Properties

Label 7524.2.a.q.1.3
Level $7524$
Weight $2$
Character 7524.1
Self dual yes
Analytic conductor $60.079$
Analytic rank $0$
Dimension $6$
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] = [7524,2,Mod(1,7524)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7524, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("7524.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7524.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: \(60.0794424808\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.744786576.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 17x^{4} + 13x^{3} + 69x^{2} - 21x - 30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 836)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-3.31717\) of defining polynomial
Character \(\chi\) \(=\) 7524.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.60797 q^{5} -4.11176 q^{7} +O(q^{10})\) \(q-1.60797 q^{5} -4.11176 q^{7} +1.00000 q^{11} -0.192283 q^{13} +7.62265 q^{17} -1.00000 q^{19} -6.73080 q^{23} -2.41443 q^{25} -6.80988 q^{29} +7.33391 q^{31} +6.61158 q^{35} +0.734914 q^{37} -0.976345 q^{41} -5.55470 q^{43} -8.83859 q^{47} +9.90653 q^{49} -11.8503 q^{53} -1.60797 q^{55} -3.30268 q^{59} +9.41840 q^{61} +0.309186 q^{65} +12.5025 q^{67} -4.12228 q^{71} -6.15694 q^{73} -4.11176 q^{77} -2.98831 q^{79} -6.33876 q^{83} -12.2570 q^{85} +13.5694 q^{89} +0.790623 q^{91} +1.60797 q^{95} -4.33130 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 5 q^{5} - 2 q^{7} + 6 q^{11} + 8 q^{13} + 2 q^{17} - 6 q^{19} - 5 q^{23} + 13 q^{25} - 10 q^{29} + 3 q^{31} + 4 q^{35} + 7 q^{37} - 6 q^{41} + 16 q^{43} + 12 q^{49} - 20 q^{53} - 5 q^{55} - 15 q^{59} + 24 q^{61} + 28 q^{65} + 25 q^{67} + 9 q^{71} - 26 q^{73} - 2 q^{77} - 16 q^{79} + 2 q^{83} + 12 q^{85} - 7 q^{89} + 8 q^{91} + 5 q^{95} + 37 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) −1.60797 −0.719106 −0.359553 0.933125i \(-0.617071\pi\)
−0.359553 + 0.933125i \(0.617071\pi\)
\(6\) 0 0
\(7\) −4.11176 −1.55410 −0.777049 0.629441i \(-0.783284\pi\)
−0.777049 + 0.629441i \(0.783284\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −0.192283 −0.0533298 −0.0266649 0.999644i \(-0.508489\pi\)
−0.0266649 + 0.999644i \(0.508489\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.62265 1.84876 0.924382 0.381469i \(-0.124582\pi\)
0.924382 + 0.381469i \(0.124582\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.73080 −1.40347 −0.701734 0.712439i \(-0.747590\pi\)
−0.701734 + 0.712439i \(0.747590\pi\)
\(24\) 0 0
\(25\) −2.41443 −0.482887
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.80988 −1.26456 −0.632282 0.774738i \(-0.717882\pi\)
−0.632282 + 0.774738i \(0.717882\pi\)
\(30\) 0 0
\(31\) 7.33391 1.31721 0.658604 0.752490i \(-0.271147\pi\)
0.658604 + 0.752490i \(0.271147\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.61158 1.11756
\(36\) 0 0
\(37\) 0.734914 0.120819 0.0604095 0.998174i \(-0.480759\pi\)
0.0604095 + 0.998174i \(0.480759\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.976345 −0.152479 −0.0762397 0.997090i \(-0.524291\pi\)
−0.0762397 + 0.997090i \(0.524291\pi\)
\(42\) 0 0
\(43\) −5.55470 −0.847084 −0.423542 0.905876i \(-0.639213\pi\)
−0.423542 + 0.905876i \(0.639213\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.83859 −1.28924 −0.644620 0.764503i \(-0.722984\pi\)
−0.644620 + 0.764503i \(0.722984\pi\)
\(48\) 0 0
\(49\) 9.90653 1.41522
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −11.8503 −1.62776 −0.813880 0.581033i \(-0.802649\pi\)
−0.813880 + 0.581033i \(0.802649\pi\)
\(54\) 0 0
\(55\) −1.60797 −0.216819
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.30268 −0.429972 −0.214986 0.976617i \(-0.568971\pi\)
−0.214986 + 0.976617i \(0.568971\pi\)
\(60\) 0 0
\(61\) 9.41840 1.20590 0.602951 0.797778i \(-0.293991\pi\)
0.602951 + 0.797778i \(0.293991\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.309186 0.0383498
\(66\) 0 0
\(67\) 12.5025 1.52743 0.763714 0.645555i \(-0.223374\pi\)
0.763714 + 0.645555i \(0.223374\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.12228 −0.489225 −0.244612 0.969621i \(-0.578661\pi\)
−0.244612 + 0.969621i \(0.578661\pi\)
\(72\) 0 0
\(73\) −6.15694 −0.720615 −0.360308 0.932834i \(-0.617328\pi\)
−0.360308 + 0.932834i \(0.617328\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.11176 −0.468578
\(78\) 0 0
\(79\) −2.98831 −0.336211 −0.168106 0.985769i \(-0.553765\pi\)
−0.168106 + 0.985769i \(0.553765\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.33876 −0.695770 −0.347885 0.937537i \(-0.613100\pi\)
−0.347885 + 0.937537i \(0.613100\pi\)
\(84\) 0 0
\(85\) −12.2570 −1.32946
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 13.5694 1.43835 0.719176 0.694828i \(-0.244520\pi\)
0.719176 + 0.694828i \(0.244520\pi\)
\(90\) 0 0
\(91\) 0.790623 0.0828798
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.60797 0.164974
\(96\) 0 0
\(97\) −4.33130 −0.439777 −0.219889 0.975525i \(-0.570569\pi\)
−0.219889 + 0.975525i \(0.570569\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.4729 1.34061 0.670303 0.742088i \(-0.266164\pi\)
0.670303 + 0.742088i \(0.266164\pi\)
\(102\) 0 0
\(103\) 8.83382 0.870422 0.435211 0.900329i \(-0.356674\pi\)
0.435211 + 0.900329i \(0.356674\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.2194 −1.18129 −0.590647 0.806930i \(-0.701127\pi\)
−0.590647 + 0.806930i \(0.701127\pi\)
\(108\) 0 0
\(109\) 7.54186 0.722379 0.361190 0.932492i \(-0.382371\pi\)
0.361190 + 0.932492i \(0.382371\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.68563 −0.346715 −0.173358 0.984859i \(-0.555462\pi\)
−0.173358 + 0.984859i \(0.555462\pi\)
\(114\) 0 0
\(115\) 10.8229 1.00924
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −31.3425 −2.87316
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.9222 1.06635
\(126\) 0 0
\(127\) −4.19292 −0.372061 −0.186031 0.982544i \(-0.559562\pi\)
−0.186031 + 0.982544i \(0.559562\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.75993 0.765359 0.382679 0.923881i \(-0.375001\pi\)
0.382679 + 0.923881i \(0.375001\pi\)
\(132\) 0 0
\(133\) 4.11176 0.356534
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.06261 0.688835 0.344418 0.938817i \(-0.388076\pi\)
0.344418 + 0.938817i \(0.388076\pi\)
\(138\) 0 0
\(139\) 13.3201 1.12979 0.564897 0.825161i \(-0.308916\pi\)
0.564897 + 0.825161i \(0.308916\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.192283 −0.0160796
\(144\) 0 0
\(145\) 10.9501 0.909355
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.6532 −1.28236 −0.641182 0.767389i \(-0.721556\pi\)
−0.641182 + 0.767389i \(0.721556\pi\)
\(150\) 0 0
\(151\) −17.8796 −1.45502 −0.727512 0.686095i \(-0.759323\pi\)
−0.727512 + 0.686095i \(0.759323\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11.7927 −0.947212
\(156\) 0 0
\(157\) 7.07368 0.564541 0.282271 0.959335i \(-0.408912\pi\)
0.282271 + 0.959335i \(0.408912\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 27.6754 2.18113
\(162\) 0 0
\(163\) −3.44357 −0.269721 −0.134861 0.990865i \(-0.543059\pi\)
−0.134861 + 0.990865i \(0.543059\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.330041 0.0255394 0.0127697 0.999918i \(-0.495935\pi\)
0.0127697 + 0.999918i \(0.495935\pi\)
\(168\) 0 0
\(169\) −12.9630 −0.997156
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4.62957 −0.351979 −0.175990 0.984392i \(-0.556313\pi\)
−0.175990 + 0.984392i \(0.556313\pi\)
\(174\) 0 0
\(175\) 9.92756 0.750453
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.15071 0.384982 0.192491 0.981299i \(-0.438343\pi\)
0.192491 + 0.981299i \(0.438343\pi\)
\(180\) 0 0
\(181\) 12.3061 0.914708 0.457354 0.889285i \(-0.348797\pi\)
0.457354 + 0.889285i \(0.348797\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.18172 −0.0868817
\(186\) 0 0
\(187\) 7.62265 0.557423
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.7999 1.14324 0.571620 0.820518i \(-0.306315\pi\)
0.571620 + 0.820518i \(0.306315\pi\)
\(192\) 0 0
\(193\) 26.6087 1.91534 0.957669 0.287871i \(-0.0929475\pi\)
0.957669 + 0.287871i \(0.0929475\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.61255 0.114890 0.0574448 0.998349i \(-0.481705\pi\)
0.0574448 + 0.998349i \(0.481705\pi\)
\(198\) 0 0
\(199\) −14.2001 −1.00662 −0.503310 0.864106i \(-0.667885\pi\)
−0.503310 + 0.864106i \(0.667885\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 28.0006 1.96525
\(204\) 0 0
\(205\) 1.56993 0.109649
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 9.58917 0.660146 0.330073 0.943955i \(-0.392927\pi\)
0.330073 + 0.943955i \(0.392927\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.93179 0.609143
\(216\) 0 0
\(217\) −30.1552 −2.04707
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.46571 −0.0985943
\(222\) 0 0
\(223\) 2.74913 0.184095 0.0920476 0.995755i \(-0.470659\pi\)
0.0920476 + 0.995755i \(0.470659\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.67193 −0.177342 −0.0886711 0.996061i \(-0.528262\pi\)
−0.0886711 + 0.996061i \(0.528262\pi\)
\(228\) 0 0
\(229\) 19.9350 1.31734 0.658672 0.752430i \(-0.271119\pi\)
0.658672 + 0.752430i \(0.271119\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.74051 −0.376073 −0.188037 0.982162i \(-0.560212\pi\)
−0.188037 + 0.982162i \(0.560212\pi\)
\(234\) 0 0
\(235\) 14.2122 0.927100
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 12.9106 0.835120 0.417560 0.908649i \(-0.362885\pi\)
0.417560 + 0.908649i \(0.362885\pi\)
\(240\) 0 0
\(241\) 26.3067 1.69457 0.847283 0.531142i \(-0.178237\pi\)
0.847283 + 0.531142i \(0.178237\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −15.9294 −1.01769
\(246\) 0 0
\(247\) 0.192283 0.0122347
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.77775 0.364688 0.182344 0.983235i \(-0.441631\pi\)
0.182344 + 0.983235i \(0.441631\pi\)
\(252\) 0 0
\(253\) −6.73080 −0.423161
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 20.6302 1.28688 0.643439 0.765498i \(-0.277507\pi\)
0.643439 + 0.765498i \(0.277507\pi\)
\(258\) 0 0
\(259\) −3.02179 −0.187765
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.4936 −0.832048 −0.416024 0.909354i \(-0.636577\pi\)
−0.416024 + 0.909354i \(0.636577\pi\)
\(264\) 0 0
\(265\) 19.0549 1.17053
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.54562 0.399094 0.199547 0.979888i \(-0.436053\pi\)
0.199547 + 0.979888i \(0.436053\pi\)
\(270\) 0 0
\(271\) 0.121298 0.00736831 0.00368415 0.999993i \(-0.498827\pi\)
0.00368415 + 0.999993i \(0.498827\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.41443 −0.145596
\(276\) 0 0
\(277\) 13.4770 0.809757 0.404878 0.914371i \(-0.367314\pi\)
0.404878 + 0.914371i \(0.367314\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.63154 0.216639 0.108320 0.994116i \(-0.465453\pi\)
0.108320 + 0.994116i \(0.465453\pi\)
\(282\) 0 0
\(283\) 16.9545 1.00784 0.503919 0.863751i \(-0.331891\pi\)
0.503919 + 0.863751i \(0.331891\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.01449 0.236968
\(288\) 0 0
\(289\) 41.1048 2.41793
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.8307 0.632739 0.316369 0.948636i \(-0.397536\pi\)
0.316369 + 0.948636i \(0.397536\pi\)
\(294\) 0 0
\(295\) 5.31061 0.309195
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.29422 0.0748467
\(300\) 0 0
\(301\) 22.8396 1.31645
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −15.1445 −0.867171
\(306\) 0 0
\(307\) 2.43981 0.139247 0.0696235 0.997573i \(-0.477820\pi\)
0.0696235 + 0.997573i \(0.477820\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 26.3308 1.49308 0.746541 0.665340i \(-0.231713\pi\)
0.746541 + 0.665340i \(0.231713\pi\)
\(312\) 0 0
\(313\) −3.76724 −0.212937 −0.106468 0.994316i \(-0.533954\pi\)
−0.106468 + 0.994316i \(0.533954\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.02324 −0.0574711 −0.0287356 0.999587i \(-0.509148\pi\)
−0.0287356 + 0.999587i \(0.509148\pi\)
\(318\) 0 0
\(319\) −6.80988 −0.381280
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7.62265 −0.424135
\(324\) 0 0
\(325\) 0.464256 0.0257523
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 36.3421 2.00361
\(330\) 0 0
\(331\) 13.5921 0.747090 0.373545 0.927612i \(-0.378142\pi\)
0.373545 + 0.927612i \(0.378142\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −20.1037 −1.09838
\(336\) 0 0
\(337\) −13.0615 −0.711503 −0.355752 0.934581i \(-0.615775\pi\)
−0.355752 + 0.934581i \(0.615775\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7.33391 0.397153
\(342\) 0 0
\(343\) −11.9509 −0.645290
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.78370 0.525217 0.262608 0.964903i \(-0.415417\pi\)
0.262608 + 0.964903i \(0.415417\pi\)
\(348\) 0 0
\(349\) 4.57188 0.244727 0.122364 0.992485i \(-0.460953\pi\)
0.122364 + 0.992485i \(0.460953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.57171 0.403001 0.201501 0.979488i \(-0.435418\pi\)
0.201501 + 0.979488i \(0.435418\pi\)
\(354\) 0 0
\(355\) 6.62850 0.351804
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.7533 −0.673094 −0.336547 0.941667i \(-0.609259\pi\)
−0.336547 + 0.941667i \(0.609259\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.90017 0.518199
\(366\) 0 0
\(367\) 25.2916 1.32021 0.660104 0.751174i \(-0.270512\pi\)
0.660104 + 0.751174i \(0.270512\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 48.7254 2.52970
\(372\) 0 0
\(373\) 16.8451 0.872209 0.436104 0.899896i \(-0.356358\pi\)
0.436104 + 0.899896i \(0.356358\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.30943 0.0674390
\(378\) 0 0
\(379\) 24.1556 1.24079 0.620394 0.784290i \(-0.286973\pi\)
0.620394 + 0.784290i \(0.286973\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.06487 −0.156608 −0.0783039 0.996930i \(-0.524950\pi\)
−0.0783039 + 0.996930i \(0.524950\pi\)
\(384\) 0 0
\(385\) 6.61158 0.336957
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.3879 −0.932304 −0.466152 0.884705i \(-0.654360\pi\)
−0.466152 + 0.884705i \(0.654360\pi\)
\(390\) 0 0
\(391\) −51.3065 −2.59468
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.80511 0.241771
\(396\) 0 0
\(397\) −10.1799 −0.510917 −0.255458 0.966820i \(-0.582226\pi\)
−0.255458 + 0.966820i \(0.582226\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −18.0851 −0.903128 −0.451564 0.892239i \(-0.649134\pi\)
−0.451564 + 0.892239i \(0.649134\pi\)
\(402\) 0 0
\(403\) −1.41019 −0.0702465
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.734914 0.0364283
\(408\) 0 0
\(409\) 20.3087 1.00420 0.502100 0.864810i \(-0.332561\pi\)
0.502100 + 0.864810i \(0.332561\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 13.5798 0.668219
\(414\) 0 0
\(415\) 10.1925 0.500332
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9.98616 −0.487856 −0.243928 0.969793i \(-0.578436\pi\)
−0.243928 + 0.969793i \(0.578436\pi\)
\(420\) 0 0
\(421\) −34.7710 −1.69463 −0.847316 0.531089i \(-0.821783\pi\)
−0.847316 + 0.531089i \(0.821783\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −18.4044 −0.892744
\(426\) 0 0
\(427\) −38.7261 −1.87409
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 22.3666 1.07736 0.538681 0.842510i \(-0.318923\pi\)
0.538681 + 0.842510i \(0.318923\pi\)
\(432\) 0 0
\(433\) −35.4168 −1.70202 −0.851011 0.525148i \(-0.824010\pi\)
−0.851011 + 0.525148i \(0.824010\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.73080 0.321978
\(438\) 0 0
\(439\) 9.55446 0.456010 0.228005 0.973660i \(-0.426780\pi\)
0.228005 + 0.973660i \(0.426780\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 28.3348 1.34623 0.673113 0.739540i \(-0.264957\pi\)
0.673113 + 0.739540i \(0.264957\pi\)
\(444\) 0 0
\(445\) −21.8192 −1.03433
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −19.7315 −0.931188 −0.465594 0.884998i \(-0.654159\pi\)
−0.465594 + 0.884998i \(0.654159\pi\)
\(450\) 0 0
\(451\) −0.976345 −0.0459743
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.27130 −0.0595993
\(456\) 0 0
\(457\) 23.6281 1.10527 0.552637 0.833422i \(-0.313621\pi\)
0.552637 + 0.833422i \(0.313621\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.976802 0.0454942 0.0227471 0.999741i \(-0.492759\pi\)
0.0227471 + 0.999741i \(0.492759\pi\)
\(462\) 0 0
\(463\) 7.78708 0.361896 0.180948 0.983493i \(-0.442083\pi\)
0.180948 + 0.983493i \(0.442083\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −35.1591 −1.62697 −0.813486 0.581585i \(-0.802433\pi\)
−0.813486 + 0.581585i \(0.802433\pi\)
\(468\) 0 0
\(469\) −51.4074 −2.37377
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.55470 −0.255406
\(474\) 0 0
\(475\) 2.41443 0.110782
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −30.2805 −1.38355 −0.691777 0.722112i \(-0.743172\pi\)
−0.691777 + 0.722112i \(0.743172\pi\)
\(480\) 0 0
\(481\) −0.141312 −0.00644326
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.96460 0.316246
\(486\) 0 0
\(487\) −23.3841 −1.05964 −0.529818 0.848112i \(-0.677740\pi\)
−0.529818 + 0.848112i \(0.677740\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18.1633 −0.819696 −0.409848 0.912154i \(-0.634418\pi\)
−0.409848 + 0.912154i \(0.634418\pi\)
\(492\) 0 0
\(493\) −51.9093 −2.33788
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 16.9498 0.760303
\(498\) 0 0
\(499\) −39.7067 −1.77752 −0.888759 0.458375i \(-0.848432\pi\)
−0.888759 + 0.458375i \(0.848432\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −13.5741 −0.605241 −0.302621 0.953111i \(-0.597861\pi\)
−0.302621 + 0.953111i \(0.597861\pi\)
\(504\) 0 0
\(505\) −21.6641 −0.964038
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −28.1607 −1.24820 −0.624101 0.781343i \(-0.714535\pi\)
−0.624101 + 0.781343i \(0.714535\pi\)
\(510\) 0 0
\(511\) 25.3158 1.11991
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −14.2045 −0.625925
\(516\) 0 0
\(517\) −8.83859 −0.388721
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.2741 0.756790 0.378395 0.925644i \(-0.376476\pi\)
0.378395 + 0.925644i \(0.376476\pi\)
\(522\) 0 0
\(523\) −14.6315 −0.639789 −0.319894 0.947453i \(-0.603647\pi\)
−0.319894 + 0.947453i \(0.603647\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 55.9038 2.43521
\(528\) 0 0
\(529\) 22.3036 0.969722
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.187735 0.00813170
\(534\) 0 0
\(535\) 19.6484 0.849475
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 9.90653 0.426704
\(540\) 0 0
\(541\) −0.742620 −0.0319277 −0.0159639 0.999873i \(-0.505082\pi\)
−0.0159639 + 0.999873i \(0.505082\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.1271 −0.519467
\(546\) 0 0
\(547\) 33.5177 1.43311 0.716557 0.697528i \(-0.245717\pi\)
0.716557 + 0.697528i \(0.245717\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.80988 0.290111
\(552\) 0 0
\(553\) 12.2872 0.522505
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.6775 0.791392 0.395696 0.918381i \(-0.370503\pi\)
0.395696 + 0.918381i \(0.370503\pi\)
\(558\) 0 0
\(559\) 1.06808 0.0451749
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 28.4524 1.19913 0.599564 0.800327i \(-0.295341\pi\)
0.599564 + 0.800327i \(0.295341\pi\)
\(564\) 0 0
\(565\) 5.92638 0.249325
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7.87017 −0.329935 −0.164967 0.986299i \(-0.552752\pi\)
−0.164967 + 0.986299i \(0.552752\pi\)
\(570\) 0 0
\(571\) −37.6693 −1.57641 −0.788205 0.615413i \(-0.788989\pi\)
−0.788205 + 0.615413i \(0.788989\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16.2511 0.677716
\(576\) 0 0
\(577\) 43.9800 1.83091 0.915457 0.402417i \(-0.131830\pi\)
0.915457 + 0.402417i \(0.131830\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 26.0634 1.08129
\(582\) 0 0
\(583\) −11.8503 −0.490788
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.6515 0.480907 0.240453 0.970661i \(-0.422704\pi\)
0.240453 + 0.970661i \(0.422704\pi\)
\(588\) 0 0
\(589\) −7.33391 −0.302188
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 32.3337 1.32778 0.663892 0.747828i \(-0.268903\pi\)
0.663892 + 0.747828i \(0.268903\pi\)
\(594\) 0 0
\(595\) 50.3977 2.06611
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0.717765 0.0293271 0.0146635 0.999892i \(-0.495332\pi\)
0.0146635 + 0.999892i \(0.495332\pi\)
\(600\) 0 0
\(601\) −17.6539 −0.720117 −0.360058 0.932930i \(-0.617243\pi\)
−0.360058 + 0.932930i \(0.617243\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.60797 −0.0653733
\(606\) 0 0
\(607\) −10.2348 −0.415419 −0.207710 0.978191i \(-0.566601\pi\)
−0.207710 + 0.978191i \(0.566601\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.69951 0.0687550
\(612\) 0 0
\(613\) −13.7215 −0.554205 −0.277102 0.960840i \(-0.589374\pi\)
−0.277102 + 0.960840i \(0.589374\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.2447 0.855280 0.427640 0.903949i \(-0.359345\pi\)
0.427640 + 0.903949i \(0.359345\pi\)
\(618\) 0 0
\(619\) 16.8753 0.678274 0.339137 0.940737i \(-0.389865\pi\)
0.339137 + 0.940737i \(0.389865\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −55.7940 −2.23534
\(624\) 0 0
\(625\) −7.09834 −0.283933
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.60199 0.223366
\(630\) 0 0
\(631\) −31.7238 −1.26291 −0.631453 0.775414i \(-0.717541\pi\)
−0.631453 + 0.775414i \(0.717541\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.74208 0.267551
\(636\) 0 0
\(637\) −1.90486 −0.0754734
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −34.5505 −1.36466 −0.682332 0.731043i \(-0.739034\pi\)
−0.682332 + 0.731043i \(0.739034\pi\)
\(642\) 0 0
\(643\) −3.89781 −0.153715 −0.0768573 0.997042i \(-0.524489\pi\)
−0.0768573 + 0.997042i \(0.524489\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 19.5834 0.769904 0.384952 0.922937i \(-0.374218\pi\)
0.384952 + 0.922937i \(0.374218\pi\)
\(648\) 0 0
\(649\) −3.30268 −0.129641
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13.1173 −0.513320 −0.256660 0.966502i \(-0.582622\pi\)
−0.256660 + 0.966502i \(0.582622\pi\)
\(654\) 0 0
\(655\) −14.0857 −0.550374
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 32.3835 1.26148 0.630741 0.775993i \(-0.282751\pi\)
0.630741 + 0.775993i \(0.282751\pi\)
\(660\) 0 0
\(661\) −21.4666 −0.834954 −0.417477 0.908688i \(-0.637086\pi\)
−0.417477 + 0.908688i \(0.637086\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.61158 −0.256386
\(666\) 0 0
\(667\) 45.8359 1.77477
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9.41840 0.363593
\(672\) 0 0
\(673\) 32.8054 1.26455 0.632277 0.774742i \(-0.282120\pi\)
0.632277 + 0.774742i \(0.282120\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 38.3331 1.47326 0.736630 0.676296i \(-0.236416\pi\)
0.736630 + 0.676296i \(0.236416\pi\)
\(678\) 0 0
\(679\) 17.8093 0.683456
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −10.3756 −0.397010 −0.198505 0.980100i \(-0.563609\pi\)
−0.198505 + 0.980100i \(0.563609\pi\)
\(684\) 0 0
\(685\) −12.9644 −0.495345
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.27861 0.0868082
\(690\) 0 0
\(691\) −6.05581 −0.230374 −0.115187 0.993344i \(-0.536747\pi\)
−0.115187 + 0.993344i \(0.536747\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −21.4183 −0.812442
\(696\) 0 0
\(697\) −7.44233 −0.281898
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −0.497075 −0.0187743 −0.00938714 0.999956i \(-0.502988\pi\)
−0.00938714 + 0.999956i \(0.502988\pi\)
\(702\) 0 0
\(703\) −0.734914 −0.0277178
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −55.3974 −2.08343
\(708\) 0 0
\(709\) 12.5856 0.472661 0.236330 0.971673i \(-0.424055\pi\)
0.236330 + 0.971673i \(0.424055\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −49.3630 −1.84866
\(714\) 0 0
\(715\) 0.309186 0.0115629
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.17724 0.230372 0.115186 0.993344i \(-0.463254\pi\)
0.115186 + 0.993344i \(0.463254\pi\)
\(720\) 0 0
\(721\) −36.3225 −1.35272
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 16.4420 0.610641
\(726\) 0 0
\(727\) 5.90914 0.219158 0.109579 0.993978i \(-0.465050\pi\)
0.109579 + 0.993978i \(0.465050\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −42.3416 −1.56606
\(732\) 0 0
\(733\) 24.0990 0.890118 0.445059 0.895501i \(-0.353183\pi\)
0.445059 + 0.895501i \(0.353183\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12.5025 0.460537
\(738\) 0 0
\(739\) −5.74460 −0.211319 −0.105659 0.994402i \(-0.533695\pi\)
−0.105659 + 0.994402i \(0.533695\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16.8092 −0.616671 −0.308335 0.951278i \(-0.599772\pi\)
−0.308335 + 0.951278i \(0.599772\pi\)
\(744\) 0 0
\(745\) 25.1699 0.922155
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 50.2431 1.83584
\(750\) 0 0
\(751\) 32.6804 1.19252 0.596262 0.802790i \(-0.296652\pi\)
0.596262 + 0.802790i \(0.296652\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 28.7499 1.04632
\(756\) 0 0
\(757\) 40.3897 1.46799 0.733994 0.679156i \(-0.237654\pi\)
0.733994 + 0.679156i \(0.237654\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 45.6390 1.65441 0.827207 0.561898i \(-0.189929\pi\)
0.827207 + 0.561898i \(0.189929\pi\)
\(762\) 0 0
\(763\) −31.0103 −1.12265
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.635051 0.0229303
\(768\) 0 0
\(769\) −24.4815 −0.882826 −0.441413 0.897304i \(-0.645523\pi\)
−0.441413 + 0.897304i \(0.645523\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.74051 0.0626018 0.0313009 0.999510i \(-0.490035\pi\)
0.0313009 + 0.999510i \(0.490035\pi\)
\(774\) 0 0
\(775\) −17.7072 −0.636063
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.976345 0.0349812
\(780\) 0 0
\(781\) −4.12228 −0.147507
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −11.3743 −0.405965
\(786\) 0 0
\(787\) −25.4670 −0.907801 −0.453901 0.891052i \(-0.649968\pi\)
−0.453901 + 0.891052i \(0.649968\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 15.1544 0.538829
\(792\) 0 0
\(793\) −1.81100 −0.0643106
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −17.4228 −0.617146 −0.308573 0.951201i \(-0.599851\pi\)
−0.308573 + 0.951201i \(0.599851\pi\)
\(798\) 0 0
\(799\) −67.3734 −2.38350
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −6.15694 −0.217274
\(804\) 0 0
\(805\) −44.5012 −1.56846
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26.1897 −0.920779 −0.460390 0.887717i \(-0.652290\pi\)
−0.460390 + 0.887717i \(0.652290\pi\)
\(810\) 0 0
\(811\) 50.4597 1.77188 0.885939 0.463801i \(-0.153515\pi\)
0.885939 + 0.463801i \(0.153515\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 5.53715 0.193958
\(816\) 0 0
\(817\) 5.55470 0.194334
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −5.99962 −0.209388 −0.104694 0.994504i \(-0.533386\pi\)
−0.104694 + 0.994504i \(0.533386\pi\)
\(822\) 0 0
\(823\) 0.615783 0.0214649 0.0107324 0.999942i \(-0.496584\pi\)
0.0107324 + 0.999942i \(0.496584\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −40.7839 −1.41820 −0.709098 0.705110i \(-0.750898\pi\)
−0.709098 + 0.705110i \(0.750898\pi\)
\(828\) 0 0
\(829\) 38.6707 1.34309 0.671544 0.740964i \(-0.265631\pi\)
0.671544 + 0.740964i \(0.265631\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 75.5140 2.61640
\(834\) 0 0
\(835\) −0.530696 −0.0183655
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −18.6821 −0.644978 −0.322489 0.946573i \(-0.604520\pi\)
−0.322489 + 0.946573i \(0.604520\pi\)
\(840\) 0 0
\(841\) 17.3745 0.599121
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 20.8442 0.717061
\(846\) 0 0
\(847\) −4.11176 −0.141282
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.94655 −0.169566
\(852\) 0 0
\(853\) 44.3592 1.51883 0.759415 0.650607i \(-0.225485\pi\)
0.759415 + 0.650607i \(0.225485\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −22.4643 −0.767367 −0.383684 0.923465i \(-0.625345\pi\)
−0.383684 + 0.923465i \(0.625345\pi\)
\(858\) 0 0
\(859\) 7.80075 0.266158 0.133079 0.991105i \(-0.457514\pi\)
0.133079 + 0.991105i \(0.457514\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −42.3672 −1.44220 −0.721098 0.692833i \(-0.756362\pi\)
−0.721098 + 0.692833i \(0.756362\pi\)
\(864\) 0 0
\(865\) 7.44420 0.253110
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.98831 −0.101371
\(870\) 0 0
\(871\) −2.40403 −0.0814575
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −49.0211 −1.65722
\(876\) 0 0
\(877\) 16.7160 0.564458 0.282229 0.959347i \(-0.408926\pi\)
0.282229 + 0.959347i \(0.408926\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 34.5007 1.16236 0.581179 0.813776i \(-0.302592\pi\)
0.581179 + 0.813776i \(0.302592\pi\)
\(882\) 0 0
\(883\) 20.0083 0.673333 0.336667 0.941624i \(-0.390700\pi\)
0.336667 + 0.941624i \(0.390700\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −51.5291 −1.73018 −0.865089 0.501618i \(-0.832738\pi\)
−0.865089 + 0.501618i \(0.832738\pi\)
\(888\) 0 0
\(889\) 17.2402 0.578219
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8.83859 0.295772
\(894\) 0 0
\(895\) −8.28218 −0.276843
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −49.9430 −1.66569
\(900\) 0 0
\(901\) −90.3305 −3.00934
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −19.7879 −0.657772
\(906\) 0 0
\(907\) −46.9324 −1.55836 −0.779182 0.626798i \(-0.784365\pi\)
−0.779182 + 0.626798i \(0.784365\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −43.3927 −1.43766 −0.718831 0.695184i \(-0.755323\pi\)
−0.718831 + 0.695184i \(0.755323\pi\)
\(912\) 0 0
\(913\) −6.33876 −0.209783
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −36.0187 −1.18944
\(918\) 0 0
\(919\) 46.1195 1.52134 0.760671 0.649138i \(-0.224870\pi\)
0.760671 + 0.649138i \(0.224870\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0.792646 0.0260903
\(924\) 0 0
\(925\) −1.77440 −0.0583419
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 50.6414 1.66149 0.830745 0.556653i \(-0.187915\pi\)
0.830745 + 0.556653i \(0.187915\pi\)
\(930\) 0 0
\(931\) −9.90653 −0.324673
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −12.2570 −0.400846
\(936\) 0 0
\(937\) 52.6225 1.71910 0.859551 0.511051i \(-0.170744\pi\)
0.859551 + 0.511051i \(0.170744\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 39.1834 1.27734 0.638671 0.769480i \(-0.279484\pi\)
0.638671 + 0.769480i \(0.279484\pi\)
\(942\) 0 0
\(943\) 6.57158 0.214000
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.35590 0.0440608 0.0220304 0.999757i \(-0.492987\pi\)
0.0220304 + 0.999757i \(0.492987\pi\)
\(948\) 0 0
\(949\) 1.18388 0.0384303
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 10.3667 0.335812 0.167906 0.985803i \(-0.446299\pi\)
0.167906 + 0.985803i \(0.446299\pi\)
\(954\) 0 0
\(955\) −25.4057 −0.822111
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −33.1515 −1.07052
\(960\) 0 0
\(961\) 22.7862 0.735038
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −42.7860 −1.37733
\(966\) 0 0
\(967\) −11.8273 −0.380340 −0.190170 0.981751i \(-0.560904\pi\)
−0.190170 + 0.981751i \(0.560904\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.74148 −0.152161 −0.0760806 0.997102i \(-0.524241\pi\)
−0.0760806 + 0.997102i \(0.524241\pi\)
\(972\) 0 0
\(973\) −54.7689 −1.75581
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −35.1330 −1.12401 −0.562003 0.827135i \(-0.689969\pi\)
−0.562003 + 0.827135i \(0.689969\pi\)
\(978\) 0 0
\(979\) 13.5694 0.433679
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 13.8563 0.441948 0.220974 0.975280i \(-0.429076\pi\)
0.220974 + 0.975280i \(0.429076\pi\)
\(984\) 0 0
\(985\) −2.59293 −0.0826178
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 37.3876 1.18886
\(990\) 0 0
\(991\) 8.08672 0.256883 0.128442 0.991717i \(-0.459003\pi\)
0.128442 + 0.991717i \(0.459003\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 22.8334 0.723867
\(996\) 0 0
\(997\) −4.02300 −0.127410 −0.0637049 0.997969i \(-0.520292\pi\)
−0.0637049 + 0.997969i \(0.520292\pi\)
\(998\) 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 7524.2.a.q.1.3 6
3.2 odd 2 836.2.a.e.1.1 6
12.11 even 2 3344.2.a.w.1.6 6
33.32 even 2 9196.2.a.n.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
836.2.a.e.1.1 6 3.2 odd 2
3344.2.a.w.1.6 6 12.11 even 2
7524.2.a.q.1.3 6 1.1 even 1 trivial
9196.2.a.n.1.1 6 33.32 even 2