Properties

Label 4840.2.a.be.1.1
Level $4840$
Weight $2$
Character 4840.1
Self dual yes
Analytic conductor $38.648$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4840,2,Mod(1,4840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4840, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4840.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4840.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: \(38.6475945783\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.45753625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 41x^{2} - 30x - 20 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.87511\) of defining polynomial
Character \(\chi\) \(=\) 4840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.03399 q^{3} -1.00000 q^{5} -0.865927 q^{7} +6.20511 q^{9} +O(q^{10})\) \(q-3.03399 q^{3} -1.00000 q^{5} -0.865927 q^{7} +6.20511 q^{9} +4.43509 q^{13} +3.03399 q^{15} +0.550031 q^{17} +0.258962 q^{19} +2.62722 q^{21} +7.92701 q^{23} +1.00000 q^{25} -9.72427 q^{27} +9.36210 q^{29} -5.31588 q^{31} +0.865927 q^{35} +6.38739 q^{37} -13.4560 q^{39} -8.74218 q^{41} -6.38622 q^{43} -6.20511 q^{45} +0.823208 q^{47} -6.25017 q^{49} -1.66879 q^{51} +2.40110 q^{53} -0.785690 q^{57} -13.5148 q^{59} +6.60761 q^{61} -5.37317 q^{63} -4.43509 q^{65} +7.17725 q^{67} -24.0505 q^{69} +2.79910 q^{71} +2.89074 q^{73} -3.03399 q^{75} +5.91452 q^{79} +10.8880 q^{81} +7.09821 q^{83} -0.550031 q^{85} -28.4046 q^{87} -16.6470 q^{89} -3.84047 q^{91} +16.1283 q^{93} -0.258962 q^{95} -7.83395 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 10 q^{9} + 6 q^{13} - 2 q^{15} - 11 q^{17} + 11 q^{19} - 2 q^{21} + 18 q^{23} + 6 q^{25} - q^{27} + 6 q^{29} + q^{31} + 6 q^{35} + 4 q^{37} - 27 q^{39} + 4 q^{41} - 3 q^{43} - 10 q^{45} + 14 q^{47} + 8 q^{49} - 31 q^{51} + 14 q^{53} + 5 q^{57} + 2 q^{59} + 4 q^{61} + 16 q^{63} - 6 q^{65} + 11 q^{67} + 8 q^{69} + 7 q^{71} + 9 q^{73} + 2 q^{75} - 36 q^{79} + 30 q^{81} + 45 q^{83} + 11 q^{85} - 25 q^{87} + q^{89} - 8 q^{91} + 55 q^{93} - 11 q^{95} + 20 q^{97}+O(q^{100}) \) 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
\(3\) −3.03399 −1.75168 −0.875838 0.482605i \(-0.839691\pi\)
−0.875838 + 0.482605i \(0.839691\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.865927 −0.327290 −0.163645 0.986519i \(-0.552325\pi\)
−0.163645 + 0.986519i \(0.552325\pi\)
\(8\) 0 0
\(9\) 6.20511 2.06837
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) 4.43509 1.23007 0.615037 0.788499i \(-0.289141\pi\)
0.615037 + 0.788499i \(0.289141\pi\)
\(14\) 0 0
\(15\) 3.03399 0.783373
\(16\) 0 0
\(17\) 0.550031 0.133402 0.0667010 0.997773i \(-0.478753\pi\)
0.0667010 + 0.997773i \(0.478753\pi\)
\(18\) 0 0
\(19\) 0.258962 0.0594100 0.0297050 0.999559i \(-0.490543\pi\)
0.0297050 + 0.999559i \(0.490543\pi\)
\(20\) 0 0
\(21\) 2.62722 0.573306
\(22\) 0 0
\(23\) 7.92701 1.65290 0.826448 0.563013i \(-0.190358\pi\)
0.826448 + 0.563013i \(0.190358\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −9.72427 −1.87144
\(28\) 0 0
\(29\) 9.36210 1.73850 0.869250 0.494374i \(-0.164602\pi\)
0.869250 + 0.494374i \(0.164602\pi\)
\(30\) 0 0
\(31\) −5.31588 −0.954760 −0.477380 0.878697i \(-0.658413\pi\)
−0.477380 + 0.878697i \(0.658413\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.865927 0.146368
\(36\) 0 0
\(37\) 6.38739 1.05008 0.525040 0.851077i \(-0.324050\pi\)
0.525040 + 0.851077i \(0.324050\pi\)
\(38\) 0 0
\(39\) −13.4560 −2.15469
\(40\) 0 0
\(41\) −8.74218 −1.36530 −0.682650 0.730746i \(-0.739173\pi\)
−0.682650 + 0.730746i \(0.739173\pi\)
\(42\) 0 0
\(43\) −6.38622 −0.973890 −0.486945 0.873433i \(-0.661889\pi\)
−0.486945 + 0.873433i \(0.661889\pi\)
\(44\) 0 0
\(45\) −6.20511 −0.925003
\(46\) 0 0
\(47\) 0.823208 0.120077 0.0600386 0.998196i \(-0.480878\pi\)
0.0600386 + 0.998196i \(0.480878\pi\)
\(48\) 0 0
\(49\) −6.25017 −0.892881
\(50\) 0 0
\(51\) −1.66879 −0.233677
\(52\) 0 0
\(53\) 2.40110 0.329816 0.164908 0.986309i \(-0.447267\pi\)
0.164908 + 0.986309i \(0.447267\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.785690 −0.104067
\(58\) 0 0
\(59\) −13.5148 −1.75948 −0.879741 0.475453i \(-0.842284\pi\)
−0.879741 + 0.475453i \(0.842284\pi\)
\(60\) 0 0
\(61\) 6.60761 0.846018 0.423009 0.906126i \(-0.360974\pi\)
0.423009 + 0.906126i \(0.360974\pi\)
\(62\) 0 0
\(63\) −5.37317 −0.676956
\(64\) 0 0
\(65\) −4.43509 −0.550105
\(66\) 0 0
\(67\) 7.17725 0.876840 0.438420 0.898770i \(-0.355538\pi\)
0.438420 + 0.898770i \(0.355538\pi\)
\(68\) 0 0
\(69\) −24.0505 −2.89534
\(70\) 0 0
\(71\) 2.79910 0.332192 0.166096 0.986110i \(-0.446884\pi\)
0.166096 + 0.986110i \(0.446884\pi\)
\(72\) 0 0
\(73\) 2.89074 0.338335 0.169168 0.985587i \(-0.445892\pi\)
0.169168 + 0.985587i \(0.445892\pi\)
\(74\) 0 0
\(75\) −3.03399 −0.350335
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.91452 0.665436 0.332718 0.943026i \(-0.392034\pi\)
0.332718 + 0.943026i \(0.392034\pi\)
\(80\) 0 0
\(81\) 10.8880 1.20978
\(82\) 0 0
\(83\) 7.09821 0.779129 0.389565 0.920999i \(-0.372625\pi\)
0.389565 + 0.920999i \(0.372625\pi\)
\(84\) 0 0
\(85\) −0.550031 −0.0596592
\(86\) 0 0
\(87\) −28.4046 −3.04529
\(88\) 0 0
\(89\) −16.6470 −1.76458 −0.882291 0.470704i \(-0.844000\pi\)
−0.882291 + 0.470704i \(0.844000\pi\)
\(90\) 0 0
\(91\) −3.84047 −0.402590
\(92\) 0 0
\(93\) 16.1283 1.67243
\(94\) 0 0
\(95\) −0.258962 −0.0265690
\(96\) 0 0
\(97\) −7.83395 −0.795417 −0.397708 0.917512i \(-0.630194\pi\)
−0.397708 + 0.917512i \(0.630194\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 18.1989 1.81086 0.905431 0.424493i \(-0.139548\pi\)
0.905431 + 0.424493i \(0.139548\pi\)
\(102\) 0 0
\(103\) 11.8025 1.16294 0.581469 0.813569i \(-0.302478\pi\)
0.581469 + 0.813569i \(0.302478\pi\)
\(104\) 0 0
\(105\) −2.62722 −0.256390
\(106\) 0 0
\(107\) 0.520965 0.0503636 0.0251818 0.999683i \(-0.491984\pi\)
0.0251818 + 0.999683i \(0.491984\pi\)
\(108\) 0 0
\(109\) 6.22545 0.596290 0.298145 0.954521i \(-0.403632\pi\)
0.298145 + 0.954521i \(0.403632\pi\)
\(110\) 0 0
\(111\) −19.3793 −1.83940
\(112\) 0 0
\(113\) −9.87578 −0.929035 −0.464518 0.885564i \(-0.653772\pi\)
−0.464518 + 0.885564i \(0.653772\pi\)
\(114\) 0 0
\(115\) −7.92701 −0.739198
\(116\) 0 0
\(117\) 27.5202 2.54425
\(118\) 0 0
\(119\) −0.476287 −0.0436611
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 26.5237 2.39156
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −3.71934 −0.330038 −0.165019 0.986290i \(-0.552769\pi\)
−0.165019 + 0.986290i \(0.552769\pi\)
\(128\) 0 0
\(129\) 19.3758 1.70594
\(130\) 0 0
\(131\) −20.4259 −1.78462 −0.892308 0.451426i \(-0.850915\pi\)
−0.892308 + 0.451426i \(0.850915\pi\)
\(132\) 0 0
\(133\) −0.224243 −0.0194443
\(134\) 0 0
\(135\) 9.72427 0.836932
\(136\) 0 0
\(137\) 13.4216 1.14669 0.573344 0.819315i \(-0.305646\pi\)
0.573344 + 0.819315i \(0.305646\pi\)
\(138\) 0 0
\(139\) −14.0856 −1.19473 −0.597364 0.801970i \(-0.703785\pi\)
−0.597364 + 0.801970i \(0.703785\pi\)
\(140\) 0 0
\(141\) −2.49761 −0.210336
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −9.36210 −0.777480
\(146\) 0 0
\(147\) 18.9630 1.56404
\(148\) 0 0
\(149\) −1.79173 −0.146784 −0.0733920 0.997303i \(-0.523382\pi\)
−0.0733920 + 0.997303i \(0.523382\pi\)
\(150\) 0 0
\(151\) −19.0871 −1.55328 −0.776641 0.629943i \(-0.783078\pi\)
−0.776641 + 0.629943i \(0.783078\pi\)
\(152\) 0 0
\(153\) 3.41300 0.275925
\(154\) 0 0
\(155\) 5.31588 0.426982
\(156\) 0 0
\(157\) 9.78753 0.781130 0.390565 0.920575i \(-0.372280\pi\)
0.390565 + 0.920575i \(0.372280\pi\)
\(158\) 0 0
\(159\) −7.28492 −0.577732
\(160\) 0 0
\(161\) −6.86422 −0.540976
\(162\) 0 0
\(163\) 0.396843 0.0310831 0.0155416 0.999879i \(-0.495053\pi\)
0.0155416 + 0.999879i \(0.495053\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −13.9140 −1.07670 −0.538349 0.842722i \(-0.680952\pi\)
−0.538349 + 0.842722i \(0.680952\pi\)
\(168\) 0 0
\(169\) 6.67004 0.513080
\(170\) 0 0
\(171\) 1.60689 0.122882
\(172\) 0 0
\(173\) −5.33390 −0.405529 −0.202765 0.979228i \(-0.564993\pi\)
−0.202765 + 0.979228i \(0.564993\pi\)
\(174\) 0 0
\(175\) −0.865927 −0.0654580
\(176\) 0 0
\(177\) 41.0039 3.08204
\(178\) 0 0
\(179\) 7.63478 0.570650 0.285325 0.958431i \(-0.407898\pi\)
0.285325 + 0.958431i \(0.407898\pi\)
\(180\) 0 0
\(181\) 1.30453 0.0969647 0.0484824 0.998824i \(-0.484562\pi\)
0.0484824 + 0.998824i \(0.484562\pi\)
\(182\) 0 0
\(183\) −20.0474 −1.48195
\(184\) 0 0
\(185\) −6.38739 −0.469610
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 8.42052 0.612502
\(190\) 0 0
\(191\) 25.0833 1.81497 0.907483 0.420088i \(-0.138001\pi\)
0.907483 + 0.420088i \(0.138001\pi\)
\(192\) 0 0
\(193\) 19.9561 1.43647 0.718235 0.695801i \(-0.244950\pi\)
0.718235 + 0.695801i \(0.244950\pi\)
\(194\) 0 0
\(195\) 13.4560 0.963607
\(196\) 0 0
\(197\) 1.31088 0.0933960 0.0466980 0.998909i \(-0.485130\pi\)
0.0466980 + 0.998909i \(0.485130\pi\)
\(198\) 0 0
\(199\) −4.99115 −0.353813 −0.176907 0.984228i \(-0.556609\pi\)
−0.176907 + 0.984228i \(0.556609\pi\)
\(200\) 0 0
\(201\) −21.7757 −1.53594
\(202\) 0 0
\(203\) −8.10690 −0.568993
\(204\) 0 0
\(205\) 8.74218 0.610581
\(206\) 0 0
\(207\) 49.1880 3.41880
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 6.41108 0.441357 0.220678 0.975347i \(-0.429173\pi\)
0.220678 + 0.975347i \(0.429173\pi\)
\(212\) 0 0
\(213\) −8.49245 −0.581893
\(214\) 0 0
\(215\) 6.38622 0.435537
\(216\) 0 0
\(217\) 4.60316 0.312483
\(218\) 0 0
\(219\) −8.77047 −0.592654
\(220\) 0 0
\(221\) 2.43944 0.164094
\(222\) 0 0
\(223\) −14.8484 −0.994321 −0.497160 0.867659i \(-0.665624\pi\)
−0.497160 + 0.867659i \(0.665624\pi\)
\(224\) 0 0
\(225\) 6.20511 0.413674
\(226\) 0 0
\(227\) 23.4761 1.55816 0.779081 0.626923i \(-0.215686\pi\)
0.779081 + 0.626923i \(0.215686\pi\)
\(228\) 0 0
\(229\) 19.6330 1.29739 0.648693 0.761050i \(-0.275316\pi\)
0.648693 + 0.761050i \(0.275316\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20.9946 −1.37541 −0.687703 0.725993i \(-0.741381\pi\)
−0.687703 + 0.725993i \(0.741381\pi\)
\(234\) 0 0
\(235\) −0.823208 −0.0537002
\(236\) 0 0
\(237\) −17.9446 −1.16563
\(238\) 0 0
\(239\) 18.8533 1.21952 0.609761 0.792586i \(-0.291266\pi\)
0.609761 + 0.792586i \(0.291266\pi\)
\(240\) 0 0
\(241\) 13.8318 0.890987 0.445494 0.895285i \(-0.353028\pi\)
0.445494 + 0.895285i \(0.353028\pi\)
\(242\) 0 0
\(243\) −3.86143 −0.247711
\(244\) 0 0
\(245\) 6.25017 0.399309
\(246\) 0 0
\(247\) 1.14852 0.0730787
\(248\) 0 0
\(249\) −21.5359 −1.36478
\(250\) 0 0
\(251\) 15.2719 0.963956 0.481978 0.876183i \(-0.339919\pi\)
0.481978 + 0.876183i \(0.339919\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 1.66879 0.104504
\(256\) 0 0
\(257\) 28.7880 1.79575 0.897873 0.440254i \(-0.145112\pi\)
0.897873 + 0.440254i \(0.145112\pi\)
\(258\) 0 0
\(259\) −5.53101 −0.343681
\(260\) 0 0
\(261\) 58.0929 3.59586
\(262\) 0 0
\(263\) 9.23218 0.569281 0.284640 0.958634i \(-0.408126\pi\)
0.284640 + 0.958634i \(0.408126\pi\)
\(264\) 0 0
\(265\) −2.40110 −0.147498
\(266\) 0 0
\(267\) 50.5070 3.09098
\(268\) 0 0
\(269\) 26.8324 1.63600 0.817999 0.575220i \(-0.195084\pi\)
0.817999 + 0.575220i \(0.195084\pi\)
\(270\) 0 0
\(271\) −23.5612 −1.43124 −0.715620 0.698490i \(-0.753856\pi\)
−0.715620 + 0.698490i \(0.753856\pi\)
\(272\) 0 0
\(273\) 11.6519 0.705208
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −9.99241 −0.600386 −0.300193 0.953879i \(-0.597051\pi\)
−0.300193 + 0.953879i \(0.597051\pi\)
\(278\) 0 0
\(279\) −32.9856 −1.97480
\(280\) 0 0
\(281\) −4.09042 −0.244014 −0.122007 0.992529i \(-0.538933\pi\)
−0.122007 + 0.992529i \(0.538933\pi\)
\(282\) 0 0
\(283\) −4.77268 −0.283706 −0.141853 0.989888i \(-0.545306\pi\)
−0.141853 + 0.989888i \(0.545306\pi\)
\(284\) 0 0
\(285\) 0.785690 0.0465402
\(286\) 0 0
\(287\) 7.57010 0.446849
\(288\) 0 0
\(289\) −16.6975 −0.982204
\(290\) 0 0
\(291\) 23.7681 1.39331
\(292\) 0 0
\(293\) −0.144012 −0.00841327 −0.00420664 0.999991i \(-0.501339\pi\)
−0.00420664 + 0.999991i \(0.501339\pi\)
\(294\) 0 0
\(295\) 13.5148 0.786864
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 35.1570 2.03318
\(300\) 0 0
\(301\) 5.53001 0.318744
\(302\) 0 0
\(303\) −55.2154 −3.17204
\(304\) 0 0
\(305\) −6.60761 −0.378351
\(306\) 0 0
\(307\) 25.7576 1.47006 0.735031 0.678034i \(-0.237168\pi\)
0.735031 + 0.678034i \(0.237168\pi\)
\(308\) 0 0
\(309\) −35.8088 −2.03709
\(310\) 0 0
\(311\) 16.3915 0.929475 0.464738 0.885448i \(-0.346149\pi\)
0.464738 + 0.885448i \(0.346149\pi\)
\(312\) 0 0
\(313\) 26.5238 1.49921 0.749606 0.661885i \(-0.230243\pi\)
0.749606 + 0.661885i \(0.230243\pi\)
\(314\) 0 0
\(315\) 5.37317 0.302744
\(316\) 0 0
\(317\) 16.7158 0.938852 0.469426 0.882972i \(-0.344461\pi\)
0.469426 + 0.882972i \(0.344461\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −1.58060 −0.0882206
\(322\) 0 0
\(323\) 0.142437 0.00792542
\(324\) 0 0
\(325\) 4.43509 0.246015
\(326\) 0 0
\(327\) −18.8880 −1.04451
\(328\) 0 0
\(329\) −0.712839 −0.0393001
\(330\) 0 0
\(331\) 4.39584 0.241617 0.120809 0.992676i \(-0.461451\pi\)
0.120809 + 0.992676i \(0.461451\pi\)
\(332\) 0 0
\(333\) 39.6344 2.17195
\(334\) 0 0
\(335\) −7.17725 −0.392135
\(336\) 0 0
\(337\) −12.6035 −0.686558 −0.343279 0.939233i \(-0.611538\pi\)
−0.343279 + 0.939233i \(0.611538\pi\)
\(338\) 0 0
\(339\) 29.9630 1.62737
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 11.4737 0.619521
\(344\) 0 0
\(345\) 24.0505 1.29484
\(346\) 0 0
\(347\) 23.9827 1.28746 0.643731 0.765252i \(-0.277386\pi\)
0.643731 + 0.765252i \(0.277386\pi\)
\(348\) 0 0
\(349\) −23.5901 −1.26275 −0.631376 0.775477i \(-0.717509\pi\)
−0.631376 + 0.775477i \(0.717509\pi\)
\(350\) 0 0
\(351\) −43.1281 −2.30201
\(352\) 0 0
\(353\) 6.46751 0.344231 0.172115 0.985077i \(-0.444940\pi\)
0.172115 + 0.985077i \(0.444940\pi\)
\(354\) 0 0
\(355\) −2.79910 −0.148561
\(356\) 0 0
\(357\) 1.44505 0.0764802
\(358\) 0 0
\(359\) −11.8241 −0.624053 −0.312026 0.950073i \(-0.601008\pi\)
−0.312026 + 0.950073i \(0.601008\pi\)
\(360\) 0 0
\(361\) −18.9329 −0.996470
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.89074 −0.151308
\(366\) 0 0
\(367\) 8.38713 0.437805 0.218902 0.975747i \(-0.429752\pi\)
0.218902 + 0.975747i \(0.429752\pi\)
\(368\) 0 0
\(369\) −54.2462 −2.82394
\(370\) 0 0
\(371\) −2.07918 −0.107946
\(372\) 0 0
\(373\) −34.6263 −1.79288 −0.896441 0.443163i \(-0.853856\pi\)
−0.896441 + 0.443163i \(0.853856\pi\)
\(374\) 0 0
\(375\) 3.03399 0.156675
\(376\) 0 0
\(377\) 41.5218 2.13848
\(378\) 0 0
\(379\) 16.0726 0.825592 0.412796 0.910823i \(-0.364552\pi\)
0.412796 + 0.910823i \(0.364552\pi\)
\(380\) 0 0
\(381\) 11.2844 0.578120
\(382\) 0 0
\(383\) 8.41569 0.430022 0.215011 0.976612i \(-0.431021\pi\)
0.215011 + 0.976612i \(0.431021\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −39.6272 −2.01436
\(388\) 0 0
\(389\) 18.5917 0.942636 0.471318 0.881963i \(-0.343778\pi\)
0.471318 + 0.881963i \(0.343778\pi\)
\(390\) 0 0
\(391\) 4.36010 0.220500
\(392\) 0 0
\(393\) 61.9719 3.12607
\(394\) 0 0
\(395\) −5.91452 −0.297592
\(396\) 0 0
\(397\) −11.9897 −0.601743 −0.300872 0.953665i \(-0.597278\pi\)
−0.300872 + 0.953665i \(0.597278\pi\)
\(398\) 0 0
\(399\) 0.680350 0.0340601
\(400\) 0 0
\(401\) 18.7991 0.938781 0.469391 0.882991i \(-0.344474\pi\)
0.469391 + 0.882991i \(0.344474\pi\)
\(402\) 0 0
\(403\) −23.5764 −1.17442
\(404\) 0 0
\(405\) −10.8880 −0.541031
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 9.50429 0.469957 0.234978 0.972001i \(-0.424498\pi\)
0.234978 + 0.972001i \(0.424498\pi\)
\(410\) 0 0
\(411\) −40.7211 −2.00863
\(412\) 0 0
\(413\) 11.7029 0.575860
\(414\) 0 0
\(415\) −7.09821 −0.348437
\(416\) 0 0
\(417\) 42.7357 2.09278
\(418\) 0 0
\(419\) 32.9152 1.60801 0.804007 0.594620i \(-0.202698\pi\)
0.804007 + 0.594620i \(0.202698\pi\)
\(420\) 0 0
\(421\) −1.03559 −0.0504717 −0.0252359 0.999682i \(-0.508034\pi\)
−0.0252359 + 0.999682i \(0.508034\pi\)
\(422\) 0 0
\(423\) 5.10810 0.248364
\(424\) 0 0
\(425\) 0.550031 0.0266804
\(426\) 0 0
\(427\) −5.72171 −0.276893
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −25.7613 −1.24088 −0.620439 0.784255i \(-0.713046\pi\)
−0.620439 + 0.784255i \(0.713046\pi\)
\(432\) 0 0
\(433\) −18.4406 −0.886201 −0.443100 0.896472i \(-0.646121\pi\)
−0.443100 + 0.896472i \(0.646121\pi\)
\(434\) 0 0
\(435\) 28.4046 1.36189
\(436\) 0 0
\(437\) 2.05280 0.0981986
\(438\) 0 0
\(439\) 4.44724 0.212255 0.106128 0.994353i \(-0.466155\pi\)
0.106128 + 0.994353i \(0.466155\pi\)
\(440\) 0 0
\(441\) −38.7830 −1.84681
\(442\) 0 0
\(443\) −25.0738 −1.19129 −0.595646 0.803247i \(-0.703104\pi\)
−0.595646 + 0.803247i \(0.703104\pi\)
\(444\) 0 0
\(445\) 16.6470 0.789145
\(446\) 0 0
\(447\) 5.43609 0.257118
\(448\) 0 0
\(449\) −18.6745 −0.881306 −0.440653 0.897678i \(-0.645253\pi\)
−0.440653 + 0.897678i \(0.645253\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 57.9100 2.72085
\(454\) 0 0
\(455\) 3.84047 0.180044
\(456\) 0 0
\(457\) 14.5569 0.680941 0.340471 0.940255i \(-0.389414\pi\)
0.340471 + 0.940255i \(0.389414\pi\)
\(458\) 0 0
\(459\) −5.34865 −0.249654
\(460\) 0 0
\(461\) −20.6525 −0.961884 −0.480942 0.876752i \(-0.659705\pi\)
−0.480942 + 0.876752i \(0.659705\pi\)
\(462\) 0 0
\(463\) −21.8605 −1.01594 −0.507971 0.861374i \(-0.669604\pi\)
−0.507971 + 0.861374i \(0.669604\pi\)
\(464\) 0 0
\(465\) −16.1283 −0.747933
\(466\) 0 0
\(467\) 20.2984 0.939296 0.469648 0.882854i \(-0.344381\pi\)
0.469648 + 0.882854i \(0.344381\pi\)
\(468\) 0 0
\(469\) −6.21498 −0.286981
\(470\) 0 0
\(471\) −29.6953 −1.36829
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.258962 0.0118820
\(476\) 0 0
\(477\) 14.8991 0.682182
\(478\) 0 0
\(479\) 9.89152 0.451955 0.225978 0.974132i \(-0.427442\pi\)
0.225978 + 0.974132i \(0.427442\pi\)
\(480\) 0 0
\(481\) 28.3287 1.29168
\(482\) 0 0
\(483\) 20.8260 0.947615
\(484\) 0 0
\(485\) 7.83395 0.355721
\(486\) 0 0
\(487\) 5.93879 0.269112 0.134556 0.990906i \(-0.457039\pi\)
0.134556 + 0.990906i \(0.457039\pi\)
\(488\) 0 0
\(489\) −1.20402 −0.0544476
\(490\) 0 0
\(491\) −27.3348 −1.23360 −0.616801 0.787119i \(-0.711572\pi\)
−0.616801 + 0.787119i \(0.711572\pi\)
\(492\) 0 0
\(493\) 5.14945 0.231919
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.42382 −0.108723
\(498\) 0 0
\(499\) −12.1678 −0.544705 −0.272353 0.962198i \(-0.587802\pi\)
−0.272353 + 0.962198i \(0.587802\pi\)
\(500\) 0 0
\(501\) 42.2150 1.88603
\(502\) 0 0
\(503\) 9.49180 0.423218 0.211609 0.977354i \(-0.432130\pi\)
0.211609 + 0.977354i \(0.432130\pi\)
\(504\) 0 0
\(505\) −18.1989 −0.809842
\(506\) 0 0
\(507\) −20.2369 −0.898750
\(508\) 0 0
\(509\) −0.957696 −0.0424491 −0.0212246 0.999775i \(-0.506756\pi\)
−0.0212246 + 0.999775i \(0.506756\pi\)
\(510\) 0 0
\(511\) −2.50317 −0.110734
\(512\) 0 0
\(513\) −2.51822 −0.111182
\(514\) 0 0
\(515\) −11.8025 −0.520082
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 16.1830 0.710356
\(520\) 0 0
\(521\) −18.2415 −0.799176 −0.399588 0.916695i \(-0.630847\pi\)
−0.399588 + 0.916695i \(0.630847\pi\)
\(522\) 0 0
\(523\) −28.3274 −1.23867 −0.619335 0.785127i \(-0.712598\pi\)
−0.619335 + 0.785127i \(0.712598\pi\)
\(524\) 0 0
\(525\) 2.62722 0.114661
\(526\) 0 0
\(527\) −2.92390 −0.127367
\(528\) 0 0
\(529\) 39.8375 1.73207
\(530\) 0 0
\(531\) −83.8610 −3.63926
\(532\) 0 0
\(533\) −38.7724 −1.67942
\(534\) 0 0
\(535\) −0.520965 −0.0225233
\(536\) 0 0
\(537\) −23.1639 −0.999594
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 31.7569 1.36534 0.682668 0.730729i \(-0.260819\pi\)
0.682668 + 0.730729i \(0.260819\pi\)
\(542\) 0 0
\(543\) −3.95792 −0.169851
\(544\) 0 0
\(545\) −6.22545 −0.266669
\(546\) 0 0
\(547\) −3.58429 −0.153253 −0.0766265 0.997060i \(-0.524415\pi\)
−0.0766265 + 0.997060i \(0.524415\pi\)
\(548\) 0 0
\(549\) 41.0009 1.74988
\(550\) 0 0
\(551\) 2.42443 0.103284
\(552\) 0 0
\(553\) −5.12155 −0.217790
\(554\) 0 0
\(555\) 19.3793 0.822605
\(556\) 0 0
\(557\) 16.6556 0.705719 0.352860 0.935676i \(-0.385209\pi\)
0.352860 + 0.935676i \(0.385209\pi\)
\(558\) 0 0
\(559\) −28.3235 −1.19796
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −39.8978 −1.68149 −0.840745 0.541431i \(-0.817883\pi\)
−0.840745 + 0.541431i \(0.817883\pi\)
\(564\) 0 0
\(565\) 9.87578 0.415477
\(566\) 0 0
\(567\) −9.42826 −0.395950
\(568\) 0 0
\(569\) −45.4644 −1.90597 −0.952983 0.303024i \(-0.902004\pi\)
−0.952983 + 0.303024i \(0.902004\pi\)
\(570\) 0 0
\(571\) 15.8877 0.664880 0.332440 0.943124i \(-0.392128\pi\)
0.332440 + 0.943124i \(0.392128\pi\)
\(572\) 0 0
\(573\) −76.1027 −3.17923
\(574\) 0 0
\(575\) 7.92701 0.330579
\(576\) 0 0
\(577\) −13.1413 −0.547078 −0.273539 0.961861i \(-0.588194\pi\)
−0.273539 + 0.961861i \(0.588194\pi\)
\(578\) 0 0
\(579\) −60.5466 −2.51623
\(580\) 0 0
\(581\) −6.14653 −0.255001
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −27.5202 −1.13782
\(586\) 0 0
\(587\) 14.9640 0.617629 0.308814 0.951122i \(-0.400068\pi\)
0.308814 + 0.951122i \(0.400068\pi\)
\(588\) 0 0
\(589\) −1.37661 −0.0567223
\(590\) 0 0
\(591\) −3.97719 −0.163600
\(592\) 0 0
\(593\) 13.7967 0.566564 0.283282 0.959037i \(-0.408577\pi\)
0.283282 + 0.959037i \(0.408577\pi\)
\(594\) 0 0
\(595\) 0.476287 0.0195259
\(596\) 0 0
\(597\) 15.1431 0.619766
\(598\) 0 0
\(599\) 31.3893 1.28253 0.641267 0.767318i \(-0.278409\pi\)
0.641267 + 0.767318i \(0.278409\pi\)
\(600\) 0 0
\(601\) 2.55635 0.104276 0.0521379 0.998640i \(-0.483396\pi\)
0.0521379 + 0.998640i \(0.483396\pi\)
\(602\) 0 0
\(603\) 44.5356 1.81363
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 37.8289 1.53543 0.767713 0.640794i \(-0.221395\pi\)
0.767713 + 0.640794i \(0.221395\pi\)
\(608\) 0 0
\(609\) 24.5963 0.996692
\(610\) 0 0
\(611\) 3.65100 0.147704
\(612\) 0 0
\(613\) −11.6599 −0.470940 −0.235470 0.971882i \(-0.575663\pi\)
−0.235470 + 0.971882i \(0.575663\pi\)
\(614\) 0 0
\(615\) −26.5237 −1.06954
\(616\) 0 0
\(617\) 38.5910 1.55361 0.776807 0.629739i \(-0.216838\pi\)
0.776807 + 0.629739i \(0.216838\pi\)
\(618\) 0 0
\(619\) −8.16365 −0.328125 −0.164062 0.986450i \(-0.552460\pi\)
−0.164062 + 0.986450i \(0.552460\pi\)
\(620\) 0 0
\(621\) −77.0844 −3.09329
\(622\) 0 0
\(623\) 14.4151 0.577530
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.51326 0.140083
\(630\) 0 0
\(631\) −13.0813 −0.520759 −0.260379 0.965506i \(-0.583848\pi\)
−0.260379 + 0.965506i \(0.583848\pi\)
\(632\) 0 0
\(633\) −19.4512 −0.773114
\(634\) 0 0
\(635\) 3.71934 0.147597
\(636\) 0 0
\(637\) −27.7201 −1.09831
\(638\) 0 0
\(639\) 17.3687 0.687096
\(640\) 0 0
\(641\) 35.6499 1.40809 0.704044 0.710156i \(-0.251376\pi\)
0.704044 + 0.710156i \(0.251376\pi\)
\(642\) 0 0
\(643\) −7.65614 −0.301929 −0.150964 0.988539i \(-0.548238\pi\)
−0.150964 + 0.988539i \(0.548238\pi\)
\(644\) 0 0
\(645\) −19.3758 −0.762919
\(646\) 0 0
\(647\) 9.18246 0.361000 0.180500 0.983575i \(-0.442228\pi\)
0.180500 + 0.983575i \(0.442228\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −13.9660 −0.547369
\(652\) 0 0
\(653\) −5.85282 −0.229039 −0.114519 0.993421i \(-0.536533\pi\)
−0.114519 + 0.993421i \(0.536533\pi\)
\(654\) 0 0
\(655\) 20.4259 0.798105
\(656\) 0 0
\(657\) 17.9373 0.699802
\(658\) 0 0
\(659\) 22.6530 0.882434 0.441217 0.897400i \(-0.354547\pi\)
0.441217 + 0.897400i \(0.354547\pi\)
\(660\) 0 0
\(661\) 1.68482 0.0655320 0.0327660 0.999463i \(-0.489568\pi\)
0.0327660 + 0.999463i \(0.489568\pi\)
\(662\) 0 0
\(663\) −7.40123 −0.287440
\(664\) 0 0
\(665\) 0.224243 0.00869575
\(666\) 0 0
\(667\) 74.2135 2.87356
\(668\) 0 0
\(669\) 45.0499 1.74173
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 9.48493 0.365617 0.182809 0.983149i \(-0.441481\pi\)
0.182809 + 0.983149i \(0.441481\pi\)
\(674\) 0 0
\(675\) −9.72427 −0.374288
\(676\) 0 0
\(677\) 4.11952 0.158326 0.0791631 0.996862i \(-0.474775\pi\)
0.0791631 + 0.996862i \(0.474775\pi\)
\(678\) 0 0
\(679\) 6.78363 0.260332
\(680\) 0 0
\(681\) −71.2262 −2.72940
\(682\) 0 0
\(683\) 29.0594 1.11193 0.555963 0.831207i \(-0.312349\pi\)
0.555963 + 0.831207i \(0.312349\pi\)
\(684\) 0 0
\(685\) −13.4216 −0.512814
\(686\) 0 0
\(687\) −59.5664 −2.27260
\(688\) 0 0
\(689\) 10.6491 0.405698
\(690\) 0 0
\(691\) 19.4633 0.740418 0.370209 0.928949i \(-0.379286\pi\)
0.370209 + 0.928949i \(0.379286\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14.0856 0.534298
\(696\) 0 0
\(697\) −4.80847 −0.182134
\(698\) 0 0
\(699\) 63.6976 2.40926
\(700\) 0 0
\(701\) 15.1359 0.571675 0.285838 0.958278i \(-0.407728\pi\)
0.285838 + 0.958278i \(0.407728\pi\)
\(702\) 0 0
\(703\) 1.65409 0.0623853
\(704\) 0 0
\(705\) 2.49761 0.0940653
\(706\) 0 0
\(707\) −15.7590 −0.592677
\(708\) 0 0
\(709\) −27.0377 −1.01542 −0.507712 0.861527i \(-0.669508\pi\)
−0.507712 + 0.861527i \(0.669508\pi\)
\(710\) 0 0
\(711\) 36.7003 1.37637
\(712\) 0 0
\(713\) −42.1390 −1.57812
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −57.2009 −2.13621
\(718\) 0 0
\(719\) 3.74967 0.139839 0.0699195 0.997553i \(-0.477726\pi\)
0.0699195 + 0.997553i \(0.477726\pi\)
\(720\) 0 0
\(721\) −10.2201 −0.380618
\(722\) 0 0
\(723\) −41.9657 −1.56072
\(724\) 0 0
\(725\) 9.36210 0.347700
\(726\) 0 0
\(727\) 45.5685 1.69004 0.845022 0.534732i \(-0.179587\pi\)
0.845022 + 0.534732i \(0.179587\pi\)
\(728\) 0 0
\(729\) −20.9486 −0.775874
\(730\) 0 0
\(731\) −3.51262 −0.129919
\(732\) 0 0
\(733\) 37.1793 1.37325 0.686625 0.727012i \(-0.259091\pi\)
0.686625 + 0.727012i \(0.259091\pi\)
\(734\) 0 0
\(735\) −18.9630 −0.699460
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 3.86380 0.142132 0.0710661 0.997472i \(-0.477360\pi\)
0.0710661 + 0.997472i \(0.477360\pi\)
\(740\) 0 0
\(741\) −3.48461 −0.128010
\(742\) 0 0
\(743\) 7.73510 0.283773 0.141887 0.989883i \(-0.454683\pi\)
0.141887 + 0.989883i \(0.454683\pi\)
\(744\) 0 0
\(745\) 1.79173 0.0656438
\(746\) 0 0
\(747\) 44.0451 1.61153
\(748\) 0 0
\(749\) −0.451118 −0.0164835
\(750\) 0 0
\(751\) −19.7386 −0.720271 −0.360135 0.932900i \(-0.617269\pi\)
−0.360135 + 0.932900i \(0.617269\pi\)
\(752\) 0 0
\(753\) −46.3349 −1.68854
\(754\) 0 0
\(755\) 19.0871 0.694649
\(756\) 0 0
\(757\) 10.5828 0.384637 0.192319 0.981333i \(-0.438399\pi\)
0.192319 + 0.981333i \(0.438399\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −50.6698 −1.83678 −0.918390 0.395677i \(-0.870510\pi\)
−0.918390 + 0.395677i \(0.870510\pi\)
\(762\) 0 0
\(763\) −5.39079 −0.195160
\(764\) 0 0
\(765\) −3.41300 −0.123397
\(766\) 0 0
\(767\) −59.9395 −2.16429
\(768\) 0 0
\(769\) 16.2588 0.586306 0.293153 0.956066i \(-0.405295\pi\)
0.293153 + 0.956066i \(0.405295\pi\)
\(770\) 0 0
\(771\) −87.3426 −3.14557
\(772\) 0 0
\(773\) 16.4897 0.593095 0.296547 0.955018i \(-0.404165\pi\)
0.296547 + 0.955018i \(0.404165\pi\)
\(774\) 0 0
\(775\) −5.31588 −0.190952
\(776\) 0 0
\(777\) 16.7811 0.602017
\(778\) 0 0
\(779\) −2.26390 −0.0811125
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −91.0397 −3.25349
\(784\) 0 0
\(785\) −9.78753 −0.349332
\(786\) 0 0
\(787\) −25.7184 −0.916762 −0.458381 0.888756i \(-0.651570\pi\)
−0.458381 + 0.888756i \(0.651570\pi\)
\(788\) 0 0
\(789\) −28.0104 −0.997196
\(790\) 0 0
\(791\) 8.55171 0.304064
\(792\) 0 0
\(793\) 29.3054 1.04066
\(794\) 0 0
\(795\) 7.28492 0.258369
\(796\) 0 0
\(797\) 5.59752 0.198274 0.0991372 0.995074i \(-0.468392\pi\)
0.0991372 + 0.995074i \(0.468392\pi\)
\(798\) 0 0
\(799\) 0.452790 0.0160186
\(800\) 0 0
\(801\) −103.297 −3.64981
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 6.86422 0.241932
\(806\) 0 0
\(807\) −81.4092 −2.86574
\(808\) 0 0
\(809\) −19.6788 −0.691871 −0.345936 0.938258i \(-0.612438\pi\)
−0.345936 + 0.938258i \(0.612438\pi\)
\(810\) 0 0
\(811\) 7.41499 0.260375 0.130188 0.991489i \(-0.458442\pi\)
0.130188 + 0.991489i \(0.458442\pi\)
\(812\) 0 0
\(813\) 71.4844 2.50707
\(814\) 0 0
\(815\) −0.396843 −0.0139008
\(816\) 0 0
\(817\) −1.65379 −0.0578588
\(818\) 0 0
\(819\) −23.8305 −0.832706
\(820\) 0 0
\(821\) 5.30773 0.185241 0.0926205 0.995701i \(-0.470476\pi\)
0.0926205 + 0.995701i \(0.470476\pi\)
\(822\) 0 0
\(823\) −16.1952 −0.564528 −0.282264 0.959337i \(-0.591085\pi\)
−0.282264 + 0.959337i \(0.591085\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.97372 0.346820 0.173410 0.984850i \(-0.444521\pi\)
0.173410 + 0.984850i \(0.444521\pi\)
\(828\) 0 0
\(829\) −26.4859 −0.919893 −0.459947 0.887947i \(-0.652131\pi\)
−0.459947 + 0.887947i \(0.652131\pi\)
\(830\) 0 0
\(831\) 30.3169 1.05168
\(832\) 0 0
\(833\) −3.43779 −0.119112
\(834\) 0 0
\(835\) 13.9140 0.481514
\(836\) 0 0
\(837\) 51.6931 1.78677
\(838\) 0 0
\(839\) 24.0591 0.830613 0.415307 0.909681i \(-0.363674\pi\)
0.415307 + 0.909681i \(0.363674\pi\)
\(840\) 0 0
\(841\) 58.6490 2.02238
\(842\) 0 0
\(843\) 12.4103 0.427433
\(844\) 0 0
\(845\) −6.67004 −0.229456
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 14.4803 0.496962
\(850\) 0 0
\(851\) 50.6329 1.73567
\(852\) 0 0
\(853\) −22.5471 −0.771997 −0.385999 0.922499i \(-0.626143\pi\)
−0.385999 + 0.922499i \(0.626143\pi\)
\(854\) 0 0
\(855\) −1.60689 −0.0549545
\(856\) 0 0
\(857\) −10.0453 −0.343143 −0.171571 0.985172i \(-0.554884\pi\)
−0.171571 + 0.985172i \(0.554884\pi\)
\(858\) 0 0
\(859\) 15.7921 0.538819 0.269409 0.963026i \(-0.413172\pi\)
0.269409 + 0.963026i \(0.413172\pi\)
\(860\) 0 0
\(861\) −22.9676 −0.782734
\(862\) 0 0
\(863\) −22.6412 −0.770717 −0.385358 0.922767i \(-0.625922\pi\)
−0.385358 + 0.922767i \(0.625922\pi\)
\(864\) 0 0
\(865\) 5.33390 0.181358
\(866\) 0 0
\(867\) 50.6600 1.72050
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 31.8318 1.07858
\(872\) 0 0
\(873\) −48.6105 −1.64522
\(874\) 0 0
\(875\) 0.865927 0.0292737
\(876\) 0 0
\(877\) −23.7591 −0.802288 −0.401144 0.916015i \(-0.631387\pi\)
−0.401144 + 0.916015i \(0.631387\pi\)
\(878\) 0 0
\(879\) 0.436931 0.0147373
\(880\) 0 0
\(881\) −21.6772 −0.730323 −0.365161 0.930944i \(-0.618986\pi\)
−0.365161 + 0.930944i \(0.618986\pi\)
\(882\) 0 0
\(883\) −40.6198 −1.36697 −0.683483 0.729967i \(-0.739535\pi\)
−0.683483 + 0.729967i \(0.739535\pi\)
\(884\) 0 0
\(885\) −41.0039 −1.37833
\(886\) 0 0
\(887\) −34.1509 −1.14668 −0.573338 0.819319i \(-0.694352\pi\)
−0.573338 + 0.819319i \(0.694352\pi\)
\(888\) 0 0
\(889\) 3.22068 0.108018
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0.213180 0.00713379
\(894\) 0 0
\(895\) −7.63478 −0.255202
\(896\) 0 0
\(897\) −106.666 −3.56148
\(898\) 0 0
\(899\) −49.7678 −1.65985
\(900\) 0 0
\(901\) 1.32068 0.0439982
\(902\) 0 0
\(903\) −16.7780 −0.558337
\(904\) 0 0
\(905\) −1.30453 −0.0433639
\(906\) 0 0
\(907\) 11.5541 0.383647 0.191824 0.981429i \(-0.438560\pi\)
0.191824 + 0.981429i \(0.438560\pi\)
\(908\) 0 0
\(909\) 112.926 3.74553
\(910\) 0 0
\(911\) −14.4057 −0.477284 −0.238642 0.971108i \(-0.576702\pi\)
−0.238642 + 0.971108i \(0.576702\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 20.0474 0.662748
\(916\) 0 0
\(917\) 17.6873 0.584087
\(918\) 0 0
\(919\) 49.1155 1.62017 0.810085 0.586312i \(-0.199421\pi\)
0.810085 + 0.586312i \(0.199421\pi\)
\(920\) 0 0
\(921\) −78.1482 −2.57507
\(922\) 0 0
\(923\) 12.4143 0.408621
\(924\) 0 0
\(925\) 6.38739 0.210016
\(926\) 0 0
\(927\) 73.2360 2.40539
\(928\) 0 0
\(929\) 23.9888 0.787048 0.393524 0.919314i \(-0.371256\pi\)
0.393524 + 0.919314i \(0.371256\pi\)
\(930\) 0 0
\(931\) −1.61856 −0.0530461
\(932\) 0 0
\(933\) −49.7316 −1.62814
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −13.1022 −0.428029 −0.214014 0.976831i \(-0.568654\pi\)
−0.214014 + 0.976831i \(0.568654\pi\)
\(938\) 0 0
\(939\) −80.4729 −2.62613
\(940\) 0 0
\(941\) 36.6826 1.19582 0.597909 0.801564i \(-0.295998\pi\)
0.597909 + 0.801564i \(0.295998\pi\)
\(942\) 0 0
\(943\) −69.2994 −2.25670
\(944\) 0 0
\(945\) −8.42052 −0.273919
\(946\) 0 0
\(947\) 20.6112 0.669774 0.334887 0.942258i \(-0.391302\pi\)
0.334887 + 0.942258i \(0.391302\pi\)
\(948\) 0 0
\(949\) 12.8207 0.416177
\(950\) 0 0
\(951\) −50.7156 −1.64457
\(952\) 0 0
\(953\) −17.7949 −0.576433 −0.288216 0.957565i \(-0.593062\pi\)
−0.288216 + 0.957565i \(0.593062\pi\)
\(954\) 0 0
\(955\) −25.0833 −0.811678
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −11.6222 −0.375299
\(960\) 0 0
\(961\) −2.74144 −0.0884337
\(962\) 0 0
\(963\) 3.23264 0.104170
\(964\) 0 0
\(965\) −19.9561 −0.642409
\(966\) 0 0
\(967\) 0.828077 0.0266292 0.0133146 0.999911i \(-0.495762\pi\)
0.0133146 + 0.999911i \(0.495762\pi\)
\(968\) 0 0
\(969\) −0.432154 −0.0138828
\(970\) 0 0
\(971\) −0.124535 −0.00399653 −0.00199827 0.999998i \(-0.500636\pi\)
−0.00199827 + 0.999998i \(0.500636\pi\)
\(972\) 0 0
\(973\) 12.1971 0.391022
\(974\) 0 0
\(975\) −13.4560 −0.430938
\(976\) 0 0
\(977\) −21.4664 −0.686770 −0.343385 0.939195i \(-0.611573\pi\)
−0.343385 + 0.939195i \(0.611573\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 38.6296 1.23335
\(982\) 0 0
\(983\) 31.7566 1.01288 0.506440 0.862275i \(-0.330961\pi\)
0.506440 + 0.862275i \(0.330961\pi\)
\(984\) 0 0
\(985\) −1.31088 −0.0417680
\(986\) 0 0
\(987\) 2.16275 0.0688410
\(988\) 0 0
\(989\) −50.6237 −1.60974
\(990\) 0 0
\(991\) 46.7101 1.48379 0.741897 0.670514i \(-0.233926\pi\)
0.741897 + 0.670514i \(0.233926\pi\)
\(992\) 0 0
\(993\) −13.3370 −0.423236
\(994\) 0 0
\(995\) 4.99115 0.158230
\(996\) 0 0
\(997\) −51.6548 −1.63592 −0.817962 0.575273i \(-0.804896\pi\)
−0.817962 + 0.575273i \(0.804896\pi\)
\(998\) 0 0
\(999\) −62.1127 −1.96516
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 4840.2.a.be.1.1 6
4.3 odd 2 9680.2.a.cy.1.6 6
11.7 odd 10 440.2.y.b.401.3 yes 12
11.8 odd 10 440.2.y.b.361.3 12
11.10 odd 2 4840.2.a.bf.1.1 6
44.7 even 10 880.2.bo.j.401.1 12
44.19 even 10 880.2.bo.j.801.1 12
44.43 even 2 9680.2.a.cx.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.y.b.361.3 12 11.8 odd 10
440.2.y.b.401.3 yes 12 11.7 odd 10
880.2.bo.j.401.1 12 44.7 even 10
880.2.bo.j.801.1 12 44.19 even 10
4840.2.a.be.1.1 6 1.1 even 1 trivial
4840.2.a.bf.1.1 6 11.10 odd 2
9680.2.a.cx.1.6 6 44.43 even 2
9680.2.a.cy.1.6 6 4.3 odd 2