Properties

Label 3332.2.a.m.1.1
Level $3332$
Weight $2$
Character 3332.1
Self dual yes
Analytic conductor $26.606$
Analytic rank $1$
Dimension $2$
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] = [3332,2,Mod(1,3332)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3332, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3332.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.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: \(26.6061539535\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{21}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.79129\) of defining polynomial
Character \(\chi\) \(=\) 3332.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.79129 q^{3} +2.79129 q^{5} +0.208712 q^{9} +O(q^{10})\) \(q-1.79129 q^{3} +2.79129 q^{5} +0.208712 q^{9} +5.58258 q^{11} -4.00000 q^{13} -5.00000 q^{15} -1.00000 q^{17} -2.00000 q^{19} -7.58258 q^{23} +2.79129 q^{25} +5.00000 q^{27} -4.79129 q^{31} -10.0000 q^{33} -3.58258 q^{37} +7.16515 q^{39} -5.79129 q^{41} +1.79129 q^{43} +0.582576 q^{45} -7.58258 q^{47} +1.79129 q^{51} -5.20871 q^{53} +15.5826 q^{55} +3.58258 q^{57} -2.41742 q^{59} -2.20871 q^{61} -11.1652 q^{65} +11.9564 q^{67} +13.5826 q^{69} +13.5826 q^{71} -10.2087 q^{73} -5.00000 q^{75} -10.0000 q^{79} -9.58258 q^{81} +0.417424 q^{83} -2.79129 q^{85} -7.16515 q^{89} +8.58258 q^{93} -5.58258 q^{95} -5.20871 q^{97} +1.16515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + q^{5} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} + q^{5} + 5 q^{9} + 2 q^{11} - 8 q^{13} - 10 q^{15} - 2 q^{17} - 4 q^{19} - 6 q^{23} + q^{25} + 10 q^{27} - 5 q^{31} - 20 q^{33} + 2 q^{37} - 4 q^{39} - 7 q^{41} - q^{43} - 8 q^{45} - 6 q^{47} - q^{51} - 15 q^{53} + 22 q^{55} - 2 q^{57} - 14 q^{59} - 9 q^{61} - 4 q^{65} + q^{67} + 18 q^{69} + 18 q^{71} - 25 q^{73} - 10 q^{75} - 20 q^{79} - 10 q^{81} + 10 q^{83} - q^{85} + 4 q^{89} + 8 q^{93} - 2 q^{95} - 15 q^{97} - 16 q^{99}+O(q^{100}) \) 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
\(3\) −1.79129 −1.03420 −0.517100 0.855925i \(-0.672989\pi\)
−0.517100 + 0.855925i \(0.672989\pi\)
\(4\) 0 0
\(5\) 2.79129 1.24830 0.624151 0.781304i \(-0.285445\pi\)
0.624151 + 0.781304i \(0.285445\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.208712 0.0695707
\(10\) 0 0
\(11\) 5.58258 1.68321 0.841605 0.540094i \(-0.181611\pi\)
0.841605 + 0.540094i \(0.181611\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −5.00000 −1.29099
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.58258 −1.58108 −0.790538 0.612413i \(-0.790199\pi\)
−0.790538 + 0.612413i \(0.790199\pi\)
\(24\) 0 0
\(25\) 2.79129 0.558258
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −4.79129 −0.860541 −0.430270 0.902700i \(-0.641582\pi\)
−0.430270 + 0.902700i \(0.641582\pi\)
\(32\) 0 0
\(33\) −10.0000 −1.74078
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.58258 −0.588972 −0.294486 0.955656i \(-0.595148\pi\)
−0.294486 + 0.955656i \(0.595148\pi\)
\(38\) 0 0
\(39\) 7.16515 1.14734
\(40\) 0 0
\(41\) −5.79129 −0.904447 −0.452224 0.891905i \(-0.649369\pi\)
−0.452224 + 0.891905i \(0.649369\pi\)
\(42\) 0 0
\(43\) 1.79129 0.273169 0.136584 0.990628i \(-0.456388\pi\)
0.136584 + 0.990628i \(0.456388\pi\)
\(44\) 0 0
\(45\) 0.582576 0.0868453
\(46\) 0 0
\(47\) −7.58258 −1.10603 −0.553016 0.833171i \(-0.686523\pi\)
−0.553016 + 0.833171i \(0.686523\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.79129 0.250830
\(52\) 0 0
\(53\) −5.20871 −0.715472 −0.357736 0.933823i \(-0.616451\pi\)
−0.357736 + 0.933823i \(0.616451\pi\)
\(54\) 0 0
\(55\) 15.5826 2.10115
\(56\) 0 0
\(57\) 3.58258 0.474524
\(58\) 0 0
\(59\) −2.41742 −0.314722 −0.157361 0.987541i \(-0.550299\pi\)
−0.157361 + 0.987541i \(0.550299\pi\)
\(60\) 0 0
\(61\) −2.20871 −0.282797 −0.141398 0.989953i \(-0.545160\pi\)
−0.141398 + 0.989953i \(0.545160\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −11.1652 −1.38487
\(66\) 0 0
\(67\) 11.9564 1.46071 0.730356 0.683067i \(-0.239354\pi\)
0.730356 + 0.683067i \(0.239354\pi\)
\(68\) 0 0
\(69\) 13.5826 1.63515
\(70\) 0 0
\(71\) 13.5826 1.61196 0.805978 0.591946i \(-0.201640\pi\)
0.805978 + 0.591946i \(0.201640\pi\)
\(72\) 0 0
\(73\) −10.2087 −1.19484 −0.597420 0.801929i \(-0.703807\pi\)
−0.597420 + 0.801929i \(0.703807\pi\)
\(74\) 0 0
\(75\) −5.00000 −0.577350
\(76\) 0 0
\(77\) 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
\(81\) −9.58258 −1.06473
\(82\) 0 0
\(83\) 0.417424 0.0458183 0.0229091 0.999738i \(-0.492707\pi\)
0.0229091 + 0.999738i \(0.492707\pi\)
\(84\) 0 0
\(85\) −2.79129 −0.302758
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.16515 −0.759505 −0.379752 0.925088i \(-0.623991\pi\)
−0.379752 + 0.925088i \(0.623991\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 8.58258 0.889972
\(94\) 0 0
\(95\) −5.58258 −0.572760
\(96\) 0 0
\(97\) −5.20871 −0.528865 −0.264432 0.964404i \(-0.585185\pi\)
−0.264432 + 0.964404i \(0.585185\pi\)
\(98\) 0 0
\(99\) 1.16515 0.117102
\(100\) 0 0
\(101\) 19.1652 1.90700 0.953502 0.301387i \(-0.0974496\pi\)
0.953502 + 0.301387i \(0.0974496\pi\)
\(102\) 0 0
\(103\) −1.58258 −0.155936 −0.0779679 0.996956i \(-0.524843\pi\)
−0.0779679 + 0.996956i \(0.524843\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.5826 1.50642 0.753212 0.657778i \(-0.228503\pi\)
0.753212 + 0.657778i \(0.228503\pi\)
\(108\) 0 0
\(109\) 10.4174 0.997808 0.498904 0.866657i \(-0.333736\pi\)
0.498904 + 0.866657i \(0.333736\pi\)
\(110\) 0 0
\(111\) 6.41742 0.609115
\(112\) 0 0
\(113\) −10.4174 −0.979989 −0.489994 0.871726i \(-0.663001\pi\)
−0.489994 + 0.871726i \(0.663001\pi\)
\(114\) 0 0
\(115\) −21.1652 −1.97366
\(116\) 0 0
\(117\) −0.834849 −0.0771818
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 20.1652 1.83320
\(122\) 0 0
\(123\) 10.3739 0.935380
\(124\) 0 0
\(125\) −6.16515 −0.551428
\(126\) 0 0
\(127\) 15.2087 1.34955 0.674777 0.738021i \(-0.264240\pi\)
0.674777 + 0.738021i \(0.264240\pi\)
\(128\) 0 0
\(129\) −3.20871 −0.282511
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 13.9564 1.20118
\(136\) 0 0
\(137\) −16.5390 −1.41302 −0.706512 0.707701i \(-0.749732\pi\)
−0.706512 + 0.707701i \(0.749732\pi\)
\(138\) 0 0
\(139\) −12.7913 −1.08494 −0.542471 0.840074i \(-0.682511\pi\)
−0.542471 + 0.840074i \(0.682511\pi\)
\(140\) 0 0
\(141\) 13.5826 1.14386
\(142\) 0 0
\(143\) −22.3303 −1.86735
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −16.5390 −1.35493 −0.677464 0.735556i \(-0.736921\pi\)
−0.677464 + 0.735556i \(0.736921\pi\)
\(150\) 0 0
\(151\) 16.9564 1.37990 0.689948 0.723859i \(-0.257633\pi\)
0.689948 + 0.723859i \(0.257633\pi\)
\(152\) 0 0
\(153\) −0.208712 −0.0168734
\(154\) 0 0
\(155\) −13.3739 −1.07421
\(156\) 0 0
\(157\) −13.1652 −1.05069 −0.525347 0.850888i \(-0.676064\pi\)
−0.525347 + 0.850888i \(0.676064\pi\)
\(158\) 0 0
\(159\) 9.33030 0.739941
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.58258 0.750565 0.375283 0.926910i \(-0.377546\pi\)
0.375283 + 0.926910i \(0.377546\pi\)
\(164\) 0 0
\(165\) −27.9129 −2.17301
\(166\) 0 0
\(167\) −9.79129 −0.757673 −0.378836 0.925464i \(-0.623676\pi\)
−0.378836 + 0.925464i \(0.623676\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −0.417424 −0.0319212
\(172\) 0 0
\(173\) −25.3739 −1.92914 −0.964570 0.263829i \(-0.915015\pi\)
−0.964570 + 0.263829i \(0.915015\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.33030 0.325485
\(178\) 0 0
\(179\) −17.7913 −1.32978 −0.664892 0.746940i \(-0.731522\pi\)
−0.664892 + 0.746940i \(0.731522\pi\)
\(180\) 0 0
\(181\) 17.1652 1.27588 0.637938 0.770088i \(-0.279788\pi\)
0.637938 + 0.770088i \(0.279788\pi\)
\(182\) 0 0
\(183\) 3.95644 0.292468
\(184\) 0 0
\(185\) −10.0000 −0.735215
\(186\) 0 0
\(187\) −5.58258 −0.408238
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.20871 −0.232174 −0.116087 0.993239i \(-0.537035\pi\)
−0.116087 + 0.993239i \(0.537035\pi\)
\(192\) 0 0
\(193\) −6.74773 −0.485712 −0.242856 0.970062i \(-0.578084\pi\)
−0.242856 + 0.970062i \(0.578084\pi\)
\(194\) 0 0
\(195\) 20.0000 1.43223
\(196\) 0 0
\(197\) 4.83485 0.344469 0.172234 0.985056i \(-0.444901\pi\)
0.172234 + 0.985056i \(0.444901\pi\)
\(198\) 0 0
\(199\) 16.5390 1.17242 0.586210 0.810159i \(-0.300619\pi\)
0.586210 + 0.810159i \(0.300619\pi\)
\(200\) 0 0
\(201\) −21.4174 −1.51067
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −16.1652 −1.12902
\(206\) 0 0
\(207\) −1.58258 −0.109997
\(208\) 0 0
\(209\) −11.1652 −0.772310
\(210\) 0 0
\(211\) −23.9129 −1.64623 −0.823115 0.567874i \(-0.807766\pi\)
−0.823115 + 0.567874i \(0.807766\pi\)
\(212\) 0 0
\(213\) −24.3303 −1.66708
\(214\) 0 0
\(215\) 5.00000 0.340997
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 18.2867 1.23570
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) 3.16515 0.211954 0.105977 0.994369i \(-0.466203\pi\)
0.105977 + 0.994369i \(0.466203\pi\)
\(224\) 0 0
\(225\) 0.582576 0.0388384
\(226\) 0 0
\(227\) −13.6261 −0.904398 −0.452199 0.891917i \(-0.649360\pi\)
−0.452199 + 0.891917i \(0.649360\pi\)
\(228\) 0 0
\(229\) 10.7477 0.710230 0.355115 0.934823i \(-0.384442\pi\)
0.355115 + 0.934823i \(0.384442\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.7477 −0.835131 −0.417566 0.908647i \(-0.637117\pi\)
−0.417566 + 0.908647i \(0.637117\pi\)
\(234\) 0 0
\(235\) −21.1652 −1.38066
\(236\) 0 0
\(237\) 17.9129 1.16357
\(238\) 0 0
\(239\) −1.37386 −0.0888678 −0.0444339 0.999012i \(-0.514148\pi\)
−0.0444339 + 0.999012i \(0.514148\pi\)
\(240\) 0 0
\(241\) −19.5390 −1.25862 −0.629309 0.777155i \(-0.716662\pi\)
−0.629309 + 0.777155i \(0.716662\pi\)
\(242\) 0 0
\(243\) 2.16515 0.138895
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 0.509028
\(248\) 0 0
\(249\) −0.747727 −0.0473853
\(250\) 0 0
\(251\) 19.5826 1.23604 0.618021 0.786162i \(-0.287935\pi\)
0.618021 + 0.786162i \(0.287935\pi\)
\(252\) 0 0
\(253\) −42.3303 −2.66128
\(254\) 0 0
\(255\) 5.00000 0.313112
\(256\) 0 0
\(257\) −28.3303 −1.76720 −0.883598 0.468247i \(-0.844886\pi\)
−0.883598 + 0.468247i \(0.844886\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.33030 −0.390343 −0.195172 0.980769i \(-0.562526\pi\)
−0.195172 + 0.980769i \(0.562526\pi\)
\(264\) 0 0
\(265\) −14.5390 −0.893125
\(266\) 0 0
\(267\) 12.8348 0.785480
\(268\) 0 0
\(269\) 21.1652 1.29046 0.645231 0.763988i \(-0.276761\pi\)
0.645231 + 0.763988i \(0.276761\pi\)
\(270\) 0 0
\(271\) −15.1652 −0.921217 −0.460609 0.887603i \(-0.652369\pi\)
−0.460609 + 0.887603i \(0.652369\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15.5826 0.939665
\(276\) 0 0
\(277\) 0.747727 0.0449266 0.0224633 0.999748i \(-0.492849\pi\)
0.0224633 + 0.999748i \(0.492849\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 5.20871 0.310726 0.155363 0.987857i \(-0.450345\pi\)
0.155363 + 0.987857i \(0.450345\pi\)
\(282\) 0 0
\(283\) 15.1216 0.898885 0.449443 0.893309i \(-0.351623\pi\)
0.449443 + 0.893309i \(0.351623\pi\)
\(284\) 0 0
\(285\) 10.0000 0.592349
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 9.33030 0.546952
\(292\) 0 0
\(293\) 14.7477 0.861571 0.430786 0.902454i \(-0.358236\pi\)
0.430786 + 0.902454i \(0.358236\pi\)
\(294\) 0 0
\(295\) −6.74773 −0.392868
\(296\) 0 0
\(297\) 27.9129 1.61967
\(298\) 0 0
\(299\) 30.3303 1.75405
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −34.3303 −1.97222
\(304\) 0 0
\(305\) −6.16515 −0.353016
\(306\) 0 0
\(307\) 1.58258 0.0903224 0.0451612 0.998980i \(-0.485620\pi\)
0.0451612 + 0.998980i \(0.485620\pi\)
\(308\) 0 0
\(309\) 2.83485 0.161269
\(310\) 0 0
\(311\) 24.7913 1.40578 0.702892 0.711296i \(-0.251891\pi\)
0.702892 + 0.711296i \(0.251891\pi\)
\(312\) 0 0
\(313\) −18.7042 −1.05722 −0.528611 0.848864i \(-0.677287\pi\)
−0.528611 + 0.848864i \(0.677287\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.3303 −1.47886 −0.739429 0.673235i \(-0.764904\pi\)
−0.739429 + 0.673235i \(0.764904\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −27.9129 −1.55794
\(322\) 0 0
\(323\) 2.00000 0.111283
\(324\) 0 0
\(325\) −11.1652 −0.619331
\(326\) 0 0
\(327\) −18.6606 −1.03193
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6.37386 0.350339 0.175170 0.984538i \(-0.443953\pi\)
0.175170 + 0.984538i \(0.443953\pi\)
\(332\) 0 0
\(333\) −0.747727 −0.0409752
\(334\) 0 0
\(335\) 33.3739 1.82341
\(336\) 0 0
\(337\) 1.16515 0.0634698 0.0317349 0.999496i \(-0.489897\pi\)
0.0317349 + 0.999496i \(0.489897\pi\)
\(338\) 0 0
\(339\) 18.6606 1.01350
\(340\) 0 0
\(341\) −26.7477 −1.44847
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 37.9129 2.04116
\(346\) 0 0
\(347\) 19.1652 1.02884 0.514420 0.857539i \(-0.328007\pi\)
0.514420 + 0.857539i \(0.328007\pi\)
\(348\) 0 0
\(349\) −9.58258 −0.512944 −0.256472 0.966552i \(-0.582560\pi\)
−0.256472 + 0.966552i \(0.582560\pi\)
\(350\) 0 0
\(351\) −20.0000 −1.06752
\(352\) 0 0
\(353\) 8.83485 0.470232 0.235116 0.971967i \(-0.424453\pi\)
0.235116 + 0.971967i \(0.424453\pi\)
\(354\) 0 0
\(355\) 37.9129 2.01221
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.95644 −0.208813 −0.104406 0.994535i \(-0.533294\pi\)
−0.104406 + 0.994535i \(0.533294\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) −36.1216 −1.89589
\(364\) 0 0
\(365\) −28.4955 −1.49152
\(366\) 0 0
\(367\) −14.6261 −0.763478 −0.381739 0.924270i \(-0.624675\pi\)
−0.381739 + 0.924270i \(0.624675\pi\)
\(368\) 0 0
\(369\) −1.20871 −0.0629230
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −24.1216 −1.24897 −0.624484 0.781037i \(-0.714691\pi\)
−0.624484 + 0.781037i \(0.714691\pi\)
\(374\) 0 0
\(375\) 11.0436 0.570287
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −26.3303 −1.35250 −0.676248 0.736674i \(-0.736395\pi\)
−0.676248 + 0.736674i \(0.736395\pi\)
\(380\) 0 0
\(381\) −27.2432 −1.39571
\(382\) 0 0
\(383\) 17.5826 0.898428 0.449214 0.893424i \(-0.351704\pi\)
0.449214 + 0.893424i \(0.351704\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.373864 0.0190046
\(388\) 0 0
\(389\) 21.1216 1.07091 0.535454 0.844565i \(-0.320141\pi\)
0.535454 + 0.844565i \(0.320141\pi\)
\(390\) 0 0
\(391\) 7.58258 0.383467
\(392\) 0 0
\(393\) 21.4955 1.08430
\(394\) 0 0
\(395\) −27.9129 −1.40445
\(396\) 0 0
\(397\) 28.2867 1.41967 0.709835 0.704368i \(-0.248769\pi\)
0.709835 + 0.704368i \(0.248769\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −21.1652 −1.05694 −0.528469 0.848953i \(-0.677234\pi\)
−0.528469 + 0.848953i \(0.677234\pi\)
\(402\) 0 0
\(403\) 19.1652 0.954684
\(404\) 0 0
\(405\) −26.7477 −1.32911
\(406\) 0 0
\(407\) −20.0000 −0.991363
\(408\) 0 0
\(409\) 4.00000 0.197787 0.0988936 0.995098i \(-0.468470\pi\)
0.0988936 + 0.995098i \(0.468470\pi\)
\(410\) 0 0
\(411\) 29.6261 1.46135
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1.16515 0.0571950
\(416\) 0 0
\(417\) 22.9129 1.12205
\(418\) 0 0
\(419\) 28.7913 1.40655 0.703273 0.710920i \(-0.251721\pi\)
0.703273 + 0.710920i \(0.251721\pi\)
\(420\) 0 0
\(421\) −13.7913 −0.672146 −0.336073 0.941836i \(-0.609099\pi\)
−0.336073 + 0.941836i \(0.609099\pi\)
\(422\) 0 0
\(423\) −1.58258 −0.0769475
\(424\) 0 0
\(425\) −2.79129 −0.135397
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 40.0000 1.93122
\(430\) 0 0
\(431\) −9.58258 −0.461576 −0.230788 0.973004i \(-0.574130\pi\)
−0.230788 + 0.973004i \(0.574130\pi\)
\(432\) 0 0
\(433\) −24.4174 −1.17343 −0.586713 0.809795i \(-0.699578\pi\)
−0.586713 + 0.809795i \(0.699578\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.1652 0.725448
\(438\) 0 0
\(439\) 20.9564 1.00020 0.500098 0.865969i \(-0.333297\pi\)
0.500098 + 0.865969i \(0.333297\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −38.3303 −1.82113 −0.910564 0.413369i \(-0.864352\pi\)
−0.910564 + 0.413369i \(0.864352\pi\)
\(444\) 0 0
\(445\) −20.0000 −0.948091
\(446\) 0 0
\(447\) 29.6261 1.40127
\(448\) 0 0
\(449\) 7.58258 0.357844 0.178922 0.983863i \(-0.442739\pi\)
0.178922 + 0.983863i \(0.442739\pi\)
\(450\) 0 0
\(451\) −32.3303 −1.52237
\(452\) 0 0
\(453\) −30.3739 −1.42709
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.20871 0.243653 0.121827 0.992551i \(-0.461125\pi\)
0.121827 + 0.992551i \(0.461125\pi\)
\(458\) 0 0
\(459\) −5.00000 −0.233380
\(460\) 0 0
\(461\) −3.25227 −0.151473 −0.0757367 0.997128i \(-0.524131\pi\)
−0.0757367 + 0.997128i \(0.524131\pi\)
\(462\) 0 0
\(463\) 18.6261 0.865630 0.432815 0.901483i \(-0.357520\pi\)
0.432815 + 0.901483i \(0.357520\pi\)
\(464\) 0 0
\(465\) 23.9564 1.11095
\(466\) 0 0
\(467\) −12.8348 −0.593926 −0.296963 0.954889i \(-0.595974\pi\)
−0.296963 + 0.954889i \(0.595974\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 23.5826 1.08663
\(472\) 0 0
\(473\) 10.0000 0.459800
\(474\) 0 0
\(475\) −5.58258 −0.256146
\(476\) 0 0
\(477\) −1.08712 −0.0497759
\(478\) 0 0
\(479\) −34.8693 −1.59322 −0.796610 0.604494i \(-0.793375\pi\)
−0.796610 + 0.604494i \(0.793375\pi\)
\(480\) 0 0
\(481\) 14.3303 0.653406
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −14.5390 −0.660183
\(486\) 0 0
\(487\) −5.25227 −0.238003 −0.119002 0.992894i \(-0.537969\pi\)
−0.119002 + 0.992894i \(0.537969\pi\)
\(488\) 0 0
\(489\) −17.1652 −0.776235
\(490\) 0 0
\(491\) 23.9564 1.08114 0.540569 0.841299i \(-0.318209\pi\)
0.540569 + 0.841299i \(0.318209\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 3.25227 0.146179
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −9.58258 −0.428975 −0.214488 0.976727i \(-0.568808\pi\)
−0.214488 + 0.976727i \(0.568808\pi\)
\(500\) 0 0
\(501\) 17.5390 0.783585
\(502\) 0 0
\(503\) −0.791288 −0.0352818 −0.0176409 0.999844i \(-0.505616\pi\)
−0.0176409 + 0.999844i \(0.505616\pi\)
\(504\) 0 0
\(505\) 53.4955 2.38052
\(506\) 0 0
\(507\) −5.37386 −0.238662
\(508\) 0 0
\(509\) 28.3303 1.25572 0.627859 0.778327i \(-0.283931\pi\)
0.627859 + 0.778327i \(0.283931\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −10.0000 −0.441511
\(514\) 0 0
\(515\) −4.41742 −0.194655
\(516\) 0 0
\(517\) −42.3303 −1.86168
\(518\) 0 0
\(519\) 45.4519 1.99512
\(520\) 0 0
\(521\) 28.9564 1.26860 0.634302 0.773085i \(-0.281287\pi\)
0.634302 + 0.773085i \(0.281287\pi\)
\(522\) 0 0
\(523\) −31.0780 −1.35895 −0.679474 0.733700i \(-0.737792\pi\)
−0.679474 + 0.733700i \(0.737792\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.79129 0.208712
\(528\) 0 0
\(529\) 34.4955 1.49980
\(530\) 0 0
\(531\) −0.504546 −0.0218954
\(532\) 0 0
\(533\) 23.1652 1.00339
\(534\) 0 0
\(535\) 43.4955 1.88047
\(536\) 0 0
\(537\) 31.8693 1.37526
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 31.1652 1.33989 0.669947 0.742409i \(-0.266317\pi\)
0.669947 + 0.742409i \(0.266317\pi\)
\(542\) 0 0
\(543\) −30.7477 −1.31951
\(544\) 0 0
\(545\) 29.0780 1.24557
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) −0.460985 −0.0196744
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 17.9129 0.760359
\(556\) 0 0
\(557\) 12.3303 0.522452 0.261226 0.965278i \(-0.415873\pi\)
0.261226 + 0.965278i \(0.415873\pi\)
\(558\) 0 0
\(559\) −7.16515 −0.303054
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) 0 0
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) −29.0780 −1.22332
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7.04356 −0.295281 −0.147641 0.989041i \(-0.547168\pi\)
−0.147641 + 0.989041i \(0.547168\pi\)
\(570\) 0 0
\(571\) −6.41742 −0.268561 −0.134280 0.990943i \(-0.542872\pi\)
−0.134280 + 0.990943i \(0.542872\pi\)
\(572\) 0 0
\(573\) 5.74773 0.240115
\(574\) 0 0
\(575\) −21.1652 −0.882648
\(576\) 0 0
\(577\) 35.9129 1.49507 0.747536 0.664221i \(-0.231237\pi\)
0.747536 + 0.664221i \(0.231237\pi\)
\(578\) 0 0
\(579\) 12.0871 0.502324
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −29.0780 −1.20429
\(584\) 0 0
\(585\) −2.33030 −0.0963462
\(586\) 0 0
\(587\) −35.5826 −1.46865 −0.734325 0.678798i \(-0.762501\pi\)
−0.734325 + 0.678798i \(0.762501\pi\)
\(588\) 0 0
\(589\) 9.58258 0.394843
\(590\) 0 0
\(591\) −8.66061 −0.356250
\(592\) 0 0
\(593\) 39.0780 1.60474 0.802371 0.596825i \(-0.203571\pi\)
0.802371 + 0.596825i \(0.203571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −29.6261 −1.21252
\(598\) 0 0
\(599\) −17.7913 −0.726932 −0.363466 0.931607i \(-0.618407\pi\)
−0.363466 + 0.931607i \(0.618407\pi\)
\(600\) 0 0
\(601\) −31.4955 −1.28473 −0.642363 0.766400i \(-0.722046\pi\)
−0.642363 + 0.766400i \(0.722046\pi\)
\(602\) 0 0
\(603\) 2.49545 0.101623
\(604\) 0 0
\(605\) 56.2867 2.28838
\(606\) 0 0
\(607\) 25.6261 1.04013 0.520066 0.854126i \(-0.325907\pi\)
0.520066 + 0.854126i \(0.325907\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 30.3303 1.22703
\(612\) 0 0
\(613\) 36.2867 1.46561 0.732804 0.680440i \(-0.238211\pi\)
0.732804 + 0.680440i \(0.238211\pi\)
\(614\) 0 0
\(615\) 28.9564 1.16764
\(616\) 0 0
\(617\) 39.4955 1.59003 0.795014 0.606592i \(-0.207464\pi\)
0.795014 + 0.606592i \(0.207464\pi\)
\(618\) 0 0
\(619\) −44.6606 −1.79506 −0.897531 0.440952i \(-0.854641\pi\)
−0.897531 + 0.440952i \(0.854641\pi\)
\(620\) 0 0
\(621\) −37.9129 −1.52139
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −31.1652 −1.24661
\(626\) 0 0
\(627\) 20.0000 0.798723
\(628\) 0 0
\(629\) 3.58258 0.142847
\(630\) 0 0
\(631\) 3.95644 0.157503 0.0787517 0.996894i \(-0.474907\pi\)
0.0787517 + 0.996894i \(0.474907\pi\)
\(632\) 0 0
\(633\) 42.8348 1.70253
\(634\) 0 0
\(635\) 42.4519 1.68465
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.83485 0.112145
\(640\) 0 0
\(641\) 3.91288 0.154549 0.0772747 0.997010i \(-0.475378\pi\)
0.0772747 + 0.997010i \(0.475378\pi\)
\(642\) 0 0
\(643\) 20.9564 0.826441 0.413221 0.910631i \(-0.364404\pi\)
0.413221 + 0.910631i \(0.364404\pi\)
\(644\) 0 0
\(645\) −8.95644 −0.352659
\(646\) 0 0
\(647\) 23.1652 0.910716 0.455358 0.890308i \(-0.349511\pi\)
0.455358 + 0.890308i \(0.349511\pi\)
\(648\) 0 0
\(649\) −13.4955 −0.529743
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −25.9129 −1.01405 −0.507025 0.861932i \(-0.669255\pi\)
−0.507025 + 0.861932i \(0.669255\pi\)
\(654\) 0 0
\(655\) −33.4955 −1.30878
\(656\) 0 0
\(657\) −2.13068 −0.0831258
\(658\) 0 0
\(659\) −4.04356 −0.157515 −0.0787574 0.996894i \(-0.525095\pi\)
−0.0787574 + 0.996894i \(0.525095\pi\)
\(660\) 0 0
\(661\) 11.4955 0.447121 0.223561 0.974690i \(-0.428232\pi\)
0.223561 + 0.974690i \(0.428232\pi\)
\(662\) 0 0
\(663\) −7.16515 −0.278271
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −5.66970 −0.219203
\(670\) 0 0
\(671\) −12.3303 −0.476006
\(672\) 0 0
\(673\) 51.0780 1.96891 0.984457 0.175628i \(-0.0561955\pi\)
0.984457 + 0.175628i \(0.0561955\pi\)
\(674\) 0 0
\(675\) 13.9564 0.537184
\(676\) 0 0
\(677\) 45.1652 1.73584 0.867919 0.496706i \(-0.165457\pi\)
0.867919 + 0.496706i \(0.165457\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 24.4083 0.935329
\(682\) 0 0
\(683\) 5.25227 0.200973 0.100486 0.994938i \(-0.467960\pi\)
0.100486 + 0.994938i \(0.467960\pi\)
\(684\) 0 0
\(685\) −46.1652 −1.76388
\(686\) 0 0
\(687\) −19.2523 −0.734520
\(688\) 0 0
\(689\) 20.8348 0.793745
\(690\) 0 0
\(691\) 33.3739 1.26960 0.634801 0.772676i \(-0.281082\pi\)
0.634801 + 0.772676i \(0.281082\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −35.7042 −1.35434
\(696\) 0 0
\(697\) 5.79129 0.219361
\(698\) 0 0
\(699\) 22.8348 0.863693
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 7.16515 0.270239
\(704\) 0 0
\(705\) 37.9129 1.42788
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 49.1652 1.84644 0.923218 0.384277i \(-0.125549\pi\)
0.923218 + 0.384277i \(0.125549\pi\)
\(710\) 0 0
\(711\) −2.08712 −0.0782732
\(712\) 0 0
\(713\) 36.3303 1.36058
\(714\) 0 0
\(715\) −62.3303 −2.33102
\(716\) 0 0
\(717\) 2.46099 0.0919072
\(718\) 0 0
\(719\) 50.8693 1.89711 0.948553 0.316619i \(-0.102548\pi\)
0.948553 + 0.316619i \(0.102548\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 35.0000 1.30166
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4.33030 0.160602 0.0803010 0.996771i \(-0.474412\pi\)
0.0803010 + 0.996771i \(0.474412\pi\)
\(728\) 0 0
\(729\) 24.8693 0.921086
\(730\) 0 0
\(731\) −1.79129 −0.0662532
\(732\) 0 0
\(733\) −12.7477 −0.470848 −0.235424 0.971893i \(-0.575648\pi\)
−0.235424 + 0.971893i \(0.575648\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 66.7477 2.45868
\(738\) 0 0
\(739\) 7.04356 0.259102 0.129551 0.991573i \(-0.458646\pi\)
0.129551 + 0.991573i \(0.458646\pi\)
\(740\) 0 0
\(741\) −14.3303 −0.526437
\(742\) 0 0
\(743\) 26.8348 0.984475 0.492238 0.870461i \(-0.336179\pi\)
0.492238 + 0.870461i \(0.336179\pi\)
\(744\) 0 0
\(745\) −46.1652 −1.69136
\(746\) 0 0
\(747\) 0.0871215 0.00318761
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 25.1652 0.918289 0.459145 0.888361i \(-0.348156\pi\)
0.459145 + 0.888361i \(0.348156\pi\)
\(752\) 0 0
\(753\) −35.0780 −1.27831
\(754\) 0 0
\(755\) 47.3303 1.72253
\(756\) 0 0
\(757\) −41.6170 −1.51260 −0.756299 0.654227i \(-0.772994\pi\)
−0.756299 + 0.654227i \(0.772994\pi\)
\(758\) 0 0
\(759\) 75.8258 2.75230
\(760\) 0 0
\(761\) 12.8348 0.465263 0.232631 0.972565i \(-0.425266\pi\)
0.232631 + 0.972565i \(0.425266\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.582576 −0.0210631
\(766\) 0 0
\(767\) 9.66970 0.349153
\(768\) 0 0
\(769\) 17.4955 0.630902 0.315451 0.948942i \(-0.397844\pi\)
0.315451 + 0.948942i \(0.397844\pi\)
\(770\) 0 0
\(771\) 50.7477 1.82763
\(772\) 0 0
\(773\) 13.9129 0.500411 0.250206 0.968193i \(-0.419502\pi\)
0.250206 + 0.968193i \(0.419502\pi\)
\(774\) 0 0
\(775\) −13.3739 −0.480403
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.5826 0.414989
\(780\) 0 0
\(781\) 75.8258 2.71326
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −36.7477 −1.31158
\(786\) 0 0
\(787\) 14.3303 0.510820 0.255410 0.966833i \(-0.417790\pi\)
0.255410 + 0.966833i \(0.417790\pi\)
\(788\) 0 0
\(789\) 11.3394 0.403693
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 8.83485 0.313735
\(794\) 0 0
\(795\) 26.0436 0.923670
\(796\) 0 0
\(797\) −41.0780 −1.45506 −0.727529 0.686077i \(-0.759331\pi\)
−0.727529 + 0.686077i \(0.759331\pi\)
\(798\) 0 0
\(799\) 7.58258 0.268252
\(800\) 0 0
\(801\) −1.49545 −0.0528393
\(802\) 0 0
\(803\) −56.9909 −2.01117
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −37.9129 −1.33460
\(808\) 0 0
\(809\) 27.4955 0.966689 0.483344 0.875430i \(-0.339422\pi\)
0.483344 + 0.875430i \(0.339422\pi\)
\(810\) 0 0
\(811\) −51.7042 −1.81558 −0.907789 0.419426i \(-0.862231\pi\)
−0.907789 + 0.419426i \(0.862231\pi\)
\(812\) 0 0
\(813\) 27.1652 0.952723
\(814\) 0 0
\(815\) 26.7477 0.936932
\(816\) 0 0
\(817\) −3.58258 −0.125338
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 0 0
\(823\) −53.0780 −1.85018 −0.925092 0.379743i \(-0.876012\pi\)
−0.925092 + 0.379743i \(0.876012\pi\)
\(824\) 0 0
\(825\) −27.9129 −0.971802
\(826\) 0 0
\(827\) 3.66970 0.127608 0.0638039 0.997962i \(-0.479677\pi\)
0.0638039 + 0.997962i \(0.479677\pi\)
\(828\) 0 0
\(829\) −38.0000 −1.31979 −0.659897 0.751356i \(-0.729400\pi\)
−0.659897 + 0.751356i \(0.729400\pi\)
\(830\) 0 0
\(831\) −1.33939 −0.0464631
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −27.3303 −0.945804
\(836\) 0 0
\(837\) −23.9564 −0.828056
\(838\) 0 0
\(839\) 32.8348 1.13358 0.566792 0.823861i \(-0.308184\pi\)
0.566792 + 0.823861i \(0.308184\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −9.33030 −0.321353
\(844\) 0 0
\(845\) 8.37386 0.288070
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −27.0871 −0.929628
\(850\) 0 0
\(851\) 27.1652 0.931209
\(852\) 0 0
\(853\) −43.4955 −1.48926 −0.744628 0.667480i \(-0.767373\pi\)
−0.744628 + 0.667480i \(0.767373\pi\)
\(854\) 0 0
\(855\) −1.16515 −0.0398473
\(856\) 0 0
\(857\) −56.2867 −1.92272 −0.961359 0.275297i \(-0.911224\pi\)
−0.961359 + 0.275297i \(0.911224\pi\)
\(858\) 0 0
\(859\) 37.9129 1.29357 0.646785 0.762672i \(-0.276113\pi\)
0.646785 + 0.762672i \(0.276113\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.37386 0.0808073 0.0404036 0.999183i \(-0.487136\pi\)
0.0404036 + 0.999183i \(0.487136\pi\)
\(864\) 0 0
\(865\) −70.8258 −2.40815
\(866\) 0 0
\(867\) −1.79129 −0.0608353
\(868\) 0 0
\(869\) −55.8258 −1.89376
\(870\) 0 0
\(871\) −47.8258 −1.62051
\(872\) 0 0
\(873\) −1.08712 −0.0367935
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 21.9129 0.739945 0.369973 0.929043i \(-0.379367\pi\)
0.369973 + 0.929043i \(0.379367\pi\)
\(878\) 0 0
\(879\) −26.4174 −0.891038
\(880\) 0 0
\(881\) −1.12159 −0.0377873 −0.0188937 0.999821i \(-0.506014\pi\)
−0.0188937 + 0.999821i \(0.506014\pi\)
\(882\) 0 0
\(883\) −2.46099 −0.0828187 −0.0414094 0.999142i \(-0.513185\pi\)
−0.0414094 + 0.999142i \(0.513185\pi\)
\(884\) 0 0
\(885\) 12.0871 0.406304
\(886\) 0 0
\(887\) −24.7913 −0.832410 −0.416205 0.909271i \(-0.636640\pi\)
−0.416205 + 0.909271i \(0.636640\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −53.4955 −1.79217
\(892\) 0 0
\(893\) 15.1652 0.507482
\(894\) 0 0
\(895\) −49.6606 −1.65997
\(896\) 0 0
\(897\) −54.3303 −1.81404
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 5.20871 0.173527
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 47.9129 1.59268
\(906\) 0 0
\(907\) −4.41742 −0.146678 −0.0733391 0.997307i \(-0.523366\pi\)
−0.0733391 + 0.997307i \(0.523366\pi\)
\(908\) 0 0
\(909\) 4.00000 0.132672
\(910\) 0 0
\(911\) −46.3303 −1.53499 −0.767496 0.641054i \(-0.778497\pi\)
−0.767496 + 0.641054i \(0.778497\pi\)
\(912\) 0 0
\(913\) 2.33030 0.0771218
\(914\) 0 0
\(915\) 11.0436 0.365089
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −56.1216 −1.85128 −0.925640 0.378405i \(-0.876473\pi\)
−0.925640 + 0.378405i \(0.876473\pi\)
\(920\) 0 0
\(921\) −2.83485 −0.0934114
\(922\) 0 0
\(923\) −54.3303 −1.78830
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) 0 0
\(927\) −0.330303 −0.0108486
\(928\) 0 0
\(929\) 8.37386 0.274738 0.137369 0.990520i \(-0.456135\pi\)
0.137369 + 0.990520i \(0.456135\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −44.4083 −1.45386
\(934\) 0 0
\(935\) −15.5826 −0.509605
\(936\) 0 0
\(937\) 56.6606 1.85102 0.925511 0.378722i \(-0.123636\pi\)
0.925511 + 0.378722i \(0.123636\pi\)
\(938\) 0 0
\(939\) 33.5045 1.09338
\(940\) 0 0
\(941\) 55.2867 1.80230 0.901148 0.433511i \(-0.142726\pi\)
0.901148 + 0.433511i \(0.142726\pi\)
\(942\) 0 0
\(943\) 43.9129 1.43000
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 45.9129 1.49197 0.745984 0.665964i \(-0.231979\pi\)
0.745984 + 0.665964i \(0.231979\pi\)
\(948\) 0 0
\(949\) 40.8348 1.32556
\(950\) 0 0
\(951\) 47.1652 1.52943
\(952\) 0 0
\(953\) −58.7042 −1.90161 −0.950807 0.309783i \(-0.899744\pi\)
−0.950807 + 0.309783i \(0.899744\pi\)
\(954\) 0 0
\(955\) −8.95644 −0.289824
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −8.04356 −0.259470
\(962\) 0 0
\(963\) 3.25227 0.104803
\(964\) 0 0
\(965\) −18.8348 −0.606315
\(966\) 0 0
\(967\) 7.46099 0.239929 0.119965 0.992778i \(-0.461722\pi\)
0.119965 + 0.992778i \(0.461722\pi\)
\(968\) 0 0
\(969\) −3.58258 −0.115089
\(970\) 0 0
\(971\) 38.8348 1.24627 0.623135 0.782114i \(-0.285859\pi\)
0.623135 + 0.782114i \(0.285859\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 20.0000 0.640513
\(976\) 0 0
\(977\) −16.4610 −0.526634 −0.263317 0.964709i \(-0.584816\pi\)
−0.263317 + 0.964709i \(0.584816\pi\)
\(978\) 0 0
\(979\) −40.0000 −1.27841
\(980\) 0 0
\(981\) 2.17424 0.0694182
\(982\) 0 0
\(983\) 22.3739 0.713615 0.356808 0.934178i \(-0.383865\pi\)
0.356808 + 0.934178i \(0.383865\pi\)
\(984\) 0 0
\(985\) 13.4955 0.430001
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −13.5826 −0.431901
\(990\) 0 0
\(991\) −19.0780 −0.606034 −0.303017 0.952985i \(-0.597994\pi\)
−0.303017 + 0.952985i \(0.597994\pi\)
\(992\) 0 0
\(993\) −11.4174 −0.362321
\(994\) 0 0
\(995\) 46.1652 1.46353
\(996\) 0 0
\(997\) −51.7042 −1.63749 −0.818744 0.574159i \(-0.805329\pi\)
−0.818744 + 0.574159i \(0.805329\pi\)
\(998\) 0 0
\(999\) −17.9129 −0.566738
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 3332.2.a.m.1.1 yes 2
7.6 odd 2 3332.2.a.i.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.2.a.i.1.2 2 7.6 odd 2
3332.2.a.m.1.1 yes 2 1.1 even 1 trivial