Properties

Label 7220.2.a.n.1.2
Level $7220$
Weight $2$
Character 7220.1
Self dual yes
Analytic conductor $57.652$
Analytic rank $0$
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] = [7220,2,Mod(1,7220)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7220, 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("7220.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7220.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: \(57.6519902594\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 4x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 380)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.19869\) of defining polynomial
Character \(\chi\) \(=\) 7220.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.364448 q^{3} -1.00000 q^{5} +0.635552 q^{7} -2.86718 q^{9} +O(q^{10})\) \(q-0.364448 q^{3} -1.00000 q^{5} +0.635552 q^{7} -2.86718 q^{9} +1.63555 q^{11} -1.00000 q^{13} +0.364448 q^{15} -6.59607 q^{17} -0.231626 q^{21} +0.867178 q^{23} +1.00000 q^{25} +2.13828 q^{27} -9.09880 q^{29} -1.86718 q^{31} -0.596074 q^{33} -0.635552 q^{35} +0.635552 q^{37} +0.364448 q^{39} +1.90666 q^{41} +3.96052 q^{43} +2.86718 q^{45} +9.09880 q^{47} -6.59607 q^{49} +2.40393 q^{51} -9.86718 q^{53} -1.63555 q^{55} +9.09880 q^{59} +2.27110 q^{61} -1.82224 q^{63} +1.00000 q^{65} +12.4633 q^{67} -0.316041 q^{69} +2.50273 q^{71} -0.403926 q^{73} -0.364448 q^{75} +1.03948 q^{77} +10.7289 q^{79} +7.82224 q^{81} -15.8672 q^{83} +6.59607 q^{85} +3.31604 q^{87} +0.542208 q^{89} -0.635552 q^{91} +0.680489 q^{93} -7.36991 q^{97} -4.68942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} - 3 q^{5} + 2 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{3} - 3 q^{5} + 2 q^{7} + 8 q^{9} + 5 q^{11} - 3 q^{13} + q^{15} - 3 q^{17} + 16 q^{21} - 14 q^{23} + 3 q^{25} - 10 q^{27} + 6 q^{29} + 11 q^{31} + 15 q^{33} - 2 q^{35} + 2 q^{37} + q^{39} + 6 q^{41} - 5 q^{43} - 8 q^{45} - 6 q^{47} - 3 q^{49} + 24 q^{51} - 13 q^{53} - 5 q^{55} - 6 q^{59} + 7 q^{61} - 5 q^{63} + 3 q^{65} + 4 q^{67} + 15 q^{69} - 9 q^{71} - 18 q^{73} - q^{75} + 20 q^{77} + 32 q^{79} + 23 q^{81} - 31 q^{83} + 3 q^{85} - 6 q^{87} + 2 q^{89} - 2 q^{91} - 14 q^{93} + 11 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.364448 −0.210414 −0.105207 0.994450i \(-0.533551\pi\)
−0.105207 + 0.994450i \(0.533551\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.635552 0.240216 0.120108 0.992761i \(-0.461676\pi\)
0.120108 + 0.992761i \(0.461676\pi\)
\(8\) 0 0
\(9\) −2.86718 −0.955726
\(10\) 0 0
\(11\) 1.63555 0.493137 0.246569 0.969125i \(-0.420697\pi\)
0.246569 + 0.969125i \(0.420697\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 0.364448 0.0941001
\(16\) 0 0
\(17\) −6.59607 −1.59978 −0.799891 0.600145i \(-0.795110\pi\)
−0.799891 + 0.600145i \(0.795110\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) 0 0
\(21\) −0.231626 −0.0505449
\(22\) 0 0
\(23\) 0.867178 0.180819 0.0904095 0.995905i \(-0.471182\pi\)
0.0904095 + 0.995905i \(0.471182\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 2.13828 0.411512
\(28\) 0 0
\(29\) −9.09880 −1.68961 −0.844803 0.535078i \(-0.820282\pi\)
−0.844803 + 0.535078i \(0.820282\pi\)
\(30\) 0 0
\(31\) −1.86718 −0.335355 −0.167677 0.985842i \(-0.553627\pi\)
−0.167677 + 0.985842i \(0.553627\pi\)
\(32\) 0 0
\(33\) −0.596074 −0.103763
\(34\) 0 0
\(35\) −0.635552 −0.107428
\(36\) 0 0
\(37\) 0.635552 0.104484 0.0522420 0.998634i \(-0.483363\pi\)
0.0522420 + 0.998634i \(0.483363\pi\)
\(38\) 0 0
\(39\) 0.364448 0.0583584
\(40\) 0 0
\(41\) 1.90666 0.297770 0.148885 0.988855i \(-0.452432\pi\)
0.148885 + 0.988855i \(0.452432\pi\)
\(42\) 0 0
\(43\) 3.96052 0.603974 0.301987 0.953312i \(-0.402350\pi\)
0.301987 + 0.953312i \(0.402350\pi\)
\(44\) 0 0
\(45\) 2.86718 0.427414
\(46\) 0 0
\(47\) 9.09880 1.32720 0.663598 0.748089i \(-0.269028\pi\)
0.663598 + 0.748089i \(0.269028\pi\)
\(48\) 0 0
\(49\) −6.59607 −0.942296
\(50\) 0 0
\(51\) 2.40393 0.336617
\(52\) 0 0
\(53\) −9.86718 −1.35536 −0.677681 0.735356i \(-0.737015\pi\)
−0.677681 + 0.735356i \(0.737015\pi\)
\(54\) 0 0
\(55\) −1.63555 −0.220538
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.09880 1.18456 0.592282 0.805731i \(-0.298227\pi\)
0.592282 + 0.805731i \(0.298227\pi\)
\(60\) 0 0
\(61\) 2.27110 0.290785 0.145393 0.989374i \(-0.453555\pi\)
0.145393 + 0.989374i \(0.453555\pi\)
\(62\) 0 0
\(63\) −1.82224 −0.229581
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 12.4633 1.52263 0.761314 0.648383i \(-0.224554\pi\)
0.761314 + 0.648383i \(0.224554\pi\)
\(68\) 0 0
\(69\) −0.316041 −0.0380469
\(70\) 0 0
\(71\) 2.50273 0.297019 0.148510 0.988911i \(-0.452552\pi\)
0.148510 + 0.988911i \(0.452552\pi\)
\(72\) 0 0
\(73\) −0.403926 −0.0472760 −0.0236380 0.999721i \(-0.507525\pi\)
−0.0236380 + 0.999721i \(0.507525\pi\)
\(74\) 0 0
\(75\) −0.364448 −0.0420828
\(76\) 0 0
\(77\) 1.03948 0.118460
\(78\) 0 0
\(79\) 10.7289 1.20710 0.603548 0.797327i \(-0.293753\pi\)
0.603548 + 0.797327i \(0.293753\pi\)
\(80\) 0 0
\(81\) 7.82224 0.869138
\(82\) 0 0
\(83\) −15.8672 −1.74165 −0.870825 0.491594i \(-0.836414\pi\)
−0.870825 + 0.491594i \(0.836414\pi\)
\(84\) 0 0
\(85\) 6.59607 0.715445
\(86\) 0 0
\(87\) 3.31604 0.355517
\(88\) 0 0
\(89\) 0.542208 0.0574739 0.0287370 0.999587i \(-0.490851\pi\)
0.0287370 + 0.999587i \(0.490851\pi\)
\(90\) 0 0
\(91\) −0.635552 −0.0666239
\(92\) 0 0
\(93\) 0.680489 0.0705634
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −7.36991 −0.748301 −0.374150 0.927368i \(-0.622066\pi\)
−0.374150 + 0.927368i \(0.622066\pi\)
\(98\) 0 0
\(99\) −4.68942 −0.471304
\(100\) 0 0
\(101\) −9.32497 −0.927869 −0.463935 0.885869i \(-0.653563\pi\)
−0.463935 + 0.885869i \(0.653563\pi\)
\(102\) 0 0
\(103\) −10.8672 −1.07077 −0.535387 0.844607i \(-0.679834\pi\)
−0.535387 + 0.844607i \(0.679834\pi\)
\(104\) 0 0
\(105\) 0.231626 0.0226044
\(106\) 0 0
\(107\) 11.3304 1.09535 0.547677 0.836690i \(-0.315512\pi\)
0.547677 + 0.836690i \(0.315512\pi\)
\(108\) 0 0
\(109\) 13.2316 1.26736 0.633680 0.773595i \(-0.281544\pi\)
0.633680 + 0.773595i \(0.281544\pi\)
\(110\) 0 0
\(111\) −0.231626 −0.0219849
\(112\) 0 0
\(113\) 7.09334 0.667286 0.333643 0.942700i \(-0.391722\pi\)
0.333643 + 0.942700i \(0.391722\pi\)
\(114\) 0 0
\(115\) −0.867178 −0.0808647
\(116\) 0 0
\(117\) 2.86718 0.265071
\(118\) 0 0
\(119\) −4.19215 −0.384294
\(120\) 0 0
\(121\) −8.32497 −0.756815
\(122\) 0 0
\(123\) −0.694877 −0.0626550
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.2766 1.44431 0.722156 0.691731i \(-0.243151\pi\)
0.722156 + 0.691731i \(0.243151\pi\)
\(128\) 0 0
\(129\) −1.44340 −0.127085
\(130\) 0 0
\(131\) −10.6356 −0.929232 −0.464616 0.885512i \(-0.653808\pi\)
−0.464616 + 0.885512i \(0.653808\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.13828 −0.184034
\(136\) 0 0
\(137\) 3.49727 0.298792 0.149396 0.988777i \(-0.452267\pi\)
0.149396 + 0.988777i \(0.452267\pi\)
\(138\) 0 0
\(139\) 0.734355 0.0622872 0.0311436 0.999515i \(-0.490085\pi\)
0.0311436 + 0.999515i \(0.490085\pi\)
\(140\) 0 0
\(141\) −3.31604 −0.279261
\(142\) 0 0
\(143\) −1.63555 −0.136772
\(144\) 0 0
\(145\) 9.09880 0.755614
\(146\) 0 0
\(147\) 2.40393 0.198272
\(148\) 0 0
\(149\) 10.1383 0.830560 0.415280 0.909694i \(-0.363684\pi\)
0.415280 + 0.909694i \(0.363684\pi\)
\(150\) 0 0
\(151\) 2.81331 0.228944 0.114472 0.993426i \(-0.463482\pi\)
0.114472 + 0.993426i \(0.463482\pi\)
\(152\) 0 0
\(153\) 18.9121 1.52895
\(154\) 0 0
\(155\) 1.86718 0.149975
\(156\) 0 0
\(157\) 0.960522 0.0766580 0.0383290 0.999265i \(-0.487797\pi\)
0.0383290 + 0.999265i \(0.487797\pi\)
\(158\) 0 0
\(159\) 3.59607 0.285187
\(160\) 0 0
\(161\) 0.551136 0.0434356
\(162\) 0 0
\(163\) 3.13828 0.245809 0.122905 0.992418i \(-0.460779\pi\)
0.122905 + 0.992418i \(0.460779\pi\)
\(164\) 0 0
\(165\) 0.596074 0.0464043
\(166\) 0 0
\(167\) −10.6356 −0.823004 −0.411502 0.911409i \(-0.634996\pi\)
−0.411502 + 0.911409i \(0.634996\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.3699 0.940467 0.470233 0.882542i \(-0.344170\pi\)
0.470233 + 0.882542i \(0.344170\pi\)
\(174\) 0 0
\(175\) 0.635552 0.0480432
\(176\) 0 0
\(177\) −3.31604 −0.249249
\(178\) 0 0
\(179\) −0.324970 −0.0242894 −0.0121447 0.999926i \(-0.503866\pi\)
−0.0121447 + 0.999926i \(0.503866\pi\)
\(180\) 0 0
\(181\) 8.81331 0.655088 0.327544 0.944836i \(-0.393779\pi\)
0.327544 + 0.944836i \(0.393779\pi\)
\(182\) 0 0
\(183\) −0.827699 −0.0611853
\(184\) 0 0
\(185\) −0.635552 −0.0467267
\(186\) 0 0
\(187\) −10.7882 −0.788913
\(188\) 0 0
\(189\) 1.35899 0.0988519
\(190\) 0 0
\(191\) 25.1921 1.82284 0.911420 0.411478i \(-0.134987\pi\)
0.911420 + 0.411478i \(0.134987\pi\)
\(192\) 0 0
\(193\) −18.8726 −1.35848 −0.679241 0.733915i \(-0.737691\pi\)
−0.679241 + 0.733915i \(0.737691\pi\)
\(194\) 0 0
\(195\) −0.364448 −0.0260987
\(196\) 0 0
\(197\) −7.36445 −0.524695 −0.262348 0.964973i \(-0.584497\pi\)
−0.262348 + 0.964973i \(0.584497\pi\)
\(198\) 0 0
\(199\) 2.76837 0.196245 0.0981224 0.995174i \(-0.468716\pi\)
0.0981224 + 0.995174i \(0.468716\pi\)
\(200\) 0 0
\(201\) −4.54221 −0.320383
\(202\) 0 0
\(203\) −5.78276 −0.405870
\(204\) 0 0
\(205\) −1.90666 −0.133167
\(206\) 0 0
\(207\) −2.48635 −0.172813
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 16.9265 1.16527 0.582634 0.812734i \(-0.302022\pi\)
0.582634 + 0.812734i \(0.302022\pi\)
\(212\) 0 0
\(213\) −0.912115 −0.0624971
\(214\) 0 0
\(215\) −3.96052 −0.270105
\(216\) 0 0
\(217\) −1.18669 −0.0805577
\(218\) 0 0
\(219\) 0.147210 0.00994754
\(220\) 0 0
\(221\) 6.59607 0.443700
\(222\) 0 0
\(223\) 8.64101 0.578645 0.289322 0.957232i \(-0.406570\pi\)
0.289322 + 0.957232i \(0.406570\pi\)
\(224\) 0 0
\(225\) −2.86718 −0.191145
\(226\) 0 0
\(227\) 20.9265 1.38894 0.694470 0.719521i \(-0.255639\pi\)
0.694470 + 0.719521i \(0.255639\pi\)
\(228\) 0 0
\(229\) 22.3754 1.47861 0.739303 0.673373i \(-0.235155\pi\)
0.739303 + 0.673373i \(0.235155\pi\)
\(230\) 0 0
\(231\) −0.378836 −0.0249256
\(232\) 0 0
\(233\) −19.2371 −1.26026 −0.630132 0.776488i \(-0.716999\pi\)
−0.630132 + 0.776488i \(0.716999\pi\)
\(234\) 0 0
\(235\) −9.09880 −0.593540
\(236\) 0 0
\(237\) −3.91013 −0.253990
\(238\) 0 0
\(239\) −2.13282 −0.137961 −0.0689804 0.997618i \(-0.521975\pi\)
−0.0689804 + 0.997618i \(0.521975\pi\)
\(240\) 0 0
\(241\) 24.4633 1.57582 0.787908 0.615793i \(-0.211164\pi\)
0.787908 + 0.615793i \(0.211164\pi\)
\(242\) 0 0
\(243\) −9.26564 −0.594391
\(244\) 0 0
\(245\) 6.59607 0.421408
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 5.78276 0.366468
\(250\) 0 0
\(251\) 3.28003 0.207034 0.103517 0.994628i \(-0.466990\pi\)
0.103517 + 0.994628i \(0.466990\pi\)
\(252\) 0 0
\(253\) 1.41831 0.0891686
\(254\) 0 0
\(255\) −2.40393 −0.150540
\(256\) 0 0
\(257\) −7.63555 −0.476293 −0.238146 0.971229i \(-0.576540\pi\)
−0.238146 + 0.971229i \(0.576540\pi\)
\(258\) 0 0
\(259\) 0.403926 0.0250988
\(260\) 0 0
\(261\) 26.0879 1.61480
\(262\) 0 0
\(263\) 14.7289 0.908223 0.454111 0.890945i \(-0.349957\pi\)
0.454111 + 0.890945i \(0.349957\pi\)
\(264\) 0 0
\(265\) 9.86718 0.606136
\(266\) 0 0
\(267\) −0.197607 −0.0120933
\(268\) 0 0
\(269\) −13.4633 −0.820869 −0.410434 0.911890i \(-0.634623\pi\)
−0.410434 + 0.911890i \(0.634623\pi\)
\(270\) 0 0
\(271\) 3.86172 0.234583 0.117291 0.993098i \(-0.462579\pi\)
0.117291 + 0.993098i \(0.462579\pi\)
\(272\) 0 0
\(273\) 0.231626 0.0140186
\(274\) 0 0
\(275\) 1.63555 0.0986275
\(276\) 0 0
\(277\) −24.2766 −1.45864 −0.729319 0.684174i \(-0.760163\pi\)
−0.729319 + 0.684174i \(0.760163\pi\)
\(278\) 0 0
\(279\) 5.35353 0.320507
\(280\) 0 0
\(281\) 0.497270 0.0296647 0.0148323 0.999890i \(-0.495279\pi\)
0.0148323 + 0.999890i \(0.495279\pi\)
\(282\) 0 0
\(283\) −15.1581 −0.901057 −0.450529 0.892762i \(-0.648764\pi\)
−0.450529 + 0.892762i \(0.648764\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.21178 0.0715290
\(288\) 0 0
\(289\) 26.5082 1.55931
\(290\) 0 0
\(291\) 2.68595 0.157453
\(292\) 0 0
\(293\) −13.4094 −0.783385 −0.391692 0.920096i \(-0.628110\pi\)
−0.391692 + 0.920096i \(0.628110\pi\)
\(294\) 0 0
\(295\) −9.09880 −0.529753
\(296\) 0 0
\(297\) 3.49727 0.202932
\(298\) 0 0
\(299\) −0.867178 −0.0501502
\(300\) 0 0
\(301\) 2.51712 0.145084
\(302\) 0 0
\(303\) 3.39847 0.195237
\(304\) 0 0
\(305\) −2.27110 −0.130043
\(306\) 0 0
\(307\) 32.2065 1.83812 0.919062 0.394113i \(-0.128948\pi\)
0.919062 + 0.394113i \(0.128948\pi\)
\(308\) 0 0
\(309\) 3.96052 0.225306
\(310\) 0 0
\(311\) 12.3699 0.701433 0.350717 0.936482i \(-0.385938\pi\)
0.350717 + 0.936482i \(0.385938\pi\)
\(312\) 0 0
\(313\) 24.7882 1.40111 0.700557 0.713597i \(-0.252935\pi\)
0.700557 + 0.713597i \(0.252935\pi\)
\(314\) 0 0
\(315\) 1.82224 0.102672
\(316\) 0 0
\(317\) 7.31058 0.410603 0.205302 0.978699i \(-0.434182\pi\)
0.205302 + 0.978699i \(0.434182\pi\)
\(318\) 0 0
\(319\) −14.8816 −0.833208
\(320\) 0 0
\(321\) −4.12935 −0.230478
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) −4.82224 −0.266670
\(328\) 0 0
\(329\) 5.78276 0.318814
\(330\) 0 0
\(331\) 18.4722 1.01532 0.507661 0.861557i \(-0.330510\pi\)
0.507661 + 0.861557i \(0.330510\pi\)
\(332\) 0 0
\(333\) −1.82224 −0.0998582
\(334\) 0 0
\(335\) −12.4633 −0.680940
\(336\) 0 0
\(337\) 30.4633 1.65944 0.829720 0.558181i \(-0.188500\pi\)
0.829720 + 0.558181i \(0.188500\pi\)
\(338\) 0 0
\(339\) −2.58516 −0.140406
\(340\) 0 0
\(341\) −3.05387 −0.165376
\(342\) 0 0
\(343\) −8.64101 −0.466571
\(344\) 0 0
\(345\) 0.316041 0.0170151
\(346\) 0 0
\(347\) 23.3215 1.25196 0.625982 0.779838i \(-0.284698\pi\)
0.625982 + 0.779838i \(0.284698\pi\)
\(348\) 0 0
\(349\) −17.6894 −0.946893 −0.473446 0.880823i \(-0.656990\pi\)
−0.473446 + 0.880823i \(0.656990\pi\)
\(350\) 0 0
\(351\) −2.13828 −0.114133
\(352\) 0 0
\(353\) −7.13828 −0.379932 −0.189966 0.981791i \(-0.560838\pi\)
−0.189966 + 0.981791i \(0.560838\pi\)
\(354\) 0 0
\(355\) −2.50273 −0.132831
\(356\) 0 0
\(357\) 1.52782 0.0808608
\(358\) 0 0
\(359\) −30.1437 −1.59093 −0.795463 0.606002i \(-0.792772\pi\)
−0.795463 + 0.606002i \(0.792772\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 3.03402 0.159245
\(364\) 0 0
\(365\) 0.403926 0.0211425
\(366\) 0 0
\(367\) −30.2031 −1.57659 −0.788294 0.615299i \(-0.789035\pi\)
−0.788294 + 0.615299i \(0.789035\pi\)
\(368\) 0 0
\(369\) −5.46672 −0.284586
\(370\) 0 0
\(371\) −6.27110 −0.325579
\(372\) 0 0
\(373\) 29.0449 1.50389 0.751945 0.659226i \(-0.229116\pi\)
0.751945 + 0.659226i \(0.229116\pi\)
\(374\) 0 0
\(375\) 0.364448 0.0188200
\(376\) 0 0
\(377\) 9.09880 0.468612
\(378\) 0 0
\(379\) 2.76837 0.142202 0.0711009 0.997469i \(-0.477349\pi\)
0.0711009 + 0.997469i \(0.477349\pi\)
\(380\) 0 0
\(381\) −5.93196 −0.303904
\(382\) 0 0
\(383\) 26.6105 1.35973 0.679866 0.733337i \(-0.262038\pi\)
0.679866 + 0.733337i \(0.262038\pi\)
\(384\) 0 0
\(385\) −1.03948 −0.0529767
\(386\) 0 0
\(387\) −11.3555 −0.577233
\(388\) 0 0
\(389\) −5.55660 −0.281731 −0.140865 0.990029i \(-0.544988\pi\)
−0.140865 + 0.990029i \(0.544988\pi\)
\(390\) 0 0
\(391\) −5.71997 −0.289271
\(392\) 0 0
\(393\) 3.87611 0.195524
\(394\) 0 0
\(395\) −10.7289 −0.539829
\(396\) 0 0
\(397\) 2.71451 0.136237 0.0681186 0.997677i \(-0.478300\pi\)
0.0681186 + 0.997677i \(0.478300\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.8816 −0.892963 −0.446481 0.894793i \(-0.647323\pi\)
−0.446481 + 0.894793i \(0.647323\pi\)
\(402\) 0 0
\(403\) 1.86718 0.0930107
\(404\) 0 0
\(405\) −7.82224 −0.388690
\(406\) 0 0
\(407\) 1.03948 0.0515250
\(408\) 0 0
\(409\) 26.3250 1.30169 0.650843 0.759212i \(-0.274416\pi\)
0.650843 + 0.759212i \(0.274416\pi\)
\(410\) 0 0
\(411\) −1.27457 −0.0628701
\(412\) 0 0
\(413\) 5.78276 0.284551
\(414\) 0 0
\(415\) 15.8672 0.778889
\(416\) 0 0
\(417\) −0.267634 −0.0131061
\(418\) 0 0
\(419\) 15.3250 0.748674 0.374337 0.927293i \(-0.377870\pi\)
0.374337 + 0.927293i \(0.377870\pi\)
\(420\) 0 0
\(421\) 21.8332 1.06408 0.532042 0.846718i \(-0.321425\pi\)
0.532042 + 0.846718i \(0.321425\pi\)
\(422\) 0 0
\(423\) −26.0879 −1.26844
\(424\) 0 0
\(425\) −6.59607 −0.319957
\(426\) 0 0
\(427\) 1.44340 0.0698512
\(428\) 0 0
\(429\) 0.596074 0.0287787
\(430\) 0 0
\(431\) 23.2855 1.12162 0.560811 0.827944i \(-0.310489\pi\)
0.560811 + 0.827944i \(0.310489\pi\)
\(432\) 0 0
\(433\) −3.90120 −0.187480 −0.0937398 0.995597i \(-0.529882\pi\)
−0.0937398 + 0.995597i \(0.529882\pi\)
\(434\) 0 0
\(435\) −3.31604 −0.158992
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −19.4776 −0.929617 −0.464808 0.885411i \(-0.653877\pi\)
−0.464808 + 0.885411i \(0.653877\pi\)
\(440\) 0 0
\(441\) 18.9121 0.900577
\(442\) 0 0
\(443\) 1.90666 0.0905880 0.0452940 0.998974i \(-0.485578\pi\)
0.0452940 + 0.998974i \(0.485578\pi\)
\(444\) 0 0
\(445\) −0.542208 −0.0257031
\(446\) 0 0
\(447\) −3.69488 −0.174762
\(448\) 0 0
\(449\) −8.05933 −0.380343 −0.190172 0.981751i \(-0.560904\pi\)
−0.190172 + 0.981751i \(0.560904\pi\)
\(450\) 0 0
\(451\) 3.11843 0.146841
\(452\) 0 0
\(453\) −1.02531 −0.0481731
\(454\) 0 0
\(455\) 0.635552 0.0297951
\(456\) 0 0
\(457\) 11.3250 0.529760 0.264880 0.964281i \(-0.414668\pi\)
0.264880 + 0.964281i \(0.414668\pi\)
\(458\) 0 0
\(459\) −14.1043 −0.658331
\(460\) 0 0
\(461\) 20.1043 0.936349 0.468174 0.883636i \(-0.344912\pi\)
0.468174 + 0.883636i \(0.344912\pi\)
\(462\) 0 0
\(463\) 1.33043 0.0618303 0.0309151 0.999522i \(-0.490158\pi\)
0.0309151 + 0.999522i \(0.490158\pi\)
\(464\) 0 0
\(465\) −0.680489 −0.0315569
\(466\) 0 0
\(467\) 10.0844 0.466651 0.233326 0.972399i \(-0.425039\pi\)
0.233326 + 0.972399i \(0.425039\pi\)
\(468\) 0 0
\(469\) 7.92104 0.365760
\(470\) 0 0
\(471\) −0.350060 −0.0161299
\(472\) 0 0
\(473\) 6.47764 0.297842
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 28.2910 1.29535
\(478\) 0 0
\(479\) 8.88157 0.405809 0.202905 0.979199i \(-0.434962\pi\)
0.202905 + 0.979199i \(0.434962\pi\)
\(480\) 0 0
\(481\) −0.635552 −0.0289787
\(482\) 0 0
\(483\) −0.200861 −0.00913947
\(484\) 0 0
\(485\) 7.36991 0.334650
\(486\) 0 0
\(487\) 5.32497 0.241297 0.120649 0.992695i \(-0.461503\pi\)
0.120649 + 0.992695i \(0.461503\pi\)
\(488\) 0 0
\(489\) −1.14374 −0.0517217
\(490\) 0 0
\(491\) −19.4094 −0.875933 −0.437967 0.898991i \(-0.644301\pi\)
−0.437967 + 0.898991i \(0.644301\pi\)
\(492\) 0 0
\(493\) 60.0164 2.70300
\(494\) 0 0
\(495\) 4.68942 0.210774
\(496\) 0 0
\(497\) 1.59061 0.0713488
\(498\) 0 0
\(499\) 11.5871 0.518712 0.259356 0.965782i \(-0.416490\pi\)
0.259356 + 0.965782i \(0.416490\pi\)
\(500\) 0 0
\(501\) 3.87611 0.173172
\(502\) 0 0
\(503\) 35.1043 1.56522 0.782611 0.622511i \(-0.213888\pi\)
0.782611 + 0.622511i \(0.213888\pi\)
\(504\) 0 0
\(505\) 9.32497 0.414956
\(506\) 0 0
\(507\) 4.37338 0.194228
\(508\) 0 0
\(509\) −15.8672 −0.703300 −0.351650 0.936131i \(-0.614379\pi\)
−0.351650 + 0.936131i \(0.614379\pi\)
\(510\) 0 0
\(511\) −0.256716 −0.0113565
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.8672 0.478865
\(516\) 0 0
\(517\) 14.8816 0.654490
\(518\) 0 0
\(519\) −4.50819 −0.197888
\(520\) 0 0
\(521\) 36.6949 1.60763 0.803816 0.594878i \(-0.202800\pi\)
0.803816 + 0.594878i \(0.202800\pi\)
\(522\) 0 0
\(523\) −31.0253 −1.35664 −0.678321 0.734766i \(-0.737292\pi\)
−0.678321 + 0.734766i \(0.737292\pi\)
\(524\) 0 0
\(525\) −0.231626 −0.0101090
\(526\) 0 0
\(527\) 12.3160 0.536495
\(528\) 0 0
\(529\) −22.2480 −0.967304
\(530\) 0 0
\(531\) −26.0879 −1.13212
\(532\) 0 0
\(533\) −1.90666 −0.0825864
\(534\) 0 0
\(535\) −11.3304 −0.489857
\(536\) 0 0
\(537\) 0.118435 0.00511083
\(538\) 0 0
\(539\) −10.7882 −0.464682
\(540\) 0 0
\(541\) −7.58715 −0.326197 −0.163098 0.986610i \(-0.552149\pi\)
−0.163098 + 0.986610i \(0.552149\pi\)
\(542\) 0 0
\(543\) −3.21199 −0.137840
\(544\) 0 0
\(545\) −13.2316 −0.566781
\(546\) 0 0
\(547\) −30.7828 −1.31618 −0.658088 0.752941i \(-0.728635\pi\)
−0.658088 + 0.752941i \(0.728635\pi\)
\(548\) 0 0
\(549\) −6.51166 −0.277911
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 6.81877 0.289964
\(554\) 0 0
\(555\) 0.231626 0.00983196
\(556\) 0 0
\(557\) 31.0737 1.31664 0.658318 0.752740i \(-0.271268\pi\)
0.658318 + 0.752740i \(0.271268\pi\)
\(558\) 0 0
\(559\) −3.96052 −0.167512
\(560\) 0 0
\(561\) 3.93175 0.165998
\(562\) 0 0
\(563\) −23.2766 −0.980990 −0.490495 0.871444i \(-0.663184\pi\)
−0.490495 + 0.871444i \(0.663184\pi\)
\(564\) 0 0
\(565\) −7.09334 −0.298419
\(566\) 0 0
\(567\) 4.97144 0.208781
\(568\) 0 0
\(569\) 24.1976 1.01442 0.507208 0.861824i \(-0.330678\pi\)
0.507208 + 0.861824i \(0.330678\pi\)
\(570\) 0 0
\(571\) 29.8475 1.24908 0.624540 0.780992i \(-0.285286\pi\)
0.624540 + 0.780992i \(0.285286\pi\)
\(572\) 0 0
\(573\) −9.18123 −0.383551
\(574\) 0 0
\(575\) 0.867178 0.0361638
\(576\) 0 0
\(577\) 33.7882 1.40662 0.703311 0.710882i \(-0.251704\pi\)
0.703311 + 0.710882i \(0.251704\pi\)
\(578\) 0 0
\(579\) 6.87810 0.285844
\(580\) 0 0
\(581\) −10.0844 −0.418372
\(582\) 0 0
\(583\) −16.1383 −0.668379
\(584\) 0 0
\(585\) −2.86718 −0.118543
\(586\) 0 0
\(587\) −30.6949 −1.26691 −0.633457 0.773778i \(-0.718364\pi\)
−0.633457 + 0.773778i \(0.718364\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 2.68396 0.110403
\(592\) 0 0
\(593\) 6.99454 0.287231 0.143616 0.989634i \(-0.454127\pi\)
0.143616 + 0.989634i \(0.454127\pi\)
\(594\) 0 0
\(595\) 4.19215 0.171861
\(596\) 0 0
\(597\) −1.00893 −0.0412927
\(598\) 0 0
\(599\) −4.53675 −0.185367 −0.0926833 0.995696i \(-0.529544\pi\)
−0.0926833 + 0.995696i \(0.529544\pi\)
\(600\) 0 0
\(601\) 16.0790 0.655874 0.327937 0.944700i \(-0.393647\pi\)
0.327937 + 0.944700i \(0.393647\pi\)
\(602\) 0 0
\(603\) −35.7344 −1.45522
\(604\) 0 0
\(605\) 8.32497 0.338458
\(606\) 0 0
\(607\) −34.0702 −1.38287 −0.691434 0.722439i \(-0.743021\pi\)
−0.691434 + 0.722439i \(0.743021\pi\)
\(608\) 0 0
\(609\) 2.10752 0.0854009
\(610\) 0 0
\(611\) −9.09880 −0.368098
\(612\) 0 0
\(613\) −39.4382 −1.59289 −0.796446 0.604709i \(-0.793289\pi\)
−0.796446 + 0.604709i \(0.793289\pi\)
\(614\) 0 0
\(615\) 0.694877 0.0280201
\(616\) 0 0
\(617\) −39.2515 −1.58020 −0.790102 0.612975i \(-0.789973\pi\)
−0.790102 + 0.612975i \(0.789973\pi\)
\(618\) 0 0
\(619\) 24.3644 0.979290 0.489645 0.871922i \(-0.337126\pi\)
0.489645 + 0.871922i \(0.337126\pi\)
\(620\) 0 0
\(621\) 1.85427 0.0744093
\(622\) 0 0
\(623\) 0.344601 0.0138062
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.19215 −0.167152
\(630\) 0 0
\(631\) −35.3898 −1.40884 −0.704422 0.709781i \(-0.748794\pi\)
−0.704422 + 0.709781i \(0.748794\pi\)
\(632\) 0 0
\(633\) −6.16883 −0.245189
\(634\) 0 0
\(635\) −16.2766 −0.645916
\(636\) 0 0
\(637\) 6.59607 0.261346
\(638\) 0 0
\(639\) −7.17577 −0.283869
\(640\) 0 0
\(641\) 35.7093 1.41043 0.705216 0.708993i \(-0.250850\pi\)
0.705216 + 0.708993i \(0.250850\pi\)
\(642\) 0 0
\(643\) 21.1097 0.832486 0.416243 0.909253i \(-0.363347\pi\)
0.416243 + 0.909253i \(0.363347\pi\)
\(644\) 0 0
\(645\) 1.44340 0.0568340
\(646\) 0 0
\(647\) 43.7058 1.71825 0.859126 0.511764i \(-0.171008\pi\)
0.859126 + 0.511764i \(0.171008\pi\)
\(648\) 0 0
\(649\) 14.8816 0.584153
\(650\) 0 0
\(651\) 0.432486 0.0169505
\(652\) 0 0
\(653\) −24.1887 −0.946576 −0.473288 0.880908i \(-0.656933\pi\)
−0.473288 + 0.880908i \(0.656933\pi\)
\(654\) 0 0
\(655\) 10.6356 0.415565
\(656\) 0 0
\(657\) 1.15813 0.0451829
\(658\) 0 0
\(659\) 33.9913 1.32411 0.662056 0.749454i \(-0.269684\pi\)
0.662056 + 0.749454i \(0.269684\pi\)
\(660\) 0 0
\(661\) 4.55660 0.177231 0.0886155 0.996066i \(-0.471756\pi\)
0.0886155 + 0.996066i \(0.471756\pi\)
\(662\) 0 0
\(663\) −2.40393 −0.0933608
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7.89028 −0.305513
\(668\) 0 0
\(669\) −3.14920 −0.121755
\(670\) 0 0
\(671\) 3.71451 0.143397
\(672\) 0 0
\(673\) −22.7487 −0.876900 −0.438450 0.898756i \(-0.644472\pi\)
−0.438450 + 0.898756i \(0.644472\pi\)
\(674\) 0 0
\(675\) 2.13828 0.0823025
\(676\) 0 0
\(677\) −15.6949 −0.603203 −0.301602 0.953434i \(-0.597521\pi\)
−0.301602 + 0.953434i \(0.597521\pi\)
\(678\) 0 0
\(679\) −4.68396 −0.179754
\(680\) 0 0
\(681\) −7.62662 −0.292253
\(682\) 0 0
\(683\) −8.82770 −0.337783 −0.168891 0.985635i \(-0.554019\pi\)
−0.168891 + 0.985635i \(0.554019\pi\)
\(684\) 0 0
\(685\) −3.49727 −0.133624
\(686\) 0 0
\(687\) −8.15466 −0.311120
\(688\) 0 0
\(689\) 9.86718 0.375910
\(690\) 0 0
\(691\) −23.0198 −0.875716 −0.437858 0.899044i \(-0.644263\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(692\) 0 0
\(693\) −2.98037 −0.113215
\(694\) 0 0
\(695\) −0.734355 −0.0278557
\(696\) 0 0
\(697\) −12.5764 −0.476367
\(698\) 0 0
\(699\) 7.01092 0.265177
\(700\) 0 0
\(701\) −9.91211 −0.374375 −0.187188 0.982324i \(-0.559937\pi\)
−0.187188 + 0.982324i \(0.559937\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 3.31604 0.124889
\(706\) 0 0
\(707\) −5.92650 −0.222889
\(708\) 0 0
\(709\) −36.1043 −1.35592 −0.677962 0.735097i \(-0.737137\pi\)
−0.677962 + 0.735097i \(0.737137\pi\)
\(710\) 0 0
\(711\) −30.7617 −1.15365
\(712\) 0 0
\(713\) −1.61917 −0.0606386
\(714\) 0 0
\(715\) 1.63555 0.0611662
\(716\) 0 0
\(717\) 0.777303 0.0290289
\(718\) 0 0
\(719\) −19.0109 −0.708988 −0.354494 0.935058i \(-0.615347\pi\)
−0.354494 + 0.935058i \(0.615347\pi\)
\(720\) 0 0
\(721\) −6.90666 −0.257217
\(722\) 0 0
\(723\) −8.91558 −0.331574
\(724\) 0 0
\(725\) −9.09880 −0.337921
\(726\) 0 0
\(727\) −2.88702 −0.107074 −0.0535369 0.998566i \(-0.517049\pi\)
−0.0535369 + 0.998566i \(0.517049\pi\)
\(728\) 0 0
\(729\) −20.0899 −0.744069
\(730\) 0 0
\(731\) −26.1239 −0.966227
\(732\) 0 0
\(733\) 44.9463 1.66013 0.830066 0.557666i \(-0.188303\pi\)
0.830066 + 0.557666i \(0.188303\pi\)
\(734\) 0 0
\(735\) −2.40393 −0.0886702
\(736\) 0 0
\(737\) 20.3843 0.750865
\(738\) 0 0
\(739\) 50.9913 1.87574 0.937872 0.346980i \(-0.112793\pi\)
0.937872 + 0.346980i \(0.112793\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18.8761 0.692497 0.346249 0.938143i \(-0.387455\pi\)
0.346249 + 0.938143i \(0.387455\pi\)
\(744\) 0 0
\(745\) −10.1383 −0.371438
\(746\) 0 0
\(747\) 45.4940 1.66454
\(748\) 0 0
\(749\) 7.20108 0.263122
\(750\) 0 0
\(751\) 26.0253 0.949677 0.474838 0.880073i \(-0.342506\pi\)
0.474838 + 0.880073i \(0.342506\pi\)
\(752\) 0 0
\(753\) −1.19540 −0.0435629
\(754\) 0 0
\(755\) −2.81331 −0.102387
\(756\) 0 0
\(757\) −11.9156 −0.433079 −0.216540 0.976274i \(-0.569477\pi\)
−0.216540 + 0.976274i \(0.569477\pi\)
\(758\) 0 0
\(759\) −0.516902 −0.0187623
\(760\) 0 0
\(761\) −2.39500 −0.0868186 −0.0434093 0.999057i \(-0.513822\pi\)
−0.0434093 + 0.999057i \(0.513822\pi\)
\(762\) 0 0
\(763\) 8.40939 0.304440
\(764\) 0 0
\(765\) −18.9121 −0.683769
\(766\) 0 0
\(767\) −9.09880 −0.328539
\(768\) 0 0
\(769\) 5.32497 0.192023 0.0960117 0.995380i \(-0.469391\pi\)
0.0960117 + 0.995380i \(0.469391\pi\)
\(770\) 0 0
\(771\) 2.78276 0.100219
\(772\) 0 0
\(773\) −24.4973 −0.881106 −0.440553 0.897727i \(-0.645218\pi\)
−0.440553 + 0.897727i \(0.645218\pi\)
\(774\) 0 0
\(775\) −1.86718 −0.0670710
\(776\) 0 0
\(777\) −0.147210 −0.00528113
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 4.09334 0.146471
\(782\) 0 0
\(783\) −19.4558 −0.695294
\(784\) 0 0
\(785\) −0.960522 −0.0342825
\(786\) 0 0
\(787\) −20.5171 −0.731356 −0.365678 0.930741i \(-0.619163\pi\)
−0.365678 + 0.930741i \(0.619163\pi\)
\(788\) 0 0
\(789\) −5.36792 −0.191103
\(790\) 0 0
\(791\) 4.50819 0.160293
\(792\) 0 0
\(793\) −2.27110 −0.0806493
\(794\) 0 0
\(795\) −3.59607 −0.127540
\(796\) 0 0
\(797\) −23.0144 −0.815211 −0.407606 0.913158i \(-0.633636\pi\)
−0.407606 + 0.913158i \(0.633636\pi\)
\(798\) 0 0
\(799\) −60.0164 −2.12323
\(800\) 0 0
\(801\) −1.55461 −0.0549293
\(802\) 0 0
\(803\) −0.660642 −0.0233136
\(804\) 0 0
\(805\) −0.551136 −0.0194250
\(806\) 0 0
\(807\) 4.90666 0.172722
\(808\) 0 0
\(809\) −28.3195 −0.995661 −0.497830 0.867274i \(-0.665870\pi\)
−0.497830 + 0.867274i \(0.665870\pi\)
\(810\) 0 0
\(811\) 39.5531 1.38890 0.694449 0.719542i \(-0.255648\pi\)
0.694449 + 0.719542i \(0.255648\pi\)
\(812\) 0 0
\(813\) −1.40740 −0.0493595
\(814\) 0 0
\(815\) −3.13828 −0.109929
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 1.82224 0.0636742
\(820\) 0 0
\(821\) 30.8026 1.07502 0.537509 0.843258i \(-0.319365\pi\)
0.537509 + 0.843258i \(0.319365\pi\)
\(822\) 0 0
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 0 0
\(825\) −0.596074 −0.0207526
\(826\) 0 0
\(827\) 20.2855 0.705396 0.352698 0.935737i \(-0.385264\pi\)
0.352698 + 0.935737i \(0.385264\pi\)
\(828\) 0 0
\(829\) 44.0792 1.53093 0.765466 0.643476i \(-0.222508\pi\)
0.765466 + 0.643476i \(0.222508\pi\)
\(830\) 0 0
\(831\) 8.84755 0.306918
\(832\) 0 0
\(833\) 43.5082 1.50747
\(834\) 0 0
\(835\) 10.6356 0.368058
\(836\) 0 0
\(837\) −3.99255 −0.138003
\(838\) 0 0
\(839\) 53.9069 1.86107 0.930536 0.366201i \(-0.119342\pi\)
0.930536 + 0.366201i \(0.119342\pi\)
\(840\) 0 0
\(841\) 53.7882 1.85477
\(842\) 0 0
\(843\) −0.181229 −0.00624187
\(844\) 0 0
\(845\) 12.0000 0.412813
\(846\) 0 0
\(847\) −5.29095 −0.181799
\(848\) 0 0
\(849\) 5.52435 0.189595
\(850\) 0 0
\(851\) 0.551136 0.0188927
\(852\) 0 0
\(853\) 27.0648 0.926681 0.463340 0.886180i \(-0.346651\pi\)
0.463340 + 0.886180i \(0.346651\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.35353 −0.114554 −0.0572772 0.998358i \(-0.518242\pi\)
−0.0572772 + 0.998358i \(0.518242\pi\)
\(858\) 0 0
\(859\) −53.7058 −1.83242 −0.916209 0.400701i \(-0.868767\pi\)
−0.916209 + 0.400701i \(0.868767\pi\)
\(860\) 0 0
\(861\) −0.441630 −0.0150507
\(862\) 0 0
\(863\) −39.1527 −1.33277 −0.666386 0.745607i \(-0.732160\pi\)
−0.666386 + 0.745607i \(0.732160\pi\)
\(864\) 0 0
\(865\) −12.3699 −0.420589
\(866\) 0 0
\(867\) −9.66086 −0.328100
\(868\) 0 0
\(869\) 17.5477 0.595264
\(870\) 0 0
\(871\) −12.4633 −0.422301
\(872\) 0 0
\(873\) 21.1308 0.715170
\(874\) 0 0
\(875\) −0.635552 −0.0214856
\(876\) 0 0
\(877\) −29.6519 −1.00127 −0.500637 0.865657i \(-0.666901\pi\)
−0.500637 + 0.865657i \(0.666901\pi\)
\(878\) 0 0
\(879\) 4.88702 0.164835
\(880\) 0 0
\(881\) 43.2820 1.45821 0.729104 0.684403i \(-0.239937\pi\)
0.729104 + 0.684403i \(0.239937\pi\)
\(882\) 0 0
\(883\) 56.9660 1.91706 0.958529 0.284995i \(-0.0919920\pi\)
0.958529 + 0.284995i \(0.0919920\pi\)
\(884\) 0 0
\(885\) 3.31604 0.111468
\(886\) 0 0
\(887\) 20.2316 0.679312 0.339656 0.940550i \(-0.389689\pi\)
0.339656 + 0.940550i \(0.389689\pi\)
\(888\) 0 0
\(889\) 10.3446 0.346947
\(890\) 0 0
\(891\) 12.7937 0.428604
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0.324970 0.0108625
\(896\) 0 0
\(897\) 0.316041 0.0105523
\(898\) 0 0
\(899\) 16.9891 0.566618
\(900\) 0 0
\(901\) 65.0846 2.16828
\(902\) 0 0
\(903\) −0.917359 −0.0305278
\(904\) 0 0
\(905\) −8.81331 −0.292964
\(906\) 0 0
\(907\) −10.0000 −0.332045 −0.166022 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) 0 0
\(909\) 26.7363 0.886789
\(910\) 0 0
\(911\) −55.0109 −1.82259 −0.911297 0.411751i \(-0.864917\pi\)
−0.911297 + 0.411751i \(0.864917\pi\)
\(912\) 0 0
\(913\) −25.9516 −0.858872
\(914\) 0 0
\(915\) 0.827699 0.0273629
\(916\) 0 0
\(917\) −6.75945 −0.223217
\(918\) 0 0
\(919\) 48.6159 1.60369 0.801846 0.597531i \(-0.203852\pi\)
0.801846 + 0.597531i \(0.203852\pi\)
\(920\) 0 0
\(921\) −11.7376 −0.386767
\(922\) 0 0
\(923\) −2.50273 −0.0823783
\(924\) 0 0
\(925\) 0.635552 0.0208968
\(926\) 0 0
\(927\) 31.1581 1.02337
\(928\) 0 0
\(929\) 11.3215 0.371446 0.185723 0.982602i \(-0.440537\pi\)
0.185723 + 0.982602i \(0.440537\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −4.50819 −0.147591
\(934\) 0 0
\(935\) 10.7882 0.352813
\(936\) 0 0
\(937\) −10.4973 −0.342931 −0.171465 0.985190i \(-0.554850\pi\)
−0.171465 + 0.985190i \(0.554850\pi\)
\(938\) 0 0
\(939\) −9.03402 −0.294814
\(940\) 0 0
\(941\) −2.81877 −0.0918893 −0.0459447 0.998944i \(-0.514630\pi\)
−0.0459447 + 0.998944i \(0.514630\pi\)
\(942\) 0 0
\(943\) 1.65341 0.0538424
\(944\) 0 0
\(945\) −1.35899 −0.0442079
\(946\) 0 0
\(947\) −45.5136 −1.47899 −0.739497 0.673159i \(-0.764937\pi\)
−0.739497 + 0.673159i \(0.764937\pi\)
\(948\) 0 0
\(949\) 0.403926 0.0131120
\(950\) 0 0
\(951\) −2.66433 −0.0863967
\(952\) 0 0
\(953\) −20.7200 −0.671186 −0.335593 0.942007i \(-0.608937\pi\)
−0.335593 + 0.942007i \(0.608937\pi\)
\(954\) 0 0
\(955\) −25.1921 −0.815199
\(956\) 0 0
\(957\) 5.42356 0.175319
\(958\) 0 0
\(959\) 2.22270 0.0717746
\(960\) 0 0
\(961\) −27.5136 −0.887537
\(962\) 0 0
\(963\) −32.4864 −1.04686
\(964\) 0 0
\(965\) 18.8726 0.607532
\(966\) 0 0
\(967\) −13.4687 −0.433125 −0.216562 0.976269i \(-0.569484\pi\)
−0.216562 + 0.976269i \(0.569484\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −47.0504 −1.50992 −0.754960 0.655771i \(-0.772344\pi\)
−0.754960 + 0.655771i \(0.772344\pi\)
\(972\) 0 0
\(973\) 0.466721 0.0149624
\(974\) 0 0
\(975\) 0.364448 0.0116717
\(976\) 0 0
\(977\) 43.0648 1.37776 0.688882 0.724873i \(-0.258102\pi\)
0.688882 + 0.724873i \(0.258102\pi\)
\(978\) 0 0
\(979\) 0.886809 0.0283425
\(980\) 0 0
\(981\) −37.9374 −1.21125
\(982\) 0 0
\(983\) −54.0792 −1.72486 −0.862429 0.506178i \(-0.831058\pi\)
−0.862429 + 0.506178i \(0.831058\pi\)
\(984\) 0 0
\(985\) 7.36445 0.234651
\(986\) 0 0
\(987\) −2.10752 −0.0670830
\(988\) 0 0
\(989\) 3.43448 0.109210
\(990\) 0 0
\(991\) 41.2711 1.31102 0.655510 0.755187i \(-0.272454\pi\)
0.655510 + 0.755187i \(0.272454\pi\)
\(992\) 0 0
\(993\) −6.73215 −0.213638
\(994\) 0 0
\(995\) −2.76837 −0.0877634
\(996\) 0 0
\(997\) −1.08987 −0.0345167 −0.0172583 0.999851i \(-0.505494\pi\)
−0.0172583 + 0.999851i \(0.505494\pi\)
\(998\) 0 0
\(999\) 1.35899 0.0429965
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 7220.2.a.n.1.2 3
19.7 even 3 380.2.i.b.201.2 yes 6
19.11 even 3 380.2.i.b.121.2 6
19.18 odd 2 7220.2.a.o.1.2 3
57.11 odd 6 3420.2.t.v.1261.2 6
57.26 odd 6 3420.2.t.v.3241.2 6
76.7 odd 6 1520.2.q.i.961.2 6
76.11 odd 6 1520.2.q.i.881.2 6
95.7 odd 12 1900.2.s.c.49.3 12
95.49 even 6 1900.2.i.c.501.2 6
95.64 even 6 1900.2.i.c.201.2 6
95.68 odd 12 1900.2.s.c.349.3 12
95.83 odd 12 1900.2.s.c.49.4 12
95.87 odd 12 1900.2.s.c.349.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.i.b.121.2 6 19.11 even 3
380.2.i.b.201.2 yes 6 19.7 even 3
1520.2.q.i.881.2 6 76.11 odd 6
1520.2.q.i.961.2 6 76.7 odd 6
1900.2.i.c.201.2 6 95.64 even 6
1900.2.i.c.501.2 6 95.49 even 6
1900.2.s.c.49.3 12 95.7 odd 12
1900.2.s.c.49.4 12 95.83 odd 12
1900.2.s.c.349.3 12 95.68 odd 12
1900.2.s.c.349.4 12 95.87 odd 12
3420.2.t.v.1261.2 6 57.11 odd 6
3420.2.t.v.3241.2 6 57.26 odd 6
7220.2.a.n.1.2 3 1.1 even 1 trivial
7220.2.a.o.1.2 3 19.18 odd 2