Properties

Label 2925.2.a.bp.1.5
Level $2925$
Weight $2$
Character 2925.1
Self dual yes
Analytic conductor $23.356$
Analytic rank $0$
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] = [2925,2,Mod(1,2925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2925, 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("2925.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2925.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: \(23.3562425912\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.1509051136.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 13x^{4} + 43x^{2} - 19 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(2.16355\) of defining polynomial
Character \(\chi\) \(=\) 2925.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.16355 q^{2} +2.68093 q^{4} +3.26817 q^{7} +1.47322 q^{8} +O(q^{10})\) \(q+2.16355 q^{2} +2.68093 q^{4} +3.26817 q^{7} +1.47322 q^{8} -2.85387 q^{11} -1.00000 q^{13} +7.07083 q^{14} -2.17448 q^{16} +6.38050 q^{17} +3.68093 q^{19} -6.17448 q^{22} +5.01742 q^{23} -2.16355 q^{26} +8.76172 q^{28} -2.05341 q^{29} +5.58724 q^{31} -7.65103 q^{32} +13.8045 q^{34} +10.2173 q^{37} +7.96385 q^{38} -5.01742 q^{41} +0.319072 q^{43} -7.65103 q^{44} +10.8554 q^{46} -2.16355 q^{47} +3.68093 q^{49} -2.68093 q^{52} +2.96401 q^{53} +4.81472 q^{56} -4.44265 q^{58} +6.49064 q^{59} +12.1745 q^{61} +12.0882 q^{62} -12.2044 q^{64} -7.58724 q^{67} +17.1057 q^{68} -16.3978 q^{71} -5.04278 q^{73} +22.1055 q^{74} +9.86830 q^{76} -9.32694 q^{77} +0.957217 q^{79} -10.8554 q^{82} +10.5975 q^{83} +0.690328 q^{86} -4.20438 q^{88} +7.05326 q^{89} -3.26817 q^{91} +13.4513 q^{92} -4.68093 q^{94} -10.5363 q^{97} +7.96385 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 14 q^{4} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 14 q^{4} - 6 q^{7} - 6 q^{13} + 34 q^{16} + 20 q^{19} + 10 q^{22} - 18 q^{28} + 10 q^{31} + 6 q^{34} + 8 q^{37} + 4 q^{43} + 16 q^{46} + 20 q^{49} - 14 q^{52} + 46 q^{58} + 26 q^{61} + 70 q^{64} - 22 q^{67} - 24 q^{73} + 100 q^{76} + 12 q^{79} - 16 q^{82} + 118 q^{88} + 6 q^{91} - 26 q^{94} - 12 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.16355 1.52986 0.764929 0.644115i \(-0.222774\pi\)
0.764929 + 0.644115i \(0.222774\pi\)
\(3\) 0 0
\(4\) 2.68093 1.34046
\(5\) 0 0
\(6\) 0 0
\(7\) 3.26817 1.23525 0.617626 0.786472i \(-0.288095\pi\)
0.617626 + 0.786472i \(0.288095\pi\)
\(8\) 1.47322 0.520861
\(9\) 0 0
\(10\) 0 0
\(11\) −2.85387 −0.860475 −0.430238 0.902716i \(-0.641570\pi\)
−0.430238 + 0.902716i \(0.641570\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 7.07083 1.88976
\(15\) 0 0
\(16\) −2.17448 −0.543621
\(17\) 6.38050 1.54750 0.773750 0.633491i \(-0.218379\pi\)
0.773750 + 0.633491i \(0.218379\pi\)
\(18\) 0 0
\(19\) 3.68093 0.844463 0.422231 0.906488i \(-0.361247\pi\)
0.422231 + 0.906488i \(0.361247\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −6.17448 −1.31640
\(23\) 5.01742 1.04620 0.523102 0.852270i \(-0.324775\pi\)
0.523102 + 0.852270i \(0.324775\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.16355 −0.424306
\(27\) 0 0
\(28\) 8.76172 1.65581
\(29\) −2.05341 −0.381309 −0.190655 0.981657i \(-0.561061\pi\)
−0.190655 + 0.981657i \(0.561061\pi\)
\(30\) 0 0
\(31\) 5.58724 1.00350 0.501749 0.865013i \(-0.332690\pi\)
0.501749 + 0.865013i \(0.332690\pi\)
\(32\) −7.65103 −1.35252
\(33\) 0 0
\(34\) 13.8045 2.36745
\(35\) 0 0
\(36\) 0 0
\(37\) 10.2173 1.67971 0.839854 0.542812i \(-0.182641\pi\)
0.839854 + 0.542812i \(0.182641\pi\)
\(38\) 7.96385 1.29191
\(39\) 0 0
\(40\) 0 0
\(41\) −5.01742 −0.783589 −0.391795 0.920053i \(-0.628146\pi\)
−0.391795 + 0.920053i \(0.628146\pi\)
\(42\) 0 0
\(43\) 0.319072 0.0486581 0.0243290 0.999704i \(-0.492255\pi\)
0.0243290 + 0.999704i \(0.492255\pi\)
\(44\) −7.65103 −1.15344
\(45\) 0 0
\(46\) 10.8554 1.60054
\(47\) −2.16355 −0.315585 −0.157793 0.987472i \(-0.550438\pi\)
−0.157793 + 0.987472i \(0.550438\pi\)
\(48\) 0 0
\(49\) 3.68093 0.525847
\(50\) 0 0
\(51\) 0 0
\(52\) −2.68093 −0.371778
\(53\) 2.96401 0.407137 0.203569 0.979061i \(-0.434746\pi\)
0.203569 + 0.979061i \(0.434746\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 4.81472 0.643394
\(57\) 0 0
\(58\) −4.44265 −0.583349
\(59\) 6.49064 0.845009 0.422504 0.906361i \(-0.361151\pi\)
0.422504 + 0.906361i \(0.361151\pi\)
\(60\) 0 0
\(61\) 12.1745 1.55878 0.779391 0.626537i \(-0.215528\pi\)
0.779391 + 0.626537i \(0.215528\pi\)
\(62\) 12.0882 1.53521
\(63\) 0 0
\(64\) −12.2044 −1.52555
\(65\) 0 0
\(66\) 0 0
\(67\) −7.58724 −0.926929 −0.463465 0.886115i \(-0.653394\pi\)
−0.463465 + 0.886115i \(0.653394\pi\)
\(68\) 17.1057 2.07437
\(69\) 0 0
\(70\) 0 0
\(71\) −16.3978 −1.94606 −0.973029 0.230685i \(-0.925903\pi\)
−0.973029 + 0.230685i \(0.925903\pi\)
\(72\) 0 0
\(73\) −5.04278 −0.590213 −0.295107 0.955464i \(-0.595355\pi\)
−0.295107 + 0.955464i \(0.595355\pi\)
\(74\) 22.1055 2.56971
\(75\) 0 0
\(76\) 9.86830 1.13197
\(77\) −9.32694 −1.06290
\(78\) 0 0
\(79\) 0.957217 0.107695 0.0538477 0.998549i \(-0.482851\pi\)
0.0538477 + 0.998549i \(0.482851\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −10.8554 −1.19878
\(83\) 10.5975 1.16322 0.581611 0.813467i \(-0.302423\pi\)
0.581611 + 0.813467i \(0.302423\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.690328 0.0744399
\(87\) 0 0
\(88\) −4.20438 −0.448188
\(89\) 7.05326 0.747644 0.373822 0.927500i \(-0.378047\pi\)
0.373822 + 0.927500i \(0.378047\pi\)
\(90\) 0 0
\(91\) −3.26817 −0.342597
\(92\) 13.4513 1.40240
\(93\) 0 0
\(94\) −4.68093 −0.482801
\(95\) 0 0
\(96\) 0 0
\(97\) −10.5363 −1.06980 −0.534902 0.844914i \(-0.679651\pi\)
−0.534902 + 0.844914i \(0.679651\pi\)
\(98\) 7.96385 0.804471
\(99\) 0 0
\(100\) 0 0
\(101\) −7.29110 −0.725491 −0.362746 0.931888i \(-0.618161\pi\)
−0.362746 + 0.931888i \(0.618161\pi\)
\(102\) 0 0
\(103\) 5.68093 0.559758 0.279879 0.960035i \(-0.409706\pi\)
0.279879 + 0.960035i \(0.409706\pi\)
\(104\) −1.47322 −0.144461
\(105\) 0 0
\(106\) 6.41276 0.622862
\(107\) −5.70775 −0.551789 −0.275894 0.961188i \(-0.588974\pi\)
−0.275894 + 0.961188i \(0.588974\pi\)
\(108\) 0 0
\(109\) 4.95722 0.474815 0.237408 0.971410i \(-0.423702\pi\)
0.237408 + 0.971410i \(0.423702\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −7.10658 −0.671508
\(113\) −17.0881 −1.60751 −0.803756 0.594958i \(-0.797168\pi\)
−0.803756 + 0.594958i \(0.797168\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −5.50505 −0.511131
\(117\) 0 0
\(118\) 14.0428 1.29274
\(119\) 20.8526 1.91155
\(120\) 0 0
\(121\) −2.85541 −0.259583
\(122\) 26.3400 2.38472
\(123\) 0 0
\(124\) 14.9790 1.34515
\(125\) 0 0
\(126\) 0 0
\(127\) 11.5791 1.02748 0.513740 0.857946i \(-0.328259\pi\)
0.513740 + 0.857946i \(0.328259\pi\)
\(128\) −11.1027 −0.981346
\(129\) 0 0
\(130\) 0 0
\(131\) 9.12424 0.797189 0.398594 0.917127i \(-0.369498\pi\)
0.398594 + 0.917127i \(0.369498\pi\)
\(132\) 0 0
\(133\) 12.0299 1.04312
\(134\) −16.4153 −1.41807
\(135\) 0 0
\(136\) 9.39987 0.806032
\(137\) −17.0881 −1.45993 −0.729967 0.683482i \(-0.760465\pi\)
−0.729967 + 0.683482i \(0.760465\pi\)
\(138\) 0 0
\(139\) −18.4345 −1.56360 −0.781798 0.623531i \(-0.785697\pi\)
−0.781798 + 0.623531i \(0.785697\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −35.4773 −2.97719
\(143\) 2.85387 0.238653
\(144\) 0 0
\(145\) 0 0
\(146\) −10.9103 −0.902942
\(147\) 0 0
\(148\) 27.3917 2.25159
\(149\) −2.94643 −0.241381 −0.120691 0.992690i \(-0.538511\pi\)
−0.120691 + 0.992690i \(0.538511\pi\)
\(150\) 0 0
\(151\) 2.54446 0.207065 0.103533 0.994626i \(-0.466985\pi\)
0.103533 + 0.994626i \(0.466985\pi\)
\(152\) 5.42281 0.439848
\(153\) 0 0
\(154\) −20.1793 −1.62609
\(155\) 0 0
\(156\) 0 0
\(157\) 8.04278 0.641884 0.320942 0.947099i \(-0.396001\pi\)
0.320942 + 0.947099i \(0.396001\pi\)
\(158\) 2.07098 0.164759
\(159\) 0 0
\(160\) 0 0
\(161\) 16.3978 1.29233
\(162\) 0 0
\(163\) −13.3917 −1.04892 −0.524461 0.851434i \(-0.675733\pi\)
−0.524461 + 0.851434i \(0.675733\pi\)
\(164\) −13.4513 −1.05037
\(165\) 0 0
\(166\) 22.9281 1.77956
\(167\) −17.9987 −1.39278 −0.696390 0.717663i \(-0.745212\pi\)
−0.696390 + 0.717663i \(0.745212\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0.855410 0.0652244
\(173\) −7.29110 −0.554332 −0.277166 0.960822i \(-0.589395\pi\)
−0.277166 + 0.960822i \(0.589395\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.20570 0.467772
\(177\) 0 0
\(178\) 15.2600 1.14379
\(179\) −7.96385 −0.595246 −0.297623 0.954683i \(-0.596194\pi\)
−0.297623 + 0.954683i \(0.596194\pi\)
\(180\) 0 0
\(181\) −17.3028 −1.28611 −0.643055 0.765820i \(-0.722333\pi\)
−0.643055 + 0.765820i \(0.722333\pi\)
\(182\) −7.07083 −0.524125
\(183\) 0 0
\(184\) 7.39175 0.544927
\(185\) 0 0
\(186\) 0 0
\(187\) −18.2091 −1.33158
\(188\) −5.80031 −0.423031
\(189\) 0 0
\(190\) 0 0
\(191\) −11.3804 −0.823453 −0.411727 0.911307i \(-0.635074\pi\)
−0.411727 + 0.911307i \(0.635074\pi\)
\(192\) 0 0
\(193\) 20.1155 1.44794 0.723971 0.689830i \(-0.242315\pi\)
0.723971 + 0.689830i \(0.242315\pi\)
\(194\) −22.7958 −1.63665
\(195\) 0 0
\(196\) 9.86830 0.704879
\(197\) 15.0523 1.07243 0.536214 0.844082i \(-0.319854\pi\)
0.536214 + 0.844082i \(0.319854\pi\)
\(198\) 0 0
\(199\) −10.4345 −0.739684 −0.369842 0.929095i \(-0.620588\pi\)
−0.369842 + 0.929095i \(0.620588\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −15.7746 −1.10990
\(203\) −6.71090 −0.471013
\(204\) 0 0
\(205\) 0 0
\(206\) 12.2909 0.856351
\(207\) 0 0
\(208\) 2.17448 0.150773
\(209\) −10.5049 −0.726639
\(210\) 0 0
\(211\) 16.8554 1.16037 0.580187 0.814483i \(-0.302979\pi\)
0.580187 + 0.814483i \(0.302979\pi\)
\(212\) 7.94628 0.545753
\(213\) 0 0
\(214\) −12.3490 −0.844158
\(215\) 0 0
\(216\) 0 0
\(217\) 18.2600 1.23957
\(218\) 10.7252 0.726400
\(219\) 0 0
\(220\) 0 0
\(221\) −6.38050 −0.429199
\(222\) 0 0
\(223\) −21.3917 −1.43250 −0.716249 0.697845i \(-0.754142\pi\)
−0.716249 + 0.697845i \(0.754142\pi\)
\(224\) −25.0048 −1.67071
\(225\) 0 0
\(226\) −36.9709 −2.45927
\(227\) −8.78188 −0.582874 −0.291437 0.956590i \(-0.594133\pi\)
−0.291437 + 0.956590i \(0.594133\pi\)
\(228\) 0 0
\(229\) 21.7964 1.44035 0.720173 0.693795i \(-0.244062\pi\)
0.720173 + 0.693795i \(0.244062\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.02512 −0.198609
\(233\) 15.7074 1.02903 0.514514 0.857482i \(-0.327972\pi\)
0.514514 + 0.857482i \(0.327972\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 17.4009 1.13270
\(237\) 0 0
\(238\) 45.1155 2.92440
\(239\) 24.9594 1.61449 0.807244 0.590217i \(-0.200958\pi\)
0.807244 + 0.590217i \(0.200958\pi\)
\(240\) 0 0
\(241\) −9.39175 −0.604976 −0.302488 0.953153i \(-0.597817\pi\)
−0.302488 + 0.953153i \(0.597817\pi\)
\(242\) −6.17781 −0.397125
\(243\) 0 0
\(244\) 32.6389 2.08949
\(245\) 0 0
\(246\) 0 0
\(247\) −3.68093 −0.234212
\(248\) 8.23122 0.522683
\(249\) 0 0
\(250\) 0 0
\(251\) 12.1058 0.764113 0.382056 0.924139i \(-0.375216\pi\)
0.382056 + 0.924139i \(0.375216\pi\)
\(252\) 0 0
\(253\) −14.3191 −0.900232
\(254\) 25.0519 1.57190
\(255\) 0 0
\(256\) 0.387635 0.0242272
\(257\) −11.6182 −0.724723 −0.362361 0.932038i \(-0.618029\pi\)
−0.362361 + 0.932038i \(0.618029\pi\)
\(258\) 0 0
\(259\) 33.3917 2.07486
\(260\) 0 0
\(261\) 0 0
\(262\) 19.7407 1.21959
\(263\) −26.2123 −1.61632 −0.808161 0.588962i \(-0.799537\pi\)
−0.808161 + 0.588962i \(0.799537\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 26.0272 1.59583
\(267\) 0 0
\(268\) −20.3408 −1.24251
\(269\) 22.3433 1.36230 0.681149 0.732145i \(-0.261481\pi\)
0.681149 + 0.732145i \(0.261481\pi\)
\(270\) 0 0
\(271\) 23.8045 1.44602 0.723010 0.690837i \(-0.242758\pi\)
0.723010 + 0.690837i \(0.242758\pi\)
\(272\) −13.8743 −0.841253
\(273\) 0 0
\(274\) −36.9709 −2.23349
\(275\) 0 0
\(276\) 0 0
\(277\) 32.8853 1.97589 0.987943 0.154817i \(-0.0494788\pi\)
0.987943 + 0.154817i \(0.0494788\pi\)
\(278\) −39.8839 −2.39208
\(279\) 0 0
\(280\) 0 0
\(281\) −11.3804 −0.678895 −0.339447 0.940625i \(-0.610240\pi\)
−0.339447 + 0.940625i \(0.610240\pi\)
\(282\) 0 0
\(283\) 3.91443 0.232689 0.116344 0.993209i \(-0.462882\pi\)
0.116344 + 0.993209i \(0.462882\pi\)
\(284\) −43.9612 −2.60862
\(285\) 0 0
\(286\) 6.17448 0.365105
\(287\) −16.3978 −0.967930
\(288\) 0 0
\(289\) 23.7108 1.39475
\(290\) 0 0
\(291\) 0 0
\(292\) −13.5193 −0.791159
\(293\) −34.2113 −1.99865 −0.999324 0.0367711i \(-0.988293\pi\)
−0.999324 + 0.0367711i \(0.988293\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 15.0523 0.874894
\(297\) 0 0
\(298\) −6.37475 −0.369279
\(299\) −5.01742 −0.290165
\(300\) 0 0
\(301\) 1.04278 0.0601050
\(302\) 5.50505 0.316780
\(303\) 0 0
\(304\) −8.00411 −0.459067
\(305\) 0 0
\(306\) 0 0
\(307\) −25.9281 −1.47979 −0.739897 0.672720i \(-0.765126\pi\)
−0.739897 + 0.672720i \(0.765126\pi\)
\(308\) −25.0048 −1.42478
\(309\) 0 0
\(310\) 0 0
\(311\) 20.0345 1.13605 0.568027 0.823010i \(-0.307707\pi\)
0.568027 + 0.823010i \(0.307707\pi\)
\(312\) 0 0
\(313\) 13.7536 0.777400 0.388700 0.921364i \(-0.372924\pi\)
0.388700 + 0.921364i \(0.372924\pi\)
\(314\) 17.4009 0.981991
\(315\) 0 0
\(316\) 2.56623 0.144362
\(317\) −17.9987 −1.01091 −0.505454 0.862854i \(-0.668675\pi\)
−0.505454 + 0.862854i \(0.668675\pi\)
\(318\) 0 0
\(319\) 5.86018 0.328107
\(320\) 0 0
\(321\) 0 0
\(322\) 35.4773 1.97707
\(323\) 23.4862 1.30681
\(324\) 0 0
\(325\) 0 0
\(326\) −28.9737 −1.60470
\(327\) 0 0
\(328\) −7.39175 −0.408141
\(329\) −7.07083 −0.389828
\(330\) 0 0
\(331\) 8.31907 0.457258 0.228629 0.973514i \(-0.426576\pi\)
0.228629 + 0.973514i \(0.426576\pi\)
\(332\) 28.4110 1.55926
\(333\) 0 0
\(334\) −38.9410 −2.13076
\(335\) 0 0
\(336\) 0 0
\(337\) −27.0137 −1.47153 −0.735764 0.677238i \(-0.763177\pi\)
−0.735764 + 0.677238i \(0.763177\pi\)
\(338\) 2.16355 0.117681
\(339\) 0 0
\(340\) 0 0
\(341\) −15.9453 −0.863485
\(342\) 0 0
\(343\) −10.8473 −0.585699
\(344\) 0.470063 0.0253441
\(345\) 0 0
\(346\) −15.7746 −0.848048
\(347\) 24.1765 1.29786 0.648931 0.760847i \(-0.275216\pi\)
0.648931 + 0.760847i \(0.275216\pi\)
\(348\) 0 0
\(349\) −6.21727 −0.332803 −0.166401 0.986058i \(-0.553215\pi\)
−0.166401 + 0.986058i \(0.553215\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 21.8351 1.16381
\(353\) −30.9800 −1.64890 −0.824448 0.565937i \(-0.808515\pi\)
−0.824448 + 0.565937i \(0.808515\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 18.9093 1.00219
\(357\) 0 0
\(358\) −17.2302 −0.910642
\(359\) 3.50906 0.185201 0.0926006 0.995703i \(-0.470482\pi\)
0.0926006 + 0.995703i \(0.470482\pi\)
\(360\) 0 0
\(361\) −5.45077 −0.286883
\(362\) −37.4355 −1.96756
\(363\) 0 0
\(364\) −8.76172 −0.459239
\(365\) 0 0
\(366\) 0 0
\(367\) −5.71082 −0.298102 −0.149051 0.988829i \(-0.547622\pi\)
−0.149051 + 0.988829i \(0.547622\pi\)
\(368\) −10.9103 −0.568738
\(369\) 0 0
\(370\) 0 0
\(371\) 9.68687 0.502917
\(372\) 0 0
\(373\) −26.4936 −1.37178 −0.685892 0.727703i \(-0.740588\pi\)
−0.685892 + 0.727703i \(0.740588\pi\)
\(374\) −39.3963 −2.03713
\(375\) 0 0
\(376\) −3.18737 −0.164376
\(377\) 2.05341 0.105756
\(378\) 0 0
\(379\) 22.3110 1.14604 0.573018 0.819543i \(-0.305772\pi\)
0.573018 + 0.819543i \(0.305772\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −24.6219 −1.25977
\(383\) −26.4326 −1.35064 −0.675322 0.737523i \(-0.735995\pi\)
−0.675322 + 0.737523i \(0.735995\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 43.5207 2.21515
\(387\) 0 0
\(388\) −28.2472 −1.43403
\(389\) −2.98158 −0.151172 −0.0755859 0.997139i \(-0.524083\pi\)
−0.0755859 + 0.997139i \(0.524083\pi\)
\(390\) 0 0
\(391\) 32.0137 1.61900
\(392\) 5.42281 0.273893
\(393\) 0 0
\(394\) 32.5662 1.64066
\(395\) 0 0
\(396\) 0 0
\(397\) 21.8982 1.09904 0.549519 0.835481i \(-0.314811\pi\)
0.549519 + 0.835481i \(0.314811\pi\)
\(398\) −22.5756 −1.13161
\(399\) 0 0
\(400\) 0 0
\(401\) −19.1591 −0.956759 −0.478379 0.878153i \(-0.658776\pi\)
−0.478379 + 0.878153i \(0.658776\pi\)
\(402\) 0 0
\(403\) −5.58724 −0.278320
\(404\) −19.5469 −0.972495
\(405\) 0 0
\(406\) −14.5193 −0.720582
\(407\) −29.1588 −1.44535
\(408\) 0 0
\(409\) 20.0137 0.989611 0.494806 0.869004i \(-0.335239\pi\)
0.494806 + 0.869004i \(0.335239\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 15.2302 0.750336
\(413\) 21.2125 1.04380
\(414\) 0 0
\(415\) 0 0
\(416\) 7.65103 0.375122
\(417\) 0 0
\(418\) −22.7278 −1.11165
\(419\) −19.3793 −0.946743 −0.473371 0.880863i \(-0.656963\pi\)
−0.473371 + 0.880863i \(0.656963\pi\)
\(420\) 0 0
\(421\) −34.3490 −1.67407 −0.837033 0.547152i \(-0.815712\pi\)
−0.837033 + 0.547152i \(0.815712\pi\)
\(422\) 36.4674 1.77521
\(423\) 0 0
\(424\) 4.36662 0.212062
\(425\) 0 0
\(426\) 0 0
\(427\) 39.7883 1.92549
\(428\) −15.3021 −0.739653
\(429\) 0 0
\(430\) 0 0
\(431\) 12.3261 0.593727 0.296863 0.954920i \(-0.404059\pi\)
0.296863 + 0.954920i \(0.404059\pi\)
\(432\) 0 0
\(433\) −30.3327 −1.45770 −0.728849 0.684675i \(-0.759944\pi\)
−0.728849 + 0.684675i \(0.759944\pi\)
\(434\) 39.5064 1.89637
\(435\) 0 0
\(436\) 13.2899 0.636473
\(437\) 18.4688 0.883480
\(438\) 0 0
\(439\) 14.1317 0.674469 0.337235 0.941421i \(-0.390508\pi\)
0.337235 + 0.941421i \(0.390508\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −13.8045 −0.656613
\(443\) −14.8320 −0.704689 −0.352345 0.935870i \(-0.614615\pi\)
−0.352345 + 0.935870i \(0.614615\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −46.2820 −2.19152
\(447\) 0 0
\(448\) −39.8860 −1.88443
\(449\) −36.9375 −1.74319 −0.871594 0.490228i \(-0.836914\pi\)
−0.871594 + 0.490228i \(0.836914\pi\)
\(450\) 0 0
\(451\) 14.3191 0.674259
\(452\) −45.8119 −2.15481
\(453\) 0 0
\(454\) −19.0000 −0.891714
\(455\) 0 0
\(456\) 0 0
\(457\) 7.78273 0.364061 0.182030 0.983293i \(-0.441733\pi\)
0.182030 + 0.983293i \(0.441733\pi\)
\(458\) 47.1575 2.20352
\(459\) 0 0
\(460\) 0 0
\(461\) −24.1765 −1.12601 −0.563006 0.826453i \(-0.690355\pi\)
−0.563006 + 0.826453i \(0.690355\pi\)
\(462\) 0 0
\(463\) −5.13647 −0.238712 −0.119356 0.992852i \(-0.538083\pi\)
−0.119356 + 0.992852i \(0.538083\pi\)
\(464\) 4.46511 0.207288
\(465\) 0 0
\(466\) 33.9838 1.57427
\(467\) −8.87445 −0.410660 −0.205330 0.978693i \(-0.565827\pi\)
−0.205330 + 0.978693i \(0.565827\pi\)
\(468\) 0 0
\(469\) −24.7964 −1.14499
\(470\) 0 0
\(471\) 0 0
\(472\) 9.56212 0.440132
\(473\) −0.910592 −0.0418691
\(474\) 0 0
\(475\) 0 0
\(476\) 55.9042 2.56237
\(477\) 0 0
\(478\) 54.0008 2.46994
\(479\) −42.7027 −1.95113 −0.975567 0.219700i \(-0.929492\pi\)
−0.975567 + 0.219700i \(0.929492\pi\)
\(480\) 0 0
\(481\) −10.2173 −0.465867
\(482\) −20.3195 −0.925527
\(483\) 0 0
\(484\) −7.65515 −0.347961
\(485\) 0 0
\(486\) 0 0
\(487\) −30.1073 −1.36429 −0.682147 0.731215i \(-0.738954\pi\)
−0.682147 + 0.731215i \(0.738954\pi\)
\(488\) 17.9357 0.811909
\(489\) 0 0
\(490\) 0 0
\(491\) −31.4500 −1.41932 −0.709660 0.704544i \(-0.751151\pi\)
−0.709660 + 0.704544i \(0.751151\pi\)
\(492\) 0 0
\(493\) −13.1018 −0.590076
\(494\) −7.96385 −0.358311
\(495\) 0 0
\(496\) −12.1494 −0.545522
\(497\) −53.5907 −2.40387
\(498\) 0 0
\(499\) 22.0937 0.989049 0.494525 0.869164i \(-0.335342\pi\)
0.494525 + 0.869164i \(0.335342\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 26.1915 1.16898
\(503\) −3.67190 −0.163722 −0.0818610 0.996644i \(-0.526086\pi\)
−0.0818610 + 0.996644i \(0.526086\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −30.9800 −1.37723
\(507\) 0 0
\(508\) 31.0428 1.37730
\(509\) 43.5558 1.93058 0.965289 0.261183i \(-0.0841125\pi\)
0.965289 + 0.261183i \(0.0841125\pi\)
\(510\) 0 0
\(511\) −16.4807 −0.729062
\(512\) 23.0440 1.01841
\(513\) 0 0
\(514\) −25.1365 −1.10872
\(515\) 0 0
\(516\) 0 0
\(517\) 6.17448 0.271553
\(518\) 72.2446 3.17424
\(519\) 0 0
\(520\) 0 0
\(521\) 10.0348 0.439634 0.219817 0.975541i \(-0.429454\pi\)
0.219817 + 0.975541i \(0.429454\pi\)
\(522\) 0 0
\(523\) −21.5234 −0.941155 −0.470577 0.882359i \(-0.655954\pi\)
−0.470577 + 0.882359i \(0.655954\pi\)
\(524\) 24.4614 1.06860
\(525\) 0 0
\(526\) −56.7116 −2.47274
\(527\) 35.6494 1.55291
\(528\) 0 0
\(529\) 2.17448 0.0945427
\(530\) 0 0
\(531\) 0 0
\(532\) 32.2513 1.39827
\(533\) 5.01742 0.217328
\(534\) 0 0
\(535\) 0 0
\(536\) −11.1777 −0.482801
\(537\) 0 0
\(538\) 48.3408 2.08412
\(539\) −10.5049 −0.452478
\(540\) 0 0
\(541\) −3.97011 −0.170688 −0.0853441 0.996352i \(-0.527199\pi\)
−0.0853441 + 0.996352i \(0.527199\pi\)
\(542\) 51.5021 2.21221
\(543\) 0 0
\(544\) −48.8174 −2.09303
\(545\) 0 0
\(546\) 0 0
\(547\) 43.3917 1.85530 0.927649 0.373454i \(-0.121827\pi\)
0.927649 + 0.373454i \(0.121827\pi\)
\(548\) −45.8119 −1.95699
\(549\) 0 0
\(550\) 0 0
\(551\) −7.55846 −0.322001
\(552\) 0 0
\(553\) 3.12835 0.133031
\(554\) 71.1488 3.02282
\(555\) 0 0
\(556\) −49.4216 −2.09594
\(557\) 10.6900 0.452951 0.226475 0.974017i \(-0.427280\pi\)
0.226475 + 0.974017i \(0.427280\pi\)
\(558\) 0 0
\(559\) −0.319072 −0.0134953
\(560\) 0 0
\(561\) 0 0
\(562\) −24.6219 −1.03861
\(563\) −3.19623 −0.134705 −0.0673526 0.997729i \(-0.521455\pi\)
−0.0673526 + 0.997729i \(0.521455\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 8.46906 0.355981
\(567\) 0 0
\(568\) −24.1575 −1.01363
\(569\) 16.8503 0.706400 0.353200 0.935548i \(-0.385094\pi\)
0.353200 + 0.935548i \(0.385094\pi\)
\(570\) 0 0
\(571\) −2.13170 −0.0892089 −0.0446044 0.999005i \(-0.514203\pi\)
−0.0446044 + 0.999005i \(0.514203\pi\)
\(572\) 7.65103 0.319905
\(573\) 0 0
\(574\) −35.4773 −1.48079
\(575\) 0 0
\(576\) 0 0
\(577\) 10.1018 0.420544 0.210272 0.977643i \(-0.432565\pi\)
0.210272 + 0.977643i \(0.432565\pi\)
\(578\) 51.2994 2.13377
\(579\) 0 0
\(580\) 0 0
\(581\) 34.6343 1.43687
\(582\) 0 0
\(583\) −8.45889 −0.350332
\(584\) −7.42912 −0.307419
\(585\) 0 0
\(586\) −74.0178 −3.05765
\(587\) 24.2691 1.00169 0.500846 0.865537i \(-0.333022\pi\)
0.500846 + 0.865537i \(0.333022\pi\)
\(588\) 0 0
\(589\) 20.5662 0.847417
\(590\) 0 0
\(591\) 0 0
\(592\) −22.2173 −0.913124
\(593\) 17.3435 0.712212 0.356106 0.934446i \(-0.384104\pi\)
0.356106 + 0.934446i \(0.384104\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −7.89918 −0.323563
\(597\) 0 0
\(598\) −10.8554 −0.443911
\(599\) −20.9803 −0.857230 −0.428615 0.903487i \(-0.640998\pi\)
−0.428615 + 0.903487i \(0.640998\pi\)
\(600\) 0 0
\(601\) −31.7536 −1.29526 −0.647628 0.761956i \(-0.724239\pi\)
−0.647628 + 0.761956i \(0.724239\pi\)
\(602\) 2.25611 0.0919521
\(603\) 0 0
\(604\) 6.82151 0.277563
\(605\) 0 0
\(606\) 0 0
\(607\) −2.73995 −0.111211 −0.0556056 0.998453i \(-0.517709\pi\)
−0.0556056 + 0.998453i \(0.517709\pi\)
\(608\) −28.1629 −1.14216
\(609\) 0 0
\(610\) 0 0
\(611\) 2.16355 0.0875277
\(612\) 0 0
\(613\) 23.5072 0.949447 0.474724 0.880135i \(-0.342548\pi\)
0.474724 + 0.880135i \(0.342548\pi\)
\(614\) −56.0966 −2.26387
\(615\) 0 0
\(616\) −13.7406 −0.553625
\(617\) 12.9813 0.522606 0.261303 0.965257i \(-0.415848\pi\)
0.261303 + 0.965257i \(0.415848\pi\)
\(618\) 0 0
\(619\) 28.2173 1.13415 0.567074 0.823667i \(-0.308075\pi\)
0.567074 + 0.823667i \(0.308075\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 43.3456 1.73800
\(623\) 23.0512 0.923529
\(624\) 0 0
\(625\) 0 0
\(626\) 29.7565 1.18931
\(627\) 0 0
\(628\) 21.5621 0.860422
\(629\) 65.1913 2.59935
\(630\) 0 0
\(631\) −8.65180 −0.344423 −0.172211 0.985060i \(-0.555091\pi\)
−0.172211 + 0.985060i \(0.555091\pi\)
\(632\) 1.41019 0.0560943
\(633\) 0 0
\(634\) −38.9410 −1.54654
\(635\) 0 0
\(636\) 0 0
\(637\) −3.68093 −0.145844
\(638\) 12.6788 0.501957
\(639\) 0 0
\(640\) 0 0
\(641\) 3.17866 0.125550 0.0627748 0.998028i \(-0.480005\pi\)
0.0627748 + 0.998028i \(0.480005\pi\)
\(642\) 0 0
\(643\) −4.52269 −0.178357 −0.0891787 0.996016i \(-0.528424\pi\)
−0.0891787 + 0.996016i \(0.528424\pi\)
\(644\) 43.9612 1.73232
\(645\) 0 0
\(646\) 50.8134 1.99923
\(647\) −6.61273 −0.259973 −0.129987 0.991516i \(-0.541493\pi\)
−0.129987 + 0.991516i \(0.541493\pi\)
\(648\) 0 0
\(649\) −18.5234 −0.727109
\(650\) 0 0
\(651\) 0 0
\(652\) −35.9023 −1.40604
\(653\) 45.1041 1.76506 0.882529 0.470258i \(-0.155839\pi\)
0.882529 + 0.470258i \(0.155839\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 10.9103 0.425975
\(657\) 0 0
\(658\) −15.2981 −0.596381
\(659\) 42.6157 1.66007 0.830036 0.557709i \(-0.188320\pi\)
0.830036 + 0.557709i \(0.188320\pi\)
\(660\) 0 0
\(661\) −8.42088 −0.327534 −0.163767 0.986499i \(-0.552365\pi\)
−0.163767 + 0.986499i \(0.552365\pi\)
\(662\) 17.9987 0.699539
\(663\) 0 0
\(664\) 15.6124 0.605877
\(665\) 0 0
\(666\) 0 0
\(667\) −10.3028 −0.398927
\(668\) −48.2532 −1.86697
\(669\) 0 0
\(670\) 0 0
\(671\) −34.7444 −1.34129
\(672\) 0 0
\(673\) −27.2173 −1.04915 −0.524574 0.851365i \(-0.675775\pi\)
−0.524574 + 0.851365i \(0.675775\pi\)
\(674\) −58.4453 −2.25123
\(675\) 0 0
\(676\) 2.68093 0.103113
\(677\) −15.9277 −0.612151 −0.306076 0.952007i \(-0.599016\pi\)
−0.306076 + 0.952007i \(0.599016\pi\)
\(678\) 0 0
\(679\) −34.4345 −1.32148
\(680\) 0 0
\(681\) 0 0
\(682\) −34.4983 −1.32101
\(683\) −25.3943 −0.971686 −0.485843 0.874046i \(-0.661487\pi\)
−0.485843 + 0.874046i \(0.661487\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −23.4686 −0.896035
\(687\) 0 0
\(688\) −0.693817 −0.0264515
\(689\) −2.96401 −0.112920
\(690\) 0 0
\(691\) 30.6898 1.16750 0.583748 0.811935i \(-0.301586\pi\)
0.583748 + 0.811935i \(0.301586\pi\)
\(692\) −19.5469 −0.743062
\(693\) 0 0
\(694\) 52.3069 1.98554
\(695\) 0 0
\(696\) 0 0
\(697\) −32.0137 −1.21260
\(698\) −13.4513 −0.509140
\(699\) 0 0
\(700\) 0 0
\(701\) 10.7427 0.405747 0.202874 0.979205i \(-0.434972\pi\)
0.202874 + 0.979205i \(0.434972\pi\)
\(702\) 0 0
\(703\) 37.6090 1.41845
\(704\) 34.8297 1.31270
\(705\) 0 0
\(706\) −67.0265 −2.52258
\(707\) −23.8285 −0.896164
\(708\) 0 0
\(709\) −25.2899 −0.949784 −0.474892 0.880044i \(-0.657513\pi\)
−0.474892 + 0.880044i \(0.657513\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 10.3910 0.389419
\(713\) 28.0335 1.04986
\(714\) 0 0
\(715\) 0 0
\(716\) −21.3505 −0.797906
\(717\) 0 0
\(718\) 7.59201 0.283331
\(719\) 42.1400 1.57156 0.785779 0.618507i \(-0.212262\pi\)
0.785779 + 0.618507i \(0.212262\pi\)
\(720\) 0 0
\(721\) 18.5662 0.691443
\(722\) −11.7930 −0.438890
\(723\) 0 0
\(724\) −46.3876 −1.72398
\(725\) 0 0
\(726\) 0 0
\(727\) 9.68093 0.359046 0.179523 0.983754i \(-0.442545\pi\)
0.179523 + 0.983754i \(0.442545\pi\)
\(728\) −4.81472 −0.178446
\(729\) 0 0
\(730\) 0 0
\(731\) 2.03584 0.0752984
\(732\) 0 0
\(733\) 24.9015 0.919760 0.459880 0.887981i \(-0.347893\pi\)
0.459880 + 0.887981i \(0.347893\pi\)
\(734\) −12.3556 −0.456054
\(735\) 0 0
\(736\) −38.3884 −1.41502
\(737\) 21.6530 0.797599
\(738\) 0 0
\(739\) −24.3707 −0.896492 −0.448246 0.893910i \(-0.647951\pi\)
−0.448246 + 0.893910i \(0.647951\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 20.9580 0.769392
\(743\) 16.7401 0.614136 0.307068 0.951688i \(-0.400652\pi\)
0.307068 + 0.951688i \(0.400652\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −57.3200 −2.09863
\(747\) 0 0
\(748\) −48.8174 −1.78494
\(749\) −18.6539 −0.681598
\(750\) 0 0
\(751\) −6.13170 −0.223749 −0.111874 0.993722i \(-0.535685\pi\)
−0.111874 + 0.993722i \(0.535685\pi\)
\(752\) 4.70459 0.171559
\(753\) 0 0
\(754\) 4.44265 0.161792
\(755\) 0 0
\(756\) 0 0
\(757\) 23.9871 0.871826 0.435913 0.899989i \(-0.356425\pi\)
0.435913 + 0.899989i \(0.356425\pi\)
\(758\) 48.2708 1.75327
\(759\) 0 0
\(760\) 0 0
\(761\) −20.6897 −0.750002 −0.375001 0.927024i \(-0.622358\pi\)
−0.375001 + 0.927024i \(0.622358\pi\)
\(762\) 0 0
\(763\) 16.2010 0.586516
\(764\) −30.5099 −1.10381
\(765\) 0 0
\(766\) −57.1881 −2.06629
\(767\) −6.49064 −0.234363
\(768\) 0 0
\(769\) −17.1745 −0.619328 −0.309664 0.950846i \(-0.600217\pi\)
−0.309664 + 0.950846i \(0.600217\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 53.9281 1.94091
\(773\) 24.3968 0.877491 0.438745 0.898611i \(-0.355423\pi\)
0.438745 + 0.898611i \(0.355423\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −15.5223 −0.557219
\(777\) 0 0
\(778\) −6.45077 −0.231271
\(779\) −18.4688 −0.661712
\(780\) 0 0
\(781\) 46.7971 1.67453
\(782\) 69.2630 2.47684
\(783\) 0 0
\(784\) −8.00411 −0.285861
\(785\) 0 0
\(786\) 0 0
\(787\) 12.7617 0.454906 0.227453 0.973789i \(-0.426960\pi\)
0.227453 + 0.973789i \(0.426960\pi\)
\(788\) 40.3540 1.43755
\(789\) 0 0
\(790\) 0 0
\(791\) −55.8468 −1.98568
\(792\) 0 0
\(793\) −12.1745 −0.432329
\(794\) 47.3777 1.68137
\(795\) 0 0
\(796\) −27.9742 −0.991520
\(797\) −2.01827 −0.0714909 −0.0357454 0.999361i \(-0.511381\pi\)
−0.0357454 + 0.999361i \(0.511381\pi\)
\(798\) 0 0
\(799\) −13.8045 −0.488368
\(800\) 0 0
\(801\) 0 0
\(802\) −41.4515 −1.46370
\(803\) 14.3915 0.507864
\(804\) 0 0
\(805\) 0 0
\(806\) −12.0882 −0.425790
\(807\) 0 0
\(808\) −10.7414 −0.377880
\(809\) −53.0855 −1.86639 −0.933193 0.359376i \(-0.882990\pi\)
−0.933193 + 0.359376i \(0.882990\pi\)
\(810\) 0 0
\(811\) −13.0808 −0.459329 −0.229664 0.973270i \(-0.573763\pi\)
−0.229664 + 0.973270i \(0.573763\pi\)
\(812\) −17.9914 −0.631376
\(813\) 0 0
\(814\) −63.0863 −2.21117
\(815\) 0 0
\(816\) 0 0
\(817\) 1.17448 0.0410899
\(818\) 43.3004 1.51396
\(819\) 0 0
\(820\) 0 0
\(821\) −0.910592 −0.0317799 −0.0158899 0.999874i \(-0.505058\pi\)
−0.0158899 + 0.999874i \(0.505058\pi\)
\(822\) 0 0
\(823\) 52.1616 1.81824 0.909119 0.416536i \(-0.136756\pi\)
0.909119 + 0.416536i \(0.136756\pi\)
\(824\) 8.36924 0.291556
\(825\) 0 0
\(826\) 45.8942 1.59686
\(827\) 47.5406 1.65315 0.826574 0.562828i \(-0.190287\pi\)
0.826574 + 0.562828i \(0.190287\pi\)
\(828\) 0 0
\(829\) −19.0435 −0.661410 −0.330705 0.943734i \(-0.607286\pi\)
−0.330705 + 0.943734i \(0.607286\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 12.2044 0.423111
\(833\) 23.4862 0.813748
\(834\) 0 0
\(835\) 0 0
\(836\) −28.1629 −0.974033
\(837\) 0 0
\(838\) −41.9281 −1.44838
\(839\) 39.2288 1.35433 0.677163 0.735833i \(-0.263209\pi\)
0.677163 + 0.735833i \(0.263209\pi\)
\(840\) 0 0
\(841\) −24.7835 −0.854603
\(842\) −74.3155 −2.56108
\(843\) 0 0
\(844\) 45.1881 1.55544
\(845\) 0 0
\(846\) 0 0
\(847\) −9.33196 −0.320650
\(848\) −6.44518 −0.221328
\(849\) 0 0
\(850\) 0 0
\(851\) 51.2643 1.75732
\(852\) 0 0
\(853\) −3.82887 −0.131098 −0.0655490 0.997849i \(-0.520880\pi\)
−0.0655490 + 0.997849i \(0.520880\pi\)
\(854\) 86.0837 2.94572
\(855\) 0 0
\(856\) −8.40875 −0.287405
\(857\) −14.1768 −0.484270 −0.242135 0.970243i \(-0.577848\pi\)
−0.242135 + 0.970243i \(0.577848\pi\)
\(858\) 0 0
\(859\) 37.1881 1.26884 0.634421 0.772987i \(-0.281238\pi\)
0.634421 + 0.772987i \(0.281238\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 26.6680 0.908317
\(863\) 4.41965 0.150447 0.0752234 0.997167i \(-0.476033\pi\)
0.0752234 + 0.997167i \(0.476033\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −65.6262 −2.23007
\(867\) 0 0
\(868\) 48.9539 1.66160
\(869\) −2.73178 −0.0926692
\(870\) 0 0
\(871\) 7.58724 0.257084
\(872\) 7.30306 0.247313
\(873\) 0 0
\(874\) 39.9580 1.35160
\(875\) 0 0
\(876\) 0 0
\(877\) 40.3327 1.36194 0.680970 0.732312i \(-0.261559\pi\)
0.680970 + 0.732312i \(0.261559\pi\)
\(878\) 30.5746 1.03184
\(879\) 0 0
\(880\) 0 0
\(881\) −22.9985 −0.774840 −0.387420 0.921903i \(-0.626634\pi\)
−0.387420 + 0.921903i \(0.626634\pi\)
\(882\) 0 0
\(883\) −15.6946 −0.528165 −0.264082 0.964500i \(-0.585069\pi\)
−0.264082 + 0.964500i \(0.585069\pi\)
\(884\) −17.1057 −0.575326
\(885\) 0 0
\(886\) −32.0897 −1.07807
\(887\) −25.3074 −0.849738 −0.424869 0.905255i \(-0.639680\pi\)
−0.424869 + 0.905255i \(0.639680\pi\)
\(888\) 0 0
\(889\) 37.8425 1.26920
\(890\) 0 0
\(891\) 0 0
\(892\) −57.3497 −1.92021
\(893\) −7.96385 −0.266500
\(894\) 0 0
\(895\) 0 0
\(896\) −36.2854 −1.21221
\(897\) 0 0
\(898\) −79.9160 −2.66683
\(899\) −11.4729 −0.382643
\(900\) 0 0
\(901\) 18.9118 0.630045
\(902\) 30.9800 1.03152
\(903\) 0 0
\(904\) −25.1745 −0.837291
\(905\) 0 0
\(906\) 0 0
\(907\) 10.3490 0.343632 0.171816 0.985129i \(-0.445037\pi\)
0.171816 + 0.985129i \(0.445037\pi\)
\(908\) −23.5436 −0.781322
\(909\) 0 0
\(910\) 0 0
\(911\) 41.0148 1.35888 0.679440 0.733731i \(-0.262223\pi\)
0.679440 + 0.733731i \(0.262223\pi\)
\(912\) 0 0
\(913\) −30.2438 −1.00092
\(914\) 16.8383 0.556961
\(915\) 0 0
\(916\) 58.4345 1.93073
\(917\) 29.8196 0.984729
\(918\) 0 0
\(919\) 23.3456 0.770101 0.385050 0.922896i \(-0.374184\pi\)
0.385050 + 0.922896i \(0.374184\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −52.3069 −1.72264
\(923\) 16.3978 0.539739
\(924\) 0 0
\(925\) 0 0
\(926\) −11.1130 −0.365195
\(927\) 0 0
\(928\) 15.7107 0.515730
\(929\) 32.8307 1.07714 0.538570 0.842581i \(-0.318965\pi\)
0.538570 + 0.842581i \(0.318965\pi\)
\(930\) 0 0
\(931\) 13.5492 0.444058
\(932\) 42.1105 1.37938
\(933\) 0 0
\(934\) −19.2003 −0.628252
\(935\) 0 0
\(936\) 0 0
\(937\) 7.39099 0.241453 0.120727 0.992686i \(-0.461478\pi\)
0.120727 + 0.992686i \(0.461478\pi\)
\(938\) −53.6481 −1.75167
\(939\) 0 0
\(940\) 0 0
\(941\) 38.0684 1.24099 0.620497 0.784209i \(-0.286931\pi\)
0.620497 + 0.784209i \(0.286931\pi\)
\(942\) 0 0
\(943\) −25.1745 −0.819794
\(944\) −14.1138 −0.459364
\(945\) 0 0
\(946\) −1.97011 −0.0640537
\(947\) −6.02057 −0.195642 −0.0978212 0.995204i \(-0.531187\pi\)
−0.0978212 + 0.995204i \(0.531187\pi\)
\(948\) 0 0
\(949\) 5.04278 0.163696
\(950\) 0 0
\(951\) 0 0
\(952\) 30.7204 0.995653
\(953\) 48.7760 1.58001 0.790004 0.613102i \(-0.210078\pi\)
0.790004 + 0.613102i \(0.210078\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 66.9143 2.16416
\(957\) 0 0
\(958\) −92.3892 −2.98496
\(959\) −55.8468 −1.80339
\(960\) 0 0
\(961\) 0.217265 0.00700856
\(962\) −22.1055 −0.712710
\(963\) 0 0
\(964\) −25.1786 −0.810948
\(965\) 0 0
\(966\) 0 0
\(967\) 3.19625 0.102785 0.0513923 0.998679i \(-0.483634\pi\)
0.0513923 + 0.998679i \(0.483634\pi\)
\(968\) −4.20664 −0.135207
\(969\) 0 0
\(970\) 0 0
\(971\) 34.3613 1.10271 0.551354 0.834272i \(-0.314112\pi\)
0.551354 + 0.834272i \(0.314112\pi\)
\(972\) 0 0
\(973\) −60.2472 −1.93144
\(974\) −65.1386 −2.08717
\(975\) 0 0
\(976\) −26.4732 −0.847386
\(977\) 30.1045 0.963129 0.481564 0.876411i \(-0.340069\pi\)
0.481564 + 0.876411i \(0.340069\pi\)
\(978\) 0 0
\(979\) −20.1291 −0.643329
\(980\) 0 0
\(981\) 0 0
\(982\) −68.0435 −2.17136
\(983\) −39.7914 −1.26915 −0.634574 0.772862i \(-0.718824\pi\)
−0.634574 + 0.772862i \(0.718824\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −28.3464 −0.902732
\(987\) 0 0
\(988\) −9.86830 −0.313952
\(989\) 1.60092 0.0509063
\(990\) 0 0
\(991\) 46.3028 1.47086 0.735429 0.677602i \(-0.236981\pi\)
0.735429 + 0.677602i \(0.236981\pi\)
\(992\) −42.7481 −1.35725
\(993\) 0 0
\(994\) −115.946 −3.67758
\(995\) 0 0
\(996\) 0 0
\(997\) 57.7673 1.82951 0.914754 0.404012i \(-0.132385\pi\)
0.914754 + 0.404012i \(0.132385\pi\)
\(998\) 47.8007 1.51310
\(999\) 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 2925.2.a.bp.1.5 yes 6
3.2 odd 2 inner 2925.2.a.bp.1.2 6
5.2 odd 4 2925.2.c.z.2224.10 12
5.3 odd 4 2925.2.c.z.2224.3 12
5.4 even 2 2925.2.a.bq.1.2 yes 6
15.2 even 4 2925.2.c.z.2224.4 12
15.8 even 4 2925.2.c.z.2224.9 12
15.14 odd 2 2925.2.a.bq.1.5 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2925.2.a.bp.1.2 6 3.2 odd 2 inner
2925.2.a.bp.1.5 yes 6 1.1 even 1 trivial
2925.2.a.bq.1.2 yes 6 5.4 even 2
2925.2.a.bq.1.5 yes 6 15.14 odd 2
2925.2.c.z.2224.3 12 5.3 odd 4
2925.2.c.z.2224.4 12 15.2 even 4
2925.2.c.z.2224.9 12 15.8 even 4
2925.2.c.z.2224.10 12 5.2 odd 4