0324396 | + | 0.0105403i | ||||
\(959\) | −19.4721 | − | 14.1473i | −0.628788 | − | 0.456841i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.2812 | + | 12.5555i | −0.557457 | + | 0.405016i | ||||
\(962\) | −16.0822 | + | 22.1353i | −0.518511 | + | 0.713669i | ||||
\(963\) | 9.68208 | − | 13.3262i | 0.312001 | − | 0.429432i | ||||
\(964\) | 0.836881 | − | 0.608030i | 0.0269541 | − | 0.0195833i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.1803 | + | 11.7557i | 0.520594 | + | 0.378234i | ||||
\(967\) | 33.1280 | − | 10.7639i | 1.06532 | − | 0.346145i | 0.276659 | − | 0.960968i | \(-0.410773\pi\) |
0.788665 | + | 0.614823i | \(0.210773\pi\) | |||||||
\(968\) | 1.58359i | 0.0508986i | ||||||||
\(969\) | −2.85410 | − | 8.78402i | −0.0916870 | − | 0.282183i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.03444 | + | 6.26137i | −0.0652883 | + | 0.200937i | −0.978379 | − | 0.206819i | \(-0.933689\pi\) |
0.913091 | + | 0.407756i | \(0.133689\pi\) | |||||||
\(972\) | 0.951057 | + | 0.309017i | 0.0305052 | + | 0.00991172i | ||||
\(973\) | 13.2898 | + | 18.2918i | 0.426050 | + | 0.586408i | ||||
\(974\) | 3.70820 | 0.118819 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.618034 | 0.0197828 | ||||||||
\(977\) | −26.8869 | − | 37.0066i | −0.860187 | − | 1.18395i | −0.981525 | − | 0.191334i | \(-0.938719\pi\) |
0.121338 | − | 0.992611i | \(-0.461281\pi\) | |||||||
\(978\) | 2.80017 | + | 0.909830i | 0.0895395 | + | 0.0290932i | ||||
\(979\) | −7.61803 | + | 23.4459i | −0.243473 | + | 0.749334i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.89919 | − | 18.1558i | −0.188347 | − | 0.579671i | ||||
\(982\) | 29.8885i | 0.953782i | ||||||||
\(983\) | −20.6457 | + | 6.70820i | −0.658496 | + | 0.213958i | −0.619157 | − | 0.785267i | \(-0.712525\pi\) |
−0.0393397 | + | 0.999226i | \(0.512525\pi\) | |||||||
\(984\) | 3.35410 | + | 2.43690i | 0.106925 | + | 0.0776855i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.1180 | − | 7.35118i | 0.322224 | − | 0.234109i | ||||
\(987\) | 13.7638 | − | 18.9443i | 0.438107 | − | 0.603003i | ||||
\(988\) | 6.43288 | − | 8.85410i | 0.204657 | − | 0.281687i | ||||
\(989\) | 20.6525 | − | 15.0049i | 0.656711 | − | 0.477128i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.52786 | + | 1.83660i | 0.0803002 | + | 0.0583415i | 0.627211 | − | 0.778849i | \(-0.284196\pi\) |
−0.546911 | + | 0.837191i | \(0.684196\pi\) | |||||||
\(992\) | 34.4095 | − | 11.1803i | 1.09250 | − | 0.354976i | ||||
\(993\) | 10.9443i | 0.347306i | ||||||||
\(994\) | 1.05573 | + | 3.24920i | 0.0334857 | + | 0.103058i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.09017 | + | 3.35520i | −0.0345434 | + | 0.106314i | ||||
\(997\) | −8.95554 | − | 2.90983i | −0.283625 | − | 0.0921552i | 0.163750 | − | 0.986502i | \(-0.447641\pi\) |
−0.447375 | + | 0.894347i | \(0.647641\pi\) | |||||||
\(998\) | 3.52671 | + | 4.85410i | 0.111636 | + | 0.153654i | ||||
\(999\) | −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 | 375.2.i.a.199.2 | 8 | ||
5.2 | odd | 4 | 75.2.g.a.61.1 | yes | 4 | ||
5.3 | odd | 4 | 375.2.g.a.301.1 | 4 | |||
5.4 | even | 2 | inner | 375.2.i.a.199.1 | 8 | ||
15.2 | even | 4 | 225.2.h.a.136.1 | 4 | |||
25.3 | odd | 20 | 1875.2.a.a.1.1 | 2 | |||
25.4 | even | 10 | 1875.2.b.b.1249.4 | 4 | |||
25.9 | even | 10 | inner | 375.2.i.a.49.2 | 8 | ||
25.12 | odd | 20 | 75.2.g.a.16.1 | ✓ | 4 | ||
25.13 | odd | 20 | 375.2.g.a.76.1 | 4 | |||
25.16 | even | 5 | inner | 375.2.i.a.49.1 | 8 | ||
25.21 | even | 5 | 1875.2.b.b.1249.1 | 4 | |||
25.22 | odd | 20 | 1875.2.a.d.1.2 | 2 | |||
75.47 | even | 20 | 5625.2.a.a.1.2 | 2 | |||
75.53 | even | 20 | 5625.2.a.h.1.1 | 2 | |||
75.62 | even | 20 | 225.2.h.a.91.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.a.16.1 | ✓ | 4 | 25.12 | odd | 20 | ||
75.2.g.a.61.1 | yes | 4 | 5.2 | odd | 4 | ||
225.2.h.a.91.1 | 4 | 75.62 | even | 20 | |||
225.2.h.a.136.1 | 4 | 15.2 | even | 4 | |||
375.2.g.a.76.1 | 4 | 25.13 | odd | 20 | |||
375.2.g.a.301.1 | 4 | 5.3 | odd | 4 | |||
375.2.i.a.49.1 | 8 | 25.16 | even | 5 | inner | ||
375.2.i.a.49.2 | 8 | 25.9 | even | 10 | inner | ||
375.2.i.a.199.1 | 8 | 5.4 | even | 2 | inner | ||
375.2.i.a.199.2 | 8 | 1.1 | even | 1 | trivial | ||
1875.2.a.a.1.1 | 2 | 25.3 | odd | 20 | |||
1875.2.a.d.1.2 | 2 | 25.22 | odd | 20 | |||
1875.2.b.b.1249.1 | 4 | 25.21 | even | 5 | |||
1875.2.b.b.1249.4 | 4 | 25.4 | even | 10 | |||
5625.2.a.a.1.2 | 2 | 75.47 | even | 20 | |||
5625.2.a.h.1.1 | 2 | 75.53 | even | 20 |