Properties

Label 378.2.k.b.269.1
Level $378$
Weight $2$
Character 378.269
Analytic conductor $3.018$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,2,Mod(215,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.215");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 378.269
Dual form 378.2.k.b.215.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.73205 + 3.00000i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.73205 + 3.00000i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000i q^{8} +(-3.00000 - 1.73205i) q^{10} -5.19615i q^{13} +(-2.59808 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 + 6.00000i) q^{17} +(-3.00000 + 1.73205i) q^{19} +3.46410 q^{20} +(5.19615 - 3.00000i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(2.59808 + 4.50000i) q^{26} +(2.50000 - 0.866025i) q^{28} +(7.50000 + 4.33013i) q^{31} +(0.866025 + 0.500000i) q^{32} -6.92820i q^{34} +(-1.73205 + 9.00000i) q^{35} +(2.50000 + 4.33013i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-3.00000 + 1.73205i) q^{40} -6.92820 q^{41} +1.00000 q^{43} +(-3.00000 + 5.19615i) q^{46} +(-3.46410 - 6.00000i) q^{47} +(1.00000 + 6.92820i) q^{49} -7.00000i q^{50} +(-4.50000 - 2.59808i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-1.73205 + 2.00000i) q^{56} +(3.46410 - 6.00000i) q^{59} +(-1.50000 + 0.866025i) q^{61} -8.66025 q^{62} -1.00000 q^{64} +(15.5885 - 9.00000i) q^{65} +(6.50000 - 11.2583i) q^{67} +(3.46410 + 6.00000i) q^{68} +(-3.00000 - 8.66025i) q^{70} -6.00000i q^{71} +(-6.00000 - 3.46410i) q^{73} +(-4.33013 - 2.50000i) q^{74} +3.46410i q^{76} +(3.50000 + 6.06218i) q^{79} +(1.73205 - 3.00000i) q^{80} +(6.00000 - 3.46410i) q^{82} +3.46410 q^{83} -24.0000 q^{85} +(-0.866025 + 0.500000i) q^{86} +(5.19615 + 9.00000i) q^{89} +(9.00000 - 10.3923i) q^{91} -6.00000i q^{92} +(6.00000 + 3.46410i) q^{94} +(-10.3923 - 6.00000i) q^{95} +1.73205i q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 8 q^{7} - 12 q^{10} - 2 q^{16} - 12 q^{19} - 14 q^{25} + 10 q^{28} + 30 q^{31} + 10 q^{37} - 12 q^{40} + 4 q^{43} - 12 q^{46} + 4 q^{49} - 18 q^{52} - 6 q^{61} - 4 q^{64} + 26 q^{67} - 12 q^{70} - 24 q^{73} + 14 q^{79} + 24 q^{82} - 96 q^{85} + 36 q^{91} + 24 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.73205 + 3.00000i 0.774597 + 1.34164i 0.935021 + 0.354593i \(0.115380\pi\)
−0.160424 + 0.987048i \(0.551286\pi\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0 0
\(13\) 5.19615i 1.44115i −0.693375 0.720577i \(-0.743877\pi\)
0.693375 0.720577i \(-0.256123\pi\)
\(14\) −2.59808 0.500000i −0.694365 0.133631i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.46410 + 6.00000i −0.840168 + 1.45521i 0.0495842 + 0.998770i \(0.484210\pi\)
−0.889752 + 0.456444i \(0.849123\pi\)
\(18\) 0 0
\(19\) −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i \(-0.796740\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 3.46410 0.774597
\(21\) 0 0
\(22\) 0 0
\(23\) 5.19615 3.00000i 1.08347 0.625543i 0.151642 0.988436i \(-0.451544\pi\)
0.931831 + 0.362892i \(0.118211\pi\)
\(24\) 0 0
\(25\) −3.50000 + 6.06218i −0.700000 + 1.21244i
\(26\) 2.59808 + 4.50000i 0.509525 + 0.882523i
\(27\) 0 0
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 7.50000 + 4.33013i 1.34704 + 0.777714i 0.987829 0.155543i \(-0.0497126\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 6.92820i 1.18818i
\(35\) −1.73205 + 9.00000i −0.292770 + 1.52128i
\(36\) 0 0
\(37\) 2.50000 + 4.33013i 0.410997 + 0.711868i 0.994999 0.0998840i \(-0.0318472\pi\)
−0.584002 + 0.811752i \(0.698514\pi\)
\(38\) 1.73205 3.00000i 0.280976 0.486664i
\(39\) 0 0
\(40\) −3.00000 + 1.73205i −0.474342 + 0.273861i
\(41\) −6.92820 −1.08200 −0.541002 0.841021i \(-0.681955\pi\)
−0.541002 + 0.841021i \(0.681955\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −3.46410 6.00000i −0.505291 0.875190i −0.999981 0.00612051i \(-0.998052\pi\)
0.494690 0.869069i \(-0.335282\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 7.00000i 0.989949i
\(51\) 0 0
\(52\) −4.50000 2.59808i −0.624038 0.360288i
\(53\) −5.19615 3.00000i −0.713746 0.412082i 0.0987002 0.995117i \(-0.468532\pi\)
−0.812447 + 0.583036i \(0.801865\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.73205 + 2.00000i −0.231455 + 0.267261i
\(57\) 0 0
\(58\) 0 0
\(59\) 3.46410 6.00000i 0.450988 0.781133i −0.547460 0.836832i \(-0.684405\pi\)
0.998448 + 0.0556984i \(0.0177385\pi\)
\(60\) 0 0
\(61\) −1.50000 + 0.866025i −0.192055 + 0.110883i −0.592944 0.805243i \(-0.702035\pi\)
0.400889 + 0.916127i \(0.368701\pi\)
\(62\) −8.66025 −1.09985
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 15.5885 9.00000i 1.93351 1.11631i
\(66\) 0 0
\(67\) 6.50000 11.2583i 0.794101 1.37542i −0.129307 0.991605i \(-0.541275\pi\)
0.923408 0.383819i \(-0.125391\pi\)
\(68\) 3.46410 + 6.00000i 0.420084 + 0.727607i
\(69\) 0 0
\(70\) −3.00000 8.66025i −0.358569 1.03510i
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 0 0
\(73\) −6.00000 3.46410i −0.702247 0.405442i 0.105937 0.994373i \(-0.466216\pi\)
−0.808184 + 0.588930i \(0.799549\pi\)
\(74\) −4.33013 2.50000i −0.503367 0.290619i
\(75\) 0 0
\(76\) 3.46410i 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.50000 + 6.06218i 0.393781 + 0.682048i 0.992945 0.118578i \(-0.0378336\pi\)
−0.599164 + 0.800626i \(0.704500\pi\)
\(80\) 1.73205 3.00000i 0.193649 0.335410i
\(81\) 0 0
\(82\) 6.00000 3.46410i 0.662589 0.382546i
\(83\) 3.46410 0.380235 0.190117 0.981761i \(-0.439113\pi\)
0.190117 + 0.981761i \(0.439113\pi\)
\(84\) 0 0
\(85\) −24.0000 −2.60317
\(86\) −0.866025 + 0.500000i −0.0933859 + 0.0539164i
\(87\) 0 0
\(88\) 0 0
\(89\) 5.19615 + 9.00000i 0.550791 + 0.953998i 0.998218 + 0.0596775i \(0.0190072\pi\)
−0.447427 + 0.894321i \(0.647659\pi\)
\(90\) 0 0
\(91\) 9.00000 10.3923i 0.943456 1.08941i
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 6.00000 + 3.46410i 0.618853 + 0.357295i
\(95\) −10.3923 6.00000i −1.06623 0.615587i
\(96\) 0 0
\(97\) 1.73205i 0.175863i 0.996127 + 0.0879316i \(0.0280257\pi\)
−0.996127 + 0.0879316i \(0.971974\pi\)
\(98\) −4.33013 5.50000i −0.437409 0.555584i
\(99\) 0 0
\(100\) 3.50000 + 6.06218i 0.350000 + 0.606218i
\(101\) 5.19615 9.00000i 0.517036 0.895533i −0.482768 0.875748i \(-0.660368\pi\)
0.999804 0.0197851i \(-0.00629819\pi\)
\(102\) 0 0
\(103\) 4.50000 2.59808i 0.443398 0.255996i −0.261640 0.965166i \(-0.584263\pi\)
0.705038 + 0.709170i \(0.250930\pi\)
\(104\) 5.19615 0.509525
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 5.19615 3.00000i 0.502331 0.290021i −0.227345 0.973814i \(-0.573004\pi\)
0.729676 + 0.683793i \(0.239671\pi\)
\(108\) 0 0
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) 18.0000i 1.69330i −0.532152 0.846649i \(-0.678617\pi\)
0.532152 0.846649i \(-0.321383\pi\)
\(114\) 0 0
\(115\) 18.0000 + 10.3923i 1.67851 + 0.969087i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.92820i 0.637793i
\(119\) −17.3205 + 6.00000i −1.58777 + 0.550019i
\(120\) 0 0
\(121\) −5.50000 9.52628i −0.500000 0.866025i
\(122\) 0.866025 1.50000i 0.0784063 0.135804i
\(123\) 0 0
\(124\) 7.50000 4.33013i 0.673520 0.388857i
\(125\) −6.92820 −0.619677
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −9.00000 + 15.5885i −0.789352 + 1.36720i
\(131\) 10.3923 + 18.0000i 0.907980 + 1.57267i 0.816866 + 0.576827i \(0.195709\pi\)
0.0911134 + 0.995841i \(0.470957\pi\)
\(132\) 0 0
\(133\) −9.00000 1.73205i −0.780399 0.150188i
\(134\) 13.0000i 1.12303i
\(135\) 0 0
\(136\) −6.00000 3.46410i −0.514496 0.297044i
\(137\) −15.5885 9.00000i −1.33181 0.768922i −0.346235 0.938148i \(-0.612540\pi\)
−0.985577 + 0.169226i \(0.945873\pi\)
\(138\) 0 0
\(139\) 5.19615i 0.440732i −0.975417 0.220366i \(-0.929275\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 6.92820 + 6.00000i 0.585540 + 0.507093i
\(141\) 0 0
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 6.92820 0.573382
\(147\) 0 0
\(148\) 5.00000 0.410997
\(149\) −5.19615 + 3.00000i −0.425685 + 0.245770i −0.697507 0.716578i \(-0.745707\pi\)
0.271821 + 0.962348i \(0.412374\pi\)
\(150\) 0 0
\(151\) −0.500000 + 0.866025i −0.0406894 + 0.0704761i −0.885653 0.464348i \(-0.846289\pi\)
0.844963 + 0.534824i \(0.179622\pi\)
\(152\) −1.73205 3.00000i −0.140488 0.243332i
\(153\) 0 0
\(154\) 0 0
\(155\) 30.0000i 2.40966i
\(156\) 0 0
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) −6.06218 3.50000i −0.482281 0.278445i
\(159\) 0 0
\(160\) 3.46410i 0.273861i
\(161\) 15.5885 + 3.00000i 1.22854 + 0.236433i
\(162\) 0 0
\(163\) −5.50000 9.52628i −0.430793 0.746156i 0.566149 0.824303i \(-0.308433\pi\)
−0.996942 + 0.0781474i \(0.975100\pi\)
\(164\) −3.46410 + 6.00000i −0.270501 + 0.468521i
\(165\) 0 0
\(166\) −3.00000 + 1.73205i −0.232845 + 0.134433i
\(167\) −3.46410 −0.268060 −0.134030 0.990977i \(-0.542792\pi\)
−0.134030 + 0.990977i \(0.542792\pi\)
\(168\) 0 0
\(169\) −14.0000 −1.07692
\(170\) 20.7846 12.0000i 1.59411 0.920358i
\(171\) 0 0
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) 10.3923 + 18.0000i 0.790112 + 1.36851i 0.925897 + 0.377776i \(0.123311\pi\)
−0.135785 + 0.990738i \(0.543356\pi\)
\(174\) 0 0
\(175\) −17.5000 + 6.06218i −1.32288 + 0.458258i
\(176\) 0 0
\(177\) 0 0
\(178\) −9.00000 5.19615i −0.674579 0.389468i
\(179\) −5.19615 3.00000i −0.388379 0.224231i 0.293079 0.956088i \(-0.405320\pi\)
−0.681457 + 0.731858i \(0.738654\pi\)
\(180\) 0 0
\(181\) 13.8564i 1.02994i 0.857209 + 0.514969i \(0.172197\pi\)
−0.857209 + 0.514969i \(0.827803\pi\)
\(182\) −2.59808 + 13.5000i −0.192582 + 1.00069i
\(183\) 0 0
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) −8.66025 + 15.0000i −0.636715 + 1.10282i
\(186\) 0 0
\(187\) 0 0
\(188\) −6.92820 −0.505291
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 5.19615 3.00000i 0.375980 0.217072i −0.300088 0.953912i \(-0.597016\pi\)
0.676068 + 0.736839i \(0.263683\pi\)
\(192\) 0 0
\(193\) −0.500000 + 0.866025i −0.0359908 + 0.0623379i −0.883460 0.468507i \(-0.844792\pi\)
0.847469 + 0.530845i \(0.178125\pi\)
\(194\) −0.866025 1.50000i −0.0621770 0.107694i
\(195\) 0 0
\(196\) 6.50000 + 2.59808i 0.464286 + 0.185577i
\(197\) 24.0000i 1.70993i −0.518686 0.854965i \(-0.673579\pi\)
0.518686 0.854965i \(-0.326421\pi\)
\(198\) 0 0
\(199\) −1.50000 0.866025i −0.106332 0.0613909i 0.445891 0.895087i \(-0.352887\pi\)
−0.552223 + 0.833696i \(0.686220\pi\)
\(200\) −6.06218 3.50000i −0.428661 0.247487i
\(201\) 0 0
\(202\) 10.3923i 0.731200i
\(203\) 0 0
\(204\) 0 0
\(205\) −12.0000 20.7846i −0.838116 1.45166i
\(206\) −2.59808 + 4.50000i −0.181017 + 0.313530i
\(207\) 0 0
\(208\) −4.50000 + 2.59808i −0.312019 + 0.180144i
\(209\) 0 0
\(210\) 0 0
\(211\) 25.0000 1.72107 0.860535 0.509390i \(-0.170129\pi\)
0.860535 + 0.509390i \(0.170129\pi\)
\(212\) −5.19615 + 3.00000i −0.356873 + 0.206041i
\(213\) 0 0
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 1.73205 + 3.00000i 0.118125 + 0.204598i
\(216\) 0 0
\(217\) 7.50000 + 21.6506i 0.509133 + 1.46974i
\(218\) 11.0000i 0.745014i
\(219\) 0 0
\(220\) 0 0
\(221\) 31.1769 + 18.0000i 2.09719 + 1.21081i
\(222\) 0 0
\(223\) 10.3923i 0.695920i −0.937509 0.347960i \(-0.886874\pi\)
0.937509 0.347960i \(-0.113126\pi\)
\(224\) 0.866025 + 2.50000i 0.0578638 + 0.167038i
\(225\) 0 0
\(226\) 9.00000 + 15.5885i 0.598671 + 1.03693i
\(227\) 5.19615 9.00000i 0.344881 0.597351i −0.640451 0.767999i \(-0.721253\pi\)
0.985332 + 0.170648i \(0.0545860\pi\)
\(228\) 0 0
\(229\) 1.50000 0.866025i 0.0991228 0.0572286i −0.449619 0.893220i \(-0.648440\pi\)
0.548742 + 0.835992i \(0.315107\pi\)
\(230\) −20.7846 −1.37050
\(231\) 0 0
\(232\) 0 0
\(233\) −10.3923 + 6.00000i −0.680823 + 0.393073i −0.800165 0.599780i \(-0.795255\pi\)
0.119342 + 0.992853i \(0.461921\pi\)
\(234\) 0 0
\(235\) 12.0000 20.7846i 0.782794 1.35584i
\(236\) −3.46410 6.00000i −0.225494 0.390567i
\(237\) 0 0
\(238\) 12.0000 13.8564i 0.777844 0.898177i
\(239\) 6.00000i 0.388108i 0.980991 + 0.194054i \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) 0 0
\(241\) 1.50000 + 0.866025i 0.0966235 + 0.0557856i 0.547533 0.836784i \(-0.315567\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 9.52628 + 5.50000i 0.612372 + 0.353553i
\(243\) 0 0
\(244\) 1.73205i 0.110883i
\(245\) −19.0526 + 15.0000i −1.21722 + 0.958315i
\(246\) 0 0
\(247\) 9.00000 + 15.5885i 0.572656 + 0.991870i
\(248\) −4.33013 + 7.50000i −0.274963 + 0.476250i
\(249\) 0 0
\(250\) 6.00000 3.46410i 0.379473 0.219089i
\(251\) 17.3205 1.09326 0.546630 0.837374i \(-0.315910\pi\)
0.546630 + 0.837374i \(0.315910\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 6.06218 3.50000i 0.380375 0.219610i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.19615 + 9.00000i 0.324127 + 0.561405i 0.981335 0.192304i \(-0.0615961\pi\)
−0.657208 + 0.753709i \(0.728263\pi\)
\(258\) 0 0
\(259\) −2.50000 + 12.9904i −0.155342 + 0.807183i
\(260\) 18.0000i 1.11631i
\(261\) 0 0
\(262\) −18.0000 10.3923i −1.11204 0.642039i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 20.7846i 1.27679i
\(266\) 8.66025 3.00000i 0.530994 0.183942i
\(267\) 0 0
\(268\) −6.50000 11.2583i −0.397051 0.687712i
\(269\) 13.8564 24.0000i 0.844840 1.46331i −0.0409201 0.999162i \(-0.513029\pi\)
0.885760 0.464143i \(-0.153638\pi\)
\(270\) 0 0
\(271\) −25.5000 + 14.7224i −1.54901 + 0.894324i −0.550797 + 0.834639i \(0.685676\pi\)
−0.998217 + 0.0596851i \(0.980990\pi\)
\(272\) 6.92820 0.420084
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 2.59808 + 4.50000i 0.155822 + 0.269892i
\(279\) 0 0
\(280\) −9.00000 1.73205i −0.537853 0.103510i
\(281\) 18.0000i 1.07379i 0.843649 + 0.536895i \(0.180403\pi\)
−0.843649 + 0.536895i \(0.819597\pi\)
\(282\) 0 0
\(283\) −16.5000 9.52628i −0.980823 0.566279i −0.0783046 0.996929i \(-0.524951\pi\)
−0.902519 + 0.430651i \(0.858284\pi\)
\(284\) −5.19615 3.00000i −0.308335 0.178017i
\(285\) 0 0
\(286\) 0 0
\(287\) −13.8564 12.0000i −0.817918 0.708338i
\(288\) 0 0
\(289\) −15.5000 26.8468i −0.911765 1.57922i
\(290\) 0 0
\(291\) 0 0
\(292\) −6.00000 + 3.46410i −0.351123 + 0.202721i
\(293\) −27.7128 −1.61900 −0.809500 0.587120i \(-0.800262\pi\)
−0.809500 + 0.587120i \(0.800262\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) −4.33013 + 2.50000i −0.251684 + 0.145310i
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) −15.5885 27.0000i −0.901504 1.56145i
\(300\) 0 0
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 1.00000i 0.0575435i
\(303\) 0 0
\(304\) 3.00000 + 1.73205i 0.172062 + 0.0993399i
\(305\) −5.19615 3.00000i −0.297531 0.171780i
\(306\) 0 0
\(307\) 8.66025i 0.494267i −0.968981 0.247133i \(-0.920511\pi\)
0.968981 0.247133i \(-0.0794886\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −15.0000 25.9808i −0.851943 1.47561i
\(311\) 1.73205 3.00000i 0.0982156 0.170114i −0.812731 0.582640i \(-0.802020\pi\)
0.910946 + 0.412525i \(0.135353\pi\)
\(312\) 0 0
\(313\) −6.00000 + 3.46410i −0.339140 + 0.195803i −0.659892 0.751361i \(-0.729398\pi\)
0.320752 + 0.947163i \(0.396065\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 7.00000 0.393781
\(317\) −20.7846 + 12.0000i −1.16738 + 0.673987i −0.953062 0.302777i \(-0.902086\pi\)
−0.214318 + 0.976764i \(0.568753\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.73205 3.00000i −0.0968246 0.167705i
\(321\) 0 0
\(322\) −15.0000 + 5.19615i −0.835917 + 0.289570i
\(323\) 24.0000i 1.33540i
\(324\) 0 0
\(325\) 31.5000 + 18.1865i 1.74731 + 1.00881i
\(326\) 9.52628 + 5.50000i 0.527612 + 0.304617i
\(327\) 0 0
\(328\) 6.92820i 0.382546i
\(329\) 3.46410 18.0000i 0.190982 0.992372i
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 1.73205 3.00000i 0.0950586 0.164646i
\(333\) 0 0
\(334\) 3.00000 1.73205i 0.164153 0.0947736i
\(335\) 45.0333 2.46043
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 12.1244 7.00000i 0.659478 0.380750i
\(339\) 0 0
\(340\) −12.0000 + 20.7846i −0.650791 + 1.12720i
\(341\) 0 0
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 1.00000i 0.0539164i
\(345\) 0 0
\(346\) −18.0000 10.3923i −0.967686 0.558694i
\(347\) −20.7846 12.0000i −1.11578 0.644194i −0.175457 0.984487i \(-0.556140\pi\)
−0.940319 + 0.340293i \(0.889474\pi\)
\(348\) 0 0
\(349\) 19.0526i 1.01986i 0.860216 + 0.509930i \(0.170329\pi\)
−0.860216 + 0.509930i \(0.829671\pi\)
\(350\) 12.1244 14.0000i 0.648074 0.748331i
\(351\) 0 0
\(352\) 0 0
\(353\) −3.46410 + 6.00000i −0.184376 + 0.319348i −0.943366 0.331754i \(-0.892360\pi\)
0.758990 + 0.651102i \(0.225693\pi\)
\(354\) 0 0
\(355\) 18.0000 10.3923i 0.955341 0.551566i
\(356\) 10.3923 0.550791
\(357\) 0 0
\(358\) 6.00000 0.317110
\(359\) 5.19615 3.00000i 0.274242 0.158334i −0.356572 0.934268i \(-0.616054\pi\)
0.630814 + 0.775934i \(0.282721\pi\)
\(360\) 0 0
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) −6.92820 12.0000i −0.364138 0.630706i
\(363\) 0 0
\(364\) −4.50000 12.9904i −0.235864 0.680881i
\(365\) 24.0000i 1.25622i
\(366\) 0 0
\(367\) 15.0000 + 8.66025i 0.782994 + 0.452062i 0.837490 0.546452i \(-0.184022\pi\)
−0.0544966 + 0.998514i \(0.517355\pi\)
\(368\) −5.19615 3.00000i −0.270868 0.156386i
\(369\) 0 0
\(370\) 17.3205i 0.900450i
\(371\) −5.19615 15.0000i −0.269771 0.778761i
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 6.00000 3.46410i 0.309426 0.178647i
\(377\) 0 0
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) −10.3923 + 6.00000i −0.533114 + 0.307794i
\(381\) 0 0
\(382\) −3.00000 + 5.19615i −0.153493 + 0.265858i
\(383\) −1.73205 3.00000i −0.0885037 0.153293i 0.818375 0.574684i \(-0.194875\pi\)
−0.906879 + 0.421392i \(0.861542\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.00000i 0.0508987i
\(387\) 0 0
\(388\) 1.50000 + 0.866025i 0.0761510 + 0.0439658i
\(389\) 10.3923 + 6.00000i 0.526911 + 0.304212i 0.739758 0.672874i \(-0.234940\pi\)
−0.212847 + 0.977086i \(0.568274\pi\)
\(390\) 0 0
\(391\) 41.5692i 2.10225i
\(392\) −6.92820 + 1.00000i −0.349927 + 0.0505076i
\(393\) 0 0
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) −12.1244 + 21.0000i −0.610043 + 1.05662i
\(396\) 0 0
\(397\) 7.50000 4.33013i 0.376414 0.217323i −0.299843 0.953989i \(-0.596934\pi\)
0.676257 + 0.736666i \(0.263601\pi\)
\(398\) 1.73205 0.0868199
\(399\) 0 0
\(400\) 7.00000 0.350000
\(401\) 20.7846 12.0000i 1.03793 0.599251i 0.118686 0.992932i \(-0.462132\pi\)
0.919247 + 0.393680i \(0.128798\pi\)
\(402\) 0 0
\(403\) 22.5000 38.9711i 1.12080 1.94129i
\(404\) −5.19615 9.00000i −0.258518 0.447767i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −13.5000 7.79423i −0.667532 0.385400i 0.127609 0.991825i \(-0.459270\pi\)
−0.795141 + 0.606425i \(0.792603\pi\)
\(410\) 20.7846 + 12.0000i 1.02648 + 0.592638i
\(411\) 0 0
\(412\) 5.19615i 0.255996i
\(413\) 17.3205 6.00000i 0.852286 0.295241i
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 2.59808 4.50000i 0.127381 0.220631i
\(417\) 0 0
\(418\) 0 0
\(419\) −24.2487 −1.18463 −0.592314 0.805708i \(-0.701785\pi\)
−0.592314 + 0.805708i \(0.701785\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) −21.6506 + 12.5000i −1.05394 + 0.608490i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) −24.2487 42.0000i −1.17624 2.03730i
\(426\) 0 0
\(427\) −4.50000 0.866025i −0.217770 0.0419099i
\(428\) 6.00000i 0.290021i
\(429\) 0 0
\(430\) −3.00000 1.73205i −0.144673 0.0835269i
\(431\) 31.1769 + 18.0000i 1.50174 + 0.867029i 0.999998 + 0.00201168i \(0.000640338\pi\)
0.501741 + 0.865018i \(0.332693\pi\)
\(432\) 0 0
\(433\) 39.8372i 1.91445i 0.289341 + 0.957226i \(0.406564\pi\)
−0.289341 + 0.957226i \(0.593436\pi\)
\(434\) −17.3205 15.0000i −0.831411 0.720023i
\(435\) 0 0
\(436\) −5.50000 9.52628i −0.263402 0.456226i
\(437\) −10.3923 + 18.0000i −0.497131 + 0.861057i
\(438\) 0 0
\(439\) −27.0000 + 15.5885i −1.28864 + 0.743996i −0.978412 0.206666i \(-0.933739\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −36.0000 −1.71235
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0 0
\(445\) −18.0000 + 31.1769i −0.853282 + 1.47793i
\(446\) 5.19615 + 9.00000i 0.246045 + 0.426162i
\(447\) 0 0
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) 30.0000i 1.41579i 0.706319 + 0.707894i \(0.250354\pi\)
−0.706319 + 0.707894i \(0.749646\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −15.5885 9.00000i −0.733219 0.423324i
\(453\) 0 0
\(454\) 10.3923i 0.487735i
\(455\) 46.7654 + 9.00000i 2.19239 + 0.421927i
\(456\) 0 0
\(457\) −15.5000 26.8468i −0.725059 1.25584i −0.958950 0.283577i \(-0.908479\pi\)
0.233890 0.972263i \(-0.424854\pi\)
\(458\) −0.866025 + 1.50000i −0.0404667 + 0.0700904i
\(459\) 0 0
\(460\) 18.0000 10.3923i 0.839254 0.484544i
\(461\) 13.8564 0.645357 0.322679 0.946509i \(-0.395417\pi\)
0.322679 + 0.946509i \(0.395417\pi\)
\(462\) 0 0
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 6.00000 10.3923i 0.277945 0.481414i
\(467\) −5.19615 9.00000i −0.240449 0.416470i 0.720393 0.693566i \(-0.243961\pi\)
−0.960842 + 0.277096i \(0.910628\pi\)
\(468\) 0 0
\(469\) 32.5000 11.2583i 1.50071 0.519861i
\(470\) 24.0000i 1.10704i
\(471\) 0 0
\(472\) 6.00000 + 3.46410i 0.276172 + 0.159448i
\(473\) 0 0
\(474\) 0 0
\(475\) 24.2487i 1.11261i
\(476\) −3.46410 + 18.0000i −0.158777 + 0.825029i
\(477\) 0 0
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) −1.73205 + 3.00000i −0.0791394 + 0.137073i −0.902879 0.429895i \(-0.858551\pi\)
0.823739 + 0.566969i \(0.191884\pi\)
\(480\) 0 0
\(481\) 22.5000 12.9904i 1.02591 0.592310i
\(482\) −1.73205 −0.0788928
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) −5.19615 + 3.00000i −0.235945 + 0.136223i
\(486\) 0 0
\(487\) 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i \(-0.775317\pi\)
0.942309 + 0.334744i \(0.108650\pi\)
\(488\) −0.866025 1.50000i −0.0392031 0.0679018i
\(489\) 0 0
\(490\) 9.00000 22.5167i 0.406579 1.01720i
\(491\) 6.00000i 0.270776i 0.990793 + 0.135388i \(0.0432281\pi\)
−0.990793 + 0.135388i \(0.956772\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −15.5885 9.00000i −0.701358 0.404929i
\(495\) 0 0
\(496\) 8.66025i 0.388857i
\(497\) 10.3923 12.0000i 0.466159 0.538274i
\(498\) 0 0
\(499\) 11.5000 + 19.9186i 0.514811 + 0.891678i 0.999852 + 0.0171872i \(0.00547113\pi\)
−0.485042 + 0.874491i \(0.661196\pi\)
\(500\) −3.46410 + 6.00000i −0.154919 + 0.268328i
\(501\) 0 0
\(502\) −15.0000 + 8.66025i −0.669483 + 0.386526i
\(503\) −38.1051 −1.69902 −0.849512 0.527570i \(-0.823103\pi\)
−0.849512 + 0.527570i \(0.823103\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) −3.50000 + 6.06218i −0.155287 + 0.268966i
\(509\) −12.1244 21.0000i −0.537403 0.930809i −0.999043 0.0437414i \(-0.986072\pi\)
0.461640 0.887067i \(-0.347261\pi\)
\(510\) 0 0
\(511\) −6.00000 17.3205i −0.265424 0.766214i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −9.00000 5.19615i −0.396973 0.229192i
\(515\) 15.5885 + 9.00000i 0.686909 + 0.396587i
\(516\) 0 0
\(517\) 0 0
\(518\) −4.33013 12.5000i −0.190255 0.549218i
\(519\) 0 0
\(520\) 9.00000 + 15.5885i 0.394676 + 0.683599i
\(521\) −12.1244 + 21.0000i −0.531178 + 0.920027i 0.468160 + 0.883644i \(0.344917\pi\)
−0.999338 + 0.0363831i \(0.988416\pi\)
\(522\) 0 0
\(523\) −4.50000 + 2.59808i −0.196771 + 0.113606i −0.595149 0.803616i \(-0.702907\pi\)
0.398377 + 0.917222i \(0.369573\pi\)
\(524\) 20.7846 0.907980
\(525\) 0 0
\(526\) 0 0
\(527\) −51.9615 + 30.0000i −2.26348 + 1.30682i
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 10.3923 + 18.0000i 0.451413 + 0.781870i
\(531\) 0 0
\(532\) −6.00000 + 6.92820i −0.260133 + 0.300376i
\(533\) 36.0000i 1.55933i
\(534\) 0 0
\(535\) 18.0000 + 10.3923i 0.778208 + 0.449299i
\(536\) 11.2583 + 6.50000i 0.486286 + 0.280757i
\(537\) 0 0
\(538\) 27.7128i 1.19478i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) 14.7224 25.5000i 0.632383 1.09532i
\(543\) 0 0
\(544\) −6.00000 + 3.46410i −0.257248 + 0.148522i
\(545\) 38.1051 1.63224
\(546\) 0 0
\(547\) −1.00000 −0.0427569 −0.0213785 0.999771i \(-0.506805\pi\)
−0.0213785 + 0.999771i \(0.506805\pi\)
\(548\) −15.5885 + 9.00000i −0.665906 + 0.384461i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −3.50000 + 18.1865i −0.148835 + 0.773370i
\(554\) 1.00000i 0.0424859i
\(555\) 0 0
\(556\) −4.50000 2.59808i −0.190843 0.110183i
\(557\) 15.5885 + 9.00000i 0.660504 + 0.381342i 0.792469 0.609912i \(-0.208795\pi\)
−0.131965 + 0.991254i \(0.542129\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) 8.66025 3.00000i 0.365963 0.126773i
\(561\) 0 0
\(562\) −9.00000 15.5885i −0.379642 0.657559i
\(563\) 5.19615 9.00000i 0.218992 0.379305i −0.735508 0.677516i \(-0.763057\pi\)
0.954500 + 0.298211i \(0.0963899\pi\)
\(564\) 0 0
\(565\) 54.0000 31.1769i 2.27180 1.31162i
\(566\) 19.0526 0.800839
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −5.19615 + 3.00000i −0.217834 + 0.125767i −0.604947 0.796266i \(-0.706806\pi\)
0.387113 + 0.922032i \(0.373472\pi\)
\(570\) 0 0
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 18.0000 + 3.46410i 0.751305 + 0.144589i
\(575\) 42.0000i 1.75152i
\(576\) 0 0
\(577\) 31.5000 + 18.1865i 1.31136 + 0.757115i 0.982322 0.187201i \(-0.0599414\pi\)
0.329040 + 0.944316i \(0.393275\pi\)
\(578\) 26.8468 + 15.5000i 1.11668 + 0.644715i
\(579\) 0 0
\(580\) 0 0
\(581\) 6.92820 + 6.00000i 0.287430 + 0.248922i
\(582\) 0 0
\(583\) 0 0
\(584\) 3.46410 6.00000i 0.143346 0.248282i
\(585\) 0 0
\(586\) 24.0000 13.8564i 0.991431 0.572403i
\(587\) 10.3923 0.428936 0.214468 0.976731i \(-0.431198\pi\)
0.214468 + 0.976731i \(0.431198\pi\)
\(588\) 0 0
\(589\) −30.0000 −1.23613
\(590\) −20.7846 + 12.0000i −0.855689 + 0.494032i
\(591\) 0 0
\(592\) 2.50000 4.33013i 0.102749 0.177967i
\(593\) 8.66025 + 15.0000i 0.355634 + 0.615976i 0.987226 0.159325i \(-0.0509316\pi\)
−0.631592 + 0.775301i \(0.717598\pi\)
\(594\) 0 0
\(595\) −48.0000 41.5692i −1.96781 1.70417i
\(596\) 6.00000i 0.245770i
\(597\) 0 0
\(598\) 27.0000 + 15.5885i 1.10411 + 0.637459i
\(599\) 20.7846 + 12.0000i 0.849236 + 0.490307i 0.860393 0.509631i \(-0.170218\pi\)
−0.0111569 + 0.999938i \(0.503551\pi\)
\(600\) 0 0
\(601\) 19.0526i 0.777170i −0.921413 0.388585i \(-0.872964\pi\)
0.921413 0.388585i \(-0.127036\pi\)
\(602\) −2.59808 0.500000i −0.105890 0.0203785i
\(603\) 0 0
\(604\) 0.500000 + 0.866025i 0.0203447 + 0.0352381i
\(605\) 19.0526 33.0000i 0.774597 1.34164i
\(606\) 0 0
\(607\) −15.0000 + 8.66025i −0.608831 + 0.351509i −0.772508 0.635005i \(-0.780998\pi\)
0.163677 + 0.986514i \(0.447665\pi\)
\(608\) −3.46410 −0.140488
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) −31.1769 + 18.0000i −1.26128 + 0.728202i
\(612\) 0 0
\(613\) −8.50000 + 14.7224i −0.343312 + 0.594633i −0.985046 0.172294i \(-0.944882\pi\)
0.641734 + 0.766927i \(0.278215\pi\)
\(614\) 4.33013 + 7.50000i 0.174750 + 0.302675i
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 0 0
\(619\) −13.5000 7.79423i −0.542611 0.313276i 0.203526 0.979070i \(-0.434760\pi\)
−0.746136 + 0.665793i \(0.768093\pi\)
\(620\) 25.9808 + 15.0000i 1.04341 + 0.602414i
\(621\) 0 0
\(622\) 3.46410i 0.138898i
\(623\) −5.19615 + 27.0000i −0.208179 + 1.08173i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 3.46410 6.00000i 0.138453 0.239808i
\(627\) 0 0
\(628\) 0 0
\(629\) −34.6410 −1.38123
\(630\) 0 0
\(631\) −25.0000 −0.995234 −0.497617 0.867397i \(-0.665792\pi\)
−0.497617 + 0.867397i \(0.665792\pi\)
\(632\) −6.06218 + 3.50000i −0.241140 + 0.139223i
\(633\) 0 0
\(634\) 12.0000 20.7846i 0.476581 0.825462i
\(635\) −12.1244 21.0000i −0.481140 0.833360i
\(636\) 0 0
\(637\) 36.0000 5.19615i 1.42637 0.205879i
\(638\) 0 0
\(639\) 0 0
\(640\) 3.00000 + 1.73205i 0.118585 + 0.0684653i
\(641\) −20.7846 12.0000i −0.820943 0.473972i 0.0297987 0.999556i \(-0.490513\pi\)
−0.850741 + 0.525584i \(0.823847\pi\)
\(642\) 0 0
\(643\) 43.3013i 1.70764i −0.520572 0.853818i \(-0.674281\pi\)
0.520572 0.853818i \(-0.325719\pi\)
\(644\) 10.3923 12.0000i 0.409514 0.472866i
\(645\) 0 0
\(646\) 12.0000 + 20.7846i 0.472134 + 0.817760i
\(647\) −10.3923 + 18.0000i −0.408564 + 0.707653i −0.994729 0.102538i \(-0.967304\pi\)
0.586165 + 0.810191i \(0.300637\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −36.3731 −1.42667
\(651\) 0 0
\(652\) −11.0000 −0.430793
\(653\) 5.19615 3.00000i 0.203341 0.117399i −0.394872 0.918736i \(-0.629211\pi\)
0.598213 + 0.801337i \(0.295878\pi\)
\(654\) 0 0
\(655\) −36.0000 + 62.3538i −1.40664 + 2.43637i
\(656\) 3.46410 + 6.00000i 0.135250 + 0.234261i
\(657\) 0 0
\(658\) 6.00000 + 17.3205i 0.233904 + 0.675224i
\(659\) 18.0000i 0.701180i −0.936529 0.350590i \(-0.885981\pi\)
0.936529 0.350590i \(-0.114019\pi\)
\(660\) 0 0
\(661\) −30.0000 17.3205i −1.16686 0.673690i −0.213925 0.976850i \(-0.568625\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) −6.92820 4.00000i −0.269272 0.155464i
\(663\) 0 0
\(664\) 3.46410i 0.134433i
\(665\) −10.3923 30.0000i −0.402996 1.16335i
\(666\) 0 0
\(667\) 0 0
\(668\) −1.73205 + 3.00000i −0.0670151 + 0.116073i
\(669\) 0 0
\(670\) −39.0000 + 22.5167i −1.50670 + 0.869894i
\(671\) 0 0
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −19.0526 + 11.0000i −0.733877 + 0.423704i
\(675\) 0 0
\(676\) −7.00000 + 12.1244i −0.269231 + 0.466321i
\(677\) −20.7846 36.0000i −0.798817 1.38359i −0.920387 0.391009i \(-0.872126\pi\)
0.121569 0.992583i \(-0.461207\pi\)
\(678\) 0 0
\(679\) −3.00000 + 3.46410i −0.115129 + 0.132940i
\(680\) 24.0000i 0.920358i
\(681\) 0 0
\(682\) 0 0
\(683\) 15.5885 + 9.00000i 0.596476 + 0.344375i 0.767654 0.640865i \(-0.221424\pi\)
−0.171178 + 0.985240i \(0.554757\pi\)
\(684\) 0 0
\(685\) 62.3538i 2.38242i
\(686\) 0.866025 18.5000i 0.0330650 0.706333i
\(687\) 0 0
\(688\) −0.500000 0.866025i −0.0190623 0.0330169i
\(689\) −15.5885 + 27.0000i −0.593873 + 1.02862i
\(690\) 0 0
\(691\) −28.5000 + 16.4545i −1.08419 + 0.625958i −0.932024 0.362397i \(-0.881959\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 15.5885 9.00000i 0.591304 0.341389i
\(696\) 0 0
\(697\) 24.0000 41.5692i 0.909065 1.57455i
\(698\) −9.52628 16.5000i −0.360575 0.624534i
\(699\) 0 0
\(700\) −3.50000 + 18.1865i −0.132288 + 0.687386i
\(701\) 36.0000i 1.35970i 0.733351 + 0.679851i \(0.237955\pi\)
−0.733351 + 0.679851i \(0.762045\pi\)
\(702\) 0 0
\(703\) −15.0000 8.66025i −0.565736 0.326628i
\(704\) 0 0
\(705\) 0 0
\(706\) 6.92820i 0.260746i
\(707\) 25.9808 9.00000i 0.977107 0.338480i
\(708\) 0 0
\(709\) −0.500000 0.866025i −0.0187779 0.0325243i 0.856484 0.516174i \(-0.172644\pi\)
−0.875262 + 0.483650i \(0.839311\pi\)
\(710\) −10.3923 + 18.0000i −0.390016 + 0.675528i
\(711\) 0 0
\(712\) −9.00000 + 5.19615i −0.337289 + 0.194734i
\(713\) 51.9615 1.94597
\(714\) 0 0
\(715\) 0 0
\(716\) −5.19615 + 3.00000i −0.194189 + 0.112115i
\(717\) 0 0
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) −1.73205 3.00000i −0.0645946 0.111881i 0.831919 0.554896i \(-0.187242\pi\)
−0.896514 + 0.443015i \(0.853909\pi\)
\(720\) 0 0
\(721\) 13.5000 + 2.59808i 0.502766 + 0.0967574i
\(722\) 7.00000i 0.260513i
\(723\) 0 0
\(724\) 12.0000 + 6.92820i 0.445976 + 0.257485i
\(725\) 0 0
\(726\) 0 0
\(727\) 19.0526i 0.706620i 0.935506 + 0.353310i \(0.114944\pi\)
−0.935506 + 0.353310i \(0.885056\pi\)
\(728\) 10.3923 + 9.00000i 0.385164 + 0.333562i
\(729\) 0 0
\(730\) 12.0000 + 20.7846i 0.444140 + 0.769273i
\(731\) −3.46410 + 6.00000i −0.128124 + 0.221918i
\(732\) 0 0
\(733\) −1.50000 + 0.866025i −0.0554038 + 0.0319874i −0.527446 0.849589i \(-0.676850\pi\)
0.472042 + 0.881576i \(0.343517\pi\)
\(734\) −17.3205 −0.639312
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 0 0
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) 8.66025 + 15.0000i 0.318357 + 0.551411i
\(741\) 0 0
\(742\) 12.0000 + 10.3923i 0.440534 + 0.381514i
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −18.0000 10.3923i −0.659469 0.380745i
\(746\) −19.0526 11.0000i −0.697564 0.402739i
\(747\) 0 0
\(748\) 0 0
\(749\) 15.5885 + 3.00000i 0.569590 + 0.109618i
\(750\) 0 0
\(751\) 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i \(-0.0477681\pi\)
−0.623856 + 0.781540i \(0.714435\pi\)
\(752\) −3.46410 + 6.00000i −0.126323 + 0.218797i
\(753\) 0 0
\(754\) 0 0
\(755\) −3.46410 −0.126072
\(756\) 0 0
\(757\) 25.0000 0.908640 0.454320 0.890838i \(-0.349882\pi\)
0.454320 + 0.890838i \(0.349882\pi\)
\(758\) 19.9186 11.5000i 0.723476 0.417699i
\(759\) 0 0
\(760\) 6.00000 10.3923i 0.217643 0.376969i
\(761\) 3.46410 + 6.00000i 0.125574 + 0.217500i 0.921957 0.387292i \(-0.126590\pi\)
−0.796383 + 0.604792i \(0.793256\pi\)
\(762\) 0 0
\(763\) 27.5000 9.52628i 0.995567 0.344874i
\(764\) 6.00000i 0.217072i
\(765\) 0 0
\(766\) 3.00000 + 1.73205i 0.108394 + 0.0625815i
\(767\) −31.1769 18.0000i −1.12573 0.649942i
\(768\) 0 0
\(769\) 6.92820i 0.249837i 0.992167 + 0.124919i \(0.0398670\pi\)
−0.992167 + 0.124919i \(0.960133\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.500000 + 0.866025i 0.0179954 + 0.0311689i
\(773\) 17.3205 30.0000i 0.622975 1.07903i −0.365953 0.930633i \(-0.619257\pi\)
0.988929 0.148392i \(-0.0474097\pi\)
\(774\) 0 0
\(775\) −52.5000 + 30.3109i −1.88586 + 1.08880i
\(776\) −1.73205 −0.0621770
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) 20.7846 12.0000i 0.744686 0.429945i
\(780\) 0 0
\(781\) 0 0
\(782\) −20.7846 36.0000i −0.743256 1.28736i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.50000 0.866025i −0.0534692 0.0308705i 0.473027 0.881048i \(-0.343161\pi\)
−0.526496 + 0.850177i \(0.676495\pi\)
\(788\) −20.7846 12.0000i −0.740421 0.427482i
\(789\) 0 0
\(790\) 24.2487i 0.862730i
\(791\) 31.1769 36.0000i 1.10852 1.28001i
\(792\) 0 0
\(793\) 4.50000 + 7.79423i 0.159800 + 0.276781i
\(794\) −4.33013 + 7.50000i −0.153670 + 0.266165i
\(795\) 0 0
\(796\) −1.50000 + 0.866025i −0.0531661 + 0.0306955i
\(797\) 20.7846 0.736229 0.368114 0.929781i \(-0.380004\pi\)
0.368114 + 0.929781i \(0.380004\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) −6.06218 + 3.50000i −0.214330 + 0.123744i
\(801\) 0 0
\(802\) −12.0000 + 20.7846i −0.423735 + 0.733930i
\(803\) 0 0
\(804\) 0 0
\(805\) 18.0000 + 51.9615i 0.634417 + 1.83140i
\(806\) 45.0000i 1.58506i
\(807\) 0 0
\(808\) 9.00000 + 5.19615i 0.316619 + 0.182800i
\(809\) −25.9808 15.0000i −0.913435 0.527372i −0.0319002 0.999491i \(-0.510156\pi\)
−0.881535 + 0.472119i \(0.843489\pi\)
\(810\) 0 0
\(811\) 10.3923i 0.364923i −0.983213 0.182462i \(-0.941593\pi\)
0.983213 0.182462i \(-0.0584065\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 19.0526 33.0000i 0.667382 1.15594i
\(816\) 0 0
\(817\) −3.00000 + 1.73205i −0.104957 + 0.0605968i
\(818\) 15.5885 0.545038
\(819\) 0 0
\(820\) −24.0000 −0.838116
\(821\) −15.5885 + 9.00000i −0.544041 + 0.314102i −0.746715 0.665144i \(-0.768370\pi\)
0.202674 + 0.979246i \(0.435037\pi\)
\(822\) 0 0
\(823\) 24.5000 42.4352i 0.854016 1.47920i −0.0235383 0.999723i \(-0.507493\pi\)
0.877555 0.479477i \(-0.159174\pi\)
\(824\) 2.59808 + 4.50000i 0.0905083 + 0.156765i
\(825\) 0 0
\(826\) −12.0000 + 13.8564i −0.417533 + 0.482126i
\(827\) 48.0000i 1.66912i −0.550914 0.834562i \(-0.685721\pi\)
0.550914 0.834562i \(-0.314279\pi\)
\(828\) 0 0
\(829\) −12.0000 6.92820i −0.416777 0.240626i 0.276920 0.960893i \(-0.410686\pi\)
−0.693698 + 0.720266i \(0.744020\pi\)
\(830\) −10.3923 6.00000i −0.360722 0.208263i
\(831\) 0 0
\(832\) 5.19615i 0.180144i
\(833\) −45.0333 18.0000i −1.56031 0.623663i
\(834\) 0 0
\(835\) −6.00000 10.3923i −0.207639 0.359641i
\(836\) 0 0
\(837\) 0 0
\(838\) 21.0000 12.1244i 0.725433 0.418829i
\(839\) −45.0333 −1.55472 −0.777361 0.629054i \(-0.783442\pi\)
−0.777361 + 0.629054i \(0.783442\pi\)
\(840\) 0 0
\(841\) 29.0000 1.00000
\(842\) 19.0526 11.0000i 0.656595 0.379085i
\(843\) 0 0
\(844\) 12.5000 21.6506i 0.430268 0.745246i
\(845\) −24.2487 42.0000i −0.834181 1.44484i
\(846\) 0 0
\(847\) 5.50000 28.5788i 0.188982 0.981981i
\(848\) 6.00000i 0.206041i
\(849\) 0 0
\(850\) 42.0000 + 24.2487i 1.44059 + 0.831724i
\(851\) 25.9808 + 15.0000i 0.890609 + 0.514193i
\(852\) 0 0
\(853\) 13.8564i 0.474434i 0.971457 + 0.237217i \(0.0762353\pi\)
−0.971457 + 0.237217i \(0.923765\pi\)
\(854\) 4.33013 1.50000i 0.148174 0.0513289i
\(855\) 0 0
\(856\) 3.00000 + 5.19615i 0.102538 + 0.177601i
\(857\) −8.66025 + 15.0000i −0.295829 + 0.512390i −0.975177 0.221425i \(-0.928929\pi\)
0.679349 + 0.733816i \(0.262262\pi\)
\(858\) 0 0
\(859\) −7.50000 + 4.33013i −0.255897 + 0.147742i −0.622461 0.782651i \(-0.713867\pi\)
0.366565 + 0.930393i \(0.380534\pi\)
\(860\) 3.46410 0.118125
\(861\) 0 0
\(862\) −36.0000 −1.22616
\(863\) 31.1769 18.0000i 1.06127 0.612727i 0.135490 0.990779i \(-0.456739\pi\)
0.925785 + 0.378052i \(0.123406\pi\)
\(864\) 0 0
\(865\) −36.0000 + 62.3538i −1.22404 + 2.12009i
\(866\) −19.9186 34.5000i −0.676861 1.17236i
\(867\) 0 0
\(868\) 22.5000 + 4.33013i 0.763700 + 0.146974i
\(869\) 0 0
\(870\) 0 0
\(871\) −58.5000 33.7750i −1.98220 1.14442i
\(872\) 9.52628 + 5.50000i 0.322601 + 0.186254i
\(873\) 0 0
\(874\) 20.7846i 0.703050i
\(875\) −13.8564 12.0000i −0.468432 0.405674i
\(876\) 0 0
\(877\) −20.5000 35.5070i −0.692236 1.19899i −0.971104 0.238658i \(-0.923292\pi\)
0.278868 0.960329i \(-0.410041\pi\)
\(878\) 15.5885 27.0000i 0.526085 0.911206i
\(879\) 0 0
\(880\) 0 0
\(881\) 31.1769 1.05038 0.525188 0.850986i \(-0.323995\pi\)
0.525188 + 0.850986i \(0.323995\pi\)
\(882\) 0 0
\(883\) 52.0000 1.74994 0.874970 0.484178i \(-0.160881\pi\)
0.874970 + 0.484178i \(0.160881\pi\)
\(884\) 31.1769 18.0000i 1.04859 0.605406i
\(885\) 0 0
\(886\) 0 0
\(887\) 1.73205 + 3.00000i 0.0581566 + 0.100730i 0.893638 0.448789i \(-0.148144\pi\)
−0.835481 + 0.549519i \(0.814811\pi\)
\(888\) 0 0
\(889\) −14.0000 12.1244i −0.469545 0.406638i
\(890\) 36.0000i 1.20672i
\(891\) 0 0
\(892\) −9.00000 5.19615i −0.301342 0.173980i
\(893\) 20.7846 + 12.0000i 0.695530 + 0.401565i
\(894\) 0 0
\(895\) 20.7846i 0.694753i
\(896\) 2.59808 + 0.500000i 0.0867956 + 0.0167038i
\(897\) 0 0
\(898\) −15.0000 25.9808i −0.500556 0.866989i
\(899\) 0 0
\(900\) 0 0
\(901\) 36.0000 20.7846i 1.19933 0.692436i
\(902\) 0 0
\(903\) 0 0
\(904\) 18.0000 0.598671
\(905\) −41.5692 + 24.0000i −1.38181 + 0.797787i
\(906\) 0 0
\(907\) 23.5000 40.7032i 0.780305 1.35153i −0.151460 0.988463i \(-0.548397\pi\)
0.931764 0.363064i \(-0.118269\pi\)
\(908\) −5.19615 9.00000i −0.172440 0.298675i
\(909\) 0 0
\(910\) −45.0000 + 15.5885i −1.49174 + 0.516752i
\(911\) 48.0000i 1.59031i −0.606406 0.795155i \(-0.707389\pi\)
0.606406 0.795155i \(-0.292611\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 26.8468 + 15.5000i 0.888013 + 0.512694i
\(915\) 0 0
\(916\) 1.73205i 0.0572286i
\(917\) −10.3923 + 54.0000i −0.343184 + 1.78324i
\(918\) 0 0
\(919\) −12.5000 21.6506i −0.412337 0.714189i 0.582808 0.812610i \(-0.301954\pi\)
−0.995145 + 0.0984214i \(0.968621\pi\)
\(920\) −10.3923 + 18.0000i −0.342624 + 0.593442i
\(921\) 0 0
\(922\) −12.0000 + 6.92820i −0.395199 + 0.228168i
\(923\) −31.1769 −1.02620
\(924\) 0 0
\(925\) −35.0000 −1.15079
\(926\) 34.6410 20.0000i 1.13837 0.657241i
\(927\) 0 0
\(928\) 0 0
\(929\) 22.5167 + 39.0000i 0.738748 + 1.27955i 0.953059 + 0.302783i \(0.0979158\pi\)
−0.214312 + 0.976765i \(0.568751\pi\)
\(930\) 0 0
\(931\) −15.0000 19.0526i −0.491605 0.624422i
\(932\) 12.0000i 0.393073i
\(933\) 0 0
\(934\) 9.00000 + 5.19615i 0.294489 + 0.170023i
\(935\) 0 0
\(936\) 0 0
\(937\) 5.19615i 0.169751i 0.996392 + 0.0848755i \(0.0270492\pi\)
−0.996392 + 0.0848755i \(0.972951\pi\)
\(938\) −22.5167 + 26.0000i −0.735195 + 0.848930i
\(939\) 0 0
\(940\) −12.0000 20.7846i −0.391397 0.677919i
\(941\) −6.92820 + 12.0000i −0.225853 + 0.391189i −0.956575 0.291486i \(-0.905850\pi\)
0.730722 + 0.682675i \(0.239184\pi\)
\(942\) 0 0
\(943\) −36.0000 + 20.7846i −1.17232 + 0.676840i
\(944\) −6.92820 −0.225494
\(945\) 0 0
\(946\) 0 0
\(947\) −31.1769 + 18.0000i −1.01311 + 0.584921i −0.912102 0.409964i \(-0.865541\pi\)
−0.101012 + 0.994885i \(0.532208\pi\)
\(948\) 0 0
\(949\) −18.0000 + 31.1769i −0.584305 + 1.01205i
\(950\) 12.1244 + 21.0000i 0.393366 + 0.681330i
\(951\) 0 0
\(952\) −6.00000 17.3205i −0.194461 0.561361i
\(953\) 6.00000i 0.194359i 0.995267 + 0.0971795i \(0.0309821\pi\)
−0.995267 + 0.0971795i \(0.969018\pi\)
\(954\) 0 0
\(955\) 18.0000 + 10.3923i 0.582466 + 0.336287i
\(956\) 5.19615 + 3.00000i 0.168056 + 0.0970269i
\(957\) 0 0
\(958\) 3.46410i 0.111920i
\(959\) −15.5885 45.0000i −0.503378 1.45313i
\(960\) 0 0
\(961\) 22.0000 + 38.1051i 0.709677 + 1.22920i
\(962\) −12.9904 + 22.5000i −0.418827 + 0.725429i
\(963\) 0 0
\(964\) 1.50000 0.866025i 0.0483117 0.0278928i
\(965\) −3.46410 −0.111513
\(966\) 0 0
\(967\) −31.0000 −0.996893 −0.498446 0.866921i \(-0.666096\pi\)
−0.498446 + 0.866921i \(0.666096\pi\)
\(968\) 9.52628 5.50000i 0.306186 0.176777i
\(969\) 0 0
\(970\) 3.00000 5.19615i 0.0963242 0.166838i
\(971\) 13.8564 + 24.0000i 0.444673 + 0.770197i 0.998029 0.0627481i \(-0.0199865\pi\)
−0.553356 + 0.832945i \(0.686653\pi\)
\(972\) 0 0
\(973\) 9.00000 10.3923i 0.288527 0.333162i
\(974\) 8.00000i 0.256337i
\(975\) 0 0
\(976\) 1.50000 + 0.866025i 0.0480138 + 0.0277208i
\(977\) −5.19615 3.00000i −0.166240 0.0959785i 0.414572 0.910017i \(-0.363931\pi\)
−0.580812 + 0.814038i \(0.697265\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 3.46410 + 24.0000i 0.110657 + 0.766652i
\(981\) 0 0
\(982\) −3.00000 5.19615i −0.0957338 0.165816i
\(983\) −12.1244 + 21.0000i −0.386707 + 0.669796i −0.992004 0.126203i \(-0.959721\pi\)
0.605298 + 0.795999i \(0.293054\pi\)
\(984\) 0 0
\(985\) 72.0000 41.5692i 2.29411 1.32451i
\(986\) 0 0
\(987\) 0 0
\(988\) 18.0000 0.572656
\(989\) 5.19615 3.00000i 0.165228 0.0953945i
\(990\) 0 0
\(991\) −6.50000 + 11.2583i −0.206479 + 0.357633i −0.950603 0.310409i \(-0.899534\pi\)
0.744124 + 0.668042i \(0.232867\pi\)
\(992\) 4.33013 + 7.50000i 0.137482 + 0.238125i
\(993\) 0 0
\(994\) −3.00000 + 15.5885i −0.0951542 + 0.494436i
\(995\) 6.00000i 0.190213i
\(996\) 0 0
\(997\) 28.5000 + 16.4545i 0.902604 + 0.521119i 0.878044 0.478580i \(-0.158848\pi\)
0.0245599 + 0.999698i \(0.492182\pi\)
\(998\) −19.9186 11.5000i −0.630512 0.364026i
\(999\) 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 378.2.k.b.269.1 yes 4
3.2 odd 2 inner 378.2.k.b.269.2 yes 4
7.3 odd 6 2646.2.d.b.2645.2 4
7.4 even 3 2646.2.d.b.2645.1 4
7.5 odd 6 inner 378.2.k.b.215.2 yes 4
9.2 odd 6 1134.2.t.b.1025.1 4
9.4 even 3 1134.2.l.a.269.1 4
9.5 odd 6 1134.2.l.a.269.2 4
9.7 even 3 1134.2.t.b.1025.2 4
21.5 even 6 inner 378.2.k.b.215.1 4
21.11 odd 6 2646.2.d.b.2645.4 4
21.17 even 6 2646.2.d.b.2645.3 4
63.5 even 6 1134.2.t.b.593.2 4
63.40 odd 6 1134.2.t.b.593.1 4
63.47 even 6 1134.2.l.a.215.2 4
63.61 odd 6 1134.2.l.a.215.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.k.b.215.1 4 21.5 even 6 inner
378.2.k.b.215.2 yes 4 7.5 odd 6 inner
378.2.k.b.269.1 yes 4 1.1 even 1 trivial
378.2.k.b.269.2 yes 4 3.2 odd 2 inner
1134.2.l.a.215.1 4 63.61 odd 6
1134.2.l.a.215.2 4 63.47 even 6
1134.2.l.a.269.1 4 9.4 even 3
1134.2.l.a.269.2 4 9.5 odd 6
1134.2.t.b.593.1 4 63.40 odd 6
1134.2.t.b.593.2 4 63.5 even 6
1134.2.t.b.1025.1 4 9.2 odd 6
1134.2.t.b.1025.2 4 9.7 even 3
2646.2.d.b.2645.1 4 7.4 even 3
2646.2.d.b.2645.2 4 7.3 odd 6
2646.2.d.b.2645.3 4 21.17 even 6
2646.2.d.b.2645.4 4 21.11 odd 6