Properties

Label 3332.2.a.i.1.1
Level $3332$
Weight $2$
Character 3332.1
Self dual yes
Analytic conductor $26.606$
Analytic rank $0$
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: \(0\)
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 \(2.79129\) 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)
 
\(f(q)\) \(=\) \(q-2.79129 q^{3} +1.79129 q^{5} +4.79129 q^{9} +O(q^{10})\) \(q-2.79129 q^{3} +1.79129 q^{5} +4.79129 q^{9} -3.58258 q^{11} +4.00000 q^{13} -5.00000 q^{15} +1.00000 q^{17} +2.00000 q^{19} +1.58258 q^{23} -1.79129 q^{25} -5.00000 q^{27} +0.208712 q^{31} +10.0000 q^{33} +5.58258 q^{37} -11.1652 q^{39} +1.20871 q^{41} -2.79129 q^{43} +8.58258 q^{45} -1.58258 q^{47} -2.79129 q^{51} -9.79129 q^{53} -6.41742 q^{55} -5.58258 q^{57} +11.5826 q^{59} +6.79129 q^{61} +7.16515 q^{65} -10.9564 q^{67} -4.41742 q^{69} +4.41742 q^{71} +14.7913 q^{73} +5.00000 q^{75} -10.0000 q^{79} -0.417424 q^{81} -9.58258 q^{83} +1.79129 q^{85} -11.1652 q^{89} -0.582576 q^{93} +3.58258 q^{95} +9.79129 q^{97} -17.1652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} - q^{5} + 5 q^{9}+O(q^{10}) \) 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
\(3\) −2.79129 −1.61155 −0.805775 0.592221i \(-0.798251\pi\)
−0.805775 + 0.592221i \(0.798251\pi\)
\(4\) 0 0
\(5\) 1.79129 0.801088 0.400544 0.916277i \(-0.368821\pi\)
0.400544 + 0.916277i \(0.368821\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 4.79129 1.59710
\(10\) 0 0
\(11\) −3.58258 −1.08019 −0.540094 0.841605i \(-0.681611\pi\)
−0.540094 + 0.841605i \(0.681611\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 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 \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.58258 0.329990 0.164995 0.986294i \(-0.447239\pi\)
0.164995 + 0.986294i \(0.447239\pi\)
\(24\) 0 0
\(25\) −1.79129 −0.358258
\(26\) 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
\(31\) 0.208712 0.0374858 0.0187429 0.999824i \(-0.494034\pi\)
0.0187429 + 0.999824i \(0.494034\pi\)
\(32\) 0 0
\(33\) 10.0000 1.74078
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.58258 0.917770 0.458885 0.888496i \(-0.348249\pi\)
0.458885 + 0.888496i \(0.348249\pi\)
\(38\) 0 0
\(39\) −11.1652 −1.78786
\(40\) 0 0
\(41\) 1.20871 0.188769 0.0943846 0.995536i \(-0.469912\pi\)
0.0943846 + 0.995536i \(0.469912\pi\)
\(42\) 0 0
\(43\) −2.79129 −0.425667 −0.212834 0.977088i \(-0.568269\pi\)
−0.212834 + 0.977088i \(0.568269\pi\)
\(44\) 0 0
\(45\) 8.58258 1.27941
\(46\) 0 0
\(47\) −1.58258 −0.230842 −0.115421 0.993317i \(-0.536822\pi\)
−0.115421 + 0.993317i \(0.536822\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.79129 −0.390858
\(52\) 0 0
\(53\) −9.79129 −1.34494 −0.672468 0.740126i \(-0.734766\pi\)
−0.672468 + 0.740126i \(0.734766\pi\)
\(54\) 0 0
\(55\) −6.41742 −0.865325
\(56\) 0 0
\(57\) −5.58258 −0.739430
\(58\) 0 0
\(59\) 11.5826 1.50792 0.753961 0.656919i \(-0.228141\pi\)
0.753961 + 0.656919i \(0.228141\pi\)
\(60\) 0 0
\(61\) 6.79129 0.869535 0.434768 0.900543i \(-0.356830\pi\)
0.434768 + 0.900543i \(0.356830\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.16515 0.888728
\(66\) 0 0
\(67\) −10.9564 −1.33854 −0.669271 0.743018i \(-0.733393\pi\)
−0.669271 + 0.743018i \(0.733393\pi\)
\(68\) 0 0
\(69\) −4.41742 −0.531795
\(70\) 0 0
\(71\) 4.41742 0.524252 0.262126 0.965034i \(-0.415576\pi\)
0.262126 + 0.965034i \(0.415576\pi\)
\(72\) 0 0
\(73\) 14.7913 1.73119 0.865595 0.500745i \(-0.166941\pi\)
0.865595 + 0.500745i \(0.166941\pi\)
\(74\) 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
\(81\) −0.417424 −0.0463805
\(82\) 0 0
\(83\) −9.58258 −1.05182 −0.525912 0.850539i \(-0.676276\pi\)
−0.525912 + 0.850539i \(0.676276\pi\)
\(84\) 0 0
\(85\) 1.79129 0.194292
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −11.1652 −1.18350 −0.591752 0.806120i \(-0.701563\pi\)
−0.591752 + 0.806120i \(0.701563\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.582576 −0.0604103
\(94\) 0 0
\(95\) 3.58258 0.367565
\(96\) 0 0
\(97\) 9.79129 0.994155 0.497077 0.867706i \(-0.334407\pi\)
0.497077 + 0.867706i \(0.334407\pi\)
\(98\) 0 0
\(99\) −17.1652 −1.72516
\(100\) 0 0
\(101\) −0.834849 −0.0830705 −0.0415353 0.999137i \(-0.513225\pi\)
−0.0415353 + 0.999137i \(0.513225\pi\)
\(102\) 0 0
\(103\) −7.58258 −0.747133 −0.373567 0.927603i \(-0.621865\pi\)
−0.373567 + 0.927603i \(0.621865\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.41742 0.620396 0.310198 0.950672i \(-0.399605\pi\)
0.310198 + 0.950672i \(0.399605\pi\)
\(108\) 0 0
\(109\) 19.5826 1.87567 0.937835 0.347081i \(-0.112827\pi\)
0.937835 + 0.347081i \(0.112827\pi\)
\(110\) 0 0
\(111\) −15.5826 −1.47903
\(112\) 0 0
\(113\) −19.5826 −1.84217 −0.921087 0.389357i \(-0.872697\pi\)
−0.921087 + 0.389357i \(0.872697\pi\)
\(114\) 0 0
\(115\) 2.83485 0.264351
\(116\) 0 0
\(117\) 19.1652 1.77182
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.83485 0.166804
\(122\) 0 0
\(123\) −3.37386 −0.304211
\(124\) 0 0
\(125\) −12.1652 −1.08808
\(126\) 0 0
\(127\) 19.7913 1.75619 0.878096 0.478484i \(-0.158813\pi\)
0.878096 + 0.478484i \(0.158813\pi\)
\(128\) 0 0
\(129\) 7.79129 0.685985
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −8.95644 −0.770848
\(136\) 0 0
\(137\) 15.5390 1.32759 0.663794 0.747916i \(-0.268945\pi\)
0.663794 + 0.747916i \(0.268945\pi\)
\(138\) 0 0
\(139\) 8.20871 0.696254 0.348127 0.937447i \(-0.386818\pi\)
0.348127 + 0.937447i \(0.386818\pi\)
\(140\) 0 0
\(141\) 4.41742 0.372014
\(142\) 0 0
\(143\) −14.3303 −1.19836
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.5390 1.27301 0.636503 0.771274i \(-0.280380\pi\)
0.636503 + 0.771274i \(0.280380\pi\)
\(150\) 0 0
\(151\) −5.95644 −0.484728 −0.242364 0.970185i \(-0.577923\pi\)
−0.242364 + 0.970185i \(0.577923\pi\)
\(152\) 0 0
\(153\) 4.79129 0.387353
\(154\) 0 0
\(155\) 0.373864 0.0300294
\(156\) 0 0
\(157\) −5.16515 −0.412224 −0.206112 0.978528i \(-0.566081\pi\)
−0.206112 + 0.978528i \(0.566081\pi\)
\(158\) 0 0
\(159\) 27.3303 2.16743
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.417424 0.0326952 0.0163476 0.999866i \(-0.494796\pi\)
0.0163476 + 0.999866i \(0.494796\pi\)
\(164\) 0 0
\(165\) 17.9129 1.39452
\(166\) 0 0
\(167\) 5.20871 0.403062 0.201531 0.979482i \(-0.435408\pi\)
0.201531 + 0.979482i \(0.435408\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 9.58258 0.732798
\(172\) 0 0
\(173\) 11.6261 0.883919 0.441959 0.897035i \(-0.354284\pi\)
0.441959 + 0.897035i \(0.354284\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −32.3303 −2.43009
\(178\) 0 0
\(179\) −13.2087 −0.987265 −0.493633 0.869670i \(-0.664331\pi\)
−0.493633 + 0.869670i \(0.664331\pi\)
\(180\) 0 0
\(181\) 1.16515 0.0866050 0.0433025 0.999062i \(-0.486212\pi\)
0.0433025 + 0.999062i \(0.486212\pi\)
\(182\) 0 0
\(183\) −18.9564 −1.40130
\(184\) 0 0
\(185\) 10.0000 0.735215
\(186\) 0 0
\(187\) −3.58258 −0.261984
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.79129 −0.563758 −0.281879 0.959450i \(-0.590958\pi\)
−0.281879 + 0.959450i \(0.590958\pi\)
\(192\) 0 0
\(193\) 20.7477 1.49345 0.746727 0.665131i \(-0.231624\pi\)
0.746727 + 0.665131i \(0.231624\pi\)
\(194\) 0 0
\(195\) −20.0000 −1.43223
\(196\) 0 0
\(197\) 23.1652 1.65045 0.825224 0.564805i \(-0.191049\pi\)
0.825224 + 0.564805i \(0.191049\pi\)
\(198\) 0 0
\(199\) 15.5390 1.10153 0.550766 0.834660i \(-0.314336\pi\)
0.550766 + 0.834660i \(0.314336\pi\)
\(200\) 0 0
\(201\) 30.5826 2.15713
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.16515 0.151221
\(206\) 0 0
\(207\) 7.58258 0.527025
\(208\) 0 0
\(209\) −7.16515 −0.495624
\(210\) 0 0
\(211\) 21.9129 1.50854 0.754272 0.656562i \(-0.227990\pi\)
0.754272 + 0.656562i \(0.227990\pi\)
\(212\) 0 0
\(213\) −12.3303 −0.844858
\(214\) 0 0
\(215\) −5.00000 −0.340997
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −41.2867 −2.78990
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) 15.1652 1.01553 0.507767 0.861495i \(-0.330471\pi\)
0.507767 + 0.861495i \(0.330471\pi\)
\(224\) 0 0
\(225\) −8.58258 −0.572172
\(226\) 0 0
\(227\) 27.3739 1.81687 0.908434 0.418029i \(-0.137279\pi\)
0.908434 + 0.418029i \(0.137279\pi\)
\(228\) 0 0
\(229\) 16.7477 1.10672 0.553360 0.832942i \(-0.313345\pi\)
0.553360 + 0.832942i \(0.313345\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.7477 0.966156 0.483078 0.875577i \(-0.339519\pi\)
0.483078 + 0.875577i \(0.339519\pi\)
\(234\) 0 0
\(235\) −2.83485 −0.184925
\(236\) 0 0
\(237\) 27.9129 1.81314
\(238\) 0 0
\(239\) 12.3739 0.800399 0.400199 0.916428i \(-0.368941\pi\)
0.400199 + 0.916428i \(0.368941\pi\)
\(240\) 0 0
\(241\) −12.5390 −0.807709 −0.403854 0.914823i \(-0.632330\pi\)
−0.403854 + 0.914823i \(0.632330\pi\)
\(242\) 0 0
\(243\) 16.1652 1.03699
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 0.509028
\(248\) 0 0
\(249\) 26.7477 1.69507
\(250\) 0 0
\(251\) −10.4174 −0.657542 −0.328771 0.944410i \(-0.606634\pi\)
−0.328771 + 0.944410i \(0.606634\pi\)
\(252\) 0 0
\(253\) −5.66970 −0.356451
\(254\) 0 0
\(255\) −5.00000 −0.313112
\(256\) 0 0
\(257\) −8.33030 −0.519630 −0.259815 0.965658i \(-0.583662\pi\)
−0.259815 + 0.965658i \(0.583662\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 30.3303 1.87025 0.935123 0.354322i \(-0.115288\pi\)
0.935123 + 0.354322i \(0.115288\pi\)
\(264\) 0 0
\(265\) −17.5390 −1.07741
\(266\) 0 0
\(267\) 31.1652 1.90728
\(268\) 0 0
\(269\) −2.83485 −0.172844 −0.0864219 0.996259i \(-0.527543\pi\)
−0.0864219 + 0.996259i \(0.527543\pi\)
\(270\) 0 0
\(271\) −3.16515 −0.192269 −0.0961346 0.995368i \(-0.530648\pi\)
−0.0961346 + 0.995368i \(0.530648\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.41742 0.386985
\(276\) 0 0
\(277\) −26.7477 −1.60712 −0.803558 0.595227i \(-0.797062\pi\)
−0.803558 + 0.595227i \(0.797062\pi\)
\(278\) 0 0
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 9.79129 0.584099 0.292050 0.956403i \(-0.405663\pi\)
0.292050 + 0.956403i \(0.405663\pi\)
\(282\) 0 0
\(283\) 26.1216 1.55277 0.776384 0.630261i \(-0.217052\pi\)
0.776384 + 0.630261i \(0.217052\pi\)
\(284\) 0 0
\(285\) −10.0000 −0.592349
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −27.3303 −1.60213
\(292\) 0 0
\(293\) 12.7477 0.744730 0.372365 0.928086i \(-0.378547\pi\)
0.372365 + 0.928086i \(0.378547\pi\)
\(294\) 0 0
\(295\) 20.7477 1.20798
\(296\) 0 0
\(297\) 17.9129 1.03941
\(298\) 0 0
\(299\) 6.33030 0.366091
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 2.33030 0.133872
\(304\) 0 0
\(305\) 12.1652 0.696575
\(306\) 0 0
\(307\) 7.58258 0.432760 0.216380 0.976309i \(-0.430575\pi\)
0.216380 + 0.976309i \(0.430575\pi\)
\(308\) 0 0
\(309\) 21.1652 1.20404
\(310\) 0 0
\(311\) −20.2087 −1.14593 −0.572965 0.819580i \(-0.694207\pi\)
−0.572965 + 0.819580i \(0.694207\pi\)
\(312\) 0 0
\(313\) −31.7042 −1.79203 −0.896013 0.444028i \(-0.853549\pi\)
−0.896013 + 0.444028i \(0.853549\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.3303 0.580208 0.290104 0.956995i \(-0.406310\pi\)
0.290104 + 0.956995i \(0.406310\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −17.9129 −0.999799
\(322\) 0 0
\(323\) 2.00000 0.111283
\(324\) 0 0
\(325\) −7.16515 −0.397451
\(326\) 0 0
\(327\) −54.6606 −3.02274
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.37386 −0.405304 −0.202652 0.979251i \(-0.564956\pi\)
−0.202652 + 0.979251i \(0.564956\pi\)
\(332\) 0 0
\(333\) 26.7477 1.46577
\(334\) 0 0
\(335\) −19.6261 −1.07229
\(336\) 0 0
\(337\) −17.1652 −0.935045 −0.467523 0.883981i \(-0.654853\pi\)
−0.467523 + 0.883981i \(0.654853\pi\)
\(338\) 0 0
\(339\) 54.6606 2.96876
\(340\) 0 0
\(341\) −0.747727 −0.0404917
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −7.91288 −0.426015
\(346\) 0 0
\(347\) 0.834849 0.0448170 0.0224085 0.999749i \(-0.492867\pi\)
0.0224085 + 0.999749i \(0.492867\pi\)
\(348\) 0 0
\(349\) 0.417424 0.0223442 0.0111721 0.999938i \(-0.496444\pi\)
0.0111721 + 0.999938i \(0.496444\pi\)
\(350\) 0 0
\(351\) −20.0000 −1.06752
\(352\) 0 0
\(353\) −27.1652 −1.44586 −0.722928 0.690924i \(-0.757204\pi\)
−0.722928 + 0.690924i \(0.757204\pi\)
\(354\) 0 0
\(355\) 7.91288 0.419972
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.9564 1.00048 0.500241 0.865886i \(-0.333245\pi\)
0.500241 + 0.865886i \(0.333245\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) −5.12159 −0.268814
\(364\) 0 0
\(365\) 26.4955 1.38684
\(366\) 0 0
\(367\) 28.3739 1.48110 0.740552 0.671999i \(-0.234564\pi\)
0.740552 + 0.671999i \(0.234564\pi\)
\(368\) 0 0
\(369\) 5.79129 0.301482
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 17.1216 0.886522 0.443261 0.896393i \(-0.353821\pi\)
0.443261 + 0.896393i \(0.353821\pi\)
\(374\) 0 0
\(375\) 33.9564 1.75350
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 10.3303 0.530632 0.265316 0.964162i \(-0.414524\pi\)
0.265316 + 0.964162i \(0.414524\pi\)
\(380\) 0 0
\(381\) −55.2432 −2.83019
\(382\) 0 0
\(383\) −8.41742 −0.430110 −0.215055 0.976602i \(-0.568993\pi\)
−0.215055 + 0.976602i \(0.568993\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −13.3739 −0.679832
\(388\) 0 0
\(389\) −20.1216 −1.02021 −0.510103 0.860114i \(-0.670393\pi\)
−0.510103 + 0.860114i \(0.670393\pi\)
\(390\) 0 0
\(391\) 1.58258 0.0800343
\(392\) 0 0
\(393\) −33.4955 −1.68962
\(394\) 0 0
\(395\) −17.9129 −0.901295
\(396\) 0 0
\(397\) 31.2867 1.57024 0.785118 0.619346i \(-0.212602\pi\)
0.785118 + 0.619346i \(0.212602\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.83485 −0.141566 −0.0707828 0.997492i \(-0.522550\pi\)
−0.0707828 + 0.997492i \(0.522550\pi\)
\(402\) 0 0
\(403\) 0.834849 0.0415868
\(404\) 0 0
\(405\) −0.747727 −0.0371549
\(406\) 0 0
\(407\) −20.0000 −0.991363
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 0 0
\(411\) −43.3739 −2.13947
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −17.1652 −0.842604
\(416\) 0 0
\(417\) −22.9129 −1.12205
\(418\) 0 0
\(419\) −24.2087 −1.18267 −0.591336 0.806425i \(-0.701399\pi\)
−0.591336 + 0.806425i \(0.701399\pi\)
\(420\) 0 0
\(421\) −9.20871 −0.448805 −0.224403 0.974497i \(-0.572043\pi\)
−0.224403 + 0.974497i \(0.572043\pi\)
\(422\) 0 0
\(423\) −7.58258 −0.368677
\(424\) 0 0
\(425\) −1.79129 −0.0868902
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 40.0000 1.93122
\(430\) 0 0
\(431\) −0.417424 −0.0201066 −0.0100533 0.999949i \(-0.503200\pi\)
−0.0100533 + 0.999949i \(0.503200\pi\)
\(432\) 0 0
\(433\) 33.5826 1.61388 0.806938 0.590636i \(-0.201123\pi\)
0.806938 + 0.590636i \(0.201123\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.16515 0.151410
\(438\) 0 0
\(439\) 1.95644 0.0933758 0.0466879 0.998910i \(-0.485133\pi\)
0.0466879 + 0.998910i \(0.485133\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.66970 −0.0793297 −0.0396649 0.999213i \(-0.512629\pi\)
−0.0396649 + 0.999213i \(0.512629\pi\)
\(444\) 0 0
\(445\) −20.0000 −0.948091
\(446\) 0 0
\(447\) −43.3739 −2.05151
\(448\) 0 0
\(449\) −1.58258 −0.0746864 −0.0373432 0.999303i \(-0.511889\pi\)
−0.0373432 + 0.999303i \(0.511889\pi\)
\(450\) 0 0
\(451\) −4.33030 −0.203906
\(452\) 0 0
\(453\) 16.6261 0.781164
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.79129 0.458017 0.229009 0.973424i \(-0.426452\pi\)
0.229009 + 0.973424i \(0.426452\pi\)
\(458\) 0 0
\(459\) −5.00000 −0.233380
\(460\) 0 0
\(461\) 30.7477 1.43206 0.716032 0.698067i \(-0.245956\pi\)
0.716032 + 0.698067i \(0.245956\pi\)
\(462\) 0 0
\(463\) 32.3739 1.50454 0.752271 0.658854i \(-0.228959\pi\)
0.752271 + 0.658854i \(0.228959\pi\)
\(464\) 0 0
\(465\) −1.04356 −0.0483940
\(466\) 0 0
\(467\) 31.1652 1.44215 0.721076 0.692856i \(-0.243648\pi\)
0.721076 + 0.692856i \(0.243648\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 14.4174 0.664320
\(472\) 0 0
\(473\) 10.0000 0.459800
\(474\) 0 0
\(475\) −3.58258 −0.164380
\(476\) 0 0
\(477\) −46.9129 −2.14799
\(478\) 0 0
\(479\) −33.8693 −1.54753 −0.773764 0.633474i \(-0.781629\pi\)
−0.773764 + 0.633474i \(0.781629\pi\)
\(480\) 0 0
\(481\) 22.3303 1.01817
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 17.5390 0.796406
\(486\) 0 0
\(487\) −32.7477 −1.48394 −0.741971 0.670432i \(-0.766109\pi\)
−0.741971 + 0.670432i \(0.766109\pi\)
\(488\) 0 0
\(489\) −1.16515 −0.0526900
\(490\) 0 0
\(491\) 1.04356 0.0470952 0.0235476 0.999723i \(-0.492504\pi\)
0.0235476 + 0.999723i \(0.492504\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −30.7477 −1.38201
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −0.417424 −0.0186865 −0.00934324 0.999956i \(-0.502974\pi\)
−0.00934324 + 0.999956i \(0.502974\pi\)
\(500\) 0 0
\(501\) −14.5390 −0.649555
\(502\) 0 0
\(503\) −3.79129 −0.169045 −0.0845226 0.996422i \(-0.526937\pi\)
−0.0845226 + 0.996422i \(0.526937\pi\)
\(504\) 0 0
\(505\) −1.49545 −0.0665468
\(506\) 0 0
\(507\) −8.37386 −0.371896
\(508\) 0 0
\(509\) 8.33030 0.369234 0.184617 0.982811i \(-0.440896\pi\)
0.184617 + 0.982811i \(0.440896\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −10.0000 −0.441511
\(514\) 0 0
\(515\) −13.5826 −0.598520
\(516\) 0 0
\(517\) 5.66970 0.249353
\(518\) 0 0
\(519\) −32.4519 −1.42448
\(520\) 0 0
\(521\) −6.04356 −0.264773 −0.132387 0.991198i \(-0.542264\pi\)
−0.132387 + 0.991198i \(0.542264\pi\)
\(522\) 0 0
\(523\) −33.0780 −1.44640 −0.723201 0.690638i \(-0.757330\pi\)
−0.723201 + 0.690638i \(0.757330\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.208712 0.00909164
\(528\) 0 0
\(529\) −20.4955 −0.891107
\(530\) 0 0
\(531\) 55.4955 2.40830
\(532\) 0 0
\(533\) 4.83485 0.209421
\(534\) 0 0
\(535\) 11.4955 0.496992
\(536\) 0 0
\(537\) 36.8693 1.59103
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.8348 0.551813 0.275907 0.961184i \(-0.411022\pi\)
0.275907 + 0.961184i \(0.411022\pi\)
\(542\) 0 0
\(543\) −3.25227 −0.139568
\(544\) 0 0
\(545\) 35.0780 1.50258
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) 32.5390 1.38873
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −27.9129 −1.18484
\(556\) 0 0
\(557\) −24.3303 −1.03091 −0.515454 0.856917i \(-0.672377\pi\)
−0.515454 + 0.856917i \(0.672377\pi\)
\(558\) 0 0
\(559\) −11.1652 −0.472236
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) 0 0
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) −35.0780 −1.47574
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −29.9564 −1.25584 −0.627920 0.778278i \(-0.716093\pi\)
−0.627920 + 0.778278i \(0.716093\pi\)
\(570\) 0 0
\(571\) −15.5826 −0.652110 −0.326055 0.945351i \(-0.605720\pi\)
−0.326055 + 0.945351i \(0.605720\pi\)
\(572\) 0 0
\(573\) 21.7477 0.908524
\(574\) 0 0
\(575\) −2.83485 −0.118221
\(576\) 0 0
\(577\) 9.91288 0.412679 0.206339 0.978481i \(-0.433845\pi\)
0.206339 + 0.978481i \(0.433845\pi\)
\(578\) 0 0
\(579\) −57.9129 −2.40678
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 35.0780 1.45278
\(584\) 0 0
\(585\) 34.3303 1.41938
\(586\) 0 0
\(587\) 26.4174 1.09036 0.545182 0.838318i \(-0.316461\pi\)
0.545182 + 0.838318i \(0.316461\pi\)
\(588\) 0 0
\(589\) 0.417424 0.0171997
\(590\) 0 0
\(591\) −64.6606 −2.65978
\(592\) 0 0
\(593\) 25.0780 1.02983 0.514916 0.857241i \(-0.327823\pi\)
0.514916 + 0.857241i \(0.327823\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −43.3739 −1.77517
\(598\) 0 0
\(599\) −13.2087 −0.539693 −0.269847 0.962903i \(-0.586973\pi\)
−0.269847 + 0.962903i \(0.586973\pi\)
\(600\) 0 0
\(601\) −23.4955 −0.958400 −0.479200 0.877706i \(-0.659073\pi\)
−0.479200 + 0.877706i \(0.659073\pi\)
\(602\) 0 0
\(603\) −52.4955 −2.13778
\(604\) 0 0
\(605\) 3.28674 0.133625
\(606\) 0 0
\(607\) −39.3739 −1.59814 −0.799068 0.601241i \(-0.794673\pi\)
−0.799068 + 0.601241i \(0.794673\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.33030 −0.256097
\(612\) 0 0
\(613\) −23.2867 −0.940543 −0.470271 0.882522i \(-0.655844\pi\)
−0.470271 + 0.882522i \(0.655844\pi\)
\(614\) 0 0
\(615\) −6.04356 −0.243700
\(616\) 0 0
\(617\) −15.4955 −0.623823 −0.311912 0.950111i \(-0.600969\pi\)
−0.311912 + 0.950111i \(0.600969\pi\)
\(618\) 0 0
\(619\) −28.6606 −1.15197 −0.575983 0.817461i \(-0.695381\pi\)
−0.575983 + 0.817461i \(0.695381\pi\)
\(620\) 0 0
\(621\) −7.91288 −0.317533
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12.8348 −0.513394
\(626\) 0 0
\(627\) 20.0000 0.798723
\(628\) 0 0
\(629\) 5.58258 0.222592
\(630\) 0 0
\(631\) −18.9564 −0.754644 −0.377322 0.926082i \(-0.623155\pi\)
−0.377322 + 0.926082i \(0.623155\pi\)
\(632\) 0 0
\(633\) −61.1652 −2.43110
\(634\) 0 0
\(635\) 35.4519 1.40687
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 21.1652 0.837280
\(640\) 0 0
\(641\) −41.9129 −1.65546 −0.827730 0.561127i \(-0.810368\pi\)
−0.827730 + 0.561127i \(0.810368\pi\)
\(642\) 0 0
\(643\) 1.95644 0.0771544 0.0385772 0.999256i \(-0.487717\pi\)
0.0385772 + 0.999256i \(0.487717\pi\)
\(644\) 0 0
\(645\) 13.9564 0.549534
\(646\) 0 0
\(647\) −4.83485 −0.190078 −0.0950388 0.995474i \(-0.530298\pi\)
−0.0950388 + 0.995474i \(0.530298\pi\)
\(648\) 0 0
\(649\) −41.4955 −1.62884
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.9129 0.779251 0.389626 0.920973i \(-0.372604\pi\)
0.389626 + 0.920973i \(0.372604\pi\)
\(654\) 0 0
\(655\) 21.4955 0.839897
\(656\) 0 0
\(657\) 70.8693 2.76488
\(658\) 0 0
\(659\) −26.9564 −1.05007 −0.525037 0.851079i \(-0.675948\pi\)
−0.525037 + 0.851079i \(0.675948\pi\)
\(660\) 0 0
\(661\) 43.4955 1.69178 0.845889 0.533360i \(-0.179071\pi\)
0.845889 + 0.533360i \(0.179071\pi\)
\(662\) 0 0
\(663\) −11.1652 −0.433619
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −42.3303 −1.63658
\(670\) 0 0
\(671\) −24.3303 −0.939261
\(672\) 0 0
\(673\) −13.0780 −0.504121 −0.252061 0.967711i \(-0.581108\pi\)
−0.252061 + 0.967711i \(0.581108\pi\)
\(674\) 0 0
\(675\) 8.95644 0.344734
\(676\) 0 0
\(677\) −26.8348 −1.03135 −0.515674 0.856785i \(-0.672458\pi\)
−0.515674 + 0.856785i \(0.672458\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −76.4083 −2.92797
\(682\) 0 0
\(683\) 32.7477 1.25306 0.626528 0.779399i \(-0.284475\pi\)
0.626528 + 0.779399i \(0.284475\pi\)
\(684\) 0 0
\(685\) 27.8348 1.06351
\(686\) 0 0
\(687\) −46.7477 −1.78354
\(688\) 0 0
\(689\) −39.1652 −1.49207
\(690\) 0 0
\(691\) −19.6261 −0.746613 −0.373307 0.927708i \(-0.621776\pi\)
−0.373307 + 0.927708i \(0.621776\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14.7042 0.557761
\(696\) 0 0
\(697\) 1.20871 0.0457832
\(698\) 0 0
\(699\) −41.1652 −1.55701
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 11.1652 0.421102
\(704\) 0 0
\(705\) 7.91288 0.298016
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 30.8348 1.15803 0.579014 0.815318i \(-0.303438\pi\)
0.579014 + 0.815318i \(0.303438\pi\)
\(710\) 0 0
\(711\) −47.9129 −1.79687
\(712\) 0 0
\(713\) 0.330303 0.0123699
\(714\) 0 0
\(715\) −25.6697 −0.959992
\(716\) 0 0
\(717\) −34.5390 −1.28988
\(718\) 0 0
\(719\) 17.8693 0.666413 0.333207 0.942854i \(-0.391869\pi\)
0.333207 + 0.942854i \(0.391869\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 35.0000 1.30166
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 32.3303 1.19906 0.599532 0.800351i \(-0.295353\pi\)
0.599532 + 0.800351i \(0.295353\pi\)
\(728\) 0 0
\(729\) −43.8693 −1.62479
\(730\) 0 0
\(731\) −2.79129 −0.103240
\(732\) 0 0
\(733\) −14.7477 −0.544720 −0.272360 0.962195i \(-0.587804\pi\)
−0.272360 + 0.962195i \(0.587804\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 39.2523 1.44588
\(738\) 0 0
\(739\) 29.9564 1.10197 0.550983 0.834517i \(-0.314253\pi\)
0.550983 + 0.834517i \(0.314253\pi\)
\(740\) 0 0
\(741\) −22.3303 −0.820324
\(742\) 0 0
\(743\) 45.1652 1.65695 0.828474 0.560027i \(-0.189209\pi\)
0.828474 + 0.560027i \(0.189209\pi\)
\(744\) 0 0
\(745\) 27.8348 1.01979
\(746\) 0 0
\(747\) −45.9129 −1.67986
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 6.83485 0.249407 0.124704 0.992194i \(-0.460202\pi\)
0.124704 + 0.992194i \(0.460202\pi\)
\(752\) 0 0
\(753\) 29.0780 1.05966
\(754\) 0 0
\(755\) −10.6697 −0.388310
\(756\) 0 0
\(757\) 54.6170 1.98509 0.992545 0.121878i \(-0.0388916\pi\)
0.992545 + 0.121878i \(0.0388916\pi\)
\(758\) 0 0
\(759\) 15.8258 0.574439
\(760\) 0 0
\(761\) −31.1652 −1.12974 −0.564868 0.825181i \(-0.691073\pi\)
−0.564868 + 0.825181i \(0.691073\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 8.58258 0.310304
\(766\) 0 0
\(767\) 46.3303 1.67289
\(768\) 0 0
\(769\) 37.4955 1.35212 0.676060 0.736846i \(-0.263686\pi\)
0.676060 + 0.736846i \(0.263686\pi\)
\(770\) 0 0
\(771\) 23.2523 0.837410
\(772\) 0 0
\(773\) 31.9129 1.14783 0.573913 0.818916i \(-0.305425\pi\)
0.573913 + 0.818916i \(0.305425\pi\)
\(774\) 0 0
\(775\) −0.373864 −0.0134296
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.41742 0.0866132
\(780\) 0 0
\(781\) −15.8258 −0.566290
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9.25227 −0.330228
\(786\) 0 0
\(787\) 22.3303 0.795989 0.397995 0.917388i \(-0.369706\pi\)
0.397995 + 0.917388i \(0.369706\pi\)
\(788\) 0 0
\(789\) −84.6606 −3.01400
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 27.1652 0.964663
\(794\) 0 0
\(795\) 48.9564 1.73631
\(796\) 0 0
\(797\) −23.0780 −0.817466 −0.408733 0.912654i \(-0.634029\pi\)
−0.408733 + 0.912654i \(0.634029\pi\)
\(798\) 0 0
\(799\) −1.58258 −0.0559875
\(800\) 0 0
\(801\) −53.4955 −1.89017
\(802\) 0 0
\(803\) −52.9909 −1.87001
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 7.91288 0.278547
\(808\) 0 0
\(809\) −27.4955 −0.966689 −0.483344 0.875430i \(-0.660578\pi\)
−0.483344 + 0.875430i \(0.660578\pi\)
\(810\) 0 0
\(811\) 1.29583 0.0455029 0.0227514 0.999741i \(-0.492757\pi\)
0.0227514 + 0.999741i \(0.492757\pi\)
\(812\) 0 0
\(813\) 8.83485 0.309852
\(814\) 0 0
\(815\) 0.747727 0.0261917
\(816\) 0 0
\(817\) −5.58258 −0.195310
\(818\) 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
\(823\) 11.0780 0.386156 0.193078 0.981183i \(-0.438153\pi\)
0.193078 + 0.981183i \(0.438153\pi\)
\(824\) 0 0
\(825\) −17.9129 −0.623646
\(826\) 0 0
\(827\) 40.3303 1.40242 0.701211 0.712954i \(-0.252643\pi\)
0.701211 + 0.712954i \(0.252643\pi\)
\(828\) 0 0
\(829\) 38.0000 1.31979 0.659897 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(830\) 0 0
\(831\) 74.6606 2.58995
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 9.33030 0.322888
\(836\) 0 0
\(837\) −1.04356 −0.0360707
\(838\) 0 0
\(839\) −51.1652 −1.76642 −0.883209 0.468980i \(-0.844622\pi\)
−0.883209 + 0.468980i \(0.844622\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −27.3303 −0.941306
\(844\) 0 0
\(845\) 5.37386 0.184867
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −72.9129 −2.50236
\(850\) 0 0
\(851\) 8.83485 0.302855
\(852\) 0 0
\(853\) −11.4955 −0.393597 −0.196798 0.980444i \(-0.563054\pi\)
−0.196798 + 0.980444i \(0.563054\pi\)
\(854\) 0 0
\(855\) 17.1652 0.587036
\(856\) 0 0
\(857\) −3.28674 −0.112273 −0.0561365 0.998423i \(-0.517878\pi\)
−0.0561365 + 0.998423i \(0.517878\pi\)
\(858\) 0 0
\(859\) 7.91288 0.269984 0.134992 0.990847i \(-0.456899\pi\)
0.134992 + 0.990847i \(0.456899\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −11.3739 −0.387171 −0.193585 0.981083i \(-0.562012\pi\)
−0.193585 + 0.981083i \(0.562012\pi\)
\(864\) 0 0
\(865\) 20.8258 0.708097
\(866\) 0 0
\(867\) −2.79129 −0.0947971
\(868\) 0 0
\(869\) 35.8258 1.21531
\(870\) 0 0
\(871\) −43.8258 −1.48498
\(872\) 0 0
\(873\) 46.9129 1.58776
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −23.9129 −0.807481 −0.403740 0.914874i \(-0.632290\pi\)
−0.403740 + 0.914874i \(0.632290\pi\)
\(878\) 0 0
\(879\) −35.5826 −1.20017
\(880\) 0 0
\(881\) −40.1216 −1.35173 −0.675865 0.737025i \(-0.736230\pi\)
−0.675865 + 0.737025i \(0.736230\pi\)
\(882\) 0 0
\(883\) −34.5390 −1.16233 −0.581165 0.813786i \(-0.697403\pi\)
−0.581165 + 0.813786i \(0.697403\pi\)
\(884\) 0 0
\(885\) −57.9129 −1.94672
\(886\) 0 0
\(887\) 20.2087 0.678542 0.339271 0.940689i \(-0.389820\pi\)
0.339271 + 0.940689i \(0.389820\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.49545 0.0500996
\(892\) 0 0
\(893\) −3.16515 −0.105918
\(894\) 0 0
\(895\) −23.6606 −0.790887
\(896\) 0 0
\(897\) −17.6697 −0.589974
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −9.79129 −0.326195
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.08712 0.0693783
\(906\) 0 0
\(907\) −13.5826 −0.451002 −0.225501 0.974243i \(-0.572402\pi\)
−0.225501 + 0.974243i \(0.572402\pi\)
\(908\) 0 0
\(909\) −4.00000 −0.132672
\(910\) 0 0
\(911\) −9.66970 −0.320371 −0.160186 0.987087i \(-0.551209\pi\)
−0.160186 + 0.987087i \(0.551209\pi\)
\(912\) 0 0
\(913\) 34.3303 1.13617
\(914\) 0 0
\(915\) −33.9564 −1.12257
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −14.8784 −0.490793 −0.245397 0.969423i \(-0.578918\pi\)
−0.245397 + 0.969423i \(0.578918\pi\)
\(920\) 0 0
\(921\) −21.1652 −0.697415
\(922\) 0 0
\(923\) 17.6697 0.581605
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) 0 0
\(927\) −36.3303 −1.19324
\(928\) 0 0
\(929\) 5.37386 0.176311 0.0881554 0.996107i \(-0.471903\pi\)
0.0881554 + 0.996107i \(0.471903\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 56.4083 1.84673
\(934\) 0 0
\(935\) −6.41742 −0.209872
\(936\) 0 0
\(937\) 16.6606 0.544278 0.272139 0.962258i \(-0.412269\pi\)
0.272139 + 0.962258i \(0.412269\pi\)
\(938\) 0 0
\(939\) 88.4955 2.88794
\(940\) 0 0
\(941\) 4.28674 0.139744 0.0698719 0.997556i \(-0.477741\pi\)
0.0698719 + 0.997556i \(0.477741\pi\)
\(942\) 0 0
\(943\) 1.91288 0.0622919
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0.0871215 0.00283107 0.00141553 0.999999i \(-0.499549\pi\)
0.00141553 + 0.999999i \(0.499549\pi\)
\(948\) 0 0
\(949\) 59.1652 1.92058
\(950\) 0 0
\(951\) −28.8348 −0.935034
\(952\) 0 0
\(953\) −8.29583 −0.268728 −0.134364 0.990932i \(-0.542899\pi\)
−0.134364 + 0.990932i \(0.542899\pi\)
\(954\) 0 0
\(955\) −13.9564 −0.451620
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.9564 −0.998595
\(962\) 0 0
\(963\) 30.7477 0.990832
\(964\) 0 0
\(965\) 37.1652 1.19639
\(966\) 0 0
\(967\) 39.5390 1.27149 0.635745 0.771900i \(-0.280693\pi\)
0.635745 + 0.771900i \(0.280693\pi\)
\(968\) 0 0
\(969\) −5.58258 −0.179338
\(970\) 0 0
\(971\) −57.1652 −1.83452 −0.917259 0.398292i \(-0.869603\pi\)
−0.917259 + 0.398292i \(0.869603\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 20.0000 0.640513
\(976\) 0 0
\(977\) −48.5390 −1.55290 −0.776450 0.630178i \(-0.782982\pi\)
−0.776450 + 0.630178i \(0.782982\pi\)
\(978\) 0 0
\(979\) 40.0000 1.27841
\(980\) 0 0
\(981\) 93.8258 2.99563
\(982\) 0 0
\(983\) −8.62614 −0.275131 −0.137566 0.990493i \(-0.543928\pi\)
−0.137566 + 0.990493i \(0.543928\pi\)
\(984\) 0 0
\(985\) 41.4955 1.32216
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.41742 −0.140466
\(990\) 0 0
\(991\) 45.0780 1.43195 0.715975 0.698126i \(-0.245982\pi\)
0.715975 + 0.698126i \(0.245982\pi\)
\(992\) 0 0
\(993\) 20.5826 0.653168
\(994\) 0 0
\(995\) 27.8348 0.882424
\(996\) 0 0
\(997\) 1.29583 0.0410395 0.0205197 0.999789i \(-0.493468\pi\)
0.0205197 + 0.999789i \(0.493468\pi\)
\(998\) 0 0
\(999\) −27.9129 −0.883124
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.i.1.1 2
7.6 odd 2 3332.2.a.m.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.2.a.i.1.1 2 1.1 even 1 trivial
3332.2.a.m.1.2 yes 2 7.6 odd 2