Properties

Label 6024.2.a.o.1.2
Level $6024$
Weight $2$
Character 6024.1
Self dual yes
Analytic conductor $48.102$
Analytic rank $1$
Dimension $14$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6024,2,Mod(1,6024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6024, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6024.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6024 = 2^{3} \cdot 3 \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6024.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: \(48.1018821776\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 3 x^{13} - 43 x^{12} + 119 x^{11} + 679 x^{10} - 1667 x^{9} - 4890 x^{8} + 9662 x^{7} + 16575 x^{6} - 20277 x^{5} - 25196 x^{4} + 8040 x^{3} + 10776 x^{2} + \cdots - 416 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.42255\) of defining polynomial
Character \(\chi\) \(=\) 6024.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -3.42255 q^{5} -3.90388 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -3.42255 q^{5} -3.90388 q^{7} +1.00000 q^{9} -4.19109 q^{11} -1.32382 q^{13} +3.42255 q^{15} +2.02268 q^{17} -0.592230 q^{19} +3.90388 q^{21} +2.66343 q^{23} +6.71385 q^{25} -1.00000 q^{27} +6.79017 q^{29} +0.654960 q^{31} +4.19109 q^{33} +13.3612 q^{35} +7.41699 q^{37} +1.32382 q^{39} +7.06823 q^{41} +6.29612 q^{43} -3.42255 q^{45} +4.83861 q^{47} +8.24026 q^{49} -2.02268 q^{51} -1.29738 q^{53} +14.3442 q^{55} +0.592230 q^{57} -9.96586 q^{59} -1.18394 q^{61} -3.90388 q^{63} +4.53085 q^{65} -5.19525 q^{67} -2.66343 q^{69} -7.71718 q^{71} -14.9445 q^{73} -6.71385 q^{75} +16.3615 q^{77} +6.29169 q^{79} +1.00000 q^{81} -14.1069 q^{83} -6.92272 q^{85} -6.79017 q^{87} +1.06762 q^{89} +5.16805 q^{91} -0.654960 q^{93} +2.02694 q^{95} +5.41590 q^{97} -4.19109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 14 q^{3} - 3 q^{5} + 7 q^{7} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 14 q^{3} - 3 q^{5} + 7 q^{7} + 14 q^{9} - 22 q^{11} + 9 q^{13} + 3 q^{15} - 7 q^{21} - 17 q^{23} + 25 q^{25} - 14 q^{27} - 18 q^{29} - 7 q^{31} + 22 q^{33} - 27 q^{35} + 9 q^{37} - 9 q^{39} - 6 q^{41} - 14 q^{43} - 3 q^{45} - 15 q^{47} + 15 q^{49} - 11 q^{53} + 2 q^{55} - 36 q^{59} + 2 q^{61} + 7 q^{63} + 8 q^{65} + 3 q^{67} + 17 q^{69} - 29 q^{71} + 2 q^{73} - 25 q^{75} + 8 q^{77} + 23 q^{79} + 14 q^{81} - 55 q^{83} + 7 q^{85} + 18 q^{87} + 9 q^{89} - 22 q^{91} + 7 q^{93} - 27 q^{95} + 17 q^{97} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −3.42255 −1.53061 −0.765305 0.643667i \(-0.777412\pi\)
−0.765305 + 0.643667i \(0.777412\pi\)
\(6\) 0 0
\(7\) −3.90388 −1.47553 −0.737763 0.675059i \(-0.764118\pi\)
−0.737763 + 0.675059i \(0.764118\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.19109 −1.26366 −0.631830 0.775107i \(-0.717696\pi\)
−0.631830 + 0.775107i \(0.717696\pi\)
\(12\) 0 0
\(13\) −1.32382 −0.367163 −0.183581 0.983005i \(-0.558769\pi\)
−0.183581 + 0.983005i \(0.558769\pi\)
\(14\) 0 0
\(15\) 3.42255 0.883699
\(16\) 0 0
\(17\) 2.02268 0.490572 0.245286 0.969451i \(-0.421118\pi\)
0.245286 + 0.969451i \(0.421118\pi\)
\(18\) 0 0
\(19\) −0.592230 −0.135867 −0.0679334 0.997690i \(-0.521641\pi\)
−0.0679334 + 0.997690i \(0.521641\pi\)
\(20\) 0 0
\(21\) 3.90388 0.851896
\(22\) 0 0
\(23\) 2.66343 0.555363 0.277682 0.960673i \(-0.410434\pi\)
0.277682 + 0.960673i \(0.410434\pi\)
\(24\) 0 0
\(25\) 6.71385 1.34277
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 6.79017 1.26090 0.630451 0.776229i \(-0.282870\pi\)
0.630451 + 0.776229i \(0.282870\pi\)
\(30\) 0 0
\(31\) 0.654960 0.117634 0.0588171 0.998269i \(-0.481267\pi\)
0.0588171 + 0.998269i \(0.481267\pi\)
\(32\) 0 0
\(33\) 4.19109 0.729575
\(34\) 0 0
\(35\) 13.3612 2.25846
\(36\) 0 0
\(37\) 7.41699 1.21935 0.609673 0.792653i \(-0.291301\pi\)
0.609673 + 0.792653i \(0.291301\pi\)
\(38\) 0 0
\(39\) 1.32382 0.211982
\(40\) 0 0
\(41\) 7.06823 1.10387 0.551936 0.833886i \(-0.313889\pi\)
0.551936 + 0.833886i \(0.313889\pi\)
\(42\) 0 0
\(43\) 6.29612 0.960149 0.480075 0.877228i \(-0.340610\pi\)
0.480075 + 0.877228i \(0.340610\pi\)
\(44\) 0 0
\(45\) −3.42255 −0.510204
\(46\) 0 0
\(47\) 4.83861 0.705784 0.352892 0.935664i \(-0.385198\pi\)
0.352892 + 0.935664i \(0.385198\pi\)
\(48\) 0 0
\(49\) 8.24026 1.17718
\(50\) 0 0
\(51\) −2.02268 −0.283232
\(52\) 0 0
\(53\) −1.29738 −0.178209 −0.0891046 0.996022i \(-0.528401\pi\)
−0.0891046 + 0.996022i \(0.528401\pi\)
\(54\) 0 0
\(55\) 14.3442 1.93417
\(56\) 0 0
\(57\) 0.592230 0.0784427
\(58\) 0 0
\(59\) −9.96586 −1.29744 −0.648722 0.761025i \(-0.724696\pi\)
−0.648722 + 0.761025i \(0.724696\pi\)
\(60\) 0 0
\(61\) −1.18394 −0.151589 −0.0757943 0.997123i \(-0.524149\pi\)
−0.0757943 + 0.997123i \(0.524149\pi\)
\(62\) 0 0
\(63\) −3.90388 −0.491842
\(64\) 0 0
\(65\) 4.53085 0.561983
\(66\) 0 0
\(67\) −5.19525 −0.634701 −0.317351 0.948308i \(-0.602793\pi\)
−0.317351 + 0.948308i \(0.602793\pi\)
\(68\) 0 0
\(69\) −2.66343 −0.320639
\(70\) 0 0
\(71\) −7.71718 −0.915861 −0.457930 0.888988i \(-0.651409\pi\)
−0.457930 + 0.888988i \(0.651409\pi\)
\(72\) 0 0
\(73\) −14.9445 −1.74913 −0.874563 0.484912i \(-0.838852\pi\)
−0.874563 + 0.484912i \(0.838852\pi\)
\(74\) 0 0
\(75\) −6.71385 −0.775248
\(76\) 0 0
\(77\) 16.3615 1.86457
\(78\) 0 0
\(79\) 6.29169 0.707871 0.353935 0.935270i \(-0.384843\pi\)
0.353935 + 0.935270i \(0.384843\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.1069 −1.54844 −0.774219 0.632918i \(-0.781857\pi\)
−0.774219 + 0.632918i \(0.781857\pi\)
\(84\) 0 0
\(85\) −6.92272 −0.750875
\(86\) 0 0
\(87\) −6.79017 −0.727983
\(88\) 0 0
\(89\) 1.06762 0.113167 0.0565836 0.998398i \(-0.481979\pi\)
0.0565836 + 0.998398i \(0.481979\pi\)
\(90\) 0 0
\(91\) 5.16805 0.541759
\(92\) 0 0
\(93\) −0.654960 −0.0679162
\(94\) 0 0
\(95\) 2.02694 0.207959
\(96\) 0 0
\(97\) 5.41590 0.549902 0.274951 0.961458i \(-0.411338\pi\)
0.274951 + 0.961458i \(0.411338\pi\)
\(98\) 0 0
\(99\) −4.19109 −0.421220
\(100\) 0 0
\(101\) −8.01940 −0.797960 −0.398980 0.916960i \(-0.630636\pi\)
−0.398980 + 0.916960i \(0.630636\pi\)
\(102\) 0 0
\(103\) 13.0264 1.28353 0.641765 0.766901i \(-0.278202\pi\)
0.641765 + 0.766901i \(0.278202\pi\)
\(104\) 0 0
\(105\) −13.3612 −1.30392
\(106\) 0 0
\(107\) −4.57643 −0.442420 −0.221210 0.975226i \(-0.571001\pi\)
−0.221210 + 0.975226i \(0.571001\pi\)
\(108\) 0 0
\(109\) −6.22019 −0.595786 −0.297893 0.954599i \(-0.596284\pi\)
−0.297893 + 0.954599i \(0.596284\pi\)
\(110\) 0 0
\(111\) −7.41699 −0.703990
\(112\) 0 0
\(113\) 1.37635 0.129476 0.0647379 0.997902i \(-0.479379\pi\)
0.0647379 + 0.997902i \(0.479379\pi\)
\(114\) 0 0
\(115\) −9.11572 −0.850045
\(116\) 0 0
\(117\) −1.32382 −0.122388
\(118\) 0 0
\(119\) −7.89630 −0.723852
\(120\) 0 0
\(121\) 6.56522 0.596839
\(122\) 0 0
\(123\) −7.06823 −0.637321
\(124\) 0 0
\(125\) −5.86572 −0.524646
\(126\) 0 0
\(127\) 11.2459 0.997916 0.498958 0.866626i \(-0.333716\pi\)
0.498958 + 0.866626i \(0.333716\pi\)
\(128\) 0 0
\(129\) −6.29612 −0.554342
\(130\) 0 0
\(131\) −6.91756 −0.604390 −0.302195 0.953246i \(-0.597719\pi\)
−0.302195 + 0.953246i \(0.597719\pi\)
\(132\) 0 0
\(133\) 2.31199 0.200475
\(134\) 0 0
\(135\) 3.42255 0.294566
\(136\) 0 0
\(137\) 0.468996 0.0400691 0.0200345 0.999799i \(-0.493622\pi\)
0.0200345 + 0.999799i \(0.493622\pi\)
\(138\) 0 0
\(139\) 11.3818 0.965393 0.482696 0.875788i \(-0.339657\pi\)
0.482696 + 0.875788i \(0.339657\pi\)
\(140\) 0 0
\(141\) −4.83861 −0.407485
\(142\) 0 0
\(143\) 5.54827 0.463969
\(144\) 0 0
\(145\) −23.2397 −1.92995
\(146\) 0 0
\(147\) −8.24026 −0.679645
\(148\) 0 0
\(149\) 12.9159 1.05811 0.529054 0.848588i \(-0.322547\pi\)
0.529054 + 0.848588i \(0.322547\pi\)
\(150\) 0 0
\(151\) 4.99361 0.406374 0.203187 0.979140i \(-0.434870\pi\)
0.203187 + 0.979140i \(0.434870\pi\)
\(152\) 0 0
\(153\) 2.02268 0.163524
\(154\) 0 0
\(155\) −2.24163 −0.180052
\(156\) 0 0
\(157\) 18.4359 1.47134 0.735671 0.677339i \(-0.236867\pi\)
0.735671 + 0.677339i \(0.236867\pi\)
\(158\) 0 0
\(159\) 1.29738 0.102889
\(160\) 0 0
\(161\) −10.3977 −0.819454
\(162\) 0 0
\(163\) 4.47891 0.350815 0.175408 0.984496i \(-0.443876\pi\)
0.175408 + 0.984496i \(0.443876\pi\)
\(164\) 0 0
\(165\) −14.3442 −1.11670
\(166\) 0 0
\(167\) −12.0001 −0.928594 −0.464297 0.885680i \(-0.653693\pi\)
−0.464297 + 0.885680i \(0.653693\pi\)
\(168\) 0 0
\(169\) −11.2475 −0.865191
\(170\) 0 0
\(171\) −0.592230 −0.0452889
\(172\) 0 0
\(173\) −9.01711 −0.685558 −0.342779 0.939416i \(-0.611368\pi\)
−0.342779 + 0.939416i \(0.611368\pi\)
\(174\) 0 0
\(175\) −26.2100 −1.98129
\(176\) 0 0
\(177\) 9.96586 0.749080
\(178\) 0 0
\(179\) 8.47311 0.633310 0.316655 0.948541i \(-0.397440\pi\)
0.316655 + 0.948541i \(0.397440\pi\)
\(180\) 0 0
\(181\) 14.0206 1.04214 0.521072 0.853513i \(-0.325532\pi\)
0.521072 + 0.853513i \(0.325532\pi\)
\(182\) 0 0
\(183\) 1.18394 0.0875197
\(184\) 0 0
\(185\) −25.3850 −1.86634
\(186\) 0 0
\(187\) −8.47723 −0.619917
\(188\) 0 0
\(189\) 3.90388 0.283965
\(190\) 0 0
\(191\) −8.96559 −0.648727 −0.324364 0.945932i \(-0.605150\pi\)
−0.324364 + 0.945932i \(0.605150\pi\)
\(192\) 0 0
\(193\) 10.0671 0.724645 0.362323 0.932053i \(-0.381984\pi\)
0.362323 + 0.932053i \(0.381984\pi\)
\(194\) 0 0
\(195\) −4.53085 −0.324461
\(196\) 0 0
\(197\) −14.5224 −1.03468 −0.517340 0.855780i \(-0.673078\pi\)
−0.517340 + 0.855780i \(0.673078\pi\)
\(198\) 0 0
\(199\) −16.7736 −1.18905 −0.594525 0.804077i \(-0.702660\pi\)
−0.594525 + 0.804077i \(0.702660\pi\)
\(200\) 0 0
\(201\) 5.19525 0.366445
\(202\) 0 0
\(203\) −26.5080 −1.86050
\(204\) 0 0
\(205\) −24.1914 −1.68960
\(206\) 0 0
\(207\) 2.66343 0.185121
\(208\) 0 0
\(209\) 2.48209 0.171690
\(210\) 0 0
\(211\) 4.01992 0.276743 0.138371 0.990380i \(-0.455813\pi\)
0.138371 + 0.990380i \(0.455813\pi\)
\(212\) 0 0
\(213\) 7.71718 0.528772
\(214\) 0 0
\(215\) −21.5488 −1.46961
\(216\) 0 0
\(217\) −2.55688 −0.173573
\(218\) 0 0
\(219\) 14.9445 1.00986
\(220\) 0 0
\(221\) −2.67767 −0.180120
\(222\) 0 0
\(223\) 8.04684 0.538856 0.269428 0.963021i \(-0.413165\pi\)
0.269428 + 0.963021i \(0.413165\pi\)
\(224\) 0 0
\(225\) 6.71385 0.447590
\(226\) 0 0
\(227\) −19.2181 −1.27555 −0.637776 0.770222i \(-0.720145\pi\)
−0.637776 + 0.770222i \(0.720145\pi\)
\(228\) 0 0
\(229\) 1.84628 0.122006 0.0610029 0.998138i \(-0.480570\pi\)
0.0610029 + 0.998138i \(0.480570\pi\)
\(230\) 0 0
\(231\) −16.3615 −1.07651
\(232\) 0 0
\(233\) −0.372758 −0.0244202 −0.0122101 0.999925i \(-0.503887\pi\)
−0.0122101 + 0.999925i \(0.503887\pi\)
\(234\) 0 0
\(235\) −16.5604 −1.08028
\(236\) 0 0
\(237\) −6.29169 −0.408689
\(238\) 0 0
\(239\) 24.9151 1.61162 0.805812 0.592171i \(-0.201729\pi\)
0.805812 + 0.592171i \(0.201729\pi\)
\(240\) 0 0
\(241\) 13.3473 0.859774 0.429887 0.902883i \(-0.358553\pi\)
0.429887 + 0.902883i \(0.358553\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −28.2027 −1.80180
\(246\) 0 0
\(247\) 0.784008 0.0498852
\(248\) 0 0
\(249\) 14.1069 0.893991
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) −11.1627 −0.701791
\(254\) 0 0
\(255\) 6.92272 0.433518
\(256\) 0 0
\(257\) 13.2700 0.827757 0.413879 0.910332i \(-0.364174\pi\)
0.413879 + 0.910332i \(0.364174\pi\)
\(258\) 0 0
\(259\) −28.9550 −1.79918
\(260\) 0 0
\(261\) 6.79017 0.420301
\(262\) 0 0
\(263\) 6.30949 0.389060 0.194530 0.980897i \(-0.437682\pi\)
0.194530 + 0.980897i \(0.437682\pi\)
\(264\) 0 0
\(265\) 4.44035 0.272769
\(266\) 0 0
\(267\) −1.06762 −0.0653371
\(268\) 0 0
\(269\) −14.3581 −0.875432 −0.437716 0.899113i \(-0.644212\pi\)
−0.437716 + 0.899113i \(0.644212\pi\)
\(270\) 0 0
\(271\) 22.4332 1.36272 0.681361 0.731948i \(-0.261388\pi\)
0.681361 + 0.731948i \(0.261388\pi\)
\(272\) 0 0
\(273\) −5.16805 −0.312784
\(274\) 0 0
\(275\) −28.1383 −1.69680
\(276\) 0 0
\(277\) 16.3951 0.985087 0.492544 0.870288i \(-0.336067\pi\)
0.492544 + 0.870288i \(0.336067\pi\)
\(278\) 0 0
\(279\) 0.654960 0.0392114
\(280\) 0 0
\(281\) 16.1631 0.964208 0.482104 0.876114i \(-0.339873\pi\)
0.482104 + 0.876114i \(0.339873\pi\)
\(282\) 0 0
\(283\) −12.6630 −0.752735 −0.376368 0.926470i \(-0.622827\pi\)
−0.376368 + 0.926470i \(0.622827\pi\)
\(284\) 0 0
\(285\) −2.02694 −0.120065
\(286\) 0 0
\(287\) −27.5935 −1.62879
\(288\) 0 0
\(289\) −12.9088 −0.759339
\(290\) 0 0
\(291\) −5.41590 −0.317486
\(292\) 0 0
\(293\) 16.7646 0.979396 0.489698 0.871892i \(-0.337107\pi\)
0.489698 + 0.871892i \(0.337107\pi\)
\(294\) 0 0
\(295\) 34.1087 1.98588
\(296\) 0 0
\(297\) 4.19109 0.243192
\(298\) 0 0
\(299\) −3.52591 −0.203909
\(300\) 0 0
\(301\) −24.5793 −1.41673
\(302\) 0 0
\(303\) 8.01940 0.460702
\(304\) 0 0
\(305\) 4.05211 0.232023
\(306\) 0 0
\(307\) −21.4014 −1.22144 −0.610722 0.791845i \(-0.709121\pi\)
−0.610722 + 0.791845i \(0.709121\pi\)
\(308\) 0 0
\(309\) −13.0264 −0.741047
\(310\) 0 0
\(311\) −7.73908 −0.438843 −0.219422 0.975630i \(-0.570417\pi\)
−0.219422 + 0.975630i \(0.570417\pi\)
\(312\) 0 0
\(313\) 5.66051 0.319951 0.159976 0.987121i \(-0.448858\pi\)
0.159976 + 0.987121i \(0.448858\pi\)
\(314\) 0 0
\(315\) 13.3612 0.752819
\(316\) 0 0
\(317\) 1.88564 0.105908 0.0529539 0.998597i \(-0.483136\pi\)
0.0529539 + 0.998597i \(0.483136\pi\)
\(318\) 0 0
\(319\) −28.4582 −1.59335
\(320\) 0 0
\(321\) 4.57643 0.255432
\(322\) 0 0
\(323\) −1.19789 −0.0666525
\(324\) 0 0
\(325\) −8.88795 −0.493015
\(326\) 0 0
\(327\) 6.22019 0.343977
\(328\) 0 0
\(329\) −18.8893 −1.04140
\(330\) 0 0
\(331\) −22.8190 −1.25425 −0.627123 0.778920i \(-0.715768\pi\)
−0.627123 + 0.778920i \(0.715768\pi\)
\(332\) 0 0
\(333\) 7.41699 0.406449
\(334\) 0 0
\(335\) 17.7810 0.971481
\(336\) 0 0
\(337\) 7.08711 0.386059 0.193030 0.981193i \(-0.438169\pi\)
0.193030 + 0.981193i \(0.438169\pi\)
\(338\) 0 0
\(339\) −1.37635 −0.0747528
\(340\) 0 0
\(341\) −2.74500 −0.148650
\(342\) 0 0
\(343\) −4.84181 −0.261433
\(344\) 0 0
\(345\) 9.11572 0.490774
\(346\) 0 0
\(347\) 12.7890 0.686552 0.343276 0.939235i \(-0.388463\pi\)
0.343276 + 0.939235i \(0.388463\pi\)
\(348\) 0 0
\(349\) −28.4637 −1.52363 −0.761814 0.647796i \(-0.775691\pi\)
−0.761814 + 0.647796i \(0.775691\pi\)
\(350\) 0 0
\(351\) 1.32382 0.0706605
\(352\) 0 0
\(353\) −24.2046 −1.28828 −0.644142 0.764906i \(-0.722785\pi\)
−0.644142 + 0.764906i \(0.722785\pi\)
\(354\) 0 0
\(355\) 26.4124 1.40183
\(356\) 0 0
\(357\) 7.89630 0.417916
\(358\) 0 0
\(359\) −22.0683 −1.16472 −0.582361 0.812930i \(-0.697871\pi\)
−0.582361 + 0.812930i \(0.697871\pi\)
\(360\) 0 0
\(361\) −18.6493 −0.981540
\(362\) 0 0
\(363\) −6.56522 −0.344585
\(364\) 0 0
\(365\) 51.1484 2.67723
\(366\) 0 0
\(367\) 25.0165 1.30585 0.652925 0.757423i \(-0.273542\pi\)
0.652925 + 0.757423i \(0.273542\pi\)
\(368\) 0 0
\(369\) 7.06823 0.367957
\(370\) 0 0
\(371\) 5.06482 0.262952
\(372\) 0 0
\(373\) 22.9992 1.19085 0.595427 0.803409i \(-0.296983\pi\)
0.595427 + 0.803409i \(0.296983\pi\)
\(374\) 0 0
\(375\) 5.86572 0.302905
\(376\) 0 0
\(377\) −8.98899 −0.462957
\(378\) 0 0
\(379\) −5.40672 −0.277725 −0.138862 0.990312i \(-0.544345\pi\)
−0.138862 + 0.990312i \(0.544345\pi\)
\(380\) 0 0
\(381\) −11.2459 −0.576147
\(382\) 0 0
\(383\) 0.0852658 0.00435688 0.00217844 0.999998i \(-0.499307\pi\)
0.00217844 + 0.999998i \(0.499307\pi\)
\(384\) 0 0
\(385\) −55.9980 −2.85392
\(386\) 0 0
\(387\) 6.29612 0.320050
\(388\) 0 0
\(389\) −38.2372 −1.93870 −0.969351 0.245680i \(-0.920989\pi\)
−0.969351 + 0.245680i \(0.920989\pi\)
\(390\) 0 0
\(391\) 5.38727 0.272446
\(392\) 0 0
\(393\) 6.91756 0.348945
\(394\) 0 0
\(395\) −21.5336 −1.08347
\(396\) 0 0
\(397\) 15.5580 0.780835 0.390417 0.920638i \(-0.372331\pi\)
0.390417 + 0.920638i \(0.372331\pi\)
\(398\) 0 0
\(399\) −2.31199 −0.115744
\(400\) 0 0
\(401\) 14.1348 0.705860 0.352930 0.935650i \(-0.385185\pi\)
0.352930 + 0.935650i \(0.385185\pi\)
\(402\) 0 0
\(403\) −0.867052 −0.0431909
\(404\) 0 0
\(405\) −3.42255 −0.170068
\(406\) 0 0
\(407\) −31.0853 −1.54084
\(408\) 0 0
\(409\) 28.1895 1.39388 0.696940 0.717130i \(-0.254544\pi\)
0.696940 + 0.717130i \(0.254544\pi\)
\(410\) 0 0
\(411\) −0.468996 −0.0231339
\(412\) 0 0
\(413\) 38.9055 1.91441
\(414\) 0 0
\(415\) 48.2817 2.37005
\(416\) 0 0
\(417\) −11.3818 −0.557370
\(418\) 0 0
\(419\) 2.13793 0.104445 0.0522224 0.998635i \(-0.483370\pi\)
0.0522224 + 0.998635i \(0.483370\pi\)
\(420\) 0 0
\(421\) −23.4041 −1.14065 −0.570324 0.821420i \(-0.693182\pi\)
−0.570324 + 0.821420i \(0.693182\pi\)
\(422\) 0 0
\(423\) 4.83861 0.235261
\(424\) 0 0
\(425\) 13.5800 0.658725
\(426\) 0 0
\(427\) 4.62197 0.223673
\(428\) 0 0
\(429\) −5.54827 −0.267873
\(430\) 0 0
\(431\) 5.07250 0.244334 0.122167 0.992510i \(-0.461016\pi\)
0.122167 + 0.992510i \(0.461016\pi\)
\(432\) 0 0
\(433\) −10.7359 −0.515933 −0.257967 0.966154i \(-0.583052\pi\)
−0.257967 + 0.966154i \(0.583052\pi\)
\(434\) 0 0
\(435\) 23.2397 1.11426
\(436\) 0 0
\(437\) −1.57736 −0.0754554
\(438\) 0 0
\(439\) −9.61779 −0.459032 −0.229516 0.973305i \(-0.573714\pi\)
−0.229516 + 0.973305i \(0.573714\pi\)
\(440\) 0 0
\(441\) 8.24026 0.392393
\(442\) 0 0
\(443\) 5.06313 0.240557 0.120278 0.992740i \(-0.461621\pi\)
0.120278 + 0.992740i \(0.461621\pi\)
\(444\) 0 0
\(445\) −3.65397 −0.173215
\(446\) 0 0
\(447\) −12.9159 −0.610899
\(448\) 0 0
\(449\) −14.9630 −0.706147 −0.353074 0.935596i \(-0.614863\pi\)
−0.353074 + 0.935596i \(0.614863\pi\)
\(450\) 0 0
\(451\) −29.6236 −1.39492
\(452\) 0 0
\(453\) −4.99361 −0.234620
\(454\) 0 0
\(455\) −17.6879 −0.829222
\(456\) 0 0
\(457\) 24.1616 1.13023 0.565116 0.825012i \(-0.308831\pi\)
0.565116 + 0.825012i \(0.308831\pi\)
\(458\) 0 0
\(459\) −2.02268 −0.0944106
\(460\) 0 0
\(461\) 17.3181 0.806582 0.403291 0.915072i \(-0.367866\pi\)
0.403291 + 0.915072i \(0.367866\pi\)
\(462\) 0 0
\(463\) −5.45093 −0.253326 −0.126663 0.991946i \(-0.540427\pi\)
−0.126663 + 0.991946i \(0.540427\pi\)
\(464\) 0 0
\(465\) 2.24163 0.103953
\(466\) 0 0
\(467\) −40.7328 −1.88489 −0.942445 0.334362i \(-0.891479\pi\)
−0.942445 + 0.334362i \(0.891479\pi\)
\(468\) 0 0
\(469\) 20.2816 0.936519
\(470\) 0 0
\(471\) −18.4359 −0.849480
\(472\) 0 0
\(473\) −26.3876 −1.21330
\(474\) 0 0
\(475\) −3.97614 −0.182438
\(476\) 0 0
\(477\) −1.29738 −0.0594030
\(478\) 0 0
\(479\) −30.7273 −1.40397 −0.701984 0.712193i \(-0.747702\pi\)
−0.701984 + 0.712193i \(0.747702\pi\)
\(480\) 0 0
\(481\) −9.81879 −0.447698
\(482\) 0 0
\(483\) 10.3977 0.473112
\(484\) 0 0
\(485\) −18.5362 −0.841685
\(486\) 0 0
\(487\) 31.0244 1.40585 0.702924 0.711265i \(-0.251877\pi\)
0.702924 + 0.711265i \(0.251877\pi\)
\(488\) 0 0
\(489\) −4.47891 −0.202543
\(490\) 0 0
\(491\) −11.8207 −0.533461 −0.266730 0.963771i \(-0.585943\pi\)
−0.266730 + 0.963771i \(0.585943\pi\)
\(492\) 0 0
\(493\) 13.7343 0.618564
\(494\) 0 0
\(495\) 14.3442 0.644724
\(496\) 0 0
\(497\) 30.1269 1.35138
\(498\) 0 0
\(499\) 22.5459 1.00930 0.504648 0.863325i \(-0.331622\pi\)
0.504648 + 0.863325i \(0.331622\pi\)
\(500\) 0 0
\(501\) 12.0001 0.536124
\(502\) 0 0
\(503\) −36.0088 −1.60555 −0.802775 0.596281i \(-0.796644\pi\)
−0.802775 + 0.596281i \(0.796644\pi\)
\(504\) 0 0
\(505\) 27.4468 1.22137
\(506\) 0 0
\(507\) 11.2475 0.499519
\(508\) 0 0
\(509\) −3.10751 −0.137738 −0.0688691 0.997626i \(-0.521939\pi\)
−0.0688691 + 0.997626i \(0.521939\pi\)
\(510\) 0 0
\(511\) 58.3416 2.58088
\(512\) 0 0
\(513\) 0.592230 0.0261476
\(514\) 0 0
\(515\) −44.5835 −1.96459
\(516\) 0 0
\(517\) −20.2791 −0.891872
\(518\) 0 0
\(519\) 9.01711 0.395807
\(520\) 0 0
\(521\) 16.6481 0.729365 0.364682 0.931132i \(-0.381178\pi\)
0.364682 + 0.931132i \(0.381178\pi\)
\(522\) 0 0
\(523\) −9.66216 −0.422497 −0.211248 0.977432i \(-0.567753\pi\)
−0.211248 + 0.977432i \(0.567753\pi\)
\(524\) 0 0
\(525\) 26.2100 1.14390
\(526\) 0 0
\(527\) 1.32477 0.0577081
\(528\) 0 0
\(529\) −15.9061 −0.691571
\(530\) 0 0
\(531\) −9.96586 −0.432481
\(532\) 0 0
\(533\) −9.35710 −0.405301
\(534\) 0 0
\(535\) 15.6631 0.677173
\(536\) 0 0
\(537\) −8.47311 −0.365642
\(538\) 0 0
\(539\) −34.5356 −1.48756
\(540\) 0 0
\(541\) −10.9248 −0.469692 −0.234846 0.972033i \(-0.575459\pi\)
−0.234846 + 0.972033i \(0.575459\pi\)
\(542\) 0 0
\(543\) −14.0206 −0.601682
\(544\) 0 0
\(545\) 21.2889 0.911917
\(546\) 0 0
\(547\) −44.5636 −1.90540 −0.952701 0.303908i \(-0.901708\pi\)
−0.952701 + 0.303908i \(0.901708\pi\)
\(548\) 0 0
\(549\) −1.18394 −0.0505295
\(550\) 0 0
\(551\) −4.02134 −0.171315
\(552\) 0 0
\(553\) −24.5620 −1.04448
\(554\) 0 0
\(555\) 25.3850 1.07753
\(556\) 0 0
\(557\) −0.626224 −0.0265340 −0.0132670 0.999912i \(-0.504223\pi\)
−0.0132670 + 0.999912i \(0.504223\pi\)
\(558\) 0 0
\(559\) −8.33496 −0.352531
\(560\) 0 0
\(561\) 8.47723 0.357909
\(562\) 0 0
\(563\) 16.6656 0.702372 0.351186 0.936306i \(-0.385779\pi\)
0.351186 + 0.936306i \(0.385779\pi\)
\(564\) 0 0
\(565\) −4.71061 −0.198177
\(566\) 0 0
\(567\) −3.90388 −0.163947
\(568\) 0 0
\(569\) −6.34649 −0.266059 −0.133029 0.991112i \(-0.542470\pi\)
−0.133029 + 0.991112i \(0.542470\pi\)
\(570\) 0 0
\(571\) −3.53134 −0.147782 −0.0738909 0.997266i \(-0.523542\pi\)
−0.0738909 + 0.997266i \(0.523542\pi\)
\(572\) 0 0
\(573\) 8.96559 0.374543
\(574\) 0 0
\(575\) 17.8819 0.745725
\(576\) 0 0
\(577\) 33.4936 1.39436 0.697179 0.716898i \(-0.254438\pi\)
0.697179 + 0.716898i \(0.254438\pi\)
\(578\) 0 0
\(579\) −10.0671 −0.418374
\(580\) 0 0
\(581\) 55.0717 2.28476
\(582\) 0 0
\(583\) 5.43744 0.225196
\(584\) 0 0
\(585\) 4.53085 0.187328
\(586\) 0 0
\(587\) −44.3552 −1.83073 −0.915367 0.402621i \(-0.868099\pi\)
−0.915367 + 0.402621i \(0.868099\pi\)
\(588\) 0 0
\(589\) −0.387887 −0.0159826
\(590\) 0 0
\(591\) 14.5224 0.597372
\(592\) 0 0
\(593\) 18.0365 0.740669 0.370335 0.928898i \(-0.379243\pi\)
0.370335 + 0.928898i \(0.379243\pi\)
\(594\) 0 0
\(595\) 27.0255 1.10794
\(596\) 0 0
\(597\) 16.7736 0.686498
\(598\) 0 0
\(599\) 3.89875 0.159299 0.0796493 0.996823i \(-0.474620\pi\)
0.0796493 + 0.996823i \(0.474620\pi\)
\(600\) 0 0
\(601\) −26.5753 −1.08403 −0.542014 0.840370i \(-0.682338\pi\)
−0.542014 + 0.840370i \(0.682338\pi\)
\(602\) 0 0
\(603\) −5.19525 −0.211567
\(604\) 0 0
\(605\) −22.4698 −0.913528
\(606\) 0 0
\(607\) 8.31269 0.337402 0.168701 0.985667i \(-0.446043\pi\)
0.168701 + 0.985667i \(0.446043\pi\)
\(608\) 0 0
\(609\) 26.5080 1.07416
\(610\) 0 0
\(611\) −6.40547 −0.259138
\(612\) 0 0
\(613\) 4.82520 0.194888 0.0974439 0.995241i \(-0.468933\pi\)
0.0974439 + 0.995241i \(0.468933\pi\)
\(614\) 0 0
\(615\) 24.1914 0.975490
\(616\) 0 0
\(617\) −20.4154 −0.821895 −0.410948 0.911659i \(-0.634802\pi\)
−0.410948 + 0.911659i \(0.634802\pi\)
\(618\) 0 0
\(619\) −25.3880 −1.02043 −0.510215 0.860047i \(-0.670434\pi\)
−0.510215 + 0.860047i \(0.670434\pi\)
\(620\) 0 0
\(621\) −2.66343 −0.106880
\(622\) 0 0
\(623\) −4.16785 −0.166981
\(624\) 0 0
\(625\) −13.4935 −0.539740
\(626\) 0 0
\(627\) −2.48209 −0.0991250
\(628\) 0 0
\(629\) 15.0022 0.598177
\(630\) 0 0
\(631\) 22.9024 0.911729 0.455864 0.890049i \(-0.349330\pi\)
0.455864 + 0.890049i \(0.349330\pi\)
\(632\) 0 0
\(633\) −4.01992 −0.159777
\(634\) 0 0
\(635\) −38.4898 −1.52742
\(636\) 0 0
\(637\) −10.9087 −0.432217
\(638\) 0 0
\(639\) −7.71718 −0.305287
\(640\) 0 0
\(641\) −2.30989 −0.0912352 −0.0456176 0.998959i \(-0.514526\pi\)
−0.0456176 + 0.998959i \(0.514526\pi\)
\(642\) 0 0
\(643\) −10.4908 −0.413718 −0.206859 0.978371i \(-0.566324\pi\)
−0.206859 + 0.978371i \(0.566324\pi\)
\(644\) 0 0
\(645\) 21.5488 0.848482
\(646\) 0 0
\(647\) 0.285006 0.0112047 0.00560237 0.999984i \(-0.498217\pi\)
0.00560237 + 0.999984i \(0.498217\pi\)
\(648\) 0 0
\(649\) 41.7678 1.63953
\(650\) 0 0
\(651\) 2.55688 0.100212
\(652\) 0 0
\(653\) 2.73617 0.107074 0.0535372 0.998566i \(-0.482950\pi\)
0.0535372 + 0.998566i \(0.482950\pi\)
\(654\) 0 0
\(655\) 23.6757 0.925086
\(656\) 0 0
\(657\) −14.9445 −0.583042
\(658\) 0 0
\(659\) 34.9986 1.36335 0.681676 0.731655i \(-0.261252\pi\)
0.681676 + 0.731655i \(0.261252\pi\)
\(660\) 0 0
\(661\) 34.6372 1.34723 0.673616 0.739082i \(-0.264740\pi\)
0.673616 + 0.739082i \(0.264740\pi\)
\(662\) 0 0
\(663\) 2.67767 0.103992
\(664\) 0 0
\(665\) −7.91291 −0.306849
\(666\) 0 0
\(667\) 18.0851 0.700259
\(668\) 0 0
\(669\) −8.04684 −0.311109
\(670\) 0 0
\(671\) 4.96202 0.191557
\(672\) 0 0
\(673\) 3.12234 0.120357 0.0601787 0.998188i \(-0.480833\pi\)
0.0601787 + 0.998188i \(0.480833\pi\)
\(674\) 0 0
\(675\) −6.71385 −0.258416
\(676\) 0 0
\(677\) 41.5426 1.59661 0.798307 0.602251i \(-0.205729\pi\)
0.798307 + 0.602251i \(0.205729\pi\)
\(678\) 0 0
\(679\) −21.1430 −0.811395
\(680\) 0 0
\(681\) 19.2181 0.736440
\(682\) 0 0
\(683\) −4.46317 −0.170778 −0.0853892 0.996348i \(-0.527213\pi\)
−0.0853892 + 0.996348i \(0.527213\pi\)
\(684\) 0 0
\(685\) −1.60516 −0.0613301
\(686\) 0 0
\(687\) −1.84628 −0.0704401
\(688\) 0 0
\(689\) 1.71751 0.0654318
\(690\) 0 0
\(691\) −26.8149 −1.02009 −0.510044 0.860148i \(-0.670371\pi\)
−0.510044 + 0.860148i \(0.670371\pi\)
\(692\) 0 0
\(693\) 16.3615 0.621522
\(694\) 0 0
\(695\) −38.9548 −1.47764
\(696\) 0 0
\(697\) 14.2968 0.541529
\(698\) 0 0
\(699\) 0.372758 0.0140990
\(700\) 0 0
\(701\) −2.53215 −0.0956380 −0.0478190 0.998856i \(-0.515227\pi\)
−0.0478190 + 0.998856i \(0.515227\pi\)
\(702\) 0 0
\(703\) −4.39256 −0.165669
\(704\) 0 0
\(705\) 16.5604 0.623700
\(706\) 0 0
\(707\) 31.3067 1.17741
\(708\) 0 0
\(709\) 31.8029 1.19438 0.597192 0.802098i \(-0.296283\pi\)
0.597192 + 0.802098i \(0.296283\pi\)
\(710\) 0 0
\(711\) 6.29169 0.235957
\(712\) 0 0
\(713\) 1.74444 0.0653298
\(714\) 0 0
\(715\) −18.9892 −0.710156
\(716\) 0 0
\(717\) −24.9151 −0.930472
\(718\) 0 0
\(719\) 47.0081 1.75311 0.876554 0.481304i \(-0.159837\pi\)
0.876554 + 0.481304i \(0.159837\pi\)
\(720\) 0 0
\(721\) −50.8535 −1.89388
\(722\) 0 0
\(723\) −13.3473 −0.496391
\(724\) 0 0
\(725\) 45.5882 1.69310
\(726\) 0 0
\(727\) −29.3615 −1.08896 −0.544479 0.838774i \(-0.683273\pi\)
−0.544479 + 0.838774i \(0.683273\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 12.7350 0.471022
\(732\) 0 0
\(733\) 37.7676 1.39498 0.697490 0.716595i \(-0.254300\pi\)
0.697490 + 0.716595i \(0.254300\pi\)
\(734\) 0 0
\(735\) 28.2027 1.04027
\(736\) 0 0
\(737\) 21.7738 0.802047
\(738\) 0 0
\(739\) −27.3273 −1.00525 −0.502626 0.864504i \(-0.667633\pi\)
−0.502626 + 0.864504i \(0.667633\pi\)
\(740\) 0 0
\(741\) −0.784008 −0.0288013
\(742\) 0 0
\(743\) −37.9503 −1.39226 −0.696131 0.717915i \(-0.745097\pi\)
−0.696131 + 0.717915i \(0.745097\pi\)
\(744\) 0 0
\(745\) −44.2052 −1.61955
\(746\) 0 0
\(747\) −14.1069 −0.516146
\(748\) 0 0
\(749\) 17.8658 0.652803
\(750\) 0 0
\(751\) −14.8835 −0.543108 −0.271554 0.962423i \(-0.587538\pi\)
−0.271554 + 0.962423i \(0.587538\pi\)
\(752\) 0 0
\(753\) −1.00000 −0.0364420
\(754\) 0 0
\(755\) −17.0909 −0.622001
\(756\) 0 0
\(757\) 39.3672 1.43083 0.715413 0.698702i \(-0.246238\pi\)
0.715413 + 0.698702i \(0.246238\pi\)
\(758\) 0 0
\(759\) 11.1627 0.405179
\(760\) 0 0
\(761\) −12.3941 −0.449287 −0.224643 0.974441i \(-0.572122\pi\)
−0.224643 + 0.974441i \(0.572122\pi\)
\(762\) 0 0
\(763\) 24.2829 0.879098
\(764\) 0 0
\(765\) −6.92272 −0.250292
\(766\) 0 0
\(767\) 13.1930 0.476373
\(768\) 0 0
\(769\) −15.4371 −0.556677 −0.278339 0.960483i \(-0.589784\pi\)
−0.278339 + 0.960483i \(0.589784\pi\)
\(770\) 0 0
\(771\) −13.2700 −0.477906
\(772\) 0 0
\(773\) 46.4766 1.67165 0.835823 0.548999i \(-0.184991\pi\)
0.835823 + 0.548999i \(0.184991\pi\)
\(774\) 0 0
\(775\) 4.39730 0.157956
\(776\) 0 0
\(777\) 28.9550 1.03876
\(778\) 0 0
\(779\) −4.18602 −0.149980
\(780\) 0 0
\(781\) 32.3434 1.15734
\(782\) 0 0
\(783\) −6.79017 −0.242661
\(784\) 0 0
\(785\) −63.0977 −2.25205
\(786\) 0 0
\(787\) −50.0653 −1.78463 −0.892317 0.451409i \(-0.850922\pi\)
−0.892317 + 0.451409i \(0.850922\pi\)
\(788\) 0 0
\(789\) −6.30949 −0.224624
\(790\) 0 0
\(791\) −5.37309 −0.191045
\(792\) 0 0
\(793\) 1.56733 0.0556577
\(794\) 0 0
\(795\) −4.44035 −0.157483
\(796\) 0 0
\(797\) 1.78837 0.0633473 0.0316737 0.999498i \(-0.489916\pi\)
0.0316737 + 0.999498i \(0.489916\pi\)
\(798\) 0 0
\(799\) 9.78697 0.346238
\(800\) 0 0
\(801\) 1.06762 0.0377224
\(802\) 0 0
\(803\) 62.6339 2.21030
\(804\) 0 0
\(805\) 35.5866 1.25426
\(806\) 0 0
\(807\) 14.3581 0.505431
\(808\) 0 0
\(809\) 25.8439 0.908622 0.454311 0.890843i \(-0.349886\pi\)
0.454311 + 0.890843i \(0.349886\pi\)
\(810\) 0 0
\(811\) −20.2004 −0.709332 −0.354666 0.934993i \(-0.615405\pi\)
−0.354666 + 0.934993i \(0.615405\pi\)
\(812\) 0 0
\(813\) −22.4332 −0.786768
\(814\) 0 0
\(815\) −15.3293 −0.536961
\(816\) 0 0
\(817\) −3.72875 −0.130452
\(818\) 0 0
\(819\) 5.16805 0.180586
\(820\) 0 0
\(821\) −42.7491 −1.49195 −0.745977 0.665971i \(-0.768017\pi\)
−0.745977 + 0.665971i \(0.768017\pi\)
\(822\) 0 0
\(823\) 19.5627 0.681913 0.340957 0.940079i \(-0.389249\pi\)
0.340957 + 0.940079i \(0.389249\pi\)
\(824\) 0 0
\(825\) 28.1383 0.979651
\(826\) 0 0
\(827\) −47.3179 −1.64540 −0.822702 0.568472i \(-0.807535\pi\)
−0.822702 + 0.568472i \(0.807535\pi\)
\(828\) 0 0
\(829\) −15.6109 −0.542189 −0.271095 0.962553i \(-0.587386\pi\)
−0.271095 + 0.962553i \(0.587386\pi\)
\(830\) 0 0
\(831\) −16.3951 −0.568740
\(832\) 0 0
\(833\) 16.6674 0.577491
\(834\) 0 0
\(835\) 41.0708 1.42132
\(836\) 0 0
\(837\) −0.654960 −0.0226387
\(838\) 0 0
\(839\) −24.8474 −0.857828 −0.428914 0.903345i \(-0.641104\pi\)
−0.428914 + 0.903345i \(0.641104\pi\)
\(840\) 0 0
\(841\) 17.1064 0.589876
\(842\) 0 0
\(843\) −16.1631 −0.556686
\(844\) 0 0
\(845\) 38.4951 1.32427
\(846\) 0 0
\(847\) −25.6298 −0.880651
\(848\) 0 0
\(849\) 12.6630 0.434592
\(850\) 0 0
\(851\) 19.7546 0.677180
\(852\) 0 0
\(853\) −56.5910 −1.93764 −0.968819 0.247769i \(-0.920303\pi\)
−0.968819 + 0.247769i \(0.920303\pi\)
\(854\) 0 0
\(855\) 2.02694 0.0693197
\(856\) 0 0
\(857\) −14.7125 −0.502570 −0.251285 0.967913i \(-0.580853\pi\)
−0.251285 + 0.967913i \(0.580853\pi\)
\(858\) 0 0
\(859\) −1.98566 −0.0677497 −0.0338749 0.999426i \(-0.510785\pi\)
−0.0338749 + 0.999426i \(0.510785\pi\)
\(860\) 0 0
\(861\) 27.5935 0.940384
\(862\) 0 0
\(863\) −13.1719 −0.448378 −0.224189 0.974546i \(-0.571973\pi\)
−0.224189 + 0.974546i \(0.571973\pi\)
\(864\) 0 0
\(865\) 30.8615 1.04932
\(866\) 0 0
\(867\) 12.9088 0.438405
\(868\) 0 0
\(869\) −26.3690 −0.894508
\(870\) 0 0
\(871\) 6.87760 0.233039
\(872\) 0 0
\(873\) 5.41590 0.183301
\(874\) 0 0
\(875\) 22.8991 0.774130
\(876\) 0 0
\(877\) −32.4241 −1.09488 −0.547442 0.836844i \(-0.684398\pi\)
−0.547442 + 0.836844i \(0.684398\pi\)
\(878\) 0 0
\(879\) −16.7646 −0.565454
\(880\) 0 0
\(881\) −50.1840 −1.69074 −0.845372 0.534178i \(-0.820621\pi\)
−0.845372 + 0.534178i \(0.820621\pi\)
\(882\) 0 0
\(883\) 33.2133 1.11772 0.558858 0.829263i \(-0.311240\pi\)
0.558858 + 0.829263i \(0.311240\pi\)
\(884\) 0 0
\(885\) −34.1087 −1.14655
\(886\) 0 0
\(887\) −16.8362 −0.565306 −0.282653 0.959222i \(-0.591214\pi\)
−0.282653 + 0.959222i \(0.591214\pi\)
\(888\) 0 0
\(889\) −43.9028 −1.47245
\(890\) 0 0
\(891\) −4.19109 −0.140407
\(892\) 0 0
\(893\) −2.86557 −0.0958926
\(894\) 0 0
\(895\) −28.9997 −0.969352
\(896\) 0 0
\(897\) 3.52591 0.117727
\(898\) 0 0
\(899\) 4.44729 0.148325
\(900\) 0 0
\(901\) −2.62419 −0.0874244
\(902\) 0 0
\(903\) 24.5793 0.817947
\(904\) 0 0
\(905\) −47.9862 −1.59512
\(906\) 0 0
\(907\) 51.3866 1.70626 0.853131 0.521696i \(-0.174701\pi\)
0.853131 + 0.521696i \(0.174701\pi\)
\(908\) 0 0
\(909\) −8.01940 −0.265987
\(910\) 0 0
\(911\) 4.76579 0.157898 0.0789489 0.996879i \(-0.474844\pi\)
0.0789489 + 0.996879i \(0.474844\pi\)
\(912\) 0 0
\(913\) 59.1234 1.95670
\(914\) 0 0
\(915\) −4.05211 −0.133959
\(916\) 0 0
\(917\) 27.0053 0.891794
\(918\) 0 0
\(919\) −26.2194 −0.864897 −0.432449 0.901659i \(-0.642350\pi\)
−0.432449 + 0.901659i \(0.642350\pi\)
\(920\) 0 0
\(921\) 21.4014 0.705201
\(922\) 0 0
\(923\) 10.2162 0.336270
\(924\) 0 0
\(925\) 49.7965 1.63730
\(926\) 0 0
\(927\) 13.0264 0.427844
\(928\) 0 0
\(929\) 4.44801 0.145934 0.0729672 0.997334i \(-0.476753\pi\)
0.0729672 + 0.997334i \(0.476753\pi\)
\(930\) 0 0
\(931\) −4.88012 −0.159940
\(932\) 0 0
\(933\) 7.73908 0.253366
\(934\) 0 0
\(935\) 29.0138 0.948851
\(936\) 0 0
\(937\) 10.1565 0.331798 0.165899 0.986143i \(-0.446947\pi\)
0.165899 + 0.986143i \(0.446947\pi\)
\(938\) 0 0
\(939\) −5.66051 −0.184724
\(940\) 0 0
\(941\) −21.1089 −0.688131 −0.344066 0.938946i \(-0.611804\pi\)
−0.344066 + 0.938946i \(0.611804\pi\)
\(942\) 0 0
\(943\) 18.8257 0.613050
\(944\) 0 0
\(945\) −13.3612 −0.434640
\(946\) 0 0
\(947\) 33.4529 1.08707 0.543536 0.839386i \(-0.317085\pi\)
0.543536 + 0.839386i \(0.317085\pi\)
\(948\) 0 0
\(949\) 19.7839 0.642214
\(950\) 0 0
\(951\) −1.88564 −0.0611460
\(952\) 0 0
\(953\) −1.24793 −0.0404244 −0.0202122 0.999796i \(-0.506434\pi\)
−0.0202122 + 0.999796i \(0.506434\pi\)
\(954\) 0 0
\(955\) 30.6852 0.992949
\(956\) 0 0
\(957\) 28.4582 0.919923
\(958\) 0 0
\(959\) −1.83090 −0.0591230
\(960\) 0 0
\(961\) −30.5710 −0.986162
\(962\) 0 0
\(963\) −4.57643 −0.147473
\(964\) 0 0
\(965\) −34.4551 −1.10915
\(966\) 0 0
\(967\) 32.5263 1.04597 0.522987 0.852340i \(-0.324818\pi\)
0.522987 + 0.852340i \(0.324818\pi\)
\(968\) 0 0
\(969\) 1.19789 0.0384818
\(970\) 0 0
\(971\) −8.25222 −0.264826 −0.132413 0.991195i \(-0.542273\pi\)
−0.132413 + 0.991195i \(0.542273\pi\)
\(972\) 0 0
\(973\) −44.4332 −1.42446
\(974\) 0 0
\(975\) 8.88795 0.284642
\(976\) 0 0
\(977\) 43.7036 1.39820 0.699101 0.715023i \(-0.253584\pi\)
0.699101 + 0.715023i \(0.253584\pi\)
\(978\) 0 0
\(979\) −4.47448 −0.143005
\(980\) 0 0
\(981\) −6.22019 −0.198595
\(982\) 0 0
\(983\) −51.0267 −1.62750 −0.813750 0.581215i \(-0.802578\pi\)
−0.813750 + 0.581215i \(0.802578\pi\)
\(984\) 0 0
\(985\) 49.7037 1.58369
\(986\) 0 0
\(987\) 18.8893 0.601255
\(988\) 0 0
\(989\) 16.7693 0.533232
\(990\) 0 0
\(991\) −19.2203 −0.610554 −0.305277 0.952264i \(-0.598749\pi\)
−0.305277 + 0.952264i \(0.598749\pi\)
\(992\) 0 0
\(993\) 22.8190 0.724139
\(994\) 0 0
\(995\) 57.4085 1.81997
\(996\) 0 0
\(997\) −11.7823 −0.373149 −0.186574 0.982441i \(-0.559739\pi\)
−0.186574 + 0.982441i \(0.559739\pi\)
\(998\) 0 0
\(999\) −7.41699 −0.234663
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 6024.2.a.o.1.2 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6024.2.a.o.1.2 14 1.1 even 1 trivial