Properties

Label 4840.2.a.s.1.2
Level $4840$
Weight $2$
Character 4840.1
Self dual yes
Analytic conductor $38.648$
Analytic rank $1$
Dimension $3$
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: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.788.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 7x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.476452\) 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)
 
\(f(q)\) \(=\) \(q-0.476452 q^{3} -1.00000 q^{5} -3.34364 q^{7} -2.77299 q^{9} +O(q^{10})\) \(q-0.476452 q^{3} -1.00000 q^{5} -3.34364 q^{7} -2.77299 q^{9} +3.82009 q^{13} +0.476452 q^{15} +6.59308 q^{17} -1.82009 q^{19} +1.59308 q^{21} +2.77299 q^{23} +1.00000 q^{25} +2.75055 q^{27} +0.952904 q^{29} -4.17991 q^{31} +3.34364 q^{35} -2.95290 q^{37} -1.82009 q^{39} -4.82009 q^{41} -9.93672 q^{43} +2.77299 q^{45} +3.16373 q^{47} +4.17991 q^{49} -3.14129 q^{51} +7.46027 q^{53} +0.867185 q^{57} +2.77299 q^{59} +11.7730 q^{61} +9.27188 q^{63} -3.82009 q^{65} +7.42936 q^{67} -1.32120 q^{69} +14.0534 q^{71} +7.64018 q^{73} -0.476452 q^{75} -8.59308 q^{79} +7.00847 q^{81} -4.86719 q^{83} -6.59308 q^{85} -0.454013 q^{87} -1.59308 q^{89} -12.7730 q^{91} +1.99153 q^{93} +1.82009 q^{95} -3.82009 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{3} - 3 q^{5} - 3 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{3} - 3 q^{5} - 3 q^{7} + 6 q^{9} + 2 q^{13} - q^{15} - 4 q^{17} + 4 q^{19} - 19 q^{21} - 6 q^{23} + 3 q^{25} + 25 q^{27} - 2 q^{29} - 22 q^{31} + 3 q^{35} - 4 q^{37} + 4 q^{39} - 5 q^{41} + q^{43} - 6 q^{45} - 7 q^{47} + 22 q^{49} - 24 q^{51} - 6 q^{53} - 2 q^{57} - 6 q^{59} + 21 q^{61} - 20 q^{63} - 2 q^{65} + 15 q^{67} - 28 q^{69} - 10 q^{71} + 4 q^{73} + q^{75} - 2 q^{79} + 31 q^{81} - 10 q^{83} + 4 q^{85} - 30 q^{87} + 19 q^{89} - 24 q^{91} - 4 q^{93} - 4 q^{95} - 2 q^{97}+O(q^{100}) \) 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
\(3\) −0.476452 −0.275080 −0.137540 0.990496i \(-0.543920\pi\)
−0.137540 + 0.990496i \(0.543920\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −3.34364 −1.26378 −0.631888 0.775060i \(-0.717720\pi\)
−0.631888 + 0.775060i \(0.717720\pi\)
\(8\) 0 0
\(9\) −2.77299 −0.924331
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) 3.82009 1.05950 0.529751 0.848153i \(-0.322285\pi\)
0.529751 + 0.848153i \(0.322285\pi\)
\(14\) 0 0
\(15\) 0.476452 0.123019
\(16\) 0 0
\(17\) 6.59308 1.59906 0.799529 0.600628i \(-0.205083\pi\)
0.799529 + 0.600628i \(0.205083\pi\)
\(18\) 0 0
\(19\) −1.82009 −0.417557 −0.208779 0.977963i \(-0.566949\pi\)
−0.208779 + 0.977963i \(0.566949\pi\)
\(20\) 0 0
\(21\) 1.59308 0.347639
\(22\) 0 0
\(23\) 2.77299 0.578209 0.289105 0.957298i \(-0.406642\pi\)
0.289105 + 0.957298i \(0.406642\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 2.75055 0.529344
\(28\) 0 0
\(29\) 0.952904 0.176950 0.0884749 0.996078i \(-0.471801\pi\)
0.0884749 + 0.996078i \(0.471801\pi\)
\(30\) 0 0
\(31\) −4.17991 −0.750734 −0.375367 0.926876i \(-0.622483\pi\)
−0.375367 + 0.926876i \(0.622483\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.34364 0.565178
\(36\) 0 0
\(37\) −2.95290 −0.485454 −0.242727 0.970095i \(-0.578042\pi\)
−0.242727 + 0.970095i \(0.578042\pi\)
\(38\) 0 0
\(39\) −1.82009 −0.291448
\(40\) 0 0
\(41\) −4.82009 −0.752771 −0.376386 0.926463i \(-0.622833\pi\)
−0.376386 + 0.926463i \(0.622833\pi\)
\(42\) 0 0
\(43\) −9.93672 −1.51534 −0.757668 0.652640i \(-0.773661\pi\)
−0.757668 + 0.652640i \(0.773661\pi\)
\(44\) 0 0
\(45\) 2.77299 0.413373
\(46\) 0 0
\(47\) 3.16373 0.461477 0.230738 0.973016i \(-0.425886\pi\)
0.230738 + 0.973016i \(0.425886\pi\)
\(48\) 0 0
\(49\) 4.17991 0.597130
\(50\) 0 0
\(51\) −3.14129 −0.439868
\(52\) 0 0
\(53\) 7.46027 1.02475 0.512373 0.858763i \(-0.328766\pi\)
0.512373 + 0.858763i \(0.328766\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.867185 0.114861
\(58\) 0 0
\(59\) 2.77299 0.361013 0.180506 0.983574i \(-0.442226\pi\)
0.180506 + 0.983574i \(0.442226\pi\)
\(60\) 0 0
\(61\) 11.7730 1.50738 0.753689 0.657232i \(-0.228273\pi\)
0.753689 + 0.657232i \(0.228273\pi\)
\(62\) 0 0
\(63\) 9.27188 1.16815
\(64\) 0 0
\(65\) −3.82009 −0.473824
\(66\) 0 0
\(67\) 7.42936 0.907640 0.453820 0.891093i \(-0.350061\pi\)
0.453820 + 0.891093i \(0.350061\pi\)
\(68\) 0 0
\(69\) −1.32120 −0.159054
\(70\) 0 0
\(71\) 14.0534 1.66783 0.833913 0.551896i \(-0.186095\pi\)
0.833913 + 0.551896i \(0.186095\pi\)
\(72\) 0 0
\(73\) 7.64018 0.894215 0.447108 0.894480i \(-0.352454\pi\)
0.447108 + 0.894480i \(0.352454\pi\)
\(74\) 0 0
\(75\) −0.476452 −0.0550159
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −8.59308 −0.966797 −0.483399 0.875400i \(-0.660598\pi\)
−0.483399 + 0.875400i \(0.660598\pi\)
\(80\) 0 0
\(81\) 7.00847 0.778719
\(82\) 0 0
\(83\) −4.86719 −0.534243 −0.267121 0.963663i \(-0.586073\pi\)
−0.267121 + 0.963663i \(0.586073\pi\)
\(84\) 0 0
\(85\) −6.59308 −0.715120
\(86\) 0 0
\(87\) −0.454013 −0.0486753
\(88\) 0 0
\(89\) −1.59308 −0.168866 −0.0844332 0.996429i \(-0.526908\pi\)
−0.0844332 + 0.996429i \(0.526908\pi\)
\(90\) 0 0
\(91\) −12.7730 −1.33897
\(92\) 0 0
\(93\) 1.99153 0.206512
\(94\) 0 0
\(95\) 1.82009 0.186737
\(96\) 0 0
\(97\) −3.82009 −0.387871 −0.193936 0.981014i \(-0.562125\pi\)
−0.193936 + 0.981014i \(0.562125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −15.3275 −1.52514 −0.762569 0.646907i \(-0.776062\pi\)
−0.762569 + 0.646907i \(0.776062\pi\)
\(102\) 0 0
\(103\) −18.0534 −1.77885 −0.889425 0.457082i \(-0.848895\pi\)
−0.889425 + 0.457082i \(0.848895\pi\)
\(104\) 0 0
\(105\) −1.59308 −0.155469
\(106\) 0 0
\(107\) −10.1166 −0.978012 −0.489006 0.872281i \(-0.662640\pi\)
−0.489006 + 0.872281i \(0.662640\pi\)
\(108\) 0 0
\(109\) −17.6788 −1.69332 −0.846661 0.532133i \(-0.821391\pi\)
−0.846661 + 0.532133i \(0.821391\pi\)
\(110\) 0 0
\(111\) 1.40692 0.133539
\(112\) 0 0
\(113\) −15.3745 −1.44632 −0.723158 0.690683i \(-0.757310\pi\)
−0.723158 + 0.690683i \(0.757310\pi\)
\(114\) 0 0
\(115\) −2.77299 −0.258583
\(116\) 0 0
\(117\) −10.5931 −0.979331
\(118\) 0 0
\(119\) −22.0449 −2.02085
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 2.29654 0.207072
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −15.0695 −1.33720 −0.668602 0.743620i \(-0.733107\pi\)
−0.668602 + 0.743620i \(0.733107\pi\)
\(128\) 0 0
\(129\) 4.73437 0.416838
\(130\) 0 0
\(131\) 11.5545 1.00952 0.504759 0.863260i \(-0.331581\pi\)
0.504759 + 0.863260i \(0.331581\pi\)
\(132\) 0 0
\(133\) 6.08572 0.527699
\(134\) 0 0
\(135\) −2.75055 −0.236730
\(136\) 0 0
\(137\) 20.1475 1.72132 0.860660 0.509179i \(-0.170051\pi\)
0.860660 + 0.509179i \(0.170051\pi\)
\(138\) 0 0
\(139\) −2.27410 −0.192887 −0.0964434 0.995338i \(-0.530747\pi\)
−0.0964434 + 0.995338i \(0.530747\pi\)
\(140\) 0 0
\(141\) −1.50736 −0.126943
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −0.952904 −0.0791344
\(146\) 0 0
\(147\) −1.99153 −0.164258
\(148\) 0 0
\(149\) −8.46027 −0.693092 −0.346546 0.938033i \(-0.612646\pi\)
−0.346546 + 0.938033i \(0.612646\pi\)
\(150\) 0 0
\(151\) 16.1475 1.31407 0.657034 0.753861i \(-0.271811\pi\)
0.657034 + 0.753861i \(0.271811\pi\)
\(152\) 0 0
\(153\) −18.2826 −1.47806
\(154\) 0 0
\(155\) 4.17991 0.335739
\(156\) 0 0
\(157\) −1.73437 −0.138418 −0.0692089 0.997602i \(-0.522048\pi\)
−0.0692089 + 0.997602i \(0.522048\pi\)
\(158\) 0 0
\(159\) −3.55446 −0.281887
\(160\) 0 0
\(161\) −9.27188 −0.730727
\(162\) 0 0
\(163\) −10.6564 −0.834671 −0.417335 0.908753i \(-0.637036\pi\)
−0.417335 + 0.908753i \(0.637036\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −21.7483 −1.68294 −0.841468 0.540306i \(-0.818308\pi\)
−0.841468 + 0.540306i \(0.818308\pi\)
\(168\) 0 0
\(169\) 1.59308 0.122545
\(170\) 0 0
\(171\) 5.04710 0.385961
\(172\) 0 0
\(173\) −5.91428 −0.449654 −0.224827 0.974399i \(-0.572182\pi\)
−0.224827 + 0.974399i \(0.572182\pi\)
\(174\) 0 0
\(175\) −3.34364 −0.252755
\(176\) 0 0
\(177\) −1.32120 −0.0993074
\(178\) 0 0
\(179\) −13.6402 −1.01951 −0.509757 0.860318i \(-0.670265\pi\)
−0.509757 + 0.860318i \(0.670265\pi\)
\(180\) 0 0
\(181\) −12.8734 −0.956875 −0.478438 0.878122i \(-0.658797\pi\)
−0.478438 + 0.878122i \(0.658797\pi\)
\(182\) 0 0
\(183\) −5.60927 −0.414649
\(184\) 0 0
\(185\) 2.95290 0.217102
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −9.19686 −0.668973
\(190\) 0 0
\(191\) 12.4132 0.898186 0.449093 0.893485i \(-0.351747\pi\)
0.449093 + 0.893485i \(0.351747\pi\)
\(192\) 0 0
\(193\) 12.9529 0.932370 0.466185 0.884687i \(-0.345628\pi\)
0.466185 + 0.884687i \(0.345628\pi\)
\(194\) 0 0
\(195\) 1.82009 0.130339
\(196\) 0 0
\(197\) −10.8587 −0.773651 −0.386826 0.922153i \(-0.626428\pi\)
−0.386826 + 0.922153i \(0.626428\pi\)
\(198\) 0 0
\(199\) 3.73437 0.264723 0.132361 0.991202i \(-0.457744\pi\)
0.132361 + 0.991202i \(0.457744\pi\)
\(200\) 0 0
\(201\) −3.53973 −0.249673
\(202\) 0 0
\(203\) −3.18617 −0.223625
\(204\) 0 0
\(205\) 4.82009 0.336650
\(206\) 0 0
\(207\) −7.68949 −0.534457
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 13.7259 0.944930 0.472465 0.881349i \(-0.343364\pi\)
0.472465 + 0.881349i \(0.343364\pi\)
\(212\) 0 0
\(213\) −6.69575 −0.458785
\(214\) 0 0
\(215\) 9.93672 0.677679
\(216\) 0 0
\(217\) 13.9761 0.948760
\(218\) 0 0
\(219\) −3.64018 −0.245980
\(220\) 0 0
\(221\) 25.1862 1.69420
\(222\) 0 0
\(223\) −23.2494 −1.55690 −0.778449 0.627708i \(-0.783993\pi\)
−0.778449 + 0.627708i \(0.783993\pi\)
\(224\) 0 0
\(225\) −2.77299 −0.184866
\(226\) 0 0
\(227\) −9.01618 −0.598425 −0.299213 0.954186i \(-0.596724\pi\)
−0.299213 + 0.954186i \(0.596724\pi\)
\(228\) 0 0
\(229\) 7.68727 0.507989 0.253995 0.967206i \(-0.418255\pi\)
0.253995 + 0.967206i \(0.418255\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.94665 −0.127529 −0.0637646 0.997965i \(-0.520311\pi\)
−0.0637646 + 0.997965i \(0.520311\pi\)
\(234\) 0 0
\(235\) −3.16373 −0.206379
\(236\) 0 0
\(237\) 4.09419 0.265946
\(238\) 0 0
\(239\) −24.7406 −1.60034 −0.800169 0.599775i \(-0.795257\pi\)
−0.800169 + 0.599775i \(0.795257\pi\)
\(240\) 0 0
\(241\) −18.0063 −1.15988 −0.579942 0.814657i \(-0.696925\pi\)
−0.579942 + 0.814657i \(0.696925\pi\)
\(242\) 0 0
\(243\) −11.5909 −0.743554
\(244\) 0 0
\(245\) −4.17991 −0.267045
\(246\) 0 0
\(247\) −6.95290 −0.442403
\(248\) 0 0
\(249\) 2.31898 0.146959
\(250\) 0 0
\(251\) 4.86719 0.307214 0.153607 0.988132i \(-0.450911\pi\)
0.153607 + 0.988132i \(0.450911\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 3.14129 0.196715
\(256\) 0 0
\(257\) −13.8201 −0.862073 −0.431037 0.902334i \(-0.641852\pi\)
−0.431037 + 0.902334i \(0.641852\pi\)
\(258\) 0 0
\(259\) 9.87344 0.613506
\(260\) 0 0
\(261\) −2.64240 −0.163560
\(262\) 0 0
\(263\) −0.539732 −0.0332813 −0.0166406 0.999862i \(-0.505297\pi\)
−0.0166406 + 0.999862i \(0.505297\pi\)
\(264\) 0 0
\(265\) −7.46027 −0.458281
\(266\) 0 0
\(267\) 0.759028 0.0464517
\(268\) 0 0
\(269\) 19.1475 1.16745 0.583723 0.811953i \(-0.301595\pi\)
0.583723 + 0.811953i \(0.301595\pi\)
\(270\) 0 0
\(271\) −8.32745 −0.505857 −0.252928 0.967485i \(-0.581394\pi\)
−0.252928 + 0.967485i \(0.581394\pi\)
\(272\) 0 0
\(273\) 6.08572 0.368324
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −24.9529 −1.49927 −0.749637 0.661849i \(-0.769772\pi\)
−0.749637 + 0.661849i \(0.769772\pi\)
\(278\) 0 0
\(279\) 11.5909 0.693927
\(280\) 0 0
\(281\) 13.8116 0.823932 0.411966 0.911199i \(-0.364842\pi\)
0.411966 + 0.911199i \(0.364842\pi\)
\(282\) 0 0
\(283\) −30.3499 −1.80411 −0.902057 0.431617i \(-0.857943\pi\)
−0.902057 + 0.431617i \(0.857943\pi\)
\(284\) 0 0
\(285\) −0.867185 −0.0513676
\(286\) 0 0
\(287\) 16.1166 0.951335
\(288\) 0 0
\(289\) 26.4687 1.55698
\(290\) 0 0
\(291\) 1.82009 0.106696
\(292\) 0 0
\(293\) −1.49264 −0.0872007 −0.0436004 0.999049i \(-0.513883\pi\)
−0.0436004 + 0.999049i \(0.513883\pi\)
\(294\) 0 0
\(295\) −2.77299 −0.161450
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10.5931 0.612614
\(300\) 0 0
\(301\) 33.2248 1.91504
\(302\) 0 0
\(303\) 7.30280 0.419535
\(304\) 0 0
\(305\) −11.7730 −0.674120
\(306\) 0 0
\(307\) −16.8672 −0.962661 −0.481331 0.876539i \(-0.659846\pi\)
−0.481331 + 0.876539i \(0.659846\pi\)
\(308\) 0 0
\(309\) 8.60156 0.489325
\(310\) 0 0
\(311\) −31.3661 −1.77861 −0.889304 0.457317i \(-0.848810\pi\)
−0.889304 + 0.457317i \(0.848810\pi\)
\(312\) 0 0
\(313\) 33.5051 1.89382 0.946911 0.321495i \(-0.104185\pi\)
0.946911 + 0.321495i \(0.104185\pi\)
\(314\) 0 0
\(315\) −9.27188 −0.522412
\(316\) 0 0
\(317\) 27.1862 1.52693 0.763464 0.645851i \(-0.223497\pi\)
0.763464 + 0.645851i \(0.223497\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 4.82009 0.269031
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 3.82009 0.211900
\(326\) 0 0
\(327\) 8.42310 0.465799
\(328\) 0 0
\(329\) −10.5784 −0.583204
\(330\) 0 0
\(331\) 33.7877 1.85714 0.928571 0.371156i \(-0.121038\pi\)
0.928571 + 0.371156i \(0.121038\pi\)
\(332\) 0 0
\(333\) 8.18838 0.448721
\(334\) 0 0
\(335\) −7.42936 −0.405909
\(336\) 0 0
\(337\) −7.63171 −0.415725 −0.207863 0.978158i \(-0.566651\pi\)
−0.207863 + 0.978158i \(0.566651\pi\)
\(338\) 0 0
\(339\) 7.32524 0.397852
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 9.42936 0.509137
\(344\) 0 0
\(345\) 1.32120 0.0711309
\(346\) 0 0
\(347\) −35.7483 −1.91907 −0.959536 0.281587i \(-0.909139\pi\)
−0.959536 + 0.281587i \(0.909139\pi\)
\(348\) 0 0
\(349\) 13.3127 0.712614 0.356307 0.934369i \(-0.384036\pi\)
0.356307 + 0.934369i \(0.384036\pi\)
\(350\) 0 0
\(351\) 10.5074 0.560842
\(352\) 0 0
\(353\) 0.601556 0.0320176 0.0160088 0.999872i \(-0.494904\pi\)
0.0160088 + 0.999872i \(0.494904\pi\)
\(354\) 0 0
\(355\) −14.0534 −0.745874
\(356\) 0 0
\(357\) 10.5033 0.555895
\(358\) 0 0
\(359\) −16.5846 −0.875302 −0.437651 0.899145i \(-0.644189\pi\)
−0.437651 + 0.899145i \(0.644189\pi\)
\(360\) 0 0
\(361\) −15.6873 −0.825646
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.64018 −0.399905
\(366\) 0 0
\(367\) 1.39699 0.0729222 0.0364611 0.999335i \(-0.488391\pi\)
0.0364611 + 0.999335i \(0.488391\pi\)
\(368\) 0 0
\(369\) 13.3661 0.695810
\(370\) 0 0
\(371\) −24.9444 −1.29505
\(372\) 0 0
\(373\) 4.60156 0.238260 0.119130 0.992879i \(-0.461990\pi\)
0.119130 + 0.992879i \(0.461990\pi\)
\(374\) 0 0
\(375\) 0.476452 0.0246039
\(376\) 0 0
\(377\) 3.64018 0.187479
\(378\) 0 0
\(379\) 33.9507 1.74393 0.871965 0.489569i \(-0.162846\pi\)
0.871965 + 0.489569i \(0.162846\pi\)
\(380\) 0 0
\(381\) 7.17991 0.367838
\(382\) 0 0
\(383\) −18.9121 −0.966361 −0.483181 0.875521i \(-0.660519\pi\)
−0.483181 + 0.875521i \(0.660519\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 27.5545 1.40067
\(388\) 0 0
\(389\) −21.2866 −1.07927 −0.539637 0.841898i \(-0.681439\pi\)
−0.539637 + 0.841898i \(0.681439\pi\)
\(390\) 0 0
\(391\) 18.2826 0.924590
\(392\) 0 0
\(393\) −5.50515 −0.277698
\(394\) 0 0
\(395\) 8.59308 0.432365
\(396\) 0 0
\(397\) −17.7344 −0.890063 −0.445031 0.895515i \(-0.646807\pi\)
−0.445031 + 0.895515i \(0.646807\pi\)
\(398\) 0 0
\(399\) −2.89955 −0.145159
\(400\) 0 0
\(401\) −12.8116 −0.639782 −0.319891 0.947454i \(-0.603646\pi\)
−0.319891 + 0.947454i \(0.603646\pi\)
\(402\) 0 0
\(403\) −15.9676 −0.795404
\(404\) 0 0
\(405\) −7.00847 −0.348254
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 16.4603 0.813908 0.406954 0.913449i \(-0.366591\pi\)
0.406954 + 0.913449i \(0.366591\pi\)
\(410\) 0 0
\(411\) −9.59934 −0.473500
\(412\) 0 0
\(413\) −9.27188 −0.456240
\(414\) 0 0
\(415\) 4.86719 0.238921
\(416\) 0 0
\(417\) 1.08350 0.0530593
\(418\) 0 0
\(419\) 1.32120 0.0645448 0.0322724 0.999479i \(-0.489726\pi\)
0.0322724 + 0.999479i \(0.489726\pi\)
\(420\) 0 0
\(421\) 15.7406 0.767151 0.383576 0.923509i \(-0.374693\pi\)
0.383576 + 0.923509i \(0.374693\pi\)
\(422\) 0 0
\(423\) −8.77299 −0.426558
\(424\) 0 0
\(425\) 6.59308 0.319811
\(426\) 0 0
\(427\) −39.3646 −1.90499
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 21.7792 1.04907 0.524535 0.851389i \(-0.324239\pi\)
0.524535 + 0.851389i \(0.324239\pi\)
\(432\) 0 0
\(433\) 17.6317 0.847326 0.423663 0.905820i \(-0.360744\pi\)
0.423663 + 0.905820i \(0.360744\pi\)
\(434\) 0 0
\(435\) 0.454013 0.0217683
\(436\) 0 0
\(437\) −5.04710 −0.241435
\(438\) 0 0
\(439\) 10.4047 0.496589 0.248295 0.968685i \(-0.420130\pi\)
0.248295 + 0.968685i \(0.420130\pi\)
\(440\) 0 0
\(441\) −11.5909 −0.551946
\(442\) 0 0
\(443\) 25.4827 1.21072 0.605360 0.795952i \(-0.293029\pi\)
0.605360 + 0.795952i \(0.293029\pi\)
\(444\) 0 0
\(445\) 1.59308 0.0755194
\(446\) 0 0
\(447\) 4.03091 0.190656
\(448\) 0 0
\(449\) 19.9614 0.942036 0.471018 0.882124i \(-0.343887\pi\)
0.471018 + 0.882124i \(0.343887\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −7.69353 −0.361474
\(454\) 0 0
\(455\) 12.7730 0.598807
\(456\) 0 0
\(457\) −12.9121 −0.604001 −0.302000 0.953308i \(-0.597654\pi\)
−0.302000 + 0.953308i \(0.597654\pi\)
\(458\) 0 0
\(459\) 18.1346 0.846452
\(460\) 0 0
\(461\) −13.5931 −0.633093 −0.316546 0.948577i \(-0.602523\pi\)
−0.316546 + 0.948577i \(0.602523\pi\)
\(462\) 0 0
\(463\) −7.96909 −0.370355 −0.185177 0.982705i \(-0.559286\pi\)
−0.185177 + 0.982705i \(0.559286\pi\)
\(464\) 0 0
\(465\) −1.99153 −0.0923549
\(466\) 0 0
\(467\) 12.8039 0.592494 0.296247 0.955111i \(-0.404265\pi\)
0.296247 + 0.955111i \(0.404265\pi\)
\(468\) 0 0
\(469\) −24.8411 −1.14705
\(470\) 0 0
\(471\) 0.826344 0.0380759
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.82009 −0.0835114
\(476\) 0 0
\(477\) −20.6873 −0.947205
\(478\) 0 0
\(479\) −33.4194 −1.52697 −0.763486 0.645824i \(-0.776514\pi\)
−0.763486 + 0.645824i \(0.776514\pi\)
\(480\) 0 0
\(481\) −11.2804 −0.514340
\(482\) 0 0
\(483\) 4.41761 0.201008
\(484\) 0 0
\(485\) 3.82009 0.173461
\(486\) 0 0
\(487\) −8.69575 −0.394042 −0.197021 0.980399i \(-0.563127\pi\)
−0.197021 + 0.980399i \(0.563127\pi\)
\(488\) 0 0
\(489\) 5.07725 0.229601
\(490\) 0 0
\(491\) 11.5136 0.519602 0.259801 0.965662i \(-0.416343\pi\)
0.259801 + 0.965662i \(0.416343\pi\)
\(492\) 0 0
\(493\) 6.28258 0.282953
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −46.9893 −2.10776
\(498\) 0 0
\(499\) −38.6549 −1.73043 −0.865216 0.501400i \(-0.832819\pi\)
−0.865216 + 0.501400i \(0.832819\pi\)
\(500\) 0 0
\(501\) 10.3620 0.462942
\(502\) 0 0
\(503\) 8.99229 0.400946 0.200473 0.979699i \(-0.435752\pi\)
0.200473 + 0.979699i \(0.435752\pi\)
\(504\) 0 0
\(505\) 15.3275 0.682063
\(506\) 0 0
\(507\) −0.759028 −0.0337096
\(508\) 0 0
\(509\) −22.1538 −0.981950 −0.490975 0.871174i \(-0.663359\pi\)
−0.490975 + 0.871174i \(0.663359\pi\)
\(510\) 0 0
\(511\) −25.5460 −1.13009
\(512\) 0 0
\(513\) −5.00626 −0.221032
\(514\) 0 0
\(515\) 18.0534 0.795526
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.81787 0.123691
\(520\) 0 0
\(521\) 31.1391 1.36423 0.682114 0.731246i \(-0.261061\pi\)
0.682114 + 0.731246i \(0.261061\pi\)
\(522\) 0 0
\(523\) −1.36608 −0.0597343 −0.0298672 0.999554i \(-0.509508\pi\)
−0.0298672 + 0.999554i \(0.509508\pi\)
\(524\) 0 0
\(525\) 1.59308 0.0695278
\(526\) 0 0
\(527\) −27.5585 −1.20047
\(528\) 0 0
\(529\) −15.3105 −0.665674
\(530\) 0 0
\(531\) −7.68949 −0.333696
\(532\) 0 0
\(533\) −18.4132 −0.797563
\(534\) 0 0
\(535\) 10.1166 0.437380
\(536\) 0 0
\(537\) 6.49889 0.280448
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 22.3745 0.961957 0.480979 0.876732i \(-0.340282\pi\)
0.480979 + 0.876732i \(0.340282\pi\)
\(542\) 0 0
\(543\) 6.13358 0.263217
\(544\) 0 0
\(545\) 17.6788 0.757277
\(546\) 0 0
\(547\) 16.3359 0.698474 0.349237 0.937034i \(-0.386441\pi\)
0.349237 + 0.937034i \(0.386441\pi\)
\(548\) 0 0
\(549\) −32.6464 −1.39332
\(550\) 0 0
\(551\) −1.73437 −0.0738867
\(552\) 0 0
\(553\) 28.7322 1.22182
\(554\) 0 0
\(555\) −1.40692 −0.0597203
\(556\) 0 0
\(557\) 12.3275 0.522331 0.261165 0.965294i \(-0.415893\pi\)
0.261165 + 0.965294i \(0.415893\pi\)
\(558\) 0 0
\(559\) −37.9592 −1.60550
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.85947 −0.331237 −0.165619 0.986190i \(-0.552962\pi\)
−0.165619 + 0.986190i \(0.552962\pi\)
\(564\) 0 0
\(565\) 15.3745 0.646812
\(566\) 0 0
\(567\) −23.4338 −0.984127
\(568\) 0 0
\(569\) 21.1475 0.886551 0.443276 0.896385i \(-0.353816\pi\)
0.443276 + 0.896385i \(0.353816\pi\)
\(570\) 0 0
\(571\) −4.78147 −0.200098 −0.100049 0.994983i \(-0.531900\pi\)
−0.100049 + 0.994983i \(0.531900\pi\)
\(572\) 0 0
\(573\) −5.91428 −0.247073
\(574\) 0 0
\(575\) 2.77299 0.115642
\(576\) 0 0
\(577\) 4.30647 0.179281 0.0896404 0.995974i \(-0.471428\pi\)
0.0896404 + 0.995974i \(0.471428\pi\)
\(578\) 0 0
\(579\) −6.17144 −0.256476
\(580\) 0 0
\(581\) 16.2741 0.675164
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 10.5931 0.437970
\(586\) 0 0
\(587\) −16.2965 −0.672630 −0.336315 0.941750i \(-0.609181\pi\)
−0.336315 + 0.941750i \(0.609181\pi\)
\(588\) 0 0
\(589\) 7.60781 0.313474
\(590\) 0 0
\(591\) 5.17366 0.212816
\(592\) 0 0
\(593\) −3.10045 −0.127320 −0.0636600 0.997972i \(-0.520277\pi\)
−0.0636600 + 0.997972i \(0.520277\pi\)
\(594\) 0 0
\(595\) 22.0449 0.903752
\(596\) 0 0
\(597\) −1.77925 −0.0728198
\(598\) 0 0
\(599\) −13.2888 −0.542967 −0.271483 0.962443i \(-0.587514\pi\)
−0.271483 + 0.962443i \(0.587514\pi\)
\(600\) 0 0
\(601\) 31.1538 1.27079 0.635395 0.772187i \(-0.280837\pi\)
0.635395 + 0.772187i \(0.280837\pi\)
\(602\) 0 0
\(603\) −20.6016 −0.838960
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −16.8348 −0.683304 −0.341652 0.939827i \(-0.610986\pi\)
−0.341652 + 0.939827i \(0.610986\pi\)
\(608\) 0 0
\(609\) 1.51806 0.0615147
\(610\) 0 0
\(611\) 12.0857 0.488936
\(612\) 0 0
\(613\) 31.6851 1.27975 0.639874 0.768480i \(-0.278987\pi\)
0.639874 + 0.768480i \(0.278987\pi\)
\(614\) 0 0
\(615\) −2.29654 −0.0926055
\(616\) 0 0
\(617\) −35.8650 −1.44387 −0.721935 0.691961i \(-0.756747\pi\)
−0.721935 + 0.691961i \(0.756747\pi\)
\(618\) 0 0
\(619\) 48.6380 1.95492 0.977462 0.211110i \(-0.0677078\pi\)
0.977462 + 0.211110i \(0.0677078\pi\)
\(620\) 0 0
\(621\) 7.62727 0.306072
\(622\) 0 0
\(623\) 5.32669 0.213409
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −19.4687 −0.776270
\(630\) 0 0
\(631\) −3.10892 −0.123764 −0.0618821 0.998083i \(-0.519710\pi\)
−0.0618821 + 0.998083i \(0.519710\pi\)
\(632\) 0 0
\(633\) −6.53973 −0.259931
\(634\) 0 0
\(635\) 15.0695 0.598016
\(636\) 0 0
\(637\) 15.9676 0.632661
\(638\) 0 0
\(639\) −38.9699 −1.54162
\(640\) 0 0
\(641\) −38.2951 −1.51256 −0.756282 0.654245i \(-0.772986\pi\)
−0.756282 + 0.654245i \(0.772986\pi\)
\(642\) 0 0
\(643\) 24.1251 0.951401 0.475701 0.879607i \(-0.342195\pi\)
0.475701 + 0.879607i \(0.342195\pi\)
\(644\) 0 0
\(645\) −4.73437 −0.186416
\(646\) 0 0
\(647\) 35.7160 1.40414 0.702070 0.712108i \(-0.252259\pi\)
0.702070 + 0.712108i \(0.252259\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −6.65894 −0.260985
\(652\) 0 0
\(653\) 33.0596 1.29372 0.646861 0.762608i \(-0.276081\pi\)
0.646861 + 0.762608i \(0.276081\pi\)
\(654\) 0 0
\(655\) −11.5545 −0.451470
\(656\) 0 0
\(657\) −21.1862 −0.826551
\(658\) 0 0
\(659\) 35.6851 1.39009 0.695046 0.718965i \(-0.255384\pi\)
0.695046 + 0.718965i \(0.255384\pi\)
\(660\) 0 0
\(661\) −33.2094 −1.29169 −0.645847 0.763467i \(-0.723496\pi\)
−0.645847 + 0.763467i \(0.723496\pi\)
\(662\) 0 0
\(663\) −12.0000 −0.466041
\(664\) 0 0
\(665\) −6.08572 −0.235994
\(666\) 0 0
\(667\) 2.64240 0.102314
\(668\) 0 0
\(669\) 11.0772 0.428271
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −34.4581 −1.32826 −0.664130 0.747617i \(-0.731198\pi\)
−0.664130 + 0.747617i \(0.731198\pi\)
\(674\) 0 0
\(675\) 2.75055 0.105869
\(676\) 0 0
\(677\) 12.4665 0.479127 0.239564 0.970881i \(-0.422996\pi\)
0.239564 + 0.970881i \(0.422996\pi\)
\(678\) 0 0
\(679\) 12.7730 0.490183
\(680\) 0 0
\(681\) 4.29578 0.164615
\(682\) 0 0
\(683\) 16.4680 0.630130 0.315065 0.949070i \(-0.397974\pi\)
0.315065 + 0.949070i \(0.397974\pi\)
\(684\) 0 0
\(685\) −20.1475 −0.769798
\(686\) 0 0
\(687\) −3.66262 −0.139738
\(688\) 0 0
\(689\) 28.4989 1.08572
\(690\) 0 0
\(691\) 12.9614 0.493074 0.246537 0.969133i \(-0.420707\pi\)
0.246537 + 0.969133i \(0.420707\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.27410 0.0862616
\(696\) 0 0
\(697\) −31.7792 −1.20372
\(698\) 0 0
\(699\) 0.927485 0.0350807
\(700\) 0 0
\(701\) −25.0596 −0.946488 −0.473244 0.880931i \(-0.656917\pi\)
−0.473244 + 0.880931i \(0.656917\pi\)
\(702\) 0 0
\(703\) 5.37455 0.202705
\(704\) 0 0
\(705\) 1.50736 0.0567706
\(706\) 0 0
\(707\) 51.2494 1.92743
\(708\) 0 0
\(709\) −7.07725 −0.265792 −0.132896 0.991130i \(-0.542428\pi\)
−0.132896 + 0.991130i \(0.542428\pi\)
\(710\) 0 0
\(711\) 23.8286 0.893641
\(712\) 0 0
\(713\) −11.5909 −0.434081
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 11.7877 0.440221
\(718\) 0 0
\(719\) −21.9592 −0.818938 −0.409469 0.912324i \(-0.634286\pi\)
−0.409469 + 0.912324i \(0.634286\pi\)
\(720\) 0 0
\(721\) 60.3639 2.24807
\(722\) 0 0
\(723\) 8.57912 0.319061
\(724\) 0 0
\(725\) 0.952904 0.0353900
\(726\) 0 0
\(727\) −25.9044 −0.960739 −0.480370 0.877066i \(-0.659497\pi\)
−0.480370 + 0.877066i \(0.659497\pi\)
\(728\) 0 0
\(729\) −15.5029 −0.574183
\(730\) 0 0
\(731\) −65.5136 −2.42311
\(732\) 0 0
\(733\) 23.5909 0.871348 0.435674 0.900104i \(-0.356510\pi\)
0.435674 + 0.900104i \(0.356510\pi\)
\(734\) 0 0
\(735\) 1.99153 0.0734586
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 9.50111 0.349504 0.174752 0.984612i \(-0.444088\pi\)
0.174752 + 0.984612i \(0.444088\pi\)
\(740\) 0 0
\(741\) 3.31273 0.121696
\(742\) 0 0
\(743\) −35.9901 −1.32035 −0.660174 0.751113i \(-0.729517\pi\)
−0.660174 + 0.751113i \(0.729517\pi\)
\(744\) 0 0
\(745\) 8.46027 0.309960
\(746\) 0 0
\(747\) 13.4967 0.493817
\(748\) 0 0
\(749\) 33.8263 1.23599
\(750\) 0 0
\(751\) −50.4665 −1.84155 −0.920775 0.390095i \(-0.872442\pi\)
−0.920775 + 0.390095i \(0.872442\pi\)
\(752\) 0 0
\(753\) −2.31898 −0.0845083
\(754\) 0 0
\(755\) −16.1475 −0.587669
\(756\) 0 0
\(757\) −26.5846 −0.966234 −0.483117 0.875556i \(-0.660495\pi\)
−0.483117 + 0.875556i \(0.660495\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.3745 0.557327 0.278663 0.960389i \(-0.410109\pi\)
0.278663 + 0.960389i \(0.410109\pi\)
\(762\) 0 0
\(763\) 59.1115 2.13998
\(764\) 0 0
\(765\) 18.2826 0.661008
\(766\) 0 0
\(767\) 10.5931 0.382494
\(768\) 0 0
\(769\) 37.4364 1.34999 0.674995 0.737822i \(-0.264146\pi\)
0.674995 + 0.737822i \(0.264146\pi\)
\(770\) 0 0
\(771\) 6.58461 0.237139
\(772\) 0 0
\(773\) 37.0511 1.33264 0.666318 0.745667i \(-0.267869\pi\)
0.666318 + 0.745667i \(0.267869\pi\)
\(774\) 0 0
\(775\) −4.17991 −0.150147
\(776\) 0 0
\(777\) −4.70422 −0.168763
\(778\) 0 0
\(779\) 8.77299 0.314325
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 2.62101 0.0936674
\(784\) 0 0
\(785\) 1.73437 0.0619023
\(786\) 0 0
\(787\) −43.6626 −1.55640 −0.778202 0.628014i \(-0.783868\pi\)
−0.778202 + 0.628014i \(0.783868\pi\)
\(788\) 0 0
\(789\) 0.257156 0.00915501
\(790\) 0 0
\(791\) 51.4069 1.82782
\(792\) 0 0
\(793\) 44.9739 1.59707
\(794\) 0 0
\(795\) 3.55446 0.126064
\(796\) 0 0
\(797\) −23.0386 −0.816070 −0.408035 0.912966i \(-0.633786\pi\)
−0.408035 + 0.912966i \(0.633786\pi\)
\(798\) 0 0
\(799\) 20.8587 0.737928
\(800\) 0 0
\(801\) 4.41761 0.156089
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 9.27188 0.326791
\(806\) 0 0
\(807\) −9.12289 −0.321141
\(808\) 0 0
\(809\) −50.3275 −1.76942 −0.884710 0.466143i \(-0.845643\pi\)
−0.884710 + 0.466143i \(0.845643\pi\)
\(810\) 0 0
\(811\) −55.9268 −1.96386 −0.981928 0.189257i \(-0.939392\pi\)
−0.981928 + 0.189257i \(0.939392\pi\)
\(812\) 0 0
\(813\) 3.96763 0.139151
\(814\) 0 0
\(815\) 10.6564 0.373276
\(816\) 0 0
\(817\) 18.0857 0.632739
\(818\) 0 0
\(819\) 35.4194 1.23765
\(820\) 0 0
\(821\) 34.3661 1.19938 0.599692 0.800231i \(-0.295290\pi\)
0.599692 + 0.800231i \(0.295290\pi\)
\(822\) 0 0
\(823\) 16.5832 0.578052 0.289026 0.957321i \(-0.406669\pi\)
0.289026 + 0.957321i \(0.406669\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 37.7693 1.31337 0.656684 0.754166i \(-0.271959\pi\)
0.656684 + 0.754166i \(0.271959\pi\)
\(828\) 0 0
\(829\) 27.8348 0.966743 0.483372 0.875415i \(-0.339412\pi\)
0.483372 + 0.875415i \(0.339412\pi\)
\(830\) 0 0
\(831\) 11.8889 0.412420
\(832\) 0 0
\(833\) 27.5585 0.954845
\(834\) 0 0
\(835\) 21.7483 0.752632
\(836\) 0 0
\(837\) −11.4971 −0.397397
\(838\) 0 0
\(839\) −22.2951 −0.769712 −0.384856 0.922977i \(-0.625749\pi\)
−0.384856 + 0.922977i \(0.625749\pi\)
\(840\) 0 0
\(841\) −28.0920 −0.968689
\(842\) 0 0
\(843\) −6.58057 −0.226647
\(844\) 0 0
\(845\) −1.59308 −0.0548037
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 14.4603 0.496275
\(850\) 0 0
\(851\) −8.18838 −0.280694
\(852\) 0 0
\(853\) −17.3745 −0.594893 −0.297447 0.954738i \(-0.596135\pi\)
−0.297447 + 0.954738i \(0.596135\pi\)
\(854\) 0 0
\(855\) −5.04710 −0.172607
\(856\) 0 0
\(857\) 2.39219 0.0817156 0.0408578 0.999165i \(-0.486991\pi\)
0.0408578 + 0.999165i \(0.486991\pi\)
\(858\) 0 0
\(859\) −46.1475 −1.57453 −0.787267 0.616612i \(-0.788505\pi\)
−0.787267 + 0.616612i \(0.788505\pi\)
\(860\) 0 0
\(861\) −7.67880 −0.261693
\(862\) 0 0
\(863\) −19.1961 −0.653443 −0.326721 0.945121i \(-0.605944\pi\)
−0.326721 + 0.945121i \(0.605944\pi\)
\(864\) 0 0
\(865\) 5.91428 0.201092
\(866\) 0 0
\(867\) −12.6111 −0.428295
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 28.3808 0.961647
\(872\) 0 0
\(873\) 10.5931 0.358522
\(874\) 0 0
\(875\) 3.34364 0.113036
\(876\) 0 0
\(877\) 5.30425 0.179112 0.0895559 0.995982i \(-0.471455\pi\)
0.0895559 + 0.995982i \(0.471455\pi\)
\(878\) 0 0
\(879\) 0.711169 0.0239872
\(880\) 0 0
\(881\) 38.0681 1.28255 0.641273 0.767313i \(-0.278407\pi\)
0.641273 + 0.767313i \(0.278407\pi\)
\(882\) 0 0
\(883\) 24.6788 0.830508 0.415254 0.909706i \(-0.363693\pi\)
0.415254 + 0.909706i \(0.363693\pi\)
\(884\) 0 0
\(885\) 1.32120 0.0444116
\(886\) 0 0
\(887\) −10.8124 −0.363044 −0.181522 0.983387i \(-0.558102\pi\)
−0.181522 + 0.983387i \(0.558102\pi\)
\(888\) 0 0
\(889\) 50.3871 1.68993
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.75827 −0.192693
\(894\) 0 0
\(895\) 13.6402 0.455941
\(896\) 0 0
\(897\) −5.04710 −0.168518
\(898\) 0 0
\(899\) −3.98305 −0.132842
\(900\) 0 0
\(901\) 49.1862 1.63863
\(902\) 0 0
\(903\) −15.8300 −0.526790
\(904\) 0 0
\(905\) 12.8734 0.427928
\(906\) 0 0
\(907\) 8.56217 0.284302 0.142151 0.989845i \(-0.454598\pi\)
0.142151 + 0.989845i \(0.454598\pi\)
\(908\) 0 0
\(909\) 42.5029 1.40973
\(910\) 0 0
\(911\) −15.8734 −0.525911 −0.262955 0.964808i \(-0.584697\pi\)
−0.262955 + 0.964808i \(0.584697\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 5.60927 0.185437
\(916\) 0 0
\(917\) −38.6339 −1.27580
\(918\) 0 0
\(919\) −11.0386 −0.364131 −0.182065 0.983286i \(-0.558278\pi\)
−0.182065 + 0.983286i \(0.558278\pi\)
\(920\) 0 0
\(921\) 8.03640 0.264809
\(922\) 0 0
\(923\) 53.6851 1.76707
\(924\) 0 0
\(925\) −2.95290 −0.0970909
\(926\) 0 0
\(927\) 50.0618 1.64425
\(928\) 0 0
\(929\) −56.2009 −1.84389 −0.921946 0.387319i \(-0.873401\pi\)
−0.921946 + 0.387319i \(0.873401\pi\)
\(930\) 0 0
\(931\) −7.60781 −0.249336
\(932\) 0 0
\(933\) 14.9444 0.489259
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −25.0596 −0.818662 −0.409331 0.912386i \(-0.634238\pi\)
−0.409331 + 0.912386i \(0.634238\pi\)
\(938\) 0 0
\(939\) −15.9636 −0.520952
\(940\) 0 0
\(941\) 5.01695 0.163548 0.0817739 0.996651i \(-0.473941\pi\)
0.0817739 + 0.996651i \(0.473941\pi\)
\(942\) 0 0
\(943\) −13.3661 −0.435259
\(944\) 0 0
\(945\) 9.19686 0.299174
\(946\) 0 0
\(947\) 35.4603 1.15230 0.576152 0.817343i \(-0.304554\pi\)
0.576152 + 0.817343i \(0.304554\pi\)
\(948\) 0 0
\(949\) 29.1862 0.947423
\(950\) 0 0
\(951\) −12.9529 −0.420027
\(952\) 0 0
\(953\) −42.5283 −1.37763 −0.688814 0.724938i \(-0.741868\pi\)
−0.688814 + 0.724938i \(0.741868\pi\)
\(954\) 0 0
\(955\) −12.4132 −0.401681
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −67.3661 −2.17536
\(960\) 0 0
\(961\) −13.5283 −0.436398
\(962\) 0 0
\(963\) 28.0534 0.904007
\(964\) 0 0
\(965\) −12.9529 −0.416969
\(966\) 0 0
\(967\) −24.6788 −0.793617 −0.396808 0.917901i \(-0.629882\pi\)
−0.396808 + 0.917901i \(0.629882\pi\)
\(968\) 0 0
\(969\) 5.71742 0.183670
\(970\) 0 0
\(971\) 47.2480 1.51626 0.758130 0.652103i \(-0.226113\pi\)
0.758130 + 0.652103i \(0.226113\pi\)
\(972\) 0 0
\(973\) 7.60377 0.243766
\(974\) 0 0
\(975\) −1.82009 −0.0582895
\(976\) 0 0
\(977\) 25.8734 0.827765 0.413882 0.910330i \(-0.364172\pi\)
0.413882 + 0.910330i \(0.364172\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 49.0232 1.56519
\(982\) 0 0
\(983\) −42.3948 −1.35218 −0.676092 0.736818i \(-0.736328\pi\)
−0.676092 + 0.736818i \(0.736328\pi\)
\(984\) 0 0
\(985\) 10.8587 0.345987
\(986\) 0 0
\(987\) 5.04008 0.160427
\(988\) 0 0
\(989\) −27.5545 −0.876181
\(990\) 0 0
\(991\) −30.0982 −0.956102 −0.478051 0.878332i \(-0.658657\pi\)
−0.478051 + 0.878332i \(0.658657\pi\)
\(992\) 0 0
\(993\) −16.0982 −0.510862
\(994\) 0 0
\(995\) −3.73437 −0.118388
\(996\) 0 0
\(997\) −3.66407 −0.116042 −0.0580212 0.998315i \(-0.518479\pi\)
−0.0580212 + 0.998315i \(0.518479\pi\)
\(998\) 0 0
\(999\) −8.12212 −0.256973
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.s.1.2 3
4.3 odd 2 9680.2.a.cd.1.2 3
11.10 odd 2 4840.2.a.v.1.2 yes 3
44.43 even 2 9680.2.a.by.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4840.2.a.s.1.2 3 1.1 even 1 trivial
4840.2.a.v.1.2 yes 3 11.10 odd 2
9680.2.a.by.1.2 3 44.43 even 2
9680.2.a.cd.1.2 3 4.3 odd 2