Properties

Label 9196.2.a.n.1.3
Level $9196$
Weight $2$
Character 9196.1
Self dual yes
Analytic conductor $73.430$
Analytic rank $0$
Dimension $6$
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] = [9196,2,Mod(1,9196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9196, 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("9196.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9196 = 2^{2} \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9196.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: \(73.4304296988\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.744786576.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 17x^{4} + 13x^{3} + 69x^{2} - 21x - 30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 836)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.566270\) of defining polynomial
Character \(\chi\) \(=\) 9196.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.566270 q^{3} -3.92909 q^{5} +2.44546 q^{7} -2.67934 q^{9} +O(q^{10})\) \(q-0.566270 q^{3} -3.92909 q^{5} +2.44546 q^{7} -2.67934 q^{9} -6.76733 q^{13} +2.22493 q^{15} +0.175988 q^{17} +1.00000 q^{19} -1.38479 q^{21} +8.30079 q^{23} +10.4377 q^{25} +3.21604 q^{27} +0.843595 q^{29} -0.224925 q^{31} -9.60842 q^{35} -3.49175 q^{37} +3.83214 q^{39} -5.09084 q^{41} -9.48647 q^{43} +10.5273 q^{45} -9.68218 q^{47} -1.01972 q^{49} -0.0996567 q^{51} -4.72563 q^{53} -0.566270 q^{57} -7.88318 q^{59} -14.9907 q^{61} -6.55221 q^{63} +26.5894 q^{65} +2.09858 q^{67} -4.70049 q^{69} -7.53352 q^{71} +1.36696 q^{73} -5.91057 q^{75} +1.04345 q^{79} +6.21686 q^{81} -2.37170 q^{83} -0.691471 q^{85} -0.477703 q^{87} +3.38140 q^{89} -16.5492 q^{91} +0.127369 q^{93} -3.92909 q^{95} +19.0920 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 5 q^{5} + 2 q^{7} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 5 q^{5} + 2 q^{7} + 17 q^{9} - 8 q^{13} + 9 q^{15} + 2 q^{17} + 6 q^{19} - 18 q^{21} + 5 q^{23} + 13 q^{25} + 7 q^{27} - 10 q^{29} + 3 q^{31} + 4 q^{35} + 7 q^{37} + 10 q^{39} - 6 q^{41} - 16 q^{43} + 42 q^{45} + 12 q^{49} - 8 q^{51} + 20 q^{53} + q^{57} + 15 q^{59} - 24 q^{61} + 20 q^{63} + 28 q^{65} + 25 q^{67} - 33 q^{69} - 9 q^{71} + 26 q^{73} + 28 q^{75} + 16 q^{79} + 58 q^{81} + 2 q^{83} - 12 q^{85} + 36 q^{87} + 7 q^{89} + 8 q^{91} - 55 q^{93} + 5 q^{95} + 37 q^{97}+O(q^{100}) \) 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
\(3\) −0.566270 −0.326936 −0.163468 0.986549i \(-0.552268\pi\)
−0.163468 + 0.986549i \(0.552268\pi\)
\(4\) 0 0
\(5\) −3.92909 −1.75714 −0.878570 0.477613i \(-0.841502\pi\)
−0.878570 + 0.477613i \(0.841502\pi\)
\(6\) 0 0
\(7\) 2.44546 0.924297 0.462149 0.886803i \(-0.347079\pi\)
0.462149 + 0.886803i \(0.347079\pi\)
\(8\) 0 0
\(9\) −2.67934 −0.893113
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −6.76733 −1.87692 −0.938460 0.345388i \(-0.887747\pi\)
−0.938460 + 0.345388i \(0.887747\pi\)
\(14\) 0 0
\(15\) 2.22493 0.574473
\(16\) 0 0
\(17\) 0.175988 0.0426833 0.0213417 0.999772i \(-0.493206\pi\)
0.0213417 + 0.999772i \(0.493206\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −1.38479 −0.302186
\(22\) 0 0
\(23\) 8.30079 1.73083 0.865417 0.501053i \(-0.167054\pi\)
0.865417 + 0.501053i \(0.167054\pi\)
\(24\) 0 0
\(25\) 10.4377 2.08754
\(26\) 0 0
\(27\) 3.21604 0.618927
\(28\) 0 0
\(29\) 0.843595 0.156652 0.0783258 0.996928i \(-0.475043\pi\)
0.0783258 + 0.996928i \(0.475043\pi\)
\(30\) 0 0
\(31\) −0.224925 −0.0403978 −0.0201989 0.999796i \(-0.506430\pi\)
−0.0201989 + 0.999796i \(0.506430\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.60842 −1.62412
\(36\) 0 0
\(37\) −3.49175 −0.574041 −0.287020 0.957924i \(-0.592665\pi\)
−0.287020 + 0.957924i \(0.592665\pi\)
\(38\) 0 0
\(39\) 3.83214 0.613634
\(40\) 0 0
\(41\) −5.09084 −0.795056 −0.397528 0.917590i \(-0.630132\pi\)
−0.397528 + 0.917590i \(0.630132\pi\)
\(42\) 0 0
\(43\) −9.48647 −1.44667 −0.723337 0.690495i \(-0.757393\pi\)
−0.723337 + 0.690495i \(0.757393\pi\)
\(44\) 0 0
\(45\) 10.5273 1.56932
\(46\) 0 0
\(47\) −9.68218 −1.41229 −0.706146 0.708066i \(-0.749568\pi\)
−0.706146 + 0.708066i \(0.749568\pi\)
\(48\) 0 0
\(49\) −1.01972 −0.145675
\(50\) 0 0
\(51\) −0.0996567 −0.0139547
\(52\) 0 0
\(53\) −4.72563 −0.649115 −0.324558 0.945866i \(-0.605215\pi\)
−0.324558 + 0.945866i \(0.605215\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.566270 −0.0750044
\(58\) 0 0
\(59\) −7.88318 −1.02630 −0.513151 0.858298i \(-0.671522\pi\)
−0.513151 + 0.858298i \(0.671522\pi\)
\(60\) 0 0
\(61\) −14.9907 −1.91936 −0.959682 0.281088i \(-0.909305\pi\)
−0.959682 + 0.281088i \(0.909305\pi\)
\(62\) 0 0
\(63\) −6.55221 −0.825501
\(64\) 0 0
\(65\) 26.5894 3.29801
\(66\) 0 0
\(67\) 2.09858 0.256383 0.128191 0.991749i \(-0.459083\pi\)
0.128191 + 0.991749i \(0.459083\pi\)
\(68\) 0 0
\(69\) −4.70049 −0.565872
\(70\) 0 0
\(71\) −7.53352 −0.894065 −0.447032 0.894518i \(-0.647519\pi\)
−0.447032 + 0.894518i \(0.647519\pi\)
\(72\) 0 0
\(73\) 1.36696 0.159990 0.0799950 0.996795i \(-0.474510\pi\)
0.0799950 + 0.996795i \(0.474510\pi\)
\(74\) 0 0
\(75\) −5.91057 −0.682494
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.04345 0.117397 0.0586985 0.998276i \(-0.481305\pi\)
0.0586985 + 0.998276i \(0.481305\pi\)
\(80\) 0 0
\(81\) 6.21686 0.690763
\(82\) 0 0
\(83\) −2.37170 −0.260328 −0.130164 0.991492i \(-0.541550\pi\)
−0.130164 + 0.991492i \(0.541550\pi\)
\(84\) 0 0
\(85\) −0.691471 −0.0750006
\(86\) 0 0
\(87\) −0.477703 −0.0512151
\(88\) 0 0
\(89\) 3.38140 0.358428 0.179214 0.983810i \(-0.442645\pi\)
0.179214 + 0.983810i \(0.442645\pi\)
\(90\) 0 0
\(91\) −16.5492 −1.73483
\(92\) 0 0
\(93\) 0.127369 0.0132075
\(94\) 0 0
\(95\) −3.92909 −0.403116
\(96\) 0 0
\(97\) 19.0920 1.93850 0.969252 0.246070i \(-0.0791394\pi\)
0.969252 + 0.246070i \(0.0791394\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −10.5496 −1.04973 −0.524864 0.851186i \(-0.675884\pi\)
−0.524864 + 0.851186i \(0.675884\pi\)
\(102\) 0 0
\(103\) −10.9384 −1.07779 −0.538895 0.842373i \(-0.681158\pi\)
−0.538895 + 0.842373i \(0.681158\pi\)
\(104\) 0 0
\(105\) 5.44097 0.530984
\(106\) 0 0
\(107\) −14.6835 −1.41950 −0.709752 0.704452i \(-0.751193\pi\)
−0.709752 + 0.704452i \(0.751193\pi\)
\(108\) 0 0
\(109\) −17.9401 −1.71835 −0.859173 0.511685i \(-0.829021\pi\)
−0.859173 + 0.511685i \(0.829021\pi\)
\(110\) 0 0
\(111\) 1.97728 0.187675
\(112\) 0 0
\(113\) 12.9266 1.21603 0.608017 0.793924i \(-0.291965\pi\)
0.608017 + 0.793924i \(0.291965\pi\)
\(114\) 0 0
\(115\) −32.6145 −3.04132
\(116\) 0 0
\(117\) 18.1320 1.67630
\(118\) 0 0
\(119\) 0.430371 0.0394521
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 2.88279 0.259933
\(124\) 0 0
\(125\) −21.3653 −1.91097
\(126\) 0 0
\(127\) 18.3365 1.62710 0.813550 0.581495i \(-0.197532\pi\)
0.813550 + 0.581495i \(0.197532\pi\)
\(128\) 0 0
\(129\) 5.37191 0.472970
\(130\) 0 0
\(131\) 2.97871 0.260251 0.130126 0.991498i \(-0.458462\pi\)
0.130126 + 0.991498i \(0.458462\pi\)
\(132\) 0 0
\(133\) 2.44546 0.212048
\(134\) 0 0
\(135\) −12.6361 −1.08754
\(136\) 0 0
\(137\) 8.90447 0.760760 0.380380 0.924830i \(-0.375793\pi\)
0.380380 + 0.924830i \(0.375793\pi\)
\(138\) 0 0
\(139\) −5.34451 −0.453315 −0.226658 0.973974i \(-0.572780\pi\)
−0.226658 + 0.973974i \(0.572780\pi\)
\(140\) 0 0
\(141\) 5.48274 0.461730
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −3.31456 −0.275259
\(146\) 0 0
\(147\) 0.577440 0.0476264
\(148\) 0 0
\(149\) 9.26958 0.759394 0.379697 0.925111i \(-0.376028\pi\)
0.379697 + 0.925111i \(0.376028\pi\)
\(150\) 0 0
\(151\) −2.51548 −0.204707 −0.102354 0.994748i \(-0.532637\pi\)
−0.102354 + 0.994748i \(0.532637\pi\)
\(152\) 0 0
\(153\) −0.471531 −0.0381210
\(154\) 0 0
\(155\) 0.883751 0.0709846
\(156\) 0 0
\(157\) −1.12005 −0.0893900 −0.0446950 0.999001i \(-0.514232\pi\)
−0.0446950 + 0.999001i \(0.514232\pi\)
\(158\) 0 0
\(159\) 2.67599 0.212219
\(160\) 0 0
\(161\) 20.2992 1.59980
\(162\) 0 0
\(163\) 16.7598 1.31273 0.656364 0.754444i \(-0.272094\pi\)
0.656364 + 0.754444i \(0.272094\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 16.0057 1.23856 0.619279 0.785171i \(-0.287425\pi\)
0.619279 + 0.785171i \(0.287425\pi\)
\(168\) 0 0
\(169\) 32.7968 2.52283
\(170\) 0 0
\(171\) −2.67934 −0.204894
\(172\) 0 0
\(173\) 2.12366 0.161459 0.0807293 0.996736i \(-0.474275\pi\)
0.0807293 + 0.996736i \(0.474275\pi\)
\(174\) 0 0
\(175\) 25.5250 1.92951
\(176\) 0 0
\(177\) 4.46401 0.335536
\(178\) 0 0
\(179\) 9.36816 0.700210 0.350105 0.936711i \(-0.386146\pi\)
0.350105 + 0.936711i \(0.386146\pi\)
\(180\) 0 0
\(181\) 14.6585 1.08955 0.544777 0.838581i \(-0.316614\pi\)
0.544777 + 0.838581i \(0.316614\pi\)
\(182\) 0 0
\(183\) 8.48880 0.627510
\(184\) 0 0
\(185\) 13.7194 1.00867
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 7.86470 0.572073
\(190\) 0 0
\(191\) 2.41984 0.175093 0.0875467 0.996160i \(-0.472097\pi\)
0.0875467 + 0.996160i \(0.472097\pi\)
\(192\) 0 0
\(193\) −16.4050 −1.18086 −0.590429 0.807090i \(-0.701041\pi\)
−0.590429 + 0.807090i \(0.701041\pi\)
\(194\) 0 0
\(195\) −15.0568 −1.07824
\(196\) 0 0
\(197\) 7.67149 0.546571 0.273285 0.961933i \(-0.411890\pi\)
0.273285 + 0.961933i \(0.411890\pi\)
\(198\) 0 0
\(199\) −6.97781 −0.494644 −0.247322 0.968933i \(-0.579551\pi\)
−0.247322 + 0.968933i \(0.579551\pi\)
\(200\) 0 0
\(201\) −1.18837 −0.0838209
\(202\) 0 0
\(203\) 2.06298 0.144793
\(204\) 0 0
\(205\) 20.0024 1.39702
\(206\) 0 0
\(207\) −22.2406 −1.54583
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −11.7584 −0.809480 −0.404740 0.914432i \(-0.632638\pi\)
−0.404740 + 0.914432i \(0.632638\pi\)
\(212\) 0 0
\(213\) 4.26601 0.292302
\(214\) 0 0
\(215\) 37.2732 2.54201
\(216\) 0 0
\(217\) −0.550046 −0.0373396
\(218\) 0 0
\(219\) −0.774067 −0.0523066
\(220\) 0 0
\(221\) −1.19097 −0.0801132
\(222\) 0 0
\(223\) −20.7798 −1.39152 −0.695759 0.718275i \(-0.744932\pi\)
−0.695759 + 0.718275i \(0.744932\pi\)
\(224\) 0 0
\(225\) −27.9662 −1.86441
\(226\) 0 0
\(227\) 18.2424 1.21079 0.605395 0.795925i \(-0.293015\pi\)
0.605395 + 0.795925i \(0.293015\pi\)
\(228\) 0 0
\(229\) 3.93873 0.260278 0.130139 0.991496i \(-0.458458\pi\)
0.130139 + 0.991496i \(0.458458\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.86045 0.645980 0.322990 0.946402i \(-0.395312\pi\)
0.322990 + 0.946402i \(0.395312\pi\)
\(234\) 0 0
\(235\) 38.0421 2.48160
\(236\) 0 0
\(237\) −0.590873 −0.0383813
\(238\) 0 0
\(239\) −3.81226 −0.246595 −0.123297 0.992370i \(-0.539347\pi\)
−0.123297 + 0.992370i \(0.539347\pi\)
\(240\) 0 0
\(241\) 17.4880 1.12650 0.563251 0.826286i \(-0.309550\pi\)
0.563251 + 0.826286i \(0.309550\pi\)
\(242\) 0 0
\(243\) −13.1686 −0.844763
\(244\) 0 0
\(245\) 4.00658 0.255971
\(246\) 0 0
\(247\) −6.76733 −0.430595
\(248\) 0 0
\(249\) 1.34302 0.0851107
\(250\) 0 0
\(251\) 29.9887 1.89287 0.946434 0.322898i \(-0.104657\pi\)
0.946434 + 0.322898i \(0.104657\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0.391560 0.0245204
\(256\) 0 0
\(257\) −20.9251 −1.30527 −0.652635 0.757672i \(-0.726337\pi\)
−0.652635 + 0.757672i \(0.726337\pi\)
\(258\) 0 0
\(259\) −8.53894 −0.530584
\(260\) 0 0
\(261\) −2.26028 −0.139908
\(262\) 0 0
\(263\) −5.29450 −0.326473 −0.163236 0.986587i \(-0.552193\pi\)
−0.163236 + 0.986587i \(0.552193\pi\)
\(264\) 0 0
\(265\) 18.5674 1.14059
\(266\) 0 0
\(267\) −1.91479 −0.117183
\(268\) 0 0
\(269\) 17.9602 1.09506 0.547528 0.836787i \(-0.315569\pi\)
0.547528 + 0.836787i \(0.315569\pi\)
\(270\) 0 0
\(271\) −0.957856 −0.0581856 −0.0290928 0.999577i \(-0.509262\pi\)
−0.0290928 + 0.999577i \(0.509262\pi\)
\(272\) 0 0
\(273\) 9.37135 0.567180
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 16.3422 0.981907 0.490953 0.871186i \(-0.336649\pi\)
0.490953 + 0.871186i \(0.336649\pi\)
\(278\) 0 0
\(279\) 0.602651 0.0360798
\(280\) 0 0
\(281\) −8.36035 −0.498737 −0.249368 0.968409i \(-0.580223\pi\)
−0.249368 + 0.968409i \(0.580223\pi\)
\(282\) 0 0
\(283\) 9.02926 0.536734 0.268367 0.963317i \(-0.413516\pi\)
0.268367 + 0.963317i \(0.413516\pi\)
\(284\) 0 0
\(285\) 2.22493 0.131793
\(286\) 0 0
\(287\) −12.4494 −0.734868
\(288\) 0 0
\(289\) −16.9690 −0.998178
\(290\) 0 0
\(291\) −10.8113 −0.633768
\(292\) 0 0
\(293\) −7.42733 −0.433909 −0.216955 0.976182i \(-0.569612\pi\)
−0.216955 + 0.976182i \(0.569612\pi\)
\(294\) 0 0
\(295\) 30.9737 1.80336
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −56.1742 −3.24864
\(300\) 0 0
\(301\) −23.1988 −1.33716
\(302\) 0 0
\(303\) 5.97395 0.343195
\(304\) 0 0
\(305\) 58.8998 3.37259
\(306\) 0 0
\(307\) −17.1405 −0.978261 −0.489130 0.872211i \(-0.662686\pi\)
−0.489130 + 0.872211i \(0.662686\pi\)
\(308\) 0 0
\(309\) 6.19408 0.352369
\(310\) 0 0
\(311\) 6.52618 0.370066 0.185033 0.982732i \(-0.440761\pi\)
0.185033 + 0.982732i \(0.440761\pi\)
\(312\) 0 0
\(313\) −17.3089 −0.978359 −0.489180 0.872183i \(-0.662704\pi\)
−0.489180 + 0.872183i \(0.662704\pi\)
\(314\) 0 0
\(315\) 25.7442 1.45052
\(316\) 0 0
\(317\) 33.6814 1.89174 0.945868 0.324551i \(-0.105213\pi\)
0.945868 + 0.324551i \(0.105213\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 8.31481 0.464087
\(322\) 0 0
\(323\) 0.175988 0.00979222
\(324\) 0 0
\(325\) −70.6355 −3.91815
\(326\) 0 0
\(327\) 10.1589 0.561790
\(328\) 0 0
\(329\) −23.6774 −1.30538
\(330\) 0 0
\(331\) −6.51703 −0.358208 −0.179104 0.983830i \(-0.557320\pi\)
−0.179104 + 0.983830i \(0.557320\pi\)
\(332\) 0 0
\(333\) 9.35559 0.512683
\(334\) 0 0
\(335\) −8.24551 −0.450501
\(336\) 0 0
\(337\) −29.8951 −1.62849 −0.814245 0.580522i \(-0.802849\pi\)
−0.814245 + 0.580522i \(0.802849\pi\)
\(338\) 0 0
\(339\) −7.31997 −0.397566
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −19.6119 −1.05894
\(344\) 0 0
\(345\) 18.4686 0.994318
\(346\) 0 0
\(347\) −8.24960 −0.442862 −0.221431 0.975176i \(-0.571073\pi\)
−0.221431 + 0.975176i \(0.571073\pi\)
\(348\) 0 0
\(349\) 8.18396 0.438078 0.219039 0.975716i \(-0.429708\pi\)
0.219039 + 0.975716i \(0.429708\pi\)
\(350\) 0 0
\(351\) −21.7640 −1.16168
\(352\) 0 0
\(353\) −14.4897 −0.771207 −0.385604 0.922664i \(-0.626007\pi\)
−0.385604 + 0.922664i \(0.626007\pi\)
\(354\) 0 0
\(355\) 29.5999 1.57100
\(356\) 0 0
\(357\) −0.243706 −0.0128983
\(358\) 0 0
\(359\) 15.7807 0.832872 0.416436 0.909165i \(-0.363279\pi\)
0.416436 + 0.909165i \(0.363279\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.37089 −0.281125
\(366\) 0 0
\(367\) 17.8387 0.931174 0.465587 0.885002i \(-0.345843\pi\)
0.465587 + 0.885002i \(0.345843\pi\)
\(368\) 0 0
\(369\) 13.6401 0.710074
\(370\) 0 0
\(371\) −11.5563 −0.599975
\(372\) 0 0
\(373\) 30.0896 1.55798 0.778990 0.627036i \(-0.215732\pi\)
0.778990 + 0.627036i \(0.215732\pi\)
\(374\) 0 0
\(375\) 12.0985 0.624765
\(376\) 0 0
\(377\) −5.70889 −0.294023
\(378\) 0 0
\(379\) 12.2583 0.629667 0.314834 0.949147i \(-0.398051\pi\)
0.314834 + 0.949147i \(0.398051\pi\)
\(380\) 0 0
\(381\) −10.3834 −0.531958
\(382\) 0 0
\(383\) −22.5978 −1.15469 −0.577346 0.816499i \(-0.695912\pi\)
−0.577346 + 0.816499i \(0.695912\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 25.4175 1.29204
\(388\) 0 0
\(389\) 29.7216 1.50695 0.753473 0.657479i \(-0.228377\pi\)
0.753473 + 0.657479i \(0.228377\pi\)
\(390\) 0 0
\(391\) 1.46084 0.0738777
\(392\) 0 0
\(393\) −1.68676 −0.0850856
\(394\) 0 0
\(395\) −4.09979 −0.206283
\(396\) 0 0
\(397\) 24.3750 1.22335 0.611674 0.791110i \(-0.290496\pi\)
0.611674 + 0.791110i \(0.290496\pi\)
\(398\) 0 0
\(399\) −1.38479 −0.0693263
\(400\) 0 0
\(401\) −28.9859 −1.44749 −0.723744 0.690069i \(-0.757580\pi\)
−0.723744 + 0.690069i \(0.757580\pi\)
\(402\) 0 0
\(403\) 1.52214 0.0758234
\(404\) 0 0
\(405\) −24.4266 −1.21377
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −21.0718 −1.04193 −0.520967 0.853577i \(-0.674428\pi\)
−0.520967 + 0.853577i \(0.674428\pi\)
\(410\) 0 0
\(411\) −5.04234 −0.248720
\(412\) 0 0
\(413\) −19.2780 −0.948608
\(414\) 0 0
\(415\) 9.31861 0.457433
\(416\) 0 0
\(417\) 3.02644 0.148205
\(418\) 0 0
\(419\) 8.59929 0.420103 0.210051 0.977690i \(-0.432637\pi\)
0.210051 + 0.977690i \(0.432637\pi\)
\(420\) 0 0
\(421\) 4.07441 0.198575 0.0992874 0.995059i \(-0.468344\pi\)
0.0992874 + 0.995059i \(0.468344\pi\)
\(422\) 0 0
\(423\) 25.9418 1.26134
\(424\) 0 0
\(425\) 1.83691 0.0891033
\(426\) 0 0
\(427\) −36.6592 −1.77406
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.8572 0.619308 0.309654 0.950849i \(-0.399787\pi\)
0.309654 + 0.950849i \(0.399787\pi\)
\(432\) 0 0
\(433\) 5.97021 0.286910 0.143455 0.989657i \(-0.454179\pi\)
0.143455 + 0.989657i \(0.454179\pi\)
\(434\) 0 0
\(435\) 1.87694 0.0899922
\(436\) 0 0
\(437\) 8.30079 0.397080
\(438\) 0 0
\(439\) −34.9965 −1.67029 −0.835146 0.550029i \(-0.814617\pi\)
−0.835146 + 0.550029i \(0.814617\pi\)
\(440\) 0 0
\(441\) 2.73219 0.130104
\(442\) 0 0
\(443\) 31.3469 1.48934 0.744669 0.667434i \(-0.232607\pi\)
0.744669 + 0.667434i \(0.232607\pi\)
\(444\) 0 0
\(445\) −13.2858 −0.629808
\(446\) 0 0
\(447\) −5.24909 −0.248273
\(448\) 0 0
\(449\) 29.7198 1.40256 0.701282 0.712884i \(-0.252611\pi\)
0.701282 + 0.712884i \(0.252611\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 1.42444 0.0669262
\(454\) 0 0
\(455\) 65.0234 3.04834
\(456\) 0 0
\(457\) −24.4809 −1.14517 −0.572585 0.819846i \(-0.694059\pi\)
−0.572585 + 0.819846i \(0.694059\pi\)
\(458\) 0 0
\(459\) 0.565984 0.0264179
\(460\) 0 0
\(461\) 21.5138 1.00200 0.500999 0.865448i \(-0.332966\pi\)
0.500999 + 0.865448i \(0.332966\pi\)
\(462\) 0 0
\(463\) −2.04695 −0.0951300 −0.0475650 0.998868i \(-0.515146\pi\)
−0.0475650 + 0.998868i \(0.515146\pi\)
\(464\) 0 0
\(465\) −0.500442 −0.0232075
\(466\) 0 0
\(467\) −23.7411 −1.09861 −0.549303 0.835623i \(-0.685107\pi\)
−0.549303 + 0.835623i \(0.685107\pi\)
\(468\) 0 0
\(469\) 5.13200 0.236974
\(470\) 0 0
\(471\) 0.634253 0.0292249
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 10.4377 0.478915
\(476\) 0 0
\(477\) 12.6616 0.579733
\(478\) 0 0
\(479\) 28.4414 1.29952 0.649759 0.760140i \(-0.274870\pi\)
0.649759 + 0.760140i \(0.274870\pi\)
\(480\) 0 0
\(481\) 23.6299 1.07743
\(482\) 0 0
\(483\) −11.4949 −0.523034
\(484\) 0 0
\(485\) −75.0143 −3.40622
\(486\) 0 0
\(487\) −1.40149 −0.0635074 −0.0317537 0.999496i \(-0.510109\pi\)
−0.0317537 + 0.999496i \(0.510109\pi\)
\(488\) 0 0
\(489\) −9.49057 −0.429179
\(490\) 0 0
\(491\) −30.2244 −1.36401 −0.682005 0.731348i \(-0.738892\pi\)
−0.682005 + 0.731348i \(0.738892\pi\)
\(492\) 0 0
\(493\) 0.148462 0.00668641
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −18.4229 −0.826381
\(498\) 0 0
\(499\) 24.5835 1.10051 0.550255 0.834997i \(-0.314530\pi\)
0.550255 + 0.834997i \(0.314530\pi\)
\(500\) 0 0
\(501\) −9.06355 −0.404930
\(502\) 0 0
\(503\) −12.9000 −0.575184 −0.287592 0.957753i \(-0.592855\pi\)
−0.287592 + 0.957753i \(0.592855\pi\)
\(504\) 0 0
\(505\) 41.4505 1.84452
\(506\) 0 0
\(507\) −18.5718 −0.824805
\(508\) 0 0
\(509\) −15.2890 −0.677674 −0.338837 0.940845i \(-0.610034\pi\)
−0.338837 + 0.940845i \(0.610034\pi\)
\(510\) 0 0
\(511\) 3.34284 0.147878
\(512\) 0 0
\(513\) 3.21604 0.141992
\(514\) 0 0
\(515\) 42.9778 1.89383
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.20256 −0.0527867
\(520\) 0 0
\(521\) 38.6252 1.69220 0.846100 0.533024i \(-0.178944\pi\)
0.846100 + 0.533024i \(0.178944\pi\)
\(522\) 0 0
\(523\) 1.26936 0.0555054 0.0277527 0.999615i \(-0.491165\pi\)
0.0277527 + 0.999615i \(0.491165\pi\)
\(524\) 0 0
\(525\) −14.4541 −0.630827
\(526\) 0 0
\(527\) −0.0395841 −0.00172431
\(528\) 0 0
\(529\) 45.9030 1.99578
\(530\) 0 0
\(531\) 21.1217 0.916604
\(532\) 0 0
\(533\) 34.4514 1.49226
\(534\) 0 0
\(535\) 57.6926 2.49427
\(536\) 0 0
\(537\) −5.30492 −0.228924
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −24.5110 −1.05381 −0.526904 0.849925i \(-0.676647\pi\)
−0.526904 + 0.849925i \(0.676647\pi\)
\(542\) 0 0
\(543\) −8.30065 −0.356215
\(544\) 0 0
\(545\) 70.4880 3.01938
\(546\) 0 0
\(547\) 27.2833 1.16655 0.583274 0.812276i \(-0.301771\pi\)
0.583274 + 0.812276i \(0.301771\pi\)
\(548\) 0 0
\(549\) 40.1652 1.71421
\(550\) 0 0
\(551\) 0.843595 0.0359383
\(552\) 0 0
\(553\) 2.55171 0.108510
\(554\) 0 0
\(555\) −7.76889 −0.329771
\(556\) 0 0
\(557\) 10.7434 0.455212 0.227606 0.973753i \(-0.426910\pi\)
0.227606 + 0.973753i \(0.426910\pi\)
\(558\) 0 0
\(559\) 64.1981 2.71529
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 30.0868 1.26801 0.634003 0.773330i \(-0.281411\pi\)
0.634003 + 0.773330i \(0.281411\pi\)
\(564\) 0 0
\(565\) −50.7898 −2.13674
\(566\) 0 0
\(567\) 15.2031 0.638470
\(568\) 0 0
\(569\) −22.0838 −0.925803 −0.462901 0.886410i \(-0.653192\pi\)
−0.462901 + 0.886410i \(0.653192\pi\)
\(570\) 0 0
\(571\) 36.7811 1.53924 0.769621 0.638500i \(-0.220445\pi\)
0.769621 + 0.638500i \(0.220445\pi\)
\(572\) 0 0
\(573\) −1.37028 −0.0572444
\(574\) 0 0
\(575\) 86.6413 3.61319
\(576\) 0 0
\(577\) −32.2242 −1.34151 −0.670755 0.741679i \(-0.734030\pi\)
−0.670755 + 0.741679i \(0.734030\pi\)
\(578\) 0 0
\(579\) 9.28966 0.386065
\(580\) 0 0
\(581\) −5.79990 −0.240620
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −71.2421 −2.94550
\(586\) 0 0
\(587\) −16.3940 −0.676654 −0.338327 0.941029i \(-0.609861\pi\)
−0.338327 + 0.941029i \(0.609861\pi\)
\(588\) 0 0
\(589\) −0.224925 −0.00926789
\(590\) 0 0
\(591\) −4.34414 −0.178694
\(592\) 0 0
\(593\) 7.33700 0.301294 0.150647 0.988588i \(-0.451864\pi\)
0.150647 + 0.988588i \(0.451864\pi\)
\(594\) 0 0
\(595\) −1.69097 −0.0693228
\(596\) 0 0
\(597\) 3.95133 0.161717
\(598\) 0 0
\(599\) −38.0717 −1.55557 −0.777784 0.628532i \(-0.783656\pi\)
−0.777784 + 0.628532i \(0.783656\pi\)
\(600\) 0 0
\(601\) 13.8342 0.564310 0.282155 0.959369i \(-0.408951\pi\)
0.282155 + 0.959369i \(0.408951\pi\)
\(602\) 0 0
\(603\) −5.62281 −0.228979
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −20.2603 −0.822340 −0.411170 0.911559i \(-0.634880\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(608\) 0 0
\(609\) −1.16820 −0.0473380
\(610\) 0 0
\(611\) 65.5226 2.65076
\(612\) 0 0
\(613\) −34.9954 −1.41345 −0.706726 0.707488i \(-0.749829\pi\)
−0.706726 + 0.707488i \(0.749829\pi\)
\(614\) 0 0
\(615\) −11.3267 −0.456738
\(616\) 0 0
\(617\) 3.87381 0.155954 0.0779769 0.996955i \(-0.475154\pi\)
0.0779769 + 0.996955i \(0.475154\pi\)
\(618\) 0 0
\(619\) −5.80250 −0.233222 −0.116611 0.993178i \(-0.537203\pi\)
−0.116611 + 0.993178i \(0.537203\pi\)
\(620\) 0 0
\(621\) 26.6957 1.07126
\(622\) 0 0
\(623\) 8.26908 0.331294
\(624\) 0 0
\(625\) 31.7574 1.27029
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.614506 −0.0245020
\(630\) 0 0
\(631\) 18.5664 0.739115 0.369558 0.929208i \(-0.379509\pi\)
0.369558 + 0.929208i \(0.379509\pi\)
\(632\) 0 0
\(633\) 6.65842 0.264649
\(634\) 0 0
\(635\) −72.0456 −2.85904
\(636\) 0 0
\(637\) 6.90081 0.273420
\(638\) 0 0
\(639\) 20.1849 0.798500
\(640\) 0 0
\(641\) 8.91056 0.351946 0.175973 0.984395i \(-0.443693\pi\)
0.175973 + 0.984395i \(0.443693\pi\)
\(642\) 0 0
\(643\) −36.9688 −1.45791 −0.728953 0.684564i \(-0.759993\pi\)
−0.728953 + 0.684564i \(0.759993\pi\)
\(644\) 0 0
\(645\) −21.1067 −0.831075
\(646\) 0 0
\(647\) 21.3503 0.839367 0.419683 0.907671i \(-0.362141\pi\)
0.419683 + 0.907671i \(0.362141\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.311475 0.0122077
\(652\) 0 0
\(653\) −9.01791 −0.352898 −0.176449 0.984310i \(-0.556461\pi\)
−0.176449 + 0.984310i \(0.556461\pi\)
\(654\) 0 0
\(655\) −11.7036 −0.457298
\(656\) 0 0
\(657\) −3.66254 −0.142889
\(658\) 0 0
\(659\) −0.402928 −0.0156958 −0.00784792 0.999969i \(-0.502498\pi\)
−0.00784792 + 0.999969i \(0.502498\pi\)
\(660\) 0 0
\(661\) −0.400038 −0.0155597 −0.00777983 0.999970i \(-0.502476\pi\)
−0.00777983 + 0.999970i \(0.502476\pi\)
\(662\) 0 0
\(663\) 0.674410 0.0261919
\(664\) 0 0
\(665\) −9.60842 −0.372599
\(666\) 0 0
\(667\) 7.00250 0.271138
\(668\) 0 0
\(669\) 11.7670 0.454938
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 42.9949 1.65733 0.828666 0.559743i \(-0.189100\pi\)
0.828666 + 0.559743i \(0.189100\pi\)
\(674\) 0 0
\(675\) 33.5681 1.29204
\(676\) 0 0
\(677\) −12.7272 −0.489148 −0.244574 0.969631i \(-0.578648\pi\)
−0.244574 + 0.969631i \(0.578648\pi\)
\(678\) 0 0
\(679\) 46.6888 1.79175
\(680\) 0 0
\(681\) −10.3301 −0.395851
\(682\) 0 0
\(683\) 47.4876 1.81706 0.908532 0.417816i \(-0.137204\pi\)
0.908532 + 0.417816i \(0.137204\pi\)
\(684\) 0 0
\(685\) −34.9864 −1.33676
\(686\) 0 0
\(687\) −2.23038 −0.0850945
\(688\) 0 0
\(689\) 31.9799 1.21834
\(690\) 0 0
\(691\) −15.9991 −0.608636 −0.304318 0.952570i \(-0.598429\pi\)
−0.304318 + 0.952570i \(0.598429\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.9990 0.796539
\(696\) 0 0
\(697\) −0.895926 −0.0339356
\(698\) 0 0
\(699\) −5.58368 −0.211194
\(700\) 0 0
\(701\) 2.12285 0.0801789 0.0400895 0.999196i \(-0.487236\pi\)
0.0400895 + 0.999196i \(0.487236\pi\)
\(702\) 0 0
\(703\) −3.49175 −0.131694
\(704\) 0 0
\(705\) −21.5421 −0.811324
\(706\) 0 0
\(707\) −25.7987 −0.970261
\(708\) 0 0
\(709\) 25.4377 0.955334 0.477667 0.878541i \(-0.341483\pi\)
0.477667 + 0.878541i \(0.341483\pi\)
\(710\) 0 0
\(711\) −2.79575 −0.104849
\(712\) 0 0
\(713\) −1.86706 −0.0699219
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.15877 0.0806208
\(718\) 0 0
\(719\) 4.59583 0.171395 0.0856977 0.996321i \(-0.472688\pi\)
0.0856977 + 0.996321i \(0.472688\pi\)
\(720\) 0 0
\(721\) −26.7494 −0.996199
\(722\) 0 0
\(723\) −9.90295 −0.368295
\(724\) 0 0
\(725\) 8.80520 0.327017
\(726\) 0 0
\(727\) 11.8175 0.438288 0.219144 0.975692i \(-0.429673\pi\)
0.219144 + 0.975692i \(0.429673\pi\)
\(728\) 0 0
\(729\) −11.1936 −0.414579
\(730\) 0 0
\(731\) −1.66950 −0.0617488
\(732\) 0 0
\(733\) −6.16798 −0.227819 −0.113910 0.993491i \(-0.536337\pi\)
−0.113910 + 0.993491i \(0.536337\pi\)
\(734\) 0 0
\(735\) −2.26881 −0.0836863
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.40065 0.0515239 0.0257619 0.999668i \(-0.491799\pi\)
0.0257619 + 0.999668i \(0.491799\pi\)
\(740\) 0 0
\(741\) 3.83214 0.140777
\(742\) 0 0
\(743\) −2.10767 −0.0773228 −0.0386614 0.999252i \(-0.512309\pi\)
−0.0386614 + 0.999252i \(0.512309\pi\)
\(744\) 0 0
\(745\) −36.4210 −1.33436
\(746\) 0 0
\(747\) 6.35458 0.232502
\(748\) 0 0
\(749\) −35.9078 −1.31204
\(750\) 0 0
\(751\) −48.6988 −1.77704 −0.888522 0.458833i \(-0.848268\pi\)
−0.888522 + 0.458833i \(0.848268\pi\)
\(752\) 0 0
\(753\) −16.9817 −0.618847
\(754\) 0 0
\(755\) 9.88355 0.359699
\(756\) 0 0
\(757\) −12.4787 −0.453545 −0.226773 0.973948i \(-0.572817\pi\)
−0.226773 + 0.973948i \(0.572817\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 40.0185 1.45067 0.725334 0.688397i \(-0.241685\pi\)
0.725334 + 0.688397i \(0.241685\pi\)
\(762\) 0 0
\(763\) −43.8717 −1.58826
\(764\) 0 0
\(765\) 1.85269 0.0669840
\(766\) 0 0
\(767\) 53.3481 1.92629
\(768\) 0 0
\(769\) 17.9730 0.648125 0.324062 0.946036i \(-0.394951\pi\)
0.324062 + 0.946036i \(0.394951\pi\)
\(770\) 0 0
\(771\) 11.8493 0.426740
\(772\) 0 0
\(773\) 13.8605 0.498526 0.249263 0.968436i \(-0.419812\pi\)
0.249263 + 0.968436i \(0.419812\pi\)
\(774\) 0 0
\(775\) −2.34771 −0.0843322
\(776\) 0 0
\(777\) 4.83535 0.173467
\(778\) 0 0
\(779\) −5.09084 −0.182398
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 2.71304 0.0969560
\(784\) 0 0
\(785\) 4.40079 0.157071
\(786\) 0 0
\(787\) 36.9065 1.31557 0.657787 0.753204i \(-0.271493\pi\)
0.657787 + 0.753204i \(0.271493\pi\)
\(788\) 0 0
\(789\) 2.99812 0.106736
\(790\) 0 0
\(791\) 31.6115 1.12398
\(792\) 0 0
\(793\) 101.447 3.60249
\(794\) 0 0
\(795\) −10.5142 −0.372899
\(796\) 0 0
\(797\) −31.6732 −1.12192 −0.560961 0.827843i \(-0.689568\pi\)
−0.560961 + 0.827843i \(0.689568\pi\)
\(798\) 0 0
\(799\) −1.70395 −0.0602813
\(800\) 0 0
\(801\) −9.05991 −0.320116
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −79.7575 −2.81108
\(806\) 0 0
\(807\) −10.1704 −0.358014
\(808\) 0 0
\(809\) 55.5256 1.95218 0.976089 0.217372i \(-0.0697486\pi\)
0.976089 + 0.217372i \(0.0697486\pi\)
\(810\) 0 0
\(811\) −30.7281 −1.07901 −0.539505 0.841983i \(-0.681389\pi\)
−0.539505 + 0.841983i \(0.681389\pi\)
\(812\) 0 0
\(813\) 0.542405 0.0190230
\(814\) 0 0
\(815\) −65.8507 −2.30665
\(816\) 0 0
\(817\) −9.48647 −0.331890
\(818\) 0 0
\(819\) 44.3410 1.54940
\(820\) 0 0
\(821\) −26.6887 −0.931444 −0.465722 0.884931i \(-0.654205\pi\)
−0.465722 + 0.884931i \(0.654205\pi\)
\(822\) 0 0
\(823\) −37.6630 −1.31285 −0.656424 0.754392i \(-0.727932\pi\)
−0.656424 + 0.754392i \(0.727932\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 50.4754 1.75520 0.877601 0.479391i \(-0.159143\pi\)
0.877601 + 0.479391i \(0.159143\pi\)
\(828\) 0 0
\(829\) −49.8921 −1.73282 −0.866411 0.499331i \(-0.833579\pi\)
−0.866411 + 0.499331i \(0.833579\pi\)
\(830\) 0 0
\(831\) −9.25410 −0.321021
\(832\) 0 0
\(833\) −0.179459 −0.00621789
\(834\) 0 0
\(835\) −62.8877 −2.17632
\(836\) 0 0
\(837\) −0.723369 −0.0250033
\(838\) 0 0
\(839\) −36.7818 −1.26985 −0.634924 0.772574i \(-0.718969\pi\)
−0.634924 + 0.772574i \(0.718969\pi\)
\(840\) 0 0
\(841\) −28.2883 −0.975460
\(842\) 0 0
\(843\) 4.73422 0.163055
\(844\) 0 0
\(845\) −128.861 −4.43297
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −5.11301 −0.175478
\(850\) 0 0
\(851\) −28.9843 −0.993569
\(852\) 0 0
\(853\) 27.1023 0.927964 0.463982 0.885845i \(-0.346420\pi\)
0.463982 + 0.885845i \(0.346420\pi\)
\(854\) 0 0
\(855\) 10.5273 0.360028
\(856\) 0 0
\(857\) 9.71381 0.331817 0.165909 0.986141i \(-0.446944\pi\)
0.165909 + 0.986141i \(0.446944\pi\)
\(858\) 0 0
\(859\) −3.38681 −0.115556 −0.0577782 0.998329i \(-0.518402\pi\)
−0.0577782 + 0.998329i \(0.518402\pi\)
\(860\) 0 0
\(861\) 7.04975 0.240255
\(862\) 0 0
\(863\) 44.8663 1.52727 0.763634 0.645650i \(-0.223413\pi\)
0.763634 + 0.645650i \(0.223413\pi\)
\(864\) 0 0
\(865\) −8.34403 −0.283706
\(866\) 0 0
\(867\) 9.60906 0.326341
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −14.2018 −0.481210
\(872\) 0 0
\(873\) −51.1540 −1.73130
\(874\) 0 0
\(875\) −52.2479 −1.76630
\(876\) 0 0
\(877\) −5.09806 −0.172149 −0.0860746 0.996289i \(-0.527432\pi\)
−0.0860746 + 0.996289i \(0.527432\pi\)
\(878\) 0 0
\(879\) 4.20588 0.141861
\(880\) 0 0
\(881\) 35.7531 1.20455 0.602276 0.798288i \(-0.294261\pi\)
0.602276 + 0.798288i \(0.294261\pi\)
\(882\) 0 0
\(883\) 36.1681 1.21715 0.608577 0.793495i \(-0.291741\pi\)
0.608577 + 0.793495i \(0.291741\pi\)
\(884\) 0 0
\(885\) −17.5395 −0.589583
\(886\) 0 0
\(887\) 8.68127 0.291489 0.145744 0.989322i \(-0.453442\pi\)
0.145744 + 0.989322i \(0.453442\pi\)
\(888\) 0 0
\(889\) 44.8412 1.50392
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −9.68218 −0.324002
\(894\) 0 0
\(895\) −36.8083 −1.23037
\(896\) 0 0
\(897\) 31.8098 1.06210
\(898\) 0 0
\(899\) −0.189746 −0.00632838
\(900\) 0 0
\(901\) −0.831653 −0.0277064
\(902\) 0 0
\(903\) 13.1368 0.437165
\(904\) 0 0
\(905\) −57.5943 −1.91450
\(906\) 0 0
\(907\) 23.1887 0.769970 0.384985 0.922923i \(-0.374207\pi\)
0.384985 + 0.922923i \(0.374207\pi\)
\(908\) 0 0
\(909\) 28.2661 0.937526
\(910\) 0 0
\(911\) 12.1119 0.401284 0.200642 0.979665i \(-0.435697\pi\)
0.200642 + 0.979665i \(0.435697\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −33.3532 −1.10262
\(916\) 0 0
\(917\) 7.28432 0.240549
\(918\) 0 0
\(919\) −41.2716 −1.36142 −0.680711 0.732552i \(-0.738329\pi\)
−0.680711 + 0.732552i \(0.738329\pi\)
\(920\) 0 0
\(921\) 9.70617 0.319829
\(922\) 0 0
\(923\) 50.9818 1.67809
\(924\) 0 0
\(925\) −36.4459 −1.19834
\(926\) 0 0
\(927\) 29.3076 0.962589
\(928\) 0 0
\(929\) 33.3106 1.09288 0.546442 0.837497i \(-0.315982\pi\)
0.546442 + 0.837497i \(0.315982\pi\)
\(930\) 0 0
\(931\) −1.01972 −0.0334201
\(932\) 0 0
\(933\) −3.69558 −0.120988
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 16.4558 0.537586 0.268793 0.963198i \(-0.413375\pi\)
0.268793 + 0.963198i \(0.413375\pi\)
\(938\) 0 0
\(939\) 9.80154 0.319861
\(940\) 0 0
\(941\) −36.1773 −1.17934 −0.589672 0.807642i \(-0.700743\pi\)
−0.589672 + 0.807642i \(0.700743\pi\)
\(942\) 0 0
\(943\) −42.2580 −1.37611
\(944\) 0 0
\(945\) −30.9011 −1.00521
\(946\) 0 0
\(947\) 53.5210 1.73920 0.869600 0.493758i \(-0.164377\pi\)
0.869600 + 0.493758i \(0.164377\pi\)
\(948\) 0 0
\(949\) −9.25064 −0.300289
\(950\) 0 0
\(951\) −19.0728 −0.618478
\(952\) 0 0
\(953\) −3.55665 −0.115211 −0.0576056 0.998339i \(-0.518347\pi\)
−0.0576056 + 0.998339i \(0.518347\pi\)
\(954\) 0 0
\(955\) −9.50776 −0.307664
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 21.7755 0.703168
\(960\) 0 0
\(961\) −30.9494 −0.998368
\(962\) 0 0
\(963\) 39.3419 1.26778
\(964\) 0 0
\(965\) 64.4566 2.07493
\(966\) 0 0
\(967\) −29.3275 −0.943108 −0.471554 0.881837i \(-0.656307\pi\)
−0.471554 + 0.881837i \(0.656307\pi\)
\(968\) 0 0
\(969\) −0.0996567 −0.00320143
\(970\) 0 0
\(971\) −27.8992 −0.895327 −0.447663 0.894202i \(-0.647744\pi\)
−0.447663 + 0.894202i \(0.647744\pi\)
\(972\) 0 0
\(973\) −13.0698 −0.418998
\(974\) 0 0
\(975\) 39.9988 1.28099
\(976\) 0 0
\(977\) 38.7061 1.23832 0.619158 0.785266i \(-0.287474\pi\)
0.619158 + 0.785266i \(0.287474\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 48.0675 1.53468
\(982\) 0 0
\(983\) 54.6223 1.74218 0.871090 0.491124i \(-0.163414\pi\)
0.871090 + 0.491124i \(0.163414\pi\)
\(984\) 0 0
\(985\) −30.1419 −0.960402
\(986\) 0 0
\(987\) 13.4078 0.426775
\(988\) 0 0
\(989\) −78.7452 −2.50395
\(990\) 0 0
\(991\) 25.9988 0.825879 0.412939 0.910759i \(-0.364502\pi\)
0.412939 + 0.910759i \(0.364502\pi\)
\(992\) 0 0
\(993\) 3.69040 0.117111
\(994\) 0 0
\(995\) 27.4164 0.869159
\(996\) 0 0
\(997\) 28.6019 0.905830 0.452915 0.891554i \(-0.350384\pi\)
0.452915 + 0.891554i \(0.350384\pi\)
\(998\) 0 0
\(999\) −11.2296 −0.355290
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 9196.2.a.n.1.3 6
11.10 odd 2 836.2.a.e.1.3 6
33.32 even 2 7524.2.a.q.1.6 6
44.43 even 2 3344.2.a.w.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
836.2.a.e.1.3 6 11.10 odd 2
3344.2.a.w.1.4 6 44.43 even 2
7524.2.a.q.1.6 6 33.32 even 2
9196.2.a.n.1.3 6 1.1 even 1 trivial