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Properties

Label 9360.2.a.x.1.1
Level $9360$
Weight $2$
Character 9360.1
Self dual yes
Analytic conductor $74.740$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9360,2,Mod(1,9360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9360.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9360.a (trivial)

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: yes
Analytic conductor: \(74.7399762919\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9360.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} +3.00000 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +3.00000 q^{7} -3.00000 q^{11} -1.00000 q^{13} +1.00000 q^{17} +6.00000 q^{19} -5.00000 q^{23} +1.00000 q^{25} +6.00000 q^{29} -2.00000 q^{31} -3.00000 q^{35} +7.00000 q^{37} -3.00000 q^{41} +8.00000 q^{43} -2.00000 q^{47} +2.00000 q^{49} +1.00000 q^{53} +3.00000 q^{55} -15.0000 q^{61} +1.00000 q^{65} -12.0000 q^{67} +5.00000 q^{71} -6.00000 q^{73} -9.00000 q^{77} +13.0000 q^{79} +12.0000 q^{83} -1.00000 q^{85} -1.00000 q^{89} -3.00000 q^{91} -6.00000 q^{95} +17.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.00000 1.13389 0.566947 − 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 0.242536 0.121268 − 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 − 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.00000 −1.04257 −0.521286 − 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) 7.00000 1.15079 0.575396 − 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 − 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 − 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.00000 −0.291730 −0.145865 − 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.00000 0.137361 0.0686803 − 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −15.0000 −1.92055 −0.960277 − 0.279050i \(-0.909981\pi\)
−0.960277 + 0.279050i \(0.909981\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 − 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 0.593391 0.296695 − 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 − 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.00000 −1.02565
\(78\) 0 0
\(79\) 13.0000 1.46261 0.731307 − 0.682048i \(-0.238911\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 − 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.00000 −0.106000 −0.0529999 − 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.00000 −0.615587
\(96\) 0 0
\(97\) 17.0000 1.72609 0.863044 − 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.00000 −0.483368 −0.241684 − 0.970355i \(-0.577700\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(108\) 0 0
\(109\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 − 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 5.00000 0.466252
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 6.00000 0.532414 0.266207 − 0.963916i \(-0.414230\pi\)
0.266207 + 0.963916i \(0.414230\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 − 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 18.0000 1.56080
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.0000 1.19610 0.598050 − 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) 19.0000 1.61156 0.805779 − 0.592216i \(-0.201747\pi\)
0.805779 + 0.592216i \(0.201747\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 0.250873
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.00000 −0.0819232 −0.0409616 − 0.999161i \(-0.513042\pi\)
−0.0409616 + 0.999161i \(0.513042\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 − 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −15.0000 −1.18217
\(162\) 0 0
\(163\) 7.00000 0.548282 0.274141 − 0.961689i \(-0.411606\pi\)
0.274141 + 0.961689i \(0.411606\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 − 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 3.00000 0.226779
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.00000 −0.149487 −0.0747435 − 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 − 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −7.00000 −0.514650
\(186\) 0 0
\(187\) −3.00000 −0.219382
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 − 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) 11.0000 0.791797 0.395899 − 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 − 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 − 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 18.0000 1.26335
\(204\) 0 0
\(205\) 3.00000 0.209529
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −18.0000 −1.24509
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 − 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.00000 −0.0672673
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 − 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.0000 0.663723 0.331862 − 0.943328i \(-0.392323\pi\)
0.331862 + 0.943328i \(0.392323\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 − 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.0000 −1.37576 −0.687878 − 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 0 0
\(235\) 2.00000 0.130466
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.0000 −0.711531 −0.355765 − 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 − 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.00000 −0.127775
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 − 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 15.0000 0.943042
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −22.0000 −1.37232 −0.686161 − 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) 0 0
\(259\) 21.0000 1.30488
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −1.00000 −0.0614295
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.00000 0.243884 0.121942 − 0.992537i \(-0.461088\pi\)
0.121942 + 0.992537i \(0.461088\pi\)
\(270\) 0 0
\(271\) −10.0000 −0.607457 −0.303728 − 0.952759i \(-0.598232\pi\)
−0.303728 + 0.952759i \(0.598232\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.00000 −0.180907
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 − 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 − 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −20.0000 −1.18888 −0.594438 − 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.00000 −0.531253
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 16.0000 0.934730 0.467365 − 0.884064i \(-0.345203\pi\)
0.467365 + 0.884064i \(0.345203\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.00000 0.289157
\(300\) 0 0
\(301\) 24.0000 1.38334
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 15.0000 0.858898
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 − 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.00000 −0.226819 −0.113410 − 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 − 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 32.0000 1.79730 0.898650 − 0.438667i \(-0.144549\pi\)
0.898650 + 0.438667i \(0.144549\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.00000 −0.330791
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 − 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) 32.0000 1.74315 0.871576 − 0.490261i \(-0.163099\pi\)
0.871576 + 0.490261i \(0.163099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 0.324918
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.0000 1.23470 0.617352 − 0.786687i \(-0.288205\pi\)
0.617352 + 0.786687i \(0.288205\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 − 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −26.0000 −1.38384 −0.691920 − 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 0 0
\(355\) −5.00000 −0.265372
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 32.0000 1.68890 0.844448 − 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) −24.0000 −1.25279 −0.626395 − 0.779506i \(-0.715470\pi\)
−0.626395 + 0.779506i \(0.715470\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.00000 0.155752
\(372\) 0 0
\(373\) 8.00000 0.414224 0.207112 − 0.978317i \(-0.433593\pi\)
0.207112 + 0.978317i \(0.433593\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −10.0000 −0.513665 −0.256833 − 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6.00000 0.306586 0.153293 − 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 9.00000 0.458682
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) −5.00000 −0.252861
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −13.0000 −0.654101
\(396\) 0 0
\(397\) 7.00000 0.351320 0.175660 − 0.984451i \(-0.443794\pi\)
0.175660 + 0.984451i \(0.443794\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.00000 −0.299626 −0.149813 − 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 0 0
\(403\) 2.00000 0.0996271
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −21.0000 −1.04093
\(408\) 0 0
\(409\) 6.00000 0.296681 0.148340 − 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 − 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) 12.0000 0.584844 0.292422 − 0.956289i \(-0.405539\pi\)
0.292422 + 0.956289i \(0.405539\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.00000 0.0485071
\(426\) 0 0
\(427\) −45.0000 −2.17770
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.0000 0.770693 0.385346 − 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 0 0
\(433\) −24.0000 −1.15337 −0.576683 − 0.816968i \(-0.695653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −30.0000 −1.43509
\(438\) 0 0
\(439\) 7.00000 0.334092 0.167046 − 0.985949i \(-0.446577\pi\)
0.167046 + 0.985949i \(0.446577\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −29.0000 −1.37783 −0.688916 − 0.724841i \(-0.741913\pi\)
−0.688916 + 0.724841i \(0.741913\pi\)
\(444\) 0 0
\(445\) 1.00000 0.0474045
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 37.0000 1.74614 0.873069 − 0.487597i \(-0.162126\pi\)
0.873069 + 0.487597i \(0.162126\pi\)
\(450\) 0 0
\(451\) 9.00000 0.423793
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.00000 0.140642
\(456\) 0 0
\(457\) −3.00000 −0.140334 −0.0701670 − 0.997535i \(-0.522353\pi\)
−0.0701670 + 0.997535i \(0.522353\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 29.0000 1.35066 0.675332 − 0.737514i \(-0.264000\pi\)
0.675332 + 0.737514i \(0.264000\pi\)
\(462\) 0 0
\(463\) −5.00000 −0.232370 −0.116185 − 0.993228i \(-0.537067\pi\)
−0.116185 + 0.993228i \(0.537067\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 27.0000 1.24941 0.624705 − 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 0 0
\(469\) −36.0000 −1.66233
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −24.0000 −1.10352
\(474\) 0 0
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.0000 0.685367 0.342684 − 0.939451i \(-0.388664\pi\)
0.342684 + 0.939451i \(0.388664\pi\)
\(480\) 0 0
\(481\) −7.00000 −0.319173
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17.0000 −0.771930
\(486\) 0 0
\(487\) 9.00000 0.407829 0.203914 − 0.978989i \(-0.434634\pi\)
0.203914 + 0.978989i \(0.434634\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16.0000 0.722070 0.361035 − 0.932552i \(-0.382424\pi\)
0.361035 + 0.932552i \(0.382424\pi\)
\(492\) 0 0
\(493\) 6.00000 0.270226
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 15.0000 0.672842
\(498\) 0 0
\(499\) −6.00000 −0.268597 −0.134298 − 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 36.0000 1.60516 0.802580 − 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 35.0000 1.55135 0.775674 − 0.631134i \(-0.217410\pi\)
0.775674 + 0.631134i \(0.217410\pi\)
\(510\) 0 0
\(511\) −18.0000 −0.796273
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 − 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) 44.0000 1.92399 0.961993 − 0.273075i \(-0.0880406\pi\)
0.961993 + 0.273075i \(0.0880406\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.00000 −0.0871214
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.00000 0.129944
\(534\) 0 0
\(535\) 5.00000 0.216169
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) −38.0000 −1.63375 −0.816874 − 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 24.0000 1.02617 0.513083 − 0.858339i \(-0.328503\pi\)
0.513083 + 0.858339i \(0.328503\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 36.0000 1.53365
\(552\) 0 0
\(553\) 39.0000 1.65845
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.00000 0.0847427 0.0423714 − 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15.0000 0.632175 0.316087 − 0.948730i \(-0.397631\pi\)
0.316087 + 0.948730i \(0.397631\pi\)
\(564\) 0 0
\(565\) 14.0000 0.588984
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.00000 −0.167689 −0.0838444 − 0.996479i \(-0.526720\pi\)
−0.0838444 + 0.996479i \(0.526720\pi\)
\(570\) 0 0
\(571\) −19.0000 −0.795125 −0.397563 − 0.917575i \(-0.630144\pi\)
−0.397563 + 0.917575i \(0.630144\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.00000 −0.208514
\(576\) 0 0
\(577\) −11.0000 −0.457936 −0.228968 − 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 36.0000 1.49353
\(582\) 0 0
\(583\) −3.00000 −0.124247
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.0000 −0.577842 −0.288921 − 0.957353i \(-0.593296\pi\)
−0.288921 + 0.957353i \(0.593296\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −36.0000 −1.47834 −0.739171 − 0.673517i \(-0.764783\pi\)
−0.739171 + 0.673517i \(0.764783\pi\)
\(594\) 0 0
\(595\) −3.00000 −0.122988
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −32.0000 −1.30748 −0.653742 − 0.756717i \(-0.726802\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) 0 0
\(601\) 19.0000 0.775026 0.387513 − 0.921864i \(-0.373334\pi\)
0.387513 + 0.921864i \(0.373334\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.00000 0.0813116
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 − 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.00000 0.0809113
\(612\) 0 0
\(613\) −15.0000 −0.605844 −0.302922 − 0.953015i \(-0.597962\pi\)
−0.302922 + 0.953015i \(0.597962\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 − 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) 10.0000 0.401934 0.200967 − 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.00000 −0.120192
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.00000 0.279108
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 − 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.00000 −0.238103
\(636\) 0 0
\(637\) −2.00000 −0.0792429
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 24.0000 0.947943 0.473972 − 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(642\) 0 0
\(643\) 35.0000 1.38027 0.690133 − 0.723683i \(-0.257552\pi\)
0.690133 + 0.723683i \(0.257552\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.0000 0.668339 0.334169 − 0.942513i \(-0.391544\pi\)
0.334169 + 0.942513i \(0.391544\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.0000 0.391330 0.195665 − 0.980671i \(-0.437313\pi\)
0.195665 + 0.980671i \(0.437313\pi\)
\(654\) 0 0
\(655\) −18.0000 −0.703318
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 44.0000 1.71400 0.856998 − 0.515319i \(-0.172327\pi\)
0.856998 + 0.515319i \(0.172327\pi\)
\(660\) 0 0
\(661\) 16.0000 0.622328 0.311164 − 0.950356i \(-0.399281\pi\)
0.311164 + 0.950356i \(0.399281\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −18.0000 −0.698010
\(666\) 0 0
\(667\) −30.0000 −1.16160
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 45.0000 1.73721
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 − 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.0000 −0.576497 −0.288248 − 0.957556i \(-0.593073\pi\)
−0.288248 + 0.957556i \(0.593073\pi\)
\(678\) 0 0
\(679\) 51.0000 1.95720
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −14.0000 −0.534913
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.00000 −0.0380970
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 − 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −19.0000 −0.720711
\(696\) 0 0
\(697\) −3.00000 −0.113633
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 − 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) 42.0000 1.58406
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 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
\(712\) 0 0
\(713\) 10.0000 0.374503
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −40.0000 −1.49175 −0.745874 − 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) −2.00000 −0.0741759 −0.0370879 − 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.00000 0.295891
\(732\) 0 0
\(733\) 19.0000 0.701781 0.350891 − 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 36.0000 1.32608
\(738\) 0 0
\(739\) 34.0000 1.25071 0.625355 − 0.780340i \(-0.284954\pi\)
0.625355 + 0.780340i \(0.284954\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14.0000 −0.513610 −0.256805 − 0.966463i \(-0.582670\pi\)
−0.256805 + 0.966463i \(0.582670\pi\)
\(744\) 0 0
\(745\) 1.00000 0.0366372
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −15.0000 −0.548088
\(750\) 0 0
\(751\) −13.0000 −0.474377 −0.237188 − 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −8.00000 −0.290765 −0.145382 − 0.989376i \(-0.546441\pi\)
−0.145382 + 0.989376i \(0.546441\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 38.0000 1.37750 0.688749 − 0.724999i \(-0.258160\pi\)
0.688749 + 0.724999i \(0.258160\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −12.0000 −0.432731 −0.216366 − 0.976312i \(-0.569420\pi\)
−0.216366 + 0.976312i \(0.569420\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 28.0000 1.00709 0.503545 − 0.863969i \(-0.332029\pi\)
0.503545 + 0.863969i \(0.332029\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −18.0000 −0.644917
\(780\) 0 0
\(781\) −15.0000 −0.536742
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10.0000 0.356915
\(786\) 0 0
\(787\) 12.0000 0.427754 0.213877 − 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −42.0000 −1.49335
\(792\) 0 0
\(793\) 15.0000 0.532666
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 51.0000 1.80651 0.903256 − 0.429101i \(-0.141170\pi\)
0.903256 + 0.429101i \(0.141170\pi\)
\(798\) 0 0
\(799\) −2.00000 −0.0707549
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 18.0000 0.635206
\(804\) 0 0
\(805\) 15.0000 0.528681
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 18.0000 0.632846 0.316423 − 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 − 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −7.00000 −0.245199
\(816\) 0 0
\(817\) 48.0000 1.67931
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 33.0000 1.15171 0.575854 − 0.817553i \(-0.304670\pi\)
0.575854 + 0.817553i \(0.304670\pi\)
\(822\) 0 0
\(823\) −12.0000 −0.418294 −0.209147 − 0.977884i \(-0.567069\pi\)
−0.209147 + 0.977884i \(0.567069\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −38.0000 −1.32139 −0.660695 − 0.750655i \(-0.729738\pi\)
−0.660695 + 0.750655i \(0.729738\pi\)
\(828\) 0 0
\(829\) −50.0000 −1.73657 −0.868286 − 0.496064i \(-0.834778\pi\)
−0.868286 + 0.496064i \(0.834778\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.00000 0.0692959
\(834\) 0 0
\(835\) 12.0000 0.415277
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.00000 −0.103572 −0.0517858 − 0.998658i \(-0.516491\pi\)
−0.0517858 + 0.998658i \(0.516491\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −6.00000 −0.206162
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −35.0000 −1.19978
\(852\) 0 0
\(853\) −23.0000 −0.787505 −0.393753 − 0.919216i \(-0.628823\pi\)
−0.393753 + 0.919216i \(0.628823\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 51.0000 1.74213 0.871063 − 0.491171i \(-0.163431\pi\)
0.871063 + 0.491171i \(0.163431\pi\)
\(858\) 0 0
\(859\) 15.0000 0.511793 0.255897 − 0.966704i \(-0.417629\pi\)
0.255897 + 0.966704i \(0.417629\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18.0000 −0.612727 −0.306364 − 0.951915i \(-0.599112\pi\)
−0.306364 + 0.951915i \(0.599112\pi\)
\(864\) 0 0
\(865\) −6.00000 −0.204006
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −39.0000 −1.32298
\(870\) 0 0
\(871\) 12.0000 0.406604
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3.00000 −0.101419
\(876\) 0 0
\(877\) 10.0000 0.337676 0.168838 − 0.985644i \(-0.445999\pi\)
0.168838 + 0.985644i \(0.445999\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −6.00000 −0.202145 −0.101073 − 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) 0 0
\(883\) 56.0000 1.88455 0.942275 − 0.334840i \(-0.108682\pi\)
0.942275 + 0.334840i \(0.108682\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.00000 −0.100730 −0.0503651 − 0.998731i \(-0.516038\pi\)
−0.0503651 + 0.998731i \(0.516038\pi\)
\(888\) 0 0
\(889\) 18.0000 0.603701
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −12.0000 −0.401565
\(894\) 0 0
\(895\) 2.00000 0.0668526
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −12.0000 −0.400222
\(900\) 0 0
\(901\) 1.00000 0.0333148
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5.00000 −0.166206
\(906\) 0 0
\(907\) 6.00000 0.199227 0.0996134 − 0.995026i \(-0.468239\pi\)
0.0996134 + 0.995026i \(0.468239\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 − 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 0 0
\(913\) −36.0000 −1.19143
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 54.0000 1.78324
\(918\) 0 0
\(919\) −27.0000 −0.890648 −0.445324 − 0.895370i \(-0.646911\pi\)
−0.445324 + 0.895370i \(0.646911\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5.00000 −0.164577
\(924\) 0 0
\(925\) 7.00000 0.230159
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −9.00000 −0.295280 −0.147640 − 0.989041i \(-0.547168\pi\)
−0.147640 + 0.989041i \(0.547168\pi\)
\(930\) 0 0
\(931\) 12.0000 0.393284
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 3.00000 0.0981105
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 − 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.00000 −0.0325991 −0.0162995 − 0.999867i \(-0.505189\pi\)
−0.0162995 + 0.999867i \(0.505189\pi\)
\(942\) 0 0
\(943\) 15.0000 0.488467
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 56.0000 1.81976 0.909878 − 0.414876i \(-0.136175\pi\)
0.909878 + 0.414876i \(0.136175\pi\)
\(948\) 0 0
\(949\) 6.00000 0.194768
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 17.0000 0.550684 0.275342 − 0.961346i \(-0.411209\pi\)
0.275342 + 0.961346i \(0.411209\pi\)
\(954\) 0 0
\(955\) −4.00000 −0.129437
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 42.0000 1.35625
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −11.0000 −0.354103
\(966\) 0 0
\(967\) 8.00000 0.257263 0.128631 − 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 40.0000 1.28366 0.641831 − 0.766846i \(-0.278175\pi\)
0.641831 + 0.766846i \(0.278175\pi\)
\(972\) 0 0
\(973\) 57.0000 1.82734
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 12.0000 0.383914 0.191957 − 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) 0 0
\(979\) 3.00000 0.0958804
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −28.0000 −0.893061 −0.446531 − 0.894768i \(-0.647341\pi\)
−0.446531 + 0.894768i \(0.647341\pi\)
\(984\) 0 0
\(985\) 12.0000 0.382352
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −40.0000 −1.27193
\(990\) 0 0
\(991\) −41.0000 −1.30241 −0.651204 − 0.758903i \(-0.725736\pi\)
−0.651204 + 0.758903i \(0.725736\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −20.0000 −0.634043
\(996\) 0 0
\(997\) −28.0000 −0.886769 −0.443384 − 0.896332i \(-0.646222\pi\)
−0.443384 + 0.896332i \(0.646222\pi\)
\(998\) 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 9360.2.a.x.1.1 1
3.2 odd 2 3120.2.a.m.1.1 1
4.3 odd 2 4680.2.a.c.1.1 1
12.11 even 2 1560.2.a.j.1.1 ✓ 1
60.59 even 2 7800.2.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.a.j.1.1 ✓ 1 12.11 even 2
3120.2.a.m.1.1 1 3.2 odd 2
4680.2.a.c.1.1 1 4.3 odd 2
7800.2.a.i.1.1 1 60.59 even 2
9360.2.a.x.1.1 1 1.1 even 1 trivial