Properties

Label 1064.2.a.b.1.2
Level $1064$
Weight $2$
Character 1064.1
Self dual yes
Analytic conductor $8.496$
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] = [1064,2,Mod(1,1064)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1064, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1064.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.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: \(8.49608277506\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) 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 1.2
Root \(-1.30278\) of defining polynomial
Character \(\chi\) \(=\) 1064.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.30278 q^{3} -1.00000 q^{5} -1.00000 q^{7} -1.30278 q^{9} +O(q^{10})\) \(q+1.30278 q^{3} -1.00000 q^{5} -1.00000 q^{7} -1.30278 q^{9} -2.30278 q^{11} -3.60555 q^{13} -1.30278 q^{15} +1.69722 q^{17} +1.00000 q^{19} -1.30278 q^{21} -0.394449 q^{23} -4.00000 q^{25} -5.60555 q^{27} -4.30278 q^{29} -8.30278 q^{31} -3.00000 q^{33} +1.00000 q^{35} +3.60555 q^{37} -4.69722 q^{39} +0.302776 q^{41} +7.21110 q^{43} +1.30278 q^{45} -7.60555 q^{47} +1.00000 q^{49} +2.21110 q^{51} -3.90833 q^{53} +2.30278 q^{55} +1.30278 q^{57} +5.60555 q^{59} +8.21110 q^{61} +1.30278 q^{63} +3.60555 q^{65} -10.9083 q^{67} -0.513878 q^{69} +8.81665 q^{71} -5.90833 q^{73} -5.21110 q^{75} +2.30278 q^{77} -14.0000 q^{79} -3.39445 q^{81} -10.5139 q^{83} -1.69722 q^{85} -5.60555 q^{87} +13.8167 q^{89} +3.60555 q^{91} -10.8167 q^{93} -1.00000 q^{95} +16.8167 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} - 2 q^{5} - 2 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} - 2 q^{5} - 2 q^{7} + q^{9} - q^{11} + q^{15} + 7 q^{17} + 2 q^{19} + q^{21} - 8 q^{23} - 8 q^{25} - 4 q^{27} - 5 q^{29} - 13 q^{31} - 6 q^{33} + 2 q^{35} - 13 q^{39} - 3 q^{41} - q^{45} - 8 q^{47} + 2 q^{49} - 10 q^{51} + 3 q^{53} + q^{55} - q^{57} + 4 q^{59} + 2 q^{61} - q^{63} - 11 q^{67} + 17 q^{69} - 4 q^{71} - q^{73} + 4 q^{75} + q^{77} - 28 q^{79} - 14 q^{81} - 3 q^{83} - 7 q^{85} - 4 q^{87} + 6 q^{89} - 2 q^{95} + 12 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.30278 0.752158 0.376079 0.926588i \(-0.377272\pi\)
0.376079 + 0.926588i \(0.377272\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −1.30278 −0.434259
\(10\) 0 0
\(11\) −2.30278 −0.694313 −0.347156 0.937807i \(-0.612853\pi\)
−0.347156 + 0.937807i \(0.612853\pi\)
\(12\) 0 0
\(13\) −3.60555 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 0 0
\(15\) −1.30278 −0.336375
\(16\) 0 0
\(17\) 1.69722 0.411637 0.205819 0.978590i \(-0.434014\pi\)
0.205819 + 0.978590i \(0.434014\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −1.30278 −0.284289
\(22\) 0 0
\(23\) −0.394449 −0.0822482 −0.0411241 0.999154i \(-0.513094\pi\)
−0.0411241 + 0.999154i \(0.513094\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) −5.60555 −1.07879
\(28\) 0 0
\(29\) −4.30278 −0.799005 −0.399503 0.916732i \(-0.630817\pi\)
−0.399503 + 0.916732i \(0.630817\pi\)
\(30\) 0 0
\(31\) −8.30278 −1.49122 −0.745611 0.666381i \(-0.767842\pi\)
−0.745611 + 0.666381i \(0.767842\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) 3.60555 0.592749 0.296374 0.955072i \(-0.404222\pi\)
0.296374 + 0.955072i \(0.404222\pi\)
\(38\) 0 0
\(39\) −4.69722 −0.752158
\(40\) 0 0
\(41\) 0.302776 0.0472856 0.0236428 0.999720i \(-0.492474\pi\)
0.0236428 + 0.999720i \(0.492474\pi\)
\(42\) 0 0
\(43\) 7.21110 1.09968 0.549841 0.835269i \(-0.314688\pi\)
0.549841 + 0.835269i \(0.314688\pi\)
\(44\) 0 0
\(45\) 1.30278 0.194206
\(46\) 0 0
\(47\) −7.60555 −1.10938 −0.554692 0.832056i \(-0.687164\pi\)
−0.554692 + 0.832056i \(0.687164\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 2.21110 0.309616
\(52\) 0 0
\(53\) −3.90833 −0.536850 −0.268425 0.963301i \(-0.586503\pi\)
−0.268425 + 0.963301i \(0.586503\pi\)
\(54\) 0 0
\(55\) 2.30278 0.310506
\(56\) 0 0
\(57\) 1.30278 0.172557
\(58\) 0 0
\(59\) 5.60555 0.729781 0.364890 0.931051i \(-0.381106\pi\)
0.364890 + 0.931051i \(0.381106\pi\)
\(60\) 0 0
\(61\) 8.21110 1.05132 0.525662 0.850694i \(-0.323818\pi\)
0.525662 + 0.850694i \(0.323818\pi\)
\(62\) 0 0
\(63\) 1.30278 0.164134
\(64\) 0 0
\(65\) 3.60555 0.447214
\(66\) 0 0
\(67\) −10.9083 −1.33266 −0.666332 0.745655i \(-0.732137\pi\)
−0.666332 + 0.745655i \(0.732137\pi\)
\(68\) 0 0
\(69\) −0.513878 −0.0618637
\(70\) 0 0
\(71\) 8.81665 1.04634 0.523172 0.852227i \(-0.324748\pi\)
0.523172 + 0.852227i \(0.324748\pi\)
\(72\) 0 0
\(73\) −5.90833 −0.691517 −0.345759 0.938323i \(-0.612378\pi\)
−0.345759 + 0.938323i \(0.612378\pi\)
\(74\) 0 0
\(75\) −5.21110 −0.601726
\(76\) 0 0
\(77\) 2.30278 0.262426
\(78\) 0 0
\(79\) −14.0000 −1.57512 −0.787562 0.616236i \(-0.788657\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(80\) 0 0
\(81\) −3.39445 −0.377161
\(82\) 0 0
\(83\) −10.5139 −1.15405 −0.577024 0.816727i \(-0.695786\pi\)
−0.577024 + 0.816727i \(0.695786\pi\)
\(84\) 0 0
\(85\) −1.69722 −0.184090
\(86\) 0 0
\(87\) −5.60555 −0.600978
\(88\) 0 0
\(89\) 13.8167 1.46456 0.732281 0.681002i \(-0.238456\pi\)
0.732281 + 0.681002i \(0.238456\pi\)
\(90\) 0 0
\(91\) 3.60555 0.377964
\(92\) 0 0
\(93\) −10.8167 −1.12163
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) 16.8167 1.70747 0.853736 0.520706i \(-0.174331\pi\)
0.853736 + 0.520706i \(0.174331\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) 2.39445 0.238257 0.119128 0.992879i \(-0.461990\pi\)
0.119128 + 0.992879i \(0.461990\pi\)
\(102\) 0 0
\(103\) −4.39445 −0.432998 −0.216499 0.976283i \(-0.569464\pi\)
−0.216499 + 0.976283i \(0.569464\pi\)
\(104\) 0 0
\(105\) 1.30278 0.127138
\(106\) 0 0
\(107\) 10.8167 1.04569 0.522843 0.852429i \(-0.324872\pi\)
0.522843 + 0.852429i \(0.324872\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) 4.69722 0.445841
\(112\) 0 0
\(113\) 17.1194 1.61046 0.805230 0.592962i \(-0.202042\pi\)
0.805230 + 0.592962i \(0.202042\pi\)
\(114\) 0 0
\(115\) 0.394449 0.0367825
\(116\) 0 0
\(117\) 4.69722 0.434259
\(118\) 0 0
\(119\) −1.69722 −0.155584
\(120\) 0 0
\(121\) −5.69722 −0.517929
\(122\) 0 0
\(123\) 0.394449 0.0355662
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −15.0278 −1.33350 −0.666749 0.745282i \(-0.732315\pi\)
−0.666749 + 0.745282i \(0.732315\pi\)
\(128\) 0 0
\(129\) 9.39445 0.827135
\(130\) 0 0
\(131\) −14.3028 −1.24964 −0.624820 0.780769i \(-0.714828\pi\)
−0.624820 + 0.780769i \(0.714828\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 5.60555 0.482449
\(136\) 0 0
\(137\) 0.788897 0.0674001 0.0337000 0.999432i \(-0.489271\pi\)
0.0337000 + 0.999432i \(0.489271\pi\)
\(138\) 0 0
\(139\) 4.39445 0.372732 0.186366 0.982480i \(-0.440329\pi\)
0.186366 + 0.982480i \(0.440329\pi\)
\(140\) 0 0
\(141\) −9.90833 −0.834432
\(142\) 0 0
\(143\) 8.30278 0.694313
\(144\) 0 0
\(145\) 4.30278 0.357326
\(146\) 0 0
\(147\) 1.30278 0.107451
\(148\) 0 0
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0 0
\(151\) −5.09167 −0.414354 −0.207177 0.978303i \(-0.566428\pi\)
−0.207177 + 0.978303i \(0.566428\pi\)
\(152\) 0 0
\(153\) −2.21110 −0.178757
\(154\) 0 0
\(155\) 8.30278 0.666895
\(156\) 0 0
\(157\) −2.48612 −0.198414 −0.0992071 0.995067i \(-0.531631\pi\)
−0.0992071 + 0.995067i \(0.531631\pi\)
\(158\) 0 0
\(159\) −5.09167 −0.403796
\(160\) 0 0
\(161\) 0.394449 0.0310869
\(162\) 0 0
\(163\) −0.513878 −0.0402500 −0.0201250 0.999797i \(-0.506406\pi\)
−0.0201250 + 0.999797i \(0.506406\pi\)
\(164\) 0 0
\(165\) 3.00000 0.233550
\(166\) 0 0
\(167\) −21.4222 −1.65770 −0.828850 0.559471i \(-0.811004\pi\)
−0.828850 + 0.559471i \(0.811004\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) −1.30278 −0.0996257
\(172\) 0 0
\(173\) 13.8167 1.05046 0.525230 0.850960i \(-0.323979\pi\)
0.525230 + 0.850960i \(0.323979\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) 7.30278 0.548910
\(178\) 0 0
\(179\) −8.30278 −0.620579 −0.310289 0.950642i \(-0.600426\pi\)
−0.310289 + 0.950642i \(0.600426\pi\)
\(180\) 0 0
\(181\) 5.69722 0.423471 0.211736 0.977327i \(-0.432088\pi\)
0.211736 + 0.977327i \(0.432088\pi\)
\(182\) 0 0
\(183\) 10.6972 0.790762
\(184\) 0 0
\(185\) −3.60555 −0.265085
\(186\) 0 0
\(187\) −3.90833 −0.285805
\(188\) 0 0
\(189\) 5.60555 0.407744
\(190\) 0 0
\(191\) −9.72498 −0.703675 −0.351837 0.936061i \(-0.614443\pi\)
−0.351837 + 0.936061i \(0.614443\pi\)
\(192\) 0 0
\(193\) −15.6972 −1.12991 −0.564955 0.825121i \(-0.691107\pi\)
−0.564955 + 0.825121i \(0.691107\pi\)
\(194\) 0 0
\(195\) 4.69722 0.336375
\(196\) 0 0
\(197\) 3.90833 0.278457 0.139228 0.990260i \(-0.455538\pi\)
0.139228 + 0.990260i \(0.455538\pi\)
\(198\) 0 0
\(199\) 5.60555 0.397367 0.198683 0.980064i \(-0.436333\pi\)
0.198683 + 0.980064i \(0.436333\pi\)
\(200\) 0 0
\(201\) −14.2111 −1.00237
\(202\) 0 0
\(203\) 4.30278 0.301996
\(204\) 0 0
\(205\) −0.302776 −0.0211468
\(206\) 0 0
\(207\) 0.513878 0.0357170
\(208\) 0 0
\(209\) −2.30278 −0.159286
\(210\) 0 0
\(211\) 10.6972 0.736427 0.368214 0.929741i \(-0.379969\pi\)
0.368214 + 0.929741i \(0.379969\pi\)
\(212\) 0 0
\(213\) 11.4861 0.787016
\(214\) 0 0
\(215\) −7.21110 −0.491793
\(216\) 0 0
\(217\) 8.30278 0.563629
\(218\) 0 0
\(219\) −7.69722 −0.520130
\(220\) 0 0
\(221\) −6.11943 −0.411637
\(222\) 0 0
\(223\) 8.21110 0.549856 0.274928 0.961465i \(-0.411346\pi\)
0.274928 + 0.961465i \(0.411346\pi\)
\(224\) 0 0
\(225\) 5.21110 0.347407
\(226\) 0 0
\(227\) 11.6972 0.776372 0.388186 0.921581i \(-0.373102\pi\)
0.388186 + 0.921581i \(0.373102\pi\)
\(228\) 0 0
\(229\) 3.21110 0.212196 0.106098 0.994356i \(-0.466164\pi\)
0.106098 + 0.994356i \(0.466164\pi\)
\(230\) 0 0
\(231\) 3.00000 0.197386
\(232\) 0 0
\(233\) 29.5139 1.93352 0.966759 0.255688i \(-0.0823021\pi\)
0.966759 + 0.255688i \(0.0823021\pi\)
\(234\) 0 0
\(235\) 7.60555 0.496131
\(236\) 0 0
\(237\) −18.2389 −1.18474
\(238\) 0 0
\(239\) −14.0278 −0.907380 −0.453690 0.891160i \(-0.649893\pi\)
−0.453690 + 0.891160i \(0.649893\pi\)
\(240\) 0 0
\(241\) −0.183346 −0.0118104 −0.00590518 0.999983i \(-0.501880\pi\)
−0.00590518 + 0.999983i \(0.501880\pi\)
\(242\) 0 0
\(243\) 12.3944 0.795104
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −3.60555 −0.229416
\(248\) 0 0
\(249\) −13.6972 −0.868026
\(250\) 0 0
\(251\) 26.7250 1.68687 0.843433 0.537235i \(-0.180531\pi\)
0.843433 + 0.537235i \(0.180531\pi\)
\(252\) 0 0
\(253\) 0.908327 0.0571060
\(254\) 0 0
\(255\) −2.21110 −0.138465
\(256\) 0 0
\(257\) 5.90833 0.368551 0.184276 0.982875i \(-0.441006\pi\)
0.184276 + 0.982875i \(0.441006\pi\)
\(258\) 0 0
\(259\) −3.60555 −0.224038
\(260\) 0 0
\(261\) 5.60555 0.346975
\(262\) 0 0
\(263\) −4.69722 −0.289643 −0.144822 0.989458i \(-0.546261\pi\)
−0.144822 + 0.989458i \(0.546261\pi\)
\(264\) 0 0
\(265\) 3.90833 0.240087
\(266\) 0 0
\(267\) 18.0000 1.10158
\(268\) 0 0
\(269\) −2.51388 −0.153274 −0.0766369 0.997059i \(-0.524418\pi\)
−0.0766369 + 0.997059i \(0.524418\pi\)
\(270\) 0 0
\(271\) −5.09167 −0.309297 −0.154649 0.987970i \(-0.549425\pi\)
−0.154649 + 0.987970i \(0.549425\pi\)
\(272\) 0 0
\(273\) 4.69722 0.284289
\(274\) 0 0
\(275\) 9.21110 0.555450
\(276\) 0 0
\(277\) −27.8167 −1.67134 −0.835670 0.549231i \(-0.814921\pi\)
−0.835670 + 0.549231i \(0.814921\pi\)
\(278\) 0 0
\(279\) 10.8167 0.647576
\(280\) 0 0
\(281\) 19.4222 1.15863 0.579316 0.815103i \(-0.303320\pi\)
0.579316 + 0.815103i \(0.303320\pi\)
\(282\) 0 0
\(283\) 22.5139 1.33831 0.669156 0.743122i \(-0.266656\pi\)
0.669156 + 0.743122i \(0.266656\pi\)
\(284\) 0 0
\(285\) −1.30278 −0.0771698
\(286\) 0 0
\(287\) −0.302776 −0.0178723
\(288\) 0 0
\(289\) −14.1194 −0.830555
\(290\) 0 0
\(291\) 21.9083 1.28429
\(292\) 0 0
\(293\) 18.6333 1.08857 0.544285 0.838901i \(-0.316801\pi\)
0.544285 + 0.838901i \(0.316801\pi\)
\(294\) 0 0
\(295\) −5.60555 −0.326368
\(296\) 0 0
\(297\) 12.9083 0.749017
\(298\) 0 0
\(299\) 1.42221 0.0822482
\(300\) 0 0
\(301\) −7.21110 −0.415641
\(302\) 0 0
\(303\) 3.11943 0.179207
\(304\) 0 0
\(305\) −8.21110 −0.470166
\(306\) 0 0
\(307\) −14.1194 −0.805838 −0.402919 0.915236i \(-0.632004\pi\)
−0.402919 + 0.915236i \(0.632004\pi\)
\(308\) 0 0
\(309\) −5.72498 −0.325683
\(310\) 0 0
\(311\) 7.33053 0.415676 0.207838 0.978163i \(-0.433357\pi\)
0.207838 + 0.978163i \(0.433357\pi\)
\(312\) 0 0
\(313\) −27.8167 −1.57229 −0.786145 0.618042i \(-0.787926\pi\)
−0.786145 + 0.618042i \(0.787926\pi\)
\(314\) 0 0
\(315\) −1.30278 −0.0734031
\(316\) 0 0
\(317\) −11.2111 −0.629678 −0.314839 0.949145i \(-0.601951\pi\)
−0.314839 + 0.949145i \(0.601951\pi\)
\(318\) 0 0
\(319\) 9.90833 0.554760
\(320\) 0 0
\(321\) 14.0917 0.786520
\(322\) 0 0
\(323\) 1.69722 0.0944361
\(324\) 0 0
\(325\) 14.4222 0.800000
\(326\) 0 0
\(327\) −9.11943 −0.504306
\(328\) 0 0
\(329\) 7.60555 0.419308
\(330\) 0 0
\(331\) −9.48612 −0.521404 −0.260702 0.965419i \(-0.583954\pi\)
−0.260702 + 0.965419i \(0.583954\pi\)
\(332\) 0 0
\(333\) −4.69722 −0.257406
\(334\) 0 0
\(335\) 10.9083 0.595986
\(336\) 0 0
\(337\) −29.6972 −1.61771 −0.808855 0.588008i \(-0.799913\pi\)
−0.808855 + 0.588008i \(0.799913\pi\)
\(338\) 0 0
\(339\) 22.3028 1.21132
\(340\) 0 0
\(341\) 19.1194 1.03538
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0.513878 0.0276663
\(346\) 0 0
\(347\) −10.6972 −0.574257 −0.287129 0.957892i \(-0.592701\pi\)
−0.287129 + 0.957892i \(0.592701\pi\)
\(348\) 0 0
\(349\) 6.51388 0.348680 0.174340 0.984686i \(-0.444221\pi\)
0.174340 + 0.984686i \(0.444221\pi\)
\(350\) 0 0
\(351\) 20.2111 1.07879
\(352\) 0 0
\(353\) 1.27502 0.0678624 0.0339312 0.999424i \(-0.489197\pi\)
0.0339312 + 0.999424i \(0.489197\pi\)
\(354\) 0 0
\(355\) −8.81665 −0.467939
\(356\) 0 0
\(357\) −2.21110 −0.117024
\(358\) 0 0
\(359\) −10.3028 −0.543760 −0.271880 0.962331i \(-0.587645\pi\)
−0.271880 + 0.962331i \(0.587645\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −7.42221 −0.389565
\(364\) 0 0
\(365\) 5.90833 0.309256
\(366\) 0 0
\(367\) 18.2111 0.950612 0.475306 0.879821i \(-0.342337\pi\)
0.475306 + 0.879821i \(0.342337\pi\)
\(368\) 0 0
\(369\) −0.394449 −0.0205342
\(370\) 0 0
\(371\) 3.90833 0.202910
\(372\) 0 0
\(373\) 19.9083 1.03081 0.515407 0.856945i \(-0.327641\pi\)
0.515407 + 0.856945i \(0.327641\pi\)
\(374\) 0 0
\(375\) 11.7250 0.605475
\(376\) 0 0
\(377\) 15.5139 0.799005
\(378\) 0 0
\(379\) 21.4222 1.10038 0.550192 0.835038i \(-0.314554\pi\)
0.550192 + 0.835038i \(0.314554\pi\)
\(380\) 0 0
\(381\) −19.5778 −1.00300
\(382\) 0 0
\(383\) −32.4500 −1.65812 −0.829058 0.559163i \(-0.811123\pi\)
−0.829058 + 0.559163i \(0.811123\pi\)
\(384\) 0 0
\(385\) −2.30278 −0.117360
\(386\) 0 0
\(387\) −9.39445 −0.477547
\(388\) 0 0
\(389\) −3.69722 −0.187457 −0.0937284 0.995598i \(-0.529879\pi\)
−0.0937284 + 0.995598i \(0.529879\pi\)
\(390\) 0 0
\(391\) −0.669468 −0.0338565
\(392\) 0 0
\(393\) −18.6333 −0.939926
\(394\) 0 0
\(395\) 14.0000 0.704416
\(396\) 0 0
\(397\) −4.60555 −0.231146 −0.115573 0.993299i \(-0.536870\pi\)
−0.115573 + 0.993299i \(0.536870\pi\)
\(398\) 0 0
\(399\) −1.30278 −0.0652204
\(400\) 0 0
\(401\) −12.9083 −0.644611 −0.322306 0.946636i \(-0.604458\pi\)
−0.322306 + 0.946636i \(0.604458\pi\)
\(402\) 0 0
\(403\) 29.9361 1.49122
\(404\) 0 0
\(405\) 3.39445 0.168672
\(406\) 0 0
\(407\) −8.30278 −0.411553
\(408\) 0 0
\(409\) −38.7527 −1.91620 −0.958100 0.286435i \(-0.907530\pi\)
−0.958100 + 0.286435i \(0.907530\pi\)
\(410\) 0 0
\(411\) 1.02776 0.0506955
\(412\) 0 0
\(413\) −5.60555 −0.275831
\(414\) 0 0
\(415\) 10.5139 0.516106
\(416\) 0 0
\(417\) 5.72498 0.280354
\(418\) 0 0
\(419\) −2.81665 −0.137603 −0.0688013 0.997630i \(-0.521917\pi\)
−0.0688013 + 0.997630i \(0.521917\pi\)
\(420\) 0 0
\(421\) −15.1833 −0.739991 −0.369996 0.929034i \(-0.620641\pi\)
−0.369996 + 0.929034i \(0.620641\pi\)
\(422\) 0 0
\(423\) 9.90833 0.481759
\(424\) 0 0
\(425\) −6.78890 −0.329310
\(426\) 0 0
\(427\) −8.21110 −0.397363
\(428\) 0 0
\(429\) 10.8167 0.522233
\(430\) 0 0
\(431\) −36.4222 −1.75440 −0.877198 0.480129i \(-0.840590\pi\)
−0.877198 + 0.480129i \(0.840590\pi\)
\(432\) 0 0
\(433\) 7.78890 0.374311 0.187155 0.982330i \(-0.440073\pi\)
0.187155 + 0.982330i \(0.440073\pi\)
\(434\) 0 0
\(435\) 5.60555 0.268766
\(436\) 0 0
\(437\) −0.394449 −0.0188690
\(438\) 0 0
\(439\) 5.21110 0.248712 0.124356 0.992238i \(-0.460313\pi\)
0.124356 + 0.992238i \(0.460313\pi\)
\(440\) 0 0
\(441\) −1.30278 −0.0620369
\(442\) 0 0
\(443\) 14.0917 0.669516 0.334758 0.942304i \(-0.391345\pi\)
0.334758 + 0.942304i \(0.391345\pi\)
\(444\) 0 0
\(445\) −13.8167 −0.654972
\(446\) 0 0
\(447\) 3.90833 0.184858
\(448\) 0 0
\(449\) −17.1194 −0.807916 −0.403958 0.914778i \(-0.632366\pi\)
−0.403958 + 0.914778i \(0.632366\pi\)
\(450\) 0 0
\(451\) −0.697224 −0.0328310
\(452\) 0 0
\(453\) −6.63331 −0.311660
\(454\) 0 0
\(455\) −3.60555 −0.169031
\(456\) 0 0
\(457\) −24.9361 −1.16646 −0.583230 0.812307i \(-0.698212\pi\)
−0.583230 + 0.812307i \(0.698212\pi\)
\(458\) 0 0
\(459\) −9.51388 −0.444070
\(460\) 0 0
\(461\) 15.1194 0.704182 0.352091 0.935966i \(-0.385471\pi\)
0.352091 + 0.935966i \(0.385471\pi\)
\(462\) 0 0
\(463\) −12.2111 −0.567498 −0.283749 0.958899i \(-0.591578\pi\)
−0.283749 + 0.958899i \(0.591578\pi\)
\(464\) 0 0
\(465\) 10.8167 0.501610
\(466\) 0 0
\(467\) −29.1194 −1.34749 −0.673743 0.738966i \(-0.735315\pi\)
−0.673743 + 0.738966i \(0.735315\pi\)
\(468\) 0 0
\(469\) 10.9083 0.503700
\(470\) 0 0
\(471\) −3.23886 −0.149239
\(472\) 0 0
\(473\) −16.6056 −0.763524
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 5.09167 0.233132
\(478\) 0 0
\(479\) 10.3028 0.470746 0.235373 0.971905i \(-0.424369\pi\)
0.235373 + 0.971905i \(0.424369\pi\)
\(480\) 0 0
\(481\) −13.0000 −0.592749
\(482\) 0 0
\(483\) 0.513878 0.0233823
\(484\) 0 0
\(485\) −16.8167 −0.763605
\(486\) 0 0
\(487\) −37.2389 −1.68745 −0.843727 0.536773i \(-0.819643\pi\)
−0.843727 + 0.536773i \(0.819643\pi\)
\(488\) 0 0
\(489\) −0.669468 −0.0302744
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) −7.30278 −0.328900
\(494\) 0 0
\(495\) −3.00000 −0.134840
\(496\) 0 0
\(497\) −8.81665 −0.395481
\(498\) 0 0
\(499\) −18.3305 −0.820587 −0.410294 0.911953i \(-0.634574\pi\)
−0.410294 + 0.911953i \(0.634574\pi\)
\(500\) 0 0
\(501\) −27.9083 −1.24685
\(502\) 0 0
\(503\) 24.8444 1.10776 0.553879 0.832597i \(-0.313147\pi\)
0.553879 + 0.832597i \(0.313147\pi\)
\(504\) 0 0
\(505\) −2.39445 −0.106552
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.78890 −0.389561 −0.194781 0.980847i \(-0.562399\pi\)
−0.194781 + 0.980847i \(0.562399\pi\)
\(510\) 0 0
\(511\) 5.90833 0.261369
\(512\) 0 0
\(513\) −5.60555 −0.247491
\(514\) 0 0
\(515\) 4.39445 0.193643
\(516\) 0 0
\(517\) 17.5139 0.770259
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) −13.4222 −0.588037 −0.294019 0.955800i \(-0.594993\pi\)
−0.294019 + 0.955800i \(0.594993\pi\)
\(522\) 0 0
\(523\) 5.42221 0.237096 0.118548 0.992948i \(-0.462176\pi\)
0.118548 + 0.992948i \(0.462176\pi\)
\(524\) 0 0
\(525\) 5.21110 0.227431
\(526\) 0 0
\(527\) −14.0917 −0.613843
\(528\) 0 0
\(529\) −22.8444 −0.993235
\(530\) 0 0
\(531\) −7.30278 −0.316913
\(532\) 0 0
\(533\) −1.09167 −0.0472856
\(534\) 0 0
\(535\) −10.8167 −0.467645
\(536\) 0 0
\(537\) −10.8167 −0.466773
\(538\) 0 0
\(539\) −2.30278 −0.0991876
\(540\) 0 0
\(541\) −39.2111 −1.68582 −0.842908 0.538057i \(-0.819159\pi\)
−0.842908 + 0.538057i \(0.819159\pi\)
\(542\) 0 0
\(543\) 7.42221 0.318517
\(544\) 0 0
\(545\) 7.00000 0.299847
\(546\) 0 0
\(547\) −6.51388 −0.278513 −0.139257 0.990256i \(-0.544471\pi\)
−0.139257 + 0.990256i \(0.544471\pi\)
\(548\) 0 0
\(549\) −10.6972 −0.456546
\(550\) 0 0
\(551\) −4.30278 −0.183304
\(552\) 0 0
\(553\) 14.0000 0.595341
\(554\) 0 0
\(555\) −4.69722 −0.199386
\(556\) 0 0
\(557\) 35.7527 1.51489 0.757446 0.652898i \(-0.226447\pi\)
0.757446 + 0.652898i \(0.226447\pi\)
\(558\) 0 0
\(559\) −26.0000 −1.09968
\(560\) 0 0
\(561\) −5.09167 −0.214971
\(562\) 0 0
\(563\) −20.0278 −0.844069 −0.422035 0.906580i \(-0.638684\pi\)
−0.422035 + 0.906580i \(0.638684\pi\)
\(564\) 0 0
\(565\) −17.1194 −0.720220
\(566\) 0 0
\(567\) 3.39445 0.142553
\(568\) 0 0
\(569\) −14.0278 −0.588074 −0.294037 0.955794i \(-0.594999\pi\)
−0.294037 + 0.955794i \(0.594999\pi\)
\(570\) 0 0
\(571\) −17.7889 −0.744442 −0.372221 0.928144i \(-0.621404\pi\)
−0.372221 + 0.928144i \(0.621404\pi\)
\(572\) 0 0
\(573\) −12.6695 −0.529275
\(574\) 0 0
\(575\) 1.57779 0.0657986
\(576\) 0 0
\(577\) 3.72498 0.155073 0.0775365 0.996990i \(-0.475295\pi\)
0.0775365 + 0.996990i \(0.475295\pi\)
\(578\) 0 0
\(579\) −20.4500 −0.849871
\(580\) 0 0
\(581\) 10.5139 0.436189
\(582\) 0 0
\(583\) 9.00000 0.372742
\(584\) 0 0
\(585\) −4.69722 −0.194206
\(586\) 0 0
\(587\) −9.63331 −0.397609 −0.198805 0.980039i \(-0.563706\pi\)
−0.198805 + 0.980039i \(0.563706\pi\)
\(588\) 0 0
\(589\) −8.30278 −0.342110
\(590\) 0 0
\(591\) 5.09167 0.209443
\(592\) 0 0
\(593\) 23.1833 0.952026 0.476013 0.879438i \(-0.342082\pi\)
0.476013 + 0.879438i \(0.342082\pi\)
\(594\) 0 0
\(595\) 1.69722 0.0695794
\(596\) 0 0
\(597\) 7.30278 0.298883
\(598\) 0 0
\(599\) 14.3305 0.585530 0.292765 0.956184i \(-0.405425\pi\)
0.292765 + 0.956184i \(0.405425\pi\)
\(600\) 0 0
\(601\) 30.1472 1.22973 0.614865 0.788633i \(-0.289211\pi\)
0.614865 + 0.788633i \(0.289211\pi\)
\(602\) 0 0
\(603\) 14.2111 0.578721
\(604\) 0 0
\(605\) 5.69722 0.231625
\(606\) 0 0
\(607\) −8.81665 −0.357857 −0.178928 0.983862i \(-0.557263\pi\)
−0.178928 + 0.983862i \(0.557263\pi\)
\(608\) 0 0
\(609\) 5.60555 0.227148
\(610\) 0 0
\(611\) 27.4222 1.10938
\(612\) 0 0
\(613\) 39.3583 1.58967 0.794833 0.606828i \(-0.207558\pi\)
0.794833 + 0.606828i \(0.207558\pi\)
\(614\) 0 0
\(615\) −0.394449 −0.0159057
\(616\) 0 0
\(617\) −42.5416 −1.71266 −0.856331 0.516428i \(-0.827262\pi\)
−0.856331 + 0.516428i \(0.827262\pi\)
\(618\) 0 0
\(619\) −46.5694 −1.87178 −0.935891 0.352290i \(-0.885403\pi\)
−0.935891 + 0.352290i \(0.885403\pi\)
\(620\) 0 0
\(621\) 2.21110 0.0887285
\(622\) 0 0
\(623\) −13.8167 −0.553553
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) −3.00000 −0.119808
\(628\) 0 0
\(629\) 6.11943 0.243998
\(630\) 0 0
\(631\) −8.21110 −0.326879 −0.163439 0.986553i \(-0.552259\pi\)
−0.163439 + 0.986553i \(0.552259\pi\)
\(632\) 0 0
\(633\) 13.9361 0.553910
\(634\) 0 0
\(635\) 15.0278 0.596358
\(636\) 0 0
\(637\) −3.60555 −0.142857
\(638\) 0 0
\(639\) −11.4861 −0.454384
\(640\) 0 0
\(641\) −40.3028 −1.59186 −0.795932 0.605386i \(-0.793019\pi\)
−0.795932 + 0.605386i \(0.793019\pi\)
\(642\) 0 0
\(643\) 14.5778 0.574892 0.287446 0.957797i \(-0.407194\pi\)
0.287446 + 0.957797i \(0.407194\pi\)
\(644\) 0 0
\(645\) −9.39445 −0.369906
\(646\) 0 0
\(647\) −0.816654 −0.0321060 −0.0160530 0.999871i \(-0.505110\pi\)
−0.0160530 + 0.999871i \(0.505110\pi\)
\(648\) 0 0
\(649\) −12.9083 −0.506696
\(650\) 0 0
\(651\) 10.8167 0.423938
\(652\) 0 0
\(653\) −24.0278 −0.940279 −0.470139 0.882592i \(-0.655796\pi\)
−0.470139 + 0.882592i \(0.655796\pi\)
\(654\) 0 0
\(655\) 14.3028 0.558856
\(656\) 0 0
\(657\) 7.69722 0.300297
\(658\) 0 0
\(659\) 6.90833 0.269110 0.134555 0.990906i \(-0.457039\pi\)
0.134555 + 0.990906i \(0.457039\pi\)
\(660\) 0 0
\(661\) −16.7889 −0.653012 −0.326506 0.945195i \(-0.605871\pi\)
−0.326506 + 0.945195i \(0.605871\pi\)
\(662\) 0 0
\(663\) −7.97224 −0.309616
\(664\) 0 0
\(665\) 1.00000 0.0387783
\(666\) 0 0
\(667\) 1.69722 0.0657168
\(668\) 0 0
\(669\) 10.6972 0.413579
\(670\) 0 0
\(671\) −18.9083 −0.729948
\(672\) 0 0
\(673\) −31.7250 −1.22291 −0.611454 0.791280i \(-0.709415\pi\)
−0.611454 + 0.791280i \(0.709415\pi\)
\(674\) 0 0
\(675\) 22.4222 0.863031
\(676\) 0 0
\(677\) 17.4861 0.672046 0.336023 0.941854i \(-0.390918\pi\)
0.336023 + 0.941854i \(0.390918\pi\)
\(678\) 0 0
\(679\) −16.8167 −0.645364
\(680\) 0 0
\(681\) 15.2389 0.583954
\(682\) 0 0
\(683\) −21.2389 −0.812682 −0.406341 0.913721i \(-0.633196\pi\)
−0.406341 + 0.913721i \(0.633196\pi\)
\(684\) 0 0
\(685\) −0.788897 −0.0301422
\(686\) 0 0
\(687\) 4.18335 0.159605
\(688\) 0 0
\(689\) 14.0917 0.536850
\(690\) 0 0
\(691\) −5.39445 −0.205215 −0.102607 0.994722i \(-0.532718\pi\)
−0.102607 + 0.994722i \(0.532718\pi\)
\(692\) 0 0
\(693\) −3.00000 −0.113961
\(694\) 0 0
\(695\) −4.39445 −0.166691
\(696\) 0 0
\(697\) 0.513878 0.0194645
\(698\) 0 0
\(699\) 38.4500 1.45431
\(700\) 0 0
\(701\) −27.6333 −1.04370 −0.521848 0.853039i \(-0.674757\pi\)
−0.521848 + 0.853039i \(0.674757\pi\)
\(702\) 0 0
\(703\) 3.60555 0.135986
\(704\) 0 0
\(705\) 9.90833 0.373169
\(706\) 0 0
\(707\) −2.39445 −0.0900525
\(708\) 0 0
\(709\) −21.2389 −0.797642 −0.398821 0.917029i \(-0.630581\pi\)
−0.398821 + 0.917029i \(0.630581\pi\)
\(710\) 0 0
\(711\) 18.2389 0.684011
\(712\) 0 0
\(713\) 3.27502 0.122650
\(714\) 0 0
\(715\) −8.30278 −0.310506
\(716\) 0 0
\(717\) −18.2750 −0.682493
\(718\) 0 0
\(719\) 23.6333 0.881374 0.440687 0.897661i \(-0.354735\pi\)
0.440687 + 0.897661i \(0.354735\pi\)
\(720\) 0 0
\(721\) 4.39445 0.163658
\(722\) 0 0
\(723\) −0.238859 −0.00888326
\(724\) 0 0
\(725\) 17.2111 0.639204
\(726\) 0 0
\(727\) −0.577795 −0.0214292 −0.0107146 0.999943i \(-0.503411\pi\)
−0.0107146 + 0.999943i \(0.503411\pi\)
\(728\) 0 0
\(729\) 26.3305 0.975205
\(730\) 0 0
\(731\) 12.2389 0.452671
\(732\) 0 0
\(733\) 52.8444 1.95185 0.975926 0.218100i \(-0.0699859\pi\)
0.975926 + 0.218100i \(0.0699859\pi\)
\(734\) 0 0
\(735\) −1.30278 −0.0480536
\(736\) 0 0
\(737\) 25.1194 0.925286
\(738\) 0 0
\(739\) −24.8167 −0.912895 −0.456448 0.889750i \(-0.650878\pi\)
−0.456448 + 0.889750i \(0.650878\pi\)
\(740\) 0 0
\(741\) −4.69722 −0.172557
\(742\) 0 0
\(743\) 23.2389 0.852551 0.426276 0.904593i \(-0.359825\pi\)
0.426276 + 0.904593i \(0.359825\pi\)
\(744\) 0 0
\(745\) −3.00000 −0.109911
\(746\) 0 0
\(747\) 13.6972 0.501155
\(748\) 0 0
\(749\) −10.8167 −0.395232
\(750\) 0 0
\(751\) −42.1472 −1.53797 −0.768986 0.639265i \(-0.779239\pi\)
−0.768986 + 0.639265i \(0.779239\pi\)
\(752\) 0 0
\(753\) 34.8167 1.26879
\(754\) 0 0
\(755\) 5.09167 0.185305
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 0 0
\(759\) 1.18335 0.0429527
\(760\) 0 0
\(761\) 3.00000 0.108750 0.0543750 0.998521i \(-0.482683\pi\)
0.0543750 + 0.998521i \(0.482683\pi\)
\(762\) 0 0
\(763\) 7.00000 0.253417
\(764\) 0 0
\(765\) 2.21110 0.0799426
\(766\) 0 0
\(767\) −20.2111 −0.729781
\(768\) 0 0
\(769\) 26.7889 0.966032 0.483016 0.875611i \(-0.339541\pi\)
0.483016 + 0.875611i \(0.339541\pi\)
\(770\) 0 0
\(771\) 7.69722 0.277209
\(772\) 0 0
\(773\) 27.8167 1.00050 0.500248 0.865882i \(-0.333242\pi\)
0.500248 + 0.865882i \(0.333242\pi\)
\(774\) 0 0
\(775\) 33.2111 1.19298
\(776\) 0 0
\(777\) −4.69722 −0.168512
\(778\) 0 0
\(779\) 0.302776 0.0108481
\(780\) 0 0
\(781\) −20.3028 −0.726490
\(782\) 0 0
\(783\) 24.1194 0.861958
\(784\) 0 0
\(785\) 2.48612 0.0887335
\(786\) 0 0
\(787\) 11.6333 0.414683 0.207341 0.978269i \(-0.433519\pi\)
0.207341 + 0.978269i \(0.433519\pi\)
\(788\) 0 0
\(789\) −6.11943 −0.217857
\(790\) 0 0
\(791\) −17.1194 −0.608697
\(792\) 0 0
\(793\) −29.6056 −1.05132
\(794\) 0 0
\(795\) 5.09167 0.180583
\(796\) 0 0
\(797\) −38.7250 −1.37171 −0.685855 0.727739i \(-0.740571\pi\)
−0.685855 + 0.727739i \(0.740571\pi\)
\(798\) 0 0
\(799\) −12.9083 −0.456664
\(800\) 0 0
\(801\) −18.0000 −0.635999
\(802\) 0 0
\(803\) 13.6056 0.480129
\(804\) 0 0
\(805\) −0.394449 −0.0139025
\(806\) 0 0
\(807\) −3.27502 −0.115286
\(808\) 0 0
\(809\) −11.1833 −0.393186 −0.196593 0.980485i \(-0.562988\pi\)
−0.196593 + 0.980485i \(0.562988\pi\)
\(810\) 0 0
\(811\) −24.4222 −0.857580 −0.428790 0.903404i \(-0.641060\pi\)
−0.428790 + 0.903404i \(0.641060\pi\)
\(812\) 0 0
\(813\) −6.63331 −0.232640
\(814\) 0 0
\(815\) 0.513878 0.0180004
\(816\) 0 0
\(817\) 7.21110 0.252285
\(818\) 0 0
\(819\) −4.69722 −0.164134
\(820\) 0 0
\(821\) 47.6333 1.66241 0.831207 0.555963i \(-0.187650\pi\)
0.831207 + 0.555963i \(0.187650\pi\)
\(822\) 0 0
\(823\) −6.23886 −0.217473 −0.108736 0.994071i \(-0.534680\pi\)
−0.108736 + 0.994071i \(0.534680\pi\)
\(824\) 0 0
\(825\) 12.0000 0.417786
\(826\) 0 0
\(827\) −9.60555 −0.334018 −0.167009 0.985955i \(-0.553411\pi\)
−0.167009 + 0.985955i \(0.553411\pi\)
\(828\) 0 0
\(829\) −42.0555 −1.46065 −0.730324 0.683101i \(-0.760631\pi\)
−0.730324 + 0.683101i \(0.760631\pi\)
\(830\) 0 0
\(831\) −36.2389 −1.25711
\(832\) 0 0
\(833\) 1.69722 0.0588053
\(834\) 0 0
\(835\) 21.4222 0.741346
\(836\) 0 0
\(837\) 46.5416 1.60871
\(838\) 0 0
\(839\) −8.36669 −0.288850 −0.144425 0.989516i \(-0.546133\pi\)
−0.144425 + 0.989516i \(0.546133\pi\)
\(840\) 0 0
\(841\) −10.4861 −0.361590
\(842\) 0 0
\(843\) 25.3028 0.871474
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 5.69722 0.195759
\(848\) 0 0
\(849\) 29.3305 1.00662
\(850\) 0 0
\(851\) −1.42221 −0.0487526
\(852\) 0 0
\(853\) 7.48612 0.256320 0.128160 0.991754i \(-0.459093\pi\)
0.128160 + 0.991754i \(0.459093\pi\)
\(854\) 0 0
\(855\) 1.30278 0.0445540
\(856\) 0 0
\(857\) 39.7527 1.35793 0.678964 0.734172i \(-0.262429\pi\)
0.678964 + 0.734172i \(0.262429\pi\)
\(858\) 0 0
\(859\) 35.7527 1.21987 0.609934 0.792452i \(-0.291196\pi\)
0.609934 + 0.792452i \(0.291196\pi\)
\(860\) 0 0
\(861\) −0.394449 −0.0134428
\(862\) 0 0
\(863\) −50.5139 −1.71951 −0.859756 0.510705i \(-0.829385\pi\)
−0.859756 + 0.510705i \(0.829385\pi\)
\(864\) 0 0
\(865\) −13.8167 −0.469780
\(866\) 0 0
\(867\) −18.3944 −0.624708
\(868\) 0 0
\(869\) 32.2389 1.09363
\(870\) 0 0
\(871\) 39.3305 1.33266
\(872\) 0 0
\(873\) −21.9083 −0.741485
\(874\) 0 0
\(875\) −9.00000 −0.304256
\(876\) 0 0
\(877\) 51.8722 1.75160 0.875799 0.482675i \(-0.160335\pi\)
0.875799 + 0.482675i \(0.160335\pi\)
\(878\) 0 0
\(879\) 24.2750 0.818776
\(880\) 0 0
\(881\) −29.9638 −1.00951 −0.504754 0.863263i \(-0.668417\pi\)
−0.504754 + 0.863263i \(0.668417\pi\)
\(882\) 0 0
\(883\) 35.6611 1.20009 0.600045 0.799966i \(-0.295149\pi\)
0.600045 + 0.799966i \(0.295149\pi\)
\(884\) 0 0
\(885\) −7.30278 −0.245480
\(886\) 0 0
\(887\) −37.7889 −1.26883 −0.634413 0.772994i \(-0.718758\pi\)
−0.634413 + 0.772994i \(0.718758\pi\)
\(888\) 0 0
\(889\) 15.0278 0.504015
\(890\) 0 0
\(891\) 7.81665 0.261868
\(892\) 0 0
\(893\) −7.60555 −0.254510
\(894\) 0 0
\(895\) 8.30278 0.277531
\(896\) 0 0
\(897\) 1.85281 0.0618637
\(898\) 0 0
\(899\) 35.7250 1.19149
\(900\) 0 0
\(901\) −6.63331 −0.220988
\(902\) 0 0
\(903\) −9.39445 −0.312628
\(904\) 0 0
\(905\) −5.69722 −0.189382
\(906\) 0 0
\(907\) 0.577795 0.0191854 0.00959268 0.999954i \(-0.496947\pi\)
0.00959268 + 0.999954i \(0.496947\pi\)
\(908\) 0 0
\(909\) −3.11943 −0.103465
\(910\) 0 0
\(911\) 12.7889 0.423715 0.211858 0.977301i \(-0.432049\pi\)
0.211858 + 0.977301i \(0.432049\pi\)
\(912\) 0 0
\(913\) 24.2111 0.801271
\(914\) 0 0
\(915\) −10.6972 −0.353639
\(916\) 0 0
\(917\) 14.3028 0.472319
\(918\) 0 0
\(919\) −3.84441 −0.126815 −0.0634077 0.997988i \(-0.520197\pi\)
−0.0634077 + 0.997988i \(0.520197\pi\)
\(920\) 0 0
\(921\) −18.3944 −0.606118
\(922\) 0 0
\(923\) −31.7889 −1.04634
\(924\) 0 0
\(925\) −14.4222 −0.474199
\(926\) 0 0
\(927\) 5.72498 0.188033
\(928\) 0 0
\(929\) 17.3028 0.567686 0.283843 0.958871i \(-0.408391\pi\)
0.283843 + 0.958871i \(0.408391\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 9.55004 0.312654
\(934\) 0 0
\(935\) 3.90833 0.127816
\(936\) 0 0
\(937\) −9.93608 −0.324598 −0.162299 0.986742i \(-0.551891\pi\)
−0.162299 + 0.986742i \(0.551891\pi\)
\(938\) 0 0
\(939\) −36.2389 −1.18261
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 0 0
\(943\) −0.119429 −0.00388916
\(944\) 0 0
\(945\) −5.60555 −0.182349
\(946\) 0 0
\(947\) −14.5139 −0.471638 −0.235819 0.971797i \(-0.575777\pi\)
−0.235819 + 0.971797i \(0.575777\pi\)
\(948\) 0 0
\(949\) 21.3028 0.691517
\(950\) 0 0
\(951\) −14.6056 −0.473617
\(952\) 0 0
\(953\) 42.1194 1.36438 0.682191 0.731174i \(-0.261027\pi\)
0.682191 + 0.731174i \(0.261027\pi\)
\(954\) 0 0
\(955\) 9.72498 0.314693
\(956\) 0 0
\(957\) 12.9083 0.417267
\(958\) 0 0
\(959\) −0.788897 −0.0254748
\(960\) 0 0
\(961\) 37.9361 1.22374
\(962\) 0 0
\(963\) −14.0917 −0.454098
\(964\) 0 0
\(965\) 15.6972 0.505312
\(966\) 0 0
\(967\) −6.48612 −0.208580 −0.104290 0.994547i \(-0.533257\pi\)
−0.104290 + 0.994547i \(0.533257\pi\)
\(968\) 0 0
\(969\) 2.21110 0.0710308
\(970\) 0 0
\(971\) 4.81665 0.154574 0.0772869 0.997009i \(-0.475374\pi\)
0.0772869 + 0.997009i \(0.475374\pi\)
\(972\) 0 0
\(973\) −4.39445 −0.140880
\(974\) 0 0
\(975\) 18.7889 0.601726
\(976\) 0 0
\(977\) 34.6056 1.10713 0.553565 0.832806i \(-0.313267\pi\)
0.553565 + 0.832806i \(0.313267\pi\)
\(978\) 0 0
\(979\) −31.8167 −1.01686
\(980\) 0 0
\(981\) 9.11943 0.291161
\(982\) 0 0
\(983\) −43.6611 −1.39257 −0.696286 0.717765i \(-0.745165\pi\)
−0.696286 + 0.717765i \(0.745165\pi\)
\(984\) 0 0
\(985\) −3.90833 −0.124530
\(986\) 0 0
\(987\) 9.90833 0.315386
\(988\) 0 0
\(989\) −2.84441 −0.0904470
\(990\) 0 0
\(991\) −22.2389 −0.706441 −0.353220 0.935540i \(-0.614913\pi\)
−0.353220 + 0.935540i \(0.614913\pi\)
\(992\) 0 0
\(993\) −12.3583 −0.392178
\(994\) 0 0
\(995\) −5.60555 −0.177708
\(996\) 0 0
\(997\) −13.7250 −0.434675 −0.217337 0.976097i \(-0.569737\pi\)
−0.217337 + 0.976097i \(0.569737\pi\)
\(998\) 0 0
\(999\) −20.2111 −0.639451
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 1064.2.a.b.1.2 2
3.2 odd 2 9576.2.a.bs.1.2 2
4.3 odd 2 2128.2.a.i.1.1 2
7.6 odd 2 7448.2.a.bb.1.1 2
8.3 odd 2 8512.2.a.r.1.2 2
8.5 even 2 8512.2.a.x.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.a.b.1.2 2 1.1 even 1 trivial
2128.2.a.i.1.1 2 4.3 odd 2
7448.2.a.bb.1.1 2 7.6 odd 2
8512.2.a.r.1.2 2 8.3 odd 2
8512.2.a.x.1.1 2 8.5 even 2
9576.2.a.bs.1.2 2 3.2 odd 2