Properties

Label 7605.2.a.bq.1.3
Level $7605$
Weight $2$
Character 7605.1
Self dual yes
Analytic conductor $60.726$
Analytic rank $1$
Dimension $3$
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] = [7605,2,Mod(1,7605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7605, 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("7605.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7605.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: \(60.7262307372\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2535)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 7605.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.24698 q^{2} -0.445042 q^{4} +1.00000 q^{5} -2.24698 q^{7} -3.04892 q^{8} +O(q^{10})\) \(q+1.24698 q^{2} -0.445042 q^{4} +1.00000 q^{5} -2.24698 q^{7} -3.04892 q^{8} +1.24698 q^{10} -1.00000 q^{11} -2.80194 q^{14} -2.91185 q^{16} +6.49396 q^{17} +2.33513 q^{19} -0.445042 q^{20} -1.24698 q^{22} -0.198062 q^{23} +1.00000 q^{25} +1.00000 q^{28} -3.82908 q^{29} +1.71379 q^{31} +2.46681 q^{32} +8.09783 q^{34} -2.24698 q^{35} +4.54288 q^{37} +2.91185 q^{38} -3.04892 q^{40} -5.75302 q^{41} -3.75302 q^{43} +0.445042 q^{44} -0.246980 q^{46} +1.97285 q^{47} -1.95108 q^{49} +1.24698 q^{50} -12.0586 q^{53} -1.00000 q^{55} +6.85086 q^{56} -4.77479 q^{58} -9.83877 q^{59} -13.6136 q^{61} +2.13706 q^{62} +8.89977 q^{64} +7.91185 q^{67} -2.89008 q^{68} -2.80194 q^{70} -7.14675 q^{71} +14.3545 q^{73} +5.66487 q^{74} -1.03923 q^{76} +2.24698 q^{77} +10.6189 q^{79} -2.91185 q^{80} -7.17390 q^{82} +12.7192 q^{83} +6.49396 q^{85} -4.67994 q^{86} +3.04892 q^{88} +6.87263 q^{89} +0.0881460 q^{92} +2.46011 q^{94} +2.33513 q^{95} -11.1414 q^{97} -2.43296 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} - q^{4} + 3 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} - q^{4} + 3 q^{5} - 2 q^{7} - q^{10} - 3 q^{11} - 4 q^{14} - 5 q^{16} + 10 q^{17} + 6 q^{19} - q^{20} + q^{22} - 5 q^{23} + 3 q^{25} + 3 q^{28} - q^{29} - 3 q^{31} + 4 q^{32} + 6 q^{34} - 2 q^{35} - 5 q^{37} + 5 q^{38} - 22 q^{41} - 16 q^{43} + q^{44} + 4 q^{46} + 12 q^{47} - 15 q^{49} - q^{50} - 5 q^{53} - 3 q^{55} + 7 q^{56} - 16 q^{58} + 3 q^{59} - 10 q^{61} + q^{62} + 4 q^{64} + 20 q^{67} - 8 q^{68} - 4 q^{70} + 6 q^{71} - 2 q^{73} + 18 q^{74} - 16 q^{76} + 2 q^{77} - 2 q^{79} - 5 q^{80} + 12 q^{82} + 27 q^{83} + 10 q^{85} + 10 q^{86} + 4 q^{89} + 4 q^{92} - 18 q^{94} + 6 q^{95} - 9 q^{97} + 12 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24698 0.881748 0.440874 0.897569i \(-0.354669\pi\)
0.440874 + 0.897569i \(0.354669\pi\)
\(3\) 0 0
\(4\) −0.445042 −0.222521
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.24698 −0.849278 −0.424639 0.905363i \(-0.639599\pi\)
−0.424639 + 0.905363i \(0.639599\pi\)
\(8\) −3.04892 −1.07796
\(9\) 0 0
\(10\) 1.24698 0.394330
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −2.80194 −0.748849
\(15\) 0 0
\(16\) −2.91185 −0.727963
\(17\) 6.49396 1.57502 0.787508 0.616304i \(-0.211371\pi\)
0.787508 + 0.616304i \(0.211371\pi\)
\(18\) 0 0
\(19\) 2.33513 0.535715 0.267857 0.963459i \(-0.413684\pi\)
0.267857 + 0.963459i \(0.413684\pi\)
\(20\) −0.445042 −0.0995144
\(21\) 0 0
\(22\) −1.24698 −0.265857
\(23\) −0.198062 −0.0412988 −0.0206494 0.999787i \(-0.506573\pi\)
−0.0206494 + 0.999787i \(0.506573\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −3.82908 −0.711043 −0.355522 0.934668i \(-0.615697\pi\)
−0.355522 + 0.934668i \(0.615697\pi\)
\(30\) 0 0
\(31\) 1.71379 0.307806 0.153903 0.988086i \(-0.450816\pi\)
0.153903 + 0.988086i \(0.450816\pi\)
\(32\) 2.46681 0.436075
\(33\) 0 0
\(34\) 8.09783 1.38877
\(35\) −2.24698 −0.379809
\(36\) 0 0
\(37\) 4.54288 0.746844 0.373422 0.927662i \(-0.378184\pi\)
0.373422 + 0.927662i \(0.378184\pi\)
\(38\) 2.91185 0.472365
\(39\) 0 0
\(40\) −3.04892 −0.482076
\(41\) −5.75302 −0.898471 −0.449235 0.893413i \(-0.648304\pi\)
−0.449235 + 0.893413i \(0.648304\pi\)
\(42\) 0 0
\(43\) −3.75302 −0.572330 −0.286165 0.958180i \(-0.592381\pi\)
−0.286165 + 0.958180i \(0.592381\pi\)
\(44\) 0.445042 0.0670926
\(45\) 0 0
\(46\) −0.246980 −0.0364152
\(47\) 1.97285 0.287770 0.143885 0.989594i \(-0.454040\pi\)
0.143885 + 0.989594i \(0.454040\pi\)
\(48\) 0 0
\(49\) −1.95108 −0.278726
\(50\) 1.24698 0.176350
\(51\) 0 0
\(52\) 0 0
\(53\) −12.0586 −1.65638 −0.828188 0.560450i \(-0.810628\pi\)
−0.828188 + 0.560450i \(0.810628\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 6.85086 0.915484
\(57\) 0 0
\(58\) −4.77479 −0.626961
\(59\) −9.83877 −1.28090 −0.640450 0.768000i \(-0.721252\pi\)
−0.640450 + 0.768000i \(0.721252\pi\)
\(60\) 0 0
\(61\) −13.6136 −1.74304 −0.871519 0.490361i \(-0.836865\pi\)
−0.871519 + 0.490361i \(0.836865\pi\)
\(62\) 2.13706 0.271407
\(63\) 0 0
\(64\) 8.89977 1.11247
\(65\) 0 0
\(66\) 0 0
\(67\) 7.91185 0.966587 0.483293 0.875458i \(-0.339440\pi\)
0.483293 + 0.875458i \(0.339440\pi\)
\(68\) −2.89008 −0.350474
\(69\) 0 0
\(70\) −2.80194 −0.334896
\(71\) −7.14675 −0.848163 −0.424082 0.905624i \(-0.639403\pi\)
−0.424082 + 0.905624i \(0.639403\pi\)
\(72\) 0 0
\(73\) 14.3545 1.68007 0.840034 0.542534i \(-0.182535\pi\)
0.840034 + 0.542534i \(0.182535\pi\)
\(74\) 5.66487 0.658528
\(75\) 0 0
\(76\) −1.03923 −0.119208
\(77\) 2.24698 0.256067
\(78\) 0 0
\(79\) 10.6189 1.19472 0.597362 0.801972i \(-0.296216\pi\)
0.597362 + 0.801972i \(0.296216\pi\)
\(80\) −2.91185 −0.325555
\(81\) 0 0
\(82\) −7.17390 −0.792225
\(83\) 12.7192 1.39611 0.698055 0.716044i \(-0.254049\pi\)
0.698055 + 0.716044i \(0.254049\pi\)
\(84\) 0 0
\(85\) 6.49396 0.704369
\(86\) −4.67994 −0.504651
\(87\) 0 0
\(88\) 3.04892 0.325016
\(89\) 6.87263 0.728497 0.364248 0.931302i \(-0.381326\pi\)
0.364248 + 0.931302i \(0.381326\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.0881460 0.00918986
\(93\) 0 0
\(94\) 2.46011 0.253741
\(95\) 2.33513 0.239579
\(96\) 0 0
\(97\) −11.1414 −1.13124 −0.565618 0.824668i \(-0.691362\pi\)
−0.565618 + 0.824668i \(0.691362\pi\)
\(98\) −2.43296 −0.245766
\(99\) 0 0
\(100\) −0.445042 −0.0445042
\(101\) 8.19136 0.815071 0.407535 0.913189i \(-0.366388\pi\)
0.407535 + 0.913189i \(0.366388\pi\)
\(102\) 0 0
\(103\) −9.52111 −0.938142 −0.469071 0.883160i \(-0.655411\pi\)
−0.469071 + 0.883160i \(0.655411\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −15.0368 −1.46051
\(107\) 14.1836 1.37118 0.685590 0.727988i \(-0.259544\pi\)
0.685590 + 0.727988i \(0.259544\pi\)
\(108\) 0 0
\(109\) −10.1957 −0.976568 −0.488284 0.872685i \(-0.662377\pi\)
−0.488284 + 0.872685i \(0.662377\pi\)
\(110\) −1.24698 −0.118895
\(111\) 0 0
\(112\) 6.54288 0.618244
\(113\) −6.88769 −0.647939 −0.323970 0.946067i \(-0.605018\pi\)
−0.323970 + 0.946067i \(0.605018\pi\)
\(114\) 0 0
\(115\) −0.198062 −0.0184694
\(116\) 1.70410 0.158222
\(117\) 0 0
\(118\) −12.2687 −1.12943
\(119\) −14.5918 −1.33763
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −16.9758 −1.53692
\(123\) 0 0
\(124\) −0.762709 −0.0684933
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −18.4547 −1.63759 −0.818796 0.574084i \(-0.805358\pi\)
−0.818796 + 0.574084i \(0.805358\pi\)
\(128\) 6.16421 0.544844
\(129\) 0 0
\(130\) 0 0
\(131\) −8.11960 −0.709413 −0.354707 0.934978i \(-0.615419\pi\)
−0.354707 + 0.934978i \(0.615419\pi\)
\(132\) 0 0
\(133\) −5.24698 −0.454971
\(134\) 9.86592 0.852286
\(135\) 0 0
\(136\) −19.7995 −1.69780
\(137\) −21.7778 −1.86060 −0.930300 0.366798i \(-0.880454\pi\)
−0.930300 + 0.366798i \(0.880454\pi\)
\(138\) 0 0
\(139\) −19.4058 −1.64598 −0.822990 0.568056i \(-0.807696\pi\)
−0.822990 + 0.568056i \(0.807696\pi\)
\(140\) 1.00000 0.0845154
\(141\) 0 0
\(142\) −8.91185 −0.747866
\(143\) 0 0
\(144\) 0 0
\(145\) −3.82908 −0.317988
\(146\) 17.8998 1.48140
\(147\) 0 0
\(148\) −2.02177 −0.166188
\(149\) −11.4668 −0.939398 −0.469699 0.882827i \(-0.655638\pi\)
−0.469699 + 0.882827i \(0.655638\pi\)
\(150\) 0 0
\(151\) 6.17092 0.502182 0.251091 0.967963i \(-0.419211\pi\)
0.251091 + 0.967963i \(0.419211\pi\)
\(152\) −7.11960 −0.577476
\(153\) 0 0
\(154\) 2.80194 0.225787
\(155\) 1.71379 0.137655
\(156\) 0 0
\(157\) −15.3080 −1.22171 −0.610855 0.791743i \(-0.709174\pi\)
−0.610855 + 0.791743i \(0.709174\pi\)
\(158\) 13.2416 1.05345
\(159\) 0 0
\(160\) 2.46681 0.195019
\(161\) 0.445042 0.0350742
\(162\) 0 0
\(163\) −19.5918 −1.53455 −0.767274 0.641320i \(-0.778387\pi\)
−0.767274 + 0.641320i \(0.778387\pi\)
\(164\) 2.56033 0.199929
\(165\) 0 0
\(166\) 15.8605 1.23102
\(167\) −9.05429 −0.700642 −0.350321 0.936630i \(-0.613928\pi\)
−0.350321 + 0.936630i \(0.613928\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 8.09783 0.621076
\(171\) 0 0
\(172\) 1.67025 0.127355
\(173\) 13.4547 1.02294 0.511472 0.859300i \(-0.329100\pi\)
0.511472 + 0.859300i \(0.329100\pi\)
\(174\) 0 0
\(175\) −2.24698 −0.169856
\(176\) 2.91185 0.219489
\(177\) 0 0
\(178\) 8.57002 0.642350
\(179\) −21.3980 −1.59936 −0.799682 0.600423i \(-0.794999\pi\)
−0.799682 + 0.600423i \(0.794999\pi\)
\(180\) 0 0
\(181\) −14.1032 −1.04828 −0.524142 0.851631i \(-0.675614\pi\)
−0.524142 + 0.851631i \(0.675614\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.603875 0.0445183
\(185\) 4.54288 0.333999
\(186\) 0 0
\(187\) −6.49396 −0.474885
\(188\) −0.878002 −0.0640349
\(189\) 0 0
\(190\) 2.91185 0.211248
\(191\) −7.19136 −0.520348 −0.260174 0.965562i \(-0.583780\pi\)
−0.260174 + 0.965562i \(0.583780\pi\)
\(192\) 0 0
\(193\) −11.3013 −0.813483 −0.406742 0.913543i \(-0.633335\pi\)
−0.406742 + 0.913543i \(0.633335\pi\)
\(194\) −13.8931 −0.997464
\(195\) 0 0
\(196\) 0.868313 0.0620224
\(197\) 20.5066 1.46104 0.730519 0.682893i \(-0.239278\pi\)
0.730519 + 0.682893i \(0.239278\pi\)
\(198\) 0 0
\(199\) 19.9681 1.41550 0.707749 0.706464i \(-0.249711\pi\)
0.707749 + 0.706464i \(0.249711\pi\)
\(200\) −3.04892 −0.215591
\(201\) 0 0
\(202\) 10.2145 0.718687
\(203\) 8.60388 0.603874
\(204\) 0 0
\(205\) −5.75302 −0.401808
\(206\) −11.8726 −0.827205
\(207\) 0 0
\(208\) 0 0
\(209\) −2.33513 −0.161524
\(210\) 0 0
\(211\) −9.74632 −0.670964 −0.335482 0.942047i \(-0.608899\pi\)
−0.335482 + 0.942047i \(0.608899\pi\)
\(212\) 5.36658 0.368579
\(213\) 0 0
\(214\) 17.6866 1.20903
\(215\) −3.75302 −0.255954
\(216\) 0 0
\(217\) −3.85086 −0.261413
\(218\) −12.7138 −0.861087
\(219\) 0 0
\(220\) 0.445042 0.0300047
\(221\) 0 0
\(222\) 0 0
\(223\) −24.5351 −1.64299 −0.821496 0.570214i \(-0.806860\pi\)
−0.821496 + 0.570214i \(0.806860\pi\)
\(224\) −5.54288 −0.370349
\(225\) 0 0
\(226\) −8.58881 −0.571319
\(227\) −0.0217703 −0.00144494 −0.000722472 1.00000i \(-0.500230\pi\)
−0.000722472 1.00000i \(0.500230\pi\)
\(228\) 0 0
\(229\) 7.36898 0.486956 0.243478 0.969906i \(-0.421712\pi\)
0.243478 + 0.969906i \(0.421712\pi\)
\(230\) −0.246980 −0.0162854
\(231\) 0 0
\(232\) 11.6746 0.766473
\(233\) 8.10992 0.531298 0.265649 0.964070i \(-0.414414\pi\)
0.265649 + 0.964070i \(0.414414\pi\)
\(234\) 0 0
\(235\) 1.97285 0.128695
\(236\) 4.37867 0.285027
\(237\) 0 0
\(238\) −18.1957 −1.17945
\(239\) 6.38165 0.412795 0.206397 0.978468i \(-0.433826\pi\)
0.206397 + 0.978468i \(0.433826\pi\)
\(240\) 0 0
\(241\) −1.30127 −0.0838224 −0.0419112 0.999121i \(-0.513345\pi\)
−0.0419112 + 0.999121i \(0.513345\pi\)
\(242\) −12.4698 −0.801589
\(243\) 0 0
\(244\) 6.05861 0.387863
\(245\) −1.95108 −0.124650
\(246\) 0 0
\(247\) 0 0
\(248\) −5.22521 −0.331801
\(249\) 0 0
\(250\) 1.24698 0.0788659
\(251\) −9.51142 −0.600355 −0.300178 0.953883i \(-0.597046\pi\)
−0.300178 + 0.953883i \(0.597046\pi\)
\(252\) 0 0
\(253\) 0.198062 0.0124521
\(254\) −23.0127 −1.44394
\(255\) 0 0
\(256\) −10.1129 −0.632056
\(257\) −7.38942 −0.460939 −0.230470 0.973080i \(-0.574026\pi\)
−0.230470 + 0.973080i \(0.574026\pi\)
\(258\) 0 0
\(259\) −10.2078 −0.634279
\(260\) 0 0
\(261\) 0 0
\(262\) −10.1250 −0.625523
\(263\) 3.06398 0.188933 0.0944666 0.995528i \(-0.469885\pi\)
0.0944666 + 0.995528i \(0.469885\pi\)
\(264\) 0 0
\(265\) −12.0586 −0.740754
\(266\) −6.54288 −0.401170
\(267\) 0 0
\(268\) −3.52111 −0.215086
\(269\) 18.2687 1.11387 0.556933 0.830558i \(-0.311978\pi\)
0.556933 + 0.830558i \(0.311978\pi\)
\(270\) 0 0
\(271\) −4.04892 −0.245954 −0.122977 0.992410i \(-0.539244\pi\)
−0.122977 + 0.992410i \(0.539244\pi\)
\(272\) −18.9095 −1.14655
\(273\) 0 0
\(274\) −27.1564 −1.64058
\(275\) −1.00000 −0.0603023
\(276\) 0 0
\(277\) 28.1608 1.69202 0.846008 0.533170i \(-0.179000\pi\)
0.846008 + 0.533170i \(0.179000\pi\)
\(278\) −24.1987 −1.45134
\(279\) 0 0
\(280\) 6.85086 0.409417
\(281\) 24.3937 1.45521 0.727604 0.685997i \(-0.240634\pi\)
0.727604 + 0.685997i \(0.240634\pi\)
\(282\) 0 0
\(283\) −7.16315 −0.425805 −0.212902 0.977073i \(-0.568292\pi\)
−0.212902 + 0.977073i \(0.568292\pi\)
\(284\) 3.18060 0.188734
\(285\) 0 0
\(286\) 0 0
\(287\) 12.9269 0.763052
\(288\) 0 0
\(289\) 25.1715 1.48068
\(290\) −4.77479 −0.280385
\(291\) 0 0
\(292\) −6.38835 −0.373850
\(293\) 5.01075 0.292731 0.146366 0.989231i \(-0.453242\pi\)
0.146366 + 0.989231i \(0.453242\pi\)
\(294\) 0 0
\(295\) −9.83877 −0.572836
\(296\) −13.8509 −0.805065
\(297\) 0 0
\(298\) −14.2989 −0.828312
\(299\) 0 0
\(300\) 0 0
\(301\) 8.43296 0.486068
\(302\) 7.69501 0.442798
\(303\) 0 0
\(304\) −6.79954 −0.389981
\(305\) −13.6136 −0.779510
\(306\) 0 0
\(307\) −29.8213 −1.70199 −0.850996 0.525172i \(-0.824001\pi\)
−0.850996 + 0.525172i \(0.824001\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 0 0
\(310\) 2.13706 0.121377
\(311\) 6.22952 0.353244 0.176622 0.984279i \(-0.443483\pi\)
0.176622 + 0.984279i \(0.443483\pi\)
\(312\) 0 0
\(313\) 8.22713 0.465025 0.232512 0.972593i \(-0.425305\pi\)
0.232512 + 0.972593i \(0.425305\pi\)
\(314\) −19.0887 −1.07724
\(315\) 0 0
\(316\) −4.72587 −0.265851
\(317\) 20.2010 1.13460 0.567302 0.823510i \(-0.307987\pi\)
0.567302 + 0.823510i \(0.307987\pi\)
\(318\) 0 0
\(319\) 3.82908 0.214388
\(320\) 8.89977 0.497512
\(321\) 0 0
\(322\) 0.554958 0.0309266
\(323\) 15.1642 0.843759
\(324\) 0 0
\(325\) 0 0
\(326\) −24.4306 −1.35308
\(327\) 0 0
\(328\) 17.5405 0.968511
\(329\) −4.43296 −0.244397
\(330\) 0 0
\(331\) −11.2771 −0.619846 −0.309923 0.950762i \(-0.600303\pi\)
−0.309923 + 0.950762i \(0.600303\pi\)
\(332\) −5.66056 −0.310664
\(333\) 0 0
\(334\) −11.2905 −0.617790
\(335\) 7.91185 0.432271
\(336\) 0 0
\(337\) −21.1075 −1.14980 −0.574900 0.818224i \(-0.694959\pi\)
−0.574900 + 0.818224i \(0.694959\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −2.89008 −0.156737
\(341\) −1.71379 −0.0928070
\(342\) 0 0
\(343\) 20.1129 1.08599
\(344\) 11.4426 0.616946
\(345\) 0 0
\(346\) 16.7778 0.901979
\(347\) −21.3744 −1.14744 −0.573718 0.819053i \(-0.694499\pi\)
−0.573718 + 0.819053i \(0.694499\pi\)
\(348\) 0 0
\(349\) −4.31527 −0.230991 −0.115496 0.993308i \(-0.536846\pi\)
−0.115496 + 0.993308i \(0.536846\pi\)
\(350\) −2.80194 −0.149770
\(351\) 0 0
\(352\) −2.46681 −0.131482
\(353\) 10.2198 0.543947 0.271973 0.962305i \(-0.412324\pi\)
0.271973 + 0.962305i \(0.412324\pi\)
\(354\) 0 0
\(355\) −7.14675 −0.379310
\(356\) −3.05861 −0.162106
\(357\) 0 0
\(358\) −26.6829 −1.41024
\(359\) 8.71678 0.460054 0.230027 0.973184i \(-0.426119\pi\)
0.230027 + 0.973184i \(0.426119\pi\)
\(360\) 0 0
\(361\) −13.5472 −0.713010
\(362\) −17.5864 −0.924322
\(363\) 0 0
\(364\) 0 0
\(365\) 14.3545 0.751349
\(366\) 0 0
\(367\) −5.37973 −0.280820 −0.140410 0.990093i \(-0.544842\pi\)
−0.140410 + 0.990093i \(0.544842\pi\)
\(368\) 0.576728 0.0300640
\(369\) 0 0
\(370\) 5.66487 0.294503
\(371\) 27.0954 1.40673
\(372\) 0 0
\(373\) −12.6843 −0.656766 −0.328383 0.944545i \(-0.606504\pi\)
−0.328383 + 0.944545i \(0.606504\pi\)
\(374\) −8.09783 −0.418729
\(375\) 0 0
\(376\) −6.01507 −0.310203
\(377\) 0 0
\(378\) 0 0
\(379\) 7.99223 0.410533 0.205267 0.978706i \(-0.434194\pi\)
0.205267 + 0.978706i \(0.434194\pi\)
\(380\) −1.03923 −0.0533113
\(381\) 0 0
\(382\) −8.96748 −0.458816
\(383\) 0.763774 0.0390270 0.0195135 0.999810i \(-0.493788\pi\)
0.0195135 + 0.999810i \(0.493788\pi\)
\(384\) 0 0
\(385\) 2.24698 0.114517
\(386\) −14.0925 −0.717287
\(387\) 0 0
\(388\) 4.95838 0.251724
\(389\) 28.8799 1.46427 0.732135 0.681159i \(-0.238524\pi\)
0.732135 + 0.681159i \(0.238524\pi\)
\(390\) 0 0
\(391\) −1.28621 −0.0650463
\(392\) 5.94869 0.300454
\(393\) 0 0
\(394\) 25.5714 1.28827
\(395\) 10.6189 0.534297
\(396\) 0 0
\(397\) −33.1347 −1.66298 −0.831491 0.555539i \(-0.812512\pi\)
−0.831491 + 0.555539i \(0.812512\pi\)
\(398\) 24.8998 1.24811
\(399\) 0 0
\(400\) −2.91185 −0.145593
\(401\) 11.0435 0.551488 0.275744 0.961231i \(-0.411076\pi\)
0.275744 + 0.961231i \(0.411076\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −3.64550 −0.181370
\(405\) 0 0
\(406\) 10.7289 0.532464
\(407\) −4.54288 −0.225182
\(408\) 0 0
\(409\) 33.3424 1.64868 0.824338 0.566097i \(-0.191547\pi\)
0.824338 + 0.566097i \(0.191547\pi\)
\(410\) −7.17390 −0.354294
\(411\) 0 0
\(412\) 4.23729 0.208756
\(413\) 22.1075 1.08784
\(414\) 0 0
\(415\) 12.7192 0.624359
\(416\) 0 0
\(417\) 0 0
\(418\) −2.91185 −0.142423
\(419\) −39.9071 −1.94959 −0.974794 0.223107i \(-0.928380\pi\)
−0.974794 + 0.223107i \(0.928380\pi\)
\(420\) 0 0
\(421\) 9.41657 0.458935 0.229468 0.973316i \(-0.426301\pi\)
0.229468 + 0.973316i \(0.426301\pi\)
\(422\) −12.1535 −0.591621
\(423\) 0 0
\(424\) 36.7657 1.78550
\(425\) 6.49396 0.315003
\(426\) 0 0
\(427\) 30.5894 1.48032
\(428\) −6.31229 −0.305116
\(429\) 0 0
\(430\) −4.67994 −0.225687
\(431\) −25.9976 −1.25226 −0.626130 0.779718i \(-0.715362\pi\)
−0.626130 + 0.779718i \(0.715362\pi\)
\(432\) 0 0
\(433\) 6.93661 0.333352 0.166676 0.986012i \(-0.446697\pi\)
0.166676 + 0.986012i \(0.446697\pi\)
\(434\) −4.80194 −0.230500
\(435\) 0 0
\(436\) 4.53750 0.217307
\(437\) −0.462500 −0.0221244
\(438\) 0 0
\(439\) 18.6775 0.891431 0.445715 0.895175i \(-0.352949\pi\)
0.445715 + 0.895175i \(0.352949\pi\)
\(440\) 3.04892 0.145351
\(441\) 0 0
\(442\) 0 0
\(443\) −36.9245 −1.75434 −0.877169 0.480183i \(-0.840570\pi\)
−0.877169 + 0.480183i \(0.840570\pi\)
\(444\) 0 0
\(445\) 6.87263 0.325794
\(446\) −30.5948 −1.44870
\(447\) 0 0
\(448\) −19.9976 −0.944798
\(449\) 15.3884 0.726221 0.363111 0.931746i \(-0.381715\pi\)
0.363111 + 0.931746i \(0.381715\pi\)
\(450\) 0 0
\(451\) 5.75302 0.270899
\(452\) 3.06531 0.144180
\(453\) 0 0
\(454\) −0.0271471 −0.00127408
\(455\) 0 0
\(456\) 0 0
\(457\) −25.2946 −1.18323 −0.591615 0.806221i \(-0.701509\pi\)
−0.591615 + 0.806221i \(0.701509\pi\)
\(458\) 9.18896 0.429372
\(459\) 0 0
\(460\) 0.0881460 0.00410983
\(461\) 8.68664 0.404577 0.202289 0.979326i \(-0.435162\pi\)
0.202289 + 0.979326i \(0.435162\pi\)
\(462\) 0 0
\(463\) 1.73663 0.0807079 0.0403539 0.999185i \(-0.487151\pi\)
0.0403539 + 0.999185i \(0.487151\pi\)
\(464\) 11.1497 0.517613
\(465\) 0 0
\(466\) 10.1129 0.468471
\(467\) −22.3177 −1.03274 −0.516369 0.856366i \(-0.672717\pi\)
−0.516369 + 0.856366i \(0.672717\pi\)
\(468\) 0 0
\(469\) −17.7778 −0.820901
\(470\) 2.46011 0.113476
\(471\) 0 0
\(472\) 29.9976 1.38075
\(473\) 3.75302 0.172564
\(474\) 0 0
\(475\) 2.33513 0.107143
\(476\) 6.49396 0.297650
\(477\) 0 0
\(478\) 7.95779 0.363981
\(479\) 26.6765 1.21888 0.609440 0.792832i \(-0.291394\pi\)
0.609440 + 0.792832i \(0.291394\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.62266 −0.0739102
\(483\) 0 0
\(484\) 4.45042 0.202292
\(485\) −11.1414 −0.505904
\(486\) 0 0
\(487\) 8.61655 0.390453 0.195227 0.980758i \(-0.437456\pi\)
0.195227 + 0.980758i \(0.437456\pi\)
\(488\) 41.5066 1.87892
\(489\) 0 0
\(490\) −2.43296 −0.109910
\(491\) 0.992230 0.0447787 0.0223894 0.999749i \(-0.492873\pi\)
0.0223894 + 0.999749i \(0.492873\pi\)
\(492\) 0 0
\(493\) −24.8659 −1.11990
\(494\) 0 0
\(495\) 0 0
\(496\) −4.99031 −0.224072
\(497\) 16.0586 0.720327
\(498\) 0 0
\(499\) 16.7138 0.748212 0.374106 0.927386i \(-0.377950\pi\)
0.374106 + 0.927386i \(0.377950\pi\)
\(500\) −0.445042 −0.0199029
\(501\) 0 0
\(502\) −11.8605 −0.529362
\(503\) −30.6547 −1.36683 −0.683413 0.730032i \(-0.739505\pi\)
−0.683413 + 0.730032i \(0.739505\pi\)
\(504\) 0 0
\(505\) 8.19136 0.364511
\(506\) 0.246980 0.0109796
\(507\) 0 0
\(508\) 8.21313 0.364399
\(509\) −25.9506 −1.15024 −0.575120 0.818069i \(-0.695045\pi\)
−0.575120 + 0.818069i \(0.695045\pi\)
\(510\) 0 0
\(511\) −32.2543 −1.42685
\(512\) −24.9390 −1.10216
\(513\) 0 0
\(514\) −9.21446 −0.406432
\(515\) −9.52111 −0.419550
\(516\) 0 0
\(517\) −1.97285 −0.0867660
\(518\) −12.7289 −0.559274
\(519\) 0 0
\(520\) 0 0
\(521\) 12.3375 0.540516 0.270258 0.962788i \(-0.412891\pi\)
0.270258 + 0.962788i \(0.412891\pi\)
\(522\) 0 0
\(523\) −20.7748 −0.908418 −0.454209 0.890895i \(-0.650078\pi\)
−0.454209 + 0.890895i \(0.650078\pi\)
\(524\) 3.61356 0.157859
\(525\) 0 0
\(526\) 3.82072 0.166591
\(527\) 11.1293 0.484800
\(528\) 0 0
\(529\) −22.9608 −0.998294
\(530\) −15.0368 −0.653158
\(531\) 0 0
\(532\) 2.33513 0.101241
\(533\) 0 0
\(534\) 0 0
\(535\) 14.1836 0.613210
\(536\) −24.1226 −1.04194
\(537\) 0 0
\(538\) 22.7808 0.982148
\(539\) 1.95108 0.0840391
\(540\) 0 0
\(541\) 45.5797 1.95962 0.979812 0.199919i \(-0.0640679\pi\)
0.979812 + 0.199919i \(0.0640679\pi\)
\(542\) −5.04892 −0.216870
\(543\) 0 0
\(544\) 16.0194 0.686825
\(545\) −10.1957 −0.436734
\(546\) 0 0
\(547\) −14.0194 −0.599425 −0.299713 0.954030i \(-0.596891\pi\)
−0.299713 + 0.954030i \(0.596891\pi\)
\(548\) 9.69202 0.414023
\(549\) 0 0
\(550\) −1.24698 −0.0531714
\(551\) −8.94139 −0.380916
\(552\) 0 0
\(553\) −23.8605 −1.01465
\(554\) 35.1159 1.49193
\(555\) 0 0
\(556\) 8.63640 0.366265
\(557\) 21.2591 0.900775 0.450388 0.892833i \(-0.351286\pi\)
0.450388 + 0.892833i \(0.351286\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 6.54288 0.276487
\(561\) 0 0
\(562\) 30.4185 1.28313
\(563\) −13.5198 −0.569791 −0.284895 0.958559i \(-0.591959\pi\)
−0.284895 + 0.958559i \(0.591959\pi\)
\(564\) 0 0
\(565\) −6.88769 −0.289767
\(566\) −8.93230 −0.375452
\(567\) 0 0
\(568\) 21.7899 0.914282
\(569\) 30.9202 1.29624 0.648121 0.761537i \(-0.275555\pi\)
0.648121 + 0.761537i \(0.275555\pi\)
\(570\) 0 0
\(571\) 5.33645 0.223324 0.111662 0.993746i \(-0.464383\pi\)
0.111662 + 0.993746i \(0.464383\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 16.1196 0.672819
\(575\) −0.198062 −0.00825977
\(576\) 0 0
\(577\) 17.3889 0.723911 0.361956 0.932195i \(-0.382109\pi\)
0.361956 + 0.932195i \(0.382109\pi\)
\(578\) 31.3884 1.30558
\(579\) 0 0
\(580\) 1.70410 0.0707590
\(581\) −28.5797 −1.18569
\(582\) 0 0
\(583\) 12.0586 0.499416
\(584\) −43.7657 −1.81104
\(585\) 0 0
\(586\) 6.24831 0.258115
\(587\) −21.4668 −0.886030 −0.443015 0.896514i \(-0.646091\pi\)
−0.443015 + 0.896514i \(0.646091\pi\)
\(588\) 0 0
\(589\) 4.00192 0.164896
\(590\) −12.2687 −0.505096
\(591\) 0 0
\(592\) −13.2282 −0.543675
\(593\) 4.27605 0.175596 0.0877981 0.996138i \(-0.472017\pi\)
0.0877981 + 0.996138i \(0.472017\pi\)
\(594\) 0 0
\(595\) −14.5918 −0.598205
\(596\) 5.10321 0.209036
\(597\) 0 0
\(598\) 0 0
\(599\) 23.2180 0.948663 0.474332 0.880346i \(-0.342690\pi\)
0.474332 + 0.880346i \(0.342690\pi\)
\(600\) 0 0
\(601\) −32.2704 −1.31634 −0.658169 0.752871i \(-0.728669\pi\)
−0.658169 + 0.752871i \(0.728669\pi\)
\(602\) 10.5157 0.428589
\(603\) 0 0
\(604\) −2.74632 −0.111746
\(605\) −10.0000 −0.406558
\(606\) 0 0
\(607\) 13.8920 0.563859 0.281929 0.959435i \(-0.409026\pi\)
0.281929 + 0.959435i \(0.409026\pi\)
\(608\) 5.76032 0.233612
\(609\) 0 0
\(610\) −16.9758 −0.687332
\(611\) 0 0
\(612\) 0 0
\(613\) 27.6668 1.11745 0.558726 0.829353i \(-0.311290\pi\)
0.558726 + 0.829353i \(0.311290\pi\)
\(614\) −37.1866 −1.50073
\(615\) 0 0
\(616\) −6.85086 −0.276029
\(617\) −10.3709 −0.417517 −0.208758 0.977967i \(-0.566942\pi\)
−0.208758 + 0.977967i \(0.566942\pi\)
\(618\) 0 0
\(619\) −43.1473 −1.73424 −0.867119 0.498101i \(-0.834031\pi\)
−0.867119 + 0.498101i \(0.834031\pi\)
\(620\) −0.762709 −0.0306311
\(621\) 0 0
\(622\) 7.76809 0.311472
\(623\) −15.4426 −0.618697
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 10.2591 0.410035
\(627\) 0 0
\(628\) 6.81269 0.271856
\(629\) 29.5013 1.17629
\(630\) 0 0
\(631\) −22.6987 −0.903622 −0.451811 0.892114i \(-0.649222\pi\)
−0.451811 + 0.892114i \(0.649222\pi\)
\(632\) −32.3763 −1.28786
\(633\) 0 0
\(634\) 25.1903 1.00043
\(635\) −18.4547 −0.732354
\(636\) 0 0
\(637\) 0 0
\(638\) 4.77479 0.189036
\(639\) 0 0
\(640\) 6.16421 0.243662
\(641\) 16.1075 0.636209 0.318104 0.948056i \(-0.396954\pi\)
0.318104 + 0.948056i \(0.396954\pi\)
\(642\) 0 0
\(643\) 32.8732 1.29639 0.648197 0.761473i \(-0.275524\pi\)
0.648197 + 0.761473i \(0.275524\pi\)
\(644\) −0.198062 −0.00780475
\(645\) 0 0
\(646\) 18.9095 0.743983
\(647\) 10.2814 0.404204 0.202102 0.979364i \(-0.435223\pi\)
0.202102 + 0.979364i \(0.435223\pi\)
\(648\) 0 0
\(649\) 9.83877 0.386206
\(650\) 0 0
\(651\) 0 0
\(652\) 8.71917 0.341469
\(653\) −14.3575 −0.561852 −0.280926 0.959729i \(-0.590642\pi\)
−0.280926 + 0.959729i \(0.590642\pi\)
\(654\) 0 0
\(655\) −8.11960 −0.317259
\(656\) 16.7520 0.654054
\(657\) 0 0
\(658\) −5.52781 −0.215497
\(659\) 16.0258 0.624277 0.312139 0.950037i \(-0.398955\pi\)
0.312139 + 0.950037i \(0.398955\pi\)
\(660\) 0 0
\(661\) 27.4282 1.06683 0.533416 0.845853i \(-0.320908\pi\)
0.533416 + 0.845853i \(0.320908\pi\)
\(662\) −14.0623 −0.546548
\(663\) 0 0
\(664\) −38.7797 −1.50494
\(665\) −5.24698 −0.203469
\(666\) 0 0
\(667\) 0.758397 0.0293653
\(668\) 4.02954 0.155908
\(669\) 0 0
\(670\) 9.86592 0.381154
\(671\) 13.6136 0.525546
\(672\) 0 0
\(673\) 1.10321 0.0425257 0.0212628 0.999774i \(-0.493231\pi\)
0.0212628 + 0.999774i \(0.493231\pi\)
\(674\) −26.3207 −1.01383
\(675\) 0 0
\(676\) 0 0
\(677\) 31.7754 1.22123 0.610614 0.791929i \(-0.290923\pi\)
0.610614 + 0.791929i \(0.290923\pi\)
\(678\) 0 0
\(679\) 25.0344 0.960734
\(680\) −19.7995 −0.759278
\(681\) 0 0
\(682\) −2.13706 −0.0818324
\(683\) −4.45606 −0.170506 −0.0852532 0.996359i \(-0.527170\pi\)
−0.0852532 + 0.996359i \(0.527170\pi\)
\(684\) 0 0
\(685\) −21.7778 −0.832086
\(686\) 25.0804 0.957573
\(687\) 0 0
\(688\) 10.9282 0.416636
\(689\) 0 0
\(690\) 0 0
\(691\) −14.1438 −0.538054 −0.269027 0.963133i \(-0.586702\pi\)
−0.269027 + 0.963133i \(0.586702\pi\)
\(692\) −5.98792 −0.227627
\(693\) 0 0
\(694\) −26.6534 −1.01175
\(695\) −19.4058 −0.736104
\(696\) 0 0
\(697\) −37.3599 −1.41511
\(698\) −5.38106 −0.203676
\(699\) 0 0
\(700\) 1.00000 0.0377964
\(701\) 4.74632 0.179266 0.0896329 0.995975i \(-0.471431\pi\)
0.0896329 + 0.995975i \(0.471431\pi\)
\(702\) 0 0
\(703\) 10.6082 0.400095
\(704\) −8.89977 −0.335423
\(705\) 0 0
\(706\) 12.7439 0.479624
\(707\) −18.4058 −0.692222
\(708\) 0 0
\(709\) 15.4112 0.578779 0.289390 0.957211i \(-0.406548\pi\)
0.289390 + 0.957211i \(0.406548\pi\)
\(710\) −8.91185 −0.334456
\(711\) 0 0
\(712\) −20.9541 −0.785287
\(713\) −0.339437 −0.0127120
\(714\) 0 0
\(715\) 0 0
\(716\) 9.52303 0.355892
\(717\) 0 0
\(718\) 10.8696 0.405651
\(719\) −11.8194 −0.440789 −0.220395 0.975411i \(-0.570734\pi\)
−0.220395 + 0.975411i \(0.570734\pi\)
\(720\) 0 0
\(721\) 21.3937 0.796744
\(722\) −16.8931 −0.628695
\(723\) 0 0
\(724\) 6.27652 0.233265
\(725\) −3.82908 −0.142209
\(726\) 0 0
\(727\) −21.9675 −0.814729 −0.407364 0.913266i \(-0.633552\pi\)
−0.407364 + 0.913266i \(0.633552\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 17.8998 0.662500
\(731\) −24.3720 −0.901430
\(732\) 0 0
\(733\) −36.0586 −1.33186 −0.665928 0.746016i \(-0.731964\pi\)
−0.665928 + 0.746016i \(0.731964\pi\)
\(734\) −6.70841 −0.247612
\(735\) 0 0
\(736\) −0.488582 −0.0180094
\(737\) −7.91185 −0.291437
\(738\) 0 0
\(739\) 36.9842 1.36049 0.680243 0.732987i \(-0.261874\pi\)
0.680243 + 0.732987i \(0.261874\pi\)
\(740\) −2.02177 −0.0743218
\(741\) 0 0
\(742\) 33.7875 1.24038
\(743\) −1.42865 −0.0524120 −0.0262060 0.999657i \(-0.508343\pi\)
−0.0262060 + 0.999657i \(0.508343\pi\)
\(744\) 0 0
\(745\) −11.4668 −0.420111
\(746\) −15.8170 −0.579102
\(747\) 0 0
\(748\) 2.89008 0.105672
\(749\) −31.8702 −1.16451
\(750\) 0 0
\(751\) −37.9874 −1.38618 −0.693091 0.720850i \(-0.743752\pi\)
−0.693091 + 0.720850i \(0.743752\pi\)
\(752\) −5.74466 −0.209486
\(753\) 0 0
\(754\) 0 0
\(755\) 6.17092 0.224583
\(756\) 0 0
\(757\) 30.6805 1.11510 0.557551 0.830142i \(-0.311741\pi\)
0.557551 + 0.830142i \(0.311741\pi\)
\(758\) 9.96615 0.361987
\(759\) 0 0
\(760\) −7.11960 −0.258255
\(761\) 52.1213 1.88939 0.944697 0.327944i \(-0.106356\pi\)
0.944697 + 0.327944i \(0.106356\pi\)
\(762\) 0 0
\(763\) 22.9095 0.829378
\(764\) 3.20046 0.115788
\(765\) 0 0
\(766\) 0.952411 0.0344120
\(767\) 0 0
\(768\) 0 0
\(769\) 30.4222 1.09705 0.548526 0.836133i \(-0.315189\pi\)
0.548526 + 0.836133i \(0.315189\pi\)
\(770\) 2.80194 0.100975
\(771\) 0 0
\(772\) 5.02954 0.181017
\(773\) 23.1118 0.831275 0.415637 0.909530i \(-0.363559\pi\)
0.415637 + 0.909530i \(0.363559\pi\)
\(774\) 0 0
\(775\) 1.71379 0.0615612
\(776\) 33.9691 1.21942
\(777\) 0 0
\(778\) 36.0127 1.29112
\(779\) −13.4340 −0.481324
\(780\) 0 0
\(781\) 7.14675 0.255731
\(782\) −1.60388 −0.0573545
\(783\) 0 0
\(784\) 5.68127 0.202902
\(785\) −15.3080 −0.546365
\(786\) 0 0
\(787\) −16.2929 −0.580780 −0.290390 0.956908i \(-0.593785\pi\)
−0.290390 + 0.956908i \(0.593785\pi\)
\(788\) −9.12631 −0.325111
\(789\) 0 0
\(790\) 13.2416 0.471115
\(791\) 15.4765 0.550281
\(792\) 0 0
\(793\) 0 0
\(794\) −41.3183 −1.46633
\(795\) 0 0
\(796\) −8.88663 −0.314978
\(797\) −18.2573 −0.646705 −0.323353 0.946279i \(-0.604810\pi\)
−0.323353 + 0.946279i \(0.604810\pi\)
\(798\) 0 0
\(799\) 12.8116 0.453243
\(800\) 2.46681 0.0872150
\(801\) 0 0
\(802\) 13.7711 0.486273
\(803\) −14.3545 −0.506559
\(804\) 0 0
\(805\) 0.445042 0.0156857
\(806\) 0 0
\(807\) 0 0
\(808\) −24.9748 −0.878609
\(809\) 24.7259 0.869315 0.434658 0.900596i \(-0.356869\pi\)
0.434658 + 0.900596i \(0.356869\pi\)
\(810\) 0 0
\(811\) 3.05429 0.107251 0.0536254 0.998561i \(-0.482922\pi\)
0.0536254 + 0.998561i \(0.482922\pi\)
\(812\) −3.82908 −0.134375
\(813\) 0 0
\(814\) −5.66487 −0.198554
\(815\) −19.5918 −0.686271
\(816\) 0 0
\(817\) −8.76377 −0.306606
\(818\) 41.5773 1.45372
\(819\) 0 0
\(820\) 2.56033 0.0894108
\(821\) 17.7646 0.619990 0.309995 0.950738i \(-0.399673\pi\)
0.309995 + 0.950738i \(0.399673\pi\)
\(822\) 0 0
\(823\) 32.1333 1.12010 0.560049 0.828460i \(-0.310782\pi\)
0.560049 + 0.828460i \(0.310782\pi\)
\(824\) 29.0291 1.01128
\(825\) 0 0
\(826\) 27.5676 0.959201
\(827\) −24.5724 −0.854467 −0.427233 0.904141i \(-0.640512\pi\)
−0.427233 + 0.904141i \(0.640512\pi\)
\(828\) 0 0
\(829\) −9.57135 −0.332427 −0.166213 0.986090i \(-0.553154\pi\)
−0.166213 + 0.986090i \(0.553154\pi\)
\(830\) 15.8605 0.550528
\(831\) 0 0
\(832\) 0 0
\(833\) −12.6703 −0.438998
\(834\) 0 0
\(835\) −9.05429 −0.313337
\(836\) 1.03923 0.0359425
\(837\) 0 0
\(838\) −49.7633 −1.71904
\(839\) −48.3510 −1.66926 −0.834632 0.550808i \(-0.814320\pi\)
−0.834632 + 0.550808i \(0.814320\pi\)
\(840\) 0 0
\(841\) −14.3381 −0.494418
\(842\) 11.7423 0.404665
\(843\) 0 0
\(844\) 4.33752 0.149304
\(845\) 0 0
\(846\) 0 0
\(847\) 22.4698 0.772071
\(848\) 35.1129 1.20578
\(849\) 0 0
\(850\) 8.09783 0.277753
\(851\) −0.899772 −0.0308438
\(852\) 0 0
\(853\) 0.524090 0.0179445 0.00897225 0.999960i \(-0.497144\pi\)
0.00897225 + 0.999960i \(0.497144\pi\)
\(854\) 38.1444 1.30527
\(855\) 0 0
\(856\) −43.2446 −1.47807
\(857\) 19.9377 0.681058 0.340529 0.940234i \(-0.389394\pi\)
0.340529 + 0.940234i \(0.389394\pi\)
\(858\) 0 0
\(859\) −34.8437 −1.18885 −0.594425 0.804151i \(-0.702620\pi\)
−0.594425 + 0.804151i \(0.702620\pi\)
\(860\) 1.67025 0.0569551
\(861\) 0 0
\(862\) −32.4185 −1.10418
\(863\) −15.4416 −0.525638 −0.262819 0.964845i \(-0.584652\pi\)
−0.262819 + 0.964845i \(0.584652\pi\)
\(864\) 0 0
\(865\) 13.4547 0.457475
\(866\) 8.64981 0.293932
\(867\) 0 0
\(868\) 1.71379 0.0581699
\(869\) −10.6189 −0.360223
\(870\) 0 0
\(871\) 0 0
\(872\) 31.0858 1.05270
\(873\) 0 0
\(874\) −0.576728 −0.0195081
\(875\) −2.24698 −0.0759618
\(876\) 0 0
\(877\) 7.15751 0.241692 0.120846 0.992671i \(-0.461439\pi\)
0.120846 + 0.992671i \(0.461439\pi\)
\(878\) 23.2905 0.786017
\(879\) 0 0
\(880\) 2.91185 0.0981586
\(881\) 29.9420 1.00877 0.504386 0.863479i \(-0.331719\pi\)
0.504386 + 0.863479i \(0.331719\pi\)
\(882\) 0 0
\(883\) 18.5139 0.623043 0.311522 0.950239i \(-0.399161\pi\)
0.311522 + 0.950239i \(0.399161\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −46.0441 −1.54688
\(887\) 46.5991 1.56464 0.782322 0.622874i \(-0.214035\pi\)
0.782322 + 0.622874i \(0.214035\pi\)
\(888\) 0 0
\(889\) 41.4674 1.39077
\(890\) 8.57002 0.287268
\(891\) 0 0
\(892\) 10.9191 0.365600
\(893\) 4.60686 0.154163
\(894\) 0 0
\(895\) −21.3980 −0.715258
\(896\) −13.8509 −0.462725
\(897\) 0 0
\(898\) 19.1890 0.640344
\(899\) −6.56225 −0.218863
\(900\) 0 0
\(901\) −78.3081 −2.60882
\(902\) 7.17390 0.238865
\(903\) 0 0
\(904\) 21.0000 0.698450
\(905\) −14.1032 −0.468807
\(906\) 0 0
\(907\) 25.6004 0.850048 0.425024 0.905182i \(-0.360266\pi\)
0.425024 + 0.905182i \(0.360266\pi\)
\(908\) 0.00968868 0.000321530 0
\(909\) 0 0
\(910\) 0 0
\(911\) 24.9782 0.827566 0.413783 0.910376i \(-0.364207\pi\)
0.413783 + 0.910376i \(0.364207\pi\)
\(912\) 0 0
\(913\) −12.7192 −0.420943
\(914\) −31.5418 −1.04331
\(915\) 0 0
\(916\) −3.27950 −0.108358
\(917\) 18.2446 0.602489
\(918\) 0 0
\(919\) 38.5338 1.27111 0.635556 0.772055i \(-0.280771\pi\)
0.635556 + 0.772055i \(0.280771\pi\)
\(920\) 0.603875 0.0199092
\(921\) 0 0
\(922\) 10.8321 0.356735
\(923\) 0 0
\(924\) 0 0
\(925\) 4.54288 0.149369
\(926\) 2.16554 0.0711640
\(927\) 0 0
\(928\) −9.44563 −0.310068
\(929\) 36.7840 1.20684 0.603422 0.797422i \(-0.293803\pi\)
0.603422 + 0.797422i \(0.293803\pi\)
\(930\) 0 0
\(931\) −4.55602 −0.149318
\(932\) −3.60925 −0.118225
\(933\) 0 0
\(934\) −27.8297 −0.910615
\(935\) −6.49396 −0.212375
\(936\) 0 0
\(937\) −10.3244 −0.337283 −0.168641 0.985677i \(-0.553938\pi\)
−0.168641 + 0.985677i \(0.553938\pi\)
\(938\) −22.1685 −0.723828
\(939\) 0 0
\(940\) −0.878002 −0.0286373
\(941\) −21.8170 −0.711214 −0.355607 0.934636i \(-0.615726\pi\)
−0.355607 + 0.934636i \(0.615726\pi\)
\(942\) 0 0
\(943\) 1.13946 0.0371058
\(944\) 28.6491 0.932448
\(945\) 0 0
\(946\) 4.67994 0.152158
\(947\) 59.4476 1.93179 0.965893 0.258942i \(-0.0833738\pi\)
0.965893 + 0.258942i \(0.0833738\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 2.91185 0.0944730
\(951\) 0 0
\(952\) 44.4892 1.44190
\(953\) −21.4601 −0.695161 −0.347581 0.937650i \(-0.612997\pi\)
−0.347581 + 0.937650i \(0.612997\pi\)
\(954\) 0 0
\(955\) −7.19136 −0.232707
\(956\) −2.84010 −0.0918554
\(957\) 0 0
\(958\) 33.2650 1.07474
\(959\) 48.9342 1.58017
\(960\) 0 0
\(961\) −28.0629 −0.905255
\(962\) 0 0
\(963\) 0 0
\(964\) 0.579121 0.0186522
\(965\) −11.3013 −0.363801
\(966\) 0 0
\(967\) 8.09379 0.260279 0.130139 0.991496i \(-0.458458\pi\)
0.130139 + 0.991496i \(0.458458\pi\)
\(968\) 30.4892 0.979959
\(969\) 0 0
\(970\) −13.8931 −0.446080
\(971\) −55.6238 −1.78505 −0.892527 0.450994i \(-0.851070\pi\)
−0.892527 + 0.450994i \(0.851070\pi\)
\(972\) 0 0
\(973\) 43.6045 1.39790
\(974\) 10.7447 0.344281
\(975\) 0 0
\(976\) 39.6407 1.26887
\(977\) 38.0847 1.21844 0.609219 0.793002i \(-0.291483\pi\)
0.609219 + 0.793002i \(0.291483\pi\)
\(978\) 0 0
\(979\) −6.87263 −0.219650
\(980\) 0.868313 0.0277373
\(981\) 0 0
\(982\) 1.23729 0.0394835
\(983\) −7.66786 −0.244567 −0.122283 0.992495i \(-0.539022\pi\)
−0.122283 + 0.992495i \(0.539022\pi\)
\(984\) 0 0
\(985\) 20.5066 0.653396
\(986\) −31.0073 −0.987473
\(987\) 0 0
\(988\) 0 0
\(989\) 0.743332 0.0236366
\(990\) 0 0
\(991\) −34.7784 −1.10477 −0.552386 0.833589i \(-0.686282\pi\)
−0.552386 + 0.833589i \(0.686282\pi\)
\(992\) 4.22760 0.134227
\(993\) 0 0
\(994\) 20.0248 0.635147
\(995\) 19.9681 0.633030
\(996\) 0 0
\(997\) −59.5220 −1.88508 −0.942540 0.334094i \(-0.891570\pi\)
−0.942540 + 0.334094i \(0.891570\pi\)
\(998\) 20.8418 0.659734
\(999\) 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 7605.2.a.bq.1.3 3
3.2 odd 2 2535.2.a.bd.1.1 yes 3
13.12 even 2 7605.2.a.bz.1.1 3
39.38 odd 2 2535.2.a.v.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2535.2.a.v.1.3 3 39.38 odd 2
2535.2.a.bd.1.1 yes 3 3.2 odd 2
7605.2.a.bq.1.3 3 1.1 even 1 trivial
7605.2.a.bz.1.1 3 13.12 even 2