Properties

Label 2646.2.f.n.1765.1
Level $2646$
Weight $2$
Character 2646.1765
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2646,2,Mod(883,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.883");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1765.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1765
Dual form 2646.2.f.n.883.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} -1.00000 q^{8} -3.69963 q^{10} +(-0.738550 - 1.27921i) q^{11} +(1.34981 - 2.33795i) q^{13} +(-0.500000 - 0.866025i) q^{16} -6.57598 q^{17} -0.888736 q^{19} +(-1.84981 - 3.20397i) q^{20} +(0.738550 - 1.27921i) q^{22} +(3.14400 - 5.44556i) q^{23} +(-4.34362 - 7.52338i) q^{25} +2.69963 q^{26} +(-1.25526 - 2.17417i) q^{29} +(3.40545 - 5.89841i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.28799 - 5.69497i) q^{34} +2.77747 q^{37} +(-0.444368 - 0.769668i) q^{38} +(1.84981 - 3.20397i) q^{40} +(-2.05563 + 3.56046i) q^{41} +(0.00618986 + 0.0107211i) q^{43} +1.47710 q^{44} +6.28799 q^{46} +(3.49381 + 6.05146i) q^{47} +(4.34362 - 7.52338i) q^{50} +(1.34981 + 2.33795i) q^{52} -3.21015 q^{53} +5.46472 q^{55} +(1.25526 - 2.17417i) q^{58} +(-3.45489 + 5.98404i) q^{59} +(-2.86652 - 4.96497i) q^{61} +6.81089 q^{62} +1.00000 q^{64} +(4.99381 + 8.64953i) q^{65} +(4.73236 - 8.19669i) q^{67} +(3.28799 - 5.69497i) q^{68} +5.46472 q^{71} -12.0655 q^{73} +(1.38874 + 2.40536i) q^{74} +(0.444368 - 0.769668i) q^{76} +(-5.72617 - 9.91802i) q^{79} +3.69963 q^{80} -4.11126 q^{82} +(2.23855 + 3.87728i) q^{83} +(12.1643 - 21.0693i) q^{85} +(-0.00618986 + 0.0107211i) q^{86} +(0.738550 + 1.27921i) q^{88} +8.87636 q^{89} +(3.14400 + 5.44556i) q^{92} +(-3.49381 + 6.05146i) q^{94} +(1.64400 - 2.84748i) q^{95} +(6.58836 + 11.4114i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8} - 10 q^{10} + q^{11} + 2 q^{13} - 3 q^{16} + 8 q^{17} - 6 q^{19} - 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} + 4 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} + 18 q^{37} - 3 q^{38} + 5 q^{40} - 12 q^{41} + 18 q^{43} - 2 q^{44} + 14 q^{46} + 3 q^{47} + 2 q^{50} + 2 q^{52} + 18 q^{53} - 14 q^{55} - 5 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} - 4 q^{68} - 14 q^{71} - 50 q^{73} + 9 q^{74} + 3 q^{76} + 7 q^{79} + 10 q^{80} - 24 q^{82} + 8 q^{83} + 14 q^{85} - 18 q^{86} - q^{88} + 18 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.84981 + 3.20397i −0.827262 + 1.43286i 0.0729162 + 0.997338i \(0.476769\pi\)
−0.900178 + 0.435522i \(0.856564\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −3.69963 −1.16993
\(11\) −0.738550 1.27921i −0.222681 0.385695i 0.732940 0.680293i \(-0.238148\pi\)
−0.955621 + 0.294598i \(0.904814\pi\)
\(12\) 0 0
\(13\) 1.34981 2.33795i 0.374371 0.648430i −0.615862 0.787854i \(-0.711192\pi\)
0.990233 + 0.139425i \(0.0445253\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −6.57598 −1.59491 −0.797455 0.603378i \(-0.793821\pi\)
−0.797455 + 0.603378i \(0.793821\pi\)
\(18\) 0 0
\(19\) −0.888736 −0.203890 −0.101945 0.994790i \(-0.532507\pi\)
−0.101945 + 0.994790i \(0.532507\pi\)
\(20\) −1.84981 3.20397i −0.413631 0.716430i
\(21\) 0 0
\(22\) 0.738550 1.27921i 0.157459 0.272728i
\(23\) 3.14400 5.44556i 0.655568 1.13548i −0.326182 0.945307i \(-0.605762\pi\)
0.981751 0.190171i \(-0.0609043\pi\)
\(24\) 0 0
\(25\) −4.34362 7.52338i −0.868725 1.50468i
\(26\) 2.69963 0.529441
\(27\) 0 0
\(28\) 0 0
\(29\) −1.25526 2.17417i −0.233096 0.403734i 0.725622 0.688094i \(-0.241552\pi\)
−0.958718 + 0.284360i \(0.908219\pi\)
\(30\) 0 0
\(31\) 3.40545 5.89841i 0.611636 1.05938i −0.379329 0.925262i \(-0.623845\pi\)
0.990965 0.134123i \(-0.0428217\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.28799 5.69497i −0.563886 0.976679i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.77747 0.456614 0.228307 0.973589i \(-0.426681\pi\)
0.228307 + 0.973589i \(0.426681\pi\)
\(38\) −0.444368 0.769668i −0.0720860 0.124857i
\(39\) 0 0
\(40\) 1.84981 3.20397i 0.292481 0.506592i
\(41\) −2.05563 + 3.56046i −0.321036 + 0.556050i −0.980702 0.195508i \(-0.937364\pi\)
0.659666 + 0.751559i \(0.270698\pi\)
\(42\) 0 0
\(43\) 0.00618986 + 0.0107211i 0.000943944 + 0.00163496i 0.866497 0.499182i \(-0.166366\pi\)
−0.865553 + 0.500817i \(0.833033\pi\)
\(44\) 1.47710 0.222681
\(45\) 0 0
\(46\) 6.28799 0.927114
\(47\) 3.49381 + 6.05146i 0.509625 + 0.882696i 0.999938 + 0.0111494i \(0.00354904\pi\)
−0.490313 + 0.871546i \(0.663118\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 4.34362 7.52338i 0.614281 1.06397i
\(51\) 0 0
\(52\) 1.34981 + 2.33795i 0.187186 + 0.324215i
\(53\) −3.21015 −0.440948 −0.220474 0.975393i \(-0.570760\pi\)
−0.220474 + 0.975393i \(0.570760\pi\)
\(54\) 0 0
\(55\) 5.46472 0.736863
\(56\) 0 0
\(57\) 0 0
\(58\) 1.25526 2.17417i 0.164824 0.285483i
\(59\) −3.45489 + 5.98404i −0.449788 + 0.779056i −0.998372 0.0570397i \(-0.981834\pi\)
0.548584 + 0.836096i \(0.315167\pi\)
\(60\) 0 0
\(61\) −2.86652 4.96497i −0.367021 0.635699i 0.622077 0.782956i \(-0.286289\pi\)
−0.989098 + 0.147257i \(0.952956\pi\)
\(62\) 6.81089 0.864984
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.99381 + 8.64953i 0.619406 + 1.07284i
\(66\) 0 0
\(67\) 4.73236 8.19669i 0.578150 1.00138i −0.417542 0.908658i \(-0.637108\pi\)
0.995692 0.0927271i \(-0.0295584\pi\)
\(68\) 3.28799 5.69497i 0.398728 0.690616i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.46472 0.648543 0.324271 0.945964i \(-0.394881\pi\)
0.324271 + 0.945964i \(0.394881\pi\)
\(72\) 0 0
\(73\) −12.0655 −1.41216 −0.706078 0.708134i \(-0.749537\pi\)
−0.706078 + 0.708134i \(0.749537\pi\)
\(74\) 1.38874 + 2.40536i 0.161437 + 0.279618i
\(75\) 0 0
\(76\) 0.444368 0.769668i 0.0509725 0.0882870i
\(77\) 0 0
\(78\) 0 0
\(79\) −5.72617 9.91802i −0.644244 1.11586i −0.984475 0.175522i \(-0.943839\pi\)
0.340231 0.940342i \(-0.389495\pi\)
\(80\) 3.69963 0.413631
\(81\) 0 0
\(82\) −4.11126 −0.454013
\(83\) 2.23855 + 3.87728i 0.245713 + 0.425587i 0.962332 0.271878i \(-0.0876447\pi\)
−0.716619 + 0.697465i \(0.754311\pi\)
\(84\) 0 0
\(85\) 12.1643 21.0693i 1.31941 2.28528i
\(86\) −0.00618986 + 0.0107211i −0.000667469 + 0.00115609i
\(87\) 0 0
\(88\) 0.738550 + 1.27921i 0.0787297 + 0.136364i
\(89\) 8.87636 0.940892 0.470446 0.882429i \(-0.344093\pi\)
0.470446 + 0.882429i \(0.344093\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.14400 + 5.44556i 0.327784 + 0.567739i
\(93\) 0 0
\(94\) −3.49381 + 6.05146i −0.360359 + 0.624160i
\(95\) 1.64400 2.84748i 0.168670 0.292146i
\(96\) 0 0
\(97\) 6.58836 + 11.4114i 0.668947 + 1.15865i 0.978199 + 0.207670i \(0.0665880\pi\)
−0.309252 + 0.950980i \(0.600079\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.68725 0.868725
\(101\) −2.62729 4.55059i −0.261425 0.452801i 0.705196 0.709012i \(-0.250859\pi\)
−0.966621 + 0.256212i \(0.917526\pi\)
\(102\) 0 0
\(103\) 0.833104 1.44298i 0.0820882 0.142181i −0.822059 0.569403i \(-0.807174\pi\)
0.904147 + 0.427222i \(0.140508\pi\)
\(104\) −1.34981 + 2.33795i −0.132360 + 0.229255i
\(105\) 0 0
\(106\) −1.60507 2.78007i −0.155899 0.270024i
\(107\) −10.7651 −1.04070 −0.520350 0.853953i \(-0.674199\pi\)
−0.520350 + 0.853953i \(0.674199\pi\)
\(108\) 0 0
\(109\) 0.189108 0.0181132 0.00905662 0.999959i \(-0.497117\pi\)
0.00905662 + 0.999959i \(0.497117\pi\)
\(110\) 2.73236 + 4.73259i 0.260520 + 0.451234i
\(111\) 0 0
\(112\) 0 0
\(113\) 6.78180 11.7464i 0.637978 1.10501i −0.347897 0.937533i \(-0.613104\pi\)
0.985876 0.167478i \(-0.0535624\pi\)
\(114\) 0 0
\(115\) 11.6316 + 20.1466i 1.08465 + 1.87868i
\(116\) 2.51052 0.233096
\(117\) 0 0
\(118\) −6.90978 −0.636097
\(119\) 0 0
\(120\) 0 0
\(121\) 4.40909 7.63676i 0.400826 0.694251i
\(122\) 2.86652 4.96497i 0.259523 0.449507i
\(123\) 0 0
\(124\) 3.40545 + 5.89841i 0.305818 + 0.529692i
\(125\) 13.6414 1.22013
\(126\) 0 0
\(127\) −2.85669 −0.253490 −0.126745 0.991935i \(-0.540453\pi\)
−0.126745 + 0.991935i \(0.540453\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −4.99381 + 8.64953i −0.437986 + 0.758614i
\(131\) −0.0778435 + 0.134829i −0.00680122 + 0.0117801i −0.869406 0.494098i \(-0.835498\pi\)
0.862605 + 0.505878i \(0.168832\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 9.46472 0.817627
\(135\) 0 0
\(136\) 6.57598 0.563886
\(137\) −1.70582 2.95456i −0.145738 0.252425i 0.783910 0.620874i \(-0.213222\pi\)
−0.929648 + 0.368449i \(0.879889\pi\)
\(138\) 0 0
\(139\) 6.75526 11.7005i 0.572974 0.992420i −0.423285 0.905997i \(-0.639123\pi\)
0.996259 0.0864229i \(-0.0275436\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.73236 + 4.73259i 0.229295 + 0.397150i
\(143\) −3.98762 −0.333462
\(144\) 0 0
\(145\) 9.28799 0.771326
\(146\) −6.03273 10.4490i −0.499272 0.864765i
\(147\) 0 0
\(148\) −1.38874 + 2.40536i −0.114153 + 0.197719i
\(149\) 0.166896 0.289073i 0.0136727 0.0236818i −0.859108 0.511794i \(-0.828981\pi\)
0.872781 + 0.488112i \(0.162314\pi\)
\(150\) 0 0
\(151\) 9.95489 + 17.2424i 0.810117 + 1.40316i 0.912781 + 0.408448i \(0.133930\pi\)
−0.102664 + 0.994716i \(0.532737\pi\)
\(152\) 0.888736 0.0720860
\(153\) 0 0
\(154\) 0 0
\(155\) 12.5989 + 21.8219i 1.01197 + 1.75278i
\(156\) 0 0
\(157\) −3.48143 + 6.03001i −0.277848 + 0.481248i −0.970850 0.239689i \(-0.922955\pi\)
0.693001 + 0.720936i \(0.256288\pi\)
\(158\) 5.72617 9.91802i 0.455550 0.789035i
\(159\) 0 0
\(160\) 1.84981 + 3.20397i 0.146241 + 0.253296i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.07413 −0.632414 −0.316207 0.948690i \(-0.602409\pi\)
−0.316207 + 0.948690i \(0.602409\pi\)
\(164\) −2.05563 3.56046i −0.160518 0.278025i
\(165\) 0 0
\(166\) −2.23855 + 3.87728i −0.173745 + 0.300935i
\(167\) 9.74288 16.8752i 0.753927 1.30584i −0.191979 0.981399i \(-0.561491\pi\)
0.945906 0.324440i \(-0.105176\pi\)
\(168\) 0 0
\(169\) 2.85600 + 4.94674i 0.219693 + 0.380519i
\(170\) 24.3287 1.86593
\(171\) 0 0
\(172\) −0.0123797 −0.000943944
\(173\) −11.2818 19.5407i −0.857740 1.48565i −0.874080 0.485782i \(-0.838535\pi\)
0.0163405 0.999866i \(-0.494798\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.738550 + 1.27921i −0.0556703 + 0.0964238i
\(177\) 0 0
\(178\) 4.43818 + 7.68715i 0.332656 + 0.576176i
\(179\) 0.333792 0.0249488 0.0124744 0.999922i \(-0.496029\pi\)
0.0124744 + 0.999922i \(0.496029\pi\)
\(180\) 0 0
\(181\) −23.2422 −1.72758 −0.863789 0.503853i \(-0.831915\pi\)
−0.863789 + 0.503853i \(0.831915\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.14400 + 5.44556i −0.231778 + 0.401452i
\(185\) −5.13781 + 8.89894i −0.377739 + 0.654263i
\(186\) 0 0
\(187\) 4.85669 + 8.41204i 0.355157 + 0.615149i
\(188\) −6.98762 −0.509625
\(189\) 0 0
\(190\) 3.28799 0.238536
\(191\) −8.16071 14.1348i −0.590488 1.02276i −0.994167 0.107854i \(-0.965602\pi\)
0.403679 0.914901i \(-0.367731\pi\)
\(192\) 0 0
\(193\) 7.16071 12.4027i 0.515439 0.892766i −0.484400 0.874846i \(-0.660962\pi\)
0.999839 0.0179200i \(-0.00570443\pi\)
\(194\) −6.58836 + 11.4114i −0.473017 + 0.819289i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.42402 −0.172704 −0.0863520 0.996265i \(-0.527521\pi\)
−0.0863520 + 0.996265i \(0.527521\pi\)
\(198\) 0 0
\(199\) −6.11126 −0.433216 −0.216608 0.976259i \(-0.569499\pi\)
−0.216608 + 0.976259i \(0.569499\pi\)
\(200\) 4.34362 + 7.52338i 0.307141 + 0.531983i
\(201\) 0 0
\(202\) 2.62729 4.55059i 0.184855 0.320179i
\(203\) 0 0
\(204\) 0 0
\(205\) −7.60507 13.1724i −0.531161 0.919999i
\(206\) 1.66621 0.116090
\(207\) 0 0
\(208\) −2.69963 −0.187186
\(209\) 0.656376 + 1.13688i 0.0454025 + 0.0786394i
\(210\) 0 0
\(211\) 5.72253 9.91171i 0.393955 0.682350i −0.599012 0.800740i \(-0.704440\pi\)
0.992967 + 0.118390i \(0.0377732\pi\)
\(212\) 1.60507 2.78007i 0.110237 0.190936i
\(213\) 0 0
\(214\) −5.38255 9.32284i −0.367943 0.637296i
\(215\) −0.0458003 −0.00312356
\(216\) 0 0
\(217\) 0 0
\(218\) 0.0945538 + 0.163772i 0.00640399 + 0.0110920i
\(219\) 0 0
\(220\) −2.73236 + 4.73259i −0.184216 + 0.319071i
\(221\) −8.87636 + 15.3743i −0.597088 + 1.03419i
\(222\) 0 0
\(223\) 3.61126 + 6.25489i 0.241828 + 0.418859i 0.961235 0.275730i \(-0.0889196\pi\)
−0.719407 + 0.694589i \(0.755586\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 13.5636 0.902238
\(227\) −6.82760 11.8258i −0.453164 0.784903i 0.545417 0.838165i \(-0.316371\pi\)
−0.998581 + 0.0532622i \(0.983038\pi\)
\(228\) 0 0
\(229\) 8.68725 15.0468i 0.574070 0.994318i −0.422073 0.906562i \(-0.638697\pi\)
0.996142 0.0877555i \(-0.0279694\pi\)
\(230\) −11.6316 + 20.1466i −0.766966 + 1.32842i
\(231\) 0 0
\(232\) 1.25526 + 2.17417i 0.0824119 + 0.142742i
\(233\) 15.2422 0.998549 0.499275 0.866444i \(-0.333600\pi\)
0.499275 + 0.866444i \(0.333600\pi\)
\(234\) 0 0
\(235\) −25.8516 −1.68637
\(236\) −3.45489 5.98404i −0.224894 0.389528i
\(237\) 0 0
\(238\) 0 0
\(239\) −9.47524 + 16.4116i −0.612902 + 1.06158i 0.377846 + 0.925868i \(0.376665\pi\)
−0.990749 + 0.135710i \(0.956669\pi\)
\(240\) 0 0
\(241\) −12.2527 21.2223i −0.789267 1.36705i −0.926417 0.376500i \(-0.877128\pi\)
0.137150 0.990550i \(-0.456206\pi\)
\(242\) 8.81818 0.566854
\(243\) 0 0
\(244\) 5.73305 0.367021
\(245\) 0 0
\(246\) 0 0
\(247\) −1.19963 + 2.07782i −0.0763305 + 0.132208i
\(248\) −3.40545 + 5.89841i −0.216246 + 0.374549i
\(249\) 0 0
\(250\) 6.82072 + 11.8138i 0.431380 + 0.747173i
\(251\) −12.1236 −0.765238 −0.382619 0.923906i \(-0.624978\pi\)
−0.382619 + 0.923906i \(0.624978\pi\)
\(252\) 0 0
\(253\) −9.28799 −0.583931
\(254\) −1.42835 2.47397i −0.0896224 0.155231i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.10439 7.10900i 0.256025 0.443448i −0.709149 0.705059i \(-0.750921\pi\)
0.965173 + 0.261611i \(0.0842539\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −9.98762 −0.619406
\(261\) 0 0
\(262\) −0.155687 −0.00961838
\(263\) −2.67309 4.62992i −0.164830 0.285493i 0.771765 0.635908i \(-0.219374\pi\)
−0.936595 + 0.350414i \(0.886041\pi\)
\(264\) 0 0
\(265\) 5.93818 10.2852i 0.364779 0.631816i
\(266\) 0 0
\(267\) 0 0
\(268\) 4.73236 + 8.19669i 0.289075 + 0.500692i
\(269\) −18.4844 −1.12701 −0.563506 0.826112i \(-0.690548\pi\)
−0.563506 + 0.826112i \(0.690548\pi\)
\(270\) 0 0
\(271\) −7.35483 −0.446774 −0.223387 0.974730i \(-0.571711\pi\)
−0.223387 + 0.974730i \(0.571711\pi\)
\(272\) 3.28799 + 5.69497i 0.199364 + 0.345308i
\(273\) 0 0
\(274\) 1.70582 2.95456i 0.103052 0.178492i
\(275\) −6.41597 + 11.1128i −0.386897 + 0.670126i
\(276\) 0 0
\(277\) 4.54944 + 7.87987i 0.273349 + 0.473455i 0.969717 0.244230i \(-0.0785351\pi\)
−0.696368 + 0.717685i \(0.745202\pi\)
\(278\) 13.5105 0.810307
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00433 10.3998i −0.358188 0.620400i 0.629470 0.777025i \(-0.283272\pi\)
−0.987658 + 0.156624i \(0.949939\pi\)
\(282\) 0 0
\(283\) 4.92147 8.52423i 0.292551 0.506713i −0.681861 0.731481i \(-0.738829\pi\)
0.974412 + 0.224768i \(0.0721626\pi\)
\(284\) −2.73236 + 4.73259i −0.162136 + 0.280827i
\(285\) 0 0
\(286\) −1.99381 3.45338i −0.117896 0.204203i
\(287\) 0 0
\(288\) 0 0
\(289\) 26.2436 1.54374
\(290\) 4.64400 + 8.04364i 0.272705 + 0.472339i
\(291\) 0 0
\(292\) 6.03273 10.4490i 0.353039 0.611481i
\(293\) 10.7101 18.5505i 0.625694 1.08373i −0.362713 0.931901i \(-0.618149\pi\)
0.988406 0.151832i \(-0.0485173\pi\)
\(294\) 0 0
\(295\) −12.7818 22.1387i −0.744185 1.28897i
\(296\) −2.77747 −0.161437
\(297\) 0 0
\(298\) 0.333792 0.0193361
\(299\) −8.48762 14.7010i −0.490852 0.850180i
\(300\) 0 0
\(301\) 0 0
\(302\) −9.95489 + 17.2424i −0.572839 + 0.992187i
\(303\) 0 0
\(304\) 0.444368 + 0.769668i 0.0254862 + 0.0441435i
\(305\) 21.2101 1.21449
\(306\) 0 0
\(307\) 5.68725 0.324588 0.162294 0.986742i \(-0.448111\pi\)
0.162294 + 0.986742i \(0.448111\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −12.5989 + 21.8219i −0.715569 + 1.23940i
\(311\) 5.86033 10.1504i 0.332309 0.575576i −0.650655 0.759373i \(-0.725506\pi\)
0.982964 + 0.183797i \(0.0588390\pi\)
\(312\) 0 0
\(313\) −13.3869 23.1868i −0.756671 1.31059i −0.944539 0.328398i \(-0.893491\pi\)
0.187868 0.982194i \(-0.439842\pi\)
\(314\) −6.96286 −0.392937
\(315\) 0 0
\(316\) 11.4523 0.644244
\(317\) 0.951246 + 1.64761i 0.0534273 + 0.0925388i 0.891502 0.453016i \(-0.149652\pi\)
−0.838075 + 0.545555i \(0.816319\pi\)
\(318\) 0 0
\(319\) −1.85414 + 3.21147i −0.103812 + 0.179808i
\(320\) −1.84981 + 3.20397i −0.103408 + 0.179107i
\(321\) 0 0
\(322\) 0 0
\(323\) 5.84431 0.325186
\(324\) 0 0
\(325\) −23.4523 −1.30090
\(326\) −4.03706 6.99240i −0.223592 0.387273i
\(327\) 0 0
\(328\) 2.05563 3.56046i 0.113503 0.196593i
\(329\) 0 0
\(330\) 0 0
\(331\) −2.78366 4.82144i −0.153004 0.265010i 0.779327 0.626618i \(-0.215561\pi\)
−0.932330 + 0.361608i \(0.882228\pi\)
\(332\) −4.47710 −0.245713
\(333\) 0 0
\(334\) 19.4858 1.06621
\(335\) 17.5080 + 30.3247i 0.956563 + 1.65682i
\(336\) 0 0
\(337\) −16.8869 + 29.2489i −0.919887 + 1.59329i −0.120302 + 0.992737i \(0.538386\pi\)
−0.799585 + 0.600553i \(0.794947\pi\)
\(338\) −2.85600 + 4.94674i −0.155346 + 0.269067i
\(339\) 0 0
\(340\) 12.1643 + 21.0693i 0.659704 + 1.14264i
\(341\) −10.0604 −0.544799
\(342\) 0 0
\(343\) 0 0
\(344\) −0.00618986 0.0107211i −0.000333735 0.000578045i
\(345\) 0 0
\(346\) 11.2818 19.5407i 0.606513 1.05051i
\(347\) −15.2033 + 26.3328i −0.816154 + 1.41362i 0.0923418 + 0.995727i \(0.470565\pi\)
−0.908496 + 0.417893i \(0.862769\pi\)
\(348\) 0 0
\(349\) 6.29782 + 10.9082i 0.337115 + 0.583900i 0.983889 0.178782i \(-0.0572156\pi\)
−0.646774 + 0.762682i \(0.723882\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.47710 −0.0787297
\(353\) 3.76578 + 6.52252i 0.200432 + 0.347159i 0.948668 0.316274i \(-0.102432\pi\)
−0.748235 + 0.663433i \(0.769099\pi\)
\(354\) 0 0
\(355\) −10.1087 + 17.5088i −0.536515 + 0.929271i
\(356\) −4.43818 + 7.68715i −0.235223 + 0.407418i
\(357\) 0 0
\(358\) 0.166896 + 0.289073i 0.00882074 + 0.0152780i
\(359\) −6.89602 −0.363958 −0.181979 0.983302i \(-0.558250\pi\)
−0.181979 + 0.983302i \(0.558250\pi\)
\(360\) 0 0
\(361\) −18.2101 −0.958429
\(362\) −11.6211 20.1283i −0.610791 1.05792i
\(363\) 0 0
\(364\) 0 0
\(365\) 22.3189 38.6574i 1.16822 2.02342i
\(366\) 0 0
\(367\) 11.5618 + 20.0257i 0.603522 + 1.04533i 0.992283 + 0.123992i \(0.0395699\pi\)
−0.388761 + 0.921339i \(0.627097\pi\)
\(368\) −6.28799 −0.327784
\(369\) 0 0
\(370\) −10.2756 −0.534204
\(371\) 0 0
\(372\) 0 0
\(373\) −14.5822 + 25.2571i −0.755036 + 1.30776i 0.190320 + 0.981722i \(0.439047\pi\)
−0.945356 + 0.326039i \(0.894286\pi\)
\(374\) −4.85669 + 8.41204i −0.251134 + 0.434976i
\(375\) 0 0
\(376\) −3.49381 6.05146i −0.180180 0.312080i
\(377\) −6.77747 −0.349058
\(378\) 0 0
\(379\) −13.5622 −0.696645 −0.348322 0.937375i \(-0.613249\pi\)
−0.348322 + 0.937375i \(0.613249\pi\)
\(380\) 1.64400 + 2.84748i 0.0843352 + 0.146073i
\(381\) 0 0
\(382\) 8.16071 14.1348i 0.417538 0.723197i
\(383\) 1.41783 2.45575i 0.0724475 0.125483i −0.827526 0.561428i \(-0.810252\pi\)
0.899973 + 0.435945i \(0.143586\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.3214 0.728941
\(387\) 0 0
\(388\) −13.1767 −0.668947
\(389\) −9.30401 16.1150i −0.471732 0.817064i 0.527745 0.849403i \(-0.323038\pi\)
−0.999477 + 0.0323388i \(0.989704\pi\)
\(390\) 0 0
\(391\) −20.6749 + 35.8099i −1.04557 + 1.81099i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.21201 2.09926i −0.0610601 0.105759i
\(395\) 42.3694 2.13184
\(396\) 0 0
\(397\) −20.5760 −1.03268 −0.516340 0.856384i \(-0.672706\pi\)
−0.516340 + 0.856384i \(0.672706\pi\)
\(398\) −3.05563 5.29251i −0.153165 0.265290i
\(399\) 0 0
\(400\) −4.34362 + 7.52338i −0.217181 + 0.376169i
\(401\) −3.37704 + 5.84921i −0.168642 + 0.292096i −0.937942 0.346791i \(-0.887271\pi\)
0.769301 + 0.638887i \(0.220605\pi\)
\(402\) 0 0
\(403\) −9.19344 15.9235i −0.457958 0.793206i
\(404\) 5.25457 0.261425
\(405\) 0 0
\(406\) 0 0
\(407\) −2.05130 3.55296i −0.101679 0.176114i
\(408\) 0 0
\(409\) 7.66071 13.2687i 0.378798 0.656097i −0.612090 0.790788i \(-0.709671\pi\)
0.990888 + 0.134691i \(0.0430043\pi\)
\(410\) 7.60507 13.1724i 0.375588 0.650537i
\(411\) 0 0
\(412\) 0.833104 + 1.44298i 0.0410441 + 0.0710904i
\(413\) 0 0
\(414\) 0 0
\(415\) −16.5636 −0.813075
\(416\) −1.34981 2.33795i −0.0661801 0.114627i
\(417\) 0 0
\(418\) −0.656376 + 1.13688i −0.0321044 + 0.0556064i
\(419\) −4.32141 + 7.48491i −0.211115 + 0.365662i −0.952064 0.305900i \(-0.901043\pi\)
0.740949 + 0.671561i \(0.234376\pi\)
\(420\) 0 0
\(421\) 18.5636 + 32.1531i 0.904735 + 1.56705i 0.821273 + 0.570536i \(0.193264\pi\)
0.0834618 + 0.996511i \(0.473402\pi\)
\(422\) 11.4451 0.557137
\(423\) 0 0
\(424\) 3.21015 0.155899
\(425\) 28.5636 + 49.4736i 1.38554 + 2.39982i
\(426\) 0 0
\(427\) 0 0
\(428\) 5.38255 9.32284i 0.260175 0.450637i
\(429\) 0 0
\(430\) −0.0229002 0.0396643i −0.00110434 0.00191278i
\(431\) −9.42030 −0.453760 −0.226880 0.973923i \(-0.572852\pi\)
−0.226880 + 0.973923i \(0.572852\pi\)
\(432\) 0 0
\(433\) 0.208771 0.0100329 0.00501645 0.999987i \(-0.498403\pi\)
0.00501645 + 0.999987i \(0.498403\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.0945538 + 0.163772i −0.00452831 + 0.00784326i
\(437\) −2.79418 + 4.83967i −0.133664 + 0.231513i
\(438\) 0 0
\(439\) −4.98398 8.63250i −0.237872 0.412007i 0.722231 0.691652i \(-0.243117\pi\)
−0.960104 + 0.279645i \(0.909783\pi\)
\(440\) −5.46472 −0.260520
\(441\) 0 0
\(442\) −17.7527 −0.844410
\(443\) −7.84981 13.5963i −0.372956 0.645979i 0.617063 0.786914i \(-0.288322\pi\)
−0.990019 + 0.140935i \(0.954989\pi\)
\(444\) 0 0
\(445\) −16.4196 + 28.4396i −0.778364 + 1.34817i
\(446\) −3.61126 + 6.25489i −0.170998 + 0.296178i
\(447\) 0 0
\(448\) 0 0
\(449\) −33.6253 −1.58688 −0.793439 0.608650i \(-0.791712\pi\)
−0.793439 + 0.608650i \(0.791712\pi\)
\(450\) 0 0
\(451\) 6.07275 0.285955
\(452\) 6.78180 + 11.7464i 0.318989 + 0.552505i
\(453\) 0 0
\(454\) 6.82760 11.8258i 0.320435 0.555010i
\(455\) 0 0
\(456\) 0 0
\(457\) −16.3541 28.3262i −0.765015 1.32504i −0.940239 0.340516i \(-0.889398\pi\)
0.175224 0.984529i \(-0.443935\pi\)
\(458\) 17.3745 0.811857
\(459\) 0 0
\(460\) −23.2632 −1.08465
\(461\) −2.07165 3.58821i −0.0964865 0.167120i 0.813742 0.581227i \(-0.197427\pi\)
−0.910228 + 0.414107i \(0.864094\pi\)
\(462\) 0 0
\(463\) −8.34176 + 14.4484i −0.387675 + 0.671472i −0.992136 0.125162i \(-0.960055\pi\)
0.604462 + 0.796634i \(0.293388\pi\)
\(464\) −1.25526 + 2.17417i −0.0582740 + 0.100934i
\(465\) 0 0
\(466\) 7.62110 + 13.2001i 0.353040 + 0.611484i
\(467\) −29.9171 −1.38440 −0.692198 0.721707i \(-0.743358\pi\)
−0.692198 + 0.721707i \(0.743358\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −12.9258 22.3881i −0.596223 1.03269i
\(471\) 0 0
\(472\) 3.45489 5.98404i 0.159024 0.275438i
\(473\) 0.00914304 0.0158362i 0.000420397 0.000728149i
\(474\) 0 0
\(475\) 3.86033 + 6.68630i 0.177124 + 0.306788i
\(476\) 0 0
\(477\) 0 0
\(478\) −18.9505 −0.866775
\(479\) 1.47965 + 2.56283i 0.0676068 + 0.117098i 0.897847 0.440307i \(-0.145130\pi\)
−0.830241 + 0.557405i \(0.811797\pi\)
\(480\) 0 0
\(481\) 3.74907 6.49358i 0.170943 0.296082i
\(482\) 12.2527 21.2223i 0.558096 0.966650i
\(483\) 0 0
\(484\) 4.40909 + 7.63676i 0.200413 + 0.347126i
\(485\) −48.7490 −2.21358
\(486\) 0 0
\(487\) 28.0617 1.27160 0.635800 0.771854i \(-0.280671\pi\)
0.635800 + 0.771854i \(0.280671\pi\)
\(488\) 2.86652 + 4.96497i 0.129761 + 0.224753i
\(489\) 0 0
\(490\) 0 0
\(491\) −17.0734 + 29.5721i −0.770513 + 1.33457i 0.166769 + 0.985996i \(0.446667\pi\)
−0.937282 + 0.348572i \(0.886667\pi\)
\(492\) 0 0
\(493\) 8.25457 + 14.2973i 0.371767 + 0.643920i
\(494\) −2.39926 −0.107948
\(495\) 0 0
\(496\) −6.81089 −0.305818
\(497\) 0 0
\(498\) 0 0
\(499\) 1.14035 1.97515i 0.0510493 0.0884199i −0.839372 0.543558i \(-0.817077\pi\)
0.890421 + 0.455138i \(0.150410\pi\)
\(500\) −6.82072 + 11.8138i −0.305032 + 0.528331i
\(501\) 0 0
\(502\) −6.06182 10.4994i −0.270552 0.468610i
\(503\) 13.9890 0.623739 0.311869 0.950125i \(-0.399045\pi\)
0.311869 + 0.950125i \(0.399045\pi\)
\(504\) 0 0
\(505\) 19.4400 0.865067
\(506\) −4.64400 8.04364i −0.206451 0.357583i
\(507\) 0 0
\(508\) 1.42835 2.47397i 0.0633726 0.109765i
\(509\) −12.8090 + 22.1859i −0.567750 + 0.983373i 0.429038 + 0.903287i \(0.358853\pi\)
−0.996788 + 0.0800859i \(0.974481\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 8.20877 0.362073
\(515\) 3.08217 + 5.33848i 0.135817 + 0.235242i
\(516\) 0 0
\(517\) 5.16071 8.93861i 0.226968 0.393119i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.99381 8.64953i −0.218993 0.379307i
\(521\) 41.8255 1.83241 0.916203 0.400714i \(-0.131238\pi\)
0.916203 + 0.400714i \(0.131238\pi\)
\(522\) 0 0
\(523\) 15.7665 0.689420 0.344710 0.938709i \(-0.387977\pi\)
0.344710 + 0.938709i \(0.387977\pi\)
\(524\) −0.0778435 0.134829i −0.00340061 0.00589003i
\(525\) 0 0
\(526\) 2.67309 4.62992i 0.116552 0.201874i
\(527\) −22.3942 + 38.7878i −0.975505 + 1.68962i
\(528\) 0 0
\(529\) −8.26942 14.3231i −0.359540 0.622742i
\(530\) 11.8764 0.515876
\(531\) 0 0
\(532\) 0 0
\(533\) 5.54944 + 9.61192i 0.240373 + 0.416338i
\(534\) 0 0
\(535\) 19.9134 34.4911i 0.860932 1.49118i
\(536\) −4.73236 + 8.19669i −0.204407 + 0.354043i
\(537\) 0 0
\(538\) −9.24219 16.0079i −0.398459 0.690152i
\(539\) 0 0
\(540\) 0 0
\(541\) 42.1927 1.81400 0.907002 0.421126i \(-0.138365\pi\)
0.907002 + 0.421126i \(0.138365\pi\)
\(542\) −3.67742 6.36947i −0.157959 0.273592i
\(543\) 0 0
\(544\) −3.28799 + 5.69497i −0.140971 + 0.244170i
\(545\) −0.349814 + 0.605896i −0.0149844 + 0.0259537i
\(546\) 0 0
\(547\) 20.3356 + 35.2222i 0.869486 + 1.50599i 0.862522 + 0.506019i \(0.168883\pi\)
0.00696400 + 0.999976i \(0.497783\pi\)
\(548\) 3.41164 0.145738
\(549\) 0 0
\(550\) −12.8319 −0.547155
\(551\) 1.11559 + 1.93227i 0.0475259 + 0.0823173i
\(552\) 0 0
\(553\) 0 0
\(554\) −4.54944 + 7.87987i −0.193287 + 0.334783i
\(555\) 0 0
\(556\) 6.75526 + 11.7005i 0.286487 + 0.496210i
\(557\) 13.3759 0.566754 0.283377 0.959009i \(-0.408545\pi\)
0.283377 + 0.959009i \(0.408545\pi\)
\(558\) 0 0
\(559\) 0.0334206 0.00141354
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00433 10.3998i 0.253277 0.438689i
\(563\) 16.3807 28.3722i 0.690364 1.19574i −0.281355 0.959604i \(-0.590784\pi\)
0.971719 0.236141i \(-0.0758828\pi\)
\(564\) 0 0
\(565\) 25.0901 + 43.4574i 1.05555 + 1.82827i
\(566\) 9.84294 0.413729
\(567\) 0 0
\(568\) −5.46472 −0.229295
\(569\) −8.36398 14.4868i −0.350636 0.607320i 0.635725 0.771916i \(-0.280701\pi\)
−0.986361 + 0.164596i \(0.947368\pi\)
\(570\) 0 0
\(571\) 13.7367 23.7926i 0.574863 0.995691i −0.421194 0.906971i \(-0.638389\pi\)
0.996057 0.0887207i \(-0.0282778\pi\)
\(572\) 1.99381 3.45338i 0.0833654 0.144393i
\(573\) 0 0
\(574\) 0 0
\(575\) −54.6253 −2.27803
\(576\) 0 0
\(577\) 2.83427 0.117992 0.0589962 0.998258i \(-0.481210\pi\)
0.0589962 + 0.998258i \(0.481210\pi\)
\(578\) 13.1218 + 22.7276i 0.545794 + 0.945343i
\(579\) 0 0
\(580\) −4.64400 + 8.04364i −0.192831 + 0.333994i
\(581\) 0 0
\(582\) 0 0
\(583\) 2.37085 + 4.10644i 0.0981908 + 0.170071i
\(584\) 12.0655 0.499272
\(585\) 0 0
\(586\) 21.4203 0.884864
\(587\) −2.34795 4.06678i −0.0969105 0.167854i 0.813494 0.581573i \(-0.197563\pi\)
−0.910404 + 0.413720i \(0.864229\pi\)
\(588\) 0 0
\(589\) −3.02654 + 5.24212i −0.124706 + 0.215998i
\(590\) 12.7818 22.1387i 0.526218 0.911437i
\(591\) 0 0
\(592\) −1.38874 2.40536i −0.0570767 0.0988597i
\(593\) −1.27205 −0.0522367 −0.0261184 0.999659i \(-0.508315\pi\)
−0.0261184 + 0.999659i \(0.508315\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.166896 + 0.289073i 0.00683634 + 0.0118409i
\(597\) 0 0
\(598\) 8.48762 14.7010i 0.347085 0.601168i
\(599\) 21.9258 37.9766i 0.895864 1.55168i 0.0631320 0.998005i \(-0.479891\pi\)
0.832732 0.553676i \(-0.186776\pi\)
\(600\) 0 0
\(601\) 6.71634 + 11.6330i 0.273965 + 0.474522i 0.969874 0.243609i \(-0.0783314\pi\)
−0.695908 + 0.718131i \(0.744998\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −19.9098 −0.810117
\(605\) 16.3120 + 28.2532i 0.663177 + 1.14866i
\(606\) 0 0
\(607\) −2.29232 + 3.97042i −0.0930425 + 0.161154i −0.908790 0.417254i \(-0.862993\pi\)
0.815747 + 0.578408i \(0.196326\pi\)
\(608\) −0.444368 + 0.769668i −0.0180215 + 0.0312142i
\(609\) 0 0
\(610\) 10.6051 + 18.3685i 0.429387 + 0.743720i
\(611\) 18.8640 0.763155
\(612\) 0 0
\(613\) 22.1075 0.892915 0.446458 0.894805i \(-0.352685\pi\)
0.446458 + 0.894805i \(0.352685\pi\)
\(614\) 2.84362 + 4.92530i 0.114759 + 0.198769i
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00433 + 10.3998i −0.241725 + 0.418680i −0.961206 0.275832i \(-0.911047\pi\)
0.719481 + 0.694513i \(0.244380\pi\)
\(618\) 0 0
\(619\) −8.78180 15.2105i −0.352970 0.611363i 0.633798 0.773499i \(-0.281495\pi\)
−0.986768 + 0.162136i \(0.948162\pi\)
\(620\) −25.1978 −1.01197
\(621\) 0 0
\(622\) 11.7207 0.469956
\(623\) 0 0
\(624\) 0 0
\(625\) −3.51602 + 6.08993i −0.140641 + 0.243597i
\(626\) 13.3869 23.1868i 0.535047 0.926729i
\(627\) 0 0
\(628\) −3.48143 6.03001i −0.138924 0.240624i
\(629\) −18.2646 −0.728258
\(630\) 0 0
\(631\) −44.9381 −1.78896 −0.894479 0.447110i \(-0.852453\pi\)
−0.894479 + 0.447110i \(0.852453\pi\)
\(632\) 5.72617 + 9.91802i 0.227775 + 0.394518i
\(633\) 0 0
\(634\) −0.951246 + 1.64761i −0.0377788 + 0.0654348i
\(635\) 5.28435 9.15276i 0.209703 0.363216i
\(636\) 0 0
\(637\) 0 0
\(638\) −3.70829 −0.146813
\(639\) 0 0
\(640\) −3.69963 −0.146241
\(641\) −14.4920 25.1008i −0.572398 0.991422i −0.996319 0.0857228i \(-0.972680\pi\)
0.423921 0.905699i \(-0.360653\pi\)
\(642\) 0 0
\(643\) −6.03087 + 10.4458i −0.237834 + 0.411941i −0.960093 0.279682i \(-0.909771\pi\)
0.722258 + 0.691623i \(0.243104\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.92216 + 5.06132i 0.114971 + 0.199135i
\(647\) −37.7651 −1.48470 −0.742349 0.670013i \(-0.766289\pi\)
−0.742349 + 0.670013i \(0.766289\pi\)
\(648\) 0 0
\(649\) 10.2064 0.400637
\(650\) −11.7262 20.3103i −0.459938 0.796636i
\(651\) 0 0
\(652\) 4.03706 6.99240i 0.158104 0.273843i
\(653\) 18.7040 32.3962i 0.731942 1.26776i −0.224109 0.974564i \(-0.571947\pi\)
0.956052 0.293198i \(-0.0947194\pi\)
\(654\) 0 0
\(655\) −0.287992 0.498817i −0.0112528 0.0194904i
\(656\) 4.11126 0.160518
\(657\) 0 0
\(658\) 0 0
\(659\) −14.9356 25.8693i −0.581810 1.00772i −0.995265 0.0971993i \(-0.969012\pi\)
0.413455 0.910524i \(-0.364322\pi\)
\(660\) 0 0
\(661\) 2.80401 4.85669i 0.109063 0.188904i −0.806328 0.591469i \(-0.798548\pi\)
0.915391 + 0.402566i \(0.131881\pi\)
\(662\) 2.78366 4.82144i 0.108190 0.187391i
\(663\) 0 0
\(664\) −2.23855 3.87728i −0.0868726 0.150468i
\(665\) 0 0
\(666\) 0 0
\(667\) −15.7861 −0.611242
\(668\) 9.74288 + 16.8752i 0.376963 + 0.652920i
\(669\) 0 0
\(670\) −17.5080 + 30.3247i −0.676392 + 1.17155i
\(671\) −4.23414 + 7.33375i −0.163457 + 0.283116i
\(672\) 0 0
\(673\) −4.72253 8.17966i −0.182040 0.315303i 0.760535 0.649297i \(-0.224937\pi\)
−0.942575 + 0.333994i \(0.891603\pi\)
\(674\) −33.7738 −1.30092
\(675\) 0 0
\(676\) −5.71201 −0.219693
\(677\) −5.53087 9.57975i −0.212569 0.368180i 0.739949 0.672663i \(-0.234850\pi\)
−0.952518 + 0.304483i \(0.901516\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −12.1643 + 21.0693i −0.466481 + 0.807970i
\(681\) 0 0
\(682\) −5.03018 8.71253i −0.192616 0.333620i
\(683\) −8.83922 −0.338223 −0.169112 0.985597i \(-0.554090\pi\)
−0.169112 + 0.985597i \(0.554090\pi\)
\(684\) 0 0
\(685\) 12.6218 0.482254
\(686\) 0 0
\(687\) 0 0
\(688\) 0.00618986 0.0107211i 0.000235986 0.000408740i
\(689\) −4.33310 + 7.50516i −0.165078 + 0.285924i
\(690\) 0 0
\(691\) 12.5309 + 21.7041i 0.476697 + 0.825663i 0.999643 0.0267023i \(-0.00850061\pi\)
−0.522947 + 0.852365i \(0.675167\pi\)
\(692\) 22.5636 0.857740
\(693\) 0 0
\(694\) −30.4065 −1.15422
\(695\) 24.9920 + 43.2873i 0.947999 + 1.64198i
\(696\) 0 0
\(697\) 13.5178 23.4135i 0.512023 0.886850i
\(698\) −6.29782 + 10.9082i −0.238376 + 0.412880i
\(699\) 0 0
\(700\) 0 0
\(701\) 43.4858 1.64243 0.821217 0.570616i \(-0.193295\pi\)
0.821217 + 0.570616i \(0.193295\pi\)
\(702\) 0 0
\(703\) −2.46844 −0.0930989
\(704\) −0.738550 1.27921i −0.0278351 0.0482119i
\(705\) 0 0
\(706\) −3.76578 + 6.52252i −0.141727 + 0.245478i
\(707\) 0 0
\(708\) 0 0
\(709\) 11.3702 + 19.6937i 0.427016 + 0.739613i 0.996606 0.0823158i \(-0.0262316\pi\)
−0.569591 + 0.821928i \(0.692898\pi\)
\(710\) −20.2174 −0.758747
\(711\) 0 0
\(712\) −8.87636 −0.332656
\(713\) −21.4134 37.0891i −0.801939 1.38900i
\(714\) 0 0
\(715\) 7.37636 12.7762i 0.275860 0.477804i
\(716\) −0.166896 + 0.289073i −0.00623721 + 0.0108032i
\(717\) 0 0
\(718\) −3.44801 5.97213i −0.128679 0.222878i
\(719\) −12.1236 −0.452136 −0.226068 0.974112i \(-0.572587\pi\)
−0.226068 + 0.974112i \(0.572587\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.10507 15.7705i −0.338856 0.586915i
\(723\) 0 0
\(724\) 11.6211 20.1283i 0.431895 0.748063i
\(725\) −10.9048 + 18.8876i −0.404993 + 0.701468i
\(726\) 0 0
\(727\) −23.0908 39.9945i −0.856392 1.48331i −0.875348 0.483494i \(-0.839368\pi\)
0.0189562 0.999820i \(-0.493966\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 44.6377 1.65212
\(731\) −0.0407044 0.0705021i −0.00150551 0.00260761i
\(732\) 0 0
\(733\) −18.0149 + 31.2026i −0.665394 + 1.15250i 0.313785 + 0.949494i \(0.398403\pi\)
−0.979178 + 0.203002i \(0.934930\pi\)
\(734\) −11.5618 + 20.0257i −0.426755 + 0.739161i
\(735\) 0 0
\(736\) −3.14400 5.44556i −0.115889 0.200726i
\(737\) −13.9803 −0.514972
\(738\) 0 0
\(739\) −46.4239 −1.70773 −0.853865 0.520495i \(-0.825747\pi\)
−0.853865 + 0.520495i \(0.825747\pi\)
\(740\) −5.13781 8.89894i −0.188870 0.327132i
\(741\) 0 0
\(742\) 0 0
\(743\) −0.598884 + 1.03730i −0.0219709 + 0.0380548i −0.876802 0.480852i \(-0.840327\pi\)
0.854831 + 0.518907i \(0.173661\pi\)
\(744\) 0 0
\(745\) 0.617454 + 1.06946i 0.0226218 + 0.0391820i
\(746\) −29.1643 −1.06778
\(747\) 0 0
\(748\) −9.71339 −0.355157
\(749\) 0 0
\(750\) 0 0
\(751\) −24.0600 + 41.6731i −0.877961 + 1.52067i −0.0243853 + 0.999703i \(0.507763\pi\)
−0.853575 + 0.520970i \(0.825570\pi\)
\(752\) 3.49381 6.05146i 0.127406 0.220674i
\(753\) 0 0
\(754\) −3.38874 5.86946i −0.123410 0.213753i
\(755\) −73.6588 −2.68072
\(756\) 0 0
\(757\) 49.6006 1.80276 0.901382 0.433025i \(-0.142554\pi\)
0.901382 + 0.433025i \(0.142554\pi\)
\(758\) −6.78111 11.7452i −0.246301 0.426606i
\(759\) 0 0
\(760\) −1.64400 + 2.84748i −0.0596340 + 0.103289i
\(761\) 18.7701 32.5108i 0.680416 1.17852i −0.294438 0.955671i \(-0.595132\pi\)
0.974854 0.222845i \(-0.0715342\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 16.3214 0.590488
\(765\) 0 0
\(766\) 2.83565 0.102456
\(767\) 9.32691 + 16.1547i 0.336775 + 0.583312i
\(768\) 0 0
\(769\) 13.4592 23.3121i 0.485352 0.840654i −0.514506 0.857486i \(-0.672025\pi\)
0.999858 + 0.0168324i \(0.00535818\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7.16071 + 12.4027i 0.257719 + 0.446383i
\(773\) −50.2261 −1.80651 −0.903254 0.429107i \(-0.858828\pi\)
−0.903254 + 0.429107i \(0.858828\pi\)
\(774\) 0 0
\(775\) −59.1679 −2.12537
\(776\) −6.58836 11.4114i −0.236508 0.409645i
\(777\) 0 0
\(778\) 9.30401 16.1150i 0.333565 0.577752i
\(779\) 1.82691 3.16431i 0.0654560 0.113373i
\(780\) 0 0
\(781\) −4.03597 6.99050i −0.144418 0.250140i
\(782\) −41.3497 −1.47866
\(783\) 0 0
\(784\) 0 0
\(785\) −12.8800 22.3088i −0.459707 0.796236i
\(786\) 0 0
\(787\) −0.829462 + 1.43667i −0.0295671 + 0.0512118i −0.880430 0.474176i \(-0.842746\pi\)
0.850863 + 0.525387i \(0.176080\pi\)
\(788\) 1.21201 2.09926i 0.0431760 0.0747830i
\(789\) 0 0
\(790\) 21.1847 + 36.6930i 0.753718 + 1.30548i
\(791\) 0 0
\(792\) 0 0
\(793\) −15.4771 −0.549608
\(794\) −10.2880 17.8193i −0.365107 0.632384i
\(795\) 0 0
\(796\) 3.05563 5.29251i 0.108304 0.187588i
\(797\) −15.3702 + 26.6219i −0.544439 + 0.942996i 0.454203 + 0.890898i \(0.349924\pi\)
−0.998642 + 0.0520981i \(0.983409\pi\)
\(798\) 0 0
\(799\) −22.9752 39.7943i −0.812806 1.40782i
\(800\) −8.68725 −0.307141
\(801\) 0 0
\(802\) −6.75409 −0.238495
\(803\) 8.91095 + 15.4342i 0.314461 + 0.544662i
\(804\) 0 0
\(805\) 0 0
\(806\) 9.19344 15.9235i 0.323825 0.560881i
\(807\) 0 0
\(808\) 2.62729 + 4.55059i 0.0924276 + 0.160089i
\(809\) −2.88502 −0.101432 −0.0507159 0.998713i \(-0.516150\pi\)
−0.0507159 + 0.998713i \(0.516150\pi\)
\(810\) 0 0
\(811\) −28.5461 −1.00239 −0.501195 0.865334i \(-0.667106\pi\)
−0.501195 + 0.865334i \(0.667106\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 2.05130 3.55296i 0.0718981 0.124531i
\(815\) 14.9356 25.8693i 0.523172 0.906161i
\(816\) 0 0
\(817\) −0.00550115 0.00952827i −0.000192461 0.000333352i
\(818\) 15.3214 0.535701
\(819\) 0 0
\(820\) 15.2101 0.531161
\(821\) 3.98329 + 6.89926i 0.139018 + 0.240786i 0.927125 0.374752i \(-0.122272\pi\)
−0.788107 + 0.615538i \(0.788939\pi\)
\(822\) 0 0
\(823\) −20.2731 + 35.1140i −0.706675 + 1.22400i 0.259409 + 0.965768i \(0.416472\pi\)
−0.966084 + 0.258229i \(0.916861\pi\)
\(824\) −0.833104 + 1.44298i −0.0290225 + 0.0502685i
\(825\) 0 0
\(826\) 0 0
\(827\) −1.22115 −0.0424636 −0.0212318 0.999775i \(-0.506759\pi\)
−0.0212318 + 0.999775i \(0.506759\pi\)
\(828\) 0 0
\(829\) −14.1506 −0.491470 −0.245735 0.969337i \(-0.579029\pi\)
−0.245735 + 0.969337i \(0.579029\pi\)
\(830\) −8.28180 14.3445i −0.287466 0.497905i
\(831\) 0 0
\(832\) 1.34981 2.33795i 0.0467964 0.0810537i
\(833\) 0 0
\(834\) 0 0
\(835\) 36.0450 + 62.4318i 1.24739 + 2.16054i
\(836\) −1.31275 −0.0454025
\(837\) 0 0
\(838\) −8.64283 −0.298561
\(839\) 1.19599 + 2.07151i 0.0412900 + 0.0715164i 0.885932 0.463815i \(-0.153520\pi\)
−0.844642 + 0.535332i \(0.820187\pi\)
\(840\) 0 0
\(841\) 11.3486 19.6564i 0.391333 0.677808i
\(842\) −18.5636 + 32.1531i −0.639744 + 1.10807i
\(843\) 0 0
\(844\) 5.72253 + 9.91171i 0.196978 + 0.341175i
\(845\) −21.1323 −0.726973
\(846\) 0 0
\(847\) 0 0
\(848\) 1.60507 + 2.78007i 0.0551185 + 0.0954680i
\(849\) 0 0
\(850\) −28.5636 + 49.4736i −0.979724 + 1.69693i
\(851\) 8.73236 15.1249i 0.299341 0.518475i
\(852\) 0 0
\(853\) 8.33998 + 14.4453i 0.285556 + 0.494597i 0.972744 0.231883i \(-0.0744886\pi\)
−0.687188 + 0.726479i \(0.741155\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 10.7651 0.367943
\(857\) 6.92580 + 11.9958i 0.236581 + 0.409770i 0.959731 0.280921i \(-0.0906399\pi\)
−0.723150 + 0.690691i \(0.757307\pi\)
\(858\) 0 0
\(859\) 24.2472 41.9974i 0.827304 1.43293i −0.0728414 0.997344i \(-0.523207\pi\)
0.900146 0.435589i \(-0.143460\pi\)
\(860\) 0.0229002 0.0396643i 0.000780889 0.00135254i
\(861\) 0 0
\(862\) −4.71015 8.15822i −0.160428 0.277870i
\(863\) 5.93082 0.201887 0.100944 0.994892i \(-0.467814\pi\)
0.100944 + 0.994892i \(0.467814\pi\)
\(864\) 0 0
\(865\) 83.4769 2.83830
\(866\) 0.104386 + 0.180801i 0.00354717 + 0.00614387i
\(867\) 0 0
\(868\) 0 0
\(869\) −8.45813 + 14.6499i −0.286922 + 0.496964i
\(870\) 0 0
\(871\) −12.7756 22.1280i −0.432885 0.749779i
\(872\) −0.189108 −0.00640399
\(873\) 0 0
\(874\) −5.58836 −0.189029
\(875\) 0 0
\(876\) 0 0
\(877\) −1.96472 + 3.40300i −0.0663439 + 0.114911i −0.897289 0.441443i \(-0.854467\pi\)
0.830945 + 0.556354i \(0.187800\pi\)
\(878\) 4.98398 8.63250i 0.168201 0.291333i
\(879\) 0 0
\(880\) −2.73236 4.73259i −0.0921078 0.159535i
\(881\) 37.6552 1.26864 0.634318 0.773072i \(-0.281281\pi\)
0.634318 + 0.773072i \(0.281281\pi\)
\(882\) 0 0
\(883\) −53.2334 −1.79145 −0.895723 0.444613i \(-0.853341\pi\)
−0.895723 + 0.444613i \(0.853341\pi\)
\(884\) −8.87636 15.3743i −0.298544 0.517094i
\(885\) 0 0
\(886\) 7.84981 13.5963i 0.263720 0.456776i
\(887\) 18.4938 32.0322i 0.620961 1.07554i −0.368346 0.929689i \(-0.620076\pi\)
0.989307 0.145848i \(-0.0465910\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −32.8392 −1.10077
\(891\) 0 0
\(892\) −7.22253 −0.241828
\(893\) −3.10507 5.37815i −0.103907 0.179973i
\(894\) 0 0
\(895\) −0.617454 + 1.06946i −0.0206392 + 0.0357482i
\(896\) 0 0
\(897\) 0 0
\(898\) −16.8127 29.1204i −0.561046 0.971761i
\(899\) −17.0989 −0.570280
\(900\) 0 0
\(901\) 21.1099 0.703272
\(902\) 3.03637 + 5.25915i 0.101100 + 0.175111i
\(903\) 0 0
\(904\) −6.78180 + 11.7464i −0.225559 + 0.390680i
\(905\) 42.9937 74.4673i 1.42916 2.47538i
\(906\) 0 0
\(907\) 19.5080 + 33.7888i 0.647752 + 1.12194i 0.983659 + 0.180044i \(0.0576239\pi\)
−0.335907 + 0.941895i \(0.609043\pi\)
\(908\) 13.6552 0.453164
\(909\) 0 0
\(910\) 0 0
\(911\) 12.8090 + 22.1859i 0.424382 + 0.735052i 0.996363 0.0852158i \(-0.0271580\pi\)
−0.571980 + 0.820267i \(0.693825\pi\)
\(912\) 0 0
\(913\) 3.30656 5.72713i 0.109431 0.189540i
\(914\) 16.3541 28.3262i 0.540947 0.936948i
\(915\) 0 0
\(916\) 8.68725 + 15.0468i 0.287035 + 0.497159i
\(917\) 0 0
\(918\) 0 0
\(919\) −20.6735 −0.681956 −0.340978 0.940071i \(-0.610758\pi\)
−0.340978 + 0.940071i \(0.610758\pi\)
\(920\) −11.6316 20.1466i −0.383483 0.664212i
\(921\) 0 0
\(922\) 2.07165 3.58821i 0.0682263 0.118171i
\(923\) 7.37636 12.7762i 0.242796 0.420535i
\(924\) 0 0
\(925\) −12.0643 20.8960i −0.396672 0.687055i
\(926\) −16.6835 −0.548255
\(927\) 0 0
\(928\) −2.51052 −0.0824119
\(929\) 1.87017 + 3.23922i 0.0613582 + 0.106275i 0.895073 0.445920i \(-0.147123\pi\)
−0.833715 + 0.552196i \(0.813790\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −7.62110 + 13.2001i −0.249637 + 0.432384i
\(933\) 0 0
\(934\) −14.9585 25.9089i −0.489458 0.847766i
\(935\) −35.9359 −1.17523
\(936\) 0 0
\(937\) 27.1345 0.886445 0.443223 0.896412i \(-0.353835\pi\)
0.443223 + 0.896412i \(0.353835\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 12.9258 22.3881i 0.421593 0.730221i
\(941\) −3.16435 + 5.48081i −0.103155 + 0.178669i −0.912983 0.407998i \(-0.866227\pi\)
0.809828 + 0.586667i \(0.199560\pi\)
\(942\) 0 0
\(943\) 12.9258 + 22.3881i 0.420922 + 0.729058i
\(944\) 6.90978 0.224894
\(945\) 0 0
\(946\) 0.0182861 0.000594531
\(947\) 15.6396 + 27.0886i 0.508218 + 0.880260i 0.999955 + 0.00951587i \(0.00302904\pi\)
−0.491736 + 0.870744i \(0.663638\pi\)
\(948\) 0 0
\(949\) −16.2861 + 28.2084i −0.528670 + 0.915684i
\(950\) −3.86033 + 6.68630i −0.125246 + 0.216932i
\(951\) 0 0
\(952\) 0 0
\(953\) −4.28937 −0.138946 −0.0694732 0.997584i \(-0.522132\pi\)
−0.0694732 + 0.997584i \(0.522132\pi\)
\(954\) 0 0
\(955\) 60.3832 1.95395
\(956\) −9.47524 16.4116i −0.306451 0.530789i
\(957\) 0 0
\(958\) −1.47965 + 2.56283i −0.0478053 + 0.0828011i
\(959\) 0 0
\(960\) 0 0
\(961\) −7.69413 13.3266i −0.248198 0.429891i
\(962\) 7.49814 0.241750
\(963\) 0 0
\(964\) 24.5054 0.789267
\(965\) 26.4920 + 45.8854i 0.852806 + 1.47710i
\(966\) 0 0
\(967\) −7.59201 + 13.1497i −0.244142 + 0.422867i −0.961890 0.273436i \(-0.911840\pi\)
0.717748 + 0.696303i \(0.245173\pi\)
\(968\) −4.40909 + 7.63676i −0.141713 + 0.245455i
\(969\) 0 0
\(970\) −24.3745 42.2179i −0.782618 1.35553i
\(971\) −3.24729 −0.104210 −0.0521052 0.998642i \(-0.516593\pi\)
−0.0521052 + 0.998642i \(0.516593\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 14.0309 + 24.3022i 0.449578 + 0.778692i
\(975\) 0 0
\(976\) −2.86652 + 4.96497i −0.0917552 + 0.158925i
\(977\) 7.77197 13.4614i 0.248647 0.430670i −0.714503 0.699632i \(-0.753347\pi\)
0.963151 + 0.268962i \(0.0866806\pi\)
\(978\) 0 0
\(979\) −6.55563 11.3547i −0.209519 0.362897i
\(980\) 0 0
\(981\) 0 0
\(982\) −34.1469 −1.08967
\(983\) −6.19158 10.7241i −0.197481 0.342047i 0.750230 0.661177i \(-0.229943\pi\)
−0.947711 + 0.319130i \(0.896609\pi\)
\(984\) 0 0
\(985\) 4.48398 7.76648i 0.142871 0.247461i
\(986\) −8.25457 + 14.2973i −0.262879 + 0.455320i
\(987\) 0 0
\(988\) −1.19963 2.07782i −0.0381653 0.0661042i
\(989\) 0.0778435 0.00247528
\(990\) 0 0
\(991\) 6.65521 0.211410 0.105705 0.994398i \(-0.466290\pi\)
0.105705 + 0.994398i \(0.466290\pi\)
\(992\) −3.40545 5.89841i −0.108123 0.187275i
\(993\) 0 0
\(994\) 0 0
\(995\) 11.3047 19.5803i 0.358383 0.620738i
\(996\) 0 0
\(997\) 2.40104 + 4.15872i 0.0760417 + 0.131708i 0.901539 0.432698i \(-0.142438\pi\)
−0.825497 + 0.564406i \(0.809105\pi\)
\(998\) 2.28071 0.0721946
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 2646.2.f.n.1765.1 6
3.2 odd 2 882.2.f.m.589.1 6
7.2 even 3 2646.2.h.p.361.3 6
7.3 odd 6 378.2.e.c.37.3 6
7.4 even 3 2646.2.e.o.1549.1 6
7.5 odd 6 378.2.h.d.361.1 6
7.6 odd 2 2646.2.f.o.1765.3 6
9.2 odd 6 882.2.f.m.295.1 6
9.4 even 3 7938.2.a.bx.1.3 3
9.5 odd 6 7938.2.a.by.1.1 3
9.7 even 3 inner 2646.2.f.n.883.1 6
21.2 odd 6 882.2.h.o.67.3 6
21.5 even 6 126.2.h.c.67.1 yes 6
21.11 odd 6 882.2.e.p.373.3 6
21.17 even 6 126.2.e.d.121.1 yes 6
21.20 even 2 882.2.f.l.589.3 6
28.3 even 6 3024.2.q.h.2305.3 6
28.19 even 6 3024.2.t.g.1873.1 6
63.2 odd 6 882.2.e.p.655.3 6
63.5 even 6 1134.2.g.k.487.1 6
63.11 odd 6 882.2.h.o.79.3 6
63.13 odd 6 7938.2.a.bu.1.1 3
63.16 even 3 2646.2.e.o.2125.1 6
63.20 even 6 882.2.f.l.295.3 6
63.25 even 3 2646.2.h.p.667.3 6
63.31 odd 6 1134.2.g.n.163.3 6
63.34 odd 6 2646.2.f.o.883.3 6
63.38 even 6 126.2.h.c.79.1 yes 6
63.40 odd 6 1134.2.g.n.487.3 6
63.41 even 6 7938.2.a.cb.1.3 3
63.47 even 6 126.2.e.d.25.1 6
63.52 odd 6 378.2.h.d.289.1 6
63.59 even 6 1134.2.g.k.163.1 6
63.61 odd 6 378.2.e.c.235.3 6
84.47 odd 6 1008.2.t.g.193.3 6
84.59 odd 6 1008.2.q.h.625.3 6
252.47 odd 6 1008.2.q.h.529.3 6
252.115 even 6 3024.2.t.g.289.1 6
252.187 even 6 3024.2.q.h.2881.3 6
252.227 odd 6 1008.2.t.g.961.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.d.25.1 6 63.47 even 6
126.2.e.d.121.1 yes 6 21.17 even 6
126.2.h.c.67.1 yes 6 21.5 even 6
126.2.h.c.79.1 yes 6 63.38 even 6
378.2.e.c.37.3 6 7.3 odd 6
378.2.e.c.235.3 6 63.61 odd 6
378.2.h.d.289.1 6 63.52 odd 6
378.2.h.d.361.1 6 7.5 odd 6
882.2.e.p.373.3 6 21.11 odd 6
882.2.e.p.655.3 6 63.2 odd 6
882.2.f.l.295.3 6 63.20 even 6
882.2.f.l.589.3 6 21.20 even 2
882.2.f.m.295.1 6 9.2 odd 6
882.2.f.m.589.1 6 3.2 odd 2
882.2.h.o.67.3 6 21.2 odd 6
882.2.h.o.79.3 6 63.11 odd 6
1008.2.q.h.529.3 6 252.47 odd 6
1008.2.q.h.625.3 6 84.59 odd 6
1008.2.t.g.193.3 6 84.47 odd 6
1008.2.t.g.961.3 6 252.227 odd 6
1134.2.g.k.163.1 6 63.59 even 6
1134.2.g.k.487.1 6 63.5 even 6
1134.2.g.n.163.3 6 63.31 odd 6
1134.2.g.n.487.3 6 63.40 odd 6
2646.2.e.o.1549.1 6 7.4 even 3
2646.2.e.o.2125.1 6 63.16 even 3
2646.2.f.n.883.1 6 9.7 even 3 inner
2646.2.f.n.1765.1 6 1.1 even 1 trivial
2646.2.f.o.883.3 6 63.34 odd 6
2646.2.f.o.1765.3 6 7.6 odd 2
2646.2.h.p.361.3 6 7.2 even 3
2646.2.h.p.667.3 6 63.25 even 3
3024.2.q.h.2305.3 6 28.3 even 6
3024.2.q.h.2881.3 6 252.187 even 6
3024.2.t.g.289.1 6 252.115 even 6
3024.2.t.g.1873.1 6 28.19 even 6
7938.2.a.bu.1.1 3 63.13 odd 6
7938.2.a.bx.1.3 3 9.4 even 3
7938.2.a.by.1.1 3 9.5 odd 6
7938.2.a.cb.1.3 3 63.41 even 6