Properties

Label 2106.2.e.b.703.1
Level $2106$
Weight $2$
Character 2106.703
Analytic conductor $16.816$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2106,2,Mod(703,2106)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2106, 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("2106.703");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2106.e (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: \(16.8164946657\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 703.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2106.703
Dual form 2106.2.e.b.1405.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(3.00000 - 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +2.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(3.00000 + 5.19615i) q^{22} +(-2.00000 + 3.46410i) q^{25} +1.00000 q^{26} -1.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{35} -7.00000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(0.500000 - 0.866025i) q^{43} -6.00000 q^{44} +(1.50000 - 2.59808i) q^{47} +(3.00000 + 5.19615i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-0.500000 + 0.866025i) q^{52} -18.0000 q^{55} +(0.500000 - 0.866025i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-7.00000 - 12.1244i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(1.50000 - 2.59808i) q^{70} +3.00000 q^{71} +2.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(-4.00000 + 6.92820i) q^{79} +3.00000 q^{80} +(6.00000 - 10.3923i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(0.500000 + 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{88} +6.00000 q^{89} -1.00000 q^{91} +(1.50000 + 2.59808i) q^{94} +(-3.00000 - 5.19615i) q^{95} +(5.00000 - 8.66025i) q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 3 q^{5} + q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 3 q^{5} + q^{7} + 2 q^{8} + 6 q^{10} + 6 q^{11} - q^{13} + q^{14} - q^{16} + 6 q^{17} + 4 q^{19} - 3 q^{20} + 6 q^{22} - 4 q^{25} + 2 q^{26} - 2 q^{28} + 6 q^{29} + 4 q^{31} - q^{32} - 3 q^{34} - 6 q^{35} - 14 q^{37} - 2 q^{38} - 3 q^{40} + q^{43} - 12 q^{44} + 3 q^{47} + 6 q^{49} - 4 q^{50} - q^{52} - 36 q^{55} + q^{56} + 6 q^{58} - 6 q^{59} - 8 q^{61} - 8 q^{62} + 2 q^{64} - 3 q^{65} - 14 q^{67} - 3 q^{68} + 3 q^{70} + 6 q^{71} + 4 q^{73} + 7 q^{74} - 2 q^{76} - 6 q^{77} - 8 q^{79} + 6 q^{80} + 12 q^{83} - 9 q^{85} + q^{86} + 6 q^{88} + 12 q^{89} - 2 q^{91} + 3 q^{94} - 6 q^{95} + 10 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2106\mathbb{Z}\right)^\times\).

\(n\) \(1379\) \(1783\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 3.00000 0.948683
\(11\) 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) 3.00000 + 5.19615i 0.639602 + 1.10782i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) 0 0
\(47\) 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i \(-0.763120\pi\)
0.954441 + 0.298401i \(0.0964533\pi\)
\(48\) 0 0
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) −0.500000 + 0.866025i −0.0693375 + 0.120096i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) −18.0000 −2.42712
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 0 0
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.50000 + 2.59808i −0.186052 + 0.322252i
\(66\) 0 0
\(67\) −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 0 0
\(70\) 1.50000 2.59808i 0.179284 0.310530i
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 3.50000 6.06218i 0.406867 0.704714i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) −3.00000 5.19615i −0.341882 0.592157i
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 3.00000 0.335410
\(81\) 0 0
\(82\) 0 0
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) 0.500000 + 0.866025i 0.0539164 + 0.0933859i
\(87\) 0 0
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 0 0
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 0 0
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) −0.500000 0.866025i −0.0490290 0.0849208i
\(105\) 0 0
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 9.00000 15.5885i 0.858116 1.48630i
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) −10.5000 18.1865i −0.917389 1.58896i −0.803365 0.595487i \(-0.796959\pi\)
−0.114024 0.993478i \(-0.536374\pi\)
\(132\) 0 0
\(133\) 1.00000 1.73205i 0.0867110 0.150188i
\(134\) 14.0000 1.20942
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(138\) 0 0
\(139\) 6.50000 + 11.2583i 0.551323 + 0.954919i 0.998179 + 0.0603135i \(0.0192101\pi\)
−0.446857 + 0.894606i \(0.647457\pi\)
\(140\) 1.50000 + 2.59808i 0.126773 + 0.219578i
\(141\) 0 0
\(142\) −1.50000 + 2.59808i −0.125877 + 0.218026i
\(143\) −6.00000 −0.501745
\(144\) 0 0
\(145\) −18.0000 −1.49482
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) 3.50000 + 6.06218i 0.287698 + 0.498308i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −8.50000 + 14.7224i −0.691720 + 1.19809i 0.279554 + 0.960130i \(0.409814\pi\)
−0.971274 + 0.237964i \(0.923520\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 6.00000 10.3923i 0.481932 0.834730i
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) 0 0
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 0 0
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 9.00000 0.690268
\(171\) 0 0
\(172\) −1.00000 −0.0762493
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 3.00000 + 5.19615i 0.226134 + 0.391675i
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −3.00000 −0.224231 −0.112115 0.993695i \(-0.535763\pi\)
−0.112115 + 0.993695i \(0.535763\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0.500000 0.866025i 0.0370625 0.0641941i
\(183\) 0 0
\(184\) 0 0
\(185\) 10.5000 + 18.1865i 0.771975 + 1.33710i
\(186\) 0 0
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) −3.00000 −0.218797
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) 5.00000 + 8.66025i 0.358979 + 0.621770i
\(195\) 0 0
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) −6.00000 10.3923i −0.422159 0.731200i
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) 0 0
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) 6.00000 10.3923i 0.415029 0.718851i
\(210\) 0 0
\(211\) 6.50000 + 11.2583i 0.447478 + 0.775055i 0.998221 0.0596196i \(-0.0189888\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) −3.00000 −0.204598
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 3.50000 6.06218i 0.237050 0.410582i
\(219\) 0 0
\(220\) 9.00000 + 15.5885i 0.606780 + 1.05097i
\(221\) −1.50000 2.59808i −0.100901 0.174766i
\(222\) 0 0
\(223\) 9.50000 16.4545i 0.636167 1.10187i −0.350100 0.936713i \(-0.613852\pi\)
0.986267 0.165161i \(-0.0528144\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 6.00000 0.399114
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) 6.50000 + 11.2583i 0.429532 + 0.743971i 0.996832 0.0795401i \(-0.0253452\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 27.0000 1.76883 0.884414 0.466702i \(-0.154558\pi\)
0.884414 + 0.466702i \(0.154558\pi\)
\(234\) 0 0
\(235\) −9.00000 −0.587095
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 0 0
\(238\) 1.50000 + 2.59808i 0.0972306 + 0.168408i
\(239\) 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 25.0000 1.60706
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) 9.00000 15.5885i 0.574989 0.995910i
\(246\) 0 0
\(247\) −1.00000 1.73205i −0.0636285 0.110208i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) 0 0
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −10.0000 + 17.3205i −0.627456 + 1.08679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.50000 + 7.79423i 0.280702 + 0.486191i 0.971558 0.236802i \(-0.0760993\pi\)
−0.690856 + 0.722993i \(0.742766\pi\)
\(258\) 0 0
\(259\) −3.50000 + 6.06218i −0.217479 + 0.376685i
\(260\) 3.00000 0.186052
\(261\) 0 0
\(262\) 21.0000 1.29738
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.00000 + 1.73205i 0.0613139 + 0.106199i
\(267\) 0 0
\(268\) −7.00000 + 12.1244i −0.427593 + 0.740613i
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) 11.0000 0.668202 0.334101 0.942537i \(-0.391567\pi\)
0.334101 + 0.942537i \(0.391567\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) 0 0
\(275\) 12.0000 + 20.7846i 0.723627 + 1.25336i
\(276\) 0 0
\(277\) 14.0000 24.2487i 0.841178 1.45696i −0.0477206 0.998861i \(-0.515196\pi\)
0.888899 0.458103i \(-0.151471\pi\)
\(278\) −13.0000 −0.779688
\(279\) 0 0
\(280\) −3.00000 −0.179284
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −1.50000 2.59808i −0.0890086 0.154167i
\(285\) 0 0
\(286\) 3.00000 5.19615i 0.177394 0.307255i
\(287\) 0 0
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 9.00000 15.5885i 0.528498 0.915386i
\(291\) 0 0
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) 10.5000 + 18.1865i 0.613417 + 1.06247i 0.990660 + 0.136355i \(0.0435386\pi\)
−0.377244 + 0.926114i \(0.623128\pi\)
\(294\) 0 0
\(295\) −9.00000 + 15.5885i −0.524000 + 0.907595i
\(296\) −7.00000 −0.406867
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −0.500000 0.866025i −0.0288195 0.0499169i
\(302\) −8.50000 14.7224i −0.489120 0.847181i
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 24.0000 1.37424
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −3.00000 + 5.19615i −0.170941 + 0.296078i
\(309\) 0 0
\(310\) 6.00000 + 10.3923i 0.340777 + 0.590243i
\(311\) −15.0000 25.9808i −0.850572 1.47323i −0.880693 0.473688i \(-0.842923\pi\)
0.0301210 0.999546i \(-0.490411\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) −18.0000 31.1769i −1.00781 1.74557i
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) 4.00000 0.221880
\(326\) 8.00000 13.8564i 0.443079 0.767435i
\(327\) 0 0
\(328\) 0 0
\(329\) −1.50000 2.59808i −0.0826977 0.143237i
\(330\) 0 0
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 0 0
\(335\) −21.0000 + 36.3731i −1.14735 + 1.98727i
\(336\) 0 0
\(337\) −11.5000 19.9186i −0.626445 1.08503i −0.988260 0.152784i \(-0.951176\pi\)
0.361815 0.932250i \(-0.382157\pi\)
\(338\) −0.500000 0.866025i −0.0271964 0.0471056i
\(339\) 0 0
\(340\) −4.50000 + 7.79423i −0.244047 + 0.422701i
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0.500000 0.866025i 0.0269582 0.0466930i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) 9.50000 16.4545i 0.508523 0.880788i −0.491428 0.870918i \(-0.663525\pi\)
0.999951 0.00987003i \(-0.00314178\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) −6.00000 −0.319801
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 0 0
\(355\) −4.50000 7.79423i −0.238835 0.413675i
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) 0 0
\(358\) 1.50000 2.59808i 0.0792775 0.137313i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −10.0000 + 17.3205i −0.525588 + 0.910346i
\(363\) 0 0
\(364\) 0.500000 + 0.866025i 0.0262071 + 0.0453921i
\(365\) −3.00000 5.19615i −0.157027 0.271979i
\(366\) 0 0
\(367\) −13.0000 + 22.5167i −0.678594 + 1.17536i 0.296810 + 0.954937i \(0.404077\pi\)
−0.975404 + 0.220423i \(0.929256\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −21.0000 −1.09174
\(371\) 0 0
\(372\) 0 0
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −3.00000 + 5.19615i −0.153897 + 0.266557i
\(381\) 0 0
\(382\) −9.00000 15.5885i −0.460480 0.797575i
\(383\) 10.5000 + 18.1865i 0.536525 + 0.929288i 0.999088 + 0.0427020i \(0.0135966\pi\)
−0.462563 + 0.886586i \(0.653070\pi\)
\(384\) 0 0
\(385\) −9.00000 + 15.5885i −0.458682 + 0.794461i
\(386\) −4.00000 −0.203595
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.00000 + 5.19615i 0.151523 + 0.262445i
\(393\) 0 0
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) 24.0000 1.20757
\(396\) 0 0
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −1.00000 + 1.73205i −0.0501255 + 0.0868199i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i \(0.188949\pi\)
0.0699455 + 0.997551i \(0.477717\pi\)
\(402\) 0 0
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) −21.0000 + 36.3731i −1.04093 + 1.80295i
\(408\) 0 0
\(409\) −16.0000 27.7128i −0.791149 1.37031i −0.925256 0.379344i \(-0.876150\pi\)
0.134107 0.990967i \(-0.457183\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) −36.0000 −1.76717
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) 6.00000 + 10.3923i 0.293470 + 0.508304i
\(419\) 4.50000 + 7.79423i 0.219839 + 0.380773i 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 0 0
\(421\) −8.50000 + 14.7224i −0.414265 + 0.717527i −0.995351 0.0963145i \(-0.969295\pi\)
0.581086 + 0.813842i \(0.302628\pi\)
\(422\) −13.0000 −0.632830
\(423\) 0 0
\(424\) 0 0
\(425\) −6.00000 + 10.3923i −0.291043 + 0.504101i
\(426\) 0 0
\(427\) 4.00000 + 6.92820i 0.193574 + 0.335279i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 0 0
\(430\) 1.50000 2.59808i 0.0723364 0.125290i
\(431\) 33.0000 1.58955 0.794777 0.606902i \(-0.207588\pi\)
0.794777 + 0.606902i \(0.207588\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) −2.00000 + 3.46410i −0.0960031 + 0.166282i
\(435\) 0 0
\(436\) 3.50000 + 6.06218i 0.167620 + 0.290326i
\(437\) 0 0
\(438\) 0 0
\(439\) −13.0000 + 22.5167i −0.620456 + 1.07466i 0.368945 + 0.929451i \(0.379719\pi\)
−0.989401 + 0.145210i \(0.953614\pi\)
\(440\) −18.0000 −0.858116
\(441\) 0 0
\(442\) 3.00000 0.142695
\(443\) 10.5000 18.1865i 0.498870 0.864068i −0.501129 0.865373i \(-0.667082\pi\)
0.999999 + 0.00130426i \(0.000415158\pi\)
\(444\) 0 0
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) 9.50000 + 16.4545i 0.449838 + 0.779142i
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) 0 0
\(454\) 0 0
\(455\) 1.50000 + 2.59808i 0.0703211 + 0.121800i
\(456\) 0 0
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −13.0000 −0.607450
\(459\) 0 0
\(460\) 0 0
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) 0 0
\(463\) 20.0000 + 34.6410i 0.929479 + 1.60990i 0.784195 + 0.620515i \(0.213076\pi\)
0.145284 + 0.989390i \(0.453590\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 0 0
\(466\) −13.5000 + 23.3827i −0.625375 + 1.08318i
\(467\) −36.0000 −1.66588 −0.832941 0.553362i \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) 0 0
\(469\) −14.0000 −0.646460
\(470\) 4.50000 7.79423i 0.207570 0.359521i
\(471\) 0 0
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) 0 0
\(475\) −4.00000 + 6.92820i −0.183533 + 0.317888i
\(476\) −3.00000 −0.137505
\(477\) 0 0
\(478\) −15.0000 −0.686084
\(479\) −10.5000 + 18.1865i −0.479757 + 0.830964i −0.999730 0.0232187i \(-0.992609\pi\)
0.519973 + 0.854183i \(0.325942\pi\)
\(480\) 0 0
\(481\) 3.50000 + 6.06218i 0.159586 + 0.276412i
\(482\) 5.00000 + 8.66025i 0.227744 + 0.394464i
\(483\) 0 0
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) −30.0000 −1.36223
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 0 0
\(490\) 9.00000 + 15.5885i 0.406579 + 0.704215i
\(491\) −4.50000 7.79423i −0.203082 0.351749i 0.746438 0.665455i \(-0.231763\pi\)
−0.949520 + 0.313707i \(0.898429\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 2.00000 0.0899843
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 1.50000 2.59808i 0.0672842 0.116540i
\(498\) 0 0
\(499\) 20.0000 + 34.6410i 0.895323 + 1.55074i 0.833404 + 0.552664i \(0.186389\pi\)
0.0619186 + 0.998081i \(0.480278\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 0 0
\(502\) 12.0000 20.7846i 0.535586 0.927663i
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) −10.0000 17.3205i −0.443678 0.768473i
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) 1.00000 1.73205i 0.0442374 0.0766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −9.00000 −0.396973
\(515\) 6.00000 10.3923i 0.264392 0.457940i
\(516\) 0 0
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) −3.50000 6.06218i −0.153781 0.266357i
\(519\) 0 0
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) 9.00000 0.394297 0.197149 0.980374i \(-0.436832\pi\)
0.197149 + 0.980374i \(0.436832\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −10.5000 + 18.1865i −0.458695 + 0.794482i
\(525\) 0 0
\(526\) −6.00000 10.3923i −0.261612 0.453126i
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 0 0
\(534\) 0 0
\(535\) 18.0000 + 31.1769i 0.778208 + 1.34790i
\(536\) −7.00000 12.1244i −0.302354 0.523692i
\(537\) 0 0
\(538\) 12.0000 20.7846i 0.517357 0.896088i
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) 11.0000 0.472927 0.236463 0.971640i \(-0.424012\pi\)
0.236463 + 0.971640i \(0.424012\pi\)
\(542\) −5.50000 + 9.52628i −0.236245 + 0.409189i
\(543\) 0 0
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 10.5000 + 18.1865i 0.449771 + 0.779026i
\(546\) 0 0
\(547\) −8.50000 + 14.7224i −0.363434 + 0.629486i −0.988524 0.151067i \(-0.951729\pi\)
0.625090 + 0.780553i \(0.285062\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −24.0000 −1.02336
\(551\) 6.00000 10.3923i 0.255609 0.442727i
\(552\) 0 0
\(553\) 4.00000 + 6.92820i 0.170097 + 0.294617i
\(554\) 14.0000 + 24.2487i 0.594803 + 1.03023i
\(555\) 0 0
\(556\) 6.50000 11.2583i 0.275661 0.477460i
\(557\) −3.00000 −0.127114 −0.0635570 0.997978i \(-0.520244\pi\)
−0.0635570 + 0.997978i \(0.520244\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) 1.50000 2.59808i 0.0633866 0.109789i
\(561\) 0 0
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i \(0.140378\pi\)
−0.0824933 + 0.996592i \(0.526288\pi\)
\(564\) 0 0
\(565\) −9.00000 + 15.5885i −0.378633 + 0.655811i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 3.00000 0.125877
\(569\) 7.50000 12.9904i 0.314416 0.544585i −0.664897 0.746935i \(-0.731525\pi\)
0.979313 + 0.202350i \(0.0648579\pi\)
\(570\) 0 0
\(571\) −2.50000 4.33013i −0.104622 0.181210i 0.808962 0.587861i \(-0.200030\pi\)
−0.913584 + 0.406651i \(0.866697\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 0 0
\(580\) 9.00000 + 15.5885i 0.373705 + 0.647275i
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) 0 0
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −21.0000 −0.867502
\(587\) 12.0000 20.7846i 0.495293 0.857873i −0.504692 0.863299i \(-0.668394\pi\)
0.999985 + 0.00542667i \(0.00172737\pi\)
\(588\) 0 0
\(589\) 4.00000 + 6.92820i 0.164817 + 0.285472i
\(590\) −9.00000 15.5885i −0.370524 0.641767i
\(591\) 0 0
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) −9.00000 −0.368964
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) 3.00000 + 5.19615i 0.122577 + 0.212309i 0.920783 0.390075i \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 0 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 1.00000 0.0407570
\(603\) 0 0
\(604\) 17.0000 0.691720
\(605\) −37.5000 + 64.9519i −1.52459 + 2.64067i
\(606\) 0 0
\(607\) −7.00000 12.1244i −0.284121 0.492112i 0.688274 0.725450i \(-0.258368\pi\)
−0.972396 + 0.233338i \(0.925035\pi\)
\(608\) −1.00000 1.73205i −0.0405554 0.0702439i
\(609\) 0 0
\(610\) −12.0000 + 20.7846i −0.485866 + 0.841544i
\(611\) −3.00000 −0.121367
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) −3.00000 5.19615i −0.120873 0.209359i
\(617\) −12.0000 20.7846i −0.483102 0.836757i 0.516710 0.856161i \(-0.327157\pi\)
−0.999812 + 0.0194037i \(0.993823\pi\)
\(618\) 0 0
\(619\) 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i \(-0.643093\pi\)
0.997259 0.0739910i \(-0.0235736\pi\)
\(620\) −12.0000 −0.481932
\(621\) 0 0
\(622\) 30.0000 1.20289
\(623\) 3.00000 5.19615i 0.120192 0.208179i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0.500000 + 0.866025i 0.0199840 + 0.0346133i
\(627\) 0 0
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) −4.00000 + 6.92820i −0.159111 + 0.275589i
\(633\) 0 0
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) −30.0000 51.9615i −1.19051 2.06203i
\(636\) 0 0
\(637\) 3.00000 5.19615i 0.118864 0.205879i
\(638\) 36.0000 1.42525
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) 0 0
\(643\) −7.00000 12.1244i −0.276053 0.478138i 0.694347 0.719640i \(-0.255693\pi\)
−0.970400 + 0.241502i \(0.922360\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) 6.00000 0.235884 0.117942 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) 0 0
\(649\) −36.0000 −1.41312
\(650\) −2.00000 + 3.46410i −0.0784465 + 0.135873i
\(651\) 0 0
\(652\) 8.00000 + 13.8564i 0.313304 + 0.542659i
\(653\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(654\) 0 0
\(655\) −31.5000 + 54.5596i −1.23081 + 2.13182i
\(656\) 0 0
\(657\) 0 0
\(658\) 3.00000 0.116952
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) −4.00000 6.92820i −0.155464 0.269272i
\(663\) 0 0
\(664\) 6.00000 10.3923i 0.232845 0.403300i
\(665\) −6.00000 −0.232670
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −21.0000 36.3731i −0.811301 1.40521i
\(671\) 24.0000 + 41.5692i 0.926510 + 1.60476i
\(672\) 0 0
\(673\) 9.50000 16.4545i 0.366198 0.634274i −0.622770 0.782405i \(-0.713993\pi\)
0.988968 + 0.148132i \(0.0473259\pi\)
\(674\) 23.0000 0.885927
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 24.0000 41.5692i 0.922395 1.59763i 0.126697 0.991941i \(-0.459562\pi\)
0.795698 0.605693i \(-0.207104\pi\)
\(678\) 0 0
\(679\) −5.00000 8.66025i −0.191882 0.332350i
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) 0 0
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −6.50000 + 11.2583i −0.248171 + 0.429845i
\(687\) 0 0
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) 0 0
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −3.00000 −0.113878
\(695\) 19.5000 33.7750i 0.739677 1.28116i
\(696\) 0 0
\(697\) 0 0
\(698\) 9.50000 + 16.4545i 0.359580 + 0.622811i
\(699\) 0 0
\(700\) 2.00000 3.46410i 0.0755929 0.130931i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −14.0000 −0.528020
\(704\) 3.00000 5.19615i 0.113067 0.195837i
\(705\) 0 0
\(706\) 12.0000 + 20.7846i 0.451626 + 0.782239i
\(707\) 6.00000 + 10.3923i 0.225653 + 0.390843i
\(708\) 0 0
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 9.00000 0.337764
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) 9.00000 + 15.5885i 0.336581 + 0.582975i
\(716\) 1.50000 + 2.59808i 0.0560576 + 0.0970947i
\(717\) 0 0
\(718\) 0 0
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 7.50000 12.9904i 0.279121 0.483452i
\(723\) 0 0
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) 0 0
\(727\) 5.00000 8.66025i 0.185440 0.321191i −0.758285 0.651923i \(-0.773962\pi\)
0.943725 + 0.330732i \(0.107296\pi\)
\(728\) −1.00000 −0.0370625
\(729\) 0 0
\(730\) 6.00000 0.222070
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) −11.5000 19.9186i −0.424762 0.735710i 0.571636 0.820507i \(-0.306309\pi\)
−0.996398 + 0.0847976i \(0.972976\pi\)
\(734\) −13.0000 22.5167i −0.479839 0.831105i
\(735\) 0 0
\(736\) 0 0
\(737\) −84.0000 −3.09418
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 10.5000 18.1865i 0.385988 0.668550i
\(741\) 0 0
\(742\) 0 0
\(743\) −4.50000 7.79423i −0.165089 0.285943i 0.771598 0.636111i \(-0.219458\pi\)
−0.936687 + 0.350168i \(0.886124\pi\)
\(744\) 0 0
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) −4.00000 −0.146450
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 0 0
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 3.00000 5.19615i 0.109254 0.189233i
\(755\) 51.0000 1.85608
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 0 0
\(760\) −3.00000 5.19615i −0.108821 0.188484i
\(761\) −3.00000 5.19615i −0.108750 0.188360i 0.806514 0.591215i \(-0.201351\pi\)
−0.915264 + 0.402854i \(0.868018\pi\)
\(762\) 0 0
\(763\) −3.50000 + 6.06218i −0.126709 + 0.219466i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) −21.0000 −0.758761
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) 0 0
\(769\) −16.0000 27.7128i −0.576975 0.999350i −0.995824 0.0912938i \(-0.970900\pi\)
0.418849 0.908056i \(-0.362434\pi\)
\(770\) −9.00000 15.5885i −0.324337 0.561769i
\(771\) 0 0
\(772\) 2.00000 3.46410i 0.0719816 0.124676i
\(773\) 39.0000 1.40273 0.701366 0.712801i \(-0.252574\pi\)
0.701366 + 0.712801i \(0.252574\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) 5.00000 8.66025i 0.179490 0.310885i
\(777\) 0 0
\(778\) −3.00000 5.19615i −0.107555 0.186291i
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) 0 0
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) −21.0000 + 36.3731i −0.749522 + 1.29821i
\(786\) 0 0
\(787\) 20.0000 + 34.6410i 0.712923 + 1.23482i 0.963755 + 0.266788i \(0.0859624\pi\)
−0.250832 + 0.968031i \(0.580704\pi\)
\(788\) 1.50000 + 2.59808i 0.0534353 + 0.0925526i
\(789\) 0 0
\(790\) −12.0000 + 20.7846i −0.426941 + 0.739483i
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) 8.00000 0.284088
\(794\) 17.0000 29.4449i 0.603307 1.04496i
\(795\) 0 0
\(796\) −1.00000 1.73205i −0.0354441 0.0613909i
\(797\) −21.0000 36.3731i −0.743858 1.28840i −0.950726 0.310031i \(-0.899660\pi\)
0.206868 0.978369i \(-0.433673\pi\)
\(798\) 0 0
\(799\) 4.50000 7.79423i 0.159199 0.275740i
\(800\) 4.00000 0.141421
\(801\) 0 0
\(802\) −36.0000 −1.27120
\(803\) 6.00000 10.3923i 0.211735 0.366736i
\(804\) 0 0
\(805\) 0 0
\(806\) 2.00000 + 3.46410i 0.0704470 + 0.122018i
\(807\) 0 0
\(808\) −6.00000 + 10.3923i −0.211079 + 0.365600i
\(809\) 33.0000 1.16022 0.580109 0.814539i \(-0.303010\pi\)
0.580109 + 0.814539i \(0.303010\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −3.00000 + 5.19615i −0.105279 + 0.182349i
\(813\) 0 0
\(814\) −21.0000 36.3731i −0.736050 1.27488i
\(815\) 24.0000 + 41.5692i 0.840683 + 1.45611i
\(816\) 0 0
\(817\) 1.00000 1.73205i 0.0349856 0.0605968i
\(818\) 32.0000 1.11885
\(819\) 0 0
\(820\) 0 0
\(821\) −1.50000 + 2.59808i −0.0523504 + 0.0906735i −0.891013 0.453978i \(-0.850005\pi\)
0.838663 + 0.544651i \(0.183338\pi\)
\(822\) 0 0
\(823\) −7.00000 12.1244i −0.244005 0.422628i 0.717847 0.696201i \(-0.245128\pi\)
−0.961851 + 0.273573i \(0.911795\pi\)
\(824\) 2.00000 + 3.46410i 0.0696733 + 0.120678i
\(825\) 0 0
\(826\) 3.00000 5.19615i 0.104383 0.180797i
\(827\) −18.0000 −0.625921 −0.312961 0.949766i \(-0.601321\pi\)
−0.312961 + 0.949766i \(0.601321\pi\)
\(828\) 0 0
\(829\) 38.0000 1.31979 0.659897 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(830\) 18.0000 31.1769i 0.624789 1.08217i
\(831\) 0 0
\(832\) −0.500000 0.866025i −0.0173344 0.0300240i
\(833\) 9.00000 + 15.5885i 0.311832 + 0.540108i
\(834\) 0 0
\(835\) 0 0
\(836\) −12.0000 −0.415029
\(837\) 0 0
\(838\) −9.00000 −0.310900
\(839\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(840\) 0 0
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) −8.50000 14.7224i −0.292929 0.507369i
\(843\) 0 0
\(844\) 6.50000 11.2583i 0.223739 0.387528i
\(845\) 3.00000 0.103203
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) 0 0
\(849\) 0 0
\(850\) −6.00000 10.3923i −0.205798 0.356453i
\(851\) 0 0
\(852\) 0 0
\(853\) 18.5000 32.0429i 0.633428 1.09713i −0.353418 0.935466i \(-0.614981\pi\)
0.986846 0.161664i \(-0.0516860\pi\)
\(854\) −8.00000 −0.273754
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −21.0000 + 36.3731i −0.717346 + 1.24248i 0.244701 + 0.969599i \(0.421310\pi\)
−0.962048 + 0.272882i \(0.912023\pi\)
\(858\) 0 0
\(859\) 2.00000 + 3.46410i 0.0682391 + 0.118194i 0.898126 0.439738i \(-0.144929\pi\)
−0.829887 + 0.557931i \(0.811595\pi\)
\(860\) 1.50000 + 2.59808i 0.0511496 + 0.0885937i
\(861\) 0 0
\(862\) −16.5000 + 28.5788i −0.561992 + 0.973399i
\(863\) 45.0000 1.53182 0.765909 0.642949i \(-0.222289\pi\)
0.765909 + 0.642949i \(0.222289\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 12.5000 21.6506i 0.424767 0.735719i
\(867\) 0 0
\(868\) −2.00000 3.46410i −0.0678844 0.117579i
\(869\) 24.0000 + 41.5692i 0.814144 + 1.41014i
\(870\) 0 0
\(871\) −7.00000 + 12.1244i −0.237186 + 0.410818i
\(872\) −7.00000 −0.237050
\(873\) 0 0
\(874\) 0 0
\(875\) −1.50000 + 2.59808i −0.0507093 + 0.0878310i
\(876\) 0 0
\(877\) 6.50000 + 11.2583i 0.219489 + 0.380167i 0.954652 0.297724i \(-0.0962275\pi\)
−0.735163 + 0.677891i \(0.762894\pi\)
\(878\) −13.0000 22.5167i −0.438729 0.759900i
\(879\) 0 0
\(880\) 9.00000 15.5885i 0.303390 0.525487i
\(881\) −21.0000 −0.707508 −0.353754 0.935339i \(-0.615095\pi\)
−0.353754 + 0.935339i \(0.615095\pi\)
\(882\) 0 0
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) −1.50000 + 2.59808i −0.0504505 + 0.0873828i
\(885\) 0 0
\(886\) 10.5000 + 18.1865i 0.352754 + 0.610989i
\(887\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 0 0
\(889\) 10.0000 17.3205i 0.335389 0.580911i
\(890\) 18.0000 0.603361
\(891\) 0 0
\(892\) −19.0000 −0.636167
\(893\) 3.00000 5.19615i 0.100391 0.173883i
\(894\) 0 0
\(895\) 4.50000 + 7.79423i 0.150418 + 0.260532i
\(896\) 0.500000 + 0.866025i 0.0167038 + 0.0289319i
\(897\) 0 0
\(898\) 3.00000 5.19615i 0.100111 0.173398i
\(899\) 24.0000 0.800445
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −3.00000 5.19615i −0.0997785 0.172821i
\(905\) −30.0000 51.9615i −0.997234 1.72726i
\(906\) 0 0
\(907\) 18.5000 32.0429i 0.614282 1.06397i −0.376228 0.926527i \(-0.622779\pi\)
0.990510 0.137441i \(-0.0438878\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −3.00000 −0.0994490
\(911\) 15.0000 25.9808i 0.496972 0.860781i −0.503022 0.864274i \(-0.667778\pi\)
0.999994 + 0.00349271i \(0.00111177\pi\)
\(912\) 0 0
\(913\) −36.0000 62.3538i −1.19143 2.06361i
\(914\) 5.00000 + 8.66025i 0.165385 + 0.286456i
\(915\) 0 0
\(916\) 6.50000 11.2583i 0.214766 0.371986i
\(917\) −21.0000 −0.693481
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 4.50000 + 7.79423i 0.148200 + 0.256689i
\(923\) −1.50000 2.59808i −0.0493731 0.0855167i
\(924\) 0 0
\(925\) 14.0000 24.2487i 0.460317 0.797293i
\(926\) −40.0000 −1.31448
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) 18.0000 31.1769i 0.590561 1.02288i −0.403596 0.914937i \(-0.632240\pi\)
0.994157 0.107944i \(-0.0344268\pi\)
\(930\) 0 0
\(931\) 6.00000 + 10.3923i 0.196642 + 0.340594i
\(932\) −13.5000 23.3827i −0.442207 0.765925i
\(933\) 0 0
\(934\) 18.0000 31.1769i 0.588978 1.02014i
\(935\) −54.0000 −1.76599
\(936\) 0 0
\(937\) −34.0000 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 7.00000 12.1244i 0.228558 0.395874i
\(939\) 0 0
\(940\) 4.50000 + 7.79423i 0.146774 + 0.254220i
\(941\) −10.5000 18.1865i −0.342290 0.592864i 0.642567 0.766229i \(-0.277869\pi\)
−0.984858 + 0.173365i \(0.944536\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) 3.00000 5.19615i 0.0974869 0.168852i −0.813157 0.582045i \(-0.802253\pi\)
0.910644 + 0.413192i \(0.135586\pi\)
\(948\) 0 0
\(949\) −1.00000 1.73205i −0.0324614 0.0562247i
\(950\) −4.00000 6.92820i −0.129777 0.224781i
\(951\) 0 0
\(952\) 1.50000 2.59808i 0.0486153 0.0842041i
\(953\) −15.0000 −0.485898 −0.242949 0.970039i \(-0.578115\pi\)
−0.242949 + 0.970039i \(0.578115\pi\)
\(954\) 0 0
\(955\) 54.0000 1.74740
\(956\) 7.50000 12.9904i 0.242567 0.420139i
\(957\) 0 0
\(958\) −10.5000 18.1865i −0.339240 0.587580i
\(959\) 0 0
\(960\) 0 0
\(961\) 7.50000 12.9904i 0.241935 0.419045i
\(962\) −7.00000 −0.225689
\(963\) 0 0
\(964\) −10.0000 −0.322078
\(965\) 6.00000 10.3923i 0.193147 0.334540i
\(966\) 0 0
\(967\) 15.5000 + 26.8468i 0.498446 + 0.863334i 0.999998 0.00179302i \(-0.000570736\pi\)
−0.501552 + 0.865128i \(0.667237\pi\)
\(968\) −12.5000 21.6506i −0.401765 0.695878i
\(969\) 0 0
\(970\) 15.0000 25.9808i 0.481621 0.834192i
\(971\) 3.00000 0.0962746 0.0481373 0.998841i \(-0.484672\pi\)
0.0481373 + 0.998841i \(0.484672\pi\)
\(972\) 0 0
\(973\) 13.0000 0.416761
\(974\) 8.00000 13.8564i 0.256337 0.443988i
\(975\) 0 0
\(976\) −4.00000 6.92820i −0.128037 0.221766i
\(977\) −27.0000 46.7654i −0.863807 1.49616i −0.868227 0.496167i \(-0.834741\pi\)
0.00442082 0.999990i \(-0.498593\pi\)
\(978\) 0 0
\(979\) 18.0000 31.1769i 0.575282 0.996419i
\(980\) −18.0000 −0.574989
\(981\) 0 0
\(982\) 9.00000 0.287202
\(983\) 19.5000 33.7750i 0.621953 1.07725i −0.367168 0.930155i \(-0.619673\pi\)
0.989122 0.147100i \(-0.0469940\pi\)
\(984\) 0 0
\(985\) 4.50000 + 7.79423i 0.143382 + 0.248345i
\(986\) 9.00000 + 15.5885i 0.286618 + 0.496438i
\(987\) 0 0
\(988\) −1.00000 + 1.73205i −0.0318142 + 0.0551039i
\(989\) 0 0
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 2.00000 3.46410i 0.0635001 0.109985i
\(993\) 0 0
\(994\) 1.50000 + 2.59808i 0.0475771 + 0.0824060i
\(995\) −3.00000 5.19615i −0.0951064 0.164729i
\(996\) 0 0
\(997\) 23.0000 39.8372i 0.728417 1.26166i −0.229135 0.973395i \(-0.573590\pi\)
0.957552 0.288261i \(-0.0930771\pi\)
\(998\) −40.0000 −1.26618
\(999\) 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 2106.2.e.b.703.1 2
3.2 odd 2 2106.2.e.ba.703.1 2
9.2 odd 6 26.2.a.a.1.1 1
9.4 even 3 inner 2106.2.e.b.1405.1 2
9.5 odd 6 2106.2.e.ba.1405.1 2
9.7 even 3 234.2.a.e.1.1 1
36.7 odd 6 1872.2.a.q.1.1 1
36.11 even 6 208.2.a.a.1.1 1
45.2 even 12 650.2.b.d.599.1 2
45.7 odd 12 5850.2.e.a.5149.2 2
45.29 odd 6 650.2.a.j.1.1 1
45.34 even 6 5850.2.a.p.1.1 1
45.38 even 12 650.2.b.d.599.2 2
45.43 odd 12 5850.2.e.a.5149.1 2
63.2 odd 6 1274.2.f.p.1145.1 2
63.11 odd 6 1274.2.f.p.79.1 2
63.20 even 6 1274.2.a.d.1.1 1
63.38 even 6 1274.2.f.r.79.1 2
63.47 even 6 1274.2.f.r.1145.1 2
72.11 even 6 832.2.a.i.1.1 1
72.29 odd 6 832.2.a.d.1.1 1
72.43 odd 6 7488.2.a.h.1.1 1
72.61 even 6 7488.2.a.g.1.1 1
99.65 even 6 3146.2.a.n.1.1 1
117.2 even 12 338.2.e.a.147.1 4
117.11 even 12 338.2.e.a.147.2 4
117.20 even 12 338.2.e.a.23.1 4
117.25 even 6 3042.2.a.a.1.1 1
117.29 odd 6 338.2.c.d.191.1 2
117.34 odd 12 3042.2.b.a.1351.2 2
117.38 odd 6 338.2.a.f.1.1 1
117.47 even 12 338.2.b.c.337.1 2
117.56 odd 6 338.2.c.a.315.1 2
117.70 odd 12 3042.2.b.a.1351.1 2
117.74 odd 6 338.2.c.d.315.1 2
117.83 even 12 338.2.b.c.337.2 2
117.101 odd 6 338.2.c.a.191.1 2
117.110 even 12 338.2.e.a.23.2 4
144.11 even 12 3328.2.b.j.1665.2 2
144.29 odd 12 3328.2.b.m.1665.2 2
144.83 even 12 3328.2.b.j.1665.1 2
144.101 odd 12 3328.2.b.m.1665.1 2
153.101 odd 6 7514.2.a.c.1.1 1
171.56 even 6 9386.2.a.j.1.1 1
180.119 even 6 5200.2.a.x.1.1 1
468.47 odd 12 2704.2.f.d.337.1 2
468.83 odd 12 2704.2.f.d.337.2 2
468.155 even 6 2704.2.a.f.1.1 1
585.389 odd 6 8450.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.2.a.a.1.1 1 9.2 odd 6
208.2.a.a.1.1 1 36.11 even 6
234.2.a.e.1.1 1 9.7 even 3
338.2.a.f.1.1 1 117.38 odd 6
338.2.b.c.337.1 2 117.47 even 12
338.2.b.c.337.2 2 117.83 even 12
338.2.c.a.191.1 2 117.101 odd 6
338.2.c.a.315.1 2 117.56 odd 6
338.2.c.d.191.1 2 117.29 odd 6
338.2.c.d.315.1 2 117.74 odd 6
338.2.e.a.23.1 4 117.20 even 12
338.2.e.a.23.2 4 117.110 even 12
338.2.e.a.147.1 4 117.2 even 12
338.2.e.a.147.2 4 117.11 even 12
650.2.a.j.1.1 1 45.29 odd 6
650.2.b.d.599.1 2 45.2 even 12
650.2.b.d.599.2 2 45.38 even 12
832.2.a.d.1.1 1 72.29 odd 6
832.2.a.i.1.1 1 72.11 even 6
1274.2.a.d.1.1 1 63.20 even 6
1274.2.f.p.79.1 2 63.11 odd 6
1274.2.f.p.1145.1 2 63.2 odd 6
1274.2.f.r.79.1 2 63.38 even 6
1274.2.f.r.1145.1 2 63.47 even 6
1872.2.a.q.1.1 1 36.7 odd 6
2106.2.e.b.703.1 2 1.1 even 1 trivial
2106.2.e.b.1405.1 2 9.4 even 3 inner
2106.2.e.ba.703.1 2 3.2 odd 2
2106.2.e.ba.1405.1 2 9.5 odd 6
2704.2.a.f.1.1 1 468.155 even 6
2704.2.f.d.337.1 2 468.47 odd 12
2704.2.f.d.337.2 2 468.83 odd 12
3042.2.a.a.1.1 1 117.25 even 6
3042.2.b.a.1351.1 2 117.70 odd 12
3042.2.b.a.1351.2 2 117.34 odd 12
3146.2.a.n.1.1 1 99.65 even 6
3328.2.b.j.1665.1 2 144.83 even 12
3328.2.b.j.1665.2 2 144.11 even 12
3328.2.b.m.1665.1 2 144.101 odd 12
3328.2.b.m.1665.2 2 144.29 odd 12
5200.2.a.x.1.1 1 180.119 even 6
5850.2.a.p.1.1 1 45.34 even 6
5850.2.e.a.5149.1 2 45.43 odd 12
5850.2.e.a.5149.2 2 45.7 odd 12
7488.2.a.g.1.1 1 72.61 even 6
7488.2.a.h.1.1 1 72.43 odd 6
7514.2.a.c.1.1 1 153.101 odd 6
8450.2.a.c.1.1 1 585.389 odd 6
9386.2.a.j.1.1 1 171.56 even 6