Properties

Label 1881.2.a.k.1.3
Level $1881$
Weight $2$
Character 1881.1
Self dual yes
Analytic conductor $15.020$
Analytic rank $0$
Dimension $5$
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] = [1881,2,Mod(1,1881)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1881, 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("1881.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1881 = 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1881.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: \(15.0198606202\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.246832.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 209)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.15351\) of defining polynomial
Character \(\chi\) \(=\) 1881.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.484093 q^{2} -1.76565 q^{4} -0.637602 q^{5} +2.66942 q^{7} +1.82293 q^{8} +O(q^{10})\) \(q-0.484093 q^{2} -1.76565 q^{4} -0.637602 q^{5} +2.66942 q^{7} +1.82293 q^{8} +0.308658 q^{10} -1.00000 q^{11} -1.20725 q^{13} -1.29225 q^{14} +2.64884 q^{16} -0.222022 q^{17} -1.00000 q^{19} +1.12578 q^{20} +0.484093 q^{22} +9.48717 q^{23} -4.59346 q^{25} +0.584420 q^{26} -4.71327 q^{28} -4.94518 q^{29} -3.05563 q^{31} -4.92814 q^{32} +0.107479 q^{34} -1.70203 q^{35} +7.18015 q^{37} +0.484093 q^{38} -1.16230 q^{40} +6.92650 q^{41} +1.53538 q^{43} +1.76565 q^{44} -4.59267 q^{46} -5.94581 q^{47} +0.125785 q^{49} +2.22366 q^{50} +2.13158 q^{52} +9.63879 q^{53} +0.637602 q^{55} +4.86615 q^{56} +2.39392 q^{58} -2.65817 q^{59} -0.809792 q^{61} +1.47921 q^{62} -2.91201 q^{64} +0.769744 q^{65} -2.22447 q^{67} +0.392015 q^{68} +0.823938 q^{70} -2.58912 q^{71} +16.6108 q^{73} -3.47586 q^{74} +1.76565 q^{76} -2.66942 q^{77} +5.69298 q^{79} -1.68891 q^{80} -3.35307 q^{82} +2.93784 q^{83} +0.141562 q^{85} -0.743267 q^{86} -1.82293 q^{88} +5.54136 q^{89} -3.22265 q^{91} -16.7511 q^{92} +2.87832 q^{94} +0.637602 q^{95} +13.7728 q^{97} -0.0608914 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{7} - 6 q^{8} + 12 q^{10} - 5 q^{11} + 4 q^{13} + 14 q^{14} + 8 q^{16} + 4 q^{17} - 5 q^{19} + 8 q^{20} + 2 q^{22} - 3 q^{23} + 6 q^{25} + 6 q^{26} - 10 q^{28} - 10 q^{29} + 11 q^{31} - 14 q^{32} - 4 q^{34} + 8 q^{35} + q^{37} + 2 q^{38} - 16 q^{40} - 2 q^{41} + 20 q^{43} - 6 q^{44} - 4 q^{46} + 20 q^{47} + 3 q^{49} + 32 q^{50} + 6 q^{52} + 14 q^{53} - 5 q^{55} + 38 q^{56} - 6 q^{58} - 3 q^{59} - 10 q^{61} + 6 q^{62} + 9 q^{67} - 24 q^{68} + 50 q^{70} - 23 q^{71} - 8 q^{74} - 6 q^{76} - 6 q^{77} + 44 q^{79} + 18 q^{80} - 30 q^{82} + 14 q^{83} - 12 q^{85} - 52 q^{86} + 6 q^{88} + 27 q^{89} + 24 q^{91} - 58 q^{92} - 8 q^{94} - 5 q^{95} + 15 q^{97} + 10 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.484093 −0.342305 −0.171153 0.985245i \(-0.554749\pi\)
−0.171153 + 0.985245i \(0.554749\pi\)
\(3\) 0 0
\(4\) −1.76565 −0.882827
\(5\) −0.637602 −0.285144 −0.142572 0.989784i \(-0.545537\pi\)
−0.142572 + 0.989784i \(0.545537\pi\)
\(6\) 0 0
\(7\) 2.66942 1.00894 0.504472 0.863428i \(-0.331687\pi\)
0.504472 + 0.863428i \(0.331687\pi\)
\(8\) 1.82293 0.644502
\(9\) 0 0
\(10\) 0.308658 0.0976064
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.20725 −0.334831 −0.167415 0.985886i \(-0.553542\pi\)
−0.167415 + 0.985886i \(0.553542\pi\)
\(14\) −1.29225 −0.345367
\(15\) 0 0
\(16\) 2.64884 0.662211
\(17\) −0.222022 −0.0538483 −0.0269242 0.999637i \(-0.508571\pi\)
−0.0269242 + 0.999637i \(0.508571\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 1.12578 0.251733
\(21\) 0 0
\(22\) 0.484093 0.103209
\(23\) 9.48717 1.97821 0.989106 0.147206i \(-0.0470279\pi\)
0.989106 + 0.147206i \(0.0470279\pi\)
\(24\) 0 0
\(25\) −4.59346 −0.918693
\(26\) 0.584420 0.114614
\(27\) 0 0
\(28\) −4.71327 −0.890724
\(29\) −4.94518 −0.918297 −0.459148 0.888360i \(-0.651845\pi\)
−0.459148 + 0.888360i \(0.651845\pi\)
\(30\) 0 0
\(31\) −3.05563 −0.548808 −0.274404 0.961615i \(-0.588480\pi\)
−0.274404 + 0.961615i \(0.588480\pi\)
\(32\) −4.92814 −0.871180
\(33\) 0 0
\(34\) 0.107479 0.0184326
\(35\) −1.70203 −0.287695
\(36\) 0 0
\(37\) 7.18015 1.18041 0.590205 0.807254i \(-0.299047\pi\)
0.590205 + 0.807254i \(0.299047\pi\)
\(38\) 0.484093 0.0785302
\(39\) 0 0
\(40\) −1.16230 −0.183776
\(41\) 6.92650 1.08174 0.540869 0.841107i \(-0.318096\pi\)
0.540869 + 0.841107i \(0.318096\pi\)
\(42\) 0 0
\(43\) 1.53538 0.234144 0.117072 0.993123i \(-0.462649\pi\)
0.117072 + 0.993123i \(0.462649\pi\)
\(44\) 1.76565 0.266182
\(45\) 0 0
\(46\) −4.59267 −0.677152
\(47\) −5.94581 −0.867285 −0.433642 0.901085i \(-0.642772\pi\)
−0.433642 + 0.901085i \(0.642772\pi\)
\(48\) 0 0
\(49\) 0.125785 0.0179692
\(50\) 2.22366 0.314473
\(51\) 0 0
\(52\) 2.13158 0.295598
\(53\) 9.63879 1.32399 0.661995 0.749509i \(-0.269710\pi\)
0.661995 + 0.749509i \(0.269710\pi\)
\(54\) 0 0
\(55\) 0.637602 0.0859742
\(56\) 4.86615 0.650266
\(57\) 0 0
\(58\) 2.39392 0.314338
\(59\) −2.65817 −0.346065 −0.173032 0.984916i \(-0.555357\pi\)
−0.173032 + 0.984916i \(0.555357\pi\)
\(60\) 0 0
\(61\) −0.809792 −0.103683 −0.0518416 0.998655i \(-0.516509\pi\)
−0.0518416 + 0.998655i \(0.516509\pi\)
\(62\) 1.47921 0.187860
\(63\) 0 0
\(64\) −2.91201 −0.364001
\(65\) 0.769744 0.0954750
\(66\) 0 0
\(67\) −2.22447 −0.271763 −0.135881 0.990725i \(-0.543387\pi\)
−0.135881 + 0.990725i \(0.543387\pi\)
\(68\) 0.392015 0.0475387
\(69\) 0 0
\(70\) 0.823938 0.0984794
\(71\) −2.58912 −0.307272 −0.153636 0.988127i \(-0.549098\pi\)
−0.153636 + 0.988127i \(0.549098\pi\)
\(72\) 0 0
\(73\) 16.6108 1.94414 0.972071 0.234687i \(-0.0754065\pi\)
0.972071 + 0.234687i \(0.0754065\pi\)
\(74\) −3.47586 −0.404060
\(75\) 0 0
\(76\) 1.76565 0.202534
\(77\) −2.66942 −0.304208
\(78\) 0 0
\(79\) 5.69298 0.640510 0.320255 0.947331i \(-0.396231\pi\)
0.320255 + 0.947331i \(0.396231\pi\)
\(80\) −1.68891 −0.188826
\(81\) 0 0
\(82\) −3.35307 −0.370284
\(83\) 2.93784 0.322470 0.161235 0.986916i \(-0.448452\pi\)
0.161235 + 0.986916i \(0.448452\pi\)
\(84\) 0 0
\(85\) 0.141562 0.0153545
\(86\) −0.743267 −0.0801486
\(87\) 0 0
\(88\) −1.82293 −0.194325
\(89\) 5.54136 0.587383 0.293692 0.955900i \(-0.405116\pi\)
0.293692 + 0.955900i \(0.405116\pi\)
\(90\) 0 0
\(91\) −3.22265 −0.337826
\(92\) −16.7511 −1.74642
\(93\) 0 0
\(94\) 2.87832 0.296876
\(95\) 0.637602 0.0654166
\(96\) 0 0
\(97\) 13.7728 1.39842 0.699209 0.714917i \(-0.253536\pi\)
0.699209 + 0.714917i \(0.253536\pi\)
\(98\) −0.0608914 −0.00615096
\(99\) 0 0
\(100\) 8.11047 0.811047
\(101\) −12.0308 −1.19711 −0.598555 0.801082i \(-0.704258\pi\)
−0.598555 + 0.801082i \(0.704258\pi\)
\(102\) 0 0
\(103\) 8.53068 0.840553 0.420276 0.907396i \(-0.361933\pi\)
0.420276 + 0.907396i \(0.361933\pi\)
\(104\) −2.20073 −0.215799
\(105\) 0 0
\(106\) −4.66607 −0.453208
\(107\) −1.64585 −0.159110 −0.0795552 0.996830i \(-0.525350\pi\)
−0.0795552 + 0.996830i \(0.525350\pi\)
\(108\) 0 0
\(109\) 16.8065 1.60977 0.804886 0.593430i \(-0.202226\pi\)
0.804886 + 0.593430i \(0.202226\pi\)
\(110\) −0.308658 −0.0294294
\(111\) 0 0
\(112\) 7.07087 0.668134
\(113\) 11.2947 1.06252 0.531258 0.847210i \(-0.321720\pi\)
0.531258 + 0.847210i \(0.321720\pi\)
\(114\) 0 0
\(115\) −6.04904 −0.564076
\(116\) 8.73148 0.810697
\(117\) 0 0
\(118\) 1.28680 0.118460
\(119\) −0.592670 −0.0543300
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0.392015 0.0354913
\(123\) 0 0
\(124\) 5.39519 0.484502
\(125\) 6.11681 0.547104
\(126\) 0 0
\(127\) 18.5894 1.64954 0.824771 0.565467i \(-0.191304\pi\)
0.824771 + 0.565467i \(0.191304\pi\)
\(128\) 11.2660 0.995779
\(129\) 0 0
\(130\) −0.372628 −0.0326816
\(131\) 3.09098 0.270060 0.135030 0.990842i \(-0.456887\pi\)
0.135030 + 0.990842i \(0.456887\pi\)
\(132\) 0 0
\(133\) −2.66942 −0.231468
\(134\) 1.07685 0.0930257
\(135\) 0 0
\(136\) −0.404730 −0.0347053
\(137\) 8.67619 0.741257 0.370629 0.928781i \(-0.379142\pi\)
0.370629 + 0.928781i \(0.379142\pi\)
\(138\) 0 0
\(139\) 14.5426 1.23348 0.616742 0.787166i \(-0.288452\pi\)
0.616742 + 0.787166i \(0.288452\pi\)
\(140\) 3.00519 0.253985
\(141\) 0 0
\(142\) 1.25338 0.105181
\(143\) 1.20725 0.100955
\(144\) 0 0
\(145\) 3.15306 0.261847
\(146\) −8.04115 −0.665490
\(147\) 0 0
\(148\) −12.6777 −1.04210
\(149\) 18.4716 1.51325 0.756625 0.653849i \(-0.226847\pi\)
0.756625 + 0.653849i \(0.226847\pi\)
\(150\) 0 0
\(151\) −0.913992 −0.0743796 −0.0371898 0.999308i \(-0.511841\pi\)
−0.0371898 + 0.999308i \(0.511841\pi\)
\(152\) −1.82293 −0.147859
\(153\) 0 0
\(154\) 1.29225 0.104132
\(155\) 1.94828 0.156489
\(156\) 0 0
\(157\) −2.39421 −0.191079 −0.0955395 0.995426i \(-0.530458\pi\)
−0.0955395 + 0.995426i \(0.530458\pi\)
\(158\) −2.75593 −0.219250
\(159\) 0 0
\(160\) 3.14219 0.248412
\(161\) 25.3252 1.99591
\(162\) 0 0
\(163\) 14.1986 1.11212 0.556061 0.831141i \(-0.312312\pi\)
0.556061 + 0.831141i \(0.312312\pi\)
\(164\) −12.2298 −0.954987
\(165\) 0 0
\(166\) −1.42219 −0.110383
\(167\) −9.25056 −0.715830 −0.357915 0.933754i \(-0.616512\pi\)
−0.357915 + 0.933754i \(0.616512\pi\)
\(168\) 0 0
\(169\) −11.5426 −0.887888
\(170\) −0.0685290 −0.00525594
\(171\) 0 0
\(172\) −2.71095 −0.206708
\(173\) −5.39376 −0.410080 −0.205040 0.978754i \(-0.565732\pi\)
−0.205040 + 0.978754i \(0.565732\pi\)
\(174\) 0 0
\(175\) −12.2619 −0.926910
\(176\) −2.64884 −0.199664
\(177\) 0 0
\(178\) −2.68253 −0.201064
\(179\) −1.30720 −0.0977048 −0.0488524 0.998806i \(-0.515556\pi\)
−0.0488524 + 0.998806i \(0.515556\pi\)
\(180\) 0 0
\(181\) −10.7624 −0.799961 −0.399980 0.916524i \(-0.630983\pi\)
−0.399980 + 0.916524i \(0.630983\pi\)
\(182\) 1.56006 0.115639
\(183\) 0 0
\(184\) 17.2944 1.27496
\(185\) −4.57808 −0.336587
\(186\) 0 0
\(187\) 0.222022 0.0162359
\(188\) 10.4982 0.765663
\(189\) 0 0
\(190\) −0.308658 −0.0223924
\(191\) −15.3041 −1.10737 −0.553684 0.832727i \(-0.686778\pi\)
−0.553684 + 0.832727i \(0.686778\pi\)
\(192\) 0 0
\(193\) −18.3032 −1.31749 −0.658747 0.752364i \(-0.728913\pi\)
−0.658747 + 0.752364i \(0.728913\pi\)
\(194\) −6.66732 −0.478686
\(195\) 0 0
\(196\) −0.222092 −0.0158637
\(197\) 0.576171 0.0410505 0.0205252 0.999789i \(-0.493466\pi\)
0.0205252 + 0.999789i \(0.493466\pi\)
\(198\) 0 0
\(199\) −10.1678 −0.720778 −0.360389 0.932802i \(-0.617356\pi\)
−0.360389 + 0.932802i \(0.617356\pi\)
\(200\) −8.37354 −0.592099
\(201\) 0 0
\(202\) 5.82402 0.409777
\(203\) −13.2007 −0.926510
\(204\) 0 0
\(205\) −4.41635 −0.308451
\(206\) −4.12964 −0.287726
\(207\) 0 0
\(208\) −3.19781 −0.221728
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −7.25837 −0.499687 −0.249843 0.968286i \(-0.580379\pi\)
−0.249843 + 0.968286i \(0.580379\pi\)
\(212\) −17.0188 −1.16885
\(213\) 0 0
\(214\) 0.796745 0.0544643
\(215\) −0.978963 −0.0667647
\(216\) 0 0
\(217\) −8.15675 −0.553716
\(218\) −8.13591 −0.551033
\(219\) 0 0
\(220\) −1.12578 −0.0759004
\(221\) 0.268036 0.0180301
\(222\) 0 0
\(223\) 16.2772 1.09000 0.545000 0.838436i \(-0.316529\pi\)
0.545000 + 0.838436i \(0.316529\pi\)
\(224\) −13.1553 −0.878972
\(225\) 0 0
\(226\) −5.46768 −0.363705
\(227\) 20.9260 1.38890 0.694452 0.719539i \(-0.255647\pi\)
0.694452 + 0.719539i \(0.255647\pi\)
\(228\) 0 0
\(229\) −10.8083 −0.714234 −0.357117 0.934060i \(-0.616240\pi\)
−0.357117 + 0.934060i \(0.616240\pi\)
\(230\) 2.92830 0.193086
\(231\) 0 0
\(232\) −9.01469 −0.591844
\(233\) 25.4173 1.66514 0.832570 0.553919i \(-0.186868\pi\)
0.832570 + 0.553919i \(0.186868\pi\)
\(234\) 0 0
\(235\) 3.79106 0.247301
\(236\) 4.69342 0.305515
\(237\) 0 0
\(238\) 0.286907 0.0185974
\(239\) −0.352238 −0.0227844 −0.0113922 0.999935i \(-0.503626\pi\)
−0.0113922 + 0.999935i \(0.503626\pi\)
\(240\) 0 0
\(241\) −15.6832 −1.01024 −0.505122 0.863048i \(-0.668552\pi\)
−0.505122 + 0.863048i \(0.668552\pi\)
\(242\) −0.484093 −0.0311187
\(243\) 0 0
\(244\) 1.42981 0.0915344
\(245\) −0.0802004 −0.00512382
\(246\) 0 0
\(247\) 1.20725 0.0768154
\(248\) −5.57019 −0.353707
\(249\) 0 0
\(250\) −2.96110 −0.187277
\(251\) −1.16332 −0.0734282 −0.0367141 0.999326i \(-0.511689\pi\)
−0.0367141 + 0.999326i \(0.511689\pi\)
\(252\) 0 0
\(253\) −9.48717 −0.596453
\(254\) −8.99899 −0.564647
\(255\) 0 0
\(256\) 0.370256 0.0231410
\(257\) 15.0510 0.938857 0.469428 0.882971i \(-0.344460\pi\)
0.469428 + 0.882971i \(0.344460\pi\)
\(258\) 0 0
\(259\) 19.1668 1.19097
\(260\) −1.35910 −0.0842879
\(261\) 0 0
\(262\) −1.49632 −0.0924429
\(263\) 20.6609 1.27400 0.637002 0.770862i \(-0.280174\pi\)
0.637002 + 0.770862i \(0.280174\pi\)
\(264\) 0 0
\(265\) −6.14571 −0.377528
\(266\) 1.29225 0.0792326
\(267\) 0 0
\(268\) 3.92765 0.239919
\(269\) 2.82662 0.172342 0.0861711 0.996280i \(-0.472537\pi\)
0.0861711 + 0.996280i \(0.472537\pi\)
\(270\) 0 0
\(271\) 23.5970 1.43341 0.716707 0.697375i \(-0.245649\pi\)
0.716707 + 0.697375i \(0.245649\pi\)
\(272\) −0.588102 −0.0356589
\(273\) 0 0
\(274\) −4.20008 −0.253736
\(275\) 4.59346 0.276996
\(276\) 0 0
\(277\) −18.7773 −1.12822 −0.564110 0.825700i \(-0.690781\pi\)
−0.564110 + 0.825700i \(0.690781\pi\)
\(278\) −7.03994 −0.422228
\(279\) 0 0
\(280\) −3.10267 −0.185420
\(281\) −27.2632 −1.62639 −0.813194 0.581993i \(-0.802273\pi\)
−0.813194 + 0.581993i \(0.802273\pi\)
\(282\) 0 0
\(283\) −27.2601 −1.62044 −0.810221 0.586124i \(-0.800653\pi\)
−0.810221 + 0.586124i \(0.800653\pi\)
\(284\) 4.57149 0.271268
\(285\) 0 0
\(286\) −0.584420 −0.0345575
\(287\) 18.4897 1.09141
\(288\) 0 0
\(289\) −16.9507 −0.997100
\(290\) −1.52637 −0.0896316
\(291\) 0 0
\(292\) −29.3289 −1.71634
\(293\) −30.9996 −1.81101 −0.905507 0.424332i \(-0.860509\pi\)
−0.905507 + 0.424332i \(0.860509\pi\)
\(294\) 0 0
\(295\) 1.69486 0.0986784
\(296\) 13.0889 0.760776
\(297\) 0 0
\(298\) −8.94195 −0.517993
\(299\) −11.4534 −0.662366
\(300\) 0 0
\(301\) 4.09858 0.236238
\(302\) 0.442457 0.0254605
\(303\) 0 0
\(304\) −2.64884 −0.151922
\(305\) 0.516325 0.0295647
\(306\) 0 0
\(307\) −18.2495 −1.04156 −0.520778 0.853692i \(-0.674358\pi\)
−0.520778 + 0.853692i \(0.674358\pi\)
\(308\) 4.71327 0.268563
\(309\) 0 0
\(310\) −0.943146 −0.0535671
\(311\) −30.8931 −1.75179 −0.875894 0.482503i \(-0.839728\pi\)
−0.875894 + 0.482503i \(0.839728\pi\)
\(312\) 0 0
\(313\) 28.7973 1.62772 0.813859 0.581062i \(-0.197363\pi\)
0.813859 + 0.581062i \(0.197363\pi\)
\(314\) 1.15902 0.0654073
\(315\) 0 0
\(316\) −10.0518 −0.565460
\(317\) −5.96040 −0.334769 −0.167385 0.985892i \(-0.553532\pi\)
−0.167385 + 0.985892i \(0.553532\pi\)
\(318\) 0 0
\(319\) 4.94518 0.276877
\(320\) 1.85670 0.103793
\(321\) 0 0
\(322\) −12.2597 −0.683209
\(323\) 0.222022 0.0123536
\(324\) 0 0
\(325\) 5.54545 0.307606
\(326\) −6.87345 −0.380685
\(327\) 0 0
\(328\) 12.6265 0.697181
\(329\) −15.8718 −0.875043
\(330\) 0 0
\(331\) 33.4010 1.83589 0.917944 0.396711i \(-0.129849\pi\)
0.917944 + 0.396711i \(0.129849\pi\)
\(332\) −5.18722 −0.284686
\(333\) 0 0
\(334\) 4.47813 0.245032
\(335\) 1.41833 0.0774915
\(336\) 0 0
\(337\) 24.9988 1.36177 0.680885 0.732390i \(-0.261595\pi\)
0.680885 + 0.732390i \(0.261595\pi\)
\(338\) 5.58766 0.303929
\(339\) 0 0
\(340\) −0.249949 −0.0135554
\(341\) 3.05563 0.165472
\(342\) 0 0
\(343\) −18.3501 −0.990815
\(344\) 2.79889 0.150906
\(345\) 0 0
\(346\) 2.61108 0.140372
\(347\) 8.35577 0.448561 0.224281 0.974525i \(-0.427997\pi\)
0.224281 + 0.974525i \(0.427997\pi\)
\(348\) 0 0
\(349\) −28.3911 −1.51974 −0.759871 0.650074i \(-0.774738\pi\)
−0.759871 + 0.650074i \(0.774738\pi\)
\(350\) 5.93588 0.317286
\(351\) 0 0
\(352\) 4.92814 0.262671
\(353\) 12.4082 0.660423 0.330212 0.943907i \(-0.392880\pi\)
0.330212 + 0.943907i \(0.392880\pi\)
\(354\) 0 0
\(355\) 1.65083 0.0876169
\(356\) −9.78413 −0.518558
\(357\) 0 0
\(358\) 0.632806 0.0334448
\(359\) −12.1134 −0.639319 −0.319659 0.947533i \(-0.603568\pi\)
−0.319659 + 0.947533i \(0.603568\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 5.20999 0.273831
\(363\) 0 0
\(364\) 5.69009 0.298242
\(365\) −10.5911 −0.554361
\(366\) 0 0
\(367\) −4.06064 −0.211964 −0.105982 0.994368i \(-0.533799\pi\)
−0.105982 + 0.994368i \(0.533799\pi\)
\(368\) 25.1300 1.30999
\(369\) 0 0
\(370\) 2.21621 0.115216
\(371\) 25.7299 1.33583
\(372\) 0 0
\(373\) 35.4898 1.83759 0.918796 0.394732i \(-0.129163\pi\)
0.918796 + 0.394732i \(0.129163\pi\)
\(374\) −0.107479 −0.00555763
\(375\) 0 0
\(376\) −10.8388 −0.558967
\(377\) 5.97006 0.307474
\(378\) 0 0
\(379\) 13.5584 0.696449 0.348224 0.937411i \(-0.386785\pi\)
0.348224 + 0.937411i \(0.386785\pi\)
\(380\) −1.12578 −0.0577515
\(381\) 0 0
\(382\) 7.40862 0.379058
\(383\) 23.8326 1.21779 0.608894 0.793251i \(-0.291613\pi\)
0.608894 + 0.793251i \(0.291613\pi\)
\(384\) 0 0
\(385\) 1.70203 0.0867432
\(386\) 8.86045 0.450985
\(387\) 0 0
\(388\) −24.3180 −1.23456
\(389\) 12.7567 0.646789 0.323395 0.946264i \(-0.395176\pi\)
0.323395 + 0.946264i \(0.395176\pi\)
\(390\) 0 0
\(391\) −2.10636 −0.106523
\(392\) 0.229296 0.0115812
\(393\) 0 0
\(394\) −0.278920 −0.0140518
\(395\) −3.62986 −0.182638
\(396\) 0 0
\(397\) −30.3169 −1.52156 −0.760780 0.649009i \(-0.775184\pi\)
−0.760780 + 0.649009i \(0.775184\pi\)
\(398\) 4.92217 0.246726
\(399\) 0 0
\(400\) −12.1674 −0.608368
\(401\) −32.6370 −1.62982 −0.814908 0.579591i \(-0.803212\pi\)
−0.814908 + 0.579591i \(0.803212\pi\)
\(402\) 0 0
\(403\) 3.68891 0.183758
\(404\) 21.2422 1.05684
\(405\) 0 0
\(406\) 6.39038 0.317149
\(407\) −7.18015 −0.355907
\(408\) 0 0
\(409\) −23.1587 −1.14512 −0.572562 0.819862i \(-0.694050\pi\)
−0.572562 + 0.819862i \(0.694050\pi\)
\(410\) 2.13792 0.105584
\(411\) 0 0
\(412\) −15.0622 −0.742063
\(413\) −7.09578 −0.349160
\(414\) 0 0
\(415\) −1.87318 −0.0919506
\(416\) 5.94949 0.291698
\(417\) 0 0
\(418\) −0.484093 −0.0236777
\(419\) 14.2213 0.694755 0.347377 0.937725i \(-0.387072\pi\)
0.347377 + 0.937725i \(0.387072\pi\)
\(420\) 0 0
\(421\) 15.9605 0.777866 0.388933 0.921266i \(-0.372844\pi\)
0.388933 + 0.921266i \(0.372844\pi\)
\(422\) 3.51373 0.171045
\(423\) 0 0
\(424\) 17.5708 0.853313
\(425\) 1.01985 0.0494701
\(426\) 0 0
\(427\) −2.16167 −0.104611
\(428\) 2.90600 0.140467
\(429\) 0 0
\(430\) 0.473909 0.0228539
\(431\) −24.5100 −1.18061 −0.590304 0.807181i \(-0.700992\pi\)
−0.590304 + 0.807181i \(0.700992\pi\)
\(432\) 0 0
\(433\) −19.1839 −0.921921 −0.460961 0.887421i \(-0.652495\pi\)
−0.460961 + 0.887421i \(0.652495\pi\)
\(434\) 3.94862 0.189540
\(435\) 0 0
\(436\) −29.6745 −1.42115
\(437\) −9.48717 −0.453833
\(438\) 0 0
\(439\) 13.7961 0.658450 0.329225 0.944251i \(-0.393212\pi\)
0.329225 + 0.944251i \(0.393212\pi\)
\(440\) 1.16230 0.0554105
\(441\) 0 0
\(442\) −0.129754 −0.00617178
\(443\) −14.1259 −0.671140 −0.335570 0.942015i \(-0.608929\pi\)
−0.335570 + 0.942015i \(0.608929\pi\)
\(444\) 0 0
\(445\) −3.53318 −0.167489
\(446\) −7.87967 −0.373113
\(447\) 0 0
\(448\) −7.77337 −0.367257
\(449\) 21.0016 0.991129 0.495565 0.868571i \(-0.334961\pi\)
0.495565 + 0.868571i \(0.334961\pi\)
\(450\) 0 0
\(451\) −6.92650 −0.326156
\(452\) −19.9425 −0.938018
\(453\) 0 0
\(454\) −10.1301 −0.475429
\(455\) 2.05477 0.0963290
\(456\) 0 0
\(457\) −22.4621 −1.05073 −0.525367 0.850876i \(-0.676072\pi\)
−0.525367 + 0.850876i \(0.676072\pi\)
\(458\) 5.23223 0.244486
\(459\) 0 0
\(460\) 10.6805 0.497981
\(461\) 31.1213 1.44946 0.724732 0.689031i \(-0.241964\pi\)
0.724732 + 0.689031i \(0.241964\pi\)
\(462\) 0 0
\(463\) 31.6932 1.47291 0.736455 0.676487i \(-0.236498\pi\)
0.736455 + 0.676487i \(0.236498\pi\)
\(464\) −13.0990 −0.608106
\(465\) 0 0
\(466\) −12.3043 −0.569986
\(467\) 1.75474 0.0811995 0.0405997 0.999175i \(-0.487073\pi\)
0.0405997 + 0.999175i \(0.487073\pi\)
\(468\) 0 0
\(469\) −5.93804 −0.274193
\(470\) −1.83522 −0.0846525
\(471\) 0 0
\(472\) −4.84566 −0.223039
\(473\) −1.53538 −0.0705970
\(474\) 0 0
\(475\) 4.59346 0.210763
\(476\) 1.04645 0.0479640
\(477\) 0 0
\(478\) 0.170516 0.00779922
\(479\) 11.1294 0.508515 0.254257 0.967137i \(-0.418169\pi\)
0.254257 + 0.967137i \(0.418169\pi\)
\(480\) 0 0
\(481\) −8.66823 −0.395237
\(482\) 7.59212 0.345812
\(483\) 0 0
\(484\) −1.76565 −0.0802570
\(485\) −8.78158 −0.398751
\(486\) 0 0
\(487\) 3.27007 0.148181 0.0740905 0.997252i \(-0.476395\pi\)
0.0740905 + 0.997252i \(0.476395\pi\)
\(488\) −1.47619 −0.0668240
\(489\) 0 0
\(490\) 0.0388244 0.00175391
\(491\) −29.2686 −1.32087 −0.660437 0.750882i \(-0.729629\pi\)
−0.660437 + 0.750882i \(0.729629\pi\)
\(492\) 0 0
\(493\) 1.09794 0.0494487
\(494\) −0.584420 −0.0262943
\(495\) 0 0
\(496\) −8.09389 −0.363426
\(497\) −6.91145 −0.310021
\(498\) 0 0
\(499\) −1.04828 −0.0469275 −0.0234638 0.999725i \(-0.507469\pi\)
−0.0234638 + 0.999725i \(0.507469\pi\)
\(500\) −10.8002 −0.482998
\(501\) 0 0
\(502\) 0.563155 0.0251348
\(503\) −28.4724 −1.26952 −0.634761 0.772709i \(-0.718901\pi\)
−0.634761 + 0.772709i \(0.718901\pi\)
\(504\) 0 0
\(505\) 7.67086 0.341349
\(506\) 4.59267 0.204169
\(507\) 0 0
\(508\) −32.8224 −1.45626
\(509\) −39.6801 −1.75879 −0.879396 0.476091i \(-0.842053\pi\)
−0.879396 + 0.476091i \(0.842053\pi\)
\(510\) 0 0
\(511\) 44.3410 1.96153
\(512\) −22.7112 −1.00370
\(513\) 0 0
\(514\) −7.28609 −0.321376
\(515\) −5.43918 −0.239679
\(516\) 0 0
\(517\) 5.94581 0.261496
\(518\) −9.27852 −0.407675
\(519\) 0 0
\(520\) 1.40319 0.0615338
\(521\) 15.3168 0.671043 0.335522 0.942033i \(-0.391087\pi\)
0.335522 + 0.942033i \(0.391087\pi\)
\(522\) 0 0
\(523\) −4.17850 −0.182713 −0.0913566 0.995818i \(-0.529120\pi\)
−0.0913566 + 0.995818i \(0.529120\pi\)
\(524\) −5.45760 −0.238416
\(525\) 0 0
\(526\) −10.0018 −0.436098
\(527\) 0.678418 0.0295524
\(528\) 0 0
\(529\) 67.0064 2.91332
\(530\) 2.97509 0.129230
\(531\) 0 0
\(532\) 4.71327 0.204346
\(533\) −8.36201 −0.362199
\(534\) 0 0
\(535\) 1.04940 0.0453694
\(536\) −4.05505 −0.175151
\(537\) 0 0
\(538\) −1.36835 −0.0589937
\(539\) −0.125785 −0.00541792
\(540\) 0 0
\(541\) −14.6201 −0.628565 −0.314283 0.949329i \(-0.601764\pi\)
−0.314283 + 0.949329i \(0.601764\pi\)
\(542\) −11.4231 −0.490665
\(543\) 0 0
\(544\) 1.09416 0.0469116
\(545\) −10.7159 −0.459017
\(546\) 0 0
\(547\) −34.7220 −1.48461 −0.742303 0.670064i \(-0.766267\pi\)
−0.742303 + 0.670064i \(0.766267\pi\)
\(548\) −15.3192 −0.654402
\(549\) 0 0
\(550\) −2.22366 −0.0948173
\(551\) 4.94518 0.210672
\(552\) 0 0
\(553\) 15.1969 0.646240
\(554\) 9.08997 0.386196
\(555\) 0 0
\(556\) −25.6771 −1.08895
\(557\) 7.07603 0.299821 0.149910 0.988700i \(-0.452101\pi\)
0.149910 + 0.988700i \(0.452101\pi\)
\(558\) 0 0
\(559\) −1.85359 −0.0783985
\(560\) −4.50840 −0.190515
\(561\) 0 0
\(562\) 13.1979 0.556721
\(563\) 32.5712 1.37271 0.686357 0.727265i \(-0.259209\pi\)
0.686357 + 0.727265i \(0.259209\pi\)
\(564\) 0 0
\(565\) −7.20152 −0.302970
\(566\) 13.1964 0.554686
\(567\) 0 0
\(568\) −4.71978 −0.198037
\(569\) −32.6457 −1.36858 −0.684290 0.729210i \(-0.739888\pi\)
−0.684290 + 0.729210i \(0.739888\pi\)
\(570\) 0 0
\(571\) −35.8059 −1.49843 −0.749216 0.662326i \(-0.769569\pi\)
−0.749216 + 0.662326i \(0.769569\pi\)
\(572\) −2.13158 −0.0891260
\(573\) 0 0
\(574\) −8.95073 −0.373596
\(575\) −43.5790 −1.81737
\(576\) 0 0
\(577\) 15.7218 0.654509 0.327254 0.944936i \(-0.393877\pi\)
0.327254 + 0.944936i \(0.393877\pi\)
\(578\) 8.20571 0.341313
\(579\) 0 0
\(580\) −5.56721 −0.231166
\(581\) 7.84233 0.325355
\(582\) 0 0
\(583\) −9.63879 −0.399198
\(584\) 30.2802 1.25300
\(585\) 0 0
\(586\) 15.0067 0.619919
\(587\) −24.4810 −1.01044 −0.505220 0.862991i \(-0.668588\pi\)
−0.505220 + 0.862991i \(0.668588\pi\)
\(588\) 0 0
\(589\) 3.05563 0.125905
\(590\) −0.820468 −0.0337781
\(591\) 0 0
\(592\) 19.0191 0.781680
\(593\) 21.2995 0.874666 0.437333 0.899300i \(-0.355923\pi\)
0.437333 + 0.899300i \(0.355923\pi\)
\(594\) 0 0
\(595\) 0.377887 0.0154919
\(596\) −32.6144 −1.33594
\(597\) 0 0
\(598\) 5.54450 0.226731
\(599\) 8.90839 0.363987 0.181994 0.983300i \(-0.441745\pi\)
0.181994 + 0.983300i \(0.441745\pi\)
\(600\) 0 0
\(601\) −8.36794 −0.341335 −0.170668 0.985329i \(-0.554592\pi\)
−0.170668 + 0.985329i \(0.554592\pi\)
\(602\) −1.98409 −0.0808655
\(603\) 0 0
\(604\) 1.61379 0.0656643
\(605\) −0.637602 −0.0259222
\(606\) 0 0
\(607\) 43.2321 1.75474 0.877368 0.479819i \(-0.159298\pi\)
0.877368 + 0.479819i \(0.159298\pi\)
\(608\) 4.92814 0.199862
\(609\) 0 0
\(610\) −0.249949 −0.0101201
\(611\) 7.17807 0.290394
\(612\) 0 0
\(613\) −12.4893 −0.504438 −0.252219 0.967670i \(-0.581160\pi\)
−0.252219 + 0.967670i \(0.581160\pi\)
\(614\) 8.83447 0.356530
\(615\) 0 0
\(616\) −4.86615 −0.196063
\(617\) 18.4079 0.741073 0.370536 0.928818i \(-0.379174\pi\)
0.370536 + 0.928818i \(0.379174\pi\)
\(618\) 0 0
\(619\) −7.30900 −0.293773 −0.146887 0.989153i \(-0.546925\pi\)
−0.146887 + 0.989153i \(0.546925\pi\)
\(620\) −3.43998 −0.138153
\(621\) 0 0
\(622\) 14.9551 0.599646
\(623\) 14.7922 0.592637
\(624\) 0 0
\(625\) 19.0672 0.762689
\(626\) −13.9406 −0.557177
\(627\) 0 0
\(628\) 4.22735 0.168690
\(629\) −1.59415 −0.0635631
\(630\) 0 0
\(631\) −11.8397 −0.471329 −0.235665 0.971834i \(-0.575727\pi\)
−0.235665 + 0.971834i \(0.575727\pi\)
\(632\) 10.3779 0.412810
\(633\) 0 0
\(634\) 2.88538 0.114593
\(635\) −11.8526 −0.470357
\(636\) 0 0
\(637\) −0.151853 −0.00601664
\(638\) −2.39392 −0.0947764
\(639\) 0 0
\(640\) −7.18320 −0.283941
\(641\) 36.5974 1.44551 0.722756 0.691104i \(-0.242875\pi\)
0.722756 + 0.691104i \(0.242875\pi\)
\(642\) 0 0
\(643\) −14.0452 −0.553888 −0.276944 0.960886i \(-0.589322\pi\)
−0.276944 + 0.960886i \(0.589322\pi\)
\(644\) −44.7156 −1.76204
\(645\) 0 0
\(646\) −0.107479 −0.00422872
\(647\) 43.5266 1.71121 0.855604 0.517631i \(-0.173186\pi\)
0.855604 + 0.517631i \(0.173186\pi\)
\(648\) 0 0
\(649\) 2.65817 0.104342
\(650\) −2.68451 −0.105295
\(651\) 0 0
\(652\) −25.0699 −0.981812
\(653\) −44.0328 −1.72314 −0.861568 0.507642i \(-0.830517\pi\)
−0.861568 + 0.507642i \(0.830517\pi\)
\(654\) 0 0
\(655\) −1.97081 −0.0770060
\(656\) 18.3472 0.716338
\(657\) 0 0
\(658\) 7.68344 0.299532
\(659\) 3.86784 0.150670 0.0753349 0.997158i \(-0.475997\pi\)
0.0753349 + 0.997158i \(0.475997\pi\)
\(660\) 0 0
\(661\) 7.96999 0.309997 0.154998 0.987915i \(-0.450463\pi\)
0.154998 + 0.987915i \(0.450463\pi\)
\(662\) −16.1692 −0.628434
\(663\) 0 0
\(664\) 5.35547 0.207833
\(665\) 1.70203 0.0660017
\(666\) 0 0
\(667\) −46.9158 −1.81659
\(668\) 16.3333 0.631954
\(669\) 0 0
\(670\) −0.686602 −0.0265258
\(671\) 0.809792 0.0312617
\(672\) 0 0
\(673\) 21.7872 0.839835 0.419917 0.907562i \(-0.362059\pi\)
0.419917 + 0.907562i \(0.362059\pi\)
\(674\) −12.1017 −0.466141
\(675\) 0 0
\(676\) 20.3802 0.783852
\(677\) −33.2004 −1.27599 −0.637997 0.770039i \(-0.720237\pi\)
−0.637997 + 0.770039i \(0.720237\pi\)
\(678\) 0 0
\(679\) 36.7654 1.41093
\(680\) 0.258057 0.00989602
\(681\) 0 0
\(682\) −1.47921 −0.0566418
\(683\) 34.9595 1.33769 0.668843 0.743403i \(-0.266790\pi\)
0.668843 + 0.743403i \(0.266790\pi\)
\(684\) 0 0
\(685\) −5.53196 −0.211365
\(686\) 8.88317 0.339161
\(687\) 0 0
\(688\) 4.06699 0.155052
\(689\) −11.6364 −0.443312
\(690\) 0 0
\(691\) −30.4626 −1.15885 −0.579426 0.815025i \(-0.696723\pi\)
−0.579426 + 0.815025i \(0.696723\pi\)
\(692\) 9.52351 0.362030
\(693\) 0 0
\(694\) −4.04497 −0.153545
\(695\) −9.27236 −0.351721
\(696\) 0 0
\(697\) −1.53784 −0.0582497
\(698\) 13.7439 0.520215
\(699\) 0 0
\(700\) 21.6502 0.818301
\(701\) −10.3329 −0.390269 −0.195135 0.980776i \(-0.562514\pi\)
−0.195135 + 0.980776i \(0.562514\pi\)
\(702\) 0 0
\(703\) −7.18015 −0.270805
\(704\) 2.91201 0.109751
\(705\) 0 0
\(706\) −6.00673 −0.226066
\(707\) −32.1152 −1.20782
\(708\) 0 0
\(709\) −45.4499 −1.70691 −0.853454 0.521169i \(-0.825496\pi\)
−0.853454 + 0.521169i \(0.825496\pi\)
\(710\) −0.799154 −0.0299917
\(711\) 0 0
\(712\) 10.1015 0.378570
\(713\) −28.9893 −1.08566
\(714\) 0 0
\(715\) −0.769744 −0.0287868
\(716\) 2.30806 0.0862564
\(717\) 0 0
\(718\) 5.86399 0.218842
\(719\) 7.51239 0.280165 0.140082 0.990140i \(-0.455263\pi\)
0.140082 + 0.990140i \(0.455263\pi\)
\(720\) 0 0
\(721\) 22.7719 0.848071
\(722\) −0.484093 −0.0180161
\(723\) 0 0
\(724\) 19.0026 0.706227
\(725\) 22.7155 0.843632
\(726\) 0 0
\(727\) 4.79898 0.177984 0.0889922 0.996032i \(-0.471635\pi\)
0.0889922 + 0.996032i \(0.471635\pi\)
\(728\) −5.87465 −0.217729
\(729\) 0 0
\(730\) 5.12705 0.189761
\(731\) −0.340889 −0.0126082
\(732\) 0 0
\(733\) −8.55077 −0.315830 −0.157915 0.987453i \(-0.550477\pi\)
−0.157915 + 0.987453i \(0.550477\pi\)
\(734\) 1.96572 0.0725562
\(735\) 0 0
\(736\) −46.7541 −1.72338
\(737\) 2.22447 0.0819395
\(738\) 0 0
\(739\) 38.8820 1.43030 0.715149 0.698972i \(-0.246359\pi\)
0.715149 + 0.698972i \(0.246359\pi\)
\(740\) 8.08330 0.297148
\(741\) 0 0
\(742\) −12.4557 −0.457262
\(743\) −28.4350 −1.04318 −0.521589 0.853197i \(-0.674660\pi\)
−0.521589 + 0.853197i \(0.674660\pi\)
\(744\) 0 0
\(745\) −11.7775 −0.431494
\(746\) −17.1804 −0.629018
\(747\) 0 0
\(748\) −0.392015 −0.0143335
\(749\) −4.39346 −0.160534
\(750\) 0 0
\(751\) 18.2732 0.666799 0.333400 0.942786i \(-0.391804\pi\)
0.333400 + 0.942786i \(0.391804\pi\)
\(752\) −15.7495 −0.574326
\(753\) 0 0
\(754\) −2.89006 −0.105250
\(755\) 0.582763 0.0212089
\(756\) 0 0
\(757\) 1.10637 0.0402117 0.0201058 0.999798i \(-0.493600\pi\)
0.0201058 + 0.999798i \(0.493600\pi\)
\(758\) −6.56352 −0.238398
\(759\) 0 0
\(760\) 1.16230 0.0421611
\(761\) −1.10110 −0.0399147 −0.0199573 0.999801i \(-0.506353\pi\)
−0.0199573 + 0.999801i \(0.506353\pi\)
\(762\) 0 0
\(763\) 44.8636 1.62417
\(764\) 27.0218 0.977615
\(765\) 0 0
\(766\) −11.5372 −0.416855
\(767\) 3.20908 0.115873
\(768\) 0 0
\(769\) 30.2914 1.09234 0.546169 0.837675i \(-0.316086\pi\)
0.546169 + 0.837675i \(0.316086\pi\)
\(770\) −0.823938 −0.0296927
\(771\) 0 0
\(772\) 32.3171 1.16312
\(773\) 43.9677 1.58141 0.790704 0.612199i \(-0.209715\pi\)
0.790704 + 0.612199i \(0.209715\pi\)
\(774\) 0 0
\(775\) 14.0359 0.504186
\(776\) 25.1068 0.901283
\(777\) 0 0
\(778\) −6.17542 −0.221399
\(779\) −6.92650 −0.248168
\(780\) 0 0
\(781\) 2.58912 0.0926461
\(782\) 1.01967 0.0364635
\(783\) 0 0
\(784\) 0.333183 0.0118994
\(785\) 1.52655 0.0544851
\(786\) 0 0
\(787\) −37.8350 −1.34867 −0.674337 0.738424i \(-0.735570\pi\)
−0.674337 + 0.738424i \(0.735570\pi\)
\(788\) −1.01732 −0.0362405
\(789\) 0 0
\(790\) 1.75719 0.0625179
\(791\) 30.1502 1.07202
\(792\) 0 0
\(793\) 0.977621 0.0347163
\(794\) 14.6762 0.520838
\(795\) 0 0
\(796\) 17.9529 0.636323
\(797\) −11.2902 −0.399918 −0.199959 0.979804i \(-0.564081\pi\)
−0.199959 + 0.979804i \(0.564081\pi\)
\(798\) 0 0
\(799\) 1.32010 0.0467018
\(800\) 22.6372 0.800347
\(801\) 0 0
\(802\) 15.7993 0.557894
\(803\) −16.6108 −0.586181
\(804\) 0 0
\(805\) −16.1474 −0.569121
\(806\) −1.78577 −0.0629012
\(807\) 0 0
\(808\) −21.9313 −0.771539
\(809\) −17.8104 −0.626180 −0.313090 0.949723i \(-0.601364\pi\)
−0.313090 + 0.949723i \(0.601364\pi\)
\(810\) 0 0
\(811\) 28.1638 0.988965 0.494482 0.869188i \(-0.335358\pi\)
0.494482 + 0.869188i \(0.335358\pi\)
\(812\) 23.3079 0.817949
\(813\) 0 0
\(814\) 3.47586 0.121829
\(815\) −9.05307 −0.317115
\(816\) 0 0
\(817\) −1.53538 −0.0537162
\(818\) 11.2110 0.391982
\(819\) 0 0
\(820\) 7.79774 0.272309
\(821\) 44.2644 1.54484 0.772418 0.635114i \(-0.219047\pi\)
0.772418 + 0.635114i \(0.219047\pi\)
\(822\) 0 0
\(823\) −22.4258 −0.781716 −0.390858 0.920451i \(-0.627822\pi\)
−0.390858 + 0.920451i \(0.627822\pi\)
\(824\) 15.5508 0.541738
\(825\) 0 0
\(826\) 3.43501 0.119519
\(827\) −19.7303 −0.686090 −0.343045 0.939319i \(-0.611458\pi\)
−0.343045 + 0.939319i \(0.611458\pi\)
\(828\) 0 0
\(829\) 5.70836 0.198259 0.0991297 0.995075i \(-0.468394\pi\)
0.0991297 + 0.995075i \(0.468394\pi\)
\(830\) 0.906791 0.0314752
\(831\) 0 0
\(832\) 3.51552 0.121879
\(833\) −0.0279270 −0.000967612 0
\(834\) 0 0
\(835\) 5.89817 0.204115
\(836\) −1.76565 −0.0610664
\(837\) 0 0
\(838\) −6.88441 −0.237818
\(839\) 0.0666011 0.00229932 0.00114966 0.999999i \(-0.499634\pi\)
0.00114966 + 0.999999i \(0.499634\pi\)
\(840\) 0 0
\(841\) −4.54521 −0.156731
\(842\) −7.72635 −0.266268
\(843\) 0 0
\(844\) 12.8158 0.441137
\(845\) 7.35955 0.253176
\(846\) 0 0
\(847\) 2.66942 0.0917222
\(848\) 25.5316 0.876760
\(849\) 0 0
\(850\) −0.493703 −0.0169339
\(851\) 68.1193 2.33510
\(852\) 0 0
\(853\) −14.8615 −0.508848 −0.254424 0.967093i \(-0.581886\pi\)
−0.254424 + 0.967093i \(0.581886\pi\)
\(854\) 1.04645 0.0358088
\(855\) 0 0
\(856\) −3.00026 −0.102547
\(857\) −12.5169 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(858\) 0 0
\(859\) −21.2738 −0.725854 −0.362927 0.931818i \(-0.618223\pi\)
−0.362927 + 0.931818i \(0.618223\pi\)
\(860\) 1.72851 0.0589417
\(861\) 0 0
\(862\) 11.8651 0.404128
\(863\) 34.4402 1.17236 0.586179 0.810181i \(-0.300631\pi\)
0.586179 + 0.810181i \(0.300631\pi\)
\(864\) 0 0
\(865\) 3.43907 0.116932
\(866\) 9.28680 0.315578
\(867\) 0 0
\(868\) 14.4020 0.488836
\(869\) −5.69298 −0.193121
\(870\) 0 0
\(871\) 2.68549 0.0909944
\(872\) 30.6370 1.03750
\(873\) 0 0
\(874\) 4.59267 0.155349
\(875\) 16.3283 0.551998
\(876\) 0 0
\(877\) −0.910260 −0.0307373 −0.0153687 0.999882i \(-0.504892\pi\)
−0.0153687 + 0.999882i \(0.504892\pi\)
\(878\) −6.67857 −0.225391
\(879\) 0 0
\(880\) 1.68891 0.0569331
\(881\) −33.7502 −1.13707 −0.568537 0.822658i \(-0.692490\pi\)
−0.568537 + 0.822658i \(0.692490\pi\)
\(882\) 0 0
\(883\) 39.8800 1.34207 0.671035 0.741426i \(-0.265850\pi\)
0.671035 + 0.741426i \(0.265850\pi\)
\(884\) −0.473259 −0.0159174
\(885\) 0 0
\(886\) 6.83822 0.229735
\(887\) 16.1868 0.543500 0.271750 0.962368i \(-0.412398\pi\)
0.271750 + 0.962368i \(0.412398\pi\)
\(888\) 0 0
\(889\) 49.6228 1.66430
\(890\) 1.71039 0.0573324
\(891\) 0 0
\(892\) −28.7399 −0.962282
\(893\) 5.94581 0.198969
\(894\) 0 0
\(895\) 0.833474 0.0278599
\(896\) 30.0735 1.00469
\(897\) 0 0
\(898\) −10.1667 −0.339269
\(899\) 15.1106 0.503968
\(900\) 0 0
\(901\) −2.14003 −0.0712946
\(902\) 3.35307 0.111645
\(903\) 0 0
\(904\) 20.5894 0.684793
\(905\) 6.86211 0.228104
\(906\) 0 0
\(907\) −14.3005 −0.474839 −0.237419 0.971407i \(-0.576302\pi\)
−0.237419 + 0.971407i \(0.576302\pi\)
\(908\) −36.9480 −1.22616
\(909\) 0 0
\(910\) −0.994698 −0.0329739
\(911\) 8.50108 0.281653 0.140827 0.990034i \(-0.455024\pi\)
0.140827 + 0.990034i \(0.455024\pi\)
\(912\) 0 0
\(913\) −2.93784 −0.0972285
\(914\) 10.8738 0.359672
\(915\) 0 0
\(916\) 19.0838 0.630545
\(917\) 8.25111 0.272476
\(918\) 0 0
\(919\) −26.0156 −0.858177 −0.429088 0.903263i \(-0.641165\pi\)
−0.429088 + 0.903263i \(0.641165\pi\)
\(920\) −11.0269 −0.363548
\(921\) 0 0
\(922\) −15.0656 −0.496159
\(923\) 3.12571 0.102884
\(924\) 0 0
\(925\) −32.9818 −1.08443
\(926\) −15.3425 −0.504185
\(927\) 0 0
\(928\) 24.3705 0.800001
\(929\) −5.99773 −0.196779 −0.0983896 0.995148i \(-0.531369\pi\)
−0.0983896 + 0.995148i \(0.531369\pi\)
\(930\) 0 0
\(931\) −0.125785 −0.00412242
\(932\) −44.8781 −1.47003
\(933\) 0 0
\(934\) −0.849454 −0.0277950
\(935\) −0.141562 −0.00462957
\(936\) 0 0
\(937\) −50.5847 −1.65253 −0.826265 0.563282i \(-0.809539\pi\)
−0.826265 + 0.563282i \(0.809539\pi\)
\(938\) 2.87456 0.0938578
\(939\) 0 0
\(940\) −6.69370 −0.218324
\(941\) 21.8640 0.712747 0.356373 0.934344i \(-0.384013\pi\)
0.356373 + 0.934344i \(0.384013\pi\)
\(942\) 0 0
\(943\) 65.7129 2.13991
\(944\) −7.04109 −0.229168
\(945\) 0 0
\(946\) 0.743267 0.0241657
\(947\) 33.1722 1.07795 0.538976 0.842321i \(-0.318812\pi\)
0.538976 + 0.842321i \(0.318812\pi\)
\(948\) 0 0
\(949\) −20.0533 −0.650958
\(950\) −2.22366 −0.0721451
\(951\) 0 0
\(952\) −1.08039 −0.0350157
\(953\) −22.4494 −0.727209 −0.363604 0.931553i \(-0.618454\pi\)
−0.363604 + 0.931553i \(0.618454\pi\)
\(954\) 0 0
\(955\) 9.75794 0.315760
\(956\) 0.621931 0.0201147
\(957\) 0 0
\(958\) −5.38765 −0.174067
\(959\) 23.1604 0.747887
\(960\) 0 0
\(961\) −21.6631 −0.698810
\(962\) 4.19623 0.135292
\(963\) 0 0
\(964\) 27.6911 0.891870
\(965\) 11.6702 0.375676
\(966\) 0 0
\(967\) −0.790013 −0.0254051 −0.0127026 0.999919i \(-0.504043\pi\)
−0.0127026 + 0.999919i \(0.504043\pi\)
\(968\) 1.82293 0.0585911
\(969\) 0 0
\(970\) 4.25110 0.136495
\(971\) −51.6970 −1.65904 −0.829518 0.558479i \(-0.811385\pi\)
−0.829518 + 0.558479i \(0.811385\pi\)
\(972\) 0 0
\(973\) 38.8201 1.24452
\(974\) −1.58302 −0.0507231
\(975\) 0 0
\(976\) −2.14501 −0.0686602
\(977\) −21.4536 −0.686360 −0.343180 0.939270i \(-0.611504\pi\)
−0.343180 + 0.939270i \(0.611504\pi\)
\(978\) 0 0
\(979\) −5.54136 −0.177103
\(980\) 0.141606 0.00452345
\(981\) 0 0
\(982\) 14.1687 0.452142
\(983\) 42.9916 1.37122 0.685610 0.727969i \(-0.259536\pi\)
0.685610 + 0.727969i \(0.259536\pi\)
\(984\) 0 0
\(985\) −0.367368 −0.0117053
\(986\) −0.531505 −0.0169266
\(987\) 0 0
\(988\) −2.13158 −0.0678147
\(989\) 14.5664 0.463186
\(990\) 0 0
\(991\) 57.7319 1.83392 0.916958 0.398985i \(-0.130637\pi\)
0.916958 + 0.398985i \(0.130637\pi\)
\(992\) 15.0586 0.478110
\(993\) 0 0
\(994\) 3.34578 0.106122
\(995\) 6.48303 0.205526
\(996\) 0 0
\(997\) −30.3487 −0.961152 −0.480576 0.876953i \(-0.659572\pi\)
−0.480576 + 0.876953i \(0.659572\pi\)
\(998\) 0.507466 0.0160635
\(999\) 0 0
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 1881.2.a.k.1.3 5
3.2 odd 2 209.2.a.c.1.3 5
12.11 even 2 3344.2.a.t.1.1 5
15.14 odd 2 5225.2.a.h.1.3 5
33.32 even 2 2299.2.a.n.1.3 5
57.56 even 2 3971.2.a.h.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
209.2.a.c.1.3 5 3.2 odd 2
1881.2.a.k.1.3 5 1.1 even 1 trivial
2299.2.a.n.1.3 5 33.32 even 2
3344.2.a.t.1.1 5 12.11 even 2
3971.2.a.h.1.3 5 57.56 even 2
5225.2.a.h.1.3 5 15.14 odd 2