Properties

Label 7280.2.a.bn.1.3
Level $7280$
Weight $2$
Character 7280.1
Self dual yes
Analytic conductor $58.131$
Analytic rank $1$
Dimension $3$
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] = [7280,2,Mod(1,7280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7280.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7280.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: \(58.1310926715\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.1101.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 9x + 12 \) 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 3640)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.68740\) of defining polynomial
Character \(\chi\) \(=\) 7280.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.68740 q^{3} -1.00000 q^{5} -1.00000 q^{7} +4.22212 q^{9} +O(q^{10})\) \(q+2.68740 q^{3} -1.00000 q^{5} -1.00000 q^{7} +4.22212 q^{9} -1.00000 q^{13} -2.68740 q^{15} +1.22212 q^{17} +0.777884 q^{19} -2.68740 q^{21} -7.81903 q^{23} +1.00000 q^{25} +3.28432 q^{27} -7.13163 q^{29} -1.31260 q^{31} +1.00000 q^{35} -8.50643 q^{37} -2.68740 q^{39} +1.22212 q^{41} -1.37480 q^{43} -4.22212 q^{45} +3.81903 q^{47} +1.00000 q^{49} +3.28432 q^{51} +2.00000 q^{53} +2.09048 q^{57} +4.06220 q^{59} -10.0000 q^{61} -4.22212 q^{63} +1.00000 q^{65} -12.4159 q^{67} -21.0129 q^{69} -5.37480 q^{71} -0.930566 q^{73} +2.68740 q^{75} -0.777884 q^{79} -3.84008 q^{81} +7.81903 q^{83} -1.22212 q^{85} -19.1655 q^{87} -13.8812 q^{89} +1.00000 q^{91} -3.52748 q^{93} -0.777884 q^{95} +19.0129 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{3} - 3 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{3} - 3 q^{5} - 3 q^{7} + 10 q^{9} - 3 q^{13} - q^{15} + q^{17} + 5 q^{19} - q^{21} - 4 q^{23} + 3 q^{25} - 14 q^{27} - 9 q^{29} - 11 q^{31} + 3 q^{35} + q^{37} - q^{39} + q^{41} + 10 q^{43} - 10 q^{45} - 8 q^{47} + 3 q^{49} - 14 q^{51} + 6 q^{53} + 16 q^{57} - 9 q^{59} - 30 q^{61} - 10 q^{63} + 3 q^{65} - q^{67} - 10 q^{69} - 2 q^{71} + 6 q^{73} + q^{75} - 5 q^{79} + 7 q^{81} + 4 q^{83} - q^{85} + 7 q^{87} - q^{89} + 3 q^{91} + 15 q^{93} - 5 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.68740 1.55157 0.775785 0.630997i \(-0.217354\pi\)
0.775785 + 0.630997i \(0.217354\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 4.22212 1.40737
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −2.68740 −0.693884
\(16\) 0 0
\(17\) 1.22212 0.296407 0.148203 0.988957i \(-0.452651\pi\)
0.148203 + 0.988957i \(0.452651\pi\)
\(18\) 0 0
\(19\) 0.777884 0.178459 0.0892294 0.996011i \(-0.471560\pi\)
0.0892294 + 0.996011i \(0.471560\pi\)
\(20\) 0 0
\(21\) −2.68740 −0.586439
\(22\) 0 0
\(23\) −7.81903 −1.63038 −0.815190 0.579193i \(-0.803368\pi\)
−0.815190 + 0.579193i \(0.803368\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 3.28432 0.632067
\(28\) 0 0
\(29\) −7.13163 −1.32431 −0.662155 0.749367i \(-0.730358\pi\)
−0.662155 + 0.749367i \(0.730358\pi\)
\(30\) 0 0
\(31\) −1.31260 −0.235750 −0.117875 0.993028i \(-0.537608\pi\)
−0.117875 + 0.993028i \(0.537608\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −8.50643 −1.39845 −0.699224 0.714902i \(-0.746471\pi\)
−0.699224 + 0.714902i \(0.746471\pi\)
\(38\) 0 0
\(39\) −2.68740 −0.430328
\(40\) 0 0
\(41\) 1.22212 0.190863 0.0954313 0.995436i \(-0.469577\pi\)
0.0954313 + 0.995436i \(0.469577\pi\)
\(42\) 0 0
\(43\) −1.37480 −0.209655 −0.104827 0.994490i \(-0.533429\pi\)
−0.104827 + 0.994490i \(0.533429\pi\)
\(44\) 0 0
\(45\) −4.22212 −0.629396
\(46\) 0 0
\(47\) 3.81903 0.557063 0.278532 0.960427i \(-0.410152\pi\)
0.278532 + 0.960427i \(0.410152\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 3.28432 0.459896
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.09048 0.276891
\(58\) 0 0
\(59\) 4.06220 0.528853 0.264427 0.964406i \(-0.414817\pi\)
0.264427 + 0.964406i \(0.414817\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) −4.22212 −0.531937
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −12.4159 −1.51685 −0.758425 0.651761i \(-0.774031\pi\)
−0.758425 + 0.651761i \(0.774031\pi\)
\(68\) 0 0
\(69\) −21.0129 −2.52965
\(70\) 0 0
\(71\) −5.37480 −0.637871 −0.318936 0.947776i \(-0.603325\pi\)
−0.318936 + 0.947776i \(0.603325\pi\)
\(72\) 0 0
\(73\) −0.930566 −0.108915 −0.0544573 0.998516i \(-0.517343\pi\)
−0.0544573 + 0.998516i \(0.517343\pi\)
\(74\) 0 0
\(75\) 2.68740 0.310314
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.777884 −0.0875187 −0.0437594 0.999042i \(-0.513933\pi\)
−0.0437594 + 0.999042i \(0.513933\pi\)
\(80\) 0 0
\(81\) −3.84008 −0.426676
\(82\) 0 0
\(83\) 7.81903 0.858250 0.429125 0.903245i \(-0.358822\pi\)
0.429125 + 0.903245i \(0.358822\pi\)
\(84\) 0 0
\(85\) −1.22212 −0.132557
\(86\) 0 0
\(87\) −19.1655 −2.05476
\(88\) 0 0
\(89\) −13.8812 −1.47141 −0.735704 0.677303i \(-0.763148\pi\)
−0.735704 + 0.677303i \(0.763148\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −3.52748 −0.365783
\(94\) 0 0
\(95\) −0.777884 −0.0798092
\(96\) 0 0
\(97\) 19.0129 1.93046 0.965232 0.261395i \(-0.0841826\pi\)
0.965232 + 0.261395i \(0.0841826\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.81903 0.977030 0.488515 0.872555i \(-0.337539\pi\)
0.488515 + 0.872555i \(0.337539\pi\)
\(102\) 0 0
\(103\) 12.4159 1.22338 0.611690 0.791098i \(-0.290490\pi\)
0.611690 + 0.791098i \(0.290490\pi\)
\(104\) 0 0
\(105\) 2.68740 0.262263
\(106\) 0 0
\(107\) −13.1938 −1.27550 −0.637748 0.770245i \(-0.720134\pi\)
−0.637748 + 0.770245i \(0.720134\pi\)
\(108\) 0 0
\(109\) 9.63806 0.923159 0.461580 0.887099i \(-0.347283\pi\)
0.461580 + 0.887099i \(0.347283\pi\)
\(110\) 0 0
\(111\) −22.8602 −2.16979
\(112\) 0 0
\(113\) −11.0129 −1.03600 −0.518002 0.855380i \(-0.673324\pi\)
−0.518002 + 0.855380i \(0.673324\pi\)
\(114\) 0 0
\(115\) 7.81903 0.729128
\(116\) 0 0
\(117\) −4.22212 −0.390335
\(118\) 0 0
\(119\) −1.22212 −0.112031
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 3.28432 0.296137
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −10.9306 −0.969931 −0.484965 0.874533i \(-0.661168\pi\)
−0.484965 + 0.874533i \(0.661168\pi\)
\(128\) 0 0
\(129\) −3.69463 −0.325294
\(130\) 0 0
\(131\) −2.93057 −0.256045 −0.128022 0.991771i \(-0.540863\pi\)
−0.128022 + 0.991771i \(0.540863\pi\)
\(132\) 0 0
\(133\) −0.777884 −0.0674511
\(134\) 0 0
\(135\) −3.28432 −0.282669
\(136\) 0 0
\(137\) 8.86837 0.757676 0.378838 0.925463i \(-0.376324\pi\)
0.378838 + 0.925463i \(0.376324\pi\)
\(138\) 0 0
\(139\) 2.44423 0.207317 0.103659 0.994613i \(-0.466945\pi\)
0.103659 + 0.994613i \(0.466945\pi\)
\(140\) 0 0
\(141\) 10.2633 0.864323
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 7.13163 0.592250
\(146\) 0 0
\(147\) 2.68740 0.221653
\(148\) 0 0
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 0 0
\(151\) 2.26326 0.184182 0.0920909 0.995751i \(-0.470645\pi\)
0.0920909 + 0.995751i \(0.470645\pi\)
\(152\) 0 0
\(153\) 5.15992 0.417155
\(154\) 0 0
\(155\) 1.31260 0.105431
\(156\) 0 0
\(157\) −5.75683 −0.459445 −0.229723 0.973256i \(-0.573782\pi\)
−0.229723 + 0.973256i \(0.573782\pi\)
\(158\) 0 0
\(159\) 5.37480 0.426249
\(160\) 0 0
\(161\) 7.81903 0.616226
\(162\) 0 0
\(163\) −10.6874 −0.837102 −0.418551 0.908193i \(-0.637462\pi\)
−0.418551 + 0.908193i \(0.637462\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.486334 −0.0376336 −0.0188168 0.999823i \(-0.505990\pi\)
−0.0188168 + 0.999823i \(0.505990\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 3.28432 0.251158
\(172\) 0 0
\(173\) 9.39490 0.714281 0.357140 0.934051i \(-0.383752\pi\)
0.357140 + 0.934051i \(0.383752\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 10.9168 0.820553
\(178\) 0 0
\(179\) −11.2221 −0.838780 −0.419390 0.907806i \(-0.637756\pi\)
−0.419390 + 0.907806i \(0.637756\pi\)
\(180\) 0 0
\(181\) −15.0129 −1.11590 −0.557949 0.829875i \(-0.688411\pi\)
−0.557949 + 0.829875i \(0.688411\pi\)
\(182\) 0 0
\(183\) −26.8740 −1.98658
\(184\) 0 0
\(185\) 8.50643 0.625405
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −3.28432 −0.238899
\(190\) 0 0
\(191\) −14.6874 −1.06274 −0.531371 0.847139i \(-0.678323\pi\)
−0.531371 + 0.847139i \(0.678323\pi\)
\(192\) 0 0
\(193\) 19.6663 1.41561 0.707807 0.706405i \(-0.249684\pi\)
0.707807 + 0.706405i \(0.249684\pi\)
\(194\) 0 0
\(195\) 2.68740 0.192449
\(196\) 0 0
\(197\) 26.3676 1.87861 0.939306 0.343082i \(-0.111471\pi\)
0.939306 + 0.343082i \(0.111471\pi\)
\(198\) 0 0
\(199\) 13.0129 0.922457 0.461229 0.887281i \(-0.347409\pi\)
0.461229 + 0.887281i \(0.347409\pi\)
\(200\) 0 0
\(201\) −33.3666 −2.35350
\(202\) 0 0
\(203\) 7.13163 0.500542
\(204\) 0 0
\(205\) −1.22212 −0.0853563
\(206\) 0 0
\(207\) −33.0129 −2.29455
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −23.1655 −1.59478 −0.797391 0.603463i \(-0.793787\pi\)
−0.797391 + 0.603463i \(0.793787\pi\)
\(212\) 0 0
\(213\) −14.4442 −0.989703
\(214\) 0 0
\(215\) 1.37480 0.0937605
\(216\) 0 0
\(217\) 1.31260 0.0891051
\(218\) 0 0
\(219\) −2.50080 −0.168989
\(220\) 0 0
\(221\) −1.22212 −0.0822084
\(222\) 0 0
\(223\) −17.1938 −1.15138 −0.575692 0.817667i \(-0.695267\pi\)
−0.575692 + 0.817667i \(0.695267\pi\)
\(224\) 0 0
\(225\) 4.22212 0.281474
\(226\) 0 0
\(227\) −15.8190 −1.04995 −0.524973 0.851119i \(-0.675925\pi\)
−0.524973 + 0.851119i \(0.675925\pi\)
\(228\) 0 0
\(229\) −6.77788 −0.447895 −0.223948 0.974601i \(-0.571894\pi\)
−0.223948 + 0.974601i \(0.571894\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.18097 −0.142880 −0.0714400 0.997445i \(-0.522759\pi\)
−0.0714400 + 0.997445i \(0.522759\pi\)
\(234\) 0 0
\(235\) −3.81903 −0.249126
\(236\) 0 0
\(237\) −2.09048 −0.135792
\(238\) 0 0
\(239\) 3.81903 0.247033 0.123516 0.992343i \(-0.460583\pi\)
0.123516 + 0.992343i \(0.460583\pi\)
\(240\) 0 0
\(241\) −2.11058 −0.135955 −0.0679773 0.997687i \(-0.521655\pi\)
−0.0679773 + 0.997687i \(0.521655\pi\)
\(242\) 0 0
\(243\) −20.1728 −1.29408
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −0.777884 −0.0494955
\(248\) 0 0
\(249\) 21.0129 1.33164
\(250\) 0 0
\(251\) −3.51367 −0.221781 −0.110890 0.993833i \(-0.535370\pi\)
−0.110890 + 0.993833i \(0.535370\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −3.28432 −0.205672
\(256\) 0 0
\(257\) 31.4992 1.96487 0.982433 0.186616i \(-0.0597520\pi\)
0.982433 + 0.186616i \(0.0597520\pi\)
\(258\) 0 0
\(259\) 8.50643 0.528564
\(260\) 0 0
\(261\) −30.1106 −1.86380
\(262\) 0 0
\(263\) −8.18097 −0.504460 −0.252230 0.967667i \(-0.581164\pi\)
−0.252230 + 0.967667i \(0.581164\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) −37.3044 −2.28299
\(268\) 0 0
\(269\) 12.5686 0.766323 0.383161 0.923681i \(-0.374835\pi\)
0.383161 + 0.923681i \(0.374835\pi\)
\(270\) 0 0
\(271\) −7.63806 −0.463979 −0.231990 0.972718i \(-0.574524\pi\)
−0.231990 + 0.972718i \(0.574524\pi\)
\(272\) 0 0
\(273\) 2.68740 0.162649
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.56863 0.514839 0.257420 0.966300i \(-0.417128\pi\)
0.257420 + 0.966300i \(0.417128\pi\)
\(278\) 0 0
\(279\) −5.54195 −0.331788
\(280\) 0 0
\(281\) 31.7204 1.89228 0.946139 0.323761i \(-0.104947\pi\)
0.946139 + 0.323761i \(0.104947\pi\)
\(282\) 0 0
\(283\) −7.16555 −0.425947 −0.212974 0.977058i \(-0.568315\pi\)
−0.212974 + 0.977058i \(0.568315\pi\)
\(284\) 0 0
\(285\) −2.09048 −0.123830
\(286\) 0 0
\(287\) −1.22212 −0.0721393
\(288\) 0 0
\(289\) −15.5064 −0.912143
\(290\) 0 0
\(291\) 51.0952 2.99525
\(292\) 0 0
\(293\) 3.19383 0.186586 0.0932928 0.995639i \(-0.470261\pi\)
0.0932928 + 0.995639i \(0.470261\pi\)
\(294\) 0 0
\(295\) −4.06220 −0.236510
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.81903 0.452186
\(300\) 0 0
\(301\) 1.37480 0.0792421
\(302\) 0 0
\(303\) 26.3877 1.51593
\(304\) 0 0
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) −15.8190 −0.902840 −0.451420 0.892312i \(-0.649082\pi\)
−0.451420 + 0.892312i \(0.649082\pi\)
\(308\) 0 0
\(309\) 33.3666 1.89816
\(310\) 0 0
\(311\) −19.9434 −1.13089 −0.565444 0.824787i \(-0.691295\pi\)
−0.565444 + 0.824787i \(0.691295\pi\)
\(312\) 0 0
\(313\) −5.39490 −0.304938 −0.152469 0.988308i \(-0.548722\pi\)
−0.152469 + 0.988308i \(0.548722\pi\)
\(314\) 0 0
\(315\) 4.22212 0.237889
\(316\) 0 0
\(317\) −10.8885 −0.611557 −0.305779 0.952103i \(-0.598917\pi\)
−0.305779 + 0.952103i \(0.598917\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −35.4571 −1.97902
\(322\) 0 0
\(323\) 0.950664 0.0528964
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) 25.9013 1.43235
\(328\) 0 0
\(329\) −3.81903 −0.210550
\(330\) 0 0
\(331\) −7.63806 −0.419826 −0.209913 0.977720i \(-0.567318\pi\)
−0.209913 + 0.977720i \(0.567318\pi\)
\(332\) 0 0
\(333\) −35.9151 −1.96814
\(334\) 0 0
\(335\) 12.4159 0.678356
\(336\) 0 0
\(337\) 12.7496 0.694515 0.347257 0.937770i \(-0.387113\pi\)
0.347257 + 0.937770i \(0.387113\pi\)
\(338\) 0 0
\(339\) −29.5960 −1.60743
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 21.0129 1.13129
\(346\) 0 0
\(347\) 28.3456 1.52167 0.760835 0.648946i \(-0.224790\pi\)
0.760835 + 0.648946i \(0.224790\pi\)
\(348\) 0 0
\(349\) 6.64530 0.355715 0.177857 0.984056i \(-0.443083\pi\)
0.177857 + 0.984056i \(0.443083\pi\)
\(350\) 0 0
\(351\) −3.28432 −0.175304
\(352\) 0 0
\(353\) −4.13887 −0.220290 −0.110145 0.993916i \(-0.535131\pi\)
−0.110145 + 0.993916i \(0.535131\pi\)
\(354\) 0 0
\(355\) 5.37480 0.285265
\(356\) 0 0
\(357\) −3.28432 −0.173824
\(358\) 0 0
\(359\) −29.7204 −1.56858 −0.784290 0.620394i \(-0.786973\pi\)
−0.784290 + 0.620394i \(0.786973\pi\)
\(360\) 0 0
\(361\) −18.3949 −0.968152
\(362\) 0 0
\(363\) −29.5614 −1.55157
\(364\) 0 0
\(365\) 0.930566 0.0487081
\(366\) 0 0
\(367\) −4.36194 −0.227691 −0.113846 0.993498i \(-0.536317\pi\)
−0.113846 + 0.993498i \(0.536317\pi\)
\(368\) 0 0
\(369\) 5.15992 0.268615
\(370\) 0 0
\(371\) −2.00000 −0.103835
\(372\) 0 0
\(373\) −24.8740 −1.28793 −0.643963 0.765056i \(-0.722711\pi\)
−0.643963 + 0.765056i \(0.722711\pi\)
\(374\) 0 0
\(375\) −2.68740 −0.138777
\(376\) 0 0
\(377\) 7.13163 0.367298
\(378\) 0 0
\(379\) 19.4571 0.999444 0.499722 0.866186i \(-0.333436\pi\)
0.499722 + 0.866186i \(0.333436\pi\)
\(380\) 0 0
\(381\) −29.3748 −1.50492
\(382\) 0 0
\(383\) 3.69463 0.188787 0.0943935 0.995535i \(-0.469909\pi\)
0.0943935 + 0.995535i \(0.469909\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.80456 −0.295062
\(388\) 0 0
\(389\) 12.6390 0.640824 0.320412 0.947278i \(-0.396179\pi\)
0.320412 + 0.947278i \(0.396179\pi\)
\(390\) 0 0
\(391\) −9.55577 −0.483256
\(392\) 0 0
\(393\) −7.87560 −0.397272
\(394\) 0 0
\(395\) 0.777884 0.0391396
\(396\) 0 0
\(397\) −1.69463 −0.0850513 −0.0425256 0.999095i \(-0.513540\pi\)
−0.0425256 + 0.999095i \(0.513540\pi\)
\(398\) 0 0
\(399\) −2.09048 −0.104655
\(400\) 0 0
\(401\) −33.5815 −1.67698 −0.838490 0.544917i \(-0.816561\pi\)
−0.838490 + 0.544917i \(0.816561\pi\)
\(402\) 0 0
\(403\) 1.31260 0.0653853
\(404\) 0 0
\(405\) 3.84008 0.190815
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −26.8885 −1.32955 −0.664775 0.747044i \(-0.731472\pi\)
−0.664775 + 0.747044i \(0.731472\pi\)
\(410\) 0 0
\(411\) 23.8328 1.17559
\(412\) 0 0
\(413\) −4.06220 −0.199888
\(414\) 0 0
\(415\) −7.81903 −0.383821
\(416\) 0 0
\(417\) 6.56863 0.321667
\(418\) 0 0
\(419\) −5.55577 −0.271417 −0.135708 0.990749i \(-0.543331\pi\)
−0.135708 + 0.990749i \(0.543331\pi\)
\(420\) 0 0
\(421\) 4.74960 0.231481 0.115741 0.993279i \(-0.463076\pi\)
0.115741 + 0.993279i \(0.463076\pi\)
\(422\) 0 0
\(423\) 16.1244 0.783995
\(424\) 0 0
\(425\) 1.22212 0.0592814
\(426\) 0 0
\(427\) 10.0000 0.483934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −16.8319 −0.810764 −0.405382 0.914147i \(-0.632861\pi\)
−0.405382 + 0.914147i \(0.632861\pi\)
\(432\) 0 0
\(433\) −30.4159 −1.46170 −0.730849 0.682540i \(-0.760875\pi\)
−0.730849 + 0.682540i \(0.760875\pi\)
\(434\) 0 0
\(435\) 19.1655 0.918918
\(436\) 0 0
\(437\) −6.08230 −0.290956
\(438\) 0 0
\(439\) 3.11153 0.148505 0.0742527 0.997239i \(-0.476343\pi\)
0.0742527 + 0.997239i \(0.476343\pi\)
\(440\) 0 0
\(441\) 4.22212 0.201053
\(442\) 0 0
\(443\) 7.81903 0.371493 0.185747 0.982598i \(-0.440530\pi\)
0.185747 + 0.982598i \(0.440530\pi\)
\(444\) 0 0
\(445\) 13.8812 0.658033
\(446\) 0 0
\(447\) 5.37480 0.254219
\(448\) 0 0
\(449\) 31.0129 1.46359 0.731794 0.681526i \(-0.238683\pi\)
0.731794 + 0.681526i \(0.238683\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 6.08230 0.285771
\(454\) 0 0
\(455\) −1.00000 −0.0468807
\(456\) 0 0
\(457\) 0.868368 0.0406205 0.0203103 0.999794i \(-0.493535\pi\)
0.0203103 + 0.999794i \(0.493535\pi\)
\(458\) 0 0
\(459\) 4.01382 0.187349
\(460\) 0 0
\(461\) −14.3676 −0.669164 −0.334582 0.942367i \(-0.608595\pi\)
−0.334582 + 0.942367i \(0.608595\pi\)
\(462\) 0 0
\(463\) 4.11058 0.191035 0.0955175 0.995428i \(-0.469549\pi\)
0.0955175 + 0.995428i \(0.469549\pi\)
\(464\) 0 0
\(465\) 3.52748 0.163583
\(466\) 0 0
\(467\) −14.5548 −0.673517 −0.336758 0.941591i \(-0.609331\pi\)
−0.336758 + 0.941591i \(0.609331\pi\)
\(468\) 0 0
\(469\) 12.4159 0.573315
\(470\) 0 0
\(471\) −15.4709 −0.712862
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.777884 0.0356917
\(476\) 0 0
\(477\) 8.44423 0.386635
\(478\) 0 0
\(479\) −24.9507 −1.14002 −0.570012 0.821636i \(-0.693062\pi\)
−0.570012 + 0.821636i \(0.693062\pi\)
\(480\) 0 0
\(481\) 8.50643 0.387860
\(482\) 0 0
\(483\) 21.0129 0.956118
\(484\) 0 0
\(485\) −19.0129 −0.863330
\(486\) 0 0
\(487\) 23.1737 1.05010 0.525051 0.851071i \(-0.324046\pi\)
0.525051 + 0.851071i \(0.324046\pi\)
\(488\) 0 0
\(489\) −28.7213 −1.29882
\(490\) 0 0
\(491\) 22.3877 1.01034 0.505171 0.863020i \(-0.331430\pi\)
0.505171 + 0.863020i \(0.331430\pi\)
\(492\) 0 0
\(493\) −8.71568 −0.392535
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.37480 0.241093
\(498\) 0 0
\(499\) 36.5265 1.63515 0.817576 0.575821i \(-0.195317\pi\)
0.817576 + 0.575821i \(0.195317\pi\)
\(500\) 0 0
\(501\) −1.30697 −0.0583912
\(502\) 0 0
\(503\) −4.36194 −0.194489 −0.0972446 0.995261i \(-0.531003\pi\)
−0.0972446 + 0.995261i \(0.531003\pi\)
\(504\) 0 0
\(505\) −9.81903 −0.436941
\(506\) 0 0
\(507\) 2.68740 0.119352
\(508\) 0 0
\(509\) 9.58405 0.424806 0.212403 0.977182i \(-0.431871\pi\)
0.212403 + 0.977182i \(0.431871\pi\)
\(510\) 0 0
\(511\) 0.930566 0.0411658
\(512\) 0 0
\(513\) 2.55481 0.112798
\(514\) 0 0
\(515\) −12.4159 −0.547112
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 25.2478 1.10826
\(520\) 0 0
\(521\) 21.0952 0.924196 0.462098 0.886829i \(-0.347097\pi\)
0.462098 + 0.886829i \(0.347097\pi\)
\(522\) 0 0
\(523\) −6.13887 −0.268434 −0.134217 0.990952i \(-0.542852\pi\)
−0.134217 + 0.990952i \(0.542852\pi\)
\(524\) 0 0
\(525\) −2.68740 −0.117288
\(526\) 0 0
\(527\) −1.60415 −0.0698779
\(528\) 0 0
\(529\) 38.1373 1.65814
\(530\) 0 0
\(531\) 17.1511 0.744293
\(532\) 0 0
\(533\) −1.22212 −0.0529357
\(534\) 0 0
\(535\) 13.1938 0.570419
\(536\) 0 0
\(537\) −30.1583 −1.30143
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −31.1938 −1.34113 −0.670564 0.741852i \(-0.733948\pi\)
−0.670564 + 0.741852i \(0.733948\pi\)
\(542\) 0 0
\(543\) −40.3456 −1.73139
\(544\) 0 0
\(545\) −9.63806 −0.412849
\(546\) 0 0
\(547\) −5.06943 −0.216753 −0.108377 0.994110i \(-0.534565\pi\)
−0.108377 + 0.994110i \(0.534565\pi\)
\(548\) 0 0
\(549\) −42.2212 −1.80196
\(550\) 0 0
\(551\) −5.54758 −0.236335
\(552\) 0 0
\(553\) 0.777884 0.0330790
\(554\) 0 0
\(555\) 22.8602 0.970361
\(556\) 0 0
\(557\) −2.11058 −0.0894282 −0.0447141 0.999000i \(-0.514238\pi\)
−0.0447141 + 0.999000i \(0.514238\pi\)
\(558\) 0 0
\(559\) 1.37480 0.0581478
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.6390 0.448381 0.224191 0.974545i \(-0.428026\pi\)
0.224191 + 0.974545i \(0.428026\pi\)
\(564\) 0 0
\(565\) 11.0129 0.463315
\(566\) 0 0
\(567\) 3.84008 0.161268
\(568\) 0 0
\(569\) 12.0201 0.503909 0.251954 0.967739i \(-0.418927\pi\)
0.251954 + 0.967739i \(0.418927\pi\)
\(570\) 0 0
\(571\) 18.6874 0.782043 0.391022 0.920381i \(-0.372122\pi\)
0.391022 + 0.920381i \(0.372122\pi\)
\(572\) 0 0
\(573\) −39.4709 −1.64892
\(574\) 0 0
\(575\) −7.81903 −0.326076
\(576\) 0 0
\(577\) 43.8448 1.82528 0.912641 0.408763i \(-0.134040\pi\)
0.912641 + 0.408763i \(0.134040\pi\)
\(578\) 0 0
\(579\) 52.8513 2.19643
\(580\) 0 0
\(581\) −7.81903 −0.324388
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 4.22212 0.174563
\(586\) 0 0
\(587\) 7.33270 0.302653 0.151326 0.988484i \(-0.451646\pi\)
0.151326 + 0.988484i \(0.451646\pi\)
\(588\) 0 0
\(589\) −1.02105 −0.0420716
\(590\) 0 0
\(591\) 70.8602 2.91480
\(592\) 0 0
\(593\) −5.45710 −0.224096 −0.112048 0.993703i \(-0.535741\pi\)
−0.112048 + 0.993703i \(0.535741\pi\)
\(594\) 0 0
\(595\) 1.22212 0.0501019
\(596\) 0 0
\(597\) 34.9708 1.43126
\(598\) 0 0
\(599\) −0.361936 −0.0147883 −0.00739415 0.999973i \(-0.502354\pi\)
−0.00739415 + 0.999973i \(0.502354\pi\)
\(600\) 0 0
\(601\) 12.8740 0.525141 0.262571 0.964913i \(-0.415430\pi\)
0.262571 + 0.964913i \(0.415430\pi\)
\(602\) 0 0
\(603\) −52.4216 −2.13477
\(604\) 0 0
\(605\) 11.0000 0.447214
\(606\) 0 0
\(607\) 18.6874 0.758498 0.379249 0.925295i \(-0.376182\pi\)
0.379249 + 0.925295i \(0.376182\pi\)
\(608\) 0 0
\(609\) 19.1655 0.776627
\(610\) 0 0
\(611\) −3.81903 −0.154501
\(612\) 0 0
\(613\) 28.3877 1.14657 0.573283 0.819357i \(-0.305669\pi\)
0.573283 + 0.819357i \(0.305669\pi\)
\(614\) 0 0
\(615\) −3.28432 −0.132436
\(616\) 0 0
\(617\) 32.3337 1.30170 0.650852 0.759205i \(-0.274412\pi\)
0.650852 + 0.759205i \(0.274412\pi\)
\(618\) 0 0
\(619\) 43.7003 1.75646 0.878231 0.478237i \(-0.158724\pi\)
0.878231 + 0.478237i \(0.158724\pi\)
\(620\) 0 0
\(621\) −25.6802 −1.03051
\(622\) 0 0
\(623\) 13.8812 0.556140
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −10.3958 −0.414510
\(630\) 0 0
\(631\) 3.33270 0.132673 0.0663363 0.997797i \(-0.478869\pi\)
0.0663363 + 0.997797i \(0.478869\pi\)
\(632\) 0 0
\(633\) −62.2551 −2.47442
\(634\) 0 0
\(635\) 10.9306 0.433766
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −22.6930 −0.897722
\(640\) 0 0
\(641\) 4.99276 0.197202 0.0986012 0.995127i \(-0.468563\pi\)
0.0986012 + 0.995127i \(0.468563\pi\)
\(642\) 0 0
\(643\) 2.20669 0.0870235 0.0435118 0.999053i \(-0.486145\pi\)
0.0435118 + 0.999053i \(0.486145\pi\)
\(644\) 0 0
\(645\) 3.69463 0.145476
\(646\) 0 0
\(647\) −5.31260 −0.208860 −0.104430 0.994532i \(-0.533302\pi\)
−0.104430 + 0.994532i \(0.533302\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 3.52748 0.138253
\(652\) 0 0
\(653\) −28.6930 −1.12284 −0.561422 0.827529i \(-0.689746\pi\)
−0.561422 + 0.827529i \(0.689746\pi\)
\(654\) 0 0
\(655\) 2.93057 0.114507
\(656\) 0 0
\(657\) −3.92896 −0.153283
\(658\) 0 0
\(659\) −40.9425 −1.59489 −0.797446 0.603390i \(-0.793816\pi\)
−0.797446 + 0.603390i \(0.793816\pi\)
\(660\) 0 0
\(661\) 22.9425 0.892359 0.446179 0.894944i \(-0.352784\pi\)
0.446179 + 0.894944i \(0.352784\pi\)
\(662\) 0 0
\(663\) −3.28432 −0.127552
\(664\) 0 0
\(665\) 0.777884 0.0301650
\(666\) 0 0
\(667\) 55.7625 2.15913
\(668\) 0 0
\(669\) −46.2067 −1.78645
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 3.68016 0.141860 0.0709300 0.997481i \(-0.477403\pi\)
0.0709300 + 0.997481i \(0.477403\pi\)
\(674\) 0 0
\(675\) 3.28432 0.126413
\(676\) 0 0
\(677\) 28.3877 1.09103 0.545513 0.838102i \(-0.316335\pi\)
0.545513 + 0.838102i \(0.316335\pi\)
\(678\) 0 0
\(679\) −19.0129 −0.729647
\(680\) 0 0
\(681\) −42.5121 −1.62907
\(682\) 0 0
\(683\) 13.6098 0.520764 0.260382 0.965506i \(-0.416152\pi\)
0.260382 + 0.965506i \(0.416152\pi\)
\(684\) 0 0
\(685\) −8.86837 −0.338843
\(686\) 0 0
\(687\) −18.2149 −0.694941
\(688\) 0 0
\(689\) −2.00000 −0.0761939
\(690\) 0 0
\(691\) 9.43700 0.359000 0.179500 0.983758i \(-0.442552\pi\)
0.179500 + 0.983758i \(0.442552\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.44423 −0.0927150
\(696\) 0 0
\(697\) 1.49357 0.0565729
\(698\) 0 0
\(699\) −5.86113 −0.221688
\(700\) 0 0
\(701\) 18.4725 0.697697 0.348849 0.937179i \(-0.386573\pi\)
0.348849 + 0.937179i \(0.386573\pi\)
\(702\) 0 0
\(703\) −6.61701 −0.249565
\(704\) 0 0
\(705\) −10.2633 −0.386537
\(706\) 0 0
\(707\) −9.81903 −0.369283
\(708\) 0 0
\(709\) 27.6802 1.03955 0.519775 0.854303i \(-0.326016\pi\)
0.519775 + 0.854303i \(0.326016\pi\)
\(710\) 0 0
\(711\) −3.28432 −0.123171
\(712\) 0 0
\(713\) 10.2633 0.384362
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.2633 0.383289
\(718\) 0 0
\(719\) 41.8046 1.55905 0.779524 0.626373i \(-0.215461\pi\)
0.779524 + 0.626373i \(0.215461\pi\)
\(720\) 0 0
\(721\) −12.4159 −0.462394
\(722\) 0 0
\(723\) −5.67198 −0.210943
\(724\) 0 0
\(725\) −7.13163 −0.264862
\(726\) 0 0
\(727\) −23.5759 −0.874380 −0.437190 0.899369i \(-0.644026\pi\)
−0.437190 + 0.899369i \(0.644026\pi\)
\(728\) 0 0
\(729\) −42.6921 −1.58119
\(730\) 0 0
\(731\) −1.68016 −0.0621431
\(732\) 0 0
\(733\) −2.52653 −0.0933195 −0.0466597 0.998911i \(-0.514858\pi\)
−0.0466597 + 0.998911i \(0.514858\pi\)
\(734\) 0 0
\(735\) −2.68740 −0.0991262
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −6.80617 −0.250369 −0.125184 0.992133i \(-0.539952\pi\)
−0.125184 + 0.992133i \(0.539952\pi\)
\(740\) 0 0
\(741\) −2.09048 −0.0767958
\(742\) 0 0
\(743\) −50.4417 −1.85053 −0.925263 0.379327i \(-0.876156\pi\)
−0.925263 + 0.379327i \(0.876156\pi\)
\(744\) 0 0
\(745\) −2.00000 −0.0732743
\(746\) 0 0
\(747\) 33.0129 1.20788
\(748\) 0 0
\(749\) 13.1938 0.482092
\(750\) 0 0
\(751\) 32.4643 1.18464 0.592320 0.805703i \(-0.298212\pi\)
0.592320 + 0.805703i \(0.298212\pi\)
\(752\) 0 0
\(753\) −9.44263 −0.344108
\(754\) 0 0
\(755\) −2.26326 −0.0823686
\(756\) 0 0
\(757\) −5.63806 −0.204919 −0.102459 0.994737i \(-0.532671\pi\)
−0.102459 + 0.994737i \(0.532671\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 36.7552 1.33238 0.666188 0.745784i \(-0.267925\pi\)
0.666188 + 0.745784i \(0.267925\pi\)
\(762\) 0 0
\(763\) −9.63806 −0.348921
\(764\) 0 0
\(765\) −5.15992 −0.186557
\(766\) 0 0
\(767\) −4.06220 −0.146677
\(768\) 0 0
\(769\) 34.2488 1.23504 0.617522 0.786554i \(-0.288137\pi\)
0.617522 + 0.786554i \(0.288137\pi\)
\(770\) 0 0
\(771\) 84.6509 3.04863
\(772\) 0 0
\(773\) 33.8869 1.21883 0.609413 0.792853i \(-0.291405\pi\)
0.609413 + 0.792853i \(0.291405\pi\)
\(774\) 0 0
\(775\) −1.31260 −0.0471500
\(776\) 0 0
\(777\) 22.8602 0.820104
\(778\) 0 0
\(779\) 0.950664 0.0340611
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −23.4225 −0.837053
\(784\) 0 0
\(785\) 5.75683 0.205470
\(786\) 0 0
\(787\) 6.50080 0.231729 0.115864 0.993265i \(-0.463036\pi\)
0.115864 + 0.993265i \(0.463036\pi\)
\(788\) 0 0
\(789\) −21.9855 −0.782706
\(790\) 0 0
\(791\) 11.0129 0.391572
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) 0 0
\(795\) −5.37480 −0.190624
\(796\) 0 0
\(797\) 6.76970 0.239795 0.119897 0.992786i \(-0.461743\pi\)
0.119897 + 0.992786i \(0.461743\pi\)
\(798\) 0 0
\(799\) 4.66730 0.165117
\(800\) 0 0
\(801\) −58.6082 −2.07082
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −7.81903 −0.275585
\(806\) 0 0
\(807\) 33.7769 1.18900
\(808\) 0 0
\(809\) 6.72131 0.236309 0.118154 0.992995i \(-0.462302\pi\)
0.118154 + 0.992995i \(0.462302\pi\)
\(810\) 0 0
\(811\) −30.9142 −1.08554 −0.542772 0.839880i \(-0.682625\pi\)
−0.542772 + 0.839880i \(0.682625\pi\)
\(812\) 0 0
\(813\) −20.5265 −0.719897
\(814\) 0 0
\(815\) 10.6874 0.374363
\(816\) 0 0
\(817\) −1.06943 −0.0374147
\(818\) 0 0
\(819\) 4.22212 0.147533
\(820\) 0 0
\(821\) −10.6673 −0.372291 −0.186146 0.982522i \(-0.559600\pi\)
−0.186146 + 0.982522i \(0.559600\pi\)
\(822\) 0 0
\(823\) −6.50080 −0.226604 −0.113302 0.993561i \(-0.536143\pi\)
−0.113302 + 0.993561i \(0.536143\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −33.1373 −1.15230 −0.576148 0.817346i \(-0.695445\pi\)
−0.576148 + 0.817346i \(0.695445\pi\)
\(828\) 0 0
\(829\) 30.9563 1.07516 0.537578 0.843214i \(-0.319339\pi\)
0.537578 + 0.843214i \(0.319339\pi\)
\(830\) 0 0
\(831\) 23.0273 0.798809
\(832\) 0 0
\(833\) 1.22212 0.0423438
\(834\) 0 0
\(835\) 0.486334 0.0168303
\(836\) 0 0
\(837\) −4.31099 −0.149010
\(838\) 0 0
\(839\) 31.6381 1.09227 0.546134 0.837698i \(-0.316099\pi\)
0.546134 + 0.837698i \(0.316099\pi\)
\(840\) 0 0
\(841\) 21.8602 0.753799
\(842\) 0 0
\(843\) 85.2453 2.93600
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) 11.0000 0.377964
\(848\) 0 0
\(849\) −19.2567 −0.660888
\(850\) 0 0
\(851\) 66.5121 2.28000
\(852\) 0 0
\(853\) −36.9306 −1.26448 −0.632239 0.774773i \(-0.717864\pi\)
−0.632239 + 0.774773i \(0.717864\pi\)
\(854\) 0 0
\(855\) −3.28432 −0.112321
\(856\) 0 0
\(857\) −21.6437 −0.739334 −0.369667 0.929164i \(-0.620528\pi\)
−0.369667 + 0.929164i \(0.620528\pi\)
\(858\) 0 0
\(859\) −26.0823 −0.889916 −0.444958 0.895551i \(-0.646781\pi\)
−0.444958 + 0.895551i \(0.646781\pi\)
\(860\) 0 0
\(861\) −3.28432 −0.111929
\(862\) 0 0
\(863\) 42.8036 1.45705 0.728526 0.685018i \(-0.240206\pi\)
0.728526 + 0.685018i \(0.240206\pi\)
\(864\) 0 0
\(865\) −9.39490 −0.319436
\(866\) 0 0
\(867\) −41.6720 −1.41525
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 12.4159 0.420698
\(872\) 0 0
\(873\) 80.2745 2.71688
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) 2.99905 0.101271 0.0506353 0.998717i \(-0.483875\pi\)
0.0506353 + 0.998717i \(0.483875\pi\)
\(878\) 0 0
\(879\) 8.58310 0.289501
\(880\) 0 0
\(881\) 33.0386 1.11310 0.556549 0.830815i \(-0.312125\pi\)
0.556549 + 0.830815i \(0.312125\pi\)
\(882\) 0 0
\(883\) −32.5265 −1.09460 −0.547302 0.836935i \(-0.684345\pi\)
−0.547302 + 0.836935i \(0.684345\pi\)
\(884\) 0 0
\(885\) −10.9168 −0.366963
\(886\) 0 0
\(887\) 19.0493 0.639614 0.319807 0.947483i \(-0.396382\pi\)
0.319807 + 0.947483i \(0.396382\pi\)
\(888\) 0 0
\(889\) 10.9306 0.366599
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.97076 0.0994128
\(894\) 0 0
\(895\) 11.2221 0.375114
\(896\) 0 0
\(897\) 21.0129 0.701599
\(898\) 0 0
\(899\) 9.36098 0.312206
\(900\) 0 0
\(901\) 2.44423 0.0814292
\(902\) 0 0
\(903\) 3.69463 0.122950
\(904\) 0 0
\(905\) 15.0129 0.499044
\(906\) 0 0
\(907\) −33.8611 −1.12434 −0.562170 0.827022i \(-0.690033\pi\)
−0.562170 + 0.827022i \(0.690033\pi\)
\(908\) 0 0
\(909\) 41.4571 1.37505
\(910\) 0 0
\(911\) 2.19288 0.0726533 0.0363267 0.999340i \(-0.488434\pi\)
0.0363267 + 0.999340i \(0.488434\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 26.8740 0.888427
\(916\) 0 0
\(917\) 2.93057 0.0967758
\(918\) 0 0
\(919\) 24.9507 0.823046 0.411523 0.911399i \(-0.364997\pi\)
0.411523 + 0.911399i \(0.364997\pi\)
\(920\) 0 0
\(921\) −42.5121 −1.40082
\(922\) 0 0
\(923\) 5.37480 0.176914
\(924\) 0 0
\(925\) −8.50643 −0.279690
\(926\) 0 0
\(927\) 52.4216 1.72175
\(928\) 0 0
\(929\) −24.0201 −0.788074 −0.394037 0.919095i \(-0.628922\pi\)
−0.394037 + 0.919095i \(0.628922\pi\)
\(930\) 0 0
\(931\) 0.777884 0.0254941
\(932\) 0 0
\(933\) −53.5960 −1.75465
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −27.6663 −0.903820 −0.451910 0.892063i \(-0.649257\pi\)
−0.451910 + 0.892063i \(0.649257\pi\)
\(938\) 0 0
\(939\) −14.4982 −0.473132
\(940\) 0 0
\(941\) −24.8036 −0.808575 −0.404287 0.914632i \(-0.632480\pi\)
−0.404287 + 0.914632i \(0.632480\pi\)
\(942\) 0 0
\(943\) −9.55577 −0.311179
\(944\) 0 0
\(945\) 3.28432 0.106839
\(946\) 0 0
\(947\) 28.0540 0.911633 0.455816 0.890074i \(-0.349347\pi\)
0.455816 + 0.890074i \(0.349347\pi\)
\(948\) 0 0
\(949\) 0.930566 0.0302075
\(950\) 0 0
\(951\) −29.2617 −0.948874
\(952\) 0 0
\(953\) −52.4555 −1.69920 −0.849600 0.527428i \(-0.823157\pi\)
−0.849600 + 0.527428i \(0.823157\pi\)
\(954\) 0 0
\(955\) 14.6874 0.475273
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.86837 −0.286375
\(960\) 0 0
\(961\) −29.2771 −0.944422
\(962\) 0 0
\(963\) −55.7059 −1.79510
\(964\) 0 0
\(965\) −19.6663 −0.633082
\(966\) 0 0
\(967\) −30.2011 −0.971201 −0.485600 0.874181i \(-0.661399\pi\)
−0.485600 + 0.874181i \(0.661399\pi\)
\(968\) 0 0
\(969\) 2.55481 0.0820725
\(970\) 0 0
\(971\) −17.8611 −0.573191 −0.286596 0.958052i \(-0.592524\pi\)
−0.286596 + 0.958052i \(0.592524\pi\)
\(972\) 0 0
\(973\) −2.44423 −0.0783585
\(974\) 0 0
\(975\) −2.68740 −0.0860657
\(976\) 0 0
\(977\) 15.7506 0.503905 0.251952 0.967740i \(-0.418927\pi\)
0.251952 + 0.967740i \(0.418927\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 40.6930 1.29923
\(982\) 0 0
\(983\) 38.9306 1.24169 0.620846 0.783932i \(-0.286789\pi\)
0.620846 + 0.783932i \(0.286789\pi\)
\(984\) 0 0
\(985\) −26.3676 −0.840140
\(986\) 0 0
\(987\) −10.2633 −0.326683
\(988\) 0 0
\(989\) 10.7496 0.341817
\(990\) 0 0
\(991\) −53.9151 −1.71267 −0.856335 0.516420i \(-0.827264\pi\)
−0.856335 + 0.516420i \(0.827264\pi\)
\(992\) 0 0
\(993\) −20.5265 −0.651390
\(994\) 0 0
\(995\) −13.0129 −0.412535
\(996\) 0 0
\(997\) −62.0540 −1.96527 −0.982635 0.185548i \(-0.940594\pi\)
−0.982635 + 0.185548i \(0.940594\pi\)
\(998\) 0 0
\(999\) −27.9378 −0.883913
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 7280.2.a.bn.1.3 3
4.3 odd 2 3640.2.a.p.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.p.1.1 3 4.3 odd 2
7280.2.a.bn.1.3 3 1.1 even 1 trivial