Properties

Label 7448.2.a.bu.1.5
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $1$
Dimension $14$
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] = [7448,2,Mod(1,7448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7448, 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("7448.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.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: \(59.4725794254\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 6 x^{13} - 11 x^{12} + 114 x^{11} - 10 x^{10} - 806 x^{9} + 523 x^{8} + 2586 x^{7} - 2226 x^{6} - 3618 x^{5} + 3397 x^{4} + 1570 x^{3} - 1529 x^{2} + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.72076\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.72076 q^{3} +1.55524 q^{5} -0.0389984 q^{9} +O(q^{10})\) \(q-1.72076 q^{3} +1.55524 q^{5} -0.0389984 q^{9} +6.04360 q^{11} -2.93856 q^{13} -2.67619 q^{15} -4.38986 q^{17} -1.00000 q^{19} +1.90354 q^{23} -2.58123 q^{25} +5.22938 q^{27} +3.96246 q^{29} -4.21372 q^{31} -10.3996 q^{33} +3.98959 q^{37} +5.05654 q^{39} +7.08103 q^{41} -7.81873 q^{43} -0.0606520 q^{45} -8.40992 q^{47} +7.55387 q^{51} -1.95105 q^{53} +9.39925 q^{55} +1.72076 q^{57} -3.02110 q^{59} +7.04678 q^{61} -4.57016 q^{65} -4.42678 q^{67} -3.27552 q^{69} -6.33231 q^{71} -3.59721 q^{73} +4.44166 q^{75} +0.562901 q^{79} -8.88148 q^{81} -14.3232 q^{83} -6.82728 q^{85} -6.81843 q^{87} -6.68823 q^{89} +7.25079 q^{93} -1.55524 q^{95} -6.98549 q^{97} -0.235691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 6 q^{3} - 2 q^{5} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 6 q^{3} - 2 q^{5} + 16 q^{9} - 6 q^{11} - 16 q^{13} + 4 q^{15} + 4 q^{17} - 14 q^{19} - 4 q^{23} + 16 q^{25} - 36 q^{27} - 6 q^{29} - 16 q^{31} + 10 q^{33} + 6 q^{37} + 16 q^{39} + 14 q^{41} - 2 q^{43} - 30 q^{47} + 20 q^{51} - 6 q^{53} - 44 q^{55} + 6 q^{57} - 22 q^{59} - 10 q^{61} - 16 q^{65} + 4 q^{67} - 48 q^{69} + 6 q^{71} - 4 q^{73} - 64 q^{75} + 26 q^{79} + 30 q^{81} - 32 q^{83} - 8 q^{85} - 32 q^{87} + 54 q^{89} - 32 q^{93} + 2 q^{95} - 18 q^{97} - 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.72076 −0.993479 −0.496739 0.867900i \(-0.665470\pi\)
−0.496739 + 0.867900i \(0.665470\pi\)
\(4\) 0 0
\(5\) 1.55524 0.695525 0.347762 0.937583i \(-0.386942\pi\)
0.347762 + 0.937583i \(0.386942\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.0389984 −0.0129995
\(10\) 0 0
\(11\) 6.04360 1.82221 0.911107 0.412170i \(-0.135229\pi\)
0.911107 + 0.412170i \(0.135229\pi\)
\(12\) 0 0
\(13\) −2.93856 −0.815009 −0.407504 0.913203i \(-0.633601\pi\)
−0.407504 + 0.913203i \(0.633601\pi\)
\(14\) 0 0
\(15\) −2.67619 −0.690989
\(16\) 0 0
\(17\) −4.38986 −1.06470 −0.532348 0.846525i \(-0.678690\pi\)
−0.532348 + 0.846525i \(0.678690\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.90354 0.396915 0.198458 0.980109i \(-0.436407\pi\)
0.198458 + 0.980109i \(0.436407\pi\)
\(24\) 0 0
\(25\) −2.58123 −0.516245
\(26\) 0 0
\(27\) 5.22938 1.00639
\(28\) 0 0
\(29\) 3.96246 0.735811 0.367905 0.929863i \(-0.380075\pi\)
0.367905 + 0.929863i \(0.380075\pi\)
\(30\) 0 0
\(31\) −4.21372 −0.756807 −0.378404 0.925641i \(-0.623527\pi\)
−0.378404 + 0.925641i \(0.623527\pi\)
\(32\) 0 0
\(33\) −10.3996 −1.81033
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.98959 0.655884 0.327942 0.944698i \(-0.393645\pi\)
0.327942 + 0.944698i \(0.393645\pi\)
\(38\) 0 0
\(39\) 5.05654 0.809694
\(40\) 0 0
\(41\) 7.08103 1.10587 0.552935 0.833224i \(-0.313508\pi\)
0.552935 + 0.833224i \(0.313508\pi\)
\(42\) 0 0
\(43\) −7.81873 −1.19234 −0.596172 0.802856i \(-0.703313\pi\)
−0.596172 + 0.802856i \(0.703313\pi\)
\(44\) 0 0
\(45\) −0.0606520 −0.00904146
\(46\) 0 0
\(47\) −8.40992 −1.22671 −0.613357 0.789806i \(-0.710181\pi\)
−0.613357 + 0.789806i \(0.710181\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 7.55387 1.05775
\(52\) 0 0
\(53\) −1.95105 −0.267998 −0.133999 0.990981i \(-0.542782\pi\)
−0.133999 + 0.990981i \(0.542782\pi\)
\(54\) 0 0
\(55\) 9.39925 1.26740
\(56\) 0 0
\(57\) 1.72076 0.227920
\(58\) 0 0
\(59\) −3.02110 −0.393314 −0.196657 0.980472i \(-0.563009\pi\)
−0.196657 + 0.980472i \(0.563009\pi\)
\(60\) 0 0
\(61\) 7.04678 0.902248 0.451124 0.892461i \(-0.351023\pi\)
0.451124 + 0.892461i \(0.351023\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.57016 −0.566859
\(66\) 0 0
\(67\) −4.42678 −0.540817 −0.270409 0.962746i \(-0.587159\pi\)
−0.270409 + 0.962746i \(0.587159\pi\)
\(68\) 0 0
\(69\) −3.27552 −0.394327
\(70\) 0 0
\(71\) −6.33231 −0.751507 −0.375753 0.926720i \(-0.622616\pi\)
−0.375753 + 0.926720i \(0.622616\pi\)
\(72\) 0 0
\(73\) −3.59721 −0.421021 −0.210511 0.977592i \(-0.567513\pi\)
−0.210511 + 0.977592i \(0.567513\pi\)
\(74\) 0 0
\(75\) 4.44166 0.512879
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.562901 0.0633314 0.0316657 0.999499i \(-0.489919\pi\)
0.0316657 + 0.999499i \(0.489919\pi\)
\(80\) 0 0
\(81\) −8.88148 −0.986832
\(82\) 0 0
\(83\) −14.3232 −1.57218 −0.786089 0.618113i \(-0.787897\pi\)
−0.786089 + 0.618113i \(0.787897\pi\)
\(84\) 0 0
\(85\) −6.82728 −0.740523
\(86\) 0 0
\(87\) −6.81843 −0.731013
\(88\) 0 0
\(89\) −6.68823 −0.708951 −0.354476 0.935065i \(-0.615341\pi\)
−0.354476 + 0.935065i \(0.615341\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 7.25079 0.751872
\(94\) 0 0
\(95\) −1.55524 −0.159564
\(96\) 0 0
\(97\) −6.98549 −0.709269 −0.354634 0.935005i \(-0.615395\pi\)
−0.354634 + 0.935005i \(0.615395\pi\)
\(98\) 0 0
\(99\) −0.235691 −0.0236878
\(100\) 0 0
\(101\) −7.03369 −0.699878 −0.349939 0.936772i \(-0.613798\pi\)
−0.349939 + 0.936772i \(0.613798\pi\)
\(102\) 0 0
\(103\) 7.01658 0.691364 0.345682 0.938352i \(-0.387648\pi\)
0.345682 + 0.938352i \(0.387648\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.07461 −0.200560 −0.100280 0.994959i \(-0.531974\pi\)
−0.100280 + 0.994959i \(0.531974\pi\)
\(108\) 0 0
\(109\) 18.6130 1.78280 0.891402 0.453214i \(-0.149723\pi\)
0.891402 + 0.453214i \(0.149723\pi\)
\(110\) 0 0
\(111\) −6.86511 −0.651607
\(112\) 0 0
\(113\) 9.02528 0.849027 0.424513 0.905422i \(-0.360445\pi\)
0.424513 + 0.905422i \(0.360445\pi\)
\(114\) 0 0
\(115\) 2.96046 0.276064
\(116\) 0 0
\(117\) 0.114599 0.0105947
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 25.5251 2.32047
\(122\) 0 0
\(123\) −12.1847 −1.09866
\(124\) 0 0
\(125\) −11.7906 −1.05459
\(126\) 0 0
\(127\) −16.8080 −1.49147 −0.745734 0.666244i \(-0.767901\pi\)
−0.745734 + 0.666244i \(0.767901\pi\)
\(128\) 0 0
\(129\) 13.4541 1.18457
\(130\) 0 0
\(131\) 9.34309 0.816310 0.408155 0.912913i \(-0.366172\pi\)
0.408155 + 0.912913i \(0.366172\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 8.13294 0.699972
\(136\) 0 0
\(137\) −19.1516 −1.63623 −0.818114 0.575056i \(-0.804980\pi\)
−0.818114 + 0.575056i \(0.804980\pi\)
\(138\) 0 0
\(139\) 17.7380 1.50452 0.752261 0.658865i \(-0.228963\pi\)
0.752261 + 0.658865i \(0.228963\pi\)
\(140\) 0 0
\(141\) 14.4714 1.21871
\(142\) 0 0
\(143\) −17.7595 −1.48512
\(144\) 0 0
\(145\) 6.16258 0.511775
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 18.8408 1.54350 0.771750 0.635926i \(-0.219382\pi\)
0.771750 + 0.635926i \(0.219382\pi\)
\(150\) 0 0
\(151\) 0.0381565 0.00310513 0.00155256 0.999999i \(-0.499506\pi\)
0.00155256 + 0.999999i \(0.499506\pi\)
\(152\) 0 0
\(153\) 0.171198 0.0138405
\(154\) 0 0
\(155\) −6.55336 −0.526378
\(156\) 0 0
\(157\) −2.01333 −0.160682 −0.0803408 0.996767i \(-0.525601\pi\)
−0.0803408 + 0.996767i \(0.525601\pi\)
\(158\) 0 0
\(159\) 3.35729 0.266250
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 14.0606 1.10131 0.550657 0.834732i \(-0.314377\pi\)
0.550657 + 0.834732i \(0.314377\pi\)
\(164\) 0 0
\(165\) −16.1738 −1.25913
\(166\) 0 0
\(167\) −16.6333 −1.28712 −0.643560 0.765396i \(-0.722543\pi\)
−0.643560 + 0.765396i \(0.722543\pi\)
\(168\) 0 0
\(169\) −4.36489 −0.335761
\(170\) 0 0
\(171\) 0.0389984 0.00298229
\(172\) 0 0
\(173\) 19.9559 1.51722 0.758608 0.651548i \(-0.225880\pi\)
0.758608 + 0.651548i \(0.225880\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.19858 0.390749
\(178\) 0 0
\(179\) −20.7482 −1.55079 −0.775397 0.631473i \(-0.782450\pi\)
−0.775397 + 0.631473i \(0.782450\pi\)
\(180\) 0 0
\(181\) −0.957746 −0.0711887 −0.0355943 0.999366i \(-0.511332\pi\)
−0.0355943 + 0.999366i \(0.511332\pi\)
\(182\) 0 0
\(183\) −12.1258 −0.896364
\(184\) 0 0
\(185\) 6.20477 0.456184
\(186\) 0 0
\(187\) −26.5305 −1.94011
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.91976 −0.500696 −0.250348 0.968156i \(-0.580545\pi\)
−0.250348 + 0.968156i \(0.580545\pi\)
\(192\) 0 0
\(193\) 15.0552 1.08370 0.541849 0.840476i \(-0.317725\pi\)
0.541849 + 0.840476i \(0.317725\pi\)
\(194\) 0 0
\(195\) 7.86413 0.563162
\(196\) 0 0
\(197\) −6.95441 −0.495481 −0.247741 0.968826i \(-0.579688\pi\)
−0.247741 + 0.968826i \(0.579688\pi\)
\(198\) 0 0
\(199\) −14.3426 −1.01672 −0.508361 0.861144i \(-0.669749\pi\)
−0.508361 + 0.861144i \(0.669749\pi\)
\(200\) 0 0
\(201\) 7.61741 0.537291
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 11.0127 0.769160
\(206\) 0 0
\(207\) −0.0742350 −0.00515969
\(208\) 0 0
\(209\) −6.04360 −0.418045
\(210\) 0 0
\(211\) 18.2034 1.25317 0.626587 0.779352i \(-0.284451\pi\)
0.626587 + 0.779352i \(0.284451\pi\)
\(212\) 0 0
\(213\) 10.8964 0.746606
\(214\) 0 0
\(215\) −12.1600 −0.829305
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.18992 0.418276
\(220\) 0 0
\(221\) 12.8998 0.867737
\(222\) 0 0
\(223\) −5.15231 −0.345024 −0.172512 0.985007i \(-0.555188\pi\)
−0.172512 + 0.985007i \(0.555188\pi\)
\(224\) 0 0
\(225\) 0.100664 0.00671092
\(226\) 0 0
\(227\) −10.6722 −0.708342 −0.354171 0.935181i \(-0.615237\pi\)
−0.354171 + 0.935181i \(0.615237\pi\)
\(228\) 0 0
\(229\) 4.54146 0.300108 0.150054 0.988678i \(-0.452055\pi\)
0.150054 + 0.988678i \(0.452055\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.78977 0.313788 0.156894 0.987615i \(-0.449852\pi\)
0.156894 + 0.987615i \(0.449852\pi\)
\(234\) 0 0
\(235\) −13.0795 −0.853210
\(236\) 0 0
\(237\) −0.968616 −0.0629184
\(238\) 0 0
\(239\) −5.36268 −0.346883 −0.173441 0.984844i \(-0.555489\pi\)
−0.173441 + 0.984844i \(0.555489\pi\)
\(240\) 0 0
\(241\) −17.0096 −1.09568 −0.547842 0.836582i \(-0.684551\pi\)
−0.547842 + 0.836582i \(0.684551\pi\)
\(242\) 0 0
\(243\) −0.405258 −0.0259973
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.93856 0.186976
\(248\) 0 0
\(249\) 24.6468 1.56193
\(250\) 0 0
\(251\) −7.05059 −0.445029 −0.222515 0.974929i \(-0.571427\pi\)
−0.222515 + 0.974929i \(0.571427\pi\)
\(252\) 0 0
\(253\) 11.5042 0.723264
\(254\) 0 0
\(255\) 11.7481 0.735694
\(256\) 0 0
\(257\) 4.67823 0.291820 0.145910 0.989298i \(-0.453389\pi\)
0.145910 + 0.989298i \(0.453389\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.154530 −0.00956516
\(262\) 0 0
\(263\) 19.7009 1.21481 0.607406 0.794392i \(-0.292210\pi\)
0.607406 + 0.794392i \(0.292210\pi\)
\(264\) 0 0
\(265\) −3.03436 −0.186399
\(266\) 0 0
\(267\) 11.5088 0.704328
\(268\) 0 0
\(269\) −6.92147 −0.422009 −0.211005 0.977485i \(-0.567674\pi\)
−0.211005 + 0.977485i \(0.567674\pi\)
\(270\) 0 0
\(271\) −27.8271 −1.69037 −0.845187 0.534470i \(-0.820511\pi\)
−0.845187 + 0.534470i \(0.820511\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −15.5999 −0.940710
\(276\) 0 0
\(277\) −13.7666 −0.827155 −0.413577 0.910469i \(-0.635721\pi\)
−0.413577 + 0.910469i \(0.635721\pi\)
\(278\) 0 0
\(279\) 0.164329 0.00983810
\(280\) 0 0
\(281\) 6.14705 0.366702 0.183351 0.983047i \(-0.441305\pi\)
0.183351 + 0.983047i \(0.441305\pi\)
\(282\) 0 0
\(283\) 15.7018 0.933376 0.466688 0.884422i \(-0.345447\pi\)
0.466688 + 0.884422i \(0.345447\pi\)
\(284\) 0 0
\(285\) 2.67619 0.158524
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.27084 0.133579
\(290\) 0 0
\(291\) 12.0203 0.704644
\(292\) 0 0
\(293\) −28.6428 −1.67333 −0.836666 0.547714i \(-0.815498\pi\)
−0.836666 + 0.547714i \(0.815498\pi\)
\(294\) 0 0
\(295\) −4.69854 −0.273560
\(296\) 0 0
\(297\) 31.6043 1.83387
\(298\) 0 0
\(299\) −5.59365 −0.323489
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 12.1033 0.695314
\(304\) 0 0
\(305\) 10.9594 0.627536
\(306\) 0 0
\(307\) 14.7028 0.839131 0.419565 0.907725i \(-0.362182\pi\)
0.419565 + 0.907725i \(0.362182\pi\)
\(308\) 0 0
\(309\) −12.0738 −0.686856
\(310\) 0 0
\(311\) −20.7626 −1.17734 −0.588669 0.808374i \(-0.700348\pi\)
−0.588669 + 0.808374i \(0.700348\pi\)
\(312\) 0 0
\(313\) −9.95015 −0.562416 −0.281208 0.959647i \(-0.590735\pi\)
−0.281208 + 0.959647i \(0.590735\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.1038 0.735981 0.367990 0.929830i \(-0.380046\pi\)
0.367990 + 0.929830i \(0.380046\pi\)
\(318\) 0 0
\(319\) 23.9475 1.34081
\(320\) 0 0
\(321\) 3.56989 0.199252
\(322\) 0 0
\(323\) 4.38986 0.244258
\(324\) 0 0
\(325\) 7.58508 0.420744
\(326\) 0 0
\(327\) −32.0285 −1.77118
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −20.3836 −1.12038 −0.560191 0.828364i \(-0.689272\pi\)
−0.560191 + 0.828364i \(0.689272\pi\)
\(332\) 0 0
\(333\) −0.155588 −0.00852616
\(334\) 0 0
\(335\) −6.88471 −0.376152
\(336\) 0 0
\(337\) −18.4997 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(338\) 0 0
\(339\) −15.5303 −0.843490
\(340\) 0 0
\(341\) −25.4661 −1.37906
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −5.09423 −0.274264
\(346\) 0 0
\(347\) −24.0859 −1.29300 −0.646499 0.762915i \(-0.723768\pi\)
−0.646499 + 0.762915i \(0.723768\pi\)
\(348\) 0 0
\(349\) −15.4912 −0.829223 −0.414612 0.909998i \(-0.636083\pi\)
−0.414612 + 0.909998i \(0.636083\pi\)
\(350\) 0 0
\(351\) −15.3668 −0.820220
\(352\) 0 0
\(353\) 13.9658 0.743324 0.371662 0.928368i \(-0.378788\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(354\) 0 0
\(355\) −9.84826 −0.522692
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 25.7918 1.36124 0.680621 0.732636i \(-0.261710\pi\)
0.680621 + 0.732636i \(0.261710\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −43.9225 −2.30533
\(364\) 0 0
\(365\) −5.59452 −0.292831
\(366\) 0 0
\(367\) −36.9061 −1.92648 −0.963242 0.268633i \(-0.913428\pi\)
−0.963242 + 0.268633i \(0.913428\pi\)
\(368\) 0 0
\(369\) −0.276149 −0.0143757
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 31.9966 1.65672 0.828359 0.560197i \(-0.189275\pi\)
0.828359 + 0.560197i \(0.189275\pi\)
\(374\) 0 0
\(375\) 20.2888 1.04771
\(376\) 0 0
\(377\) −11.6439 −0.599692
\(378\) 0 0
\(379\) −31.3529 −1.61049 −0.805245 0.592943i \(-0.797966\pi\)
−0.805245 + 0.592943i \(0.797966\pi\)
\(380\) 0 0
\(381\) 28.9224 1.48174
\(382\) 0 0
\(383\) 6.28405 0.321100 0.160550 0.987028i \(-0.448673\pi\)
0.160550 + 0.987028i \(0.448673\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.304918 0.0154999
\(388\) 0 0
\(389\) −19.2715 −0.977105 −0.488553 0.872534i \(-0.662475\pi\)
−0.488553 + 0.872534i \(0.662475\pi\)
\(390\) 0 0
\(391\) −8.35626 −0.422594
\(392\) 0 0
\(393\) −16.0772 −0.810986
\(394\) 0 0
\(395\) 0.875447 0.0440485
\(396\) 0 0
\(397\) −21.6728 −1.08773 −0.543863 0.839174i \(-0.683039\pi\)
−0.543863 + 0.839174i \(0.683039\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.5694 −0.627688 −0.313844 0.949475i \(-0.601617\pi\)
−0.313844 + 0.949475i \(0.601617\pi\)
\(402\) 0 0
\(403\) 12.3823 0.616804
\(404\) 0 0
\(405\) −13.8128 −0.686366
\(406\) 0 0
\(407\) 24.1115 1.19516
\(408\) 0 0
\(409\) 2.79037 0.137975 0.0689874 0.997618i \(-0.478023\pi\)
0.0689874 + 0.997618i \(0.478023\pi\)
\(410\) 0 0
\(411\) 32.9552 1.62556
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −22.2761 −1.09349
\(416\) 0 0
\(417\) −30.5229 −1.49471
\(418\) 0 0
\(419\) −28.8393 −1.40889 −0.704445 0.709759i \(-0.748804\pi\)
−0.704445 + 0.709759i \(0.748804\pi\)
\(420\) 0 0
\(421\) −17.7241 −0.863819 −0.431909 0.901917i \(-0.642160\pi\)
−0.431909 + 0.901917i \(0.642160\pi\)
\(422\) 0 0
\(423\) 0.327974 0.0159466
\(424\) 0 0
\(425\) 11.3312 0.549645
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 30.5597 1.47544
\(430\) 0 0
\(431\) −16.4231 −0.791072 −0.395536 0.918451i \(-0.629441\pi\)
−0.395536 + 0.918451i \(0.629441\pi\)
\(432\) 0 0
\(433\) 12.6537 0.608099 0.304050 0.952656i \(-0.401661\pi\)
0.304050 + 0.952656i \(0.401661\pi\)
\(434\) 0 0
\(435\) −10.6043 −0.508437
\(436\) 0 0
\(437\) −1.90354 −0.0910586
\(438\) 0 0
\(439\) −29.1568 −1.39158 −0.695790 0.718245i \(-0.744946\pi\)
−0.695790 + 0.718245i \(0.744946\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −33.1636 −1.57565 −0.787825 0.615899i \(-0.788793\pi\)
−0.787825 + 0.615899i \(0.788793\pi\)
\(444\) 0 0
\(445\) −10.4018 −0.493093
\(446\) 0 0
\(447\) −32.4204 −1.53343
\(448\) 0 0
\(449\) 36.4179 1.71867 0.859334 0.511415i \(-0.170879\pi\)
0.859334 + 0.511415i \(0.170879\pi\)
\(450\) 0 0
\(451\) 42.7949 2.01513
\(452\) 0 0
\(453\) −0.0656580 −0.00308488
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.13478 −0.146639 −0.0733194 0.997309i \(-0.523359\pi\)
−0.0733194 + 0.997309i \(0.523359\pi\)
\(458\) 0 0
\(459\) −22.9562 −1.07150
\(460\) 0 0
\(461\) 23.0172 1.07202 0.536009 0.844212i \(-0.319931\pi\)
0.536009 + 0.844212i \(0.319931\pi\)
\(462\) 0 0
\(463\) 25.8814 1.20281 0.601406 0.798944i \(-0.294608\pi\)
0.601406 + 0.798944i \(0.294608\pi\)
\(464\) 0 0
\(465\) 11.2767 0.522946
\(466\) 0 0
\(467\) −16.2749 −0.753111 −0.376556 0.926394i \(-0.622892\pi\)
−0.376556 + 0.926394i \(0.622892\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.46446 0.159634
\(472\) 0 0
\(473\) −47.2533 −2.17271
\(474\) 0 0
\(475\) 2.58123 0.118435
\(476\) 0 0
\(477\) 0.0760880 0.00348383
\(478\) 0 0
\(479\) 6.55561 0.299533 0.149767 0.988721i \(-0.452148\pi\)
0.149767 + 0.988721i \(0.452148\pi\)
\(480\) 0 0
\(481\) −11.7236 −0.534551
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.8641 −0.493314
\(486\) 0 0
\(487\) 19.9218 0.902743 0.451372 0.892336i \(-0.350935\pi\)
0.451372 + 0.892336i \(0.350935\pi\)
\(488\) 0 0
\(489\) −24.1949 −1.09413
\(490\) 0 0
\(491\) −37.1248 −1.67542 −0.837709 0.546117i \(-0.816105\pi\)
−0.837709 + 0.546117i \(0.816105\pi\)
\(492\) 0 0
\(493\) −17.3946 −0.783415
\(494\) 0 0
\(495\) −0.366556 −0.0164755
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 4.27794 0.191507 0.0957535 0.995405i \(-0.469474\pi\)
0.0957535 + 0.995405i \(0.469474\pi\)
\(500\) 0 0
\(501\) 28.6218 1.27873
\(502\) 0 0
\(503\) 22.4931 1.00292 0.501458 0.865182i \(-0.332797\pi\)
0.501458 + 0.865182i \(0.332797\pi\)
\(504\) 0 0
\(505\) −10.9391 −0.486783
\(506\) 0 0
\(507\) 7.51091 0.333571
\(508\) 0 0
\(509\) 0.718953 0.0318670 0.0159335 0.999873i \(-0.494928\pi\)
0.0159335 + 0.999873i \(0.494928\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −5.22938 −0.230883
\(514\) 0 0
\(515\) 10.9125 0.480861
\(516\) 0 0
\(517\) −50.8262 −2.23533
\(518\) 0 0
\(519\) −34.3392 −1.50732
\(520\) 0 0
\(521\) −11.5791 −0.507291 −0.253646 0.967297i \(-0.581630\pi\)
−0.253646 + 0.967297i \(0.581630\pi\)
\(522\) 0 0
\(523\) −20.8967 −0.913749 −0.456875 0.889531i \(-0.651031\pi\)
−0.456875 + 0.889531i \(0.651031\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.4976 0.805770
\(528\) 0 0
\(529\) −19.3765 −0.842458
\(530\) 0 0
\(531\) 0.117818 0.00511288
\(532\) 0 0
\(533\) −20.8080 −0.901294
\(534\) 0 0
\(535\) −3.22651 −0.139494
\(536\) 0 0
\(537\) 35.7026 1.54068
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −40.2267 −1.72948 −0.864741 0.502218i \(-0.832518\pi\)
−0.864741 + 0.502218i \(0.832518\pi\)
\(542\) 0 0
\(543\) 1.64805 0.0707245
\(544\) 0 0
\(545\) 28.9477 1.23998
\(546\) 0 0
\(547\) −16.3996 −0.701196 −0.350598 0.936526i \(-0.614022\pi\)
−0.350598 + 0.936526i \(0.614022\pi\)
\(548\) 0 0
\(549\) −0.274813 −0.0117288
\(550\) 0 0
\(551\) −3.96246 −0.168807
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −10.6769 −0.453209
\(556\) 0 0
\(557\) −41.4238 −1.75518 −0.877592 0.479408i \(-0.840852\pi\)
−0.877592 + 0.479408i \(0.840852\pi\)
\(558\) 0 0
\(559\) 22.9758 0.971771
\(560\) 0 0
\(561\) 45.6526 1.92745
\(562\) 0 0
\(563\) 5.52573 0.232882 0.116441 0.993198i \(-0.462851\pi\)
0.116441 + 0.993198i \(0.462851\pi\)
\(564\) 0 0
\(565\) 14.0365 0.590519
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.0308 0.923580 0.461790 0.886989i \(-0.347207\pi\)
0.461790 + 0.886989i \(0.347207\pi\)
\(570\) 0 0
\(571\) 9.98240 0.417750 0.208875 0.977942i \(-0.433020\pi\)
0.208875 + 0.977942i \(0.433020\pi\)
\(572\) 0 0
\(573\) 11.9072 0.497431
\(574\) 0 0
\(575\) −4.91346 −0.204906
\(576\) 0 0
\(577\) 2.26255 0.0941913 0.0470957 0.998890i \(-0.485003\pi\)
0.0470957 + 0.998890i \(0.485003\pi\)
\(578\) 0 0
\(579\) −25.9063 −1.07663
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −11.7914 −0.488349
\(584\) 0 0
\(585\) 0.178229 0.00736887
\(586\) 0 0
\(587\) −22.8815 −0.944419 −0.472209 0.881486i \(-0.656543\pi\)
−0.472209 + 0.881486i \(0.656543\pi\)
\(588\) 0 0
\(589\) 4.21372 0.173623
\(590\) 0 0
\(591\) 11.9668 0.492250
\(592\) 0 0
\(593\) 40.7867 1.67491 0.837455 0.546507i \(-0.184043\pi\)
0.837455 + 0.546507i \(0.184043\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 24.6802 1.01009
\(598\) 0 0
\(599\) −26.7013 −1.09098 −0.545492 0.838116i \(-0.683657\pi\)
−0.545492 + 0.838116i \(0.683657\pi\)
\(600\) 0 0
\(601\) 38.2174 1.55892 0.779459 0.626453i \(-0.215494\pi\)
0.779459 + 0.626453i \(0.215494\pi\)
\(602\) 0 0
\(603\) 0.172637 0.00703034
\(604\) 0 0
\(605\) 39.6977 1.61394
\(606\) 0 0
\(607\) 6.00389 0.243690 0.121845 0.992549i \(-0.461119\pi\)
0.121845 + 0.992549i \(0.461119\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24.7130 0.999782
\(612\) 0 0
\(613\) −44.2793 −1.78843 −0.894213 0.447643i \(-0.852264\pi\)
−0.894213 + 0.447643i \(0.852264\pi\)
\(614\) 0 0
\(615\) −18.9502 −0.764145
\(616\) 0 0
\(617\) −22.2323 −0.895039 −0.447519 0.894274i \(-0.647692\pi\)
−0.447519 + 0.894274i \(0.647692\pi\)
\(618\) 0 0
\(619\) 31.3252 1.25907 0.629534 0.776973i \(-0.283246\pi\)
0.629534 + 0.776973i \(0.283246\pi\)
\(620\) 0 0
\(621\) 9.95431 0.399453
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −5.43114 −0.217246
\(626\) 0 0
\(627\) 10.3996 0.415319
\(628\) 0 0
\(629\) −17.5137 −0.698318
\(630\) 0 0
\(631\) 31.2735 1.24498 0.622488 0.782629i \(-0.286122\pi\)
0.622488 + 0.782629i \(0.286122\pi\)
\(632\) 0 0
\(633\) −31.3236 −1.24500
\(634\) 0 0
\(635\) −26.1405 −1.03735
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.246950 0.00976920
\(640\) 0 0
\(641\) −6.36977 −0.251591 −0.125795 0.992056i \(-0.540148\pi\)
−0.125795 + 0.992056i \(0.540148\pi\)
\(642\) 0 0
\(643\) −21.4825 −0.847188 −0.423594 0.905852i \(-0.639232\pi\)
−0.423594 + 0.905852i \(0.639232\pi\)
\(644\) 0 0
\(645\) 20.9244 0.823897
\(646\) 0 0
\(647\) −26.9963 −1.06133 −0.530667 0.847580i \(-0.678059\pi\)
−0.530667 + 0.847580i \(0.678059\pi\)
\(648\) 0 0
\(649\) −18.2583 −0.716703
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24.6716 −0.965473 −0.482737 0.875766i \(-0.660357\pi\)
−0.482737 + 0.875766i \(0.660357\pi\)
\(654\) 0 0
\(655\) 14.5308 0.567764
\(656\) 0 0
\(657\) 0.140285 0.00547306
\(658\) 0 0
\(659\) 39.5236 1.53962 0.769810 0.638274i \(-0.220351\pi\)
0.769810 + 0.638274i \(0.220351\pi\)
\(660\) 0 0
\(661\) −12.9541 −0.503856 −0.251928 0.967746i \(-0.581065\pi\)
−0.251928 + 0.967746i \(0.581065\pi\)
\(662\) 0 0
\(663\) −22.1975 −0.862078
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.54270 0.292054
\(668\) 0 0
\(669\) 8.86586 0.342774
\(670\) 0 0
\(671\) 42.5879 1.64409
\(672\) 0 0
\(673\) −17.6910 −0.681937 −0.340968 0.940075i \(-0.610755\pi\)
−0.340968 + 0.940075i \(0.610755\pi\)
\(674\) 0 0
\(675\) −13.4982 −0.519546
\(676\) 0 0
\(677\) 26.9395 1.03537 0.517685 0.855571i \(-0.326794\pi\)
0.517685 + 0.855571i \(0.326794\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 18.3643 0.703723
\(682\) 0 0
\(683\) 26.5395 1.01551 0.507754 0.861502i \(-0.330476\pi\)
0.507754 + 0.861502i \(0.330476\pi\)
\(684\) 0 0
\(685\) −29.7853 −1.13804
\(686\) 0 0
\(687\) −7.81475 −0.298151
\(688\) 0 0
\(689\) 5.73328 0.218420
\(690\) 0 0
\(691\) −9.80182 −0.372879 −0.186439 0.982466i \(-0.559695\pi\)
−0.186439 + 0.982466i \(0.559695\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 27.5869 1.04643
\(696\) 0 0
\(697\) −31.0847 −1.17742
\(698\) 0 0
\(699\) −8.24202 −0.311742
\(700\) 0 0
\(701\) −9.65378 −0.364618 −0.182309 0.983241i \(-0.558357\pi\)
−0.182309 + 0.983241i \(0.558357\pi\)
\(702\) 0 0
\(703\) −3.98959 −0.150470
\(704\) 0 0
\(705\) 22.5066 0.847646
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 17.3356 0.651053 0.325526 0.945533i \(-0.394459\pi\)
0.325526 + 0.945533i \(0.394459\pi\)
\(710\) 0 0
\(711\) −0.0219523 −0.000823275 0
\(712\) 0 0
\(713\) −8.02098 −0.300388
\(714\) 0 0
\(715\) −27.6202 −1.03294
\(716\) 0 0
\(717\) 9.22786 0.344621
\(718\) 0 0
\(719\) 34.9661 1.30402 0.652008 0.758212i \(-0.273927\pi\)
0.652008 + 0.758212i \(0.273927\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 29.2694 1.08854
\(724\) 0 0
\(725\) −10.2280 −0.379859
\(726\) 0 0
\(727\) 33.6942 1.24965 0.624825 0.780765i \(-0.285170\pi\)
0.624825 + 0.780765i \(0.285170\pi\)
\(728\) 0 0
\(729\) 27.3418 1.01266
\(730\) 0 0
\(731\) 34.3231 1.26949
\(732\) 0 0
\(733\) 1.99072 0.0735288 0.0367644 0.999324i \(-0.488295\pi\)
0.0367644 + 0.999324i \(0.488295\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −26.7537 −0.985485
\(738\) 0 0
\(739\) −0.565193 −0.0207910 −0.0103955 0.999946i \(-0.503309\pi\)
−0.0103955 + 0.999946i \(0.503309\pi\)
\(740\) 0 0
\(741\) −5.05654 −0.185757
\(742\) 0 0
\(743\) −11.1044 −0.407380 −0.203690 0.979035i \(-0.565293\pi\)
−0.203690 + 0.979035i \(0.565293\pi\)
\(744\) 0 0
\(745\) 29.3020 1.07354
\(746\) 0 0
\(747\) 0.558584 0.0204375
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 5.12656 0.187071 0.0935354 0.995616i \(-0.470183\pi\)
0.0935354 + 0.995616i \(0.470183\pi\)
\(752\) 0 0
\(753\) 12.1324 0.442127
\(754\) 0 0
\(755\) 0.0593425 0.00215969
\(756\) 0 0
\(757\) −18.1635 −0.660164 −0.330082 0.943952i \(-0.607076\pi\)
−0.330082 + 0.943952i \(0.607076\pi\)
\(758\) 0 0
\(759\) −19.7960 −0.718548
\(760\) 0 0
\(761\) −3.00837 −0.109053 −0.0545266 0.998512i \(-0.517365\pi\)
−0.0545266 + 0.998512i \(0.517365\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.266253 0.00962641
\(766\) 0 0
\(767\) 8.87768 0.320554
\(768\) 0 0
\(769\) −12.5047 −0.450930 −0.225465 0.974251i \(-0.572390\pi\)
−0.225465 + 0.974251i \(0.572390\pi\)
\(770\) 0 0
\(771\) −8.05009 −0.289917
\(772\) 0 0
\(773\) −14.6308 −0.526235 −0.263117 0.964764i \(-0.584751\pi\)
−0.263117 + 0.964764i \(0.584751\pi\)
\(774\) 0 0
\(775\) 10.8766 0.390698
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.08103 −0.253704
\(780\) 0 0
\(781\) −38.2699 −1.36941
\(782\) 0 0
\(783\) 20.7212 0.740516
\(784\) 0 0
\(785\) −3.13122 −0.111758
\(786\) 0 0
\(787\) −24.5644 −0.875625 −0.437813 0.899066i \(-0.644247\pi\)
−0.437813 + 0.899066i \(0.644247\pi\)
\(788\) 0 0
\(789\) −33.9005 −1.20689
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −20.7074 −0.735340
\(794\) 0 0
\(795\) 5.22139 0.185184
\(796\) 0 0
\(797\) 15.9870 0.566290 0.283145 0.959077i \(-0.408622\pi\)
0.283145 + 0.959077i \(0.408622\pi\)
\(798\) 0 0
\(799\) 36.9184 1.30608
\(800\) 0 0
\(801\) 0.260831 0.00921600
\(802\) 0 0
\(803\) −21.7401 −0.767191
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 11.9102 0.419257
\(808\) 0 0
\(809\) −13.9841 −0.491655 −0.245827 0.969314i \(-0.579060\pi\)
−0.245827 + 0.969314i \(0.579060\pi\)
\(810\) 0 0
\(811\) 47.5695 1.67039 0.835196 0.549953i \(-0.185354\pi\)
0.835196 + 0.549953i \(0.185354\pi\)
\(812\) 0 0
\(813\) 47.8836 1.67935
\(814\) 0 0
\(815\) 21.8677 0.765991
\(816\) 0 0
\(817\) 7.81873 0.273543
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33.9428 −1.18461 −0.592306 0.805713i \(-0.701782\pi\)
−0.592306 + 0.805713i \(0.701782\pi\)
\(822\) 0 0
\(823\) −14.3697 −0.500897 −0.250448 0.968130i \(-0.580578\pi\)
−0.250448 + 0.968130i \(0.580578\pi\)
\(824\) 0 0
\(825\) 26.8436 0.934575
\(826\) 0 0
\(827\) −23.4511 −0.815474 −0.407737 0.913099i \(-0.633682\pi\)
−0.407737 + 0.913099i \(0.633682\pi\)
\(828\) 0 0
\(829\) 36.1483 1.25548 0.627741 0.778422i \(-0.283980\pi\)
0.627741 + 0.778422i \(0.283980\pi\)
\(830\) 0 0
\(831\) 23.6890 0.821761
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −25.8687 −0.895224
\(836\) 0 0
\(837\) −22.0351 −0.761646
\(838\) 0 0
\(839\) 33.6909 1.16314 0.581569 0.813497i \(-0.302439\pi\)
0.581569 + 0.813497i \(0.302439\pi\)
\(840\) 0 0
\(841\) −13.2989 −0.458582
\(842\) 0 0
\(843\) −10.5776 −0.364311
\(844\) 0 0
\(845\) −6.78846 −0.233530
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −27.0190 −0.927289
\(850\) 0 0
\(851\) 7.59433 0.260330
\(852\) 0 0
\(853\) −47.1231 −1.61347 −0.806733 0.590917i \(-0.798766\pi\)
−0.806733 + 0.590917i \(0.798766\pi\)
\(854\) 0 0
\(855\) 0.0606520 0.00207425
\(856\) 0 0
\(857\) −4.80685 −0.164199 −0.0820994 0.996624i \(-0.526162\pi\)
−0.0820994 + 0.996624i \(0.526162\pi\)
\(858\) 0 0
\(859\) −19.2753 −0.657663 −0.328832 0.944389i \(-0.606655\pi\)
−0.328832 + 0.944389i \(0.606655\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.74668 −0.0594577 −0.0297288 0.999558i \(-0.509464\pi\)
−0.0297288 + 0.999558i \(0.509464\pi\)
\(864\) 0 0
\(865\) 31.0362 1.05526
\(866\) 0 0
\(867\) −3.90756 −0.132708
\(868\) 0 0
\(869\) 3.40195 0.115403
\(870\) 0 0
\(871\) 13.0083 0.440771
\(872\) 0 0
\(873\) 0.272423 0.00922013
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 42.0397 1.41958 0.709790 0.704413i \(-0.248790\pi\)
0.709790 + 0.704413i \(0.248790\pi\)
\(878\) 0 0
\(879\) 49.2873 1.66242
\(880\) 0 0
\(881\) 39.6661 1.33639 0.668193 0.743988i \(-0.267068\pi\)
0.668193 + 0.743988i \(0.267068\pi\)
\(882\) 0 0
\(883\) −11.3442 −0.381761 −0.190881 0.981613i \(-0.561134\pi\)
−0.190881 + 0.981613i \(0.561134\pi\)
\(884\) 0 0
\(885\) 8.08505 0.271776
\(886\) 0 0
\(887\) 3.09158 0.103805 0.0519025 0.998652i \(-0.483472\pi\)
0.0519025 + 0.998652i \(0.483472\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −53.6761 −1.79822
\(892\) 0 0
\(893\) 8.40992 0.281427
\(894\) 0 0
\(895\) −32.2685 −1.07862
\(896\) 0 0
\(897\) 9.62531 0.321380
\(898\) 0 0
\(899\) −16.6967 −0.556867
\(900\) 0 0
\(901\) 8.56484 0.285336
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.48953 −0.0495135
\(906\) 0 0
\(907\) 19.2594 0.639499 0.319750 0.947502i \(-0.396401\pi\)
0.319750 + 0.947502i \(0.396401\pi\)
\(908\) 0 0
\(909\) 0.274303 0.00909805
\(910\) 0 0
\(911\) −35.7350 −1.18395 −0.591977 0.805955i \(-0.701652\pi\)
−0.591977 + 0.805955i \(0.701652\pi\)
\(912\) 0 0
\(913\) −86.5639 −2.86485
\(914\) 0 0
\(915\) −18.8585 −0.623444
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −40.8292 −1.34683 −0.673416 0.739264i \(-0.735174\pi\)
−0.673416 + 0.739264i \(0.735174\pi\)
\(920\) 0 0
\(921\) −25.2999 −0.833659
\(922\) 0 0
\(923\) 18.6078 0.612484
\(924\) 0 0
\(925\) −10.2980 −0.338597
\(926\) 0 0
\(927\) −0.273636 −0.00898738
\(928\) 0 0
\(929\) −25.4124 −0.833755 −0.416877 0.908963i \(-0.636876\pi\)
−0.416877 + 0.908963i \(0.636876\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 35.7274 1.16966
\(934\) 0 0
\(935\) −41.2614 −1.34939
\(936\) 0 0
\(937\) 32.7066 1.06848 0.534239 0.845333i \(-0.320598\pi\)
0.534239 + 0.845333i \(0.320598\pi\)
\(938\) 0 0
\(939\) 17.1218 0.558748
\(940\) 0 0
\(941\) 19.5311 0.636695 0.318347 0.947974i \(-0.396872\pi\)
0.318347 + 0.947974i \(0.396872\pi\)
\(942\) 0 0
\(943\) 13.4790 0.438937
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.60632 0.0846941 0.0423470 0.999103i \(-0.486516\pi\)
0.0423470 + 0.999103i \(0.486516\pi\)
\(948\) 0 0
\(949\) 10.5706 0.343136
\(950\) 0 0
\(951\) −22.5484 −0.731182
\(952\) 0 0
\(953\) −57.7638 −1.87115 −0.935577 0.353123i \(-0.885120\pi\)
−0.935577 + 0.353123i \(0.885120\pi\)
\(954\) 0 0
\(955\) −10.7619 −0.348246
\(956\) 0 0
\(957\) −41.2079 −1.33206
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −13.2445 −0.427243
\(962\) 0 0
\(963\) 0.0809064 0.00260717
\(964\) 0 0
\(965\) 23.4145 0.753738
\(966\) 0 0
\(967\) −22.7179 −0.730557 −0.365279 0.930898i \(-0.619026\pi\)
−0.365279 + 0.930898i \(0.619026\pi\)
\(968\) 0 0
\(969\) −7.55387 −0.242665
\(970\) 0 0
\(971\) −49.5521 −1.59020 −0.795101 0.606478i \(-0.792582\pi\)
−0.795101 + 0.606478i \(0.792582\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −13.0521 −0.418001
\(976\) 0 0
\(977\) −20.0651 −0.641940 −0.320970 0.947089i \(-0.604009\pi\)
−0.320970 + 0.947089i \(0.604009\pi\)
\(978\) 0 0
\(979\) −40.4210 −1.29186
\(980\) 0 0
\(981\) −0.725878 −0.0231755
\(982\) 0 0
\(983\) 28.3692 0.904837 0.452419 0.891806i \(-0.350561\pi\)
0.452419 + 0.891806i \(0.350561\pi\)
\(984\) 0 0
\(985\) −10.8158 −0.344620
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −14.8832 −0.473260
\(990\) 0 0
\(991\) 17.7050 0.562417 0.281209 0.959647i \(-0.409265\pi\)
0.281209 + 0.959647i \(0.409265\pi\)
\(992\) 0 0
\(993\) 35.0751 1.11308
\(994\) 0 0
\(995\) −22.3063 −0.707156
\(996\) 0 0
\(997\) −49.2816 −1.56077 −0.780383 0.625302i \(-0.784976\pi\)
−0.780383 + 0.625302i \(0.784976\pi\)
\(998\) 0 0
\(999\) 20.8631 0.660078
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 7448.2.a.bu.1.5 14
7.6 odd 2 7448.2.a.bx.1.10 yes 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7448.2.a.bu.1.5 14 1.1 even 1 trivial
7448.2.a.bx.1.10 yes 14 7.6 odd 2