Properties

Label 5733.2.a.bs.1.4
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5733,2,Mod(1,5733)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5733, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5733.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.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: \(45.7782354788\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.46162368.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 8x^{4} + 17x^{2} - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 819)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.734503\) of defining polynomial
Character \(\chi\) \(=\) 5733.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.734503 q^{2} -1.46050 q^{4} -2.54175 q^{5} -2.54175 q^{8} +O(q^{10})\) \(q+0.734503 q^{2} -1.46050 q^{4} -2.54175 q^{5} -2.54175 q^{8} -1.86693 q^{10} -3.71224 q^{11} -1.00000 q^{13} +1.05408 q^{16} +2.10577 q^{17} +5.92101 q^{19} +3.71224 q^{20} -2.72665 q^{22} +6.25399 q^{23} +1.46050 q^{25} -0.734503 q^{26} +8.83547 q^{29} -5.70175 q^{31} +5.85773 q^{32} +1.54669 q^{34} +6.56867 q^{37} +4.34900 q^{38} +6.46050 q^{40} +10.3045 q^{41} -10.6477 q^{43} +5.42175 q^{44} +4.59358 q^{46} -1.46901 q^{47} +1.07275 q^{50} +1.46050 q^{52} -6.45477 q^{53} +9.43560 q^{55} +6.48968 q^{58} +11.4352 q^{59} -9.11537 q^{61} -4.18795 q^{62} +2.19436 q^{64} +2.54175 q^{65} -14.0541 q^{67} -3.07548 q^{68} -14.4527 q^{71} -6.14027 q^{73} +4.82471 q^{74} -8.64766 q^{76} -7.96790 q^{79} -2.67922 q^{80} +7.56867 q^{82} -12.1515 q^{83} -5.35234 q^{85} -7.82074 q^{86} +9.43560 q^{88} +11.8132 q^{89} -9.13399 q^{92} -1.07899 q^{94} -15.0497 q^{95} +7.10097 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 4 q^{4} - 4 q^{10} - 6 q^{13} - 12 q^{16} + 10 q^{19} - 18 q^{22} - 4 q^{25} + 8 q^{31} + 6 q^{34} - 10 q^{37} + 26 q^{40} - 40 q^{43} + 22 q^{46} - 4 q^{52} - 36 q^{58} - 2 q^{61} - 14 q^{64} - 66 q^{67} - 28 q^{73} - 28 q^{76} - 20 q^{79} - 4 q^{82} - 56 q^{85} - 32 q^{94} + 22 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.734503 0.519372 0.259686 0.965693i \(-0.416381\pi\)
0.259686 + 0.965693i \(0.416381\pi\)
\(3\) 0 0
\(4\) −1.46050 −0.730252
\(5\) −2.54175 −1.13671 −0.568353 0.822785i \(-0.692419\pi\)
−0.568353 + 0.822785i \(0.692419\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.54175 −0.898645
\(9\) 0 0
\(10\) −1.86693 −0.590374
\(11\) −3.71224 −1.11928 −0.559641 0.828735i \(-0.689061\pi\)
−0.559641 + 0.828735i \(0.689061\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 1.05408 0.263521
\(17\) 2.10577 0.510723 0.255362 0.966846i \(-0.417805\pi\)
0.255362 + 0.966846i \(0.417805\pi\)
\(18\) 0 0
\(19\) 5.92101 1.35837 0.679186 0.733966i \(-0.262333\pi\)
0.679186 + 0.733966i \(0.262333\pi\)
\(20\) 3.71224 0.830082
\(21\) 0 0
\(22\) −2.72665 −0.581325
\(23\) 6.25399 1.30405 0.652024 0.758198i \(-0.273920\pi\)
0.652024 + 0.758198i \(0.273920\pi\)
\(24\) 0 0
\(25\) 1.46050 0.292101
\(26\) −0.734503 −0.144048
\(27\) 0 0
\(28\) 0 0
\(29\) 8.83547 1.64071 0.820353 0.571858i \(-0.193777\pi\)
0.820353 + 0.571858i \(0.193777\pi\)
\(30\) 0 0
\(31\) −5.70175 −1.02406 −0.512032 0.858966i \(-0.671107\pi\)
−0.512032 + 0.858966i \(0.671107\pi\)
\(32\) 5.85773 1.03551
\(33\) 0 0
\(34\) 1.54669 0.265256
\(35\) 0 0
\(36\) 0 0
\(37\) 6.56867 1.07988 0.539942 0.841702i \(-0.318446\pi\)
0.539942 + 0.841702i \(0.318446\pi\)
\(38\) 4.34900 0.705501
\(39\) 0 0
\(40\) 6.46050 1.02150
\(41\) 10.3045 1.60929 0.804645 0.593757i \(-0.202356\pi\)
0.804645 + 0.593757i \(0.202356\pi\)
\(42\) 0 0
\(43\) −10.6477 −1.62375 −0.811877 0.583829i \(-0.801554\pi\)
−0.811877 + 0.583829i \(0.801554\pi\)
\(44\) 5.42175 0.817359
\(45\) 0 0
\(46\) 4.59358 0.677286
\(47\) −1.46901 −0.214277 −0.107138 0.994244i \(-0.534169\pi\)
−0.107138 + 0.994244i \(0.534169\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.07275 0.151709
\(51\) 0 0
\(52\) 1.46050 0.202536
\(53\) −6.45477 −0.886631 −0.443315 0.896366i \(-0.646198\pi\)
−0.443315 + 0.896366i \(0.646198\pi\)
\(54\) 0 0
\(55\) 9.43560 1.27230
\(56\) 0 0
\(57\) 0 0
\(58\) 6.48968 0.852137
\(59\) 11.4352 1.48874 0.744371 0.667766i \(-0.232750\pi\)
0.744371 + 0.667766i \(0.232750\pi\)
\(60\) 0 0
\(61\) −9.11537 −1.16710 −0.583551 0.812076i \(-0.698337\pi\)
−0.583551 + 0.812076i \(0.698337\pi\)
\(62\) −4.18795 −0.531871
\(63\) 0 0
\(64\) 2.19436 0.274294
\(65\) 2.54175 0.315266
\(66\) 0 0
\(67\) −14.0541 −1.71698 −0.858490 0.512831i \(-0.828597\pi\)
−0.858490 + 0.512831i \(0.828597\pi\)
\(68\) −3.07548 −0.372957
\(69\) 0 0
\(70\) 0 0
\(71\) −14.4527 −1.71522 −0.857610 0.514300i \(-0.828052\pi\)
−0.857610 + 0.514300i \(0.828052\pi\)
\(72\) 0 0
\(73\) −6.14027 −0.718664 −0.359332 0.933210i \(-0.616996\pi\)
−0.359332 + 0.933210i \(0.616996\pi\)
\(74\) 4.82471 0.560861
\(75\) 0 0
\(76\) −8.64766 −0.991955
\(77\) 0 0
\(78\) 0 0
\(79\) −7.96790 −0.896458 −0.448229 0.893919i \(-0.647945\pi\)
−0.448229 + 0.893919i \(0.647945\pi\)
\(80\) −2.67922 −0.299546
\(81\) 0 0
\(82\) 7.56867 0.835820
\(83\) −12.1515 −1.33380 −0.666898 0.745149i \(-0.732378\pi\)
−0.666898 + 0.745149i \(0.732378\pi\)
\(84\) 0 0
\(85\) −5.35234 −0.580542
\(86\) −7.82074 −0.843333
\(87\) 0 0
\(88\) 9.43560 1.00584
\(89\) 11.8132 1.25220 0.626099 0.779744i \(-0.284651\pi\)
0.626099 + 0.779744i \(0.284651\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −9.13399 −0.952284
\(93\) 0 0
\(94\) −1.07899 −0.111289
\(95\) −15.0497 −1.54407
\(96\) 0 0
\(97\) 7.10097 0.720994 0.360497 0.932760i \(-0.382607\pi\)
0.360497 + 0.932760i \(0.382607\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.13307 −0.213307
\(101\) 8.49723 0.845506 0.422753 0.906245i \(-0.361064\pi\)
0.422753 + 0.906245i \(0.361064\pi\)
\(102\) 0 0
\(103\) 2.18716 0.215507 0.107754 0.994178i \(-0.465634\pi\)
0.107754 + 0.994178i \(0.465634\pi\)
\(104\) 2.54175 0.249239
\(105\) 0 0
\(106\) −4.74105 −0.460491
\(107\) −7.52751 −0.727712 −0.363856 0.931455i \(-0.618540\pi\)
−0.363856 + 0.931455i \(0.618540\pi\)
\(108\) 0 0
\(109\) 0.0540842 0.00518033 0.00259016 0.999997i \(-0.499176\pi\)
0.00259016 + 0.999997i \(0.499176\pi\)
\(110\) 6.93048 0.660795
\(111\) 0 0
\(112\) 0 0
\(113\) −6.25399 −0.588326 −0.294163 0.955755i \(-0.595041\pi\)
−0.294163 + 0.955755i \(0.595041\pi\)
\(114\) 0 0
\(115\) −15.8961 −1.48232
\(116\) −12.9042 −1.19813
\(117\) 0 0
\(118\) 8.39922 0.773211
\(119\) 0 0
\(120\) 0 0
\(121\) 2.78074 0.252794
\(122\) −6.69527 −0.606161
\(123\) 0 0
\(124\) 8.32743 0.747825
\(125\) 8.99652 0.804673
\(126\) 0 0
\(127\) −2.49261 −0.221183 −0.110592 0.993866i \(-0.535275\pi\)
−0.110592 + 0.993866i \(0.535275\pi\)
\(128\) −10.1037 −0.893050
\(129\) 0 0
\(130\) 1.86693 0.163740
\(131\) −8.85376 −0.773557 −0.386779 0.922173i \(-0.626412\pi\)
−0.386779 + 0.922173i \(0.626412\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −10.3228 −0.891752
\(135\) 0 0
\(136\) −5.35234 −0.458959
\(137\) 2.71895 0.232295 0.116148 0.993232i \(-0.462945\pi\)
0.116148 + 0.993232i \(0.462945\pi\)
\(138\) 0 0
\(139\) 13.1694 1.11702 0.558509 0.829498i \(-0.311374\pi\)
0.558509 + 0.829498i \(0.311374\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.6156 −0.890838
\(143\) 3.71224 0.310433
\(144\) 0 0
\(145\) −22.4576 −1.86500
\(146\) −4.51005 −0.373254
\(147\) 0 0
\(148\) −9.59358 −0.788587
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −7.29533 −0.593685 −0.296843 0.954926i \(-0.595934\pi\)
−0.296843 + 0.954926i \(0.595934\pi\)
\(152\) −15.0497 −1.22070
\(153\) 0 0
\(154\) 0 0
\(155\) 14.4924 1.16406
\(156\) 0 0
\(157\) −5.67257 −0.452720 −0.226360 0.974044i \(-0.572683\pi\)
−0.226360 + 0.974044i \(0.572683\pi\)
\(158\) −5.85245 −0.465596
\(159\) 0 0
\(160\) −14.8889 −1.17707
\(161\) 0 0
\(162\) 0 0
\(163\) −20.7161 −1.62261 −0.811307 0.584621i \(-0.801243\pi\)
−0.811307 + 0.584621i \(0.801243\pi\)
\(164\) −15.0497 −1.17519
\(165\) 0 0
\(166\) −8.92528 −0.692736
\(167\) 14.3152 1.10775 0.553873 0.832601i \(-0.313149\pi\)
0.553873 + 0.832601i \(0.313149\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −3.93131 −0.301518
\(171\) 0 0
\(172\) 15.5510 1.18575
\(173\) −22.4162 −1.70427 −0.852136 0.523320i \(-0.824693\pi\)
−0.852136 + 0.523320i \(0.824693\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.91302 −0.294955
\(177\) 0 0
\(178\) 8.67684 0.650357
\(179\) 8.26202 0.617532 0.308766 0.951138i \(-0.400084\pi\)
0.308766 + 0.951138i \(0.400084\pi\)
\(180\) 0 0
\(181\) −0.787935 −0.0585668 −0.0292834 0.999571i \(-0.509323\pi\)
−0.0292834 + 0.999571i \(0.509323\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −15.8961 −1.17188
\(185\) −16.6959 −1.22751
\(186\) 0 0
\(187\) −7.81711 −0.571644
\(188\) 2.14549 0.156476
\(189\) 0 0
\(190\) −11.0541 −0.801948
\(191\) 0.396261 0.0286724 0.0143362 0.999897i \(-0.495436\pi\)
0.0143362 + 0.999897i \(0.495436\pi\)
\(192\) 0 0
\(193\) 3.78794 0.272662 0.136331 0.990663i \(-0.456469\pi\)
0.136331 + 0.990663i \(0.456469\pi\)
\(194\) 5.21569 0.374464
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0484 0.858415 0.429207 0.903206i \(-0.358793\pi\)
0.429207 + 0.903206i \(0.358793\pi\)
\(198\) 0 0
\(199\) −5.16225 −0.365942 −0.182971 0.983118i \(-0.558572\pi\)
−0.182971 + 0.983118i \(0.558572\pi\)
\(200\) −3.71224 −0.262495
\(201\) 0 0
\(202\) 6.24124 0.439132
\(203\) 0 0
\(204\) 0 0
\(205\) −26.1914 −1.82929
\(206\) 1.60648 0.111928
\(207\) 0 0
\(208\) −1.05408 −0.0730876
\(209\) −21.9802 −1.52040
\(210\) 0 0
\(211\) 17.9794 1.23775 0.618875 0.785489i \(-0.287589\pi\)
0.618875 + 0.785489i \(0.287589\pi\)
\(212\) 9.42722 0.647464
\(213\) 0 0
\(214\) −5.52898 −0.377954
\(215\) 27.0637 1.84573
\(216\) 0 0
\(217\) 0 0
\(218\) 0.0397250 0.00269052
\(219\) 0 0
\(220\) −13.7807 −0.929097
\(221\) −2.10577 −0.141649
\(222\) 0 0
\(223\) 1.96790 0.131780 0.0658901 0.997827i \(-0.479011\pi\)
0.0658901 + 0.997827i \(0.479011\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.59358 −0.305560
\(227\) −12.4285 −0.824911 −0.412456 0.910978i \(-0.635329\pi\)
−0.412456 + 0.910978i \(0.635329\pi\)
\(228\) 0 0
\(229\) 21.0584 1.39158 0.695788 0.718248i \(-0.255055\pi\)
0.695788 + 0.718248i \(0.255055\pi\)
\(230\) −11.6757 −0.769876
\(231\) 0 0
\(232\) −22.4576 −1.47441
\(233\) −7.26872 −0.476190 −0.238095 0.971242i \(-0.576523\pi\)
−0.238095 + 0.971242i \(0.576523\pi\)
\(234\) 0 0
\(235\) 3.73385 0.243570
\(236\) −16.7012 −1.08716
\(237\) 0 0
\(238\) 0 0
\(239\) 12.8698 0.832479 0.416239 0.909255i \(-0.363348\pi\)
0.416239 + 0.909255i \(0.363348\pi\)
\(240\) 0 0
\(241\) 13.1986 0.850198 0.425099 0.905147i \(-0.360239\pi\)
0.425099 + 0.905147i \(0.360239\pi\)
\(242\) 2.04246 0.131294
\(243\) 0 0
\(244\) 13.3130 0.852280
\(245\) 0 0
\(246\) 0 0
\(247\) −5.92101 −0.376745
\(248\) 14.4924 0.920270
\(249\) 0 0
\(250\) 6.60797 0.417925
\(251\) 10.1617 0.641402 0.320701 0.947180i \(-0.396081\pi\)
0.320701 + 0.947180i \(0.396081\pi\)
\(252\) 0 0
\(253\) −23.2163 −1.45960
\(254\) −1.83083 −0.114876
\(255\) 0 0
\(256\) −11.8099 −0.738120
\(257\) 0.240499 0.0150019 0.00750095 0.999972i \(-0.497612\pi\)
0.00750095 + 0.999972i \(0.497612\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3.71224 −0.230223
\(261\) 0 0
\(262\) −6.50312 −0.401764
\(263\) 16.7592 1.03342 0.516710 0.856161i \(-0.327157\pi\)
0.516710 + 0.856161i \(0.327157\pi\)
\(264\) 0 0
\(265\) 16.4064 1.00784
\(266\) 0 0
\(267\) 0 0
\(268\) 20.5261 1.25383
\(269\) −14.8307 −0.904242 −0.452121 0.891957i \(-0.649332\pi\)
−0.452121 + 0.891957i \(0.649332\pi\)
\(270\) 0 0
\(271\) 27.2704 1.65656 0.828280 0.560314i \(-0.189320\pi\)
0.828280 + 0.560314i \(0.189320\pi\)
\(272\) 2.21966 0.134586
\(273\) 0 0
\(274\) 1.99707 0.120648
\(275\) −5.42175 −0.326944
\(276\) 0 0
\(277\) −27.6912 −1.66381 −0.831903 0.554922i \(-0.812748\pi\)
−0.831903 + 0.554922i \(0.812748\pi\)
\(278\) 9.67300 0.580148
\(279\) 0 0
\(280\) 0 0
\(281\) −16.6959 −0.995996 −0.497998 0.867178i \(-0.665931\pi\)
−0.497998 + 0.867178i \(0.665931\pi\)
\(282\) 0 0
\(283\) −0.320233 −0.0190359 −0.00951794 0.999955i \(-0.503030\pi\)
−0.00951794 + 0.999955i \(0.503030\pi\)
\(284\) 21.1082 1.25254
\(285\) 0 0
\(286\) 2.72665 0.161230
\(287\) 0 0
\(288\) 0 0
\(289\) −12.5657 −0.739162
\(290\) −16.4952 −0.968630
\(291\) 0 0
\(292\) 8.96790 0.524806
\(293\) 8.07954 0.472012 0.236006 0.971752i \(-0.424162\pi\)
0.236006 + 0.971752i \(0.424162\pi\)
\(294\) 0 0
\(295\) −29.0656 −1.69226
\(296\) −16.6959 −0.970432
\(297\) 0 0
\(298\) 0 0
\(299\) −6.25399 −0.361678
\(300\) 0 0
\(301\) 0 0
\(302\) −5.35844 −0.308344
\(303\) 0 0
\(304\) 6.24124 0.357960
\(305\) 23.1690 1.32665
\(306\) 0 0
\(307\) −4.94299 −0.282111 −0.141056 0.990002i \(-0.545050\pi\)
−0.141056 + 0.990002i \(0.545050\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.6447 0.604581
\(311\) −4.05048 −0.229682 −0.114841 0.993384i \(-0.536636\pi\)
−0.114841 + 0.993384i \(0.536636\pi\)
\(312\) 0 0
\(313\) −10.3671 −0.585984 −0.292992 0.956115i \(-0.594651\pi\)
−0.292992 + 0.956115i \(0.594651\pi\)
\(314\) −4.16652 −0.235130
\(315\) 0 0
\(316\) 11.6372 0.654641
\(317\) 12.0773 0.678328 0.339164 0.940727i \(-0.389856\pi\)
0.339164 + 0.940727i \(0.389856\pi\)
\(318\) 0 0
\(319\) −32.7994 −1.83641
\(320\) −5.57751 −0.311792
\(321\) 0 0
\(322\) 0 0
\(323\) 12.4683 0.693753
\(324\) 0 0
\(325\) −1.46050 −0.0810142
\(326\) −15.2161 −0.842740
\(327\) 0 0
\(328\) −26.1914 −1.44618
\(329\) 0 0
\(330\) 0 0
\(331\) −22.1766 −1.21894 −0.609469 0.792810i \(-0.708617\pi\)
−0.609469 + 0.792810i \(0.708617\pi\)
\(332\) 17.7473 0.974007
\(333\) 0 0
\(334\) 10.5146 0.575333
\(335\) 35.7220 1.95170
\(336\) 0 0
\(337\) −5.95311 −0.324287 −0.162143 0.986767i \(-0.551841\pi\)
−0.162143 + 0.986767i \(0.551841\pi\)
\(338\) 0.734503 0.0399517
\(339\) 0 0
\(340\) 7.81711 0.423942
\(341\) 21.1663 1.14622
\(342\) 0 0
\(343\) 0 0
\(344\) 27.0637 1.45918
\(345\) 0 0
\(346\) −16.4648 −0.885152
\(347\) −19.0422 −1.02224 −0.511120 0.859510i \(-0.670769\pi\)
−0.511120 + 0.859510i \(0.670769\pi\)
\(348\) 0 0
\(349\) −3.61556 −0.193537 −0.0967683 0.995307i \(-0.530851\pi\)
−0.0967683 + 0.995307i \(0.530851\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −21.7453 −1.15903
\(353\) 5.97691 0.318119 0.159059 0.987269i \(-0.449154\pi\)
0.159059 + 0.987269i \(0.449154\pi\)
\(354\) 0 0
\(355\) 36.7352 1.94970
\(356\) −17.2533 −0.914420
\(357\) 0 0
\(358\) 6.06848 0.320729
\(359\) −15.1528 −0.799733 −0.399866 0.916573i \(-0.630943\pi\)
−0.399866 + 0.916573i \(0.630943\pi\)
\(360\) 0 0
\(361\) 16.0584 0.845177
\(362\) −0.578741 −0.0304180
\(363\) 0 0
\(364\) 0 0
\(365\) 15.6070 0.816910
\(366\) 0 0
\(367\) −6.75156 −0.352429 −0.176214 0.984352i \(-0.556385\pi\)
−0.176214 + 0.984352i \(0.556385\pi\)
\(368\) 6.59224 0.343644
\(369\) 0 0
\(370\) −12.2632 −0.637535
\(371\) 0 0
\(372\) 0 0
\(373\) 6.30972 0.326705 0.163352 0.986568i \(-0.447769\pi\)
0.163352 + 0.986568i \(0.447769\pi\)
\(374\) −5.74170 −0.296896
\(375\) 0 0
\(376\) 3.73385 0.192559
\(377\) −8.83547 −0.455050
\(378\) 0 0
\(379\) 0.0861875 0.00442715 0.00221358 0.999998i \(-0.499295\pi\)
0.00221358 + 0.999998i \(0.499295\pi\)
\(380\) 21.9802 1.12756
\(381\) 0 0
\(382\) 0.291055 0.0148917
\(383\) −21.3779 −1.09236 −0.546180 0.837668i \(-0.683918\pi\)
−0.546180 + 0.837668i \(0.683918\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.78225 0.141613
\(387\) 0 0
\(388\) −10.3710 −0.526508
\(389\) −32.0839 −1.62672 −0.813360 0.581761i \(-0.802364\pi\)
−0.813360 + 0.581761i \(0.802364\pi\)
\(390\) 0 0
\(391\) 13.1694 0.666008
\(392\) 0 0
\(393\) 0 0
\(394\) 8.84961 0.445837
\(395\) 20.2524 1.01901
\(396\) 0 0
\(397\) 12.1196 0.608267 0.304134 0.952629i \(-0.401633\pi\)
0.304134 + 0.952629i \(0.401633\pi\)
\(398\) −3.79169 −0.190060
\(399\) 0 0
\(400\) 1.53950 0.0769748
\(401\) 26.6277 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(402\) 0 0
\(403\) 5.70175 0.284024
\(404\) −12.4102 −0.617433
\(405\) 0 0
\(406\) 0 0
\(407\) −24.3845 −1.20869
\(408\) 0 0
\(409\) −6.48968 −0.320894 −0.160447 0.987044i \(-0.551294\pi\)
−0.160447 + 0.987044i \(0.551294\pi\)
\(410\) −19.2377 −0.950082
\(411\) 0 0
\(412\) −3.19436 −0.157375
\(413\) 0 0
\(414\) 0 0
\(415\) 30.8860 1.51613
\(416\) −5.85773 −0.287199
\(417\) 0 0
\(418\) −16.1445 −0.789655
\(419\) −31.3097 −1.52958 −0.764789 0.644280i \(-0.777157\pi\)
−0.764789 + 0.644280i \(0.777157\pi\)
\(420\) 0 0
\(421\) −24.3097 −1.18478 −0.592392 0.805650i \(-0.701816\pi\)
−0.592392 + 0.805650i \(0.701816\pi\)
\(422\) 13.2059 0.642853
\(423\) 0 0
\(424\) 16.4064 0.796766
\(425\) 3.07548 0.149183
\(426\) 0 0
\(427\) 0 0
\(428\) 10.9940 0.531414
\(429\) 0 0
\(430\) 19.8784 0.958621
\(431\) 19.7950 0.953492 0.476746 0.879041i \(-0.341816\pi\)
0.476746 + 0.879041i \(0.341816\pi\)
\(432\) 0 0
\(433\) −31.8932 −1.53269 −0.766344 0.642430i \(-0.777926\pi\)
−0.766344 + 0.642430i \(0.777926\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.0789903 −0.00378295
\(437\) 37.0300 1.77138
\(438\) 0 0
\(439\) −28.8463 −1.37676 −0.688379 0.725351i \(-0.741677\pi\)
−0.688379 + 0.725351i \(0.741677\pi\)
\(440\) −23.9830 −1.14334
\(441\) 0 0
\(442\) −1.54669 −0.0735687
\(443\) 3.25796 0.154790 0.0773952 0.997000i \(-0.475340\pi\)
0.0773952 + 0.997000i \(0.475340\pi\)
\(444\) 0 0
\(445\) −30.0263 −1.42338
\(446\) 1.44543 0.0684429
\(447\) 0 0
\(448\) 0 0
\(449\) 1.03302 0.0487513 0.0243756 0.999703i \(-0.492240\pi\)
0.0243756 + 0.999703i \(0.492240\pi\)
\(450\) 0 0
\(451\) −38.2527 −1.80125
\(452\) 9.13399 0.429627
\(453\) 0 0
\(454\) −9.12880 −0.428436
\(455\) 0 0
\(456\) 0 0
\(457\) −17.4648 −0.816968 −0.408484 0.912766i \(-0.633942\pi\)
−0.408484 + 0.912766i \(0.633942\pi\)
\(458\) 15.4674 0.722746
\(459\) 0 0
\(460\) 23.2163 1.08247
\(461\) −32.4060 −1.50930 −0.754649 0.656128i \(-0.772193\pi\)
−0.754649 + 0.656128i \(0.772193\pi\)
\(462\) 0 0
\(463\) −34.8788 −1.62095 −0.810477 0.585770i \(-0.800792\pi\)
−0.810477 + 0.585770i \(0.800792\pi\)
\(464\) 9.31333 0.432361
\(465\) 0 0
\(466\) −5.33890 −0.247320
\(467\) −32.5252 −1.50509 −0.752543 0.658543i \(-0.771173\pi\)
−0.752543 + 0.658543i \(0.771173\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 2.74253 0.126503
\(471\) 0 0
\(472\) −29.0656 −1.33785
\(473\) 39.5267 1.81744
\(474\) 0 0
\(475\) 8.64766 0.396782
\(476\) 0 0
\(477\) 0 0
\(478\) 9.45292 0.432366
\(479\) −5.04378 −0.230456 −0.115228 0.993339i \(-0.536760\pi\)
−0.115228 + 0.993339i \(0.536760\pi\)
\(480\) 0 0
\(481\) −6.56867 −0.299506
\(482\) 9.69444 0.441569
\(483\) 0 0
\(484\) −4.06128 −0.184604
\(485\) −18.0489 −0.819559
\(486\) 0 0
\(487\) −11.2019 −0.507608 −0.253804 0.967256i \(-0.581682\pi\)
−0.253804 + 0.967256i \(0.581682\pi\)
\(488\) 23.1690 1.04881
\(489\) 0 0
\(490\) 0 0
\(491\) −21.6420 −0.976689 −0.488344 0.872651i \(-0.662399\pi\)
−0.488344 + 0.872651i \(0.662399\pi\)
\(492\) 0 0
\(493\) 18.6054 0.837947
\(494\) −4.34900 −0.195671
\(495\) 0 0
\(496\) −6.01012 −0.269862
\(497\) 0 0
\(498\) 0 0
\(499\) −12.8128 −0.573582 −0.286791 0.957993i \(-0.592588\pi\)
−0.286791 + 0.957993i \(0.592588\pi\)
\(500\) −13.1395 −0.587615
\(501\) 0 0
\(502\) 7.46382 0.333127
\(503\) 24.9763 1.11364 0.556818 0.830635i \(-0.312022\pi\)
0.556818 + 0.830635i \(0.312022\pi\)
\(504\) 0 0
\(505\) −21.5979 −0.961092
\(506\) −17.0525 −0.758075
\(507\) 0 0
\(508\) 3.64047 0.161520
\(509\) 35.6007 1.57797 0.788986 0.614411i \(-0.210606\pi\)
0.788986 + 0.614411i \(0.210606\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.5330 0.509691
\(513\) 0 0
\(514\) 0.176647 0.00779157
\(515\) −5.55922 −0.244968
\(516\) 0 0
\(517\) 5.45331 0.239836
\(518\) 0 0
\(519\) 0 0
\(520\) −6.46050 −0.283312
\(521\) −36.8078 −1.61258 −0.806288 0.591523i \(-0.798527\pi\)
−0.806288 + 0.591523i \(0.798527\pi\)
\(522\) 0 0
\(523\) −15.5175 −0.678534 −0.339267 0.940690i \(-0.610179\pi\)
−0.339267 + 0.940690i \(0.610179\pi\)
\(524\) 12.9310 0.564892
\(525\) 0 0
\(526\) 12.3097 0.536729
\(527\) −12.0065 −0.523013
\(528\) 0 0
\(529\) 16.1124 0.700541
\(530\) 12.0506 0.523443
\(531\) 0 0
\(532\) 0 0
\(533\) −10.3045 −0.446336
\(534\) 0 0
\(535\) 19.1331 0.827195
\(536\) 35.7220 1.54296
\(537\) 0 0
\(538\) −10.8932 −0.469638
\(539\) 0 0
\(540\) 0 0
\(541\) 22.5261 0.968471 0.484235 0.874938i \(-0.339098\pi\)
0.484235 + 0.874938i \(0.339098\pi\)
\(542\) 20.0302 0.860371
\(543\) 0 0
\(544\) 12.3350 0.528859
\(545\) −0.137469 −0.00588851
\(546\) 0 0
\(547\) 1.73812 0.0743168 0.0371584 0.999309i \(-0.488169\pi\)
0.0371584 + 0.999309i \(0.488169\pi\)
\(548\) −3.97103 −0.169634
\(549\) 0 0
\(550\) −3.98229 −0.169805
\(551\) 52.3149 2.22869
\(552\) 0 0
\(553\) 0 0
\(554\) −20.3393 −0.864134
\(555\) 0 0
\(556\) −19.2340 −0.815705
\(557\) −26.3056 −1.11461 −0.557303 0.830309i \(-0.688164\pi\)
−0.557303 + 0.830309i \(0.688164\pi\)
\(558\) 0 0
\(559\) 10.6477 0.450348
\(560\) 0 0
\(561\) 0 0
\(562\) −12.2632 −0.517293
\(563\) 13.7365 0.578924 0.289462 0.957189i \(-0.406524\pi\)
0.289462 + 0.957189i \(0.406524\pi\)
\(564\) 0 0
\(565\) 15.8961 0.668754
\(566\) −0.235212 −0.00988671
\(567\) 0 0
\(568\) 36.7352 1.54137
\(569\) 19.6522 0.823865 0.411933 0.911214i \(-0.364854\pi\)
0.411933 + 0.911214i \(0.364854\pi\)
\(570\) 0 0
\(571\) −16.7516 −0.701031 −0.350515 0.936557i \(-0.613994\pi\)
−0.350515 + 0.936557i \(0.613994\pi\)
\(572\) −5.42175 −0.226695
\(573\) 0 0
\(574\) 0 0
\(575\) 9.13399 0.380914
\(576\) 0 0
\(577\) −23.3930 −0.973863 −0.486931 0.873440i \(-0.661884\pi\)
−0.486931 + 0.873440i \(0.661884\pi\)
\(578\) −9.22958 −0.383900
\(579\) 0 0
\(580\) 32.7994 1.36192
\(581\) 0 0
\(582\) 0 0
\(583\) 23.9617 0.992390
\(584\) 15.6070 0.645824
\(585\) 0 0
\(586\) 5.93445 0.245150
\(587\) 6.05322 0.249843 0.124922 0.992167i \(-0.460132\pi\)
0.124922 + 0.992167i \(0.460132\pi\)
\(588\) 0 0
\(589\) −33.7601 −1.39106
\(590\) −21.3487 −0.878914
\(591\) 0 0
\(592\) 6.92393 0.284572
\(593\) 6.54722 0.268862 0.134431 0.990923i \(-0.457079\pi\)
0.134431 + 0.990923i \(0.457079\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −4.59358 −0.187845
\(599\) −2.36241 −0.0965255 −0.0482627 0.998835i \(-0.515368\pi\)
−0.0482627 + 0.998835i \(0.515368\pi\)
\(600\) 0 0
\(601\) 40.5408 1.65370 0.826848 0.562426i \(-0.190132\pi\)
0.826848 + 0.562426i \(0.190132\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 10.6549 0.433540
\(605\) −7.06795 −0.287353
\(606\) 0 0
\(607\) −11.4461 −0.464583 −0.232292 0.972646i \(-0.574622\pi\)
−0.232292 + 0.972646i \(0.574622\pi\)
\(608\) 34.6837 1.40661
\(609\) 0 0
\(610\) 17.0177 0.689027
\(611\) 1.46901 0.0594296
\(612\) 0 0
\(613\) 12.7060 0.513191 0.256596 0.966519i \(-0.417399\pi\)
0.256596 + 0.966519i \(0.417399\pi\)
\(614\) −3.63064 −0.146521
\(615\) 0 0
\(616\) 0 0
\(617\) 30.9500 1.24600 0.623000 0.782221i \(-0.285913\pi\)
0.623000 + 0.782221i \(0.285913\pi\)
\(618\) 0 0
\(619\) 4.56440 0.183459 0.0917294 0.995784i \(-0.470761\pi\)
0.0917294 + 0.995784i \(0.470761\pi\)
\(620\) −21.1663 −0.850058
\(621\) 0 0
\(622\) −2.97509 −0.119290
\(623\) 0 0
\(624\) 0 0
\(625\) −30.1694 −1.20678
\(626\) −7.61468 −0.304344
\(627\) 0 0
\(628\) 8.28482 0.330600
\(629\) 13.8321 0.551522
\(630\) 0 0
\(631\) 15.0803 0.600339 0.300169 0.953886i \(-0.402957\pi\)
0.300169 + 0.953886i \(0.402957\pi\)
\(632\) 20.2524 0.805598
\(633\) 0 0
\(634\) 8.87081 0.352305
\(635\) 6.33559 0.251420
\(636\) 0 0
\(637\) 0 0
\(638\) −24.0913 −0.953783
\(639\) 0 0
\(640\) 25.6811 1.01514
\(641\) −6.04236 −0.238659 −0.119329 0.992855i \(-0.538074\pi\)
−0.119329 + 0.992855i \(0.538074\pi\)
\(642\) 0 0
\(643\) −16.2881 −0.642341 −0.321171 0.947021i \(-0.604076\pi\)
−0.321171 + 0.947021i \(0.604076\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 9.15798 0.360316
\(647\) −7.16040 −0.281505 −0.140752 0.990045i \(-0.544952\pi\)
−0.140752 + 0.990045i \(0.544952\pi\)
\(648\) 0 0
\(649\) −42.4504 −1.66632
\(650\) −1.07275 −0.0420765
\(651\) 0 0
\(652\) 30.2560 1.18492
\(653\) 23.5255 0.920625 0.460313 0.887757i \(-0.347737\pi\)
0.460313 + 0.887757i \(0.347737\pi\)
\(654\) 0 0
\(655\) 22.5041 0.879307
\(656\) 10.8618 0.424082
\(657\) 0 0
\(658\) 0 0
\(659\) −8.73459 −0.340251 −0.170126 0.985422i \(-0.554417\pi\)
−0.170126 + 0.985422i \(0.554417\pi\)
\(660\) 0 0
\(661\) 11.2016 0.435690 0.217845 0.975983i \(-0.430097\pi\)
0.217845 + 0.975983i \(0.430097\pi\)
\(662\) −16.2888 −0.633083
\(663\) 0 0
\(664\) 30.8860 1.19861
\(665\) 0 0
\(666\) 0 0
\(667\) 55.2570 2.13956
\(668\) −20.9075 −0.808934
\(669\) 0 0
\(670\) 26.2379 1.01366
\(671\) 33.8384 1.30632
\(672\) 0 0
\(673\) −11.0728 −0.426823 −0.213412 0.976962i \(-0.568458\pi\)
−0.213412 + 0.976962i \(0.568458\pi\)
\(674\) −4.37258 −0.168426
\(675\) 0 0
\(676\) −1.46050 −0.0561733
\(677\) −36.0838 −1.38681 −0.693407 0.720546i \(-0.743891\pi\)
−0.693407 + 0.720546i \(0.743891\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 13.6043 0.521702
\(681\) 0 0
\(682\) 15.5467 0.595314
\(683\) 48.9248 1.87205 0.936027 0.351928i \(-0.114474\pi\)
0.936027 + 0.351928i \(0.114474\pi\)
\(684\) 0 0
\(685\) −6.91089 −0.264051
\(686\) 0 0
\(687\) 0 0
\(688\) −11.2235 −0.427893
\(689\) 6.45477 0.245907
\(690\) 0 0
\(691\) −37.6706 −1.43306 −0.716529 0.697558i \(-0.754270\pi\)
−0.716529 + 0.697558i \(0.754270\pi\)
\(692\) 32.7390 1.24455
\(693\) 0 0
\(694\) −13.9866 −0.530923
\(695\) −33.4735 −1.26972
\(696\) 0 0
\(697\) 21.6988 0.821902
\(698\) −2.65564 −0.100517
\(699\) 0 0
\(700\) 0 0
\(701\) −19.9325 −0.752839 −0.376420 0.926449i \(-0.622845\pi\)
−0.376420 + 0.926449i \(0.622845\pi\)
\(702\) 0 0
\(703\) 38.8932 1.46688
\(704\) −8.14598 −0.307013
\(705\) 0 0
\(706\) 4.39006 0.165222
\(707\) 0 0
\(708\) 0 0
\(709\) −4.07607 −0.153080 −0.0765399 0.997067i \(-0.524387\pi\)
−0.0765399 + 0.997067i \(0.524387\pi\)
\(710\) 26.9821 1.01262
\(711\) 0 0
\(712\) −30.0263 −1.12528
\(713\) −35.6587 −1.33543
\(714\) 0 0
\(715\) −9.43560 −0.352871
\(716\) −12.0667 −0.450954
\(717\) 0 0
\(718\) −11.1298 −0.415359
\(719\) −4.12465 −0.153823 −0.0769117 0.997038i \(-0.524506\pi\)
−0.0769117 + 0.997038i \(0.524506\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 11.7949 0.438961
\(723\) 0 0
\(724\) 1.15078 0.0427685
\(725\) 12.9042 0.479252
\(726\) 0 0
\(727\) −7.39203 −0.274155 −0.137078 0.990560i \(-0.543771\pi\)
−0.137078 + 0.990560i \(0.543771\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 11.4634 0.424281
\(731\) −22.4215 −0.829289
\(732\) 0 0
\(733\) −7.05836 −0.260706 −0.130353 0.991468i \(-0.541611\pi\)
−0.130353 + 0.991468i \(0.541611\pi\)
\(734\) −4.95904 −0.183042
\(735\) 0 0
\(736\) 36.6342 1.35036
\(737\) 52.1722 1.92179
\(738\) 0 0
\(739\) −33.9033 −1.24715 −0.623577 0.781762i \(-0.714321\pi\)
−0.623577 + 0.781762i \(0.714321\pi\)
\(740\) 24.3845 0.896392
\(741\) 0 0
\(742\) 0 0
\(743\) −16.3211 −0.598763 −0.299382 0.954133i \(-0.596780\pi\)
−0.299382 + 0.954133i \(0.596780\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 4.63451 0.169682
\(747\) 0 0
\(748\) 11.4169 0.417444
\(749\) 0 0
\(750\) 0 0
\(751\) −23.5467 −0.859231 −0.429616 0.903012i \(-0.641351\pi\)
−0.429616 + 0.903012i \(0.641351\pi\)
\(752\) −1.54846 −0.0564664
\(753\) 0 0
\(754\) −6.48968 −0.236340
\(755\) 18.5429 0.674846
\(756\) 0 0
\(757\) 35.1019 1.27580 0.637901 0.770119i \(-0.279803\pi\)
0.637901 + 0.770119i \(0.279803\pi\)
\(758\) 0.0633050 0.00229934
\(759\) 0 0
\(760\) 38.2527 1.38757
\(761\) −45.4692 −1.64826 −0.824128 0.566404i \(-0.808334\pi\)
−0.824128 + 0.566404i \(0.808334\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −0.578741 −0.0209381
\(765\) 0 0
\(766\) −15.7021 −0.567341
\(767\) −11.4352 −0.412903
\(768\) 0 0
\(769\) −42.4543 −1.53094 −0.765470 0.643472i \(-0.777493\pi\)
−0.765470 + 0.643472i \(0.777493\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.53230 −0.199112
\(773\) −46.6021 −1.67616 −0.838080 0.545547i \(-0.816322\pi\)
−0.838080 + 0.545547i \(0.816322\pi\)
\(774\) 0 0
\(775\) −8.32743 −0.299130
\(776\) −18.0489 −0.647918
\(777\) 0 0
\(778\) −23.5657 −0.844873
\(779\) 61.0129 2.18601
\(780\) 0 0
\(781\) 53.6519 1.91982
\(782\) 9.67300 0.345906
\(783\) 0 0
\(784\) 0 0
\(785\) 14.4183 0.514610
\(786\) 0 0
\(787\) 26.3815 0.940399 0.470200 0.882560i \(-0.344182\pi\)
0.470200 + 0.882560i \(0.344182\pi\)
\(788\) −17.5968 −0.626859
\(789\) 0 0
\(790\) 14.8755 0.529245
\(791\) 0 0
\(792\) 0 0
\(793\) 9.11537 0.323696
\(794\) 8.90191 0.315917
\(795\) 0 0
\(796\) 7.53950 0.267230
\(797\) −17.6474 −0.625102 −0.312551 0.949901i \(-0.601183\pi\)
−0.312551 + 0.949901i \(0.601183\pi\)
\(798\) 0 0
\(799\) −3.09338 −0.109436
\(800\) 8.55525 0.302474
\(801\) 0 0
\(802\) 19.5582 0.690623
\(803\) 22.7942 0.804389
\(804\) 0 0
\(805\) 0 0
\(806\) 4.18795 0.147514
\(807\) 0 0
\(808\) −21.5979 −0.759810
\(809\) 17.9716 0.631848 0.315924 0.948784i \(-0.397686\pi\)
0.315924 + 0.948784i \(0.397686\pi\)
\(810\) 0 0
\(811\) 43.5159 1.52805 0.764026 0.645186i \(-0.223220\pi\)
0.764026 + 0.645186i \(0.223220\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −17.9105 −0.627763
\(815\) 52.6553 1.84443
\(816\) 0 0
\(817\) −63.0449 −2.20566
\(818\) −4.76669 −0.166664
\(819\) 0 0
\(820\) 38.2527 1.33584
\(821\) −36.7283 −1.28183 −0.640913 0.767613i \(-0.721444\pi\)
−0.640913 + 0.767613i \(0.721444\pi\)
\(822\) 0 0
\(823\) −41.2235 −1.43696 −0.718481 0.695547i \(-0.755162\pi\)
−0.718481 + 0.695547i \(0.755162\pi\)
\(824\) −5.55922 −0.193664
\(825\) 0 0
\(826\) 0 0
\(827\) 10.0060 0.347941 0.173971 0.984751i \(-0.444340\pi\)
0.173971 + 0.984751i \(0.444340\pi\)
\(828\) 0 0
\(829\) 14.9607 0.519607 0.259803 0.965662i \(-0.416342\pi\)
0.259803 + 0.965662i \(0.416342\pi\)
\(830\) 22.6859 0.787438
\(831\) 0 0
\(832\) −2.19436 −0.0760756
\(833\) 0 0
\(834\) 0 0
\(835\) −36.3858 −1.25918
\(836\) 32.1022 1.11028
\(837\) 0 0
\(838\) −22.9971 −0.794421
\(839\) 27.0026 0.932232 0.466116 0.884724i \(-0.345653\pi\)
0.466116 + 0.884724i \(0.345653\pi\)
\(840\) 0 0
\(841\) 49.0656 1.69192
\(842\) −17.8556 −0.615344
\(843\) 0 0
\(844\) −26.2590 −0.903870
\(845\) −2.54175 −0.0874389
\(846\) 0 0
\(847\) 0 0
\(848\) −6.80387 −0.233646
\(849\) 0 0
\(850\) 2.25895 0.0774814
\(851\) 41.0804 1.40822
\(852\) 0 0
\(853\) −10.5438 −0.361012 −0.180506 0.983574i \(-0.557773\pi\)
−0.180506 + 0.983574i \(0.557773\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 19.1331 0.653955
\(857\) 7.48035 0.255524 0.127762 0.991805i \(-0.459221\pi\)
0.127762 + 0.991805i \(0.459221\pi\)
\(858\) 0 0
\(859\) 43.3724 1.47985 0.739923 0.672692i \(-0.234862\pi\)
0.739923 + 0.672692i \(0.234862\pi\)
\(860\) −39.5267 −1.34785
\(861\) 0 0
\(862\) 14.5395 0.495217
\(863\) 32.0228 1.09007 0.545034 0.838414i \(-0.316517\pi\)
0.545034 + 0.838414i \(0.316517\pi\)
\(864\) 0 0
\(865\) 56.9764 1.93726
\(866\) −23.4256 −0.796036
\(867\) 0 0
\(868\) 0 0
\(869\) 29.5788 1.00339
\(870\) 0 0
\(871\) 14.0541 0.476204
\(872\) −0.137469 −0.00465528
\(873\) 0 0
\(874\) 27.1986 0.920007
\(875\) 0 0
\(876\) 0 0
\(877\) 32.6156 1.10135 0.550675 0.834720i \(-0.314371\pi\)
0.550675 + 0.834720i \(0.314371\pi\)
\(878\) −21.1877 −0.715050
\(879\) 0 0
\(880\) 9.94592 0.335277
\(881\) −34.6890 −1.16870 −0.584351 0.811501i \(-0.698651\pi\)
−0.584351 + 0.811501i \(0.698651\pi\)
\(882\) 0 0
\(883\) 7.36381 0.247812 0.123906 0.992294i \(-0.460458\pi\)
0.123906 + 0.992294i \(0.460458\pi\)
\(884\) 3.07548 0.103440
\(885\) 0 0
\(886\) 2.39298 0.0803939
\(887\) 31.2517 1.04933 0.524664 0.851309i \(-0.324191\pi\)
0.524664 + 0.851309i \(0.324191\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −22.0544 −0.739265
\(891\) 0 0
\(892\) −2.87412 −0.0962327
\(893\) −8.69800 −0.291068
\(894\) 0 0
\(895\) −21.0000 −0.701953
\(896\) 0 0
\(897\) 0 0
\(898\) 0.758757 0.0253201
\(899\) −50.3776 −1.68019
\(900\) 0 0
\(901\) −13.5922 −0.452823
\(902\) −28.0967 −0.935519
\(903\) 0 0
\(904\) 15.8961 0.528697
\(905\) 2.00274 0.0665732
\(906\) 0 0
\(907\) −56.7204 −1.88337 −0.941685 0.336495i \(-0.890758\pi\)
−0.941685 + 0.336495i \(0.890758\pi\)
\(908\) 18.1519 0.602393
\(909\) 0 0
\(910\) 0 0
\(911\) −22.4742 −0.744604 −0.372302 0.928112i \(-0.621431\pi\)
−0.372302 + 0.928112i \(0.621431\pi\)
\(912\) 0 0
\(913\) 45.1091 1.49289
\(914\) −12.8279 −0.424310
\(915\) 0 0
\(916\) −30.7558 −1.01620
\(917\) 0 0
\(918\) 0 0
\(919\) 2.48541 0.0819861 0.0409931 0.999159i \(-0.486948\pi\)
0.0409931 + 0.999159i \(0.486948\pi\)
\(920\) 40.4040 1.33208
\(921\) 0 0
\(922\) −23.8023 −0.783888
\(923\) 14.4527 0.475717
\(924\) 0 0
\(925\) 9.59358 0.315435
\(926\) −25.6186 −0.841879
\(927\) 0 0
\(928\) 51.7558 1.69897
\(929\) 35.1991 1.15485 0.577423 0.816445i \(-0.304058\pi\)
0.577423 + 0.816445i \(0.304058\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 10.6160 0.347739
\(933\) 0 0
\(934\) −23.8899 −0.781700
\(935\) 19.8692 0.649791
\(936\) 0 0
\(937\) 40.0613 1.30875 0.654373 0.756172i \(-0.272933\pi\)
0.654373 + 0.756172i \(0.272933\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −5.45331 −0.177867
\(941\) −32.0076 −1.04342 −0.521709 0.853123i \(-0.674705\pi\)
−0.521709 + 0.853123i \(0.674705\pi\)
\(942\) 0 0
\(943\) 64.4441 2.09859
\(944\) 12.0537 0.392315
\(945\) 0 0
\(946\) 29.0325 0.943928
\(947\) −22.7383 −0.738896 −0.369448 0.929251i \(-0.620453\pi\)
−0.369448 + 0.929251i \(0.620453\pi\)
\(948\) 0 0
\(949\) 6.14027 0.199322
\(950\) 6.35174 0.206078
\(951\) 0 0
\(952\) 0 0
\(953\) 16.7884 0.543830 0.271915 0.962321i \(-0.412343\pi\)
0.271915 + 0.962321i \(0.412343\pi\)
\(954\) 0 0
\(955\) −1.00720 −0.0325921
\(956\) −18.7964 −0.607920
\(957\) 0 0
\(958\) −3.70467 −0.119693
\(959\) 0 0
\(960\) 0 0
\(961\) 1.50993 0.0487073
\(962\) −4.82471 −0.155555
\(963\) 0 0
\(964\) −19.2767 −0.620859
\(965\) −9.62799 −0.309936
\(966\) 0 0
\(967\) 44.3533 1.42631 0.713153 0.701009i \(-0.247267\pi\)
0.713153 + 0.701009i \(0.247267\pi\)
\(968\) −7.06795 −0.227172
\(969\) 0 0
\(970\) −13.2570 −0.425656
\(971\) −4.07935 −0.130913 −0.0654563 0.997855i \(-0.520850\pi\)
−0.0654563 + 0.997855i \(0.520850\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −8.22786 −0.263638
\(975\) 0 0
\(976\) −9.60836 −0.307556
\(977\) 9.76018 0.312256 0.156128 0.987737i \(-0.450099\pi\)
0.156128 + 0.987737i \(0.450099\pi\)
\(978\) 0 0
\(979\) −43.8535 −1.40156
\(980\) 0 0
\(981\) 0 0
\(982\) −15.8961 −0.507265
\(983\) −51.3163 −1.63674 −0.818368 0.574694i \(-0.805121\pi\)
−0.818368 + 0.574694i \(0.805121\pi\)
\(984\) 0 0
\(985\) −30.6241 −0.975765
\(986\) 13.6658 0.435206
\(987\) 0 0
\(988\) 8.64766 0.275119
\(989\) −66.5904 −2.11745
\(990\) 0 0
\(991\) −0.704673 −0.0223847 −0.0111923 0.999937i \(-0.503563\pi\)
−0.0111923 + 0.999937i \(0.503563\pi\)
\(992\) −33.3993 −1.06043
\(993\) 0 0
\(994\) 0 0
\(995\) 13.1212 0.415969
\(996\) 0 0
\(997\) 34.0259 1.07761 0.538805 0.842431i \(-0.318876\pi\)
0.538805 + 0.842431i \(0.318876\pi\)
\(998\) −9.41107 −0.297902
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5733.2.a.bs.1.4 6
3.2 odd 2 inner 5733.2.a.bs.1.3 6
7.2 even 3 819.2.j.i.235.3 12
7.4 even 3 819.2.j.i.352.3 yes 12
7.6 odd 2 5733.2.a.bt.1.4 6
21.2 odd 6 819.2.j.i.235.4 yes 12
21.11 odd 6 819.2.j.i.352.4 yes 12
21.20 even 2 5733.2.a.bt.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.j.i.235.3 12 7.2 even 3
819.2.j.i.235.4 yes 12 21.2 odd 6
819.2.j.i.352.3 yes 12 7.4 even 3
819.2.j.i.352.4 yes 12 21.11 odd 6
5733.2.a.bs.1.3 6 3.2 odd 2 inner
5733.2.a.bs.1.4 6 1.1 even 1 trivial
5733.2.a.bt.1.3 6 21.20 even 2
5733.2.a.bt.1.4 6 7.6 odd 2