Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(527,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.527");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 527.11 | ||
Character | \(\chi\) | \(=\) | 1008.527 |
Dual form | 1008.2.cj.d.767.11 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.02952 | − | 1.39287i | 0.594393 | − | 0.804174i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.34742 | + | 1.35528i | −1.04980 | + | 0.606100i | −0.922592 | − | 0.385776i | \(-0.873934\pi\) |
−0.127204 | + | 0.991877i | \(0.540600\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.57527 | − | 0.606609i | 0.973361 | − | 0.229277i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.880179 | − | 2.86798i | −0.293393 | − | 0.955992i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.711483 | + | 1.23232i | −0.214520 | + | 0.371560i | −0.953124 | − | 0.302580i | \(-0.902152\pi\) |
0.738604 | + | 0.674140i | \(0.235485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.56378 | − | 4.44059i | 0.711064 | − | 1.23160i | −0.253394 | − | 0.967363i | \(-0.581547\pi\) |
0.964458 | − | 0.264236i | \(-0.0851198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.528979 | + | 4.66494i | −0.136582 | + | 1.20448i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.04103 | + | 0.601041i | −0.252488 | + | 0.145774i | −0.620903 | − | 0.783887i | \(-0.713234\pi\) |
0.368415 | + | 0.929661i | \(0.379901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.15547 | + | 3.55386i | 1.41216 | + | 0.815312i | 0.995592 | − | 0.0937915i | \(-0.0298987\pi\) |
0.416570 | + | 0.909104i | \(0.363232\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.80636 | − | 4.21154i | 0.394181 | − | 0.919033i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.74811 | − | 6.49192i | −0.781535 | − | 1.35366i | −0.931047 | − | 0.364899i | \(-0.881104\pi\) |
0.149512 | − | 0.988760i | \(-0.452230\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.17357 | − | 2.03269i | 0.234715 | − | 0.406538i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.90088 | − | 1.72666i | −0.943175 | − | 0.332296i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.90901 | − | 3.98892i | 1.28297 | − | 0.740724i | 0.305581 | − | 0.952166i | \(-0.401149\pi\) |
0.977390 | + | 0.211443i | \(0.0678161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.34842i | − | 1.31982i | −0.751347 | − | 0.659908i | \(-0.770595\pi\) | ||
0.751347 | − | 0.659908i | \(-0.229405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.983983 | + | 2.25971i | 0.171290 | + | 0.393364i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.22311 | + | 4.91418i | −0.882866 | + | 0.830648i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.194581 | + | 0.337025i | −0.0319890 | + | 0.0554065i | −0.881577 | − | 0.472041i | \(-0.843517\pi\) |
0.849588 | + | 0.527447i | \(0.176851\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.54572 | − | 8.14269i | −0.567769 | − | 1.30387i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.52819 | − | 0.882303i | −0.238664 | − | 0.137793i | 0.375899 | − | 0.926661i | \(-0.377334\pi\) |
−0.614562 | + | 0.788868i | \(0.710667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.214184 | + | 0.123659i | −0.0326628 | + | 0.0188579i | −0.516242 | − | 0.856442i | \(-0.672670\pi\) |
0.483580 | + | 0.875300i | \(0.339336\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.95306 | + | 5.53944i | 0.887430 | + | 0.825771i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.80343 | −0.992382 | −0.496191 | − | 0.868213i | \(-0.665268\pi\) | ||||
−0.496191 | + | 0.868213i | \(0.665268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.26405 | − | 3.12437i | 0.894864 | − | 0.446338i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.234592 | + | 2.06881i | −0.0328494 | + | 0.289691i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7865 | − | 6.22758i | 1.48164 | − | 0.855423i | 0.481853 | − | 0.876252i | \(-0.339964\pi\) |
0.999783 | + | 0.0208286i | \(0.00663044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.85704i | − | 0.520083i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.2873 | − | 4.91501i | 1.49503 | − | 0.651008i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.75647 | 0.619240 | 0.309620 | − | 0.950860i | \(-0.399798\pi\) | ||||
0.309620 | + | 0.950860i | \(0.399798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.204627 | −0.0261998 | −0.0130999 | − | 0.999914i | \(-0.504170\pi\) | ||||
−0.0130999 | + | 0.999914i | \(0.504170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00644 | − | 6.85189i | −0.504764 | − | 0.863257i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.8986i | 1.72390i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.33812i | 0.652155i | 0.945343 | + | 0.326077i | \(0.105727\pi\) | ||||
−0.945343 | + | 0.326077i | \(0.894273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9012 | − | 1.46292i | −1.55312 | − | 0.176115i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.22420 | 0.263964 | 0.131982 | − | 0.991252i | \(-0.457866\pi\) | ||||
0.131982 | + | 0.991252i | \(0.457866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.54731 | − | 13.0723i | −0.883345 | − | 1.53000i | −0.847598 | − | 0.530638i | \(-0.821952\pi\) |
−0.0357471 | − | 0.999361i | \(-0.511381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.62306 | − | 3.72733i | −0.187414 | − | 0.430395i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.08472 | + | 3.60516i | −0.123616 | + | 0.410846i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.62145i | 1.08250i | 0.840863 | + | 0.541249i | \(0.182048\pi\) | ||||
−0.840863 | + | 0.541249i | \(0.817952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.45057 | + | 5.04866i | −0.827841 | + | 0.560963i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.59188 | + | 4.48927i | 0.284496 | + | 0.492761i | 0.972487 | − | 0.232958i | \(-0.0748405\pi\) |
−0.687991 | + | 0.725719i | \(0.741507\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.62916 | − | 2.82179i | 0.176707 | − | 0.306066i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.55691 | − | 13.7300i | 0.166918 | − | 1.47201i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.17410 | − | 2.40992i | −0.442454 | − | 0.255451i | 0.262184 | − | 0.965018i | \(-0.415557\pi\) |
−0.704638 | + | 0.709567i | \(0.748891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.90872 | − | 12.9910i | 0.409745 | − | 1.36182i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.2354 | − | 7.56534i | −1.06136 | − | 0.784490i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.2659 | −1.97664 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.40373 | + | 4.16339i | 0.244062 | + | 0.422728i | 0.961868 | − | 0.273516i | \(-0.0881865\pi\) |
−0.717805 | + | 0.696244i | \(0.754853\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.16051 | + | 0.955849i | 0.418147 | + | 0.0960665i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.36507 | + | 1.94282i | 0.334837 | + | 0.193318i | 0.657987 | − | 0.753030i | \(-0.271408\pi\) |
−0.323150 | + | 0.946348i | \(0.604742\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0608 | + | 6.38595i | −1.08985 | + | 0.629226i | −0.933537 | − | 0.358481i | \(-0.883295\pi\) |
−0.156315 | + | 0.987707i | \(0.549961\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.46753 | + | 12.3344i | 0.143216 | + | 1.20371i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.20389 | + | 10.7455i | −0.599753 | + | 1.03880i | 0.393104 | + | 0.919494i | \(0.371401\pi\) |
−0.992857 | + | 0.119309i | \(0.961932\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.14048 | − | 10.6356i | −0.588152 | − | 1.01871i | −0.994474 | − | 0.104979i | \(-0.966523\pi\) |
0.406323 | − | 0.913730i | \(-0.366811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.269107 | + | 0.618000i | 0.0255425 | + | 0.0586579i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.2555 | + | 7.65305i | 1.24697 | + | 0.719938i | 0.970504 | − | 0.241086i | \(-0.0775035\pi\) |
0.276465 | + | 0.961024i | \(0.410837\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.5968 | + | 10.1595i | 1.64091 | + | 0.947377i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.9921 | − | 3.44434i | −1.38602 | − | 0.318429i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.31635 | + | 2.17935i | −0.212339 | + | 0.199780i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.48758 | + | 7.77272i | 0.407962 | + | 0.706611i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.80224 | + | 1.22023i | −0.252669 | + | 0.110024i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 7.19072i | − | 0.643158i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1494i | 1.34429i | 0.740418 | + | 0.672147i | \(0.234628\pi\) | ||||
−0.740418 | + | 0.672147i | \(0.765372\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.0482654 | + | 0.425641i | −0.00424953 | + | 0.0374756i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.62022 | − | 8.00246i | −0.403671 | − | 0.699178i | 0.590495 | − | 0.807041i | \(-0.298932\pi\) |
−0.994166 | + | 0.107863i | \(0.965599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.0078 | + | 5.41820i | 1.56148 | + | 0.469817i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.8445 | − | 2.58888i | 1.19155 | − | 0.222815i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.57002 | − | 2.06115i | −0.305008 | − | 0.176096i | 0.339683 | − | 0.940540i | \(-0.389680\pi\) |
−0.644690 | + | 0.764444i | \(0.723014\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.87372 | − | 2.23649i | −0.328564 | − | 0.189697i | 0.326639 | − | 0.945149i | \(-0.394084\pi\) |
−0.655204 | + | 0.755452i | \(0.727417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.00426 | + | 9.47630i | −0.589865 | + | 0.798048i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.64817 | + | 6.31881i | 0.305075 | + | 0.528406i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.8122 | + | 18.7273i | −0.897905 | + | 1.55522i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.09712 | − | 11.9416i | 0.172968 | − | 0.984927i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.5491 | − | 10.1320i | 1.43768 | − | 0.830045i | 0.439992 | − | 0.898002i | \(-0.354981\pi\) |
0.997688 | + | 0.0679562i | \(0.0216478\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.44512 | + | 3.72109i | 0.524497 | + | 0.302818i | 0.738772 | − | 0.673955i | \(-0.235406\pi\) |
−0.214276 | + | 0.976773i | \(0.568739\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.64007 | + | 2.45664i | 0.213437 | + | 0.198607i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.95918 | + | 17.2498i | 0.799940 | + | 1.38554i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.9414 | −1.19245 | −0.596226 | − | 0.802816i | \(-0.703334\pi\) | ||||
−0.596226 | + | 0.802816i | \(0.703334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.43068 | − | 21.4356i | 0.192765 | − | 1.69995i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.5905 | − | 14.4448i | −1.07108 | − | 1.13841i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3855 | + | 5.99605i | 0.813453 | + | 0.469647i | 0.848153 | − | 0.529751i | \(-0.177714\pi\) |
−0.0347008 | + | 0.999398i | \(0.511048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.37235 | − | 3.97090i | −0.418237 | − | 0.309134i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.91245 | + | 15.4368i | −0.689666 | + | 1.19454i | 0.282280 | + | 0.959332i | \(0.408909\pi\) |
−0.971946 | + | 0.235205i | \(0.924424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.64592 | − | 11.5111i | −0.511225 | − | 0.885467i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.77448 | − | 20.7818i | 0.365113 | − | 1.58922i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.2496i | 1.91969i | 0.280526 | + | 0.959847i | \(0.409491\pi\) | ||||
−0.280526 | + | 0.959847i | \(0.590509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.78922 | − | 5.94663i | 0.135253 | − | 0.449523i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.89688 | − | 6.62515i | 0.368072 | − | 0.497977i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.16327 | + | 7.21099i | 0.311177 | + | 0.538975i | 0.978617 | − | 0.205689i | \(-0.0659434\pi\) |
−0.667440 | + | 0.744663i | \(0.732610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6017 | 1.15967 | 0.579833 | − | 0.814735i | \(-0.303118\pi\) | ||||
0.579833 | + | 0.814735i | \(0.303118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.210667 | + | 0.285018i | −0.0155730 | + | 0.0210692i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.05485i | − | 0.0775540i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.71052i | − | 0.125086i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.6685 | − | 1.47370i | −0.994238 | − | 0.107196i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8565 | 0.785552 | 0.392776 | − | 0.919634i | \(-0.371515\pi\) | ||||
0.392776 | + | 0.919634i | \(0.371515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.20956 | 0.374992 | 0.187496 | − | 0.982265i | \(-0.439963\pi\) | ||||
0.187496 | + | 0.982265i | \(0.439963\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 19.3589 | + | 14.3088i | 1.38632 | + | 1.02468i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.7479i | 1.47823i | 0.673582 | + | 0.739113i | \(0.264755\pi\) | ||||
−0.673582 | + | 0.739113i | \(0.735245\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.76108 | − | 1.01676i | 0.124839 | − | 0.0720760i | −0.436280 | − | 0.899811i | \(-0.643704\pi\) |
0.561119 | + | 0.827735i | \(0.310371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.43531 | + | 5.49570i | 0.524446 | + | 0.387636i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.3729 | − | 14.4636i | 1.07896 | − | 1.01515i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.78307 | 0.334064 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.3197 | + | 16.4635i | −1.06479 | + | 1.14430i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.75902 | + | 5.05702i | −0.605874 | + | 0.349802i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.705274 | − | 0.407190i | −0.0485531 | − | 0.0280321i | 0.475527 | − | 0.879701i | \(-0.342257\pi\) |
−0.524080 | + | 0.851669i | \(0.675591\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.28986 | − | 3.09802i | 0.156898 | − | 0.212273i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.335187 | − | 0.580560i | 0.0228595 | − | 0.0395939i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.45762 | − | 18.9242i | −0.302603 | − | 1.28466i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −25.9782 | − | 2.94578i | −1.75544 | − | 0.199058i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.16375i | 0.414619i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.40736 | − | 5.43134i | 0.629963 | − | 0.363709i | −0.150775 | − | 0.988568i | \(-0.548177\pi\) |
0.780738 | + | 0.624859i | \(0.214843\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.86266 | − | 1.57665i | −0.457511 | − | 0.105110i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1494 | + | 17.5792i | −0.673638 | + | 1.16677i | 0.303227 | + | 0.952918i | \(0.401936\pi\) |
−0.976865 | + | 0.213857i | \(0.931397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.51141 | − | 4.34989i | −0.165959 | − | 0.287449i | 0.771037 | − | 0.636791i | \(-0.219738\pi\) |
−0.936995 | + | 0.349342i | \(0.886405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.90478 | + | 5.22246i | 0.256916 | + | 0.343613i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.4121 | − | 7.16616i | −0.813147 | − | 0.469470i | 0.0349007 | − | 0.999391i | \(-0.488889\pi\) |
−0.848047 | + | 0.529920i | \(0.822222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9705 | − | 9.22056i | 1.04180 | − | 0.601483i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4014 | + | 9.90547i | 0.870517 | + | 0.643429i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.71239 | − | 16.8224i | 0.628242 | − | 1.08815i | −0.359662 | − | 0.933083i | \(-0.617108\pi\) |
0.987904 | − | 0.155065i | \(-0.0495587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.05881 | − | 5.29801i | 0.197035 | − | 0.341275i | −0.750531 | − | 0.660836i | \(-0.770202\pi\) |
0.947566 | + | 0.319561i | \(0.103535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.638369 | + | 15.5754i | −0.0409514 | + | 0.999161i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.4699 | + | 15.8237i | −0.668900 | + | 1.01094i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.5625 | − | 18.2226i | 2.00828 | − | 1.15948i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.92136 | + | 1.01163i | 0.565368 | + | 0.0641097i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.54044 | 0.160351 | 0.0801757 | − | 0.996781i | \(-0.474452\pi\) | ||||
0.0801757 | + | 0.996781i | \(0.474452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.6669 | 0.670620 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.25313 | − | 5.17430i | −0.141097 | − | 0.324027i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0461 | − | 9.26423i | 1.00093 | − | 0.577886i | 0.0924058 | − | 0.995721i | \(-0.470544\pi\) |
0.908523 | + | 0.417835i | \(0.137211\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.296657 | + | 0.985964i | −0.0184334 | + | 0.0612649i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.5213 | − | 16.3039i | −1.08454 | − | 1.00919i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.21852 | + | 10.7708i | −0.383451 | + | 0.664156i | −0.991553 | − | 0.129703i | \(-0.958598\pi\) |
0.608102 | + | 0.793859i | \(0.291931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.8802 | + | 29.2374i | −1.03694 | + | 1.79604i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.65402 | + | 3.33292i | −0.468418 | + | 0.203972i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.0139 | + | 12.1324i | −1.28124 | + | 0.739723i | −0.977075 | − | 0.212897i | \(-0.931710\pi\) |
−0.304163 | + | 0.952620i | \(0.598377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.6964 | − | 10.2170i | −1.07498 | − | 0.620638i | −0.145440 | − | 0.989367i | \(-0.546460\pi\) |
−0.929537 | + | 0.368729i | \(0.879793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.0706 | − | 18.8188i | −0.851592 | − | 1.13896i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.66996 | + | 2.89245i | 0.100702 | + | 0.174421i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.63541 | + | 11.4929i | −0.398683 | + | 0.690539i | −0.993564 | − | 0.113275i | \(-0.963866\pi\) |
0.594881 | + | 0.803814i | \(0.297199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.0751 | + | 6.46793i | −1.26173 | + | 0.387225i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.56448 | − | 0.903251i | 0.0933289 | − | 0.0538835i | −0.452609 | − | 0.891709i | \(-0.649507\pi\) |
0.545938 | + | 0.837826i | \(0.316173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.1885i | 1.67563i | 0.545953 | + | 0.837816i | \(0.316168\pi\) | ||||
−0.545953 | + | 0.837816i | \(0.683832\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.8347 | + | 26.8350i | −1.17490 | + | 1.58957i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.47073 | − | 1.34515i | −0.263899 | − | 0.0794019i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.77750 | + | 13.4710i | −0.457500 | + | 0.792413i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.27376 | + | 0.938200i | 0.485016 | + | 0.0549982i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.28005 | − | 4.78049i | −0.483726 | − | 0.279279i | 0.238242 | − | 0.971206i | \(-0.423429\pi\) |
−0.721968 | + | 0.691927i | \(0.756762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.1654 | + | 6.44636i | −0.650076 | + | 0.375322i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.61470 | − | 4.81099i | 0.325798 | − | 0.279162i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.4373 | −2.22289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.476570 | + | 0.448383i | −0.0274690 | + | 0.0258444i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.17051 | − | 2.68693i | 0.354486 | − | 0.154360i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.480344 | − | 0.277327i | 0.0275044 | − | 0.0158797i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8578i | 1.13334i | 0.823944 | + | 0.566671i | \(0.191769\pi\) | ||||
−0.823944 | + | 0.566671i | \(0.808231\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.49249 | + | 21.9807i | −0.141793 | + | 1.25044i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.757772 | −0.0429693 | −0.0214846 | − | 0.999769i | \(-0.506839\pi\) | ||||
−0.0214846 | + | 0.999769i | \(0.506839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.95282 | −0.449520 | −0.224760 | − | 0.974414i | \(-0.572160\pi\) | ||||
−0.224760 | + | 0.974414i | \(0.572160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.6910 | + | 10.6544i | 1.05312 | + | 0.600307i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.1843i | 0.796667i | 0.917241 | + | 0.398334i | \(0.130411\pi\) | ||||
−0.917241 | + | 0.398334i | \(0.869589\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3522i | 0.635601i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.58001 | + | 19.7039i | 0.478889 | + | 1.09976i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.54408 | −0.475405 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.01757 | − | 10.4227i | −0.333795 | − | 0.578149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.1358 | − | 2.39669i | −1.16881 | − | 0.132537i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.5207 | + | 4.12702i | −0.965946 | + | 0.227530i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.43888i | 0.463843i | 0.972735 | + | 0.231921i | \(0.0745012\pi\) | ||||
−0.972735 | + | 0.231921i | \(0.925499\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.13784 | + | 0.261412i | 0.0623535 | + | 0.0143253i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.23465 | − | 12.5308i | −0.395271 | − | 0.684630i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.41921 | − | 11.1184i | 0.349677 | − | 0.605658i | −0.636515 | − | 0.771264i | \(-0.719625\pi\) |
0.986192 | + | 0.165606i | \(0.0529582\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.3065 | − | 10.5842i | 1.32015 | − | 0.574854i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.05564 | + | 5.22828i | 0.490390 | + | 0.283127i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2364 | − | 11.8459i | 0.768691 | − | 0.639620i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 32.2671 | − | 14.0506i | 1.73720 | − | 0.756459i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5540 | −0.566567 | −0.283283 | − | 0.959036i | \(-0.591424\pi\) | ||||
−0.283283 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.84572 | − | 13.5892i | −0.419972 | − | 0.727412i | 0.575964 | − | 0.817475i | \(-0.304627\pi\) |
−0.995936 | + | 0.0900624i | \(0.971293\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.2322 | + | 17.3361i | −1.07991 | + | 0.925330i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.0186821 | + | 0.0107861i | 0.000994348 | + | 0.000574087i | 0.500497 | − | 0.865738i | \(-0.333151\pi\) |
−0.499503 | + | 0.866312i | \(0.666484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.22112 | + | 3.01442i | −0.277108 | + | 0.159989i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.650821 | + | 5.47005i | 0.0344451 | + | 0.289506i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.41437 | − | 5.91386i | 0.180203 | − | 0.312121i | −0.761746 | − | 0.647875i | \(-0.775658\pi\) |
0.941950 | + | 0.335754i | \(0.108991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.7599 | + | 27.2969i | 0.829468 | + | 1.43668i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.4465 | + | 1.75155i | 0.810729 | + | 0.0919323i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.4333 | + | 20.4574i | 1.85467 | + | 1.07079i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.99931 | − | 1.73165i | −0.156563 | − | 0.0903916i | 0.419672 | − | 0.907676i | \(-0.362145\pi\) |
−0.576235 | + | 0.817284i | \(0.695479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.18534 | + | 5.15941i | −0.0617063 | + | 0.268588i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0004 | − | 22.5809i | 1.24604 | − | 1.17234i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.26770 | − | 7.39187i | −0.220973 | − | 0.382736i | 0.734131 | − | 0.679008i | \(-0.237590\pi\) |
−0.955104 | + | 0.296272i | \(0.904257\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.0157 | − | 7.40299i | −0.517211 | − | 0.382289i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 40.9068i | − | 2.10681i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.38671i | − | 0.328063i | −0.986455 | − | 0.164032i | \(-0.947550\pi\) | ||
0.986455 | − | 0.164032i | \(-0.0524499\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.1012 | + | 15.5966i | 1.08105 | + | 0.799039i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.2604 | − | 22.9677i | −0.677575 | − | 1.17359i | −0.975709 | − | 0.219070i | \(-0.929698\pi\) |
0.298135 | − | 0.954524i | \(-0.403636\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.33971 | − | 9.93292i | −0.119243 | − | 0.506228i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.543173 | + | 0.505433i | 0.0276110 | + | 0.0256926i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.247789 | + | 0.143061i | 0.0125634 | + | 0.00725347i | 0.506269 | − | 0.862376i | \(-0.331024\pi\) |
−0.493705 | + | 0.869629i | \(0.664358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.80382 | + | 4.50554i | 0.394656 | + | 0.227855i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.9030 | − | 1.80331i | −0.802200 | − | 0.0909652i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0398 | − | 22.5855i | −0.656102 | − | 1.13640i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.6448 | − | 27.0975i | 0.785188 | − | 1.35998i | −0.143699 | − | 0.989621i | \(-0.545900\pi\) |
0.928887 | − | 0.370363i | \(-0.120767\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 26.0863 | − | 19.5044i | 1.30595 | − | 0.976443i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5838 | + | 7.26527i | −0.628406 | + | 0.362810i | −0.780135 | − | 0.625612i | \(-0.784849\pi\) |
0.151728 | + | 0.988422i | \(0.451516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.6314 | − | 18.8397i | −1.62548 | − | 0.938474i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.6472 | − | 21.9489i | 0.529065 | − | 1.09065i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.276882 | − | 0.479574i | −0.0137245 | − | 0.0237716i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6983 | −0.924573 | −0.462286 | − | 0.886731i | \(-0.652971\pi\) | ||||
−0.462286 | + | 0.886731i | \(0.652971\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.54633 | + | 2.85058i | −0.322907 | + | 0.140609i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.2492 | − | 2.88532i | 0.602744 | − | 0.141977i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.1684 | − | 7.02545i | −0.597325 | − | 0.344866i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.10321 | + | 3.09308i | −0.347846 | + | 0.151469i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.0728005 | + | 0.126094i | −0.00355653 | + | 0.00616010i | −0.867798 | − | 0.496917i | \(-0.834465\pi\) |
0.864242 | + | 0.503077i | \(0.167799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4460 | − | 18.0930i | −0.509107 | − | 0.881799i | −0.999944 | − | 0.0105480i | \(-0.996642\pi\) |
0.490837 | − | 0.871251i | \(-0.336691\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.98823 | + | 19.5121i | 0.291158 | + | 0.948709i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82147i | 0.136861i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.526969 | + | 0.124128i | −0.0255018 | + | 0.00600699i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.5572 | + | 1.42391i | 0.606265 | + | 0.0687472i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5495 | + | 18.2723i | 0.508151 | + | 0.880144i | 0.999955 | + | 0.00943786i | \(0.00300421\pi\) |
−0.491804 | + | 0.870706i | \(0.663662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.19616 | 0.441939 | 0.220970 | − | 0.975281i | \(-0.429078\pi\) | ||||
0.220970 | + | 0.975281i | \(0.429078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.9533 | + | 34.3401i | 0.716957 | + | 1.64648i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 53.2811i | − | 2.54878i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 11.3238i | − | 0.540456i | −0.962796 | − | 0.270228i | \(-0.912901\pi\) | ||
0.962796 | − | 0.270228i | \(-0.0870991\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.4741 | − | 15.2151i | −0.689243 | − | 0.724531i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.8943 | 1.65788 | 0.828940 | − | 0.559338i | \(-0.188945\pi\) | ||||
0.828940 | + | 0.559338i | \(0.188945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0645 | 0.619315 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.95461 | − | 34.8748i | 0.187047 | − | 1.64952i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.4981i | − | 1.15614i | −0.815988 | − | 0.578069i | \(-0.803806\pi\) | ||
0.815988 | − | 0.578069i | \(-0.196194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.17457 | − | 1.25549i | 0.102396 | − | 0.0591186i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.8184 | − | 5.14629i | 0.555276 | − | 0.241794i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.43100 | + | 35.7926i | 0.395251 | + | 1.67798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.8516 | 1.58351 | 0.791756 | − | 0.610838i | \(-0.209167\pi\) | ||||
0.791756 | + | 0.610838i | \(0.209167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.13978 | − | 1.14812i | 0.286580 | − | 0.0535896i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.526552 | − | 0.304005i | 0.0245240 | − | 0.0141589i | −0.487688 | − | 0.873018i | \(-0.662160\pi\) |
0.512212 | + | 0.858859i | \(0.328826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.6357 | − | 7.87260i | −0.633707 | − | 0.365871i | 0.148479 | − | 0.988915i | \(-0.452562\pi\) |
−0.782186 | + | 0.623045i | \(0.785895\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 34.2799 | + | 3.88716i | 1.58969 | + | 0.180263i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.73247 | − | 6.46483i | 0.172718 | − | 0.299156i | −0.766651 | − | 0.642064i | \(-0.778078\pi\) |
0.939369 | + | 0.342907i | \(0.111412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.23815 | + | 13.7471i | 0.149524 | + | 0.634782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.3825 | + | 20.8114i | −0.708786 | + | 0.958940i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.351926i | − | 0.0161816i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.4478 | − | 8.34144i | 0.662910 | − | 0.382732i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.3546 | − | 25.4540i | −1.25248 | − | 1.16546i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0468 | − | 24.3297i | 0.641813 | − | 1.11165i | −0.343215 | − | 0.939257i | \(-0.611516\pi\) |
0.985028 | − | 0.172395i | \(-0.0551506\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.997726 | + | 1.72811i | 0.0454924 | + | 0.0787951i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.1114 | + | 4.05854i | −1.55212 | + | 0.184670i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.2851 | − | 6.51547i | −0.512431 | − | 0.295852i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.2895 | + | 13.4462i | −1.05535 | + | 0.609305i | −0.924141 | − | 0.382051i | \(-0.875218\pi\) |
−0.131205 | + | 0.991355i | \(0.541885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0438 | − | 8.29256i | 0.861189 | − | 0.375003i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.958840 | − | 1.66076i | 0.0432719 | − | 0.0749491i | −0.843578 | − | 0.537006i | \(-0.819555\pi\) |
0.886850 | + | 0.462057i | \(0.152889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.79501 | + | 8.30520i | −0.215956 | + | 0.374048i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.0619 | + | 3.39488i | −0.497195 | + | 0.152589i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.72792 | − | 1.34922i | 0.256932 | − | 0.0605208i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.08439 | − | 2.93547i | 0.227608 | − | 0.131410i | −0.381860 | − | 0.924220i | \(-0.624716\pi\) |
0.609468 | + | 0.792810i | \(0.291383\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.3260 | + | 28.3064i | 0.550683 | + | 1.26464i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.9558 | −0.488495 | −0.244248 | − | 0.969713i | \(-0.578541\pi\) | ||||
−0.244248 | + | 0.969713i | \(0.578541\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5323 | −0.468681 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.8755 | − | 2.59396i | −1.01594 | − | 0.115202i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.3859 | − | 19.2753i | 1.47980 | − | 0.854364i | 0.480064 | − | 0.877234i | \(-0.340614\pi\) |
0.999738 | + | 0.0228696i | \(0.00728024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.3662 | − | 29.0865i | −1.21061 | − | 1.28671i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.0309 | − | 28.0455i | −1.06099 | − | 1.23824i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.3095 | − | 29.9810i | 0.762748 | − | 1.32112i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.84052 | − | 8.38403i | 0.212886 | − | 0.368729i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.1695 | + | 25.9950i | 1.54377 | + | 1.14105i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.6259 | − | 9.59898i | 0.728395 | − | 0.420539i | −0.0894400 | − | 0.995992i | \(-0.528508\pi\) |
0.817835 | + | 0.575453i | \(0.195174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6079 | − | 7.27919i | −0.551306 | − | 0.318297i | 0.198343 | − | 0.980133i | \(-0.436444\pi\) |
−0.749649 | + | 0.661836i | \(0.769778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.44085 | − | 8.61433i | −0.281102 | − | 0.375960i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.41671 | + | 7.64996i | 0.192395 | + | 0.333237i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.5967 | + | 28.7463i | −0.721595 | + | 1.24984i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.18655 | − | 13.6415i | −0.181681 | − | 0.591989i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.83590 | + | 4.52406i | −0.339410 | + | 0.195959i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 33.6321i | − | 1.45404i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.3301 | + | 1.62496i | 0.618391 | + | 0.0701223i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.606531 | + | 9.94228i | −0.0261251 | + | 0.428244i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.33531 | + | 4.04487i | −0.100403 | + | 0.173903i | −0.911851 | − | 0.410522i | \(-0.865346\pi\) |
0.811448 | + | 0.584425i | \(0.198680\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.0623 | − | 21.7312i | 0.689298 | − | 0.932574i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.8285 | + | 16.6442i | 1.23488 | + | 0.712957i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.6708 | + | 17.7078i | −1.31139 | + | 0.757130i | −0.982326 | − | 0.187178i | \(-0.940066\pi\) |
−0.329062 | + | 0.944308i | \(0.606733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.180108 | + | 0.586864i | 0.00768683 | + | 0.0250468i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.7043 | 2.41568 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.83646 | + | 24.7778i | 0.248191 | + | 1.05366i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.46927 | − | 1.08599i | −0.0623670 | − | 0.0460976i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.7408 | + | 11.3974i | −0.836446 | + | 0.482922i | −0.856054 | − | 0.516886i | \(-0.827091\pi\) |
0.0196089 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.26814i | 0.0536367i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.38254 | − | 1.76102i | −0.100591 | − | 0.0743502i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.6920 | 1.29351 | 0.646756 | − | 0.762697i | \(-0.276125\pi\) | ||||
0.646756 | + | 0.762697i | \(0.276125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.4881 | −1.74542 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.1247 | + | 17.5213i | −0.677173 | + | 0.735824i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 39.2328i | − | 1.64472i | −0.568965 | − | 0.822362i | \(-0.692656\pi\) | ||
0.568965 | − | 0.822362i | \(-0.307344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.86834i | 0.0781877i | 0.999236 | + | 0.0390938i | \(0.0124471\pi\) | ||||
−0.999236 | + | 0.0390938i | \(0.987553\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.1770 | − | 15.1218i | 0.466927 | − | 0.631721i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.5947 | −0.733751 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.6560 | + | 35.7773i | 0.859921 | + | 1.48943i | 0.872003 | + | 0.489500i | \(0.162821\pi\) |
−0.0120819 | + | 0.999927i | \(0.503846\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.36334 | − | 7.25624i | 0.222893 | − | 0.301559i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.39802 | + | 9.98882i | 0.389896 | + | 0.414406i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.7233i | 0.734022i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 39.8607 | − | 12.2332i | 1.64804 | − | 0.505782i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.03460 | + | 12.1843i | 0.290349 | + | 0.502899i | 0.973892 | − | 0.227011i | \(-0.0728952\pi\) |
−0.683543 | + | 0.729910i | \(0.739562\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.1153 | − | 45.2330i | 1.07606 | − | 1.86379i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.8991 | + | 21.3603i | 1.18875 | + | 0.878647i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.5014 | − | 21.0741i | −1.49893 | − | 0.865410i | −0.498935 | − | 0.866639i | \(-0.666275\pi\) |
−0.999999 | + | 0.00122942i | \(0.999609\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.48381 | − | 8.25514i | 0.101826 | − | 0.338428i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.396850 | − | 3.49972i | 0.0162420 | − | 0.143234i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.3701 | 0.668865 | 0.334432 | − | 0.942420i | \(-0.391455\pi\) | ||||
0.334432 | + | 0.942420i | \(0.391455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.42868 | + | 5.93864i | 0.139859 | + | 0.242242i | 0.927443 | − | 0.373965i | \(-0.122002\pi\) |
−0.787584 | + | 0.616207i | \(0.788669\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.3096 | − | 4.69850i | 0.623455 | − | 0.191338i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.0685 | − | 12.1639i | −0.856554 | − | 0.494532i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.5705 | + | 21.1140i | −1.48435 | + | 0.856989i | −0.999842 | − | 0.0177977i | \(-0.994335\pi\) |
−0.484508 | + | 0.874787i | \(0.661001\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.31929 | − | 36.3030i | −0.175026 | − | 1.47107i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.4425 | + | 30.2113i | −0.705647 | + | 1.22222i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.14051 | + | 5.43953i | 0.126844 | + | 0.219700i | 0.922452 | − | 0.386111i | \(-0.126182\pi\) |
−0.795608 | + | 0.605812i | \(0.792849\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.92427 | − | 6.66220i | 0.198566 | − | 0.268646i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.8749 | + | 13.2068i | 0.920910 | + | 0.531688i | 0.883925 | − | 0.467628i | \(-0.154891\pi\) |
0.0369847 | + | 0.999316i | \(0.488225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.91891 | − | 3.99463i | −0.278094 | − | 0.160558i | 0.354466 | − | 0.935069i | \(-0.384663\pi\) |
−0.632560 | + | 0.774511i | \(0.717996\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.15970 | + | 38.2878i | 0.287309 | + | 1.53644i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.2113 | − | 3.67415i | −0.489236 | − | 0.147202i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6133 | + | 27.0431i | 0.624533 | + | 1.08172i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.97380 | + | 17.4065i | −0.0788261 | + | 0.695149i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.467805i | − | 0.0186526i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.8074i | 1.14681i | 0.819274 | + | 0.573403i | \(0.194377\pi\) | ||||
−0.819274 | + | 0.573403i | \(0.805623\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.29326 | + | 0.563145i | −0.0514023 | + | 0.0223830i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.5317 | − | 35.5620i | −0.814777 | − | 1.41123i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.18559 | − | 35.8263i | 0.0865963 | − | 1.41949i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.95769 | − | 6.37895i | −0.0774452 | − | 0.252347i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.0963 | + | 15.0667i | 1.03074 | + | 0.595099i | 0.917197 | − | 0.398434i | \(-0.130446\pi\) |
0.113544 | + | 0.993533i | \(0.463780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.6075 | − | 7.85629i | −0.536627 | − | 0.309822i | 0.207084 | − | 0.978323i | \(-0.433603\pi\) |
−0.743711 | + | 0.668501i | \(0.766936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.463564 | − | 1.06457i | −0.0182528 | − | 0.0419174i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.3703 | − | 19.6939i | −0.447012 | − | 0.774248i | 0.551177 | − | 0.834388i | \(-0.314179\pi\) |
−0.998190 | + | 0.0601397i | \(0.980845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.38415 | + | 5.86152i | −0.132839 | + | 0.230085i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.9482 | − | 13.2739i | −1.21295 | − | 0.520246i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.2807 | + | 20.3693i | −1.38064 | + | 0.797114i | −0.992235 | − | 0.124374i | \(-0.960308\pi\) |
−0.388407 | + | 0.921488i | \(0.626974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.6912 | + | 12.5234i | 0.847544 | + | 0.489330i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.8481 | + | 33.1515i | −1.20350 | + | 1.29336i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8968 | + | 27.5340i | 0.619251 | + | 1.07257i | 0.989623 | + | 0.143690i | \(0.0458970\pi\) |
−0.370372 | + | 0.928884i | \(0.620770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.4918 | −1.53605 | −0.768026 | − | 0.640419i | \(-0.778761\pi\) | ||||
−0.768026 | + | 0.640419i | \(0.778761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.58531 | + | 6.34570i | 0.333426 | + | 0.246447i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −49.6150 | + | 11.6869i | −1.92399 | + | 0.453198i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51.7915 | − | 29.9018i | −2.00537 | − | 1.15780i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.11990 | − | 18.6949i | 0.0819601 | − | 0.722787i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.145588 | − | 0.252166i | 0.00562038 | − | 0.00973478i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.03747 | − | 10.4572i | −0.232727 | − | 0.403095i | 0.725883 | − | 0.687819i | \(-0.241432\pi\) |
−0.958610 | + | 0.284723i | \(0.908098\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.26131 | + | 7.93561i | −0.356468 | + | 0.305442i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.43834i | − | 0.362745i | −0.983414 | − | 0.181373i | \(-0.941946\pi\) | ||
0.983414 | − | 0.181373i | \(-0.0580540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.71582 | + | 9.26373i | 0.334482 | + | 0.355509i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0366 | + | 32.2349i | 0.537885 | + | 1.23525i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.4219 | − | 31.9076i | −0.704893 | − | 1.22091i | −0.966730 | − | 0.255799i | \(-0.917662\pi\) |
0.261837 | − | 0.965112i | \(-0.415672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.1738 | 0.426928 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.64437 | − | 0.980226i | −0.329803 | − | 0.0373979i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 63.8645i | − | 2.43304i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 16.4596i | − | 0.626152i | −0.949728 | − | 0.313076i | \(-0.898641\pi\) | ||
0.949728 | − | 0.313076i | \(-0.101359\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.2943 | − | 0.0622307i | 0.429034 | − | 0.00236395i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.1243 | 0.459901 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.12120 | 0.0803463 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.7601 | + | 9.91082i | −0.860865 | + | 0.374862i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.7098i | 0.895506i | 0.894157 | + | 0.447753i | \(0.147776\pi\) | ||||
−0.894157 | + | 0.447753i | \(0.852224\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.39548 | + | 1.38303i | −0.0903472 | + | 0.0521620i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.59887 | − | 31.7376i | 0.135541 | − | 1.19531i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.84450 | + | 2.96202i | 0.370241 | + | 0.111398i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.5648 | 1.41077 | 0.705387 | − | 0.708822i | \(-0.250773\pi\) | ||||
0.705387 | + | 0.708822i | \(0.250773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.5941 | − | 8.46859i | 1.03486 | − | 0.317597i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −47.7054 | + | 27.5427i | −1.78658 | + | 1.03148i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.1275 | − | 9.88859i | −0.640534 | − | 0.369812i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.4323 | − | 30.8470i | −0.501637 | − | 1.15200i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.5085 | + | 23.3975i | −0.503783 | + | 0.872578i | 0.496207 | + | 0.868204i | \(0.334726\pi\) |
−0.999990 | + | 0.00437396i | \(0.998608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.6108 | + | 23.1551i | −0.916553 | + | 0.862342i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.23034 | − | 9.71493i | −0.157328 | − | 0.361302i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 18.7252i | − | 0.695435i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.96075 | − | 4.01879i | 0.258160 | − | 0.149049i | −0.365335 | − | 0.930876i | \(-0.619046\pi\) |
0.623495 | + | 0.781827i | \(0.285712\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.0373 | + | 16.9243i | 0.779159 | + | 0.626827i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.148649 | − | 0.257467i | 0.00549798 | − | 0.00952278i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.87974 | + | 8.45196i | 0.180237 | + | 0.312180i | 0.941961 | − | 0.335721i | \(-0.108980\pi\) |
−0.761724 | + | 0.647902i | \(0.775647\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.2614 | + | 30.8741i | 0.415384 | + | 1.13881i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.57829 | − | 3.79798i | −0.242314 | − | 0.139900i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.20806 | + | 4.73893i | −0.301938 | + | 0.174324i | −0.643313 | − | 0.765603i | \(-0.722441\pi\) |
0.341375 | + | 0.939927i | \(0.389107\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.11246 | − | 62.7231i | 0.261283 | − | 2.30419i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.9246 | − | 41.4386i | 0.877709 | − | 1.52024i | 0.0238602 | − | 0.999715i | \(-0.492404\pi\) |
0.853849 | − | 0.520521i | \(-0.174262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.4634 | + | 47.5680i | −1.00618 | + | 1.74276i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.5938 | − | 11.3848i | 0.387607 | − | 0.416548i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.45842 | + | 31.4358i | −0.345603 | + | 1.14864i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.8378 | − | 10.8760i | 0.687399 | − | 0.396870i | −0.115238 | − | 0.993338i | \(-0.536763\pi\) |
0.802637 | + | 0.596468i | \(0.203430\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.61544 | − | 3.53851i | 0.0953118 | − | 0.128951i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.1725 | −0.734153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2247 | 0.662390 | 0.331195 | − | 0.943562i | \(-0.392548\pi\) | ||||
0.331195 | + | 0.943562i | \(0.392548\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.9817 | − | 14.8576i | 0.398612 | − | 0.539296i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.47507 | + | 3.73838i | −0.234721 | + | 0.135516i | −0.612748 | − | 0.790278i | \(-0.709936\pi\) |
0.378027 | + | 0.925795i | \(0.376603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.2651 | − | 23.6648i | −0.806050 | − | 0.856722i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.52677 | − | 2.18871i | −0.344441 | − | 0.0791331i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.1945 | − | 21.1216i | 0.440319 | − | 0.762656i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.1663 | + | 19.3406i | −0.402666 | + | 0.697439i | −0.994047 | − | 0.108954i | \(-0.965250\pi\) |
0.591380 | + | 0.806393i | \(0.298583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.61591 | − | 31.8879i | 0.130224 | − | 1.14841i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.7168 | − | 24.0852i | 1.50045 | − | 0.866285i | 0.500450 | − | 0.865766i | \(-0.333168\pi\) |
1.00000 | 0.000519449i | \(-0.000165346\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.9371 | − | 8.62391i | −0.536555 | − | 0.309780i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.06791 | + | 1.42828i | 0.0383109 | + | 0.0512391i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.27117 | − | 10.8620i | −0.224688 | − | 0.389171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.58248 | + | 2.74094i | −0.0566256 | + | 0.0980784i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40.7478 | + | 7.61970i | −1.45621 | + | 0.272306i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.0737 | − | 20.2498i | 1.25183 | − | 0.722746i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.18145i | 0.149053i | 0.997219 | + | 0.0745263i | \(0.0237445\pi\) | ||||
−0.997219 | + | 0.0745263i | \(0.976256\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.60024 | + | 19.7503i | 0.306177 | + | 0.703131i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.7788 | + | 11.6678i | 1.37882 | + | 0.414859i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.524617 | + | 0.908664i | −0.0186297 | + | 0.0322676i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.3454 | + | 53.6125i | 0.827977 | + | 1.90144i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.4260 | + | 16.4118i | 1.00690 | + | 0.581335i | 0.910283 | − | 0.413986i | \(-0.135864\pi\) |
0.0966189 | + | 0.995321i | \(0.469197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.08260 | − | 4.08914i | 0.250564 | − | 0.144663i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.23763 | + | 14.0924i | −0.114396 | + | 0.497930i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.4791 | 0.757982 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51.4793 | + | 15.4891i | 1.81441 | + | 0.545919i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.73537 | + | 41.7601i | −0.166693 | + | 1.47003i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.93633 | − | 2.27264i | 0.138394 | − | 0.0799018i | −0.429204 | − | 0.903207i | \(-0.641206\pi\) |
0.567598 | + | 0.823306i | \(0.307873\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.5008i | 1.10614i | 0.833133 | + | 0.553072i | \(0.186545\pi\) | ||||
−0.833133 | + | 0.553072i | \(0.813455\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.4497 | + | 14.1301i | −1.13806 | + | 0.495566i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.5053 | −1.13861 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.75787 | −0.0615003 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −40.6981 | + | 0.224244i | −1.42211 | + | 0.00783572i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2584i | 0.986223i | 0.869966 | + | 0.493112i | \(0.164141\pi\) | ||||
−0.869966 | + | 0.493112i | \(0.835859\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0066i | 0.523096i | 0.965190 | + | 0.261548i | \(0.0842329\pi\) | ||||
−0.965190 | + | 0.261548i | \(0.915767\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.74806 | + | 0.651799i | 0.200122 | + | 0.0226927i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.7519 | 0.860709 | 0.430354 | − | 0.902660i | \(-0.358389\pi\) | ||||
0.430354 | + | 0.902660i | \(0.358389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.67861 | − | 2.90744i | −0.0583005 | − | 0.100979i | 0.835402 | − | 0.549639i | \(-0.185235\pi\) |
−0.893703 | + | 0.448660i | \(0.851901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.17679 | + | 21.0744i | 0.318339 | + | 0.731063i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.64322 | + | 7.01753i | −0.160878 | + | 0.243143i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 48.3155i | − | 1.67203i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.6882 | + | 36.0137i | −0.438570 | + | 1.24482i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.54338 | − | 4.40526i | −0.0878073 | − | 0.152087i | 0.818777 | − | 0.574112i | \(-0.194653\pi\) |
−0.906584 | + | 0.422025i | \(0.861319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.3229 | − | 30.0042i | 0.597343 | − | 1.03463i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.352547 | − | 3.10903i | 0.0121424 | − | 0.107081i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.2015 | + | 18.0142i | 1.07336 | + | 0.619707i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.2718 | + | 17.2947i | 0.559104 | + | 0.594252i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 39.2629 | + | 29.0206i | 1.34750 | + | 0.995984i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.91725 | 0.100002 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.5066 | + | 35.5185i | 0.702134 | + | 1.21613i | 0.967716 | + | 0.252043i | \(0.0811024\pi\) |
−0.265582 | + | 0.964088i | \(0.585564\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.9575 | + | 55.2542i | 0.579933 | + | 1.88965i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.1819 | − | 15.6935i | −0.928515 | − | 0.536078i | −0.0421734 | − | 0.999110i | \(-0.513428\pi\) |
−0.886342 | + | 0.463032i | \(0.846762\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.9116 | − | 27.6618i | 1.63472 | − | 0.943807i | 0.652113 | − | 0.758121i | \(-0.273883\pi\) |
0.982609 | − | 0.185686i | \(-0.0594507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.47633 | + | 4.84228i | −0.220713 | + | 0.165025i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.18055 | + | 12.4371i | −0.244429 | + | 0.423363i | −0.961971 | − | 0.273152i | \(-0.911934\pi\) |
0.717542 | + | 0.696515i | \(0.245267\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.2203 | − | 59.2714i | −1.16353 | − | 2.01529i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.7563 | + | 24.7017i | 0.365303 | + | 0.838915i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.8567 | − | 6.84549i | −0.402212 | − | 0.232217i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.7044 | + | 13.6857i | 0.803193 | + | 0.463724i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.82478 | − | 10.5584i | 0.332519 | − | 0.357347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.36196 | − | 18.5181i | −0.147461 | − | 0.626025i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.5368 | − | 44.2310i | −0.862316 | − | 1.49358i | −0.869687 | − | 0.493603i | \(-0.835680\pi\) |
0.00737111 | − | 0.999973i | \(-0.497654\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.1831 | + | 6.61143i | −0.512112 | + | 0.222998i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.4851i | 1.29660i | 0.761387 | + | 0.648298i | \(0.224519\pi\) | ||||
−0.761387 | + | 0.648298i | \(0.775481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.7854i | 0.564872i | 0.959286 | + | 0.282436i | \(0.0911425\pi\) | ||||
−0.959286 | + | 0.282436i | \(0.908857\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.51607 | + | 22.1886i | −0.0845769 | + | 0.745863i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.1564 | + | 29.7157i | 0.576054 | + | 0.997755i | 0.995926 | + | 0.0901717i | \(0.0287416\pi\) |
−0.419872 | + | 0.907583i | \(0.637925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.18978 | + | 39.0139i | 0.308215 | + | 1.30848i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.920640 | − | 12.7736i | −0.0308426 | − | 0.427930i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.8783 | − | 24.1785i | −1.40140 | − | 0.809101i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.5458 | − | 11.2848i | −0.653345 | − | 0.377209i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −39.5720 | + | 53.5382i | −1.32127 | + | 1.78759i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.3123 | − | 50.7703i | −0.977618 | − | 1.69328i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.48606 | + | 12.9662i | −0.249397 | + | 0.431968i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.133901 | + | 1.12542i | 0.00445595 | + | 0.0374516i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.6237 | + | 21.1447i | −1.21741 | + | 0.702874i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.2030 | − | 15.1283i | −0.870058 | − | 0.502328i | −0.00269031 | − | 0.999996i | \(-0.500856\pi\) |
−0.867367 | + | 0.497668i | \(0.834190\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.61011 | − | 11.3610i | 0.0865718 | − | 0.376820i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.9890 | − | 39.8181i | −0.761660 | − | 1.31923i | −0.941995 | − | 0.335628i | \(-0.891052\pi\) |
0.180335 | − | 0.983605i | \(-0.442282\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.37631 | −0.244120 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.108243 | − | 0.954570i | 0.00357841 | − | 0.0315571i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.7527 | − | 17.8058i | −0.553223 | − | 0.588001i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.58006 | − | 3.79900i | −0.217056 | − | 0.125317i | 0.387530 | − | 0.921857i | \(-0.373328\pi\) |
−0.604586 | + | 0.796540i | \(0.706662\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.6593 | + | 20.4440i | 0.911405 | + | 0.673651i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.70235 | − | 9.87677i | 0.187695 | − | 0.325098i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.456711 | + | 0.791046i | 0.0150166 | + | 0.0260094i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.0502 | + | 26.1013i | 0.921290 | + | 0.857279i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 38.0118i | − | 1.24713i | −0.781773 | − | 0.623564i | \(-0.785684\pi\) | ||
0.781773 | − | 0.623564i | \(-0.214316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.6618 | + | 3.02963i | 1.62760 | + | 0.0992920i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.780141 | + | 1.05548i | −0.0255407 | + | 0.0345548i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.31824 | + | 4.01531i | 0.0758145 | + | 0.131315i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.0882 | −1.73431 | −0.867157 | − | 0.498034i | \(-0.834055\pi\) | ||||
−0.867157 | + | 0.498034i | \(0.834055\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.18759 | + | 11.0773i | −0.267192 | + | 0.361493i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.52665i | 0.310560i | 0.987871 | + | 0.155280i | \(0.0496280\pi\) | ||||
−0.987871 | + | 0.155280i | \(0.950372\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.2279i | 0.430759i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 34.0830 | − | 15.0653i | 1.10872 | − | 0.490074i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.61009 | 0.247295 | 0.123647 | − | 0.992326i | \(-0.460541\pi\) | ||||
0.123647 | + | 0.992326i | \(0.460541\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −77.3985 | −2.51246 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.7568 | + | 14.6030i | 0.640659 | + | 0.473534i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.51742i | 0.275906i | 0.990439 | + | 0.137953i | \(0.0440524\pi\) | ||||
−0.990439 | + | 0.137953i | \(0.955948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.4848 | + | 14.7137i | −0.824669 | + | 0.476123i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.8121 | + | 11.6873i | 0.511134 | + | 0.377797i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.4441 | − | 3.14242i | −0.337257 | − | 0.101474i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.9993 | −0.741913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.2783 | + | 8.33469i | 1.16905 | + | 0.268582i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.2290 | + | 7.06042i | −0.393666 | + | 0.227283i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0326 | + | 7.52437i | 0.419100 | + | 0.241967i | 0.694692 | − | 0.719307i | \(-0.255541\pi\) |
−0.275592 | + | 0.961275i | \(0.588874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.79629 | + | 11.9008i | −0.282578 | + | 0.382309i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.1706 | + | 22.8121i | −0.422664 | + | 0.732076i | −0.996199 | − | 0.0871050i | \(-0.972238\pi\) |
0.573535 | + | 0.819181i | \(0.305572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3325 | − | 3.40974i | −0.363305 | − | 0.109311i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.7127 | − | 2.34871i | −0.663338 | − | 0.0752190i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27.2504i | − | 0.871818i | −0.899991 | − | 0.435909i | \(-0.856427\pi\) | ||
0.899991 | − | 0.435909i | \(-0.143573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.93960 | − | 3.42923i | 0.189830 | − | 0.109599i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.0980 | + | 26.9720i | −0.801317 | + | 0.861150i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.1791 | + | 34.9511i | −0.643612 | + | 1.11477i | 0.341008 | + | 0.940060i | \(0.389232\pi\) |
−0.984620 | + | 0.174708i | \(0.944102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.1192 | − | 48.7039i | −0.895953 | − | 1.55184i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.2895 | + | 28.6529i | −0.391178 | + | 0.912032i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.60557 | + | 0.926979i | 0.0510543 | + | 0.0294762i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0823 | − | 13.9039i | 0.765000 | − | 0.441673i | −0.0660879 | − | 0.997814i | \(-0.521052\pi\) |
0.831088 | + | 0.556141i | \(0.187718\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.7543 | + | 8.68799i | 0.373010 | + | 0.275705i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.75598 | + | 4.77350i | −0.0873706 | + | 0.151330i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.1178 | + | 40.0413i | −0.732149 | + | 1.26812i | 0.223813 | + | 0.974632i | \(0.428149\pi\) |
−0.955963 | + | 0.293488i | \(0.905184\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.53555 | − | 1.31574i | 0.0485825 | − | 0.0416282i |
(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 | 1008.2.cj.d.527.11 | yes | 30 | |
3.2 | odd | 2 | 3024.2.cj.d.2879.13 | 30 | |||
4.3 | odd | 2 | 1008.2.cj.c.527.5 | yes | 30 | ||
7.4 | even | 3 | 1008.2.bh.d.95.1 | yes | 30 | ||
9.2 | odd | 6 | 1008.2.bh.c.191.15 | yes | 30 | ||
9.7 | even | 3 | 3024.2.bh.c.1871.3 | 30 | |||
12.11 | even | 2 | 3024.2.cj.c.2879.13 | 30 | |||
21.11 | odd | 6 | 3024.2.bh.d.2447.13 | 30 | |||
28.11 | odd | 6 | 1008.2.bh.c.95.15 | ✓ | 30 | ||
36.7 | odd | 6 | 3024.2.bh.d.1871.3 | 30 | |||
36.11 | even | 6 | 1008.2.bh.d.191.1 | yes | 30 | ||
63.11 | odd | 6 | 1008.2.cj.c.767.5 | yes | 30 | ||
63.25 | even | 3 | 3024.2.cj.c.1439.13 | 30 | |||
84.11 | even | 6 | 3024.2.bh.c.2447.13 | 30 | |||
252.11 | even | 6 | inner | 1008.2.cj.d.767.11 | yes | 30 | |
252.151 | odd | 6 | 3024.2.cj.d.1439.13 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bh.c.95.15 | ✓ | 30 | 28.11 | odd | 6 | ||
1008.2.bh.c.191.15 | yes | 30 | 9.2 | odd | 6 | ||
1008.2.bh.d.95.1 | yes | 30 | 7.4 | even | 3 | ||
1008.2.bh.d.191.1 | yes | 30 | 36.11 | even | 6 | ||
1008.2.cj.c.527.5 | yes | 30 | 4.3 | odd | 2 | ||
1008.2.cj.c.767.5 | yes | 30 | 63.11 | odd | 6 | ||
1008.2.cj.d.527.11 | yes | 30 | 1.1 | even | 1 | trivial | |
1008.2.cj.d.767.11 | yes | 30 | 252.11 | even | 6 | inner | |
3024.2.bh.c.1871.3 | 30 | 9.7 | even | 3 | |||
3024.2.bh.c.2447.13 | 30 | 84.11 | even | 6 | |||
3024.2.bh.d.1871.3 | 30 | 36.7 | odd | 6 | |||
3024.2.bh.d.2447.13 | 30 | 21.11 | odd | 6 | |||
3024.2.cj.c.1439.13 | 30 | 63.25 | even | 3 | |||
3024.2.cj.c.2879.13 | 30 | 12.11 | even | 2 | |||
3024.2.cj.d.1439.13 | 30 | 252.151 | odd | 6 | |||
3024.2.cj.d.2879.13 | 30 | 3.2 | odd | 2 |