Properties

Label 3626.2.a.n.1.1
Level $3626$
Weight $2$
Character 3626.1
Self dual yes
Analytic conductor $28.954$
Analytic rank $1$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3626,2,Mod(1,3626)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3626, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3626.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3626 = 2 \cdot 7^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3626.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: \(28.9537557729\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
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: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 3626.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} -3.00000 q^{9} +1.00000 q^{16} -2.82843 q^{17} -3.00000 q^{18} +4.24264 q^{19} -6.00000 q^{23} -5.00000 q^{25} -6.00000 q^{29} -4.24264 q^{31} +1.00000 q^{32} -2.82843 q^{34} -3.00000 q^{36} +1.00000 q^{37} +4.24264 q^{38} +7.07107 q^{41} -4.00000 q^{43} -6.00000 q^{46} -2.82843 q^{47} -5.00000 q^{50} -6.00000 q^{58} -1.41421 q^{59} -2.82843 q^{61} -4.24264 q^{62} +1.00000 q^{64} -8.00000 q^{67} -2.82843 q^{68} -3.00000 q^{72} -1.41421 q^{73} +1.00000 q^{74} +4.24264 q^{76} -10.0000 q^{79} +9.00000 q^{81} +7.07107 q^{82} +5.65685 q^{83} -4.00000 q^{86} +2.82843 q^{89} -6.00000 q^{92} -2.82843 q^{94} +16.9706 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 6 q^{9} + 2 q^{16} - 6 q^{18} - 12 q^{23} - 10 q^{25} - 12 q^{29} + 2 q^{32} - 6 q^{36} + 2 q^{37} - 8 q^{43} - 12 q^{46} - 10 q^{50} - 12 q^{58} + 2 q^{64} - 16 q^{67} - 6 q^{72} + 2 q^{74} - 20 q^{79} + 18 q^{81} - 8 q^{86} - 12 q^{92}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.82843 −0.685994 −0.342997 0.939336i \(-0.611442\pi\)
−0.342997 + 0.939336i \(0.611442\pi\)
\(18\) −3.00000 −0.707107
\(19\) 4.24264 0.973329 0.486664 0.873589i \(-0.338214\pi\)
0.486664 + 0.873589i \(0.338214\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −4.24264 −0.762001 −0.381000 0.924575i \(-0.624420\pi\)
−0.381000 + 0.924575i \(0.624420\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.82843 −0.485071
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 1.00000 0.164399
\(38\) 4.24264 0.688247
\(39\) 0 0
\(40\) 0 0
\(41\) 7.07107 1.10432 0.552158 0.833740i \(-0.313805\pi\)
0.552158 + 0.833740i \(0.313805\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −1.41421 −0.184115 −0.0920575 0.995754i \(-0.529344\pi\)
−0.0920575 + 0.995754i \(0.529344\pi\)
\(60\) 0 0
\(61\) −2.82843 −0.362143 −0.181071 0.983470i \(-0.557957\pi\)
−0.181071 + 0.983470i \(0.557957\pi\)
\(62\) −4.24264 −0.538816
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) −2.82843 −0.342997
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −3.00000 −0.353553
\(73\) −1.41421 −0.165521 −0.0827606 0.996569i \(-0.526374\pi\)
−0.0827606 + 0.996569i \(0.526374\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) 4.24264 0.486664
\(77\) 0 0
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 7.07107 0.780869
\(83\) 5.65685 0.620920 0.310460 0.950586i \(-0.399517\pi\)
0.310460 + 0.950586i \(0.399517\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 0 0
\(89\) 2.82843 0.299813 0.149906 0.988700i \(-0.452103\pi\)
0.149906 + 0.988700i \(0.452103\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) −2.82843 −0.291730
\(95\) 0 0
\(96\) 0 0
\(97\) 16.9706 1.72310 0.861550 0.507673i \(-0.169494\pi\)
0.861550 + 0.507673i \(0.169494\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) −9.89949 −0.985037 −0.492518 0.870302i \(-0.663924\pi\)
−0.492518 + 0.870302i \(0.663924\pi\)
\(102\) 0 0
\(103\) −15.5563 −1.53281 −0.766406 0.642356i \(-0.777957\pi\)
−0.766406 + 0.642356i \(0.777957\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) −1.41421 −0.130189
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −2.82843 −0.256074
\(123\) 0 0
\(124\) −4.24264 −0.381000
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −1.41421 −0.123560 −0.0617802 0.998090i \(-0.519678\pi\)
−0.0617802 + 0.998090i \(0.519678\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −2.82843 −0.242536
\(137\) −4.00000 −0.341743 −0.170872 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(138\) 0 0
\(139\) −2.82843 −0.239904 −0.119952 0.992780i \(-0.538274\pi\)
−0.119952 + 0.992780i \(0.538274\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) −1.41421 −0.117041
\(147\) 0 0
\(148\) 1.00000 0.0821995
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) 0 0
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 4.24264 0.344124
\(153\) 8.48528 0.685994
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.7279 −1.01580 −0.507899 0.861416i \(-0.669578\pi\)
−0.507899 + 0.861416i \(0.669578\pi\)
\(158\) −10.0000 −0.795557
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 9.00000 0.707107
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 7.07107 0.552158
\(165\) 0 0
\(166\) 5.65685 0.439057
\(167\) 24.0416 1.86040 0.930199 0.367057i \(-0.119634\pi\)
0.930199 + 0.367057i \(0.119634\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) −12.7279 −0.973329
\(172\) −4.00000 −0.304997
\(173\) 15.5563 1.18273 0.591364 0.806405i \(-0.298590\pi\)
0.591364 + 0.806405i \(0.298590\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 2.82843 0.212000
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −4.24264 −0.315353 −0.157676 0.987491i \(-0.550400\pi\)
−0.157676 + 0.987491i \(0.550400\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −2.82843 −0.206284
\(189\) 0 0
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 16.9706 1.21842
\(195\) 0 0
\(196\) 0 0
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) 4.24264 0.300753 0.150376 0.988629i \(-0.451951\pi\)
0.150376 + 0.988629i \(0.451951\pi\)
\(200\) −5.00000 −0.353553
\(201\) 0 0
\(202\) −9.89949 −0.696526
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −15.5563 −1.08386
\(207\) 18.0000 1.25109
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 16.0000 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 15.0000 1.00000
\(226\) 10.0000 0.665190
\(227\) −26.8701 −1.78343 −0.891714 0.452599i \(-0.850497\pi\)
−0.891714 + 0.452599i \(0.850497\pi\)
\(228\) 0 0
\(229\) 12.7279 0.841085 0.420542 0.907273i \(-0.361840\pi\)
0.420542 + 0.907273i \(0.361840\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.41421 −0.0920575
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −22.6274 −1.45756 −0.728780 0.684748i \(-0.759912\pi\)
−0.728780 + 0.684748i \(0.759912\pi\)
\(242\) −11.0000 −0.707107
\(243\) 0 0
\(244\) −2.82843 −0.181071
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −4.24264 −0.269408
\(249\) 0 0
\(250\) 0 0
\(251\) 15.5563 0.981908 0.490954 0.871185i \(-0.336648\pi\)
0.490954 + 0.871185i \(0.336648\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 25.4558 1.58789 0.793946 0.607988i \(-0.208023\pi\)
0.793946 + 0.607988i \(0.208023\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 18.0000 1.11417
\(262\) −1.41421 −0.0873704
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −8.00000 −0.488678
\(269\) −24.0416 −1.46584 −0.732922 0.680313i \(-0.761844\pi\)
−0.732922 + 0.680313i \(0.761844\pi\)
\(270\) 0 0
\(271\) −16.9706 −1.03089 −0.515444 0.856923i \(-0.672373\pi\)
−0.515444 + 0.856923i \(0.672373\pi\)
\(272\) −2.82843 −0.171499
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −2.82843 −0.169638
\(279\) 12.7279 0.762001
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 21.2132 1.26099 0.630497 0.776192i \(-0.282851\pi\)
0.630497 + 0.776192i \(0.282851\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −3.00000 −0.176777
\(289\) −9.00000 −0.529412
\(290\) 0 0
\(291\) 0 0
\(292\) −1.41421 −0.0827606
\(293\) −9.89949 −0.578335 −0.289167 0.957279i \(-0.593378\pi\)
−0.289167 + 0.957279i \(0.593378\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) 0 0
\(298\) −12.0000 −0.695141
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 12.0000 0.690522
\(303\) 0 0
\(304\) 4.24264 0.243332
\(305\) 0 0
\(306\) 8.48528 0.485071
\(307\) −14.1421 −0.807134 −0.403567 0.914950i \(-0.632230\pi\)
−0.403567 + 0.914950i \(0.632230\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.41421 0.0801927 0.0400963 0.999196i \(-0.487234\pi\)
0.0400963 + 0.999196i \(0.487234\pi\)
\(312\) 0 0
\(313\) −5.65685 −0.319744 −0.159872 0.987138i \(-0.551108\pi\)
−0.159872 + 0.987138i \(0.551108\pi\)
\(314\) −12.7279 −0.718278
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −32.0000 −1.79730 −0.898650 0.438667i \(-0.855451\pi\)
−0.898650 + 0.438667i \(0.855451\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 9.00000 0.500000
\(325\) 0 0
\(326\) 2.00000 0.110770
\(327\) 0 0
\(328\) 7.07107 0.390434
\(329\) 0 0
\(330\) 0 0
\(331\) −6.00000 −0.329790 −0.164895 0.986311i \(-0.552728\pi\)
−0.164895 + 0.986311i \(0.552728\pi\)
\(332\) 5.65685 0.310460
\(333\) −3.00000 −0.164399
\(334\) 24.0416 1.31550
\(335\) 0 0
\(336\) 0 0
\(337\) 16.0000 0.871576 0.435788 0.900049i \(-0.356470\pi\)
0.435788 + 0.900049i \(0.356470\pi\)
\(338\) −13.0000 −0.707107
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −12.7279 −0.688247
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 15.5563 0.836315
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) 0 0
\(349\) 21.2132 1.13552 0.567758 0.823195i \(-0.307811\pi\)
0.567758 + 0.823195i \(0.307811\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −11.3137 −0.602168 −0.301084 0.953598i \(-0.597348\pi\)
−0.301084 + 0.953598i \(0.597348\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.82843 0.149906
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 0 0
\(361\) −1.00000 −0.0526316
\(362\) −4.24264 −0.222988
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 36.7696 1.91936 0.959678 0.281103i \(-0.0907004\pi\)
0.959678 + 0.281103i \(0.0907004\pi\)
\(368\) −6.00000 −0.312772
\(369\) −21.2132 −1.10432
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −2.82843 −0.145865
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 8.00000 0.409316
\(383\) 1.41421 0.0722629 0.0361315 0.999347i \(-0.488496\pi\)
0.0361315 + 0.999347i \(0.488496\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) 12.0000 0.609994
\(388\) 16.9706 0.861550
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 16.9706 0.858238
\(392\) 0 0
\(393\) 0 0
\(394\) 10.0000 0.503793
\(395\) 0 0
\(396\) 0 0
\(397\) −7.07107 −0.354887 −0.177443 0.984131i \(-0.556783\pi\)
−0.177443 + 0.984131i \(0.556783\pi\)
\(398\) 4.24264 0.212664
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −9.89949 −0.492518
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −25.4558 −1.25871 −0.629355 0.777118i \(-0.716681\pi\)
−0.629355 + 0.777118i \(0.716681\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −15.5563 −0.766406
\(413\) 0 0
\(414\) 18.0000 0.884652
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.82843 −0.138178 −0.0690889 0.997611i \(-0.522009\pi\)
−0.0690889 + 0.997611i \(0.522009\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 16.0000 0.778868
\(423\) 8.48528 0.412568
\(424\) 0 0
\(425\) 14.1421 0.685994
\(426\) 0 0
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 0 0
\(431\) 10.0000 0.481683 0.240842 0.970564i \(-0.422577\pi\)
0.240842 + 0.970564i \(0.422577\pi\)
\(432\) 0 0
\(433\) −15.5563 −0.747590 −0.373795 0.927511i \(-0.621944\pi\)
−0.373795 + 0.927511i \(0.621944\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) −25.4558 −1.21772
\(438\) 0 0
\(439\) 21.2132 1.01245 0.506225 0.862401i \(-0.331040\pi\)
0.506225 + 0.862401i \(0.331040\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 15.0000 0.707107
\(451\) 0 0
\(452\) 10.0000 0.470360
\(453\) 0 0
\(454\) −26.8701 −1.26107
\(455\) 0 0
\(456\) 0 0
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) 12.7279 0.594737
\(459\) 0 0
\(460\) 0 0
\(461\) 5.65685 0.263466 0.131733 0.991285i \(-0.457946\pi\)
0.131733 + 0.991285i \(0.457946\pi\)
\(462\) 0 0
\(463\) 6.00000 0.278844 0.139422 0.990233i \(-0.455476\pi\)
0.139422 + 0.990233i \(0.455476\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) 18.3848 0.850746 0.425373 0.905018i \(-0.360143\pi\)
0.425373 + 0.905018i \(0.360143\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.41421 −0.0650945
\(473\) 0 0
\(474\) 0 0
\(475\) −21.2132 −0.973329
\(476\) 0 0
\(477\) 0 0
\(478\) 16.0000 0.731823
\(479\) −32.5269 −1.48619 −0.743096 0.669185i \(-0.766644\pi\)
−0.743096 + 0.669185i \(0.766644\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −22.6274 −1.03065
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) −2.82843 −0.128037
\(489\) 0 0
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 0 0
\(493\) 16.9706 0.764316
\(494\) 0 0
\(495\) 0 0
\(496\) −4.24264 −0.190500
\(497\) 0 0
\(498\) 0 0
\(499\) 22.0000 0.984855 0.492428 0.870353i \(-0.336110\pi\)
0.492428 + 0.870353i \(0.336110\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 15.5563 0.694314
\(503\) −7.07107 −0.315283 −0.157642 0.987496i \(-0.550389\pi\)
−0.157642 + 0.987496i \(0.550389\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −16.0000 −0.709885
\(509\) −12.7279 −0.564155 −0.282078 0.959392i \(-0.591024\pi\)
−0.282078 + 0.959392i \(0.591024\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 25.4558 1.12281
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.8701 1.17720 0.588599 0.808425i \(-0.299680\pi\)
0.588599 + 0.808425i \(0.299680\pi\)
\(522\) 18.0000 0.787839
\(523\) 21.2132 0.927589 0.463794 0.885943i \(-0.346488\pi\)
0.463794 + 0.885943i \(0.346488\pi\)
\(524\) −1.41421 −0.0617802
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 4.24264 0.184115
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −8.00000 −0.345547
\(537\) 0 0
\(538\) −24.0416 −1.03651
\(539\) 0 0
\(540\) 0 0
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) −16.9706 −0.728948
\(543\) 0 0
\(544\) −2.82843 −0.121268
\(545\) 0 0
\(546\) 0 0
\(547\) 6.00000 0.256541 0.128271 0.991739i \(-0.459057\pi\)
0.128271 + 0.991739i \(0.459057\pi\)
\(548\) −4.00000 −0.170872
\(549\) 8.48528 0.362143
\(550\) 0 0
\(551\) −25.4558 −1.08446
\(552\) 0 0
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) −2.82843 −0.119952
\(557\) 34.0000 1.44063 0.720313 0.693649i \(-0.243998\pi\)
0.720313 + 0.693649i \(0.243998\pi\)
\(558\) 12.7279 0.538816
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 7.07107 0.298010 0.149005 0.988836i \(-0.452393\pi\)
0.149005 + 0.988836i \(0.452393\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 21.2132 0.891657
\(567\) 0 0
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 30.0000 1.25109
\(576\) −3.00000 −0.125000
\(577\) 28.2843 1.17749 0.588745 0.808319i \(-0.299622\pi\)
0.588745 + 0.808319i \(0.299622\pi\)
\(578\) −9.00000 −0.374351
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.41421 −0.0585206
\(585\) 0 0
\(586\) −9.89949 −0.408944
\(587\) −21.2132 −0.875563 −0.437781 0.899081i \(-0.644236\pi\)
−0.437781 + 0.899081i \(0.644236\pi\)
\(588\) 0 0
\(589\) −18.0000 −0.741677
\(590\) 0 0
\(591\) 0 0
\(592\) 1.00000 0.0410997
\(593\) −4.24264 −0.174224 −0.0871122 0.996199i \(-0.527764\pi\)
−0.0871122 + 0.996199i \(0.527764\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −12.0000 −0.491539
\(597\) 0 0
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 26.8701 1.09605 0.548026 0.836461i \(-0.315379\pi\)
0.548026 + 0.836461i \(0.315379\pi\)
\(602\) 0 0
\(603\) 24.0000 0.977356
\(604\) 12.0000 0.488273
\(605\) 0 0
\(606\) 0 0
\(607\) −1.41421 −0.0574012 −0.0287006 0.999588i \(-0.509137\pi\)
−0.0287006 + 0.999588i \(0.509137\pi\)
\(608\) 4.24264 0.172062
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 8.48528 0.342997
\(613\) −24.0000 −0.969351 −0.484675 0.874694i \(-0.661062\pi\)
−0.484675 + 0.874694i \(0.661062\pi\)
\(614\) −14.1421 −0.570730
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 0 0
\(619\) 42.4264 1.70526 0.852631 0.522514i \(-0.175006\pi\)
0.852631 + 0.522514i \(0.175006\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 1.41421 0.0567048
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −5.65685 −0.226093
\(627\) 0 0
\(628\) −12.7279 −0.507899
\(629\) −2.82843 −0.112777
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −10.0000 −0.397779
\(633\) 0 0
\(634\) −32.0000 −1.27088
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 0 0
\(643\) −46.6690 −1.84045 −0.920224 0.391393i \(-0.871993\pi\)
−0.920224 + 0.391393i \(0.871993\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 4.24264 0.166795 0.0833977 0.996516i \(-0.473423\pi\)
0.0833977 + 0.996516i \(0.473423\pi\)
\(648\) 9.00000 0.353553
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 0.0783260
\(653\) 30.0000 1.17399 0.586995 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 7.07107 0.276079
\(657\) 4.24264 0.165521
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) −28.2843 −1.10013 −0.550065 0.835122i \(-0.685397\pi\)
−0.550065 + 0.835122i \(0.685397\pi\)
\(662\) −6.00000 −0.233197
\(663\) 0 0
\(664\) 5.65685 0.219529
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) 36.0000 1.39393
\(668\) 24.0416 0.930199
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) 16.0000 0.616297
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −12.7279 −0.489174 −0.244587 0.969627i \(-0.578652\pi\)
−0.244587 + 0.969627i \(0.578652\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −12.7279 −0.486664
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) 0 0
\(690\) 0 0
\(691\) −22.6274 −0.860788 −0.430394 0.902641i \(-0.641625\pi\)
−0.430394 + 0.902641i \(0.641625\pi\)
\(692\) 15.5563 0.591364
\(693\) 0 0
\(694\) −2.00000 −0.0759190
\(695\) 0 0
\(696\) 0 0
\(697\) −20.0000 −0.757554
\(698\) 21.2132 0.802932
\(699\) 0 0
\(700\) 0 0
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) 4.24264 0.160014
\(704\) 0 0
\(705\) 0 0
\(706\) −11.3137 −0.425797
\(707\) 0 0
\(708\) 0 0
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) 30.0000 1.12509
\(712\) 2.82843 0.106000
\(713\) 25.4558 0.953329
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 −0.224231
\(717\) 0 0
\(718\) 20.0000 0.746393
\(719\) −45.2548 −1.68772 −0.843860 0.536563i \(-0.819722\pi\)
−0.843860 + 0.536563i \(0.819722\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.00000 −0.0372161
\(723\) 0 0
\(724\) −4.24264 −0.157676
\(725\) 30.0000 1.11417
\(726\) 0 0
\(727\) −24.0416 −0.891655 −0.445827 0.895119i \(-0.647090\pi\)
−0.445827 + 0.895119i \(0.647090\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 11.3137 0.418453
\(732\) 0 0
\(733\) −12.7279 −0.470117 −0.235058 0.971981i \(-0.575528\pi\)
−0.235058 + 0.971981i \(0.575528\pi\)
\(734\) 36.7696 1.35719
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 0 0
\(738\) −21.2132 −0.780869
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 16.0000 0.585802
\(747\) −16.9706 −0.620920
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 36.0000 1.31366 0.656829 0.754039i \(-0.271897\pi\)
0.656829 + 0.754039i \(0.271897\pi\)
\(752\) −2.82843 −0.103142
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −6.00000 −0.218074 −0.109037 0.994038i \(-0.534777\pi\)
−0.109037 + 0.994038i \(0.534777\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.5563 0.563917 0.281959 0.959427i \(-0.409016\pi\)
0.281959 + 0.959427i \(0.409016\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 1.41421 0.0510976
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000 0.215945
\(773\) 43.8406 1.57684 0.788419 0.615139i \(-0.210900\pi\)
0.788419 + 0.615139i \(0.210900\pi\)
\(774\) 12.0000 0.431331
\(775\) 21.2132 0.762001
\(776\) 16.9706 0.609208
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) 0 0
\(782\) 16.9706 0.606866
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 45.2548 1.61316 0.806580 0.591125i \(-0.201316\pi\)
0.806580 + 0.591125i \(0.201316\pi\)
\(788\) 10.0000 0.356235
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −7.07107 −0.250943
\(795\) 0 0
\(796\) 4.24264 0.150376
\(797\) 25.4558 0.901692 0.450846 0.892602i \(-0.351122\pi\)
0.450846 + 0.892602i \(0.351122\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) −5.00000 −0.176777
\(801\) −8.48528 −0.299813
\(802\) 2.00000 0.0706225
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −9.89949 −0.348263
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 0 0
\(811\) −39.5980 −1.39047 −0.695237 0.718781i \(-0.744700\pi\)
−0.695237 + 0.718781i \(0.744700\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −16.9706 −0.593725
\(818\) −25.4558 −0.890043
\(819\) 0 0
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 0 0
\(823\) 16.0000 0.557725 0.278862 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) −15.5563 −0.541931
\(825\) 0 0
\(826\) 0 0
\(827\) −10.0000 −0.347734 −0.173867 0.984769i \(-0.555626\pi\)
−0.173867 + 0.984769i \(0.555626\pi\)
\(828\) 18.0000 0.625543
\(829\) 39.5980 1.37529 0.687647 0.726045i \(-0.258644\pi\)
0.687647 + 0.726045i \(0.258644\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −2.82843 −0.0977064
\(839\) 22.6274 0.781185 0.390593 0.920564i \(-0.372270\pi\)
0.390593 + 0.920564i \(0.372270\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −18.0000 −0.620321
\(843\) 0 0
\(844\) 16.0000 0.550743
\(845\) 0 0
\(846\) 8.48528 0.291730
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 14.1421 0.485071
\(851\) −6.00000 −0.205677
\(852\) 0 0
\(853\) −8.48528 −0.290531 −0.145265 0.989393i \(-0.546404\pi\)
−0.145265 + 0.989393i \(0.546404\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −4.00000 −0.136717
\(857\) −19.7990 −0.676321 −0.338160 0.941089i \(-0.609805\pi\)
−0.338160 + 0.941089i \(0.609805\pi\)
\(858\) 0 0
\(859\) −38.1838 −1.30281 −0.651407 0.758729i \(-0.725821\pi\)
−0.651407 + 0.758729i \(0.725821\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 10.0000 0.340601
\(863\) 36.0000 1.22545 0.612727 0.790295i \(-0.290072\pi\)
0.612727 + 0.790295i \(0.290072\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −15.5563 −0.528626
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −10.0000 −0.338643
\(873\) −50.9117 −1.72310
\(874\) −25.4558 −0.861057
\(875\) 0 0
\(876\) 0 0
\(877\) −8.00000 −0.270141 −0.135070 0.990836i \(-0.543126\pi\)
−0.135070 + 0.990836i \(0.543126\pi\)
\(878\) 21.2132 0.715911
\(879\) 0 0
\(880\) 0 0
\(881\) 12.7279 0.428815 0.214407 0.976744i \(-0.431218\pi\)
0.214407 + 0.976744i \(0.431218\pi\)
\(882\) 0 0
\(883\) −38.0000 −1.27880 −0.639401 0.768874i \(-0.720818\pi\)
−0.639401 + 0.768874i \(0.720818\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 4.00000 0.134383
\(887\) 14.1421 0.474846 0.237423 0.971406i \(-0.423697\pi\)
0.237423 + 0.971406i \(0.423697\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −12.0000 −0.401565
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −2.00000 −0.0667409
\(899\) 25.4558 0.849000
\(900\) 15.0000 0.500000
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) 0 0
\(906\) 0 0
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) −26.8701 −0.891714
\(909\) 29.6985 0.985037
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 2.00000 0.0661541
\(915\) 0 0
\(916\) 12.7279 0.420542
\(917\) 0 0
\(918\) 0 0
\(919\) −24.0000 −0.791687 −0.395843 0.918318i \(-0.629548\pi\)
−0.395843 + 0.918318i \(0.629548\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 5.65685 0.186299
\(923\) 0 0
\(924\) 0 0
\(925\) −5.00000 −0.164399
\(926\) 6.00000 0.197172
\(927\) 46.6690 1.53281
\(928\) −6.00000 −0.196960
\(929\) −18.3848 −0.603185 −0.301592 0.953437i \(-0.597518\pi\)
−0.301592 + 0.953437i \(0.597518\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) 18.3848 0.601568
\(935\) 0 0
\(936\) 0 0
\(937\) −29.6985 −0.970207 −0.485104 0.874457i \(-0.661218\pi\)
−0.485104 + 0.874457i \(0.661218\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.41421 0.0461020 0.0230510 0.999734i \(-0.492662\pi\)
0.0230510 + 0.999734i \(0.492662\pi\)
\(942\) 0 0
\(943\) −42.4264 −1.38159
\(944\) −1.41421 −0.0460287
\(945\) 0 0
\(946\) 0 0
\(947\) 28.0000 0.909878 0.454939 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −21.2132 −0.688247
\(951\) 0 0
\(952\) 0 0
\(953\) −8.00000 −0.259145 −0.129573 0.991570i \(-0.541361\pi\)
−0.129573 + 0.991570i \(0.541361\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 16.0000 0.517477
\(957\) 0 0
\(958\) −32.5269 −1.05090
\(959\) 0 0
\(960\) 0 0
\(961\) −13.0000 −0.419355
\(962\) 0 0
\(963\) 12.0000 0.386695
\(964\) −22.6274 −0.728780
\(965\) 0 0
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) −11.0000 −0.353553
\(969\) 0 0
\(970\) 0 0
\(971\) −39.5980 −1.27076 −0.635380 0.772200i \(-0.719156\pi\)
−0.635380 + 0.772200i \(0.719156\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −8.00000 −0.256337
\(975\) 0 0
\(976\) −2.82843 −0.0905357
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 30.0000 0.957826
\(982\) 20.0000 0.638226
\(983\) −2.82843 −0.0902128 −0.0451064 0.998982i \(-0.514363\pi\)
−0.0451064 + 0.998982i \(0.514363\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 16.9706 0.540453
\(987\) 0 0
\(988\) 0 0
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) −4.24264 −0.134704
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −2.82843 −0.0895772 −0.0447886 0.998996i \(-0.514261\pi\)
−0.0447886 + 0.998996i \(0.514261\pi\)
\(998\) 22.0000 0.696398
\(999\) 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 3626.2.a.n.1.1 2
7.6 odd 2 inner 3626.2.a.n.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3626.2.a.n.1.1 2 1.1 even 1 trivial
3626.2.a.n.1.2 yes 2 7.6 odd 2 inner