Properties

Label 1764.2.e.c.1079.2
Level $1764$
Weight $2$
Character 1764.1079
Analytic conductor $14.086$
Analytic rank $0$
Dimension $2$
CM discriminant -4
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1764,2,Mod(1079,1764)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1764.1079");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.e (of order \(2\), degree \(1\), 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: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1079.2
Root \(-1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1079
Dual form 1764.2.e.c.1079.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421i q^{2} -2.00000 q^{4} -4.24264i q^{5} -2.82843i q^{8} +O(q^{10})\) \(q+1.41421i q^{2} -2.00000 q^{4} -4.24264i q^{5} -2.82843i q^{8} +6.00000 q^{10} +6.00000 q^{13} +4.00000 q^{16} +4.24264i q^{17} +8.48528i q^{20} -13.0000 q^{25} +8.48528i q^{26} -9.89949i q^{29} +5.65685i q^{32} -6.00000 q^{34} -2.00000 q^{37} -12.0000 q^{40} -12.7279i q^{41} -18.3848i q^{50} -12.0000 q^{52} -7.07107i q^{53} +14.0000 q^{58} +12.0000 q^{61} -8.00000 q^{64} -25.4558i q^{65} -8.48528i q^{68} -6.00000 q^{73} -2.82843i q^{74} -16.9706i q^{80} +18.0000 q^{82} +18.0000 q^{85} +4.24264i q^{89} -18.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{4} + 12 q^{10} + 12 q^{13} + 8 q^{16} - 26 q^{25} - 12 q^{34} - 4 q^{37} - 24 q^{40} - 24 q^{52} + 28 q^{58} + 24 q^{61} - 16 q^{64} - 12 q^{73} + 36 q^{82} + 36 q^{85} - 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) 0 0
\(4\) −2.00000 −1.00000
\(5\) − 4.24264i − 1.89737i −0.316228 0.948683i \(-0.602416\pi\)
0.316228 0.948683i \(-0.397584\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) − 2.82843i − 1.00000i
\(9\) 0 0
\(10\) 6.00000 1.89737
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 4.24264i 1.02899i 0.857493 + 0.514496i \(0.172021\pi\)
−0.857493 + 0.514496i \(0.827979\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 8.48528i 1.89737i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −13.0000 −2.60000
\(26\) 8.48528i 1.66410i
\(27\) 0 0
\(28\) 0 0
\(29\) − 9.89949i − 1.83829i −0.393919 0.919145i \(-0.628881\pi\)
0.393919 0.919145i \(-0.371119\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −12.0000 −1.89737
\(41\) − 12.7279i − 1.98777i −0.110432 0.993884i \(-0.535223\pi\)
0.110432 0.993884i \(-0.464777\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) − 18.3848i − 2.60000i
\(51\) 0 0
\(52\) −12.0000 −1.66410
\(53\) − 7.07107i − 0.971286i −0.874157 0.485643i \(-0.838586\pi\)
0.874157 0.485643i \(-0.161414\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 14.0000 1.83829
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) − 25.4558i − 3.15741i
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) − 8.48528i − 1.02899i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) − 2.82843i − 0.328798i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) − 16.9706i − 1.89737i
\(81\) 0 0
\(82\) 18.0000 1.98777
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 18.0000 1.95237
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.24264i 0.449719i 0.974391 + 0.224860i \(0.0721923\pi\)
−0.974391 + 0.224860i \(0.927808\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −18.0000 −1.82762 −0.913812 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 26.0000 2.60000
\(101\) − 12.7279i − 1.26648i −0.773957 0.633238i \(-0.781726\pi\)
0.773957 0.633238i \(-0.218274\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) − 16.9706i − 1.66410i
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −20.0000 −1.91565 −0.957826 0.287348i \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.41421i 0.133038i 0.997785 + 0.0665190i \(0.0211893\pi\)
−0.997785 + 0.0665190i \(0.978811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 19.7990i 1.83829i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 16.9706i 1.53644i
\(123\) 0 0
\(124\) 0 0
\(125\) 33.9411i 3.03579i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) − 11.3137i − 1.00000i
\(129\) 0 0
\(130\) 36.0000 3.15741
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 12.0000 1.02899
\(137\) − 9.89949i − 0.845771i −0.906183 0.422885i \(-0.861017\pi\)
0.906183 0.422885i \(-0.138983\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −42.0000 −3.48791
\(146\) − 8.48528i − 0.702247i
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) − 24.0416i − 1.96957i −0.173785 0.984784i \(-0.555600\pi\)
0.173785 0.984784i \(-0.444400\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 24.0000 1.89737
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 25.4558i 1.98777i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 25.4558i 1.95237i
\(171\) 0 0
\(172\) 0 0
\(173\) 21.2132i 1.61281i 0.591364 + 0.806405i \(0.298590\pi\)
−0.591364 + 0.806405i \(0.701410\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.48528i 0.623850i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) − 25.4558i − 1.82762i
\(195\) 0 0
\(196\) 0 0
\(197\) 18.3848i 1.30986i 0.755689 + 0.654931i \(0.227302\pi\)
−0.755689 + 0.654931i \(0.772698\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 36.7696i 2.60000i
\(201\) 0 0
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) 0 0
\(205\) −54.0000 −3.77152
\(206\) 0 0
\(207\) 0 0
\(208\) 24.0000 1.66410
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 14.1421i 0.971286i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) − 28.2843i − 1.91565i
\(219\) 0 0
\(220\) 0 0
\(221\) 25.4558i 1.71235i
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 30.0000 1.98246 0.991228 0.132164i \(-0.0421925\pi\)
0.991228 + 0.132164i \(0.0421925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −28.0000 −1.83829
\(233\) 7.07107i 0.463241i 0.972806 + 0.231621i \(0.0744028\pi\)
−0.972806 + 0.231621i \(0.925597\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 30.0000 1.93247 0.966235 0.257663i \(-0.0829523\pi\)
0.966235 + 0.257663i \(0.0829523\pi\)
\(242\) − 15.5563i − 1.00000i
\(243\) 0 0
\(244\) −24.0000 −1.53644
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −48.0000 −3.03579
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) − 21.2132i − 1.32324i −0.749838 0.661622i \(-0.769869\pi\)
0.749838 0.661622i \(-0.230131\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 50.9117i 3.15741i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −30.0000 −1.84289
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 4.24264i − 0.258678i −0.991600 0.129339i \(-0.958714\pi\)
0.991600 0.129339i \(-0.0412856\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 16.9706i 1.02899i
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 0 0
\(276\) 0 0
\(277\) −28.0000 −1.68236 −0.841178 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 15.5563i 0.928014i 0.885832 + 0.464007i \(0.153589\pi\)
−0.885832 + 0.464007i \(0.846411\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) − 59.3970i − 3.48791i
\(291\) 0 0
\(292\) 12.0000 0.702247
\(293\) − 21.2132i − 1.23929i −0.784883 0.619644i \(-0.787277\pi\)
0.784883 0.619644i \(-0.212723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 5.65685i 0.328798i
\(297\) 0 0
\(298\) 34.0000 1.96957
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 50.9117i − 2.91519i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 24.0000 1.35656 0.678280 0.734803i \(-0.262726\pi\)
0.678280 + 0.734803i \(0.262726\pi\)
\(314\) 16.9706i 0.957704i
\(315\) 0 0
\(316\) 0 0
\(317\) 35.3553i 1.98575i 0.119145 + 0.992877i \(0.461985\pi\)
−0.119145 + 0.992877i \(0.538015\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 33.9411i 1.89737i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −78.0000 −4.32666
\(326\) 0 0
\(327\) 0 0
\(328\) −36.0000 −1.98777
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) 32.5269i 1.76923i
\(339\) 0 0
\(340\) −36.0000 −1.95237
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −30.0000 −1.61281
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 36.0000 1.92704 0.963518 0.267644i \(-0.0862451\pi\)
0.963518 + 0.267644i \(0.0862451\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.7279i 0.677439i 0.940887 + 0.338719i \(0.109994\pi\)
−0.940887 + 0.338719i \(0.890006\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) − 8.48528i − 0.449719i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 25.4558i 1.33793i
\(363\) 0 0
\(364\) 0 0
\(365\) 25.4558i 1.33242i
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) 0 0
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 59.3970i − 3.05910i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 19.7990i 1.00774i
\(387\) 0 0
\(388\) 36.0000 1.82762
\(389\) − 9.89949i − 0.501924i −0.967997 0.250962i \(-0.919253\pi\)
0.967997 0.250962i \(-0.0807470\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −26.0000 −1.30986
\(395\) 0 0
\(396\) 0 0
\(397\) −12.0000 −0.602263 −0.301131 0.953583i \(-0.597364\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −52.0000 −2.60000
\(401\) − 26.8701i − 1.34183i −0.741536 0.670913i \(-0.765902\pi\)
0.741536 0.670913i \(-0.234098\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 25.4558i 1.26648i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 6.00000 0.296681 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) − 76.3675i − 3.77152i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 33.9411i 1.66410i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −20.0000 −0.971286
\(425\) − 55.1543i − 2.67538i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 24.0000 1.15337 0.576683 0.816968i \(-0.304347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 40.0000 1.91565
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −36.0000 −1.71235
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 18.0000 0.853282
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 18.3848i 0.867631i 0.901002 + 0.433816i \(0.142833\pi\)
−0.901002 + 0.433816i \(0.857167\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) − 2.82843i − 0.133038i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 42.4264i 1.98246i
\(459\) 0 0
\(460\) 0 0
\(461\) 12.7279i 0.592798i 0.955064 + 0.296399i \(0.0957859\pi\)
−0.955064 + 0.296399i \(0.904214\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) − 39.5980i − 1.83829i
\(465\) 0 0
\(466\) −10.0000 −0.463241
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 42.4264i 1.93247i
\(483\) 0 0
\(484\) 22.0000 1.00000
\(485\) 76.3675i 3.46767i
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) − 33.9411i − 1.53644i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 42.0000 1.89158
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) − 67.8823i − 3.03579i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −54.0000 −2.40297
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 38.1838i 1.69247i 0.532813 + 0.846233i \(0.321135\pi\)
−0.532813 + 0.846233i \(0.678865\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 30.0000 1.32324
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −72.0000 −3.15741
\(521\) − 12.7279i − 0.557620i −0.960346 0.278810i \(-0.910060\pi\)
0.960346 0.278810i \(-0.0899400\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) − 42.4264i − 1.84289i
\(531\) 0 0
\(532\) 0 0
\(533\) − 76.3675i − 3.30785i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −24.0000 −1.02899
\(545\) 84.8528i 3.63470i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 19.7990i 0.845771i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) − 39.5980i − 1.68236i
\(555\) 0 0
\(556\) 0 0
\(557\) − 7.07107i − 0.299611i −0.988716 0.149805i \(-0.952135\pi\)
0.988716 0.149805i \(-0.0478647\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −22.0000 −0.928014
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 6.00000 0.252422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 9.89949i − 0.415008i −0.978234 0.207504i \(-0.933466\pi\)
0.978234 0.207504i \(-0.0665341\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 48.0000 1.99827 0.999133 0.0416305i \(-0.0132552\pi\)
0.999133 + 0.0416305i \(0.0132552\pi\)
\(578\) − 1.41421i − 0.0588235i
\(579\) 0 0
\(580\) 84.0000 3.48791
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 16.9706i 0.702247i
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) 21.2132i 0.871122i 0.900159 + 0.435561i \(0.143450\pi\)
−0.900159 + 0.435561i \(0.856550\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 48.0833i 1.96957i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −48.0000 −1.95796 −0.978980 0.203954i \(-0.934621\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 46.6690i 1.89737i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 72.0000 2.91519
\(611\) 0 0
\(612\) 0 0
\(613\) 34.0000 1.37325 0.686624 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 49.4975i 1.99269i 0.0854011 + 0.996347i \(0.472783\pi\)
−0.0854011 + 0.996347i \(0.527217\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 79.0000 3.16000
\(626\) 33.9411i 1.35656i
\(627\) 0 0
\(628\) −24.0000 −0.957704
\(629\) − 8.48528i − 0.338330i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −50.0000 −1.98575
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −48.0000 −1.89737
\(641\) 41.0122i 1.61988i 0.586510 + 0.809942i \(0.300502\pi\)
−0.586510 + 0.809942i \(0.699498\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) − 110.309i − 4.32666i
\(651\) 0 0
\(652\) 0 0
\(653\) 49.4975i 1.93699i 0.249041 + 0.968493i \(0.419885\pi\)
−0.249041 + 0.968493i \(0.580115\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) − 50.9117i − 1.98777i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −12.0000 −0.466746 −0.233373 0.972387i \(-0.574976\pi\)
−0.233373 + 0.972387i \(0.574976\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 46.0000 1.77317 0.886585 0.462566i \(-0.153071\pi\)
0.886585 + 0.462566i \(0.153071\pi\)
\(674\) − 45.2548i − 1.74315i
\(675\) 0 0
\(676\) −46.0000 −1.76923
\(677\) 38.1838i 1.46752i 0.679408 + 0.733761i \(0.262237\pi\)
−0.679408 + 0.733761i \(0.737763\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) − 50.9117i − 1.95237i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) −42.0000 −1.60474
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 42.4264i − 1.61632i
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) − 42.4264i − 1.61281i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 54.0000 2.04540
\(698\) 50.9117i 1.92704i
\(699\) 0 0
\(700\) 0 0
\(701\) − 43.8406i − 1.65584i −0.560848 0.827919i \(-0.689525\pi\)
0.560848 0.827919i \(-0.310475\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) 0 0
\(709\) −44.0000 −1.65245 −0.826227 0.563337i \(-0.809517\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 12.0000 0.449719
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 26.8701i 1.00000i
\(723\) 0 0
\(724\) −36.0000 −1.33793
\(725\) 128.693i 4.77955i
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −36.0000 −1.33242
\(731\) 0 0
\(732\) 0 0
\(733\) −54.0000 −1.99454 −0.997268 0.0738717i \(-0.976464\pi\)
−0.997268 + 0.0738717i \(0.976464\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) − 16.9706i − 0.623850i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −102.000 −3.73699
\(746\) 19.7990i 0.724893i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 84.0000 3.05910
\(755\) 0 0
\(756\) 0 0
\(757\) 52.0000 1.88997 0.944986 0.327111i \(-0.106075\pi\)
0.944986 + 0.327111i \(0.106075\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 55.1543i 1.99934i 0.0256326 + 0.999671i \(0.491840\pi\)
−0.0256326 + 0.999671i \(0.508160\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 24.0000 0.865462 0.432731 0.901523i \(-0.357550\pi\)
0.432731 + 0.901523i \(0.357550\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −28.0000 −1.00774
\(773\) − 55.1543i − 1.98376i −0.127164 0.991882i \(-0.540588\pi\)
0.127164 0.991882i \(-0.459412\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 50.9117i 1.82762i
\(777\) 0 0
\(778\) 14.0000 0.501924
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 50.9117i − 1.81712i
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) − 36.7696i − 1.30986i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 72.0000 2.55679
\(794\) − 16.9706i − 0.602263i
\(795\) 0 0
\(796\) 0 0
\(797\) 21.2132i 0.751410i 0.926739 + 0.375705i \(0.122599\pi\)
−0.926739 + 0.375705i \(0.877401\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) − 73.5391i − 2.60000i
\(801\) 0 0
\(802\) 38.0000 1.34183
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −36.0000 −1.26648
\(809\) − 32.5269i − 1.14359i −0.820398 0.571793i \(-0.806248\pi\)
0.820398 0.571793i \(-0.193752\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 8.48528i 0.296681i
\(819\) 0 0
\(820\) 108.000 3.77152
\(821\) − 15.5563i − 0.542920i −0.962450 0.271460i \(-0.912493\pi\)
0.962450 0.271460i \(-0.0875065\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 54.0000 1.87550 0.937749 0.347314i \(-0.112906\pi\)
0.937749 + 0.347314i \(0.112906\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −48.0000 −1.66410
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −69.0000 −2.37931
\(842\) − 39.5980i − 1.36464i
\(843\) 0 0
\(844\) 0 0
\(845\) − 97.5807i − 3.35688i
\(846\) 0 0
\(847\) 0 0
\(848\) − 28.2843i − 0.971286i
\(849\) 0 0
\(850\) 78.0000 2.67538
\(851\) 0 0
\(852\) 0 0
\(853\) −36.0000 −1.23262 −0.616308 0.787505i \(-0.711372\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 46.6690i − 1.59418i −0.603858 0.797092i \(-0.706370\pi\)
0.603858 0.797092i \(-0.293630\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 90.0000 3.06009
\(866\) 33.9411i 1.15337i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 56.5685i 1.91565i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 58.0000 1.95852 0.979260 0.202606i \(-0.0649409\pi\)
0.979260 + 0.202606i \(0.0649409\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 12.7279i − 0.428815i −0.976744 0.214407i \(-0.931218\pi\)
0.976744 0.214407i \(-0.0687820\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) − 50.9117i − 1.71235i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 25.4558i 0.853282i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −26.0000 −0.867631
\(899\) 0 0
\(900\) 0 0
\(901\) 30.0000 0.999445
\(902\) 0 0
\(903\) 0 0
\(904\) 4.00000 0.133038
\(905\) − 76.3675i − 2.53854i
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 11.3137i 0.374224i
\(915\) 0 0
\(916\) −60.0000 −1.98246
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −18.0000 −0.592798
\(923\) 0 0
\(924\) 0 0
\(925\) 26.0000 0.854875
\(926\) 0 0
\(927\) 0 0
\(928\) 56.0000 1.83829
\(929\) − 4.24264i − 0.139197i −0.997575 0.0695983i \(-0.977828\pi\)
0.997575 0.0695983i \(-0.0221717\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) − 14.1421i − 0.463241i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 48.0000 1.56809 0.784046 0.620703i \(-0.213153\pi\)
0.784046 + 0.620703i \(0.213153\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 55.1543i 1.79798i 0.437969 + 0.898990i \(0.355698\pi\)
−0.437969 + 0.898990i \(0.644302\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) −36.0000 −1.16861
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 57.9828i − 1.87825i −0.343582 0.939123i \(-0.611640\pi\)
0.343582 0.939123i \(-0.388360\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 31.0000 1.00000
\(962\) − 16.9706i − 0.547153i
\(963\) 0 0
\(964\) −60.0000 −1.93247
\(965\) − 59.3970i − 1.91206i
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 31.1127i 1.00000i
\(969\) 0 0
\(970\) −108.000 −3.46767
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 48.0000 1.53644
\(977\) 49.4975i 1.58356i 0.610803 + 0.791782i \(0.290847\pi\)
−0.610803 + 0.791782i \(0.709153\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 78.0000 2.48529
\(986\) 59.3970i 1.89158i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 12.0000 0.380044 0.190022 0.981780i \(-0.439144\pi\)
0.190022 + 0.981780i \(0.439144\pi\)
\(998\) 0 0
\(999\) 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 1764.2.e.c.1079.2 yes 2
3.2 odd 2 inner 1764.2.e.c.1079.1 yes 2
4.3 odd 2 CM 1764.2.e.c.1079.2 yes 2
7.6 odd 2 1764.2.e.a.1079.2 yes 2
12.11 even 2 inner 1764.2.e.c.1079.1 yes 2
21.20 even 2 1764.2.e.a.1079.1 2
28.27 even 2 1764.2.e.a.1079.2 yes 2
84.83 odd 2 1764.2.e.a.1079.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1764.2.e.a.1079.1 2 21.20 even 2
1764.2.e.a.1079.1 2 84.83 odd 2
1764.2.e.a.1079.2 yes 2 7.6 odd 2
1764.2.e.a.1079.2 yes 2 28.27 even 2
1764.2.e.c.1079.1 yes 2 3.2 odd 2 inner
1764.2.e.c.1079.1 yes 2 12.11 even 2 inner
1764.2.e.c.1079.2 yes 2 1.1 even 1 trivial
1764.2.e.c.1079.2 yes 2 4.3 odd 2 CM