Properties

Label 1323.2.f.e.442.3
Level $1323$
Weight $2$
Character 1323.442
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
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] = [1323,2,Mod(442,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.442");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 442.3
Root \(0.247934 + 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 1323.442
Dual form 1323.2.f.e.883.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.247934 - 0.429435i) q^{2} +(0.877057 - 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} -1.86155 q^{8} +O(q^{10})\) \(q+(-0.247934 - 0.429435i) q^{2} +(0.877057 - 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} -1.86155 q^{8} +1.83103 q^{10} +(-0.446284 - 0.772987i) q^{11} +(0.598355 - 1.03638i) q^{13} +(-1.29257 - 2.23880i) q^{16} -0.249983 q^{17} -2.80827 q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(1.23886 - 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} -0.593411 q^{26} +(-2.07128 - 3.58755i) q^{29} +(-1.79257 + 3.10483i) q^{31} +(-2.50249 + 4.33444i) q^{32} +(0.0619793 + 0.107351i) q^{34} +4.73136 q^{37} +(0.696267 + 1.20597i) q^{38} +(3.43695 - 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} -1.56567 q^{44} -1.22862 q^{46} +(-5.08653 - 8.81013i) q^{47} +(-2.14095 + 3.70823i) q^{50} +(-1.04958 - 1.81793i) q^{52} -9.88929 q^{53} +3.29588 q^{55} +(-1.02708 + 1.77895i) q^{58} +(0.906186 - 1.56956i) q^{59} +(-5.40205 - 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(2.20948 + 3.82692i) q^{65} +(-0.514685 + 0.891460i) q^{67} +(-0.219249 + 0.379751i) q^{68} +4.94533 q^{71} +1.83052 q^{73} +(-1.17306 - 2.03181i) q^{74} +(-2.46302 + 4.26607i) q^{76} +(0.899562 + 1.55809i) q^{79} +9.54586 q^{80} -2.37117 q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(-2.47403 + 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} -2.40741 q^{89} +(-2.17310 - 3.76392i) q^{92} +(-2.52225 + 4.36867i) q^{94} +(5.18489 - 8.98049i) q^{95} +(5.52210 + 9.56456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8} + 14 q^{10} - 4 q^{11} - 8 q^{13} + 2 q^{16} + 24 q^{17} - 2 q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 22 q^{26} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} - 20 q^{44} - 6 q^{46} - 27 q^{47} - 19 q^{50} - 10 q^{52} - 42 q^{53} + 4 q^{55} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} + 6 q^{71} - 30 q^{73} + 36 q^{74} + 5 q^{76} - 4 q^{79} + 40 q^{80} + 10 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 56 q^{89} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.247934 0.429435i −0.175316 0.303656i 0.764955 0.644084i \(-0.222761\pi\)
−0.940271 + 0.340428i \(0.889428\pi\)
\(3\) 0 0
\(4\) 0.877057 1.51911i 0.438529 0.759554i
\(5\) −1.84629 + 3.19787i −0.825686 + 1.43013i 0.0757082 + 0.997130i \(0.475878\pi\)
−0.901394 + 0.433000i \(0.857455\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.86155 −0.658156
\(9\) 0 0
\(10\) 1.83103 0.579023
\(11\) −0.446284 0.772987i −0.134560 0.233064i 0.790869 0.611985i \(-0.209629\pi\)
−0.925429 + 0.378921i \(0.876295\pi\)
\(12\) 0 0
\(13\) 0.598355 1.03638i 0.165954 0.287441i −0.771040 0.636787i \(-0.780263\pi\)
0.936994 + 0.349346i \(0.113596\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.29257 2.23880i −0.323143 0.559701i
\(17\) −0.249983 −0.0606298 −0.0303149 0.999540i \(-0.509651\pi\)
−0.0303149 + 0.999540i \(0.509651\pi\)
\(18\) 0 0
\(19\) −2.80827 −0.644262 −0.322131 0.946695i \(-0.604399\pi\)
−0.322131 + 0.946695i \(0.604399\pi\)
\(20\) 3.23860 + 5.60943i 0.724174 + 1.25431i
\(21\) 0 0
\(22\) −0.221298 + 0.383300i −0.0471809 + 0.0817198i
\(23\) 1.23886 2.14576i 0.258320 0.447423i −0.707472 0.706741i \(-0.750165\pi\)
0.965792 + 0.259318i \(0.0834979\pi\)
\(24\) 0 0
\(25\) −4.31757 7.47825i −0.863514 1.49565i
\(26\) −0.593411 −0.116377
\(27\) 0 0
\(28\) 0 0
\(29\) −2.07128 3.58755i −0.384626 0.666192i 0.607091 0.794632i \(-0.292336\pi\)
−0.991717 + 0.128440i \(0.959003\pi\)
\(30\) 0 0
\(31\) −1.79257 + 3.10483i −0.321956 + 0.557644i −0.980892 0.194555i \(-0.937674\pi\)
0.658936 + 0.752199i \(0.271007\pi\)
\(32\) −2.50249 + 4.33444i −0.442382 + 0.766229i
\(33\) 0 0
\(34\) 0.0619793 + 0.107351i 0.0106294 + 0.0184106i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.73136 0.777830 0.388915 0.921274i \(-0.372850\pi\)
0.388915 + 0.921274i \(0.372850\pi\)
\(38\) 0.696267 + 1.20597i 0.112949 + 0.195634i
\(39\) 0 0
\(40\) 3.43695 5.95298i 0.543430 0.941249i
\(41\) 2.39093 4.14121i 0.373400 0.646748i −0.616686 0.787209i \(-0.711525\pi\)
0.990086 + 0.140461i \(0.0448584\pi\)
\(42\) 0 0
\(43\) −4.98928 8.64169i −0.760859 1.31785i −0.942408 0.334464i \(-0.891445\pi\)
0.181550 0.983382i \(-0.441889\pi\)
\(44\) −1.56567 −0.236033
\(45\) 0 0
\(46\) −1.22862 −0.181150
\(47\) −5.08653 8.81013i −0.741947 1.28509i −0.951608 0.307316i \(-0.900569\pi\)
0.209661 0.977774i \(-0.432764\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.14095 + 3.70823i −0.302776 + 0.524423i
\(51\) 0 0
\(52\) −1.04958 1.81793i −0.145551 0.252102i
\(53\) −9.88929 −1.35840 −0.679199 0.733954i \(-0.737673\pi\)
−0.679199 + 0.733954i \(0.737673\pi\)
\(54\) 0 0
\(55\) 3.29588 0.444416
\(56\) 0 0
\(57\) 0 0
\(58\) −1.02708 + 1.77895i −0.134862 + 0.233588i
\(59\) 0.906186 1.56956i 0.117975 0.204339i −0.800990 0.598678i \(-0.795693\pi\)
0.918965 + 0.394339i \(0.129026\pi\)
\(60\) 0 0
\(61\) −5.40205 9.35663i −0.691662 1.19799i −0.971293 0.237886i \(-0.923545\pi\)
0.279631 0.960108i \(-0.409788\pi\)
\(62\) 1.77776 0.225776
\(63\) 0 0
\(64\) −2.68848 −0.336060
\(65\) 2.20948 + 3.82692i 0.274052 + 0.474671i
\(66\) 0 0
\(67\) −0.514685 + 0.891460i −0.0628787 + 0.108909i −0.895751 0.444556i \(-0.853361\pi\)
0.832872 + 0.553465i \(0.186695\pi\)
\(68\) −0.219249 + 0.379751i −0.0265879 + 0.0460516i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.94533 0.586903 0.293451 0.955974i \(-0.405196\pi\)
0.293451 + 0.955974i \(0.405196\pi\)
\(72\) 0 0
\(73\) 1.83052 0.214247 0.107123 0.994246i \(-0.465836\pi\)
0.107123 + 0.994246i \(0.465836\pi\)
\(74\) −1.17306 2.03181i −0.136366 0.236193i
\(75\) 0 0
\(76\) −2.46302 + 4.26607i −0.282527 + 0.489352i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.899562 + 1.55809i 0.101209 + 0.175298i 0.912183 0.409783i \(-0.134396\pi\)
−0.810974 + 0.585082i \(0.801062\pi\)
\(80\) 9.54586 1.06726
\(81\) 0 0
\(82\) −2.37117 −0.261852
\(83\) −6.16156 10.6721i −0.676319 1.17142i −0.976082 0.217405i \(-0.930241\pi\)
0.299763 0.954014i \(-0.403092\pi\)
\(84\) 0 0
\(85\) 0.461541 0.799412i 0.0500611 0.0867084i
\(86\) −2.47403 + 4.28514i −0.266781 + 0.462079i
\(87\) 0 0
\(88\) 0.830779 + 1.43895i 0.0885613 + 0.153393i
\(89\) −2.40741 −0.255185 −0.127592 0.991827i \(-0.540725\pi\)
−0.127592 + 0.991827i \(0.540725\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.17310 3.76392i −0.226561 0.392416i
\(93\) 0 0
\(94\) −2.52225 + 4.36867i −0.260150 + 0.450593i
\(95\) 5.18489 8.98049i 0.531958 0.921379i
\(96\) 0 0
\(97\) 5.52210 + 9.56456i 0.560684 + 0.971134i 0.997437 + 0.0715522i \(0.0227952\pi\)
−0.436752 + 0.899582i \(0.643871\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −15.1470 −1.51470
\(101\) −1.29982 2.25136i −0.129337 0.224018i 0.794083 0.607810i \(-0.207952\pi\)
−0.923420 + 0.383791i \(0.874618\pi\)
\(102\) 0 0
\(103\) −4.85578 + 8.41045i −0.478454 + 0.828706i −0.999695 0.0247032i \(-0.992136\pi\)
0.521241 + 0.853409i \(0.325469\pi\)
\(104\) −1.11387 + 1.92927i −0.109224 + 0.189181i
\(105\) 0 0
\(106\) 2.45189 + 4.24680i 0.238149 + 0.412486i
\(107\) −10.9005 −1.05379 −0.526896 0.849930i \(-0.676644\pi\)
−0.526896 + 0.849930i \(0.676644\pi\)
\(108\) 0 0
\(109\) 2.12193 0.203244 0.101622 0.994823i \(-0.467597\pi\)
0.101622 + 0.994823i \(0.467597\pi\)
\(110\) −0.817161 1.41536i −0.0779132 0.134950i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.91318 + 13.7060i −0.744409 + 1.28935i 0.206061 + 0.978539i \(0.433935\pi\)
−0.950470 + 0.310816i \(0.899398\pi\)
\(114\) 0 0
\(115\) 4.57458 + 7.92341i 0.426582 + 0.738861i
\(116\) −7.26651 −0.674679
\(117\) 0 0
\(118\) −0.898698 −0.0827318
\(119\) 0 0
\(120\) 0 0
\(121\) 5.10166 8.83634i 0.463787 0.803303i
\(122\) −2.67871 + 4.63966i −0.242519 + 0.420055i
\(123\) 0 0
\(124\) 3.14438 + 5.44623i 0.282374 + 0.489086i
\(125\) 13.4230 1.20059
\(126\) 0 0
\(127\) −1.26946 −0.112647 −0.0563233 0.998413i \(-0.517938\pi\)
−0.0563233 + 0.998413i \(0.517938\pi\)
\(128\) 5.67155 + 9.82342i 0.501299 + 0.868275i
\(129\) 0 0
\(130\) 1.09561 1.89765i 0.0960912 0.166435i
\(131\) −7.51444 + 13.0154i −0.656540 + 1.13716i 0.324965 + 0.945726i \(0.394647\pi\)
−0.981505 + 0.191435i \(0.938686\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.510432 0.0440946
\(135\) 0 0
\(136\) 0.465355 0.0399038
\(137\) −0.244246 0.423047i −0.0208674 0.0361433i 0.855403 0.517963i \(-0.173309\pi\)
−0.876271 + 0.481819i \(0.839976\pi\)
\(138\) 0 0
\(139\) −4.93487 + 8.54745i −0.418570 + 0.724985i −0.995796 0.0915997i \(-0.970802\pi\)
0.577226 + 0.816585i \(0.304135\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.22612 2.12370i −0.102893 0.178217i
\(143\) −1.06815 −0.0893229
\(144\) 0 0
\(145\) 15.2967 1.27032
\(146\) −0.453849 0.786090i −0.0375609 0.0650573i
\(147\) 0 0
\(148\) 4.14967 7.18744i 0.341101 0.590804i
\(149\) 10.5120 18.2073i 0.861175 1.49160i −0.00962096 0.999954i \(-0.503062\pi\)
0.870796 0.491645i \(-0.163604\pi\)
\(150\) 0 0
\(151\) −0.749191 1.29764i −0.0609683 0.105600i 0.833930 0.551870i \(-0.186086\pi\)
−0.894898 + 0.446270i \(0.852752\pi\)
\(152\) 5.22773 0.424025
\(153\) 0 0
\(154\) 0 0
\(155\) −6.61922 11.4648i −0.531669 0.920877i
\(156\) 0 0
\(157\) 8.33982 14.4450i 0.665590 1.15284i −0.313535 0.949577i \(-0.601513\pi\)
0.979125 0.203259i \(-0.0651534\pi\)
\(158\) 0.446064 0.772606i 0.0354870 0.0614652i
\(159\) 0 0
\(160\) −9.24065 16.0053i −0.730538 1.26533i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.68269 0.523429 0.261714 0.965145i \(-0.415712\pi\)
0.261714 + 0.965145i \(0.415712\pi\)
\(164\) −4.19396 7.26416i −0.327494 0.567236i
\(165\) 0 0
\(166\) −3.05532 + 5.29197i −0.237139 + 0.410737i
\(167\) −8.81549 + 15.2689i −0.682163 + 1.18154i 0.292156 + 0.956371i \(0.405627\pi\)
−0.974319 + 0.225170i \(0.927706\pi\)
\(168\) 0 0
\(169\) 5.78394 + 10.0181i 0.444919 + 0.770622i
\(170\) −0.457727 −0.0351061
\(171\) 0 0
\(172\) −17.5036 −1.33463
\(173\) −1.94342 3.36611i −0.147756 0.255920i 0.782642 0.622472i \(-0.213872\pi\)
−0.930398 + 0.366552i \(0.880538\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.15371 + 1.99829i −0.0869642 + 0.150626i
\(177\) 0 0
\(178\) 0.596879 + 1.03382i 0.0447380 + 0.0774884i
\(179\) 7.33516 0.548256 0.274128 0.961693i \(-0.411611\pi\)
0.274128 + 0.961693i \(0.411611\pi\)
\(180\) 0 0
\(181\) 11.2566 0.836693 0.418346 0.908288i \(-0.362610\pi\)
0.418346 + 0.908288i \(0.362610\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.30619 + 3.99444i −0.170015 + 0.294474i
\(185\) −8.73545 + 15.1302i −0.642243 + 1.11240i
\(186\) 0 0
\(187\) 0.111563 + 0.193234i 0.00815833 + 0.0141306i
\(188\) −17.8447 −1.30146
\(189\) 0 0
\(190\) −5.14204 −0.373043
\(191\) −11.9230 20.6512i −0.862715 1.49427i −0.869298 0.494288i \(-0.835429\pi\)
0.00658302 0.999978i \(-0.497905\pi\)
\(192\) 0 0
\(193\) −2.96728 + 5.13948i −0.213589 + 0.369948i −0.952835 0.303488i \(-0.901849\pi\)
0.739246 + 0.673436i \(0.235182\pi\)
\(194\) 2.73823 4.74276i 0.196594 0.340510i
\(195\) 0 0
\(196\) 0 0
\(197\) 15.4682 1.10206 0.551032 0.834484i \(-0.314234\pi\)
0.551032 + 0.834484i \(0.314234\pi\)
\(198\) 0 0
\(199\) −15.4964 −1.09851 −0.549254 0.835655i \(-0.685088\pi\)
−0.549254 + 0.835655i \(0.685088\pi\)
\(200\) 8.03736 + 13.9211i 0.568327 + 0.984371i
\(201\) 0 0
\(202\) −0.644540 + 1.11638i −0.0453497 + 0.0785480i
\(203\) 0 0
\(204\) 0 0
\(205\) 8.82870 + 15.2917i 0.616623 + 1.06802i
\(206\) 4.81565 0.335522
\(207\) 0 0
\(208\) −3.09367 −0.214508
\(209\) 1.25329 + 2.17076i 0.0866918 + 0.150155i
\(210\) 0 0
\(211\) 0.771898 1.33697i 0.0531397 0.0920406i −0.838232 0.545314i \(-0.816410\pi\)
0.891372 + 0.453273i \(0.149744\pi\)
\(212\) −8.67347 + 15.0229i −0.595697 + 1.03178i
\(213\) 0 0
\(214\) 2.70261 + 4.68105i 0.184746 + 0.319990i
\(215\) 36.8467 2.51292
\(216\) 0 0
\(217\) 0 0
\(218\) −0.526098 0.911229i −0.0356319 0.0617162i
\(219\) 0 0
\(220\) 2.89068 5.00680i 0.194889 0.337558i
\(221\) −0.149579 + 0.259078i −0.0100617 + 0.0174275i
\(222\) 0 0
\(223\) −2.72171 4.71414i −0.182259 0.315682i 0.760390 0.649466i \(-0.225008\pi\)
−0.942649 + 0.333784i \(0.891674\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.84779 0.522027
\(227\) −8.03818 13.9225i −0.533513 0.924072i −0.999234 0.0391399i \(-0.987538\pi\)
0.465721 0.884932i \(-0.345795\pi\)
\(228\) 0 0
\(229\) 4.98420 8.63289i 0.329365 0.570477i −0.653021 0.757340i \(-0.726499\pi\)
0.982386 + 0.186863i \(0.0598319\pi\)
\(230\) 2.26839 3.92897i 0.149573 0.259068i
\(231\) 0 0
\(232\) 3.85578 + 6.67840i 0.253144 + 0.438458i
\(233\) 16.5409 1.08363 0.541815 0.840498i \(-0.317737\pi\)
0.541815 + 0.840498i \(0.317737\pi\)
\(234\) 0 0
\(235\) 37.5648 2.45046
\(236\) −1.58955 2.75319i −0.103471 0.179217i
\(237\) 0 0
\(238\) 0 0
\(239\) 11.0119 19.0732i 0.712303 1.23375i −0.251687 0.967809i \(-0.580985\pi\)
0.963990 0.265937i \(-0.0856813\pi\)
\(240\) 0 0
\(241\) −8.36004 14.4800i −0.538517 0.932739i −0.998984 0.0450623i \(-0.985651\pi\)
0.460467 0.887677i \(-0.347682\pi\)
\(242\) −5.05950 −0.325237
\(243\) 0 0
\(244\) −18.9516 −1.21325
\(245\) 0 0
\(246\) 0 0
\(247\) −1.68035 + 2.91045i −0.106918 + 0.185187i
\(248\) 3.33696 5.77978i 0.211897 0.367017i
\(249\) 0 0
\(250\) −3.32803 5.76432i −0.210483 0.364568i
\(251\) 8.53099 0.538471 0.269236 0.963074i \(-0.413229\pi\)
0.269236 + 0.963074i \(0.413229\pi\)
\(252\) 0 0
\(253\) −2.21153 −0.139038
\(254\) 0.314743 + 0.545151i 0.0197488 + 0.0342058i
\(255\) 0 0
\(256\) 0.123861 0.214533i 0.00774131 0.0134083i
\(257\) −8.55986 + 14.8261i −0.533950 + 0.924828i 0.465264 + 0.885172i \(0.345959\pi\)
−0.999213 + 0.0396557i \(0.987374\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.75135 0.480718
\(261\) 0 0
\(262\) 7.45235 0.460408
\(263\) 10.2763 + 17.7991i 0.633666 + 1.09754i 0.986796 + 0.161967i \(0.0517838\pi\)
−0.353130 + 0.935574i \(0.614883\pi\)
\(264\) 0 0
\(265\) 18.2585 31.6246i 1.12161 1.94269i
\(266\) 0 0
\(267\) 0 0
\(268\) 0.902816 + 1.56372i 0.0551483 + 0.0955196i
\(269\) 19.8453 1.20999 0.604996 0.796229i \(-0.293175\pi\)
0.604996 + 0.796229i \(0.293175\pi\)
\(270\) 0 0
\(271\) −10.6411 −0.646402 −0.323201 0.946330i \(-0.604759\pi\)
−0.323201 + 0.946330i \(0.604759\pi\)
\(272\) 0.323121 + 0.559663i 0.0195921 + 0.0339345i
\(273\) 0 0
\(274\) −0.121114 + 0.209776i −0.00731676 + 0.0126730i
\(275\) −3.85373 + 6.67485i −0.232388 + 0.402509i
\(276\) 0 0
\(277\) 12.4407 + 21.5479i 0.747487 + 1.29469i 0.949024 + 0.315205i \(0.102073\pi\)
−0.201536 + 0.979481i \(0.564593\pi\)
\(278\) 4.89409 0.293528
\(279\) 0 0
\(280\) 0 0
\(281\) 6.83733 + 11.8426i 0.407881 + 0.706470i 0.994652 0.103282i \(-0.0329346\pi\)
−0.586771 + 0.809753i \(0.699601\pi\)
\(282\) 0 0
\(283\) −3.16089 + 5.47483i −0.187896 + 0.325445i −0.944548 0.328372i \(-0.893500\pi\)
0.756653 + 0.653817i \(0.226833\pi\)
\(284\) 4.33734 7.51249i 0.257374 0.445784i
\(285\) 0 0
\(286\) 0.264830 + 0.458699i 0.0156597 + 0.0271234i
\(287\) 0 0
\(288\) 0 0
\(289\) −16.9375 −0.996324
\(290\) −3.79257 6.56893i −0.222708 0.385741i
\(291\) 0 0
\(292\) 1.60547 2.78076i 0.0939533 0.162732i
\(293\) 1.31508 2.27778i 0.0768277 0.133069i −0.825052 0.565057i \(-0.808854\pi\)
0.901880 + 0.431987i \(0.142188\pi\)
\(294\) 0 0
\(295\) 3.34616 + 5.79573i 0.194821 + 0.337440i
\(296\) −8.80764 −0.511934
\(297\) 0 0
\(298\) −10.4251 −0.603911
\(299\) −1.48255 2.56786i −0.0857384 0.148503i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.371500 + 0.643457i −0.0213774 + 0.0370268i
\(303\) 0 0
\(304\) 3.62990 + 6.28717i 0.208189 + 0.360594i
\(305\) 39.8950 2.28438
\(306\) 0 0
\(307\) −2.79496 −0.159517 −0.0797583 0.996814i \(-0.525415\pi\)
−0.0797583 + 0.996814i \(0.525415\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.28226 + 5.68504i −0.186420 + 0.322889i
\(311\) −7.55013 + 13.0772i −0.428129 + 0.741541i −0.996707 0.0810885i \(-0.974160\pi\)
0.568578 + 0.822629i \(0.307494\pi\)
\(312\) 0 0
\(313\) 12.7392 + 22.0650i 0.720064 + 1.24719i 0.960974 + 0.276640i \(0.0892209\pi\)
−0.240910 + 0.970548i \(0.577446\pi\)
\(314\) −8.27090 −0.466754
\(315\) 0 0
\(316\) 3.15587 0.177531
\(317\) 16.2605 + 28.1639i 0.913278 + 1.58184i 0.809403 + 0.587253i \(0.199791\pi\)
0.103875 + 0.994590i \(0.466876\pi\)
\(318\) 0 0
\(319\) −1.84875 + 3.20214i −0.103510 + 0.179285i
\(320\) 4.96372 8.59741i 0.277480 0.480610i
\(321\) 0 0
\(322\) 0 0
\(323\) 0.702021 0.0390615
\(324\) 0 0
\(325\) −10.3338 −0.573214
\(326\) −1.65687 2.86978i −0.0917654 0.158942i
\(327\) 0 0
\(328\) −4.45083 + 7.70906i −0.245756 + 0.425661i
\(329\) 0 0
\(330\) 0 0
\(331\) −9.04741 15.6706i −0.497291 0.861333i 0.502704 0.864458i \(-0.332338\pi\)
−0.999995 + 0.00312545i \(0.999005\pi\)
\(332\) −21.6162 −1.18634
\(333\) 0 0
\(334\) 8.74264 0.478376
\(335\) −1.90051 3.29179i −0.103836 0.179850i
\(336\) 0 0
\(337\) −12.5086 + 21.6656i −0.681389 + 1.18020i 0.293168 + 0.956061i \(0.405290\pi\)
−0.974557 + 0.224139i \(0.928043\pi\)
\(338\) 2.86807 4.96765i 0.156003 0.270204i
\(339\) 0 0
\(340\) −0.809596 1.40226i −0.0439065 0.0760483i
\(341\) 3.19999 0.173289
\(342\) 0 0
\(343\) 0 0
\(344\) 9.28778 + 16.0869i 0.500764 + 0.867348i
\(345\) 0 0
\(346\) −0.963682 + 1.66915i −0.0518078 + 0.0897338i
\(347\) 5.37444 9.30881i 0.288515 0.499723i −0.684940 0.728599i \(-0.740172\pi\)
0.973456 + 0.228876i \(0.0735051\pi\)
\(348\) 0 0
\(349\) −1.64301 2.84577i −0.0879482 0.152331i 0.818695 0.574228i \(-0.194698\pi\)
−0.906644 + 0.421897i \(0.861364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.46729 0.238107
\(353\) 8.40960 + 14.5658i 0.447598 + 0.775262i 0.998229 0.0594866i \(-0.0189463\pi\)
−0.550631 + 0.834748i \(0.685613\pi\)
\(354\) 0 0
\(355\) −9.13051 + 15.8145i −0.484597 + 0.839347i
\(356\) −2.11144 + 3.65711i −0.111906 + 0.193827i
\(357\) 0 0
\(358\) −1.81864 3.14997i −0.0961180 0.166481i
\(359\) 23.7842 1.25528 0.627642 0.778502i \(-0.284020\pi\)
0.627642 + 0.778502i \(0.284020\pi\)
\(360\) 0 0
\(361\) −11.1136 −0.584926
\(362\) −2.79088 4.83395i −0.146686 0.254067i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.37968 + 5.85377i −0.176900 + 0.306401i
\(366\) 0 0
\(367\) 0.344992 + 0.597544i 0.0180084 + 0.0311915i 0.874889 0.484323i \(-0.160934\pi\)
−0.856881 + 0.515515i \(0.827601\pi\)
\(368\) −6.40526 −0.333897
\(369\) 0 0
\(370\) 8.66327 0.450382
\(371\) 0 0
\(372\) 0 0
\(373\) 1.88006 3.25636i 0.0973457 0.168608i −0.813239 0.581929i \(-0.802298\pi\)
0.910585 + 0.413321i \(0.135631\pi\)
\(374\) 0.0553208 0.0958184i 0.00286057 0.00495465i
\(375\) 0 0
\(376\) 9.46882 + 16.4005i 0.488317 + 0.845790i
\(377\) −4.95744 −0.255321
\(378\) 0 0
\(379\) 32.8735 1.68860 0.844300 0.535872i \(-0.180017\pi\)
0.844300 + 0.535872i \(0.180017\pi\)
\(380\) −9.09489 15.7528i −0.466558 0.808102i
\(381\) 0 0
\(382\) −5.91222 + 10.2403i −0.302495 + 0.523937i
\(383\) −0.536335 + 0.928960i −0.0274055 + 0.0474676i −0.879403 0.476078i \(-0.842058\pi\)
0.851997 + 0.523546i \(0.175391\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.94276 0.149782
\(387\) 0 0
\(388\) 19.3728 0.983505
\(389\) −11.8718 20.5626i −0.601925 1.04256i −0.992529 0.122006i \(-0.961067\pi\)
0.390605 0.920559i \(-0.372266\pi\)
\(390\) 0 0
\(391\) −0.309693 + 0.536405i −0.0156619 + 0.0271271i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.83510 6.64258i −0.193209 0.334648i
\(395\) −6.64340 −0.334266
\(396\) 0 0
\(397\) 0.0320978 0.00161094 0.000805471 1.00000i \(-0.499744\pi\)
0.000805471 1.00000i \(0.499744\pi\)
\(398\) 3.84208 + 6.65467i 0.192586 + 0.333569i
\(399\) 0 0
\(400\) −11.1616 + 19.3324i −0.558078 + 0.966619i
\(401\) 12.2628 21.2398i 0.612374 1.06066i −0.378465 0.925616i \(-0.623548\pi\)
0.990839 0.135048i \(-0.0431188\pi\)
\(402\) 0 0
\(403\) 2.14519 + 3.71558i 0.106860 + 0.185086i
\(404\) −4.56007 −0.226872
\(405\) 0 0
\(406\) 0 0
\(407\) −2.11153 3.65728i −0.104665 0.181284i
\(408\) 0 0
\(409\) −13.3948 + 23.2006i −0.662333 + 1.14719i 0.317669 + 0.948202i \(0.397100\pi\)
−0.980001 + 0.198992i \(0.936233\pi\)
\(410\) 4.37787 7.58269i 0.216208 0.374483i
\(411\) 0 0
\(412\) 8.51759 + 14.7529i 0.419631 + 0.726823i
\(413\) 0 0
\(414\) 0 0
\(415\) 45.5041 2.23371
\(416\) 2.99476 + 5.18708i 0.146830 + 0.254317i
\(417\) 0 0
\(418\) 0.621466 1.07641i 0.0303969 0.0526490i
\(419\) 10.5262 18.2320i 0.514240 0.890689i −0.485624 0.874168i \(-0.661407\pi\)
0.999864 0.0165215i \(-0.00525920\pi\)
\(420\) 0 0
\(421\) −7.44533 12.8957i −0.362863 0.628498i 0.625568 0.780170i \(-0.284867\pi\)
−0.988431 + 0.151672i \(0.951534\pi\)
\(422\) −0.765520 −0.0372649
\(423\) 0 0
\(424\) 18.4094 0.894038
\(425\) 1.07932 + 1.86944i 0.0523547 + 0.0906809i
\(426\) 0 0
\(427\) 0 0
\(428\) −9.56037 + 16.5590i −0.462118 + 0.800412i
\(429\) 0 0
\(430\) −9.13554 15.8232i −0.440555 0.763064i
\(431\) −15.9038 −0.766061 −0.383031 0.923736i \(-0.625120\pi\)
−0.383031 + 0.923736i \(0.625120\pi\)
\(432\) 0 0
\(433\) −16.3658 −0.786490 −0.393245 0.919434i \(-0.628648\pi\)
−0.393245 + 0.919434i \(0.628648\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.86105 3.22344i 0.0891282 0.154375i
\(437\) −3.47905 + 6.02590i −0.166426 + 0.288258i
\(438\) 0 0
\(439\) 7.77236 + 13.4621i 0.370954 + 0.642512i 0.989713 0.143070i \(-0.0456973\pi\)
−0.618758 + 0.785582i \(0.712364\pi\)
\(440\) −6.13543 −0.292495
\(441\) 0 0
\(442\) 0.148343 0.00705594
\(443\) 0.895027 + 1.55023i 0.0425240 + 0.0736537i 0.886504 0.462721i \(-0.153127\pi\)
−0.843980 + 0.536375i \(0.819793\pi\)
\(444\) 0 0
\(445\) 4.44477 7.69857i 0.210702 0.364947i
\(446\) −1.34961 + 2.33759i −0.0639058 + 0.110688i
\(447\) 0 0
\(448\) 0 0
\(449\) −13.5666 −0.640250 −0.320125 0.947375i \(-0.603725\pi\)
−0.320125 + 0.947375i \(0.603725\pi\)
\(450\) 0 0
\(451\) −4.26814 −0.200979
\(452\) 13.8806 + 24.0419i 0.652890 + 1.13084i
\(453\) 0 0
\(454\) −3.98588 + 6.90375i −0.187067 + 0.324009i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.28459 2.22497i −0.0600905 0.104080i 0.834415 0.551136i \(-0.185806\pi\)
−0.894506 + 0.447057i \(0.852472\pi\)
\(458\) −4.94301 −0.230972
\(459\) 0 0
\(460\) 16.0487 0.748274
\(461\) −18.0934 31.3388i −0.842695 1.45959i −0.887608 0.460600i \(-0.847634\pi\)
0.0449122 0.998991i \(-0.485699\pi\)
\(462\) 0 0
\(463\) 8.19224 14.1894i 0.380726 0.659436i −0.610440 0.792062i \(-0.709008\pi\)
0.991166 + 0.132626i \(0.0423409\pi\)
\(464\) −5.35455 + 9.27436i −0.248579 + 0.430551i
\(465\) 0 0
\(466\) −4.10105 7.10323i −0.189978 0.329051i
\(467\) −8.70044 −0.402608 −0.201304 0.979529i \(-0.564518\pi\)
−0.201304 + 0.979529i \(0.564518\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.31361 16.1316i −0.429605 0.744097i
\(471\) 0 0
\(472\) −1.68691 + 2.92181i −0.0776462 + 0.134487i
\(473\) −4.45328 + 7.71330i −0.204762 + 0.354658i
\(474\) 0 0
\(475\) 12.1249 + 21.0010i 0.556330 + 0.963591i
\(476\) 0 0
\(477\) 0 0
\(478\) −10.9209 −0.499513
\(479\) −8.88370 15.3870i −0.405907 0.703051i 0.588520 0.808483i \(-0.299711\pi\)
−0.994427 + 0.105432i \(0.966378\pi\)
\(480\) 0 0
\(481\) 2.83103 4.90349i 0.129084 0.223580i
\(482\) −4.14548 + 7.18018i −0.188821 + 0.327048i
\(483\) 0 0
\(484\) −8.94890 15.4999i −0.406768 0.704543i
\(485\) −40.7816 −1.85180
\(486\) 0 0
\(487\) −16.6553 −0.754722 −0.377361 0.926066i \(-0.623168\pi\)
−0.377361 + 0.926066i \(0.623168\pi\)
\(488\) 10.0562 + 17.4178i 0.455222 + 0.788467i
\(489\) 0 0
\(490\) 0 0
\(491\) 3.21021 5.56025i 0.144875 0.250930i −0.784451 0.620190i \(-0.787055\pi\)
0.929326 + 0.369260i \(0.120389\pi\)
\(492\) 0 0
\(493\) 0.517784 + 0.896827i 0.0233198 + 0.0403911i
\(494\) 1.66646 0.0749776
\(495\) 0 0
\(496\) 9.26814 0.416152
\(497\) 0 0
\(498\) 0 0
\(499\) −5.57296 + 9.65264i −0.249480 + 0.432112i −0.963382 0.268134i \(-0.913593\pi\)
0.713902 + 0.700246i \(0.246926\pi\)
\(500\) 11.7728 20.3911i 0.526495 0.911916i
\(501\) 0 0
\(502\) −2.11512 3.66350i −0.0944026 0.163510i
\(503\) 17.7223 0.790200 0.395100 0.918638i \(-0.370710\pi\)
0.395100 + 0.918638i \(0.370710\pi\)
\(504\) 0 0
\(505\) 9.59939 0.427167
\(506\) 0.548314 + 0.949708i 0.0243755 + 0.0422197i
\(507\) 0 0
\(508\) −1.11339 + 1.92845i −0.0493988 + 0.0855612i
\(509\) 15.5411 26.9180i 0.688848 1.19312i −0.283362 0.959013i \(-0.591450\pi\)
0.972211 0.234107i \(-0.0752167\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.5634 0.997169
\(513\) 0 0
\(514\) 8.48913 0.374439
\(515\) −17.9303 31.0563i −0.790105 1.36850i
\(516\) 0 0
\(517\) −4.54008 + 7.86365i −0.199672 + 0.345843i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.11304 7.12399i −0.180369 0.312408i
\(521\) −4.75971 −0.208527 −0.104263 0.994550i \(-0.533249\pi\)
−0.104263 + 0.994550i \(0.533249\pi\)
\(522\) 0 0
\(523\) −40.2515 −1.76008 −0.880038 0.474904i \(-0.842483\pi\)
−0.880038 + 0.474904i \(0.842483\pi\)
\(524\) 13.1812 + 22.8305i 0.575823 + 0.997355i
\(525\) 0 0
\(526\) 5.09571 8.82602i 0.222183 0.384833i
\(527\) 0.448113 0.776154i 0.0195201 0.0338098i
\(528\) 0 0
\(529\) 8.43046 + 14.6020i 0.366542 + 0.634869i
\(530\) −18.1076 −0.786545
\(531\) 0 0
\(532\) 0 0
\(533\) −2.86125 4.95583i −0.123935 0.214661i
\(534\) 0 0
\(535\) 20.1255 34.8584i 0.870101 1.50706i
\(536\) 0.958109 1.65949i 0.0413840 0.0716792i
\(537\) 0 0
\(538\) −4.92033 8.52227i −0.212131 0.367421i
\(539\) 0 0
\(540\) 0 0
\(541\) −24.1094 −1.03655 −0.518273 0.855215i \(-0.673425\pi\)
−0.518273 + 0.855215i \(0.673425\pi\)
\(542\) 2.63830 + 4.56966i 0.113325 + 0.196284i
\(543\) 0 0
\(544\) 0.625580 1.08354i 0.0268215 0.0464563i
\(545\) −3.91769 + 6.78564i −0.167815 + 0.290665i
\(546\) 0 0
\(547\) −6.17751 10.6998i −0.264131 0.457489i 0.703204 0.710988i \(-0.251752\pi\)
−0.967336 + 0.253499i \(0.918419\pi\)
\(548\) −0.856872 −0.0366038
\(549\) 0 0
\(550\) 3.82188 0.162966
\(551\) 5.81671 + 10.0748i 0.247800 + 0.429203i
\(552\) 0 0
\(553\) 0 0
\(554\) 6.16893 10.6849i 0.262093 0.453958i
\(555\) 0 0
\(556\) 8.65633 + 14.9932i 0.367110 + 0.635853i
\(557\) 8.07689 0.342229 0.171114 0.985251i \(-0.445263\pi\)
0.171114 + 0.985251i \(0.445263\pi\)
\(558\) 0 0
\(559\) −11.9415 −0.505070
\(560\) 0 0
\(561\) 0 0
\(562\) 3.39041 5.87237i 0.143016 0.247711i
\(563\) 22.6064 39.1554i 0.952744 1.65020i 0.213296 0.976988i \(-0.431580\pi\)
0.739448 0.673214i \(-0.235087\pi\)
\(564\) 0 0
\(565\) −29.2200 50.6106i −1.22930 2.12920i
\(566\) 3.13477 0.131764
\(567\) 0 0
\(568\) −9.20596 −0.386274
\(569\) 11.2149 + 19.4248i 0.470155 + 0.814332i 0.999418 0.0341263i \(-0.0108648\pi\)
−0.529263 + 0.848458i \(0.677532\pi\)
\(570\) 0 0
\(571\) 10.9134 18.9026i 0.456713 0.791050i −0.542072 0.840332i \(-0.682360\pi\)
0.998785 + 0.0492820i \(0.0156933\pi\)
\(572\) −0.936826 + 1.62263i −0.0391706 + 0.0678455i
\(573\) 0 0
\(574\) 0 0
\(575\) −21.3954 −0.892251
\(576\) 0 0
\(577\) 32.2044 1.34068 0.670342 0.742052i \(-0.266147\pi\)
0.670342 + 0.742052i \(0.266147\pi\)
\(578\) 4.19939 + 7.27355i 0.174671 + 0.302540i
\(579\) 0 0
\(580\) 13.4161 23.2373i 0.557072 0.964878i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.41343 + 7.64429i 0.182786 + 0.316594i
\(584\) −3.40761 −0.141008
\(585\) 0 0
\(586\) −1.30421 −0.0538765
\(587\) 9.72304 + 16.8408i 0.401313 + 0.695094i 0.993885 0.110424i \(-0.0352208\pi\)
−0.592572 + 0.805518i \(0.701887\pi\)
\(588\) 0 0
\(589\) 5.03404 8.71921i 0.207424 0.359269i
\(590\) 1.65926 2.87392i 0.0683105 0.118317i
\(591\) 0 0
\(592\) −6.11563 10.5926i −0.251351 0.435352i
\(593\) −28.8405 −1.18434 −0.592168 0.805815i \(-0.701728\pi\)
−0.592168 + 0.805815i \(0.701728\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.4392 31.9377i −0.755300 1.30822i
\(597\) 0 0
\(598\) −0.735152 + 1.27332i −0.0300626 + 0.0520699i
\(599\) −23.4994 + 40.7022i −0.960161 + 1.66305i −0.238072 + 0.971247i \(0.576516\pi\)
−0.722089 + 0.691800i \(0.756818\pi\)
\(600\) 0 0
\(601\) −7.80843 13.5246i −0.318512 0.551680i 0.661665 0.749799i \(-0.269850\pi\)
−0.980178 + 0.198119i \(0.936517\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.62833 −0.106945
\(605\) 18.8383 + 32.6289i 0.765885 + 1.32655i
\(606\) 0 0
\(607\) 14.3266 24.8144i 0.581500 1.00719i −0.413802 0.910367i \(-0.635800\pi\)
0.995302 0.0968200i \(-0.0308671\pi\)
\(608\) 7.02769 12.1723i 0.285010 0.493652i
\(609\) 0 0
\(610\) −9.89134 17.1323i −0.400489 0.693667i
\(611\) −12.1742 −0.492516
\(612\) 0 0
\(613\) −29.3468 −1.18531 −0.592653 0.805458i \(-0.701920\pi\)
−0.592653 + 0.805458i \(0.701920\pi\)
\(614\) 0.692965 + 1.20025i 0.0279658 + 0.0484382i
\(615\) 0 0
\(616\) 0 0
\(617\) −2.06401 + 3.57497i −0.0830938 + 0.143923i −0.904577 0.426310i \(-0.859813\pi\)
0.821484 + 0.570232i \(0.193147\pi\)
\(618\) 0 0
\(619\) −11.3565 19.6700i −0.456456 0.790605i 0.542315 0.840175i \(-0.317548\pi\)
−0.998771 + 0.0495708i \(0.984215\pi\)
\(620\) −23.2217 −0.932608
\(621\) 0 0
\(622\) 7.48774 0.300231
\(623\) 0 0
\(624\) 0 0
\(625\) −3.19498 + 5.53387i −0.127799 + 0.221355i
\(626\) 6.31698 10.9413i 0.252477 0.437304i
\(627\) 0 0
\(628\) −14.6290 25.3382i −0.583761 1.01110i
\(629\) −1.18276 −0.0471597
\(630\) 0 0
\(631\) −38.6411 −1.53828 −0.769138 0.639082i \(-0.779314\pi\)
−0.769138 + 0.639082i \(0.779314\pi\)
\(632\) −1.67458 2.90045i −0.0666110 0.115374i
\(633\) 0 0
\(634\) 8.06304 13.9656i 0.320224 0.554645i
\(635\) 2.34380 4.05958i 0.0930107 0.161099i
\(636\) 0 0
\(637\) 0 0
\(638\) 1.83348 0.0725881
\(639\) 0 0
\(640\) −41.8853 −1.65566
\(641\) −14.2363 24.6580i −0.562301 0.973933i −0.997295 0.0735002i \(-0.976583\pi\)
0.434995 0.900433i \(-0.356750\pi\)
\(642\) 0 0
\(643\) −8.52125 + 14.7592i −0.336045 + 0.582048i −0.983685 0.179899i \(-0.942423\pi\)
0.647640 + 0.761947i \(0.275756\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.174055 0.301472i −0.00684810 0.0118613i
\(647\) 3.37618 0.132731 0.0663657 0.997795i \(-0.478860\pi\)
0.0663657 + 0.997795i \(0.478860\pi\)
\(648\) 0 0
\(649\) −1.61767 −0.0634989
\(650\) 2.56209 + 4.43768i 0.100494 + 0.174060i
\(651\) 0 0
\(652\) 5.86110 10.1517i 0.229538 0.397572i
\(653\) −9.17255 + 15.8873i −0.358950 + 0.621719i −0.987786 0.155819i \(-0.950198\pi\)
0.628836 + 0.777538i \(0.283532\pi\)
\(654\) 0 0
\(655\) −27.7477 48.0604i −1.08419 1.87787i
\(656\) −12.3618 −0.482648
\(657\) 0 0
\(658\) 0 0
\(659\) 13.9248 + 24.1184i 0.542432 + 0.939519i 0.998764 + 0.0497098i \(0.0158297\pi\)
−0.456332 + 0.889810i \(0.650837\pi\)
\(660\) 0 0
\(661\) −19.5071 + 33.7872i −0.758737 + 1.31417i 0.184758 + 0.982784i \(0.440850\pi\)
−0.943495 + 0.331387i \(0.892484\pi\)
\(662\) −4.48633 + 7.77054i −0.174366 + 0.302011i
\(663\) 0 0
\(664\) 11.4700 + 19.8667i 0.445123 + 0.770976i
\(665\) 0 0
\(666\) 0 0
\(667\) −10.2641 −0.397426
\(668\) 15.4634 + 26.7834i 0.598296 + 1.03628i
\(669\) 0 0
\(670\) −0.942405 + 1.63229i −0.0364083 + 0.0630610i
\(671\) −4.82170 + 8.35143i −0.186140 + 0.322404i
\(672\) 0 0
\(673\) 24.6154 + 42.6352i 0.948856 + 1.64347i 0.747841 + 0.663878i \(0.231090\pi\)
0.201014 + 0.979588i \(0.435576\pi\)
\(674\) 12.4053 0.477833
\(675\) 0 0
\(676\) 20.2914 0.780438
\(677\) −11.6958 20.2577i −0.449505 0.778565i 0.548849 0.835922i \(-0.315066\pi\)
−0.998354 + 0.0573564i \(0.981733\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.859180 + 1.48814i −0.0329480 + 0.0570677i
\(681\) 0 0
\(682\) −0.793387 1.37419i −0.0303803 0.0526203i
\(683\) −30.3264 −1.16041 −0.580204 0.814471i \(-0.697027\pi\)
−0.580204 + 0.814471i \(0.697027\pi\)
\(684\) 0 0
\(685\) 1.80380 0.0689196
\(686\) 0 0
\(687\) 0 0
\(688\) −12.8980 + 22.3401i −0.491733 + 0.851707i
\(689\) −5.91731 + 10.2491i −0.225432 + 0.390459i
\(690\) 0 0
\(691\) 2.05665 + 3.56223i 0.0782387 + 0.135513i 0.902490 0.430711i \(-0.141737\pi\)
−0.824251 + 0.566224i \(0.808404\pi\)
\(692\) −6.81797 −0.259180
\(693\) 0 0
\(694\) −5.33003 −0.202325
\(695\) −18.2224 31.5621i −0.691215 1.19722i
\(696\) 0 0
\(697\) −0.597691 + 1.03523i −0.0226392 + 0.0392122i
\(698\) −0.814716 + 1.41113i −0.0308375 + 0.0534120i
\(699\) 0 0
\(700\) 0 0
\(701\) −29.1835 −1.10225 −0.551123 0.834424i \(-0.685800\pi\)
−0.551123 + 0.834424i \(0.685800\pi\)
\(702\) 0 0
\(703\) −13.2869 −0.501127
\(704\) 1.19983 + 2.07816i 0.0452202 + 0.0783236i
\(705\) 0 0
\(706\) 4.17005 7.22274i 0.156942 0.271831i
\(707\) 0 0
\(708\) 0 0
\(709\) 21.2309 + 36.7729i 0.797342 + 1.38104i 0.921341 + 0.388755i \(0.127095\pi\)
−0.123999 + 0.992282i \(0.539572\pi\)
\(710\) 9.05507 0.339831
\(711\) 0 0
\(712\) 4.48150 0.167951
\(713\) 4.44149 + 7.69288i 0.166335 + 0.288101i
\(714\) 0 0
\(715\) 1.97211 3.41579i 0.0737526 0.127743i
\(716\) 6.43336 11.1429i 0.240426 0.416430i
\(717\) 0 0
\(718\) −5.89692 10.2138i −0.220071 0.381175i
\(719\) −11.1425 −0.415546 −0.207773 0.978177i \(-0.566621\pi\)
−0.207773 + 0.978177i \(0.566621\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.75544 + 4.77256i 0.102547 + 0.177616i
\(723\) 0 0
\(724\) 9.87264 17.0999i 0.366914 0.635513i
\(725\) −17.8858 + 30.9790i −0.664260 + 1.15053i
\(726\) 0 0
\(727\) −14.3410 24.8393i −0.531878 0.921239i −0.999308 0.0372089i \(-0.988153\pi\)
0.467430 0.884030i \(-0.345180\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3.35175 0.124054
\(731\) 1.24724 + 2.16028i 0.0461307 + 0.0799007i
\(732\) 0 0
\(733\) 12.5264 21.6964i 0.462674 0.801375i −0.536419 0.843952i \(-0.680223\pi\)
0.999093 + 0.0425768i \(0.0135567\pi\)
\(734\) 0.171071 0.296303i 0.00631433 0.0109367i
\(735\) 0 0
\(736\) 6.20047 + 10.7395i 0.228552 + 0.395864i
\(737\) 0.918782 0.0338438
\(738\) 0 0
\(739\) −27.5216 −1.01240 −0.506198 0.862417i \(-0.668950\pi\)
−0.506198 + 0.862417i \(0.668950\pi\)
\(740\) 15.3230 + 26.5402i 0.563284 + 0.975637i
\(741\) 0 0
\(742\) 0 0
\(743\) 7.00608 12.1349i 0.257028 0.445186i −0.708416 0.705795i \(-0.750590\pi\)
0.965444 + 0.260609i \(0.0839233\pi\)
\(744\) 0 0
\(745\) 38.8163 + 67.2318i 1.42212 + 2.46318i
\(746\) −1.86452 −0.0682650
\(747\) 0 0
\(748\) 0.391390 0.0143106
\(749\) 0 0
\(750\) 0 0
\(751\) 26.1297 45.2580i 0.953486 1.65149i 0.215692 0.976461i \(-0.430799\pi\)
0.737795 0.675025i \(-0.235867\pi\)
\(752\) −13.1494 + 22.7755i −0.479511 + 0.830537i
\(753\) 0 0
\(754\) 1.22912 + 2.12889i 0.0447618 + 0.0775298i
\(755\) 5.53289 0.201363
\(756\) 0 0
\(757\) −43.3447 −1.57539 −0.787694 0.616066i \(-0.788725\pi\)
−0.787694 + 0.616066i \(0.788725\pi\)
\(758\) −8.15047 14.1170i −0.296038 0.512753i
\(759\) 0 0
\(760\) −9.65191 + 16.7176i −0.350112 + 0.606411i
\(761\) −8.62550 + 14.9398i −0.312674 + 0.541568i −0.978940 0.204146i \(-0.934558\pi\)
0.666266 + 0.745714i \(0.267891\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −41.8285 −1.51330
\(765\) 0 0
\(766\) 0.531903 0.0192184
\(767\) −1.08444 1.87831i −0.0391570 0.0678218i
\(768\) 0 0
\(769\) −10.6727 + 18.4856i −0.384867 + 0.666609i −0.991751 0.128182i \(-0.959086\pi\)
0.606884 + 0.794790i \(0.292419\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.20495 + 9.01523i 0.187330 + 0.324465i
\(773\) −13.1471 −0.472870 −0.236435 0.971647i \(-0.575979\pi\)
−0.236435 + 0.971647i \(0.575979\pi\)
\(774\) 0 0
\(775\) 30.9583 1.11205
\(776\) −10.2796 17.8049i −0.369018 0.639158i
\(777\) 0 0
\(778\) −5.88685 + 10.1963i −0.211054 + 0.365556i
\(779\) −6.71439 + 11.6297i −0.240568 + 0.416676i
\(780\) 0 0
\(781\) −2.20702 3.82268i −0.0789735 0.136786i
\(782\) 0.307134 0.0109831
\(783\) 0 0
\(784\) 0 0
\(785\) 30.7954 + 53.3393i 1.09914 + 1.90376i
\(786\) 0 0
\(787\) 14.0650 24.3614i 0.501364 0.868389i −0.498634 0.866812i \(-0.666165\pi\)
0.999999 0.00157623i \(-0.000501728\pi\)
\(788\) 13.5665 23.4979i 0.483287 0.837077i
\(789\) 0 0
\(790\) 1.64713 + 2.85291i 0.0586021 + 0.101502i
\(791\) 0 0
\(792\) 0 0
\(793\) −12.9294 −0.459136
\(794\) −0.00795814 0.0137839i −0.000282424 0.000489172i
\(795\) 0 0
\(796\) −13.5912 + 23.5406i −0.481727 + 0.834376i
\(797\) −12.8683 + 22.2885i −0.455817 + 0.789499i −0.998735 0.0502873i \(-0.983986\pi\)
0.542917 + 0.839786i \(0.317320\pi\)
\(798\) 0 0
\(799\) 1.27155 + 2.20238i 0.0449841 + 0.0779147i
\(800\) 43.2188 1.52801
\(801\) 0 0
\(802\) −12.1615 −0.429436
\(803\) −0.816934 1.41497i −0.0288290 0.0499333i
\(804\) 0 0
\(805\) 0 0
\(806\) 1.06373 1.84244i 0.0374684 0.0648972i
\(807\) 0 0
\(808\) 2.41968 + 4.19100i 0.0851240 + 0.147439i
\(809\) 31.8705 1.12051 0.560254 0.828321i \(-0.310704\pi\)
0.560254 + 0.828321i \(0.310704\pi\)
\(810\) 0 0
\(811\) 43.3860 1.52349 0.761744 0.647878i \(-0.224343\pi\)
0.761744 + 0.647878i \(0.224343\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1.04704 + 1.81353i −0.0366987 + 0.0635641i
\(815\) −12.3382 + 21.3704i −0.432188 + 0.748571i
\(816\) 0 0
\(817\) 14.0113 + 24.2682i 0.490193 + 0.849039i
\(818\) 13.2842 0.464470
\(819\) 0 0
\(820\) 30.9731 1.08163
\(821\) −8.19677 14.1972i −0.286069 0.495487i 0.686799 0.726848i \(-0.259015\pi\)
−0.972868 + 0.231361i \(0.925682\pi\)
\(822\) 0 0
\(823\) 13.1890 22.8440i 0.459739 0.796292i −0.539208 0.842173i \(-0.681276\pi\)
0.998947 + 0.0458812i \(0.0146096\pi\)
\(824\) 9.03925 15.6564i 0.314897 0.545418i
\(825\) 0 0
\(826\) 0 0
\(827\) −36.7225 −1.27697 −0.638484 0.769635i \(-0.720438\pi\)
−0.638484 + 0.769635i \(0.720438\pi\)
\(828\) 0 0
\(829\) −24.3158 −0.844522 −0.422261 0.906474i \(-0.638763\pi\)
−0.422261 + 0.906474i \(0.638763\pi\)
\(830\) −11.2820 19.5410i −0.391604 0.678279i
\(831\) 0 0
\(832\) −1.60867 + 2.78629i −0.0557705 + 0.0965974i
\(833\) 0 0
\(834\) 0 0
\(835\) −32.5519 56.3815i −1.12650 1.95116i
\(836\) 4.39682 0.152067
\(837\) 0 0
\(838\) −10.4392 −0.360618
\(839\) 12.8405 + 22.2404i 0.443303 + 0.767824i 0.997932 0.0642741i \(-0.0204732\pi\)
−0.554629 + 0.832098i \(0.687140\pi\)
\(840\) 0 0
\(841\) 5.91963 10.2531i 0.204125 0.353555i
\(842\) −3.69190 + 6.39456i −0.127231 + 0.220371i
\(843\) 0 0
\(844\) −1.35400 2.34519i −0.0466065 0.0807249i
\(845\) −42.7153 −1.46945
\(846\) 0 0
\(847\) 0 0
\(848\) 12.7826 + 22.1402i 0.438958 + 0.760297i
\(849\) 0 0
\(850\) 0.535200 0.926994i 0.0183572 0.0317956i
\(851\) 5.86148 10.1524i 0.200929 0.348019i
\(852\) 0 0
\(853\) 14.4872 + 25.0925i 0.496031 + 0.859150i 0.999990 0.00457743i \(-0.00145705\pi\)
−0.503959 + 0.863728i \(0.668124\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 20.2918 0.693559
\(857\) −12.6934 21.9856i −0.433598 0.751015i 0.563582 0.826060i \(-0.309423\pi\)
−0.997180 + 0.0750458i \(0.976090\pi\)
\(858\) 0 0
\(859\) 2.97891 5.15963i 0.101639 0.176044i −0.810721 0.585433i \(-0.800925\pi\)
0.912360 + 0.409388i \(0.134258\pi\)
\(860\) 32.3166 55.9740i 1.10199 1.90870i
\(861\) 0 0
\(862\) 3.94310 + 6.82966i 0.134303 + 0.232619i
\(863\) 16.3909 0.557953 0.278977 0.960298i \(-0.410005\pi\)
0.278977 + 0.960298i \(0.410005\pi\)
\(864\) 0 0
\(865\) 14.3525 0.487999
\(866\) 4.05764 + 7.02804i 0.137884 + 0.238822i
\(867\) 0 0
\(868\) 0 0
\(869\) 0.802920 1.39070i 0.0272372 0.0471762i
\(870\) 0 0
\(871\) 0.615929 + 1.06682i 0.0208700 + 0.0361478i
\(872\) −3.95006 −0.133766
\(873\) 0 0
\(874\) 3.45030 0.116708
\(875\) 0 0
\(876\) 0 0
\(877\) −17.6270 + 30.5308i −0.595220 + 1.03095i 0.398295 + 0.917257i \(0.369602\pi\)
−0.993516 + 0.113695i \(0.963731\pi\)
\(878\) 3.85407 6.67544i 0.130068 0.225285i
\(879\) 0 0
\(880\) −4.26017 7.37883i −0.143610 0.248740i
\(881\) −26.2582 −0.884661 −0.442331 0.896852i \(-0.645848\pi\)
−0.442331 + 0.896852i \(0.645848\pi\)
\(882\) 0 0
\(883\) 10.0087 0.336821 0.168410 0.985717i \(-0.446137\pi\)
0.168410 + 0.985717i \(0.446137\pi\)
\(884\) 0.262378 + 0.454452i 0.00882473 + 0.0152849i
\(885\) 0 0
\(886\) 0.443815 0.768711i 0.0149103 0.0258253i
\(887\) −7.95282 + 13.7747i −0.267030 + 0.462509i −0.968093 0.250590i \(-0.919376\pi\)
0.701064 + 0.713099i \(0.252709\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −4.40804 −0.147758
\(891\) 0 0
\(892\) −9.54838 −0.319703
\(893\) 14.2844 + 24.7413i 0.478009 + 0.827935i
\(894\) 0 0
\(895\) −13.5428 + 23.4569i −0.452687 + 0.784077i
\(896\) 0 0
\(897\) 0 0
\(898\) 3.36364 + 5.82599i 0.112246 + 0.194416i
\(899\) 14.8517 0.495331
\(900\) 0 0
\(901\) 2.47215 0.0823594
\(902\) 1.05822 + 1.83288i 0.0352348 + 0.0610284i
\(903\) 0 0
\(904\) 14.7307 25.5144i 0.489937 0.848597i
\(905\) −20.7829 + 35.9970i −0.690846 + 1.19658i
\(906\) 0 0
\(907\) 8.54624 + 14.8025i 0.283773 + 0.491510i 0.972311 0.233691i \(-0.0750804\pi\)
−0.688538 + 0.725201i \(0.741747\pi\)
\(908\) −28.1998 −0.935843
\(909\) 0 0
\(910\) 0 0
\(911\) −14.9435 25.8829i −0.495099 0.857537i 0.504885 0.863187i \(-0.331535\pi\)
−0.999984 + 0.00564955i \(0.998202\pi\)
\(912\) 0 0
\(913\) −5.49961 + 9.52561i −0.182011 + 0.315252i
\(914\) −0.636986 + 1.10329i −0.0210696 + 0.0364937i
\(915\) 0 0
\(916\) −8.74286 15.1431i −0.288872 0.500341i
\(917\) 0 0
\(918\) 0 0
\(919\) −23.6567 −0.780362 −0.390181 0.920738i \(-0.627588\pi\)
−0.390181 + 0.920738i \(0.627588\pi\)
\(920\) −8.51579 14.7498i −0.280757 0.486286i
\(921\) 0 0
\(922\) −8.97196 + 15.5399i −0.295476 + 0.511779i
\(923\) 2.95907 5.12525i 0.0973989 0.168700i
\(924\) 0 0
\(925\) −20.4280 35.3823i −0.671667 1.16336i
\(926\) −8.12454 −0.266989
\(927\) 0 0
\(928\) 20.7334 0.680607
\(929\) 6.30880 + 10.9272i 0.206985 + 0.358509i 0.950763 0.309918i \(-0.100302\pi\)
−0.743778 + 0.668426i \(0.766968\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 14.5073 25.1274i 0.475203 0.823075i
\(933\) 0 0
\(934\) 2.15714 + 3.73627i 0.0705836 + 0.122254i
\(935\) −0.823914 −0.0269449
\(936\) 0 0
\(937\) −26.3440 −0.860622 −0.430311 0.902681i \(-0.641596\pi\)
−0.430311 + 0.902681i \(0.641596\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 32.9465 57.0651i 1.07460 1.86126i
\(941\) 25.4699 44.1151i 0.830294 1.43811i −0.0675118 0.997718i \(-0.521506\pi\)
0.897805 0.440392i \(-0.145161\pi\)
\(942\) 0 0
\(943\) −5.92404 10.2607i −0.192913 0.334136i
\(944\) −4.68525 −0.152492
\(945\) 0 0
\(946\) 4.41648 0.143592
\(947\) 13.8399 + 23.9714i 0.449737 + 0.778967i 0.998369 0.0570968i \(-0.0181844\pi\)
−0.548632 + 0.836064i \(0.684851\pi\)
\(948\) 0 0
\(949\) 1.09530 1.89712i 0.0355551 0.0615832i
\(950\) 6.01236 10.4137i 0.195067 0.337866i
\(951\) 0 0
\(952\) 0 0
\(953\) 27.4017 0.887628 0.443814 0.896119i \(-0.353625\pi\)
0.443814 + 0.896119i \(0.353625\pi\)
\(954\) 0 0
\(955\) 88.0530 2.84933
\(956\) −19.3162 33.4567i −0.624731 1.08207i
\(957\) 0 0
\(958\) −4.40515 + 7.62994i −0.142324 + 0.246512i
\(959\) 0 0
\(960\) 0 0
\(961\) 9.07336 + 15.7155i 0.292689 + 0.506952i
\(962\) −2.80764 −0.0905219
\(963\) 0 0
\(964\) −29.3289 −0.944621
\(965\) −10.9569 18.9779i −0.352715 0.610921i
\(966\) 0 0
\(967\) 9.09069 15.7455i 0.292337 0.506342i −0.682025 0.731329i \(-0.738900\pi\)
0.974362 + 0.224986i \(0.0722338\pi\)
\(968\) −9.49698 + 16.4492i −0.305244 + 0.528699i
\(969\) 0 0
\(970\) 10.1111 + 17.5130i 0.324649 + 0.562309i
\(971\) 39.4832 1.26708 0.633538 0.773712i \(-0.281602\pi\)
0.633538 + 0.773712i \(0.281602\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 4.12941 + 7.15234i 0.132315 + 0.229176i
\(975\) 0 0
\(976\) −13.9651 + 24.1883i −0.447012 + 0.774248i
\(977\) 5.95782 10.3193i 0.190608 0.330142i −0.754844 0.655904i \(-0.772288\pi\)
0.945452 + 0.325762i \(0.105621\pi\)
\(978\) 0 0
\(979\) 1.07439 + 1.86090i 0.0343376 + 0.0594745i
\(980\) 0 0
\(981\) 0 0
\(982\) −3.18368 −0.101595
\(983\) −9.23896 16.0024i −0.294677 0.510396i 0.680233 0.732996i \(-0.261879\pi\)
−0.974910 + 0.222601i \(0.928545\pi\)
\(984\) 0 0
\(985\) −28.5588 + 49.4653i −0.909959 + 1.57609i
\(986\) 0.256752 0.444708i 0.00817666 0.0141624i
\(987\) 0 0
\(988\) 2.94752 + 5.10525i 0.0937731 + 0.162420i
\(989\) −24.7241 −0.786179
\(990\) 0 0
\(991\) 12.6970 0.403334 0.201667 0.979454i \(-0.435364\pi\)
0.201667 + 0.979454i \(0.435364\pi\)
\(992\) −8.97181 15.5396i −0.284855 0.493384i
\(993\) 0 0
\(994\) 0 0
\(995\) 28.6108 49.5553i 0.907023 1.57101i
\(996\) 0 0
\(997\) −20.9767 36.3327i −0.664338 1.15067i −0.979464 0.201617i \(-0.935380\pi\)
0.315127 0.949050i \(-0.397953\pi\)
\(998\) 5.52690 0.174951
\(999\) 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 1323.2.f.e.442.3 10
3.2 odd 2 441.2.f.e.148.3 10
7.2 even 3 189.2.g.b.172.3 10
7.3 odd 6 1323.2.h.f.226.3 10
7.4 even 3 189.2.h.b.37.3 10
7.5 odd 6 1323.2.g.f.361.3 10
7.6 odd 2 1323.2.f.f.442.3 10
9.2 odd 6 441.2.f.e.295.3 10
9.4 even 3 3969.2.a.bc.1.3 5
9.5 odd 6 3969.2.a.z.1.3 5
9.7 even 3 inner 1323.2.f.e.883.3 10
21.2 odd 6 63.2.g.b.4.3 10
21.5 even 6 441.2.g.f.67.3 10
21.11 odd 6 63.2.h.b.58.3 yes 10
21.17 even 6 441.2.h.f.373.3 10
21.20 even 2 441.2.f.f.148.3 10
28.11 odd 6 3024.2.q.i.2305.1 10
28.23 odd 6 3024.2.t.i.1873.5 10
63.2 odd 6 63.2.h.b.25.3 yes 10
63.4 even 3 567.2.e.e.163.3 10
63.11 odd 6 63.2.g.b.16.3 yes 10
63.13 odd 6 3969.2.a.bb.1.3 5
63.16 even 3 189.2.h.b.46.3 10
63.20 even 6 441.2.f.f.295.3 10
63.23 odd 6 567.2.e.f.487.3 10
63.25 even 3 189.2.g.b.100.3 10
63.32 odd 6 567.2.e.f.163.3 10
63.34 odd 6 1323.2.f.f.883.3 10
63.38 even 6 441.2.g.f.79.3 10
63.41 even 6 3969.2.a.ba.1.3 5
63.47 even 6 441.2.h.f.214.3 10
63.52 odd 6 1323.2.g.f.667.3 10
63.58 even 3 567.2.e.e.487.3 10
63.61 odd 6 1323.2.h.f.802.3 10
84.11 even 6 1008.2.q.i.625.3 10
84.23 even 6 1008.2.t.i.193.1 10
252.11 even 6 1008.2.t.i.961.1 10
252.79 odd 6 3024.2.q.i.2881.1 10
252.151 odd 6 3024.2.t.i.289.5 10
252.191 even 6 1008.2.q.i.529.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.3 10 21.2 odd 6
63.2.g.b.16.3 yes 10 63.11 odd 6
63.2.h.b.25.3 yes 10 63.2 odd 6
63.2.h.b.58.3 yes 10 21.11 odd 6
189.2.g.b.100.3 10 63.25 even 3
189.2.g.b.172.3 10 7.2 even 3
189.2.h.b.37.3 10 7.4 even 3
189.2.h.b.46.3 10 63.16 even 3
441.2.f.e.148.3 10 3.2 odd 2
441.2.f.e.295.3 10 9.2 odd 6
441.2.f.f.148.3 10 21.20 even 2
441.2.f.f.295.3 10 63.20 even 6
441.2.g.f.67.3 10 21.5 even 6
441.2.g.f.79.3 10 63.38 even 6
441.2.h.f.214.3 10 63.47 even 6
441.2.h.f.373.3 10 21.17 even 6
567.2.e.e.163.3 10 63.4 even 3
567.2.e.e.487.3 10 63.58 even 3
567.2.e.f.163.3 10 63.32 odd 6
567.2.e.f.487.3 10 63.23 odd 6
1008.2.q.i.529.3 10 252.191 even 6
1008.2.q.i.625.3 10 84.11 even 6
1008.2.t.i.193.1 10 84.23 even 6
1008.2.t.i.961.1 10 252.11 even 6
1323.2.f.e.442.3 10 1.1 even 1 trivial
1323.2.f.e.883.3 10 9.7 even 3 inner
1323.2.f.f.442.3 10 7.6 odd 2
1323.2.f.f.883.3 10 63.34 odd 6
1323.2.g.f.361.3 10 7.5 odd 6
1323.2.g.f.667.3 10 63.52 odd 6
1323.2.h.f.226.3 10 7.3 odd 6
1323.2.h.f.802.3 10 63.61 odd 6
3024.2.q.i.2305.1 10 28.11 odd 6
3024.2.q.i.2881.1 10 252.79 odd 6
3024.2.t.i.289.5 10 252.151 odd 6
3024.2.t.i.1873.5 10 28.23 odd 6
3969.2.a.z.1.3 5 9.5 odd 6
3969.2.a.ba.1.3 5 63.41 even 6
3969.2.a.bb.1.3 5 63.13 odd 6
3969.2.a.bc.1.3 5 9.4 even 3