Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.4 | ||
Root | \(0.453990 - 0.891007i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.d.757.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14412 | + | 0.831254i | −0.809017 | + | 0.587785i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | − | 1.90211i | 0.309017 | − | 0.951057i | ||||
\(5\) | 1.60758i | 0.718930i | 0.933158 | + | 0.359465i | \(0.117041\pi\) | ||||
−0.933158 | + | 0.359465i | \(0.882959\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.874032 | + | 2.68999i | 0.309017 | + | 0.951057i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.33630 | − | 1.83927i | −0.422577 | − | 0.581627i | ||||
\(11\) | − | 0.0549306i | − | 0.0165622i | −0.999966 | − | 0.00828109i | \(-0.997364\pi\) | ||
0.999966 | − | 0.00828109i | \(-0.00263598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.75621i | − | 1.04179i | −0.853622 | − | 0.520893i | \(-0.825599\pi\) | ||
0.853622 | − | 0.520893i | \(-0.174401\pi\) | |||||||
\(14\) | 1.14412 | − | 0.831254i | 0.305780 | − | 0.222162i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23607 | − | 2.35114i | −0.809017 | − | 0.587785i | ||||
\(17\) | −3.16228 | −0.766965 | −0.383482 | − | 0.923548i | \(-0.625275\pi\) | ||||
−0.383482 | + | 0.923548i | \(0.625275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.726543i | − | 0.166680i | −0.996521 | − | 0.0833401i | \(-0.973441\pi\) | ||
0.996521 | − | 0.0833401i | \(-0.0265588\pi\) | |||||||
\(20\) | 3.05779 | + | 0.993537i | 0.683743 | + | 0.222162i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0456612 | + | 0.0628473i | 0.00973501 | + | 0.0133991i | ||||
\(23\) | 7.77604 | 1.62142 | 0.810708 | − | 0.585450i | \(-0.199082\pi\) | ||||
0.810708 | + | 0.585450i | \(0.199082\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.41570 | 0.483139 | ||||||||
\(26\) | 3.12237 | + | 4.29757i | 0.612347 | + | 0.842823i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.618034 | + | 1.90211i | −0.116797 | + | 0.359466i | ||||
\(29\) | − | 2.75789i | − | 0.512128i | −0.966660 | − | 0.256064i | \(-0.917574\pi\) | ||
0.966660 | − | 0.256064i | \(-0.0824257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14475 | −0.385208 | −0.192604 | − | 0.981277i | \(-0.561693\pi\) | ||||
−0.192604 | + | 0.981277i | \(0.561693\pi\) | |||||||
\(32\) | 5.65685 | 1.00000 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.61803 | − | 2.62866i | 0.620488 | − | 0.450811i | ||||
\(35\) | − | 1.60758i | − | 0.271730i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.600848i | − | 0.0987788i | −0.998780 | − | 0.0493894i | \(-0.984272\pi\) | ||
0.998780 | − | 0.0493894i | \(-0.0157275\pi\) | |||||||
\(38\) | 0.603941 | + | 0.831254i | 0.0979722 | + | 0.134847i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.32437 | + | 1.40507i | −0.683743 | + | 0.222162i | ||||
\(41\) | 4.53658 | 0.708495 | 0.354248 | − | 0.935152i | \(-0.384737\pi\) | ||||
0.354248 | + | 0.935152i | \(0.384737\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.85004i | − | 1.04462i | −0.852755 | − | 0.522311i | \(-0.825070\pi\) | ||
0.852755 | − | 0.522311i | \(-0.174930\pi\) | |||||||
\(44\) | −0.104484 | − | 0.0339490i | −0.0157516 | − | 0.00511800i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.89675 | + | 6.46386i | −1.31175 | + | 0.953045i | ||||
\(47\) | 0.744883 | 0.108652 | 0.0543261 | − | 0.998523i | \(-0.482699\pi\) | ||||
0.0543261 | + | 0.998523i | \(0.482699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.76385 | + | 2.00806i | −0.390868 | + | 0.283982i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.14475 | − | 2.32147i | −0.990798 | − | 0.321930i | ||||
\(53\) | 10.5822i | 1.45358i | 0.686860 | + | 0.726790i | \(0.258989\pi\) | ||||
−0.686860 | + | 0.726790i | \(0.741011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0883051 | 0.0119071 | ||||||||
\(56\) | −0.874032 | − | 2.68999i | −0.116797 | − | 0.359466i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.29251 | + | 3.15537i | 0.301021 | + | 0.414320i | ||||
\(59\) | − | 2.58013i | − | 0.335905i | −0.985795 | − | 0.167952i | \(-0.946285\pi\) | ||
0.985795 | − | 0.167952i | \(-0.0537155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.80423i | 1.25530i | 0.778495 | + | 0.627651i | \(0.215984\pi\) | ||||
−0.778495 | + | 0.627651i | \(0.784016\pi\) | |||||||
\(62\) | 2.45385 | − | 1.78283i | 0.311640 | − | 0.226419i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.47214 | + | 4.70228i | −0.809017 | + | 0.587785i | ||||
\(65\) | 6.03841 | 0.748972 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.2627i | − | 1.49813i | −0.662496 | − | 0.749065i | \(-0.730503\pi\) | ||
0.662496 | − | 0.749065i | \(-0.269497\pi\) | |||||||
\(68\) | −1.95440 | + | 6.01501i | −0.237005 | + | 0.729427i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.33630 | + | 1.83927i | 0.159719 | + | 0.219834i | ||||
\(71\) | 9.19025 | 1.09068 | 0.545341 | − | 0.838214i | \(-0.316400\pi\) | ||||
0.545341 | + | 0.838214i | \(0.316400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.85224 | 0.450870 | 0.225435 | − | 0.974258i | \(-0.427620\pi\) | ||||
0.225435 | + | 0.974258i | \(0.427620\pi\) | |||||||
\(74\) | 0.499457 | + | 0.687444i | 0.0580607 | + | 0.0799137i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.38197 | − | 0.449028i | −0.158522 | − | 0.0515070i | ||||
\(77\) | 0.0549306i | 0.00625992i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9057 | 1.22698 | 0.613491 | − | 0.789701i | \(-0.289765\pi\) | ||||
0.613491 | + | 0.789701i | \(0.289765\pi\) | |||||||
\(80\) | 3.77964 | − | 5.20223i | 0.422577 | − | 0.581627i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.19041 | + | 3.77105i | −0.573185 | + | 0.416443i | ||||
\(83\) | − | 13.1624i | − | 1.44476i | −0.691499 | − | 0.722378i | \(-0.743049\pi\) | ||
0.691499 | − | 0.722378i | \(-0.256951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.08361i | − | 0.551394i | ||||||
\(86\) | 5.69413 | + | 7.83729i | 0.614013 | + | 0.845117i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.147763 | − | 0.0480111i | 0.0157516 | − | 0.00511800i | ||||
\(89\) | −7.90356 | −0.837776 | −0.418888 | − | 0.908038i | \(-0.637580\pi\) | ||||
−0.418888 | + | 0.908038i | \(0.637580\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.75621i | 0.393758i | ||||||||
\(92\) | 4.80586 | − | 14.7909i | 0.501045 | − | 1.54206i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.852237 | + | 0.619187i | −0.0879015 | + | 0.0638642i | ||||
\(95\) | 1.16797 | 0.119832 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1803 | 1.23673 | 0.618363 | − | 0.785893i | \(-0.287796\pi\) | ||||
0.618363 | + | 0.785893i | \(0.287796\pi\) | |||||||
\(98\) | −1.14412 | + | 0.831254i | −0.115574 | + | 0.0839693i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.49298 | − | 4.59493i | 0.149298 | − | 0.459493i | ||||
\(101\) | 4.35250i | 0.433090i | 0.976273 | + | 0.216545i | \(0.0694788\pi\) | ||||
−0.976273 | + | 0.216545i | \(0.930521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.5574 | 1.72998 | 0.864992 | − | 0.501785i | \(-0.167323\pi\) | ||||
0.864992 | + | 0.501785i | \(0.167323\pi\) | |||||||
\(104\) | 10.1042 | − | 3.28305i | 0.990798 | − | 0.321930i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.79651 | − | 12.1074i | −0.854392 | − | 1.17597i | ||||
\(107\) | 6.44944i | 0.623491i | 0.950166 | + | 0.311745i | \(0.100914\pi\) | ||||
−0.950166 | + | 0.311745i | \(0.899086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.03559i | − | 0.194975i | −0.995237 | − | 0.0974873i | \(-0.968919\pi\) | ||
0.995237 | − | 0.0974873i | \(-0.0310805\pi\) | |||||||
\(110\) | −0.101032 | + | 0.0734040i | −0.00963301 | + | 0.00699879i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.23607 | + | 2.35114i | 0.305780 | + | 0.222162i | ||||
\(113\) | 2.61946 | 0.246418 | 0.123209 | − | 0.992381i | \(-0.460681\pi\) | ||||
0.123209 | + | 0.992381i | \(0.460681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.5006i | 1.16569i | ||||||||
\(116\) | −5.24582 | − | 1.70447i | −0.487062 | − | 0.158256i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.14475 | + | 2.95199i | 0.197440 | + | 0.271753i | ||||
\(119\) | 3.16228 | 0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9970 | 0.999726 | ||||||||
\(122\) | −8.14980 | − | 11.2172i | −0.737848 | − | 1.01556i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.32553 | + | 4.07955i | −0.119036 | + | 0.366354i | ||||
\(125\) | 11.9213i | 1.06627i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6733 | −1.21331 | −0.606656 | − | 0.794965i | \(-0.707489\pi\) | ||||
−0.606656 | + | 0.794965i | \(0.707489\pi\) | |||||||
\(128\) | 3.49613 | − | 10.7600i | 0.309017 | − | 0.951057i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.90868 | + | 5.01945i | −0.605931 | + | 0.440235i | ||||
\(131\) | − | 11.2592i | − | 0.983721i | −0.870674 | − | 0.491861i | \(-0.836317\pi\) | ||
0.870674 | − | 0.491861i | \(-0.163683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.726543i | 0.0629992i | ||||||||
\(134\) | 10.1934 | + | 14.0301i | 0.880579 | + | 1.21201i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.76393 | − | 8.50651i | −0.237005 | − | 0.729427i | ||||
\(137\) | 1.00318 | 0.0857076 | 0.0428538 | − | 0.999081i | \(-0.486355\pi\) | ||||
0.0428538 | + | 0.999081i | \(0.486355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.60253i | − | 0.220744i | −0.993890 | − | 0.110372i | \(-0.964796\pi\) | ||
0.993890 | − | 0.110372i | \(-0.0352042\pi\) | |||||||
\(140\) | −3.05779 | − | 0.993537i | −0.258431 | − | 0.0839692i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.5148 | + | 7.63943i | −0.882381 | + | 0.641087i | ||||
\(143\) | −0.206331 | −0.0172543 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.43352 | 0.368184 | ||||||||
\(146\) | −4.40743 | + | 3.20219i | −0.364762 | + | 0.265015i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.14288 | − | 0.371344i | −0.0939442 | − | 0.0305243i | ||||
\(149\) | 19.1514i | 1.56895i | 0.620163 | + | 0.784473i | \(0.287066\pi\) | ||||
−0.620163 | + | 0.784473i | \(0.712934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8848 | 1.29269 | 0.646344 | − | 0.763046i | \(-0.276297\pi\) | ||||
0.646344 | + | 0.763046i | \(0.276297\pi\) | |||||||
\(152\) | 1.95440 | − | 0.635021i | 0.158522 | − | 0.0515070i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0456612 | − | 0.0628473i | −0.00367949 | − | 0.00506438i | ||||
\(155\) | − | 3.44784i | − | 0.276937i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.7099i | − | 1.17398i | −0.809595 | − | 0.586988i | \(-0.800313\pi\) | ||
0.809595 | − | 0.586988i | \(-0.199687\pi\) | |||||||
\(158\) | −12.4774 | + | 9.06537i | −0.992650 | + | 0.721202i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.09383i | 0.718930i | ||||||||
\(161\) | −7.77604 | −0.612838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.69687i | 0.759517i | 0.925086 | + | 0.379759i | \(0.123993\pi\) | ||||
−0.925086 | + | 0.379759i | \(0.876007\pi\) | |||||||
\(164\) | 2.80376 | − | 8.62909i | 0.218937 | − | 0.673819i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.9413 | + | 15.0593i | 0.849206 | + | 1.16883i | ||||
\(167\) | 2.57013 | 0.198882 | 0.0994412 | − | 0.995043i | \(-0.468294\pi\) | ||||
0.0994412 | + | 0.995043i | \(0.468294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.10915 | −0.0853193 | ||||||||
\(170\) | 4.22577 | + | 5.81627i | 0.324102 | + | 0.446087i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.0296 | − | 4.23356i | −0.993495 | − | 0.322806i | ||||
\(173\) | − | 1.69460i | − | 0.128838i | −0.997923 | − | 0.0644192i | \(-0.979481\pi\) | ||
0.997923 | − | 0.0644192i | \(-0.0205195\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.41570 | −0.182609 | ||||||||
\(176\) | −0.129149 | + | 0.177759i | −0.00973501 | + | 0.0133991i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.04264 | − | 6.56987i | 0.677775 | − | 0.492432i | ||||
\(179\) | 11.1383i | 0.832518i | 0.909246 | + | 0.416259i | \(0.136659\pi\) | ||||
−0.909246 | + | 0.416259i | \(0.863341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.80203i | 0.505591i | 0.967520 | + | 0.252796i | \(0.0813500\pi\) | ||||
−0.967520 | + | 0.252796i | \(0.918650\pi\) | |||||||
\(182\) | −3.12237 | − | 4.29757i | −0.231445 | − | 0.318557i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.79651 | + | 20.9175i | 0.501045 | + | 1.54206i | ||||
\(185\) | 0.965909 | 0.0710151 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.173706i | 0.0127026i | ||||||||
\(188\) | 0.460363 | − | 1.41685i | 0.0335754 | − | 0.103334i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.33630 | + | 0.970882i | −0.0969457 | + | 0.0704352i | ||||
\(191\) | 15.6397 | 1.13165 | 0.565824 | − | 0.824526i | \(-0.308558\pi\) | ||||
0.565824 | + | 0.824526i | \(0.308558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5893 | 1.41007 | 0.705034 | − | 0.709174i | \(-0.250932\pi\) | ||||
0.705034 | + | 0.709174i | \(0.250932\pi\) | |||||||
\(194\) | −13.9358 | + | 10.1250i | −1.00053 | + | 0.726929i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | − | 1.90211i | 0.0441453 | − | 0.135865i | ||||
\(197\) | − | 7.29916i | − | 0.520044i | −0.965603 | − | 0.260022i | \(-0.916270\pi\) | ||
0.965603 | − | 0.260022i | \(-0.0837298\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8002 | 0.978273 | 0.489136 | − | 0.872207i | \(-0.337312\pi\) | ||||
0.489136 | + | 0.872207i | \(0.337312\pi\) | |||||||
\(200\) | 2.11140 | + | 6.49821i | 0.149298 | + | 0.459493i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.61803 | − | 4.97980i | −0.254564 | − | 0.350377i | ||||
\(203\) | 2.75789i | 0.193566i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.29291i | 0.509359i | ||||||||
\(206\) | −20.0878 | + | 14.5947i | −1.39959 | + | 1.01686i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.83139 | + | 12.1554i | −0.612347 | + | 0.842823i | ||||
\(209\) | −0.0399094 | −0.00276059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.25731i | − | 0.361928i | −0.983490 | − | 0.180964i | \(-0.942078\pi\) | ||
0.983490 | − | 0.180964i | \(-0.0579218\pi\) | |||||||
\(212\) | 20.1286 | + | 6.54017i | 1.38244 | + | 0.449181i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.36112 | − | 7.37895i | −0.366479 | − | 0.504415i | ||||
\(215\) | 11.0120 | 0.751011 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.14475 | 0.145595 | ||||||||
\(218\) | 1.69210 | + | 2.32897i | 0.114603 | + | 0.157738i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0545756 | − | 0.167966i | 0.00367948 | − | 0.0113243i | ||||
\(221\) | 11.8782i | 0.799014i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.96512 | 0.332489 | 0.166244 | − | 0.986085i | \(-0.446836\pi\) | ||||
0.166244 | + | 0.986085i | \(0.446836\pi\) | |||||||
\(224\) | −5.65685 | −0.377964 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.99698 | + | 2.17744i | −0.199356 | + | 0.144841i | ||||
\(227\) | − | 15.1773i | − | 1.00735i | −0.863893 | − | 0.503676i | \(-0.831981\pi\) | ||
0.863893 | − | 0.503676i | \(-0.168019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.69636i | − | 0.376426i | −0.982128 | − | 0.188213i | \(-0.939730\pi\) | ||
0.982128 | − | 0.188213i | \(-0.0602695\pi\) | |||||||
\(230\) | −10.3912 | − | 14.3022i | −0.685173 | − | 0.943060i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.41871 | − | 2.41049i | 0.487062 | − | 0.158256i | ||||
\(233\) | −16.5086 | −1.08151 | −0.540756 | − | 0.841179i | \(-0.681862\pi\) | ||||
−0.540756 | + | 0.841179i | \(0.681862\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.19746i | 0.0781134i | ||||||||
\(236\) | −4.90770 | − | 1.59461i | −0.319464 | − | 0.103800i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.61803 | + | 2.62866i | −0.234522 | + | 0.170390i | ||||
\(239\) | −15.1437 | −0.979564 | −0.489782 | − | 0.871845i | \(-0.662924\pi\) | ||||
−0.489782 | + | 0.871845i | \(0.662924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.5047 | −1.83615 | −0.918075 | − | 0.396407i | \(-0.870257\pi\) | ||||
−0.918075 | + | 0.396407i | \(0.870257\pi\) | |||||||
\(242\) | −12.5819 | + | 9.14128i | −0.808795 | + | 0.587624i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.6487 | + | 6.05934i | 1.19386 | + | 0.387910i | ||||
\(245\) | 1.60758i | 0.102704i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.72905 | −0.173645 | ||||||||
\(248\) | −1.87458 | − | 5.76935i | −0.119036 | − | 0.366354i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.90963 | − | 13.6394i | −0.626740 | − | 0.862634i | ||||
\(251\) | − | 7.18930i | − | 0.453785i | −0.973920 | − | 0.226892i | \(-0.927143\pi\) | ||
0.973920 | − | 0.226892i | \(-0.0728566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.427142i | − | 0.0268542i | ||||||
\(254\) | 15.6440 | − | 11.3660i | 0.981589 | − | 0.713166i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | + | 15.2169i | 0.309017 | + | 0.951057i | ||||
\(257\) | −30.4469 | −1.89922 | −0.949612 | − | 0.313427i | \(-0.898523\pi\) | ||||
−0.949612 | + | 0.313427i | \(0.898523\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.600848i | 0.0373349i | ||||||||
\(260\) | 3.73194 | − | 11.4857i | 0.231445 | − | 0.712315i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.35926 | + | 12.8819i | 0.578217 | + | 0.795847i | ||||
\(263\) | −8.28410 | −0.510820 | −0.255410 | − | 0.966833i | \(-0.582210\pi\) | ||||
−0.255410 | + | 0.966833i | \(0.582210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.0117 | −1.04502 | ||||||||
\(266\) | −0.603941 | − | 0.831254i | −0.0370300 | − | 0.0509674i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.3251 | − | 7.57878i | −1.42481 | − | 0.462948i | ||||
\(269\) | − | 7.16222i | − | 0.436689i | −0.975872 | − | 0.218344i | \(-0.929934\pi\) | ||
0.975872 | − | 0.218344i | \(-0.0700656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4721 | 0.757628 | 0.378814 | − | 0.925473i | \(-0.376332\pi\) | ||||
0.378814 | + | 0.925473i | \(0.376332\pi\) | |||||||
\(272\) | 10.2333 | + | 7.43496i | 0.620488 | + | 0.450811i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.14776 | + | 0.833899i | −0.0693389 | + | 0.0503777i | ||||
\(275\) | − | 0.132696i | − | 0.00800184i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.91531i | − | 0.535669i | −0.963465 | − | 0.267835i | \(-0.913692\pi\) | ||
0.963465 | − | 0.267835i | \(-0.0863081\pi\) | |||||||
\(278\) | 2.16336 | + | 2.97761i | 0.129750 | + | 0.178585i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.32437 | − | 1.40507i | 0.258431 | − | 0.0839692i | ||||
\(281\) | −12.3577 | −0.737198 | −0.368599 | − | 0.929589i | \(-0.620162\pi\) | ||||
−0.368599 | + | 0.929589i | \(0.620162\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 21.4245i | − | 1.27356i | −0.771047 | − | 0.636778i | \(-0.780267\pi\) | ||
0.771047 | − | 0.636778i | \(-0.219733\pi\) | |||||||
\(284\) | 5.67989 | − | 17.4809i | 0.337039 | − | 1.03730i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.236068 | − | 0.171513i | 0.0139590 | − | 0.0101418i | ||||
\(287\) | −4.53658 | −0.267786 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | −5.07250 | + | 3.68538i | −0.297867 | + | 0.216413i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.38081 | − | 7.32739i | 0.139327 | − | 0.428803i | ||||
\(293\) | 0.0647976i | 0.00378552i | 0.999998 | + | 0.00189276i | \(0.000602484\pi\) | ||||
−0.999998 | + | 0.00189276i | \(0.999398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.14776 | 0.241492 | ||||||||
\(296\) | 1.61628 | − | 0.525160i | 0.0939442 | − | 0.0305243i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.9197 | − | 21.9116i | −0.922203 | − | 1.26930i | ||||
\(299\) | − | 29.2085i | − | 1.68917i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.85004i | 0.394830i | ||||||||
\(302\) | −18.1742 | + | 13.2043i | −1.04581 | + | 0.759823i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.70820 | + | 2.35114i | −0.0979722 | + | 0.134847i | ||||
\(305\) | −15.7611 | −0.902475 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8474i | 0.904460i | 0.891901 | + | 0.452230i | \(0.149371\pi\) | ||||
−0.891901 | + | 0.452230i | \(0.850629\pi\) | |||||||
\(308\) | 0.104484 | + | 0.0339490i | 0.00595354 | + | 0.00193442i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.86603 | + | 3.94476i | 0.162780 | + | 0.224047i | ||||
\(311\) | −13.0254 | −0.738602 | −0.369301 | − | 0.929310i | \(-0.620403\pi\) | ||||
−0.369301 | + | 0.929310i | \(0.620403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0265 | 1.35806 | 0.679030 | − | 0.734110i | \(-0.262401\pi\) | ||||
0.679030 | + | 0.734110i | \(0.262401\pi\) | |||||||
\(314\) | 12.2276 | + | 16.8299i | 0.690046 | + | 0.949767i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.74007 | − | 20.7438i | 0.379158 | − | 1.16693i | ||||
\(317\) | 3.71438i | 0.208620i | 0.994545 | + | 0.104310i | \(0.0332635\pi\) | ||||
−0.994545 | + | 0.104310i | \(0.966737\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.151493 | −0.00848195 | ||||||||
\(320\) | −7.55928 | − | 10.4045i | −0.422577 | − | 0.581627i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.89675 | − | 6.46386i | 0.495796 | − | 0.360217i | ||||
\(323\) | 2.29753i | 0.127838i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 9.07387i | − | 0.503328i | ||||||
\(326\) | −8.06056 | − | 11.0944i | −0.446433 | − | 0.614463i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.96512 | + | 12.2034i | 0.218937 | + | 0.673819i | ||||
\(329\) | −0.744883 | −0.0410667 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50059i | 0.192410i | 0.995362 | + | 0.0962048i | \(0.0306704\pi\) | ||||
−0.995362 | + | 0.0962048i | \(0.969330\pi\) | |||||||
\(332\) | −25.0363 | − | 8.13478i | −1.37404 | − | 0.446454i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.94054 | + | 2.13643i | −0.160899 | + | 0.116900i | ||||
\(335\) | 19.7133 | 1.07705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.9917 | −0.925595 | −0.462797 | − | 0.886464i | \(-0.653154\pi\) | ||||
−0.462797 | + | 0.886464i | \(0.653154\pi\) | |||||||
\(338\) | 1.26901 | − | 0.921986i | 0.0690248 | − | 0.0501494i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.66959 | − | 3.14184i | −0.524407 | − | 0.170390i | ||||
\(341\) | 0.117812i | 0.00637988i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 18.4266 | − | 5.98716i | 0.993495 | − | 0.322806i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.40865 | + | 1.93883i | 0.0757293 | + | 0.104232i | ||||
\(347\) | − | 36.6651i | − | 1.96829i | −0.177373 | − | 0.984144i | \(-0.556760\pi\) | ||
0.177373 | − | 0.984144i | \(-0.443240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.7887i | 1.86220i | 0.364770 | + | 0.931098i | \(0.381148\pi\) | ||||
−0.364770 | + | 0.931098i | \(0.618852\pi\) | |||||||
\(350\) | 2.76385 | − | 2.00806i | 0.147734 | − | 0.107335i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 0.310734i | − | 0.0165622i | ||||||
\(353\) | −12.1913 | −0.648876 | −0.324438 | − | 0.945907i | \(-0.605175\pi\) | ||||
−0.324438 | + | 0.945907i | \(0.605175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7740i | 0.784125i | ||||||||
\(356\) | −4.88467 | + | 15.0335i | −0.258887 | + | 0.796772i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.25878 | − | 12.7436i | −0.489342 | − | 0.673521i | ||||
\(359\) | 33.4411 | 1.76495 | 0.882477 | − | 0.470355i | \(-0.155874\pi\) | ||||
0.882477 | + | 0.470355i | \(0.155874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4721 | 0.972218 | ||||||||
\(362\) | −5.65422 | − | 7.78236i | −0.297179 | − | 0.409032i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.14475 | + | 2.32147i | 0.374486 | + | 0.121678i | ||||
\(365\) | 6.19277i | 0.324144i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.4869 | −0.756212 | −0.378106 | − | 0.925762i | \(-0.623425\pi\) | ||||
−0.378106 | + | 0.925762i | \(0.623425\pi\) | |||||||
\(368\) | −25.1638 | − | 18.2826i | −1.31175 | − | 0.953045i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.10512 | + | 0.802916i | −0.0574524 | + | 0.0417416i | ||||
\(371\) | − | 10.5822i | − | 0.549401i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 28.7612i | − | 1.48920i | −0.667512 | − | 0.744599i | \(-0.732641\pi\) | ||
0.667512 | − | 0.744599i | \(-0.267359\pi\) | |||||||
\(374\) | −0.144394 | − | 0.198741i | −0.00746641 | − | 0.0102766i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.651051 | + | 2.00373i | 0.0335754 | + | 0.103334i | ||||
\(377\) | −10.3592 | −0.533528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.1036i | − | 0.827188i | −0.910461 | − | 0.413594i | \(-0.864273\pi\) | ||
0.910461 | − | 0.413594i | \(-0.135727\pi\) | |||||||
\(380\) | 0.721847 | − | 2.22162i | 0.0370300 | − | 0.113967i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.8937 | + | 13.0006i | −0.915523 | + | 0.665166i | ||||
\(383\) | −25.7602 | −1.31629 | −0.658143 | − | 0.752893i | \(-0.728658\pi\) | ||||
−0.658143 | + | 0.752893i | \(0.728658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0883051 | −0.00450045 | ||||||||
\(386\) | −22.4126 | + | 16.2837i | −1.14077 | + | 0.828817i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.52786 | − | 23.1684i | 0.382169 | − | 1.17620i | ||||
\(389\) | − | 9.82322i | − | 0.498057i | −0.968496 | − | 0.249029i | \(-0.919889\pi\) | ||
0.968496 | − | 0.249029i | \(-0.0801113\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.5900 | −1.24357 | ||||||||
\(392\) | 0.874032 | + | 2.68999i | 0.0441453 | + | 0.135865i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.06746 | + | 8.35114i | 0.305674 | + | 0.420724i | ||||
\(395\) | 17.5317i | 0.882115i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 24.1824i | − | 1.21368i | −0.794824 | − | 0.606840i | \(-0.792437\pi\) | ||
0.794824 | − | 0.606840i | \(-0.207563\pi\) | |||||||
\(398\) | −15.7892 | + | 11.4715i | −0.791439 | + | 0.575014i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.81736 | − | 5.67964i | −0.390868 | − | 0.283982i | ||||
\(401\) | 23.4216 | 1.16962 | 0.584810 | − | 0.811170i | \(-0.301169\pi\) | ||||
0.584810 | + | 0.811170i | \(0.301169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.05613i | 0.401304i | ||||||||
\(404\) | 8.27895 | + | 2.68999i | 0.411893 | + | 0.133832i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.29251 | − | 3.15537i | −0.113775 | − | 0.156598i | ||||
\(407\) | −0.0330049 | −0.00163599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.6813 | −1.61599 | −0.807994 | − | 0.589191i | \(-0.799447\pi\) | ||||
−0.807994 | + | 0.589191i | \(0.799447\pi\) | |||||||
\(410\) | −6.06226 | − | 8.34398i | −0.299393 | − | 0.412080i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.8511 | − | 33.3962i | 0.534595 | − | 1.64531i | ||||
\(413\) | 2.58013i | 0.126960i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.1595 | 1.03868 | ||||||||
\(416\) | − | 21.2484i | − | 1.04179i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0456612 | − | 0.0331748i | 0.00223336 | − | 0.00162263i | ||||
\(419\) | − | 29.3981i | − | 1.43619i | −0.695945 | − | 0.718095i | \(-0.745014\pi\) | ||
0.695945 | − | 0.718095i | \(-0.254986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.59493i | 0.0777319i | 0.999244 | + | 0.0388660i | \(0.0123745\pi\) | ||||
−0.999244 | + | 0.0388660i | \(0.987625\pi\) | |||||||
\(422\) | 4.37016 | + | 6.01501i | 0.212736 | + | 0.292806i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −28.4661 | + | 9.24920i | −1.38244 | + | 0.449181i | ||||
\(425\) | −7.63910 | −0.370551 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.80423i | − | 0.474460i | ||||||
\(428\) | 12.2676 | + | 3.98597i | 0.592975 | + | 0.192669i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.5991 | + | 9.15375i | −0.607580 | + | 0.441433i | ||||
\(431\) | −10.7336 | −0.517020 | −0.258510 | − | 0.966009i | \(-0.583232\pi\) | ||||
−0.258510 | + | 0.966009i | \(0.583232\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.43352 | −0.405289 | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202645 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(434\) | −2.45385 | + | 1.78283i | −0.117789 | + | 0.0855785i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.87193 | − | 1.25807i | −0.185432 | − | 0.0602505i | ||||
\(437\) | − | 5.64962i | − | 0.270258i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.3452 | −0.827842 | −0.413921 | − | 0.910313i | \(-0.635841\pi\) | ||||
−0.413921 | + | 0.910313i | \(0.635841\pi\) | |||||||
\(440\) | 0.0771815 | + | 0.237540i | 0.00367948 | + | 0.0113243i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.87380 | − | 13.5901i | −0.469649 | − | 0.646416i | ||||
\(443\) | − | 29.8824i | − | 1.41976i | −0.704325 | − | 0.709878i | \(-0.748750\pi\) | ||
0.704325 | − | 0.709878i | \(-0.251250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.7056i | − | 0.602302i | ||||||
\(446\) | −5.68070 | + | 4.12727i | −0.268989 | + | 0.195432i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.47214 | − | 4.70228i | 0.305780 | − | 0.222162i | ||||
\(449\) | 18.6303 | 0.879217 | 0.439608 | − | 0.898190i | \(-0.355117\pi\) | ||||
0.439608 | + | 0.898190i | \(0.355117\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.249197i | − | 0.0117342i | ||||||
\(452\) | 1.61891 | − | 4.98251i | 0.0761473 | − | 0.234357i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.6162 | + | 17.3647i | 0.592106 | + | 0.814964i | ||||
\(455\) | −6.03841 | −0.283085 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.63702 | −0.310466 | −0.155233 | − | 0.987878i | \(-0.549613\pi\) | ||||
−0.155233 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(458\) | 4.73512 | + | 6.51734i | 0.221258 | + | 0.304535i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.7775 | + | 7.72579i | 1.10863 | + | 0.360217i | ||||
\(461\) | 42.1500i | 1.96312i | 0.191155 | + | 0.981560i | \(0.438777\pi\) | ||||
−0.191155 | + | 0.981560i | \(0.561223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.1209 | −1.26041 | −0.630207 | − | 0.776427i | \(-0.717030\pi\) | ||||
−0.630207 | + | 0.776427i | \(0.717030\pi\) | |||||||
\(464\) | −6.48419 | + | 8.92473i | −0.301021 | + | 0.414320i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.8878 | − | 13.7228i | 0.874962 | − | 0.635697i | ||||
\(467\) | − | 1.06443i | − | 0.0492561i | −0.999697 | − | 0.0246280i | \(-0.992160\pi\) | ||
0.999697 | − | 0.0246280i | \(-0.00784014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.2627i | 0.566240i | ||||||||
\(470\) | −0.995390 | − | 1.37004i | −0.0459139 | − | 0.0631951i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.94054 | − | 2.25512i | 0.319464 | − | 0.103800i | ||||
\(473\) | −0.376277 | −0.0173012 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.75511i | − | 0.0805298i | ||||||
\(476\) | 1.95440 | − | 6.01501i | 0.0895796 | − | 0.275698i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.3262 | − | 12.5882i | 0.792484 | − | 0.575773i | ||||
\(479\) | −32.7777 | −1.49765 | −0.748825 | − | 0.662767i | \(-0.769382\pi\) | ||||
−0.748825 | + | 0.662767i | \(0.769382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.25691 | −0.102906 | ||||||||
\(482\) | 32.6129 | − | 23.6947i | 1.48548 | − | 1.07926i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.79651 | − | 20.9175i | 0.308932 | − | 0.950796i | ||||
\(485\) | 19.5808i | 0.889120i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.44329 | −0.110716 | −0.0553580 | − | 0.998467i | \(-0.517630\pi\) | ||||
−0.0553580 | + | 0.998467i | \(0.517630\pi\) | |||||||
\(488\) | −26.3733 | + | 8.56921i | −1.19386 | + | 0.387910i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.33630 | − | 1.83927i | −0.0603681 | − | 0.0830896i | ||||
\(491\) | 25.5978i | 1.15521i | 0.816315 | + | 0.577606i | \(0.196013\pi\) | ||||
−0.816315 | + | 0.577606i | \(0.803987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.72122i | 0.392784i | ||||||||
\(494\) | 3.12237 | − | 2.26853i | 0.140482 | − | 0.102066i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.94054 | + | 5.04260i | 0.311640 | + | 0.226419i | ||||
\(497\) | −9.19025 | −0.412239 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7.96720i | − | 0.356661i | −0.983971 | − | 0.178330i | \(-0.942930\pi\) | ||
0.983971 | − | 0.178330i | \(-0.0570696\pi\) | |||||||
\(500\) | 22.6757 | + | 7.36777i | 1.01409 | + | 0.329497i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.97614 | + | 8.22545i | 0.266728 | + | 0.367120i | ||||
\(503\) | 31.3158 | 1.39630 | 0.698151 | − | 0.715951i | \(-0.254007\pi\) | ||||
0.698151 | + | 0.715951i | \(0.254007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.99698 | −0.311362 | ||||||||
\(506\) | 0.355064 | + | 0.488703i | 0.0157845 | + | 0.0217255i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.45058 | + | 26.0082i | −0.374934 | + | 1.15393i | ||||
\(509\) | 40.7362i | 1.80560i | 0.430061 | + | 0.902800i | \(0.358492\pi\) | ||||
−0.430061 | + | 0.902800i | \(0.641508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.85224 | −0.170413 | ||||||||
\(512\) | −18.3060 | − | 13.3001i | −0.809017 | − | 0.587785i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34.8350 | − | 25.3091i | 1.53651 | − | 1.11634i | ||||
\(515\) | 28.2249i | 1.24374i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.0409168i | − | 0.00179952i | ||||||
\(518\) | −0.499457 | − | 0.687444i | −0.0219449 | − | 0.0302045i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.27776 | + | 16.2433i | 0.231445 | + | 0.712315i | ||||
\(521\) | −43.3880 | −1.90086 | −0.950432 | − | 0.310931i | \(-0.899359\pi\) | ||||
−0.950432 | + | 0.310931i | \(0.899359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 17.9726i | − | 0.785887i | −0.919563 | − | 0.392944i | \(-0.871457\pi\) | ||
0.919563 | − | 0.392944i | \(-0.128543\pi\) | |||||||
\(524\) | −21.4163 | − | 6.95857i | −0.935574 | − | 0.303987i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.47803 | − | 6.88619i | 0.413262 | − | 0.300252i | ||||
\(527\) | 6.78228 | 0.295441 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.4668 | 1.62899 | ||||||||
\(530\) | 19.4635 | − | 14.1411i | 0.845441 | − | 0.614249i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.38197 | + | 0.449028i | 0.0599158 | + | 0.0194678i | ||||
\(533\) | − | 17.0404i | − | 0.738101i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.3680 | −0.448246 | ||||||||
\(536\) | 32.9867 | − | 10.7180i | 1.42481 | − | 0.462948i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.95363 | + | 8.19446i | 0.256679 | + | 0.353288i | ||||
\(539\) | − | 0.0549306i | − | 0.00236603i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5151i | 0.495074i | 0.968878 | + | 0.247537i | \(0.0796212\pi\) | ||||
−0.968878 | + | 0.247537i | \(0.920379\pi\) | |||||||
\(542\) | −14.2697 | + | 10.3675i | −0.612934 | + | 0.445323i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.8885 | −0.766965 | ||||||||
\(545\) | 3.27238 | 0.140173 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5265i | 0.621107i | 0.950556 | + | 0.310553i | \(0.100514\pi\) | ||||
−0.950556 | + | 0.310553i | \(0.899486\pi\) | |||||||
\(548\) | 0.620000 | − | 1.90816i | 0.0264851 | − | 0.0815128i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.110304 | + | 0.151820i | 0.00470336 | + | 0.00647362i | ||||
\(551\) | −2.00373 | −0.0853616 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9057 | −0.463756 | ||||||||
\(554\) | 7.41089 | + | 10.2002i | 0.314858 | + | 0.433365i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.95031 | − | 1.60845i | −0.209940 | − | 0.0682136i | ||||
\(557\) | − | 44.6492i | − | 1.89185i | −0.324387 | − | 0.945924i | \(-0.605158\pi\) | ||
0.324387 | − | 0.945924i | \(-0.394842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.7302 | −1.08827 | ||||||||
\(560\) | −3.77964 | + | 5.20223i | −0.159719 | + | 0.219834i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.1387 | − | 10.2724i | 0.596406 | − | 0.433314i | ||||
\(563\) | 4.26356i | 0.179688i | 0.995956 | + | 0.0898438i | \(0.0286368\pi\) | ||||
−0.995956 | + | 0.0898438i | \(0.971363\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.21098i | 0.177157i | ||||||||
\(566\) | 17.8092 | + | 24.5123i | 0.748577 | + | 1.03033i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.03258 | + | 24.7217i | 0.337039 | + | 1.03730i | ||||
\(569\) | 38.6045 | 1.61838 | 0.809192 | − | 0.587544i | \(-0.199905\pi\) | ||||
0.809192 | + | 0.587544i | \(0.199905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 28.0556i | − | 1.17409i | −0.809554 | − | 0.587045i | \(-0.800291\pi\) | ||
0.809554 | − | 0.587045i | \(-0.199709\pi\) | |||||||
\(572\) | −0.127520 | + | 0.392465i | −0.00533186 | + | 0.0164098i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.19041 | − | 3.77105i | 0.216643 | − | 0.157401i | ||||
\(575\) | 18.7845 | 0.783370 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.46468 | −0.102606 | −0.0513029 | − | 0.998683i | \(-0.516337\pi\) | ||||
−0.0513029 | + | 0.998683i | \(0.516337\pi\) | |||||||
\(578\) | 8.00886 | − | 5.81878i | 0.333125 | − | 0.242029i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.74007 | − | 8.43306i | 0.113775 | − | 0.350164i | ||||
\(581\) | 13.1624i | 0.546066i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.581287 | 0.0240745 | ||||||||
\(584\) | 3.36698 | + | 10.3625i | 0.139327 | + | 0.428803i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.0538633 | − | 0.0741364i | −0.00222507 | − | 0.00306255i | ||||
\(587\) | 42.7523i | 1.76458i | 0.470710 | + | 0.882288i | \(0.343998\pi\) | ||||
−0.470710 | + | 0.882288i | \(0.656002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.55825i | 0.0642065i | ||||||||
\(590\) | −4.74555 | + | 3.44784i | −0.195371 | + | 0.141945i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.41268 | + | 1.94438i | −0.0580607 | + | 0.0799137i | ||||
\(593\) | −17.7945 | −0.730733 | −0.365367 | − | 0.930864i | \(-0.619056\pi\) | ||||
−0.365367 | + | 0.930864i | \(0.619056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.08361i | 0.208408i | ||||||||
\(596\) | 36.4282 | + | 11.8362i | 1.49216 | + | 0.484831i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.2797 | + | 33.4181i | 0.992869 | + | 1.36657i | ||||
\(599\) | 14.5626 | 0.595011 | 0.297506 | − | 0.954720i | \(-0.403845\pi\) | ||||
0.297506 | + | 0.954720i | \(0.403845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1497 | −1.10746 | −0.553730 | − | 0.832696i | \(-0.686796\pi\) | ||||
−0.553730 | + | 0.832696i | \(0.686796\pi\) | |||||||
\(602\) | −5.69413 | − | 7.83729i | −0.232075 | − | 0.319424i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.81736 | − | 30.2147i | 0.399463 | − | 1.22942i | ||||
\(605\) | 17.6785i | 0.718733i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.8708 | 0.441231 | 0.220616 | − | 0.975361i | \(-0.429193\pi\) | ||||
0.220616 | + | 0.975361i | \(0.429193\pi\) | |||||||
\(608\) | − | 4.10995i | − | 0.166680i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.0326 | − | 13.1014i | 0.730118 | − | 0.530462i | ||||
\(611\) | − | 2.79794i | − | 0.113192i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.1387i | 1.05573i | 0.849327 | + | 0.527866i | \(0.177008\pi\) | ||||
−0.849327 | + | 0.527866i | \(0.822992\pi\) | |||||||
\(614\) | −13.1732 | − | 18.1314i | −0.531628 | − | 0.731724i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.147763 | + | 0.0480111i | −0.00595354 | + | 0.00193442i | ||||
\(617\) | 42.5464 | 1.71285 | 0.856427 | − | 0.516269i | \(-0.172679\pi\) | ||||
0.856427 | + | 0.516269i | \(0.172679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.0012i | 1.64798i | 0.566606 | + | 0.823989i | \(0.308256\pi\) | ||||
−0.566606 | + | 0.823989i | \(0.691744\pi\) | |||||||
\(620\) | −6.55819 | − | 2.13088i | −0.263383 | − | 0.0855784i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.9026 | − | 10.8274i | 0.597542 | − | 0.434139i | ||||
\(623\) | 7.90356 | 0.316649 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.08594 | −0.283437 | ||||||||
\(626\) | −27.4893 | + | 19.9722i | −1.09869 | + | 0.798248i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −27.9799 | − | 9.09121i | −1.11652 | − | 0.362779i | ||||
\(629\) | 1.90005i | 0.0757599i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.8045 | −1.18650 | −0.593249 | − | 0.805019i | \(-0.702155\pi\) | ||||
−0.593249 | + | 0.805019i | \(0.702155\pi\) | |||||||
\(632\) | 9.53190 | + | 29.3362i | 0.379158 | + | 1.16693i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.08759 | − | 4.24971i | −0.122624 | − | 0.168777i | ||||
\(635\) | − | 21.9809i | − | 0.872286i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.75621i | − | 0.148827i | ||||||
\(638\) | 0.173326 | − | 0.125929i | 0.00686204 | − | 0.00498557i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.2975 | + | 5.62030i | 0.683743 | + | 0.222162i | ||||
\(641\) | −18.1768 | −0.717941 | −0.358971 | − | 0.933349i | \(-0.616872\pi\) | ||||
−0.358971 | + | 0.933349i | \(0.616872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.8490i | 0.822203i | 0.911590 | + | 0.411101i | \(0.134856\pi\) | ||||
−0.911590 | + | 0.411101i | \(0.865144\pi\) | |||||||
\(644\) | −4.80586 | + | 14.7909i | −0.189377 | + | 0.582843i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.90983 | − | 2.62866i | −0.0751413 | − | 0.103423i | ||||
\(647\) | 18.7706 | 0.737948 | 0.368974 | − | 0.929440i | \(-0.379709\pi\) | ||||
0.368974 | + | 0.929440i | \(0.379709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.141728 | −0.00556332 | ||||||||
\(650\) | 7.54269 | + | 10.3816i | 0.295849 | + | 0.407201i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.4445 | + | 5.99300i | 0.722344 | + | 0.234704i | ||||
\(653\) | 25.5220i | 0.998751i | 0.866386 | + | 0.499376i | \(0.166437\pi\) | ||||
−0.866386 | + | 0.499376i | \(0.833563\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1000 | 0.707227 | ||||||||
\(656\) | −14.6807 | − | 10.6661i | −0.573185 | − | 0.416443i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.852237 | − | 0.619187i | 0.0332237 | − | 0.0241384i | ||||
\(659\) | 18.8249i | 0.733314i | 0.930356 | + | 0.366657i | \(0.119498\pi\) | ||||
−0.930356 | + | 0.366657i | \(0.880502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.1764i | 0.979247i | 0.871934 | + | 0.489623i | \(0.162866\pi\) | ||||
−0.871934 | + | 0.489623i | \(0.837134\pi\) | |||||||
\(662\) | −2.90988 | − | 4.00510i | −0.113096 | − | 0.155663i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 35.4066 | − | 11.5043i | 1.37404 | − | 0.446454i | ||||
\(665\) | −1.16797 | −0.0452921 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 21.4455i | − | 0.830372i | ||||||
\(668\) | 1.58843 | − | 4.88867i | 0.0614581 | − | 0.189148i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.5544 | + | 16.3867i | −0.871353 | + | 0.633075i | ||||
\(671\) | 0.538552 | 0.0207906 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.29322 | 0.319680 | 0.159840 | − | 0.987143i | \(-0.448902\pi\) | ||||
0.159840 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(674\) | 19.4405 | − | 14.1244i | 0.748822 | − | 0.544051i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.685493 | + | 2.10973i | −0.0263651 | + | 0.0811435i | ||||
\(677\) | − | 11.6825i | − | 0.448993i | −0.974475 | − | 0.224497i | \(-0.927926\pi\) | ||
0.974475 | − | 0.224497i | \(-0.0720738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.1803 | −0.467439 | ||||||||
\(680\) | 13.6749 | − | 4.44323i | 0.524407 | − | 0.170390i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0979317 | − | 0.134791i | −0.00375000 | − | 0.00516143i | ||||
\(683\) | − | 22.9388i | − | 0.877727i | −0.898554 | − | 0.438864i | \(-0.855381\pi\) | ||
0.898554 | − | 0.438864i | \(-0.144619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.61269i | 0.0616178i | ||||||||
\(686\) | 1.14412 | − | 0.831254i | 0.0436828 | − | 0.0317374i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.1054 | + | 22.1672i | −0.614013 | + | 0.845117i | ||||
\(689\) | 39.7491 | 1.51432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2800i | 1.57036i | 0.619265 | + | 0.785182i | \(0.287431\pi\) | ||||
−0.619265 | + | 0.785182i | \(0.712569\pi\) | |||||||
\(692\) | −3.22333 | − | 1.04732i | −0.122533 | − | 0.0398132i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.4780 | + | 41.9494i | 1.15693 | + | 1.59238i | ||||
\(695\) | 4.18377 | 0.158699 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.3459 | −0.543391 | ||||||||
\(698\) | −28.9182 | − | 39.8025i | −1.09457 | − | 1.50655i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.49298 | + | 4.59493i | −0.0564294 | + | 0.173672i | ||||
\(701\) | − | 22.9596i | − | 0.867174i | −0.901112 | − | 0.433587i | \(-0.857248\pi\) | ||
0.901112 | − | 0.433587i | \(-0.142752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.436542 | −0.0164645 | ||||||||
\(704\) | 0.258299 | + | 0.355518i | 0.00973501 | + | 0.0133991i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.9483 | − | 10.1340i | 0.524951 | − | 0.381399i | ||||
\(707\) | − | 4.35250i | − | 0.163693i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0831i | 0.829348i | 0.909970 | + | 0.414674i | \(0.136104\pi\) | ||||
−0.909970 | + | 0.414674i | \(0.863896\pi\) | |||||||
\(710\) | −12.2810 | − | 16.9033i | −0.460897 | − | 0.634370i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.90797 | − | 21.2605i | −0.258887 | − | 0.796772i | ||||
\(713\) | −16.6776 | −0.624582 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.331693i | − | 0.0124046i | ||||||
\(716\) | 21.1864 | + | 6.88387i | 0.791771 | + | 0.257262i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.2607 | + | 27.7981i | −1.42788 | + | 1.03741i | ||||
\(719\) | 29.4594 | 1.09865 | 0.549325 | − | 0.835609i | \(-0.314885\pi\) | ||||
0.549325 | + | 0.835609i | \(0.314885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5574 | −0.653873 | ||||||||
\(722\) | −21.1344 | + | 15.3550i | −0.786541 | + | 0.571455i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.9382 | + | 4.20389i | 0.480846 | + | 0.156236i | ||||
\(725\) | − | 6.66223i | − | 0.247429i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.5893 | −0.949054 | −0.474527 | − | 0.880241i | \(-0.657381\pi\) | ||||
−0.474527 | + | 0.880241i | \(0.657381\pi\) | |||||||
\(728\) | −10.1042 | + | 3.28305i | −0.374486 | + | 0.121678i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.14776 | − | 7.08529i | −0.190527 | − | 0.262238i | ||||
\(731\) | 21.6617i | 0.801189i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.3587i | 0.899711i | 0.893101 | + | 0.449855i | \(0.148524\pi\) | ||||
−0.893101 | + | 0.449855i | \(0.851476\pi\) | |||||||
\(734\) | 16.5748 | − | 12.0423i | 0.611789 | − | 0.444491i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 43.9879 | 1.62142 | ||||||||
\(737\) | −0.673598 | −0.0248123 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8064i | 0.691805i | 0.938270 | + | 0.345903i | \(0.112427\pi\) | ||||
−0.938270 | + | 0.345903i | \(0.887573\pi\) | |||||||
\(740\) | 0.596965 | − | 1.83727i | 0.0219449 | − | 0.0675393i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.79651 | + | 12.1074i | 0.322930 | + | 0.444475i | ||||
\(743\) | −29.4039 | −1.07873 | −0.539363 | − | 0.842074i | \(-0.681335\pi\) | ||||
−0.539363 | + | 0.842074i | \(0.681335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.7874 | −1.12796 | ||||||||
\(746\) | 23.9079 | + | 32.9063i | 0.875329 | + | 1.20479i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.330408 | + | 0.107356i | 0.0120809 | + | 0.00392532i | ||||
\(749\) | − | 6.44944i | − | 0.235657i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.9057 | −0.616896 | −0.308448 | − | 0.951241i | \(-0.599810\pi\) | ||||
−0.308448 | + | 0.951241i | \(0.599810\pi\) | |||||||
\(752\) | −2.41049 | − | 1.75132i | −0.0879015 | − | 0.0638642i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.8522 | − | 8.61115i | 0.431633 | − | 0.313600i | ||||
\(755\) | 25.5361i | 0.929353i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.3657i | 1.10366i | 0.833957 | + | 0.551830i | \(0.186070\pi\) | ||||
−0.833957 | + | 0.551830i | \(0.813930\pi\) | |||||||
\(758\) | 13.3862 | + | 18.4245i | 0.486209 | + | 0.669209i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.02085 | + | 3.14184i | 0.0370300 | + | 0.113967i | ||||
\(761\) | 18.0960 | 0.655979 | 0.327990 | − | 0.944681i | \(-0.393629\pi\) | ||||
0.327990 | + | 0.944681i | \(0.393629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03559i | 0.0736935i | ||||||||
\(764\) | 9.66586 | − | 29.7485i | 0.349699 | − | 1.07626i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.4728 | − | 21.4133i | 1.06490 | − | 0.773693i | ||||
\(767\) | −9.69153 | −0.349941 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.4944 | 0.558743 | 0.279371 | − | 0.960183i | \(-0.409874\pi\) | ||||
0.279371 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(770\) | 0.101032 | − | 0.0734040i | 0.00364094 | − | 0.00264530i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.1068 | − | 37.2610i | 0.435735 | − | 1.34105i | ||||
\(773\) | − | 33.1186i | − | 1.19119i | −0.803284 | − | 0.595597i | \(-0.796916\pi\) | ||
0.803284 | − | 0.595597i | \(-0.203084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.18105 | −0.186109 | ||||||||
\(776\) | 10.6460 | + | 32.7650i | 0.382169 | + | 1.17620i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.16559 | + | 11.2390i | 0.292751 | + | 0.402937i | ||||
\(779\) | − | 3.29602i | − | 0.118092i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.504826i | − | 0.0180641i | ||||||
\(782\) | 28.1340 | − | 20.4405i | 1.00607 | − | 0.730952i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.23607 | − | 2.35114i | −0.115574 | − | 0.0839693i | ||||
\(785\) | 23.6473 | 0.844008 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8484i | 0.493641i | 0.969061 | + | 0.246820i | \(0.0793858\pi\) | ||||
−0.969061 | + | 0.246820i | \(0.920614\pi\) | |||||||
\(788\) | −13.8838 | − | 4.51113i | −0.494591 | − | 0.160702i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.5733 | − | 20.0584i | −0.518494 | − | 0.713646i | ||||
\(791\) | −2.61946 | −0.0931372 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.8268 | 1.30776 | ||||||||
\(794\) | 20.1017 | + | 27.6677i | 0.713384 | + | 0.981888i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.52902 | − | 26.2496i | 0.302303 | − | 0.930393i | ||||
\(797\) | − | 27.5510i | − | 0.975908i | −0.872869 | − | 0.487954i | \(-0.837743\pi\) | ||
0.872869 | − | 0.487954i | \(-0.162257\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.35553 | −0.0833325 | ||||||||
\(800\) | 13.6652 | 0.483139 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.7972 | + | 19.4693i | −0.946243 | + | 0.687486i | ||||
\(803\) | − | 0.211606i | − | 0.00746740i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 12.5006i | − | 0.440588i | ||||||
\(806\) | −6.69669 | − | 9.21720i | −0.235881 | − | 0.324662i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.7082 | + | 3.80423i | −0.411893 | + | 0.133832i | ||||
\(809\) | −0.181117 | −0.00636775 | −0.00318388 | − | 0.999995i | \(-0.501013\pi\) | ||||
−0.00318388 | + | 0.999995i | \(0.501013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.7508i | − | 0.834003i | −0.908906 | − | 0.417002i | \(-0.863081\pi\) | ||
0.908906 | − | 0.417002i | \(-0.136919\pi\) | |||||||
\(812\) | 5.24582 | + | 1.70447i | 0.184092 | + | 0.0598152i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.0377617 | − | 0.0274355i | 0.00132355 | − | 0.000961612i | ||||
\(815\) | −15.5885 | −0.546040 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.97685 | −0.174118 | ||||||||
\(818\) | 37.3914 | − | 27.1665i | 1.30736 | − | 0.949854i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.8719 | + | 4.50726i | 0.484429 | + | 0.157400i | ||||
\(821\) | − | 8.16381i | − | 0.284919i | −0.989801 | − | 0.142460i | \(-0.954499\pi\) | ||
0.989801 | − | 0.142460i | \(-0.0455011\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.6984 | 1.38380 | 0.691900 | − | 0.721993i | \(-0.256774\pi\) | ||||
0.691900 | + | 0.721993i | \(0.256774\pi\) | |||||||
\(824\) | 15.3458 | + | 47.2294i | 0.534595 | + | 1.64531i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.14475 | − | 2.95199i | −0.0746252 | − | 0.102713i | ||||
\(827\) | 46.0390i | 1.60093i | 0.599377 | + | 0.800467i | \(0.295415\pi\) | ||||
−0.599377 | + | 0.800467i | \(0.704585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1434i | 0.491220i | 0.969369 | + | 0.245610i | \(0.0789882\pi\) | ||||
−0.969369 | + | 0.245610i | \(0.921012\pi\) | |||||||
\(830\) | −24.2091 | + | 17.5889i | −0.840309 | + | 0.610520i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17.6628 | + | 24.3107i | 0.612347 | + | 0.842823i | ||||
\(833\) | −3.16228 | −0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.13168i | 0.142983i | ||||||||
\(836\) | −0.0246654 | + | 0.0759122i | −0.000853069 | + | 0.00262548i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.4373 | + | 33.6350i | 0.844171 | + | 1.16190i | ||||
\(839\) | 31.0217 | 1.07099 | 0.535494 | − | 0.844539i | \(-0.320125\pi\) | ||||
0.535494 | + | 0.844539i | \(0.320125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3940 | 0.737725 | ||||||||
\(842\) | −1.32579 | − | 1.82479i | −0.0456897 | − | 0.0628865i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | − | 3.24920i | −0.344214 | − | 0.111842i | ||||
\(845\) | − | 1.78305i | − | 0.0613386i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9970 | −0.377861 | ||||||||
\(848\) | 24.8803 | − | 34.2448i | 0.854392 | − | 1.17597i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.74007 | − | 6.35003i | 0.299782 | − | 0.217804i | ||||
\(851\) | − | 4.67222i | − | 0.160162i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36.2812i | − | 1.24224i | −0.783714 | − | 0.621121i | \(-0.786677\pi\) | ||
0.783714 | − | 0.621121i | \(-0.213323\pi\) | |||||||
\(854\) | 8.14980 | + | 11.2172i | 0.278880 | + | 0.383846i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.3489 | + | 5.63702i | −0.592975 | + | 0.192669i | ||||
\(857\) | 27.6532 | 0.944616 | 0.472308 | − | 0.881434i | \(-0.343421\pi\) | ||||
0.472308 | + | 0.881434i | \(0.343421\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 27.0733i | − | 0.923729i | −0.886950 | − | 0.461865i | \(-0.847181\pi\) | ||
0.886950 | − | 0.461865i | \(-0.152819\pi\) | |||||||
\(860\) | 6.80578 | − | 20.9460i | 0.232075 | − | 0.714253i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.2806 | − | 8.92236i | 0.418278 | − | 0.303897i | ||||
\(863\) | 8.98203 | 0.305752 | 0.152876 | − | 0.988245i | \(-0.451147\pi\) | ||||
0.152876 | + | 0.988245i | \(0.451147\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.72421 | 0.0926258 | ||||||||
\(866\) | 9.64899 | − | 7.01040i | 0.327886 | − | 0.238223i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.32553 | − | 4.07955i | 0.0449913 | − | 0.138469i | ||||
\(869\) | − | 0.599054i | − | 0.0203215i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.0614 | −1.56073 | ||||||||
\(872\) | 5.47574 | − | 1.77917i | 0.185432 | − | 0.0602505i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.69627 | + | 6.46386i | 0.158854 | + | 0.218643i | ||||
\(875\) | − | 11.9213i | − | 0.403014i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27.9552i | − | 0.943980i | −0.881604 | − | 0.471990i | \(-0.843536\pi\) | ||
0.881604 | − | 0.471990i | \(-0.156464\pi\) | |||||||
\(878\) | 19.8451 | − | 14.4183i | 0.669738 | − | 0.486593i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.285761 | − | 0.207618i | −0.00963301 | − | 0.00699879i | ||||
\(881\) | −33.0213 | −1.11252 | −0.556258 | − | 0.831010i | \(-0.687763\pi\) | ||||
−0.556258 | + | 0.831010i | \(0.687763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.1451i | 0.644283i | 0.946692 | + | 0.322141i | \(0.104403\pi\) | ||||
−0.946692 | + | 0.322141i | \(0.895597\pi\) | |||||||
\(884\) | 22.5937 | + | 7.34113i | 0.759907 | + | 0.246909i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.8399 | + | 34.1891i | 0.834512 | + | 1.14861i | ||||
\(887\) | 8.99598 | 0.302056 | 0.151028 | − | 0.988530i | \(-0.451742\pi\) | ||||
0.151028 | + | 0.988530i | \(0.451742\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6733 | 0.458588 | ||||||||
\(890\) | 10.5616 | + | 14.5367i | 0.354024 | + | 0.487273i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.06861 | − | 9.44422i | 0.102745 | − | 0.316216i | ||||
\(893\) | − | 0.541189i | − | 0.0181102i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.9057 | −0.598522 | ||||||||
\(896\) | −3.49613 | + | 10.7600i | −0.116797 | + | 0.359466i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.3153 | + | 15.4865i | −0.711301 | + | 0.516791i | ||||
\(899\) | 5.91498i | 0.197276i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 33.4639i | − | 1.11484i | ||||||
\(902\) | 0.207146 | + | 0.285112i | 0.00689721 | + | 0.00949319i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.28949 | + | 7.04633i | 0.0761473 | + | 0.234357i | ||||
\(905\) | −10.9348 | −0.363485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 53.5978i | − | 1.77969i | −0.456267 | − | 0.889843i | \(-0.650814\pi\) | ||
0.456267 | − | 0.889843i | \(-0.349186\pi\) | |||||||
\(908\) | −28.8689 | − | 9.38007i | −0.958048 | − | 0.311289i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.90868 | − | 5.01945i | 0.229020 | − | 0.166393i | ||||
\(911\) | −47.1958 | −1.56367 | −0.781833 | − | 0.623487i | \(-0.785715\pi\) | ||||
−0.781833 | + | 0.623487i | \(0.785715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.723015 | −0.0239283 | ||||||||
\(914\) | 7.59356 | − | 5.51704i | 0.251173 | − | 0.182488i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.8351 | − | 3.52054i | −0.358002 | − | 0.116322i | ||||
\(917\) | 11.2592i | 0.371812i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.6942 | 0.748612 | 0.374306 | − | 0.927305i | \(-0.377881\pi\) | ||||
0.374306 | + | 0.927305i | \(0.377881\pi\) | |||||||
\(920\) | −33.6265 | + | 10.9259i | −1.10863 | + | 0.360217i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −35.0373 | − | 48.2247i | −1.15389 | − | 1.58820i | ||||
\(923\) | − | 34.5206i | − | 1.13626i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.45147i | − | 0.0477239i | ||||||
\(926\) | 31.0296 | − | 22.5443i | 1.01970 | − | 0.740853i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 15.6010i | − | 0.512128i | ||||||
\(929\) | 31.0001 | 1.01708 | 0.508541 | − | 0.861038i | \(-0.330185\pi\) | ||||
0.508541 | + | 0.861038i | \(0.330185\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.726543i | − | 0.0238115i | ||||||
\(932\) | −10.2029 | + | 31.4012i | −0.334206 | + | 1.02858i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.884814 | + | 1.21784i | 0.0289520 | + | 0.0398490i | ||||
\(935\) | −0.279245 | −0.00913230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.0011 | −1.60080 | −0.800398 | − | 0.599469i | \(-0.795378\pi\) | ||||
−0.800398 | + | 0.599469i | \(0.795378\pi\) | |||||||
\(938\) | −10.1934 | − | 14.0301i | −0.332827 | − | 0.458098i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.27770 | + | 0.740069i | 0.0742903 | + | 0.0241384i | ||||
\(941\) | − | 49.2485i | − | 1.60546i | −0.596345 | − | 0.802728i | \(-0.703381\pi\) | ||
0.596345 | − | 0.802728i | \(-0.296619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.2766 | 1.14877 | ||||||||
\(944\) | −6.06626 | + | 8.34949i | −0.197440 | + | 0.271753i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.430507 | − | 0.312782i | 0.0139970 | − | 0.0101694i | ||||
\(947\) | 9.28008i | 0.301562i | 0.988567 | + | 0.150781i | \(0.0481788\pi\) | ||||
−0.988567 | + | 0.150781i | \(0.951821\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 14.4698i | − | 0.469711i | ||||||
\(950\) | 1.45894 | + | 2.00806i | 0.0473342 | + | 0.0651499i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.76393 | + | 8.50651i | 0.0895796 | + | 0.275698i | ||||
\(953\) | 50.1855 | 1.62567 | 0.812834 | − | 0.582496i | \(-0.197924\pi\) | ||||
0.812834 | + | 0.582496i | \(0.197924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.1420i | 0.813576i | ||||||||
\(956\) | −9.35931 | + | 28.8050i | −0.302702 | + | 0.931620i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.5017 | − | 27.2466i | 1.21162 | − | 0.880297i | ||||
\(959\) | −1.00318 | −0.0323944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4001 | −0.851615 | ||||||||
\(962\) | 2.58219 | − | 1.87607i | 0.0832530 | − | 0.0604869i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.6169 | + | 54.2192i | −0.567402 | + | 1.74628i | ||||
\(965\) | 31.4913i | 1.01374i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.81736 | −0.251389 | −0.125695 | − | 0.992069i | \(-0.540116\pi\) | ||||
−0.125695 | + | 0.992069i | \(0.540116\pi\) | |||||||
\(968\) | 9.61172 | + | 29.5818i | 0.308932 | + | 0.950796i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.2766 | − | 22.4029i | −0.522612 | − | 0.719313i | ||||
\(971\) | − | 7.60460i | − | 0.244043i | −0.992527 | − | 0.122022i | \(-0.961062\pi\) | ||
0.992527 | − | 0.122022i | \(-0.0389377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.60253i | 0.0834333i | ||||||||
\(974\) | 2.79542 | − | 2.03099i | 0.0895711 | − | 0.0650772i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.0511 | − | 31.7271i | 0.737848 | − | 1.01556i | ||||
\(977\) | 37.9179 | 1.21310 | 0.606551 | − | 0.795044i | \(-0.292553\pi\) | ||||
0.606551 | + | 0.795044i | \(0.292553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.434147i | 0.0138754i | ||||||||
\(980\) | 3.05779 | + | 0.993537i | 0.0976776 | + | 0.0317374i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.2783 | − | 29.2870i | −0.679017 | − | 0.934587i | ||||
\(983\) | −33.7230 | −1.07560 | −0.537798 | − | 0.843074i | \(-0.680744\pi\) | ||||
−0.537798 | + | 0.843074i | \(0.680744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7340 | 0.373875 | ||||||||
\(986\) | −7.24955 | − | 9.97815i | −0.230873 | − | 0.317769i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.68665 | + | 5.19096i | −0.0536593 | + | 0.165146i | ||||
\(989\) | − | 53.2662i | − | 1.69377i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.3137 | 1.47120 | 0.735602 | − | 0.677414i | \(-0.236899\pi\) | ||||
0.735602 | + | 0.677414i | \(0.236899\pi\) | |||||||
\(992\) | −12.1325 | −0.385208 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.5148 | − | 7.63943i | 0.333509 | − | 0.242308i | ||||
\(995\) | 22.1849i | 0.703310i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.20068i | 0.164707i | 0.996603 | + | 0.0823535i | \(0.0262437\pi\) | ||||
−0.996603 | + | 0.0823535i | \(0.973756\pi\) | |||||||
\(998\) | 6.62276 | + | 9.11545i | 0.209640 | + | 0.288545i | ||||
\(999\) | 0 | 0 |
(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 | 1512.2.c.d.757.4 | yes | 16 | |
3.2 | odd | 2 | inner | 1512.2.c.d.757.13 | yes | 16 | |
4.3 | odd | 2 | 6048.2.c.d.3025.11 | 16 | |||
8.3 | odd | 2 | 6048.2.c.d.3025.6 | 16 | |||
8.5 | even | 2 | inner | 1512.2.c.d.757.1 | ✓ | 16 | |
12.11 | even | 2 | 6048.2.c.d.3025.5 | 16 | |||
24.5 | odd | 2 | inner | 1512.2.c.d.757.16 | yes | 16 | |
24.11 | even | 2 | 6048.2.c.d.3025.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.d.757.1 | ✓ | 16 | 8.5 | even | 2 | inner | |
1512.2.c.d.757.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1512.2.c.d.757.13 | yes | 16 | 3.2 | odd | 2 | inner | |
1512.2.c.d.757.16 | yes | 16 | 24.5 | odd | 2 | inner | |
6048.2.c.d.3025.5 | 16 | 12.11 | even | 2 | |||
6048.2.c.d.3025.6 | 16 | 8.3 | odd | 2 | |||
6048.2.c.d.3025.11 | 16 | 4.3 | odd | 2 | |||
6048.2.c.d.3025.12 | 16 | 24.11 | even | 2 |