Properties

Label 3332.2.a.l.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: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 476)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) 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)
 
\(f(q)\) \(=\) \(q-0.618034 q^{3} +1.61803 q^{5} -2.61803 q^{9} +O(q^{10})\) \(q-0.618034 q^{3} +1.61803 q^{5} -2.61803 q^{9} -5.23607 q^{11} +3.23607 q^{13} -1.00000 q^{15} -1.00000 q^{17} -0.472136 q^{19} +5.70820 q^{23} -2.38197 q^{25} +3.47214 q^{27} +7.70820 q^{29} +9.32624 q^{31} +3.23607 q^{33} -8.47214 q^{37} -2.00000 q^{39} -11.0902 q^{41} -0.909830 q^{43} -4.23607 q^{45} -0.472136 q^{47} +0.618034 q^{51} -13.7984 q^{53} -8.47214 q^{55} +0.291796 q^{57} -8.32624 q^{61} +5.23607 q^{65} -1.90983 q^{67} -3.52786 q^{69} -6.94427 q^{71} -13.8541 q^{73} +1.47214 q^{75} -14.9443 q^{79} +5.70820 q^{81} +11.4164 q^{83} -1.61803 q^{85} -4.76393 q^{87} -2.00000 q^{89} -5.76393 q^{93} -0.763932 q^{95} -3.90983 q^{97} +13.7082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + q^{5} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} + q^{5} - 3 q^{9} - 6 q^{11} + 2 q^{13} - 2 q^{15} - 2 q^{17} + 8 q^{19} - 2 q^{23} - 7 q^{25} - 2 q^{27} + 2 q^{29} + 3 q^{31} + 2 q^{33} - 8 q^{37} - 4 q^{39} - 11 q^{41} - 13 q^{43} - 4 q^{45} + 8 q^{47} - q^{51} - 3 q^{53} - 8 q^{55} + 14 q^{57} - q^{61} + 6 q^{65} - 15 q^{67} - 16 q^{69} + 4 q^{71} - 21 q^{73} - 6 q^{75} - 12 q^{79} - 2 q^{81} - 4 q^{83} - q^{85} - 14 q^{87} - 4 q^{89} - 16 q^{93} - 6 q^{95} - 19 q^{97} + 14 q^{99}+O(q^{100}) \) 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
\(3\) −0.618034 −0.356822 −0.178411 0.983956i \(-0.557096\pi\)
−0.178411 + 0.983956i \(0.557096\pi\)
\(4\) 0 0
\(5\) 1.61803 0.723607 0.361803 0.932254i \(-0.382161\pi\)
0.361803 + 0.932254i \(0.382161\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.61803 −0.872678
\(10\) 0 0
\(11\) −5.23607 −1.57873 −0.789367 0.613922i \(-0.789591\pi\)
−0.789367 + 0.613922i \(0.789591\pi\)
\(12\) 0 0
\(13\) 3.23607 0.897524 0.448762 0.893651i \(-0.351865\pi\)
0.448762 + 0.893651i \(0.351865\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −0.472136 −0.108315 −0.0541577 0.998532i \(-0.517247\pi\)
−0.0541577 + 0.998532i \(0.517247\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.70820 1.19024 0.595121 0.803636i \(-0.297104\pi\)
0.595121 + 0.803636i \(0.297104\pi\)
\(24\) 0 0
\(25\) −2.38197 −0.476393
\(26\) 0 0
\(27\) 3.47214 0.668213
\(28\) 0 0
\(29\) 7.70820 1.43138 0.715689 0.698419i \(-0.246113\pi\)
0.715689 + 0.698419i \(0.246113\pi\)
\(30\) 0 0
\(31\) 9.32624 1.67504 0.837521 0.546405i \(-0.184004\pi\)
0.837521 + 0.546405i \(0.184004\pi\)
\(32\) 0 0
\(33\) 3.23607 0.563327
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.47214 −1.39281 −0.696405 0.717649i \(-0.745218\pi\)
−0.696405 + 0.717649i \(0.745218\pi\)
\(38\) 0 0
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) −11.0902 −1.73199 −0.865997 0.500050i \(-0.833315\pi\)
−0.865997 + 0.500050i \(0.833315\pi\)
\(42\) 0 0
\(43\) −0.909830 −0.138748 −0.0693739 0.997591i \(-0.522100\pi\)
−0.0693739 + 0.997591i \(0.522100\pi\)
\(44\) 0 0
\(45\) −4.23607 −0.631476
\(46\) 0 0
\(47\) −0.472136 −0.0688681 −0.0344341 0.999407i \(-0.510963\pi\)
−0.0344341 + 0.999407i \(0.510963\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0.618034 0.0865421
\(52\) 0 0
\(53\) −13.7984 −1.89535 −0.947676 0.319233i \(-0.896575\pi\)
−0.947676 + 0.319233i \(0.896575\pi\)
\(54\) 0 0
\(55\) −8.47214 −1.14238
\(56\) 0 0
\(57\) 0.291796 0.0386493
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −8.32624 −1.06607 −0.533033 0.846095i \(-0.678948\pi\)
−0.533033 + 0.846095i \(0.678948\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.23607 0.649454
\(66\) 0 0
\(67\) −1.90983 −0.233323 −0.116661 0.993172i \(-0.537219\pi\)
−0.116661 + 0.993172i \(0.537219\pi\)
\(68\) 0 0
\(69\) −3.52786 −0.424705
\(70\) 0 0
\(71\) −6.94427 −0.824133 −0.412067 0.911154i \(-0.635193\pi\)
−0.412067 + 0.911154i \(0.635193\pi\)
\(72\) 0 0
\(73\) −13.8541 −1.62150 −0.810750 0.585393i \(-0.800940\pi\)
−0.810750 + 0.585393i \(0.800940\pi\)
\(74\) 0 0
\(75\) 1.47214 0.169988
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −14.9443 −1.68136 −0.840681 0.541531i \(-0.817845\pi\)
−0.840681 + 0.541531i \(0.817845\pi\)
\(80\) 0 0
\(81\) 5.70820 0.634245
\(82\) 0 0
\(83\) 11.4164 1.25311 0.626557 0.779376i \(-0.284464\pi\)
0.626557 + 0.779376i \(0.284464\pi\)
\(84\) 0 0
\(85\) −1.61803 −0.175500
\(86\) 0 0
\(87\) −4.76393 −0.510747
\(88\) 0 0
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −5.76393 −0.597692
\(94\) 0 0
\(95\) −0.763932 −0.0783778
\(96\) 0 0
\(97\) −3.90983 −0.396983 −0.198492 0.980103i \(-0.563604\pi\)
−0.198492 + 0.980103i \(0.563604\pi\)
\(98\) 0 0
\(99\) 13.7082 1.37773
\(100\) 0 0
\(101\) −8.47214 −0.843009 −0.421505 0.906826i \(-0.638498\pi\)
−0.421505 + 0.906826i \(0.638498\pi\)
\(102\) 0 0
\(103\) 11.4164 1.12489 0.562446 0.826834i \(-0.309860\pi\)
0.562446 + 0.826834i \(0.309860\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.2361 1.47293 0.736463 0.676478i \(-0.236494\pi\)
0.736463 + 0.676478i \(0.236494\pi\)
\(108\) 0 0
\(109\) −12.4721 −1.19461 −0.597307 0.802013i \(-0.703763\pi\)
−0.597307 + 0.802013i \(0.703763\pi\)
\(110\) 0 0
\(111\) 5.23607 0.496986
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 9.23607 0.861268
\(116\) 0 0
\(117\) −8.47214 −0.783249
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 16.4164 1.49240
\(122\) 0 0
\(123\) 6.85410 0.618014
\(124\) 0 0
\(125\) −11.9443 −1.06833
\(126\) 0 0
\(127\) −1.14590 −0.101682 −0.0508410 0.998707i \(-0.516190\pi\)
−0.0508410 + 0.998707i \(0.516190\pi\)
\(128\) 0 0
\(129\) 0.562306 0.0495083
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 5.61803 0.483523
\(136\) 0 0
\(137\) 4.61803 0.394545 0.197273 0.980349i \(-0.436792\pi\)
0.197273 + 0.980349i \(0.436792\pi\)
\(138\) 0 0
\(139\) −15.0344 −1.27520 −0.637602 0.770366i \(-0.720074\pi\)
−0.637602 + 0.770366i \(0.720074\pi\)
\(140\) 0 0
\(141\) 0.291796 0.0245737
\(142\) 0 0
\(143\) −16.9443 −1.41695
\(144\) 0 0
\(145\) 12.4721 1.03575
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.3820 −0.932447 −0.466223 0.884667i \(-0.654386\pi\)
−0.466223 + 0.884667i \(0.654386\pi\)
\(150\) 0 0
\(151\) −21.8541 −1.77846 −0.889231 0.457459i \(-0.848760\pi\)
−0.889231 + 0.457459i \(0.848760\pi\)
\(152\) 0 0
\(153\) 2.61803 0.211656
\(154\) 0 0
\(155\) 15.0902 1.21207
\(156\) 0 0
\(157\) −20.1803 −1.61057 −0.805283 0.592890i \(-0.797987\pi\)
−0.805283 + 0.592890i \(0.797987\pi\)
\(158\) 0 0
\(159\) 8.52786 0.676304
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −7.70820 −0.603753 −0.301877 0.953347i \(-0.597613\pi\)
−0.301877 + 0.953347i \(0.597613\pi\)
\(164\) 0 0
\(165\) 5.23607 0.407627
\(166\) 0 0
\(167\) −16.6180 −1.28594 −0.642971 0.765890i \(-0.722298\pi\)
−0.642971 + 0.765890i \(0.722298\pi\)
\(168\) 0 0
\(169\) −2.52786 −0.194451
\(170\) 0 0
\(171\) 1.23607 0.0945245
\(172\) 0 0
\(173\) 23.0902 1.75551 0.877757 0.479107i \(-0.159039\pi\)
0.877757 + 0.479107i \(0.159039\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −20.6180 −1.54106 −0.770532 0.637401i \(-0.780009\pi\)
−0.770532 + 0.637401i \(0.780009\pi\)
\(180\) 0 0
\(181\) 3.52786 0.262224 0.131112 0.991368i \(-0.458145\pi\)
0.131112 + 0.991368i \(0.458145\pi\)
\(182\) 0 0
\(183\) 5.14590 0.380396
\(184\) 0 0
\(185\) −13.7082 −1.00785
\(186\) 0 0
\(187\) 5.23607 0.382899
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.79837 −0.274841 −0.137420 0.990513i \(-0.543881\pi\)
−0.137420 + 0.990513i \(0.543881\pi\)
\(192\) 0 0
\(193\) 8.18034 0.588834 0.294417 0.955677i \(-0.404875\pi\)
0.294417 + 0.955677i \(0.404875\pi\)
\(194\) 0 0
\(195\) −3.23607 −0.231740
\(196\) 0 0
\(197\) −3.70820 −0.264199 −0.132099 0.991236i \(-0.542172\pi\)
−0.132099 + 0.991236i \(0.542172\pi\)
\(198\) 0 0
\(199\) 0.909830 0.0644961 0.0322481 0.999480i \(-0.489733\pi\)
0.0322481 + 0.999480i \(0.489733\pi\)
\(200\) 0 0
\(201\) 1.18034 0.0832548
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −17.9443 −1.25328
\(206\) 0 0
\(207\) −14.9443 −1.03870
\(208\) 0 0
\(209\) 2.47214 0.171001
\(210\) 0 0
\(211\) −15.7082 −1.08140 −0.540699 0.841216i \(-0.681840\pi\)
−0.540699 + 0.841216i \(0.681840\pi\)
\(212\) 0 0
\(213\) 4.29180 0.294069
\(214\) 0 0
\(215\) −1.47214 −0.100399
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 8.56231 0.578587
\(220\) 0 0
\(221\) −3.23607 −0.217681
\(222\) 0 0
\(223\) 14.9443 1.00074 0.500371 0.865811i \(-0.333197\pi\)
0.500371 + 0.865811i \(0.333197\pi\)
\(224\) 0 0
\(225\) 6.23607 0.415738
\(226\) 0 0
\(227\) 16.7426 1.11125 0.555624 0.831434i \(-0.312479\pi\)
0.555624 + 0.831434i \(0.312479\pi\)
\(228\) 0 0
\(229\) 14.7639 0.975628 0.487814 0.872948i \(-0.337794\pi\)
0.487814 + 0.872948i \(0.337794\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.47214 −0.161955 −0.0809775 0.996716i \(-0.525804\pi\)
−0.0809775 + 0.996716i \(0.525804\pi\)
\(234\) 0 0
\(235\) −0.763932 −0.0498334
\(236\) 0 0
\(237\) 9.23607 0.599947
\(238\) 0 0
\(239\) 23.0902 1.49358 0.746789 0.665061i \(-0.231594\pi\)
0.746789 + 0.665061i \(0.231594\pi\)
\(240\) 0 0
\(241\) 25.0344 1.61261 0.806305 0.591500i \(-0.201464\pi\)
0.806305 + 0.591500i \(0.201464\pi\)
\(242\) 0 0
\(243\) −13.9443 −0.894525
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.52786 −0.0972157
\(248\) 0 0
\(249\) −7.05573 −0.447139
\(250\) 0 0
\(251\) −9.41641 −0.594358 −0.297179 0.954822i \(-0.596046\pi\)
−0.297179 + 0.954822i \(0.596046\pi\)
\(252\) 0 0
\(253\) −29.8885 −1.87908
\(254\) 0 0
\(255\) 1.00000 0.0626224
\(256\) 0 0
\(257\) −12.2918 −0.766741 −0.383371 0.923595i \(-0.625237\pi\)
−0.383371 + 0.923595i \(0.625237\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −20.1803 −1.24913
\(262\) 0 0
\(263\) 0.944272 0.0582263 0.0291132 0.999576i \(-0.490732\pi\)
0.0291132 + 0.999576i \(0.490732\pi\)
\(264\) 0 0
\(265\) −22.3262 −1.37149
\(266\) 0 0
\(267\) 1.23607 0.0756461
\(268\) 0 0
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) 9.70820 0.589731 0.294866 0.955539i \(-0.404725\pi\)
0.294866 + 0.955539i \(0.404725\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.4721 0.752098
\(276\) 0 0
\(277\) 7.23607 0.434773 0.217387 0.976086i \(-0.430247\pi\)
0.217387 + 0.976086i \(0.430247\pi\)
\(278\) 0 0
\(279\) −24.4164 −1.46177
\(280\) 0 0
\(281\) −20.0902 −1.19848 −0.599240 0.800570i \(-0.704530\pi\)
−0.599240 + 0.800570i \(0.704530\pi\)
\(282\) 0 0
\(283\) 24.5623 1.46008 0.730039 0.683406i \(-0.239502\pi\)
0.730039 + 0.683406i \(0.239502\pi\)
\(284\) 0 0
\(285\) 0.472136 0.0279669
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 2.41641 0.141652
\(292\) 0 0
\(293\) 19.7082 1.15137 0.575683 0.817673i \(-0.304736\pi\)
0.575683 + 0.817673i \(0.304736\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −18.1803 −1.05493
\(298\) 0 0
\(299\) 18.4721 1.06827
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 5.23607 0.300804
\(304\) 0 0
\(305\) −13.4721 −0.771412
\(306\) 0 0
\(307\) −18.9443 −1.08121 −0.540603 0.841278i \(-0.681804\pi\)
−0.540603 + 0.841278i \(0.681804\pi\)
\(308\) 0 0
\(309\) −7.05573 −0.401386
\(310\) 0 0
\(311\) −24.3820 −1.38257 −0.691287 0.722580i \(-0.742956\pi\)
−0.691287 + 0.722580i \(0.742956\pi\)
\(312\) 0 0
\(313\) −32.2705 −1.82404 −0.912019 0.410149i \(-0.865477\pi\)
−0.912019 + 0.410149i \(0.865477\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.81966 −0.326865 −0.163432 0.986555i \(-0.552257\pi\)
−0.163432 + 0.986555i \(0.552257\pi\)
\(318\) 0 0
\(319\) −40.3607 −2.25976
\(320\) 0 0
\(321\) −9.41641 −0.525573
\(322\) 0 0
\(323\) 0.472136 0.0262703
\(324\) 0 0
\(325\) −7.70820 −0.427574
\(326\) 0 0
\(327\) 7.70820 0.426265
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −11.0344 −0.606508 −0.303254 0.952910i \(-0.598073\pi\)
−0.303254 + 0.952910i \(0.598073\pi\)
\(332\) 0 0
\(333\) 22.1803 1.21548
\(334\) 0 0
\(335\) −3.09017 −0.168834
\(336\) 0 0
\(337\) 18.4721 1.00624 0.503121 0.864216i \(-0.332185\pi\)
0.503121 + 0.864216i \(0.332185\pi\)
\(338\) 0 0
\(339\) −3.70820 −0.201402
\(340\) 0 0
\(341\) −48.8328 −2.64445
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −5.70820 −0.307319
\(346\) 0 0
\(347\) 13.0557 0.700868 0.350434 0.936587i \(-0.386034\pi\)
0.350434 + 0.936587i \(0.386034\pi\)
\(348\) 0 0
\(349\) 24.4721 1.30996 0.654982 0.755645i \(-0.272676\pi\)
0.654982 + 0.755645i \(0.272676\pi\)
\(350\) 0 0
\(351\) 11.2361 0.599737
\(352\) 0 0
\(353\) 17.2361 0.917383 0.458692 0.888595i \(-0.348318\pi\)
0.458692 + 0.888595i \(0.348318\pi\)
\(354\) 0 0
\(355\) −11.2361 −0.596349
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.562306 −0.0296774 −0.0148387 0.999890i \(-0.504723\pi\)
−0.0148387 + 0.999890i \(0.504723\pi\)
\(360\) 0 0
\(361\) −18.7771 −0.988268
\(362\) 0 0
\(363\) −10.1459 −0.532522
\(364\) 0 0
\(365\) −22.4164 −1.17333
\(366\) 0 0
\(367\) −18.5066 −0.966035 −0.483018 0.875611i \(-0.660459\pi\)
−0.483018 + 0.875611i \(0.660459\pi\)
\(368\) 0 0
\(369\) 29.0344 1.51147
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.1459 −0.525335 −0.262667 0.964886i \(-0.584602\pi\)
−0.262667 + 0.964886i \(0.584602\pi\)
\(374\) 0 0
\(375\) 7.38197 0.381203
\(376\) 0 0
\(377\) 24.9443 1.28470
\(378\) 0 0
\(379\) −20.6525 −1.06085 −0.530423 0.847733i \(-0.677967\pi\)
−0.530423 + 0.847733i \(0.677967\pi\)
\(380\) 0 0
\(381\) 0.708204 0.0362824
\(382\) 0 0
\(383\) −0.652476 −0.0333400 −0.0166700 0.999861i \(-0.505306\pi\)
−0.0166700 + 0.999861i \(0.505306\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.38197 0.121082
\(388\) 0 0
\(389\) −1.43769 −0.0728940 −0.0364470 0.999336i \(-0.511604\pi\)
−0.0364470 + 0.999336i \(0.511604\pi\)
\(390\) 0 0
\(391\) −5.70820 −0.288676
\(392\) 0 0
\(393\) −4.94427 −0.249406
\(394\) 0 0
\(395\) −24.1803 −1.21664
\(396\) 0 0
\(397\) −17.7984 −0.893275 −0.446637 0.894715i \(-0.647379\pi\)
−0.446637 + 0.894715i \(0.647379\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.52786 −0.0762979 −0.0381489 0.999272i \(-0.512146\pi\)
−0.0381489 + 0.999272i \(0.512146\pi\)
\(402\) 0 0
\(403\) 30.1803 1.50339
\(404\) 0 0
\(405\) 9.23607 0.458944
\(406\) 0 0
\(407\) 44.3607 2.19888
\(408\) 0 0
\(409\) −14.1803 −0.701173 −0.350586 0.936530i \(-0.614018\pi\)
−0.350586 + 0.936530i \(0.614018\pi\)
\(410\) 0 0
\(411\) −2.85410 −0.140782
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 18.4721 0.906761
\(416\) 0 0
\(417\) 9.29180 0.455021
\(418\) 0 0
\(419\) 18.4508 0.901383 0.450691 0.892680i \(-0.351177\pi\)
0.450691 + 0.892680i \(0.351177\pi\)
\(420\) 0 0
\(421\) 22.2148 1.08268 0.541341 0.840803i \(-0.317917\pi\)
0.541341 + 0.840803i \(0.317917\pi\)
\(422\) 0 0
\(423\) 1.23607 0.0600997
\(424\) 0 0
\(425\) 2.38197 0.115542
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 10.4721 0.505599
\(430\) 0 0
\(431\) 22.9443 1.10519 0.552593 0.833451i \(-0.313638\pi\)
0.552593 + 0.833451i \(0.313638\pi\)
\(432\) 0 0
\(433\) 0.944272 0.0453788 0.0226894 0.999743i \(-0.492777\pi\)
0.0226894 + 0.999743i \(0.492777\pi\)
\(434\) 0 0
\(435\) −7.70820 −0.369580
\(436\) 0 0
\(437\) −2.69505 −0.128922
\(438\) 0 0
\(439\) −12.3262 −0.588299 −0.294150 0.955759i \(-0.595036\pi\)
−0.294150 + 0.955759i \(0.595036\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.88854 −0.469819 −0.234909 0.972017i \(-0.575479\pi\)
−0.234909 + 0.972017i \(0.575479\pi\)
\(444\) 0 0
\(445\) −3.23607 −0.153404
\(446\) 0 0
\(447\) 7.03444 0.332718
\(448\) 0 0
\(449\) 4.29180 0.202542 0.101271 0.994859i \(-0.467709\pi\)
0.101271 + 0.994859i \(0.467709\pi\)
\(450\) 0 0
\(451\) 58.0689 2.73436
\(452\) 0 0
\(453\) 13.5066 0.634594
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.61803 −0.0756884 −0.0378442 0.999284i \(-0.512049\pi\)
−0.0378442 + 0.999284i \(0.512049\pi\)
\(458\) 0 0
\(459\) −3.47214 −0.162065
\(460\) 0 0
\(461\) −4.94427 −0.230278 −0.115139 0.993349i \(-0.536731\pi\)
−0.115139 + 0.993349i \(0.536731\pi\)
\(462\) 0 0
\(463\) 16.0344 0.745184 0.372592 0.927995i \(-0.378469\pi\)
0.372592 + 0.927995i \(0.378469\pi\)
\(464\) 0 0
\(465\) −9.32624 −0.432494
\(466\) 0 0
\(467\) −1.52786 −0.0707011 −0.0353506 0.999375i \(-0.511255\pi\)
−0.0353506 + 0.999375i \(0.511255\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 12.4721 0.574686
\(472\) 0 0
\(473\) 4.76393 0.219046
\(474\) 0 0
\(475\) 1.12461 0.0516007
\(476\) 0 0
\(477\) 36.1246 1.65403
\(478\) 0 0
\(479\) −9.27051 −0.423580 −0.211790 0.977315i \(-0.567929\pi\)
−0.211790 + 0.977315i \(0.567929\pi\)
\(480\) 0 0
\(481\) −27.4164 −1.25008
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.32624 −0.287260
\(486\) 0 0
\(487\) 22.3607 1.01326 0.506630 0.862164i \(-0.330891\pi\)
0.506630 + 0.862164i \(0.330891\pi\)
\(488\) 0 0
\(489\) 4.76393 0.215432
\(490\) 0 0
\(491\) 10.0902 0.455363 0.227681 0.973736i \(-0.426885\pi\)
0.227681 + 0.973736i \(0.426885\pi\)
\(492\) 0 0
\(493\) −7.70820 −0.347160
\(494\) 0 0
\(495\) 22.1803 0.996932
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 34.9443 1.56432 0.782160 0.623077i \(-0.214118\pi\)
0.782160 + 0.623077i \(0.214118\pi\)
\(500\) 0 0
\(501\) 10.2705 0.458853
\(502\) 0 0
\(503\) 8.38197 0.373733 0.186867 0.982385i \(-0.440167\pi\)
0.186867 + 0.982385i \(0.440167\pi\)
\(504\) 0 0
\(505\) −13.7082 −0.610007
\(506\) 0 0
\(507\) 1.56231 0.0693844
\(508\) 0 0
\(509\) 5.23607 0.232085 0.116042 0.993244i \(-0.462979\pi\)
0.116042 + 0.993244i \(0.462979\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.63932 −0.0723778
\(514\) 0 0
\(515\) 18.4721 0.813980
\(516\) 0 0
\(517\) 2.47214 0.108724
\(518\) 0 0
\(519\) −14.2705 −0.626406
\(520\) 0 0
\(521\) −15.7426 −0.689698 −0.344849 0.938658i \(-0.612070\pi\)
−0.344849 + 0.938658i \(0.612070\pi\)
\(522\) 0 0
\(523\) −11.8197 −0.516838 −0.258419 0.966033i \(-0.583201\pi\)
−0.258419 + 0.966033i \(0.583201\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.32624 −0.406257
\(528\) 0 0
\(529\) 9.58359 0.416678
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −35.8885 −1.55451
\(534\) 0 0
\(535\) 24.6525 1.06582
\(536\) 0 0
\(537\) 12.7426 0.549886
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.763932 −0.0328440 −0.0164220 0.999865i \(-0.505228\pi\)
−0.0164220 + 0.999865i \(0.505228\pi\)
\(542\) 0 0
\(543\) −2.18034 −0.0935673
\(544\) 0 0
\(545\) −20.1803 −0.864431
\(546\) 0 0
\(547\) −9.34752 −0.399671 −0.199836 0.979829i \(-0.564041\pi\)
−0.199836 + 0.979829i \(0.564041\pi\)
\(548\) 0 0
\(549\) 21.7984 0.930332
\(550\) 0 0
\(551\) −3.63932 −0.155040
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 8.47214 0.359622
\(556\) 0 0
\(557\) −10.3607 −0.438996 −0.219498 0.975613i \(-0.570442\pi\)
−0.219498 + 0.975613i \(0.570442\pi\)
\(558\) 0 0
\(559\) −2.94427 −0.124529
\(560\) 0 0
\(561\) −3.23607 −0.136627
\(562\) 0 0
\(563\) −11.1246 −0.468846 −0.234423 0.972135i \(-0.575320\pi\)
−0.234423 + 0.972135i \(0.575320\pi\)
\(564\) 0 0
\(565\) 9.70820 0.408427
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.49342 −0.230296 −0.115148 0.993348i \(-0.536734\pi\)
−0.115148 + 0.993348i \(0.536734\pi\)
\(570\) 0 0
\(571\) −0.472136 −0.0197583 −0.00987914 0.999951i \(-0.503145\pi\)
−0.00987914 + 0.999951i \(0.503145\pi\)
\(572\) 0 0
\(573\) 2.34752 0.0980692
\(574\) 0 0
\(575\) −13.5967 −0.567024
\(576\) 0 0
\(577\) 23.1246 0.962690 0.481345 0.876531i \(-0.340148\pi\)
0.481345 + 0.876531i \(0.340148\pi\)
\(578\) 0 0
\(579\) −5.05573 −0.210109
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 72.2492 2.99226
\(584\) 0 0
\(585\) −13.7082 −0.566764
\(586\) 0 0
\(587\) −10.8328 −0.447118 −0.223559 0.974690i \(-0.571768\pi\)
−0.223559 + 0.974690i \(0.571768\pi\)
\(588\) 0 0
\(589\) −4.40325 −0.181433
\(590\) 0 0
\(591\) 2.29180 0.0942719
\(592\) 0 0
\(593\) −22.3607 −0.918243 −0.459122 0.888373i \(-0.651836\pi\)
−0.459122 + 0.888373i \(0.651836\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.562306 −0.0230136
\(598\) 0 0
\(599\) 24.9098 1.01779 0.508894 0.860829i \(-0.330055\pi\)
0.508894 + 0.860829i \(0.330055\pi\)
\(600\) 0 0
\(601\) 32.2492 1.31547 0.657737 0.753248i \(-0.271514\pi\)
0.657737 + 0.753248i \(0.271514\pi\)
\(602\) 0 0
\(603\) 5.00000 0.203616
\(604\) 0 0
\(605\) 26.5623 1.07991
\(606\) 0 0
\(607\) 33.1459 1.34535 0.672675 0.739938i \(-0.265145\pi\)
0.672675 + 0.739938i \(0.265145\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.52786 −0.0618108
\(612\) 0 0
\(613\) 2.56231 0.103491 0.0517453 0.998660i \(-0.483522\pi\)
0.0517453 + 0.998660i \(0.483522\pi\)
\(614\) 0 0
\(615\) 11.0902 0.447199
\(616\) 0 0
\(617\) 41.0132 1.65113 0.825564 0.564309i \(-0.190857\pi\)
0.825564 + 0.564309i \(0.190857\pi\)
\(618\) 0 0
\(619\) 32.0000 1.28619 0.643094 0.765787i \(-0.277650\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) 0 0
\(621\) 19.8197 0.795336
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7.41641 −0.296656
\(626\) 0 0
\(627\) −1.52786 −0.0610170
\(628\) 0 0
\(629\) 8.47214 0.337806
\(630\) 0 0
\(631\) −25.9098 −1.03145 −0.515727 0.856753i \(-0.672478\pi\)
−0.515727 + 0.856753i \(0.672478\pi\)
\(632\) 0 0
\(633\) 9.70820 0.385866
\(634\) 0 0
\(635\) −1.85410 −0.0735778
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 18.1803 0.719203
\(640\) 0 0
\(641\) 38.9443 1.53821 0.769103 0.639125i \(-0.220703\pi\)
0.769103 + 0.639125i \(0.220703\pi\)
\(642\) 0 0
\(643\) −9.85410 −0.388608 −0.194304 0.980941i \(-0.562245\pi\)
−0.194304 + 0.980941i \(0.562245\pi\)
\(644\) 0 0
\(645\) 0.909830 0.0358245
\(646\) 0 0
\(647\) 25.2361 0.992132 0.496066 0.868285i \(-0.334777\pi\)
0.496066 + 0.868285i \(0.334777\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −23.5279 −0.920716 −0.460358 0.887733i \(-0.652279\pi\)
−0.460358 + 0.887733i \(0.652279\pi\)
\(654\) 0 0
\(655\) 12.9443 0.505775
\(656\) 0 0
\(657\) 36.2705 1.41505
\(658\) 0 0
\(659\) −40.7426 −1.58711 −0.793554 0.608500i \(-0.791772\pi\)
−0.793554 + 0.608500i \(0.791772\pi\)
\(660\) 0 0
\(661\) 22.8328 0.888094 0.444047 0.896004i \(-0.353542\pi\)
0.444047 + 0.896004i \(0.353542\pi\)
\(662\) 0 0
\(663\) 2.00000 0.0776736
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 44.0000 1.70369
\(668\) 0 0
\(669\) −9.23607 −0.357087
\(670\) 0 0
\(671\) 43.5967 1.68303
\(672\) 0 0
\(673\) −5.52786 −0.213083 −0.106542 0.994308i \(-0.533978\pi\)
−0.106542 + 0.994308i \(0.533978\pi\)
\(674\) 0 0
\(675\) −8.27051 −0.318332
\(676\) 0 0
\(677\) −37.7771 −1.45189 −0.725946 0.687752i \(-0.758598\pi\)
−0.725946 + 0.687752i \(0.758598\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −10.3475 −0.396518
\(682\) 0 0
\(683\) 5.81966 0.222683 0.111342 0.993782i \(-0.464485\pi\)
0.111342 + 0.993782i \(0.464485\pi\)
\(684\) 0 0
\(685\) 7.47214 0.285496
\(686\) 0 0
\(687\) −9.12461 −0.348126
\(688\) 0 0
\(689\) −44.6525 −1.70112
\(690\) 0 0
\(691\) −46.5066 −1.76919 −0.884597 0.466357i \(-0.845566\pi\)
−0.884597 + 0.466357i \(0.845566\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24.3262 −0.922747
\(696\) 0 0
\(697\) 11.0902 0.420070
\(698\) 0 0
\(699\) 1.52786 0.0577891
\(700\) 0 0
\(701\) −18.5836 −0.701893 −0.350946 0.936396i \(-0.614140\pi\)
−0.350946 + 0.936396i \(0.614140\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) 0.472136 0.0177817
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 9.34752 0.351054 0.175527 0.984475i \(-0.443837\pi\)
0.175527 + 0.984475i \(0.443837\pi\)
\(710\) 0 0
\(711\) 39.1246 1.46729
\(712\) 0 0
\(713\) 53.2361 1.99371
\(714\) 0 0
\(715\) −27.4164 −1.02532
\(716\) 0 0
\(717\) −14.2705 −0.532942
\(718\) 0 0
\(719\) 45.8541 1.71007 0.855035 0.518571i \(-0.173536\pi\)
0.855035 + 0.518571i \(0.173536\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −15.4721 −0.575415
\(724\) 0 0
\(725\) −18.3607 −0.681899
\(726\) 0 0
\(727\) −7.52786 −0.279193 −0.139597 0.990208i \(-0.544581\pi\)
−0.139597 + 0.990208i \(0.544581\pi\)
\(728\) 0 0
\(729\) −8.50658 −0.315058
\(730\) 0 0
\(731\) 0.909830 0.0336513
\(732\) 0 0
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.0000 0.368355
\(738\) 0 0
\(739\) −21.5623 −0.793182 −0.396591 0.917995i \(-0.629807\pi\)
−0.396591 + 0.917995i \(0.629807\pi\)
\(740\) 0 0
\(741\) 0.944272 0.0346887
\(742\) 0 0
\(743\) −26.6525 −0.977785 −0.488892 0.872344i \(-0.662599\pi\)
−0.488892 + 0.872344i \(0.662599\pi\)
\(744\) 0 0
\(745\) −18.4164 −0.674725
\(746\) 0 0
\(747\) −29.8885 −1.09356
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −6.94427 −0.253400 −0.126700 0.991941i \(-0.540439\pi\)
−0.126700 + 0.991941i \(0.540439\pi\)
\(752\) 0 0
\(753\) 5.81966 0.212080
\(754\) 0 0
\(755\) −35.3607 −1.28691
\(756\) 0 0
\(757\) −29.5623 −1.07446 −0.537230 0.843436i \(-0.680529\pi\)
−0.537230 + 0.843436i \(0.680529\pi\)
\(758\) 0 0
\(759\) 18.4721 0.670496
\(760\) 0 0
\(761\) −7.81966 −0.283462 −0.141731 0.989905i \(-0.545267\pi\)
−0.141731 + 0.989905i \(0.545267\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 4.23607 0.153155
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −33.1246 −1.19450 −0.597252 0.802054i \(-0.703741\pi\)
−0.597252 + 0.802054i \(0.703741\pi\)
\(770\) 0 0
\(771\) 7.59675 0.273590
\(772\) 0 0
\(773\) 21.4164 0.770295 0.385147 0.922855i \(-0.374151\pi\)
0.385147 + 0.922855i \(0.374151\pi\)
\(774\) 0 0
\(775\) −22.2148 −0.797979
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.23607 0.187602
\(780\) 0 0
\(781\) 36.3607 1.30109
\(782\) 0 0
\(783\) 26.7639 0.956465
\(784\) 0 0
\(785\) −32.6525 −1.16542
\(786\) 0 0
\(787\) 12.0000 0.427754 0.213877 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 0 0
\(789\) −0.583592 −0.0207764
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −26.9443 −0.956819
\(794\) 0 0
\(795\) 13.7984 0.489378
\(796\) 0 0
\(797\) 11.4164 0.404390 0.202195 0.979345i \(-0.435193\pi\)
0.202195 + 0.979345i \(0.435193\pi\)
\(798\) 0 0
\(799\) 0.472136 0.0167030
\(800\) 0 0
\(801\) 5.23607 0.185007
\(802\) 0 0
\(803\) 72.5410 2.55992
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −6.18034 −0.217558
\(808\) 0 0
\(809\) 31.4853 1.10696 0.553482 0.832861i \(-0.313299\pi\)
0.553482 + 0.832861i \(0.313299\pi\)
\(810\) 0 0
\(811\) 32.0344 1.12488 0.562441 0.826838i \(-0.309862\pi\)
0.562441 + 0.826838i \(0.309862\pi\)
\(812\) 0 0
\(813\) −6.00000 −0.210429
\(814\) 0 0
\(815\) −12.4721 −0.436880
\(816\) 0 0
\(817\) 0.429563 0.0150285
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30.3607 −1.05960 −0.529798 0.848124i \(-0.677732\pi\)
−0.529798 + 0.848124i \(0.677732\pi\)
\(822\) 0 0
\(823\) −37.4853 −1.30666 −0.653328 0.757075i \(-0.726628\pi\)
−0.653328 + 0.757075i \(0.726628\pi\)
\(824\) 0 0
\(825\) −7.70820 −0.268365
\(826\) 0 0
\(827\) 36.4721 1.26826 0.634130 0.773226i \(-0.281358\pi\)
0.634130 + 0.773226i \(0.281358\pi\)
\(828\) 0 0
\(829\) −16.1803 −0.561966 −0.280983 0.959713i \(-0.590661\pi\)
−0.280983 + 0.959713i \(0.590661\pi\)
\(830\) 0 0
\(831\) −4.47214 −0.155137
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −26.8885 −0.930516
\(836\) 0 0
\(837\) 32.3820 1.11928
\(838\) 0 0
\(839\) 22.4721 0.775824 0.387912 0.921696i \(-0.373196\pi\)
0.387912 + 0.921696i \(0.373196\pi\)
\(840\) 0 0
\(841\) 30.4164 1.04884
\(842\) 0 0
\(843\) 12.4164 0.427644
\(844\) 0 0
\(845\) −4.09017 −0.140706
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −15.1803 −0.520988
\(850\) 0 0
\(851\) −48.3607 −1.65778
\(852\) 0 0
\(853\) −6.36068 −0.217786 −0.108893 0.994054i \(-0.534731\pi\)
−0.108893 + 0.994054i \(0.534731\pi\)
\(854\) 0 0
\(855\) 2.00000 0.0683986
\(856\) 0 0
\(857\) 3.90983 0.133557 0.0667786 0.997768i \(-0.478728\pi\)
0.0667786 + 0.997768i \(0.478728\pi\)
\(858\) 0 0
\(859\) 2.94427 0.100457 0.0502286 0.998738i \(-0.484005\pi\)
0.0502286 + 0.998738i \(0.484005\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −30.6738 −1.04415 −0.522074 0.852900i \(-0.674841\pi\)
−0.522074 + 0.852900i \(0.674841\pi\)
\(864\) 0 0
\(865\) 37.3607 1.27030
\(866\) 0 0
\(867\) −0.618034 −0.0209895
\(868\) 0 0
\(869\) 78.2492 2.65442
\(870\) 0 0
\(871\) −6.18034 −0.209413
\(872\) 0 0
\(873\) 10.2361 0.346438
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 31.7082 1.07071 0.535355 0.844627i \(-0.320178\pi\)
0.535355 + 0.844627i \(0.320178\pi\)
\(878\) 0 0
\(879\) −12.1803 −0.410833
\(880\) 0 0
\(881\) 35.3262 1.19017 0.595086 0.803662i \(-0.297118\pi\)
0.595086 + 0.803662i \(0.297118\pi\)
\(882\) 0 0
\(883\) −31.9787 −1.07617 −0.538085 0.842891i \(-0.680852\pi\)
−0.538085 + 0.842891i \(0.680852\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −21.5066 −0.722120 −0.361060 0.932543i \(-0.617585\pi\)
−0.361060 + 0.932543i \(0.617585\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −29.8885 −1.00130
\(892\) 0 0
\(893\) 0.222912 0.00745948
\(894\) 0 0
\(895\) −33.3607 −1.11512
\(896\) 0 0
\(897\) −11.4164 −0.381183
\(898\) 0 0
\(899\) 71.8885 2.39762
\(900\) 0 0
\(901\) 13.7984 0.459690
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.70820 0.189747
\(906\) 0 0
\(907\) 31.3050 1.03946 0.519732 0.854329i \(-0.326032\pi\)
0.519732 + 0.854329i \(0.326032\pi\)
\(908\) 0 0
\(909\) 22.1803 0.735675
\(910\) 0 0
\(911\) −5.52786 −0.183146 −0.0915732 0.995798i \(-0.529190\pi\)
−0.0915732 + 0.995798i \(0.529190\pi\)
\(912\) 0 0
\(913\) −59.7771 −1.97833
\(914\) 0 0
\(915\) 8.32624 0.275257
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 39.1591 1.29174 0.645869 0.763448i \(-0.276495\pi\)
0.645869 + 0.763448i \(0.276495\pi\)
\(920\) 0 0
\(921\) 11.7082 0.385798
\(922\) 0 0
\(923\) −22.4721 −0.739679
\(924\) 0 0
\(925\) 20.1803 0.663525
\(926\) 0 0
\(927\) −29.8885 −0.981669
\(928\) 0 0
\(929\) 12.2705 0.402582 0.201291 0.979531i \(-0.435486\pi\)
0.201291 + 0.979531i \(0.435486\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 15.0689 0.493333
\(934\) 0 0
\(935\) 8.47214 0.277068
\(936\) 0 0
\(937\) −57.3050 −1.87207 −0.936036 0.351905i \(-0.885534\pi\)
−0.936036 + 0.351905i \(0.885534\pi\)
\(938\) 0 0
\(939\) 19.9443 0.650857
\(940\) 0 0
\(941\) 0.978714 0.0319052 0.0159526 0.999873i \(-0.494922\pi\)
0.0159526 + 0.999873i \(0.494922\pi\)
\(942\) 0 0
\(943\) −63.3050 −2.06149
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 47.1246 1.53134 0.765672 0.643231i \(-0.222407\pi\)
0.765672 + 0.643231i \(0.222407\pi\)
\(948\) 0 0
\(949\) −44.8328 −1.45533
\(950\) 0 0
\(951\) 3.59675 0.116633
\(952\) 0 0
\(953\) 16.6738 0.540116 0.270058 0.962844i \(-0.412957\pi\)
0.270058 + 0.962844i \(0.412957\pi\)
\(954\) 0 0
\(955\) −6.14590 −0.198877
\(956\) 0 0
\(957\) 24.9443 0.806334
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 55.9787 1.80576
\(962\) 0 0
\(963\) −39.8885 −1.28539
\(964\) 0 0
\(965\) 13.2361 0.426084
\(966\) 0 0
\(967\) 13.2016 0.424536 0.212268 0.977212i \(-0.431915\pi\)
0.212268 + 0.977212i \(0.431915\pi\)
\(968\) 0 0
\(969\) −0.291796 −0.00937384
\(970\) 0 0
\(971\) 19.1246 0.613738 0.306869 0.951752i \(-0.400719\pi\)
0.306869 + 0.951752i \(0.400719\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 4.76393 0.152568
\(976\) 0 0
\(977\) 49.2148 1.57452 0.787260 0.616621i \(-0.211499\pi\)
0.787260 + 0.616621i \(0.211499\pi\)
\(978\) 0 0
\(979\) 10.4721 0.334691
\(980\) 0 0
\(981\) 32.6525 1.04251
\(982\) 0 0
\(983\) −18.0902 −0.576987 −0.288493 0.957482i \(-0.593154\pi\)
−0.288493 + 0.957482i \(0.593154\pi\)
\(984\) 0 0
\(985\) −6.00000 −0.191176
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.19350 −0.165144
\(990\) 0 0
\(991\) 52.2492 1.65975 0.829876 0.557948i \(-0.188411\pi\)
0.829876 + 0.557948i \(0.188411\pi\)
\(992\) 0 0
\(993\) 6.81966 0.216415
\(994\) 0 0
\(995\) 1.47214 0.0466698
\(996\) 0 0
\(997\) 0.0344419 0.00109078 0.000545392 1.00000i \(-0.499826\pi\)
0.000545392 1.00000i \(0.499826\pi\)
\(998\) 0 0
\(999\) −29.4164 −0.930694
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.l.1.1 2
7.6 odd 2 476.2.a.b.1.2 2
21.20 even 2 4284.2.a.m.1.2 2
28.27 even 2 1904.2.a.j.1.1 2
56.13 odd 2 7616.2.a.u.1.1 2
56.27 even 2 7616.2.a.p.1.2 2
119.118 odd 2 8092.2.a.m.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
476.2.a.b.1.2 2 7.6 odd 2
1904.2.a.j.1.1 2 28.27 even 2
3332.2.a.l.1.1 2 1.1 even 1 trivial
4284.2.a.m.1.2 2 21.20 even 2
7616.2.a.p.1.2 2 56.27 even 2
7616.2.a.u.1.1 2 56.13 odd 2
8092.2.a.m.1.1 2 119.118 odd 2