Properties

Label 1183.2.c.j.337.10
Level $1183$
Weight $2$
Character 1183.337
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
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] = [1183,2,Mod(337,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1183.337");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.c (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 337.10
Character \(\chi\) \(=\) 1183.337
Dual form 1183.2.c.j.337.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.961590i q^{2} -1.98737 q^{3} +1.07534 q^{4} +3.39320i q^{5} +1.91103i q^{6} -1.00000i q^{7} -2.95722i q^{8} +0.949635 q^{9} +O(q^{10})\) \(q-0.961590i q^{2} -1.98737 q^{3} +1.07534 q^{4} +3.39320i q^{5} +1.91103i q^{6} -1.00000i q^{7} -2.95722i q^{8} +0.949635 q^{9} +3.26287 q^{10} -4.59237i q^{11} -2.13711 q^{12} -0.961590 q^{14} -6.74354i q^{15} -0.692948 q^{16} -2.44749 q^{17} -0.913160i q^{18} +4.77408i q^{19} +3.64886i q^{20} +1.98737i q^{21} -4.41598 q^{22} +4.04446 q^{23} +5.87709i q^{24} -6.51382 q^{25} +4.07483 q^{27} -1.07534i q^{28} -3.20889 q^{29} -6.48453 q^{30} -4.83171i q^{31} -5.24811i q^{32} +9.12674i q^{33} +2.35349i q^{34} +3.39320 q^{35} +1.02118 q^{36} -9.61127i q^{37} +4.59071 q^{38} +10.0344 q^{40} -8.99377i q^{41} +1.91103 q^{42} +8.90960 q^{43} -4.93838i q^{44} +3.22230i q^{45} -3.88911i q^{46} +5.37660i q^{47} +1.37714 q^{48} -1.00000 q^{49} +6.26362i q^{50} +4.86407 q^{51} +9.97733 q^{53} -3.91832i q^{54} +15.5829 q^{55} -2.95722 q^{56} -9.48786i q^{57} +3.08564i q^{58} -10.5145i q^{59} -7.25163i q^{60} +5.29731 q^{61} -4.64612 q^{62} -0.949635i q^{63} -6.43243 q^{64} +8.77619 q^{66} +14.0270i q^{67} -2.63190 q^{68} -8.03783 q^{69} -3.26287i q^{70} -8.52794i q^{71} -2.80828i q^{72} -6.62822i q^{73} -9.24211 q^{74} +12.9454 q^{75} +5.13378i q^{76} -4.59237 q^{77} -7.98042 q^{79} -2.35131i q^{80} -10.9471 q^{81} -8.64833 q^{82} -7.30165i q^{83} +2.13711i q^{84} -8.30484i q^{85} -8.56739i q^{86} +6.37725 q^{87} -13.5807 q^{88} -18.1007i q^{89} +3.09854 q^{90} +4.34918 q^{92} +9.60239i q^{93} +5.17009 q^{94} -16.1994 q^{95} +10.4299i q^{96} +6.90825i q^{97} +0.961590i q^{98} -4.36108i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 0.961590i − 0.679947i −0.940435 0.339974i \(-0.889582\pi\)
0.940435 0.339974i \(-0.110418\pi\)
\(3\) −1.98737 −1.14741 −0.573704 0.819063i \(-0.694494\pi\)
−0.573704 + 0.819063i \(0.694494\pi\)
\(4\) 1.07534 0.537672
\(5\) 3.39320i 1.51749i 0.651390 + 0.758743i \(0.274186\pi\)
−0.651390 + 0.758743i \(0.725814\pi\)
\(6\) 1.91103i 0.780177i
\(7\) − 1.00000i − 0.377964i
\(8\) − 2.95722i − 1.04554i
\(9\) 0.949635 0.316545
\(10\) 3.26287 1.03181
\(11\) − 4.59237i − 1.38465i −0.721584 0.692326i \(-0.756586\pi\)
0.721584 0.692326i \(-0.243414\pi\)
\(12\) −2.13711 −0.616929
\(13\) 0 0
\(14\) −0.961590 −0.256996
\(15\) − 6.74354i − 1.74118i
\(16\) −0.692948 −0.173237
\(17\) −2.44749 −0.593604 −0.296802 0.954939i \(-0.595920\pi\)
−0.296802 + 0.954939i \(0.595920\pi\)
\(18\) − 0.913160i − 0.215234i
\(19\) 4.77408i 1.09525i 0.836724 + 0.547625i \(0.184468\pi\)
−0.836724 + 0.547625i \(0.815532\pi\)
\(20\) 3.64886i 0.815910i
\(21\) 1.98737i 0.433679i
\(22\) −4.41598 −0.941491
\(23\) 4.04446 0.843328 0.421664 0.906752i \(-0.361446\pi\)
0.421664 + 0.906752i \(0.361446\pi\)
\(24\) 5.87709i 1.19966i
\(25\) −6.51382 −1.30276
\(26\) 0 0
\(27\) 4.07483 0.784202
\(28\) − 1.07534i − 0.203221i
\(29\) −3.20889 −0.595876 −0.297938 0.954585i \(-0.596299\pi\)
−0.297938 + 0.954585i \(0.596299\pi\)
\(30\) −6.48453 −1.18391
\(31\) − 4.83171i − 0.867800i −0.900961 0.433900i \(-0.857137\pi\)
0.900961 0.433900i \(-0.142863\pi\)
\(32\) − 5.24811i − 0.927744i
\(33\) 9.12674i 1.58876i
\(34\) 2.35349i 0.403620i
\(35\) 3.39320 0.573556
\(36\) 1.02118 0.170197
\(37\) − 9.61127i − 1.58008i −0.613053 0.790042i \(-0.710059\pi\)
0.613053 0.790042i \(-0.289941\pi\)
\(38\) 4.59071 0.744712
\(39\) 0 0
\(40\) 10.0344 1.58659
\(41\) − 8.99377i − 1.40459i −0.711885 0.702296i \(-0.752158\pi\)
0.711885 0.702296i \(-0.247842\pi\)
\(42\) 1.91103 0.294879
\(43\) 8.90960 1.35870 0.679351 0.733814i \(-0.262261\pi\)
0.679351 + 0.733814i \(0.262261\pi\)
\(44\) − 4.93838i − 0.744489i
\(45\) 3.22230i 0.480353i
\(46\) − 3.88911i − 0.573418i
\(47\) 5.37660i 0.784258i 0.919910 + 0.392129i \(0.128261\pi\)
−0.919910 + 0.392129i \(0.871739\pi\)
\(48\) 1.37714 0.198773
\(49\) −1.00000 −0.142857
\(50\) 6.26362i 0.885810i
\(51\) 4.86407 0.681106
\(52\) 0 0
\(53\) 9.97733 1.37049 0.685246 0.728312i \(-0.259695\pi\)
0.685246 + 0.728312i \(0.259695\pi\)
\(54\) − 3.91832i − 0.533216i
\(55\) 15.5829 2.10119
\(56\) −2.95722 −0.395175
\(57\) − 9.48786i − 1.25670i
\(58\) 3.08564i 0.405165i
\(59\) − 10.5145i − 1.36888i −0.729071 0.684438i \(-0.760047\pi\)
0.729071 0.684438i \(-0.239953\pi\)
\(60\) − 7.25163i − 0.936181i
\(61\) 5.29731 0.678252 0.339126 0.940741i \(-0.389869\pi\)
0.339126 + 0.940741i \(0.389869\pi\)
\(62\) −4.64612 −0.590058
\(63\) − 0.949635i − 0.119643i
\(64\) −6.43243 −0.804054
\(65\) 0 0
\(66\) 8.77619 1.08027
\(67\) 14.0270i 1.71367i 0.515588 + 0.856837i \(0.327574\pi\)
−0.515588 + 0.856837i \(0.672426\pi\)
\(68\) −2.63190 −0.319164
\(69\) −8.03783 −0.967641
\(70\) − 3.26287i − 0.389988i
\(71\) − 8.52794i − 1.01208i −0.862510 0.506040i \(-0.831109\pi\)
0.862510 0.506040i \(-0.168891\pi\)
\(72\) − 2.80828i − 0.330959i
\(73\) − 6.62822i − 0.775775i −0.921707 0.387887i \(-0.873205\pi\)
0.921707 0.387887i \(-0.126795\pi\)
\(74\) −9.24211 −1.07437
\(75\) 12.9454 1.49480
\(76\) 5.13378i 0.588885i
\(77\) −4.59237 −0.523350
\(78\) 0 0
\(79\) −7.98042 −0.897867 −0.448934 0.893565i \(-0.648196\pi\)
−0.448934 + 0.893565i \(0.648196\pi\)
\(80\) − 2.35131i − 0.262885i
\(81\) −10.9471 −1.21634
\(82\) −8.64833 −0.955048
\(83\) − 7.30165i − 0.801460i −0.916196 0.400730i \(-0.868756\pi\)
0.916196 0.400730i \(-0.131244\pi\)
\(84\) 2.13711i 0.233177i
\(85\) − 8.30484i − 0.900786i
\(86\) − 8.56739i − 0.923845i
\(87\) 6.37725 0.683713
\(88\) −13.5807 −1.44770
\(89\) − 18.1007i − 1.91867i −0.282265 0.959337i \(-0.591086\pi\)
0.282265 0.959337i \(-0.408914\pi\)
\(90\) 3.09854 0.326614
\(91\) 0 0
\(92\) 4.34918 0.453434
\(93\) 9.60239i 0.995721i
\(94\) 5.17009 0.533254
\(95\) −16.1994 −1.66203
\(96\) 10.4299i 1.06450i
\(97\) 6.90825i 0.701426i 0.936483 + 0.350713i \(0.114061\pi\)
−0.936483 + 0.350713i \(0.885939\pi\)
\(98\) 0.961590i 0.0971353i
\(99\) − 4.36108i − 0.438305i
\(100\) −7.00459 −0.700459
\(101\) −6.10247 −0.607218 −0.303609 0.952797i \(-0.598192\pi\)
−0.303609 + 0.952797i \(0.598192\pi\)
\(102\) − 4.67725i − 0.463116i
\(103\) 3.66700 0.361320 0.180660 0.983546i \(-0.442177\pi\)
0.180660 + 0.983546i \(0.442177\pi\)
\(104\) 0 0
\(105\) −6.74354 −0.658102
\(106\) − 9.59411i − 0.931862i
\(107\) 9.82398 0.949720 0.474860 0.880061i \(-0.342499\pi\)
0.474860 + 0.880061i \(0.342499\pi\)
\(108\) 4.38184 0.421643
\(109\) 1.51609i 0.145215i 0.997361 + 0.0726074i \(0.0231320\pi\)
−0.997361 + 0.0726074i \(0.976868\pi\)
\(110\) − 14.9843i − 1.42870i
\(111\) 19.1011i 1.81300i
\(112\) 0.692948i 0.0654774i
\(113\) 10.7558 1.01182 0.505908 0.862587i \(-0.331158\pi\)
0.505908 + 0.862587i \(0.331158\pi\)
\(114\) −9.12344 −0.854488
\(115\) 13.7237i 1.27974i
\(116\) −3.45066 −0.320386
\(117\) 0 0
\(118\) −10.1107 −0.930764
\(119\) 2.44749i 0.224361i
\(120\) −19.9421 −1.82046
\(121\) −10.0899 −0.917264
\(122\) − 5.09385i − 0.461175i
\(123\) 17.8739i 1.61164i
\(124\) − 5.19575i − 0.466592i
\(125\) − 5.13668i − 0.459439i
\(126\) −0.913160 −0.0813508
\(127\) 11.0034 0.976390 0.488195 0.872735i \(-0.337655\pi\)
0.488195 + 0.872735i \(0.337655\pi\)
\(128\) − 4.31086i − 0.381030i
\(129\) −17.7067 −1.55899
\(130\) 0 0
\(131\) −7.69627 −0.672426 −0.336213 0.941786i \(-0.609146\pi\)
−0.336213 + 0.941786i \(0.609146\pi\)
\(132\) 9.81439i 0.854233i
\(133\) 4.77408 0.413965
\(134\) 13.4883 1.16521
\(135\) 13.8267i 1.19001i
\(136\) 7.23778i 0.620634i
\(137\) − 2.91596i − 0.249128i −0.992212 0.124564i \(-0.960247\pi\)
0.992212 0.124564i \(-0.0397532\pi\)
\(138\) 7.72910i 0.657945i
\(139\) 7.38529 0.626412 0.313206 0.949685i \(-0.398597\pi\)
0.313206 + 0.949685i \(0.398597\pi\)
\(140\) 3.64886 0.308385
\(141\) − 10.6853i − 0.899864i
\(142\) −8.20039 −0.688161
\(143\) 0 0
\(144\) −0.658048 −0.0548373
\(145\) − 10.8884i − 0.904234i
\(146\) −6.37363 −0.527486
\(147\) 1.98737 0.163915
\(148\) − 10.3354i − 0.849567i
\(149\) − 5.62392i − 0.460730i −0.973104 0.230365i \(-0.926008\pi\)
0.973104 0.230365i \(-0.0739919\pi\)
\(150\) − 12.4481i − 1.01639i
\(151\) 8.87295i 0.722071i 0.932552 + 0.361035i \(0.117577\pi\)
−0.932552 + 0.361035i \(0.882423\pi\)
\(152\) 14.1180 1.14512
\(153\) −2.32423 −0.187903
\(154\) 4.41598i 0.355850i
\(155\) 16.3950 1.31687
\(156\) 0 0
\(157\) −14.7335 −1.17586 −0.587929 0.808913i \(-0.700056\pi\)
−0.587929 + 0.808913i \(0.700056\pi\)
\(158\) 7.67389i 0.610502i
\(159\) −19.8286 −1.57251
\(160\) 17.8079 1.40784
\(161\) − 4.04446i − 0.318748i
\(162\) 10.5266i 0.827050i
\(163\) − 17.4467i − 1.36653i −0.730170 0.683265i \(-0.760559\pi\)
0.730170 0.683265i \(-0.239441\pi\)
\(164\) − 9.67140i − 0.755209i
\(165\) −30.9689 −2.41092
\(166\) −7.02120 −0.544951
\(167\) 12.3209i 0.953422i 0.879060 + 0.476711i \(0.158171\pi\)
−0.879060 + 0.476711i \(0.841829\pi\)
\(168\) 5.87709 0.453427
\(169\) 0 0
\(170\) −7.98585 −0.612487
\(171\) 4.53364i 0.346696i
\(172\) 9.58089 0.730536
\(173\) −0.540871 −0.0411217 −0.0205608 0.999789i \(-0.506545\pi\)
−0.0205608 + 0.999789i \(0.506545\pi\)
\(174\) − 6.13231i − 0.464889i
\(175\) 6.51382i 0.492398i
\(176\) 3.18228i 0.239873i
\(177\) 20.8963i 1.57066i
\(178\) −17.4055 −1.30460
\(179\) −13.6466 −1.02000 −0.509999 0.860175i \(-0.670354\pi\)
−0.509999 + 0.860175i \(0.670354\pi\)
\(180\) 3.46509i 0.258272i
\(181\) −1.83569 −0.136446 −0.0682230 0.997670i \(-0.521733\pi\)
−0.0682230 + 0.997670i \(0.521733\pi\)
\(182\) 0 0
\(183\) −10.5277 −0.778231
\(184\) − 11.9604i − 0.881729i
\(185\) 32.6130 2.39775
\(186\) 9.23356 0.677038
\(187\) 11.2398i 0.821936i
\(188\) 5.78169i 0.421673i
\(189\) − 4.07483i − 0.296400i
\(190\) 15.5772i 1.13009i
\(191\) −10.1490 −0.734356 −0.367178 0.930151i \(-0.619676\pi\)
−0.367178 + 0.930151i \(0.619676\pi\)
\(192\) 12.7836 0.922577
\(193\) 4.66529i 0.335815i 0.985803 + 0.167908i \(0.0537010\pi\)
−0.985803 + 0.167908i \(0.946299\pi\)
\(194\) 6.64291 0.476933
\(195\) 0 0
\(196\) −1.07534 −0.0768103
\(197\) 9.10037i 0.648375i 0.945993 + 0.324187i \(0.105091\pi\)
−0.945993 + 0.324187i \(0.894909\pi\)
\(198\) −4.19357 −0.298024
\(199\) 13.4461 0.953168 0.476584 0.879129i \(-0.341875\pi\)
0.476584 + 0.879129i \(0.341875\pi\)
\(200\) 19.2628i 1.36209i
\(201\) − 27.8769i − 1.96628i
\(202\) 5.86808i 0.412876i
\(203\) 3.20889i 0.225220i
\(204\) 5.23055 0.366212
\(205\) 30.5177 2.13145
\(206\) − 3.52615i − 0.245678i
\(207\) 3.84076 0.266951
\(208\) 0 0
\(209\) 21.9244 1.51654
\(210\) 6.48453i 0.447475i
\(211\) 11.9909 0.825490 0.412745 0.910847i \(-0.364570\pi\)
0.412745 + 0.910847i \(0.364570\pi\)
\(212\) 10.7291 0.736875
\(213\) 16.9482i 1.16127i
\(214\) − 9.44664i − 0.645759i
\(215\) 30.2321i 2.06181i
\(216\) − 12.0502i − 0.819911i
\(217\) −4.83171 −0.327998
\(218\) 1.45785 0.0987384
\(219\) 13.1727i 0.890130i
\(220\) 16.7569 1.12975
\(221\) 0 0
\(222\) 18.3675 1.23274
\(223\) − 2.54948i − 0.170726i −0.996350 0.0853629i \(-0.972795\pi\)
0.996350 0.0853629i \(-0.0272050\pi\)
\(224\) −5.24811 −0.350654
\(225\) −6.18575 −0.412383
\(226\) − 10.3426i − 0.687981i
\(227\) − 8.99748i − 0.597184i −0.954381 0.298592i \(-0.903483\pi\)
0.954381 0.298592i \(-0.0965169\pi\)
\(228\) − 10.2027i − 0.675691i
\(229\) − 7.21104i − 0.476519i −0.971202 0.238259i \(-0.923423\pi\)
0.971202 0.238259i \(-0.0765769\pi\)
\(230\) 13.1965 0.870154
\(231\) 9.12674 0.600496
\(232\) 9.48941i 0.623010i
\(233\) −13.1933 −0.864323 −0.432162 0.901796i \(-0.642249\pi\)
−0.432162 + 0.901796i \(0.642249\pi\)
\(234\) 0 0
\(235\) −18.2439 −1.19010
\(236\) − 11.3067i − 0.736007i
\(237\) 15.8600 1.03022
\(238\) 2.35349 0.152554
\(239\) 15.9833i 1.03387i 0.856024 + 0.516936i \(0.172927\pi\)
−0.856024 + 0.516936i \(0.827073\pi\)
\(240\) 4.67292i 0.301636i
\(241\) 25.1342i 1.61903i 0.587096 + 0.809517i \(0.300271\pi\)
−0.587096 + 0.809517i \(0.699729\pi\)
\(242\) 9.70235i 0.623691i
\(243\) 9.53143 0.611442
\(244\) 5.69643 0.364677
\(245\) − 3.39320i − 0.216784i
\(246\) 17.1874 1.09583
\(247\) 0 0
\(248\) −14.2884 −0.907316
\(249\) 14.5111i 0.919602i
\(250\) −4.93939 −0.312394
\(251\) 2.94037 0.185594 0.0927972 0.995685i \(-0.470419\pi\)
0.0927972 + 0.995685i \(0.470419\pi\)
\(252\) − 1.02118i − 0.0643286i
\(253\) − 18.5737i − 1.16772i
\(254\) − 10.5807i − 0.663894i
\(255\) 16.5048i 1.03357i
\(256\) −17.0101 −1.06313
\(257\) −18.5537 −1.15735 −0.578675 0.815559i \(-0.696430\pi\)
−0.578675 + 0.815559i \(0.696430\pi\)
\(258\) 17.0266i 1.06003i
\(259\) −9.61127 −0.597216
\(260\) 0 0
\(261\) −3.04728 −0.188622
\(262\) 7.40066i 0.457214i
\(263\) −10.3996 −0.641269 −0.320634 0.947203i \(-0.603896\pi\)
−0.320634 + 0.947203i \(0.603896\pi\)
\(264\) 26.9898 1.66111
\(265\) 33.8551i 2.07970i
\(266\) − 4.59071i − 0.281475i
\(267\) 35.9728i 2.20150i
\(268\) 15.0839i 0.921394i
\(269\) 2.74007 0.167065 0.0835324 0.996505i \(-0.473380\pi\)
0.0835324 + 0.996505i \(0.473380\pi\)
\(270\) 13.2956 0.809147
\(271\) 11.0867i 0.673469i 0.941600 + 0.336735i \(0.109323\pi\)
−0.941600 + 0.336735i \(0.890677\pi\)
\(272\) 1.69599 0.102834
\(273\) 0 0
\(274\) −2.80396 −0.169394
\(275\) 29.9139i 1.80387i
\(276\) −8.64343 −0.520273
\(277\) −9.14278 −0.549336 −0.274668 0.961539i \(-0.588568\pi\)
−0.274668 + 0.961539i \(0.588568\pi\)
\(278\) − 7.10163i − 0.425927i
\(279\) − 4.58836i − 0.274698i
\(280\) − 10.0344i − 0.599673i
\(281\) − 0.571443i − 0.0340895i −0.999855 0.0170447i \(-0.994574\pi\)
0.999855 0.0170447i \(-0.00542577\pi\)
\(282\) −10.2749 −0.611860
\(283\) −18.7911 −1.11701 −0.558506 0.829500i \(-0.688625\pi\)
−0.558506 + 0.829500i \(0.688625\pi\)
\(284\) − 9.17047i − 0.544167i
\(285\) 32.1942 1.90702
\(286\) 0 0
\(287\) −8.99377 −0.530886
\(288\) − 4.98379i − 0.293673i
\(289\) −11.0098 −0.647634
\(290\) −10.4702 −0.614831
\(291\) − 13.7292i − 0.804822i
\(292\) − 7.12762i − 0.417112i
\(293\) − 9.39283i − 0.548735i −0.961625 0.274368i \(-0.911532\pi\)
0.961625 0.274368i \(-0.0884685\pi\)
\(294\) − 1.91103i − 0.111454i
\(295\) 35.6780 2.07725
\(296\) −28.4227 −1.65203
\(297\) − 18.7131i − 1.08585i
\(298\) −5.40791 −0.313272
\(299\) 0 0
\(300\) 13.9207 0.803713
\(301\) − 8.90960i − 0.513541i
\(302\) 8.53215 0.490970
\(303\) 12.1279 0.696727
\(304\) − 3.30819i − 0.189738i
\(305\) 17.9749i 1.02924i
\(306\) 2.23495i 0.127764i
\(307\) 1.39399i 0.0795591i 0.999208 + 0.0397796i \(0.0126656\pi\)
−0.999208 + 0.0397796i \(0.987334\pi\)
\(308\) −4.93838 −0.281390
\(309\) −7.28767 −0.414581
\(310\) − 15.7652i − 0.895405i
\(311\) 10.0430 0.569486 0.284743 0.958604i \(-0.408092\pi\)
0.284743 + 0.958604i \(0.408092\pi\)
\(312\) 0 0
\(313\) 29.0874 1.64411 0.822057 0.569405i \(-0.192826\pi\)
0.822057 + 0.569405i \(0.192826\pi\)
\(314\) 14.1675i 0.799521i
\(315\) 3.22230 0.181556
\(316\) −8.58169 −0.482758
\(317\) 4.50428i 0.252986i 0.991968 + 0.126493i \(0.0403721\pi\)
−0.991968 + 0.126493i \(0.959628\pi\)
\(318\) 19.0670i 1.06923i
\(319\) 14.7364i 0.825082i
\(320\) − 21.8265i − 1.22014i
\(321\) −19.5239 −1.08972
\(322\) −3.88911 −0.216732
\(323\) − 11.6845i − 0.650145i
\(324\) −11.7719 −0.653994
\(325\) 0 0
\(326\) −16.7766 −0.929168
\(327\) − 3.01302i − 0.166621i
\(328\) −26.5966 −1.46855
\(329\) 5.37660 0.296422
\(330\) 29.7794i 1.63930i
\(331\) 14.2992i 0.785953i 0.919549 + 0.392976i \(0.128555\pi\)
−0.919549 + 0.392976i \(0.871445\pi\)
\(332\) − 7.85179i − 0.430923i
\(333\) − 9.12721i − 0.500168i
\(334\) 11.8477 0.648277
\(335\) −47.5965 −2.60048
\(336\) − 1.37714i − 0.0751293i
\(337\) −28.4506 −1.54981 −0.774903 0.632081i \(-0.782201\pi\)
−0.774903 + 0.632081i \(0.782201\pi\)
\(338\) 0 0
\(339\) −21.3756 −1.16097
\(340\) − 8.93056i − 0.484327i
\(341\) −22.1890 −1.20160
\(342\) 4.35950 0.235735
\(343\) 1.00000i 0.0539949i
\(344\) − 26.3477i − 1.42057i
\(345\) − 27.2740i − 1.46838i
\(346\) 0.520097i 0.0279606i
\(347\) 27.4960 1.47606 0.738032 0.674766i \(-0.235755\pi\)
0.738032 + 0.674766i \(0.235755\pi\)
\(348\) 6.85774 0.367614
\(349\) 22.0281i 1.17914i 0.807718 + 0.589570i \(0.200703\pi\)
−0.807718 + 0.589570i \(0.799297\pi\)
\(350\) 6.26362 0.334805
\(351\) 0 0
\(352\) −24.1013 −1.28460
\(353\) 1.60451i 0.0853993i 0.999088 + 0.0426996i \(0.0135958\pi\)
−0.999088 + 0.0426996i \(0.986404\pi\)
\(354\) 20.0937 1.06797
\(355\) 28.9370 1.53582
\(356\) − 19.4645i − 1.03162i
\(357\) − 4.86407i − 0.257434i
\(358\) 13.1225i 0.693545i
\(359\) − 21.4030i − 1.12961i −0.825225 0.564804i \(-0.808952\pi\)
0.825225 0.564804i \(-0.191048\pi\)
\(360\) 9.52907 0.502226
\(361\) −3.79185 −0.199571
\(362\) 1.76518i 0.0927761i
\(363\) 20.0524 1.05248
\(364\) 0 0
\(365\) 22.4909 1.17723
\(366\) 10.1234i 0.529156i
\(367\) −17.8326 −0.930856 −0.465428 0.885086i \(-0.654100\pi\)
−0.465428 + 0.885086i \(0.654100\pi\)
\(368\) −2.80260 −0.146096
\(369\) − 8.54081i − 0.444617i
\(370\) − 31.3603i − 1.63035i
\(371\) − 9.97733i − 0.517997i
\(372\) 10.3259i 0.535371i
\(373\) 25.9981 1.34613 0.673066 0.739582i \(-0.264977\pi\)
0.673066 + 0.739582i \(0.264977\pi\)
\(374\) 10.8081 0.558873
\(375\) 10.2085i 0.527164i
\(376\) 15.8998 0.819969
\(377\) 0 0
\(378\) −3.91832 −0.201537
\(379\) − 23.0715i − 1.18510i −0.805532 0.592552i \(-0.798120\pi\)
0.805532 0.592552i \(-0.201880\pi\)
\(380\) −17.4199 −0.893624
\(381\) −21.8677 −1.12032
\(382\) 9.75919i 0.499323i
\(383\) − 7.91174i − 0.404271i −0.979358 0.202136i \(-0.935212\pi\)
0.979358 0.202136i \(-0.0647882\pi\)
\(384\) 8.56727i 0.437197i
\(385\) − 15.5829i − 0.794176i
\(386\) 4.48610 0.228336
\(387\) 8.46087 0.430090
\(388\) 7.42874i 0.377137i
\(389\) 6.69526 0.339463 0.169732 0.985490i \(-0.445710\pi\)
0.169732 + 0.985490i \(0.445710\pi\)
\(390\) 0 0
\(391\) −9.89878 −0.500603
\(392\) 2.95722i 0.149362i
\(393\) 15.2953 0.771547
\(394\) 8.75083 0.440861
\(395\) − 27.0792i − 1.36250i
\(396\) − 4.68966i − 0.235664i
\(397\) 38.8307i 1.94886i 0.224698 + 0.974428i \(0.427860\pi\)
−0.224698 + 0.974428i \(0.572140\pi\)
\(398\) − 12.9296i − 0.648104i
\(399\) −9.48786 −0.474987
\(400\) 4.51374 0.225687
\(401\) 25.5291i 1.27486i 0.770508 + 0.637431i \(0.220003\pi\)
−0.770508 + 0.637431i \(0.779997\pi\)
\(402\) −26.8061 −1.33697
\(403\) 0 0
\(404\) −6.56225 −0.326484
\(405\) − 37.1457i − 1.84579i
\(406\) 3.08564 0.153138
\(407\) −44.1386 −2.18787
\(408\) − 14.3841i − 0.712121i
\(409\) 11.0908i 0.548402i 0.961672 + 0.274201i \(0.0884134\pi\)
−0.961672 + 0.274201i \(0.911587\pi\)
\(410\) − 29.3455i − 1.44927i
\(411\) 5.79510i 0.285851i
\(412\) 3.94328 0.194272
\(413\) −10.5145 −0.517387
\(414\) − 3.69324i − 0.181513i
\(415\) 24.7760 1.21620
\(416\) 0 0
\(417\) −14.6773 −0.718751
\(418\) − 21.0823i − 1.03117i
\(419\) −14.9846 −0.732044 −0.366022 0.930606i \(-0.619281\pi\)
−0.366022 + 0.930606i \(0.619281\pi\)
\(420\) −7.25163 −0.353843
\(421\) 13.0941i 0.638166i 0.947727 + 0.319083i \(0.103375\pi\)
−0.947727 + 0.319083i \(0.896625\pi\)
\(422\) − 11.5304i − 0.561289i
\(423\) 5.10581i 0.248253i
\(424\) − 29.5052i − 1.43290i
\(425\) 15.9425 0.773326
\(426\) 16.2972 0.789602
\(427\) − 5.29731i − 0.256355i
\(428\) 10.5642 0.510638
\(429\) 0 0
\(430\) 29.0709 1.40192
\(431\) 25.1962i 1.21366i 0.794832 + 0.606829i \(0.207559\pi\)
−0.794832 + 0.606829i \(0.792441\pi\)
\(432\) −2.82365 −0.135853
\(433\) 20.0880 0.965369 0.482684 0.875794i \(-0.339662\pi\)
0.482684 + 0.875794i \(0.339662\pi\)
\(434\) 4.64612i 0.223021i
\(435\) 21.6393i 1.03753i
\(436\) 1.63031i 0.0780779i
\(437\) 19.3086i 0.923654i
\(438\) 12.6668 0.605241
\(439\) 29.7431 1.41956 0.709779 0.704424i \(-0.248795\pi\)
0.709779 + 0.704424i \(0.248795\pi\)
\(440\) − 46.0819i − 2.19687i
\(441\) −0.949635 −0.0452207
\(442\) 0 0
\(443\) −4.81064 −0.228560 −0.114280 0.993449i \(-0.536456\pi\)
−0.114280 + 0.993449i \(0.536456\pi\)
\(444\) 20.5403i 0.974800i
\(445\) 61.4194 2.91156
\(446\) −2.45156 −0.116085
\(447\) 11.1768i 0.528645i
\(448\) 6.43243i 0.303904i
\(449\) − 19.5128i − 0.920866i −0.887695 0.460433i \(-0.847694\pi\)
0.887695 0.460433i \(-0.152306\pi\)
\(450\) 5.94816i 0.280399i
\(451\) −41.3028 −1.94487
\(452\) 11.5661 0.544025
\(453\) − 17.6338i − 0.828510i
\(454\) −8.65189 −0.406053
\(455\) 0 0
\(456\) −28.0577 −1.31392
\(457\) 4.96981i 0.232478i 0.993221 + 0.116239i \(0.0370839\pi\)
−0.993221 + 0.116239i \(0.962916\pi\)
\(458\) −6.93407 −0.324008
\(459\) −9.97312 −0.465505
\(460\) 14.7577i 0.688079i
\(461\) − 4.13305i − 0.192495i −0.995357 0.0962476i \(-0.969316\pi\)
0.995357 0.0962476i \(-0.0306841\pi\)
\(462\) − 8.77619i − 0.408305i
\(463\) 24.3782i 1.13295i 0.824079 + 0.566475i \(0.191693\pi\)
−0.824079 + 0.566475i \(0.808307\pi\)
\(464\) 2.22360 0.103228
\(465\) −32.5828 −1.51099
\(466\) 12.6866i 0.587694i
\(467\) −16.1866 −0.749028 −0.374514 0.927221i \(-0.622190\pi\)
−0.374514 + 0.927221i \(0.622190\pi\)
\(468\) 0 0
\(469\) 14.0270 0.647708
\(470\) 17.5431i 0.809205i
\(471\) 29.2808 1.34919
\(472\) −31.0938 −1.43121
\(473\) − 40.9162i − 1.88133i
\(474\) − 15.2509i − 0.700495i
\(475\) − 31.0975i − 1.42685i
\(476\) 2.63190i 0.120633i
\(477\) 9.47483 0.433823
\(478\) 15.3694 0.702978
\(479\) 3.89449i 0.177944i 0.996034 + 0.0889719i \(0.0283581\pi\)
−0.996034 + 0.0889719i \(0.971642\pi\)
\(480\) −35.3909 −1.61536
\(481\) 0 0
\(482\) 24.1688 1.10086
\(483\) 8.03783i 0.365734i
\(484\) −10.8501 −0.493187
\(485\) −23.4411 −1.06440
\(486\) − 9.16533i − 0.415748i
\(487\) 18.1062i 0.820470i 0.911980 + 0.410235i \(0.134553\pi\)
−0.911980 + 0.410235i \(0.865447\pi\)
\(488\) − 15.6653i − 0.709136i
\(489\) 34.6730i 1.56797i
\(490\) −3.26287 −0.147401
\(491\) 15.5669 0.702524 0.351262 0.936277i \(-0.385753\pi\)
0.351262 + 0.936277i \(0.385753\pi\)
\(492\) 19.2206i 0.866533i
\(493\) 7.85374 0.353715
\(494\) 0 0
\(495\) 14.7980 0.665122
\(496\) 3.34812i 0.150335i
\(497\) −8.52794 −0.382530
\(498\) 13.9537 0.625281
\(499\) − 23.4892i − 1.05152i −0.850632 0.525761i \(-0.823781\pi\)
0.850632 0.525761i \(-0.176219\pi\)
\(500\) − 5.52370i − 0.247027i
\(501\) − 24.4862i − 1.09396i
\(502\) − 2.82743i − 0.126194i
\(503\) −15.2579 −0.680317 −0.340159 0.940368i \(-0.610481\pi\)
−0.340159 + 0.940368i \(0.610481\pi\)
\(504\) −2.80828 −0.125091
\(505\) − 20.7069i − 0.921445i
\(506\) −17.8603 −0.793985
\(507\) 0 0
\(508\) 11.8324 0.524978
\(509\) − 41.2509i − 1.82842i −0.405246 0.914208i \(-0.632814\pi\)
0.405246 0.914208i \(-0.367186\pi\)
\(510\) 15.8708 0.702772
\(511\) −6.62822 −0.293215
\(512\) 7.73507i 0.341845i
\(513\) 19.4536i 0.858896i
\(514\) 17.8411i 0.786936i
\(515\) 12.4429i 0.548298i
\(516\) −19.0408 −0.838223
\(517\) 24.6914 1.08592
\(518\) 9.24211i 0.406075i
\(519\) 1.07491 0.0471834
\(520\) 0 0
\(521\) −19.5558 −0.856756 −0.428378 0.903600i \(-0.640915\pi\)
−0.428378 + 0.903600i \(0.640915\pi\)
\(522\) 2.93023i 0.128253i
\(523\) −16.4130 −0.717689 −0.358845 0.933397i \(-0.616829\pi\)
−0.358845 + 0.933397i \(0.616829\pi\)
\(524\) −8.27613 −0.361545
\(525\) − 12.9454i − 0.564982i
\(526\) 10.0002i 0.436029i
\(527\) 11.8256i 0.515130i
\(528\) − 6.32436i − 0.275232i
\(529\) −6.64237 −0.288799
\(530\) 32.5547 1.41409
\(531\) − 9.98498i − 0.433311i
\(532\) 5.13378 0.222578
\(533\) 0 0
\(534\) 34.5911 1.49690
\(535\) 33.3347i 1.44119i
\(536\) 41.4810 1.79171
\(537\) 27.1209 1.17035
\(538\) − 2.63482i − 0.113595i
\(539\) 4.59237i 0.197808i
\(540\) 14.8685i 0.639838i
\(541\) − 33.7185i − 1.44967i −0.688922 0.724836i \(-0.741916\pi\)
0.688922 0.724836i \(-0.258084\pi\)
\(542\) 10.6609 0.457923
\(543\) 3.64820 0.156559
\(544\) 12.8447i 0.550713i
\(545\) −5.14439 −0.220361
\(546\) 0 0
\(547\) 40.0637 1.71300 0.856501 0.516145i \(-0.172634\pi\)
0.856501 + 0.516145i \(0.172634\pi\)
\(548\) − 3.13566i − 0.133949i
\(549\) 5.03052 0.214697
\(550\) 28.7649 1.22654
\(551\) − 15.3195i − 0.652633i
\(552\) 23.7696i 1.01170i
\(553\) 7.98042i 0.339362i
\(554\) 8.79161i 0.373520i
\(555\) −64.8140 −2.75120
\(556\) 7.94173 0.336804
\(557\) 6.26450i 0.265435i 0.991154 + 0.132718i \(0.0423703\pi\)
−0.991154 + 0.132718i \(0.957630\pi\)
\(558\) −4.41212 −0.186780
\(559\) 0 0
\(560\) −2.35131 −0.0993611
\(561\) − 22.3376i − 0.943096i
\(562\) −0.549494 −0.0231790
\(563\) 18.9876 0.800231 0.400115 0.916465i \(-0.368970\pi\)
0.400115 + 0.916465i \(0.368970\pi\)
\(564\) − 11.4904i − 0.483831i
\(565\) 36.4964i 1.53542i
\(566\) 18.0693i 0.759510i
\(567\) 10.9471i 0.459735i
\(568\) −25.2190 −1.05817
\(569\) −40.9151 −1.71525 −0.857626 0.514274i \(-0.828061\pi\)
−0.857626 + 0.514274i \(0.828061\pi\)
\(570\) − 30.9577i − 1.29667i
\(571\) 18.9901 0.794713 0.397356 0.917664i \(-0.369928\pi\)
0.397356 + 0.917664i \(0.369928\pi\)
\(572\) 0 0
\(573\) 20.1698 0.842606
\(574\) 8.64833i 0.360974i
\(575\) −26.3448 −1.09866
\(576\) −6.10846 −0.254519
\(577\) 6.42794i 0.267599i 0.991008 + 0.133799i \(0.0427177\pi\)
−0.991008 + 0.133799i \(0.957282\pi\)
\(578\) 10.5869i 0.440357i
\(579\) − 9.27166i − 0.385317i
\(580\) − 11.7088i − 0.486181i
\(581\) −7.30165 −0.302924
\(582\) −13.2019 −0.547237
\(583\) − 45.8196i − 1.89766i
\(584\) −19.6011 −0.811100
\(585\) 0 0
\(586\) −9.03206 −0.373111
\(587\) 10.4081i 0.429588i 0.976659 + 0.214794i \(0.0689079\pi\)
−0.976659 + 0.214794i \(0.931092\pi\)
\(588\) 2.13711 0.0881327
\(589\) 23.0670 0.950458
\(590\) − 34.3076i − 1.41242i
\(591\) − 18.0858i − 0.743950i
\(592\) 6.66011i 0.273729i
\(593\) 16.2341i 0.666654i 0.942811 + 0.333327i \(0.108171\pi\)
−0.942811 + 0.333327i \(0.891829\pi\)
\(594\) −17.9944 −0.738319
\(595\) −8.30484 −0.340465
\(596\) − 6.04765i − 0.247721i
\(597\) −26.7223 −1.09367
\(598\) 0 0
\(599\) 4.84879 0.198116 0.0990580 0.995082i \(-0.468417\pi\)
0.0990580 + 0.995082i \(0.468417\pi\)
\(600\) − 38.2823i − 1.56287i
\(601\) −35.9758 −1.46748 −0.733742 0.679428i \(-0.762228\pi\)
−0.733742 + 0.679428i \(0.762228\pi\)
\(602\) −8.56739 −0.349181
\(603\) 13.3206i 0.542455i
\(604\) 9.54148i 0.388237i
\(605\) − 34.2371i − 1.39193i
\(606\) − 11.6620i − 0.473738i
\(607\) 28.7089 1.16526 0.582629 0.812738i \(-0.302024\pi\)
0.582629 + 0.812738i \(0.302024\pi\)
\(608\) 25.0549 1.01611
\(609\) − 6.37725i − 0.258419i
\(610\) 17.2844 0.699827
\(611\) 0 0
\(612\) −2.49934 −0.101030
\(613\) − 37.1913i − 1.50214i −0.660221 0.751071i \(-0.729538\pi\)
0.660221 0.751071i \(-0.270462\pi\)
\(614\) 1.34045 0.0540960
\(615\) −60.6499 −2.44564
\(616\) 13.5807i 0.547181i
\(617\) − 0.556995i − 0.0224238i −0.999937 0.0112119i \(-0.996431\pi\)
0.999937 0.0112119i \(-0.00356893\pi\)
\(618\) 7.00776i 0.281893i
\(619\) 12.4079i 0.498715i 0.968411 + 0.249358i \(0.0802195\pi\)
−0.968411 + 0.249358i \(0.919781\pi\)
\(620\) 17.6302 0.708047
\(621\) 16.4805 0.661339
\(622\) − 9.65725i − 0.387220i
\(623\) −18.1007 −0.725190
\(624\) 0 0
\(625\) −15.1393 −0.605571
\(626\) − 27.9701i − 1.11791i
\(627\) −43.5718 −1.74009
\(628\) −15.8435 −0.632226
\(629\) 23.5235i 0.937945i
\(630\) − 3.09854i − 0.123449i
\(631\) 10.5304i 0.419208i 0.977786 + 0.209604i \(0.0672174\pi\)
−0.977786 + 0.209604i \(0.932783\pi\)
\(632\) 23.5999i 0.938752i
\(633\) −23.8304 −0.947174
\(634\) 4.33127 0.172017
\(635\) 37.3366i 1.48166i
\(636\) −21.3226 −0.845496
\(637\) 0 0
\(638\) 14.1704 0.561012
\(639\) − 8.09844i − 0.320369i
\(640\) 14.6276 0.578207
\(641\) −17.8975 −0.706910 −0.353455 0.935452i \(-0.614993\pi\)
−0.353455 + 0.935452i \(0.614993\pi\)
\(642\) 18.7740i 0.740949i
\(643\) − 11.7963i − 0.465202i −0.972572 0.232601i \(-0.925276\pi\)
0.972572 0.232601i \(-0.0747236\pi\)
\(644\) − 4.34918i − 0.171382i
\(645\) − 60.0823i − 2.36574i
\(646\) −11.2357 −0.442064
\(647\) −4.52415 −0.177863 −0.0889313 0.996038i \(-0.528345\pi\)
−0.0889313 + 0.996038i \(0.528345\pi\)
\(648\) 32.3730i 1.27173i
\(649\) −48.2867 −1.89542
\(650\) 0 0
\(651\) 9.60239 0.376347
\(652\) − 18.7612i − 0.734745i
\(653\) 46.9198 1.83611 0.918057 0.396448i \(-0.129757\pi\)
0.918057 + 0.396448i \(0.129757\pi\)
\(654\) −2.89730 −0.113293
\(655\) − 26.1150i − 1.02040i
\(656\) 6.23222i 0.243327i
\(657\) − 6.29439i − 0.245568i
\(658\) − 5.17009i − 0.201551i
\(659\) −39.3468 −1.53273 −0.766366 0.642404i \(-0.777937\pi\)
−0.766366 + 0.642404i \(0.777937\pi\)
\(660\) −33.3022 −1.29629
\(661\) − 23.0664i − 0.897179i −0.893738 0.448590i \(-0.851926\pi\)
0.893738 0.448590i \(-0.148074\pi\)
\(662\) 13.7499 0.534406
\(663\) 0 0
\(664\) −21.5926 −0.837955
\(665\) 16.1994i 0.628187i
\(666\) −8.77663 −0.340088
\(667\) −12.9782 −0.502519
\(668\) 13.2492i 0.512628i
\(669\) 5.06676i 0.195892i
\(670\) 45.7684i 1.76819i
\(671\) − 24.3272i − 0.939143i
\(672\) 10.4299 0.402343
\(673\) 15.7225 0.606057 0.303028 0.952981i \(-0.402002\pi\)
0.303028 + 0.952981i \(0.402002\pi\)
\(674\) 27.3579i 1.05379i
\(675\) −26.5427 −1.02163
\(676\) 0 0
\(677\) 1.59613 0.0613443 0.0306721 0.999529i \(-0.490235\pi\)
0.0306721 + 0.999529i \(0.490235\pi\)
\(678\) 20.5546i 0.789395i
\(679\) 6.90825 0.265114
\(680\) −24.5592 −0.941804
\(681\) 17.8813i 0.685213i
\(682\) 21.3367i 0.817026i
\(683\) − 18.4740i − 0.706889i −0.935455 0.353445i \(-0.885010\pi\)
0.935455 0.353445i \(-0.114990\pi\)
\(684\) 4.87522i 0.186409i
\(685\) 9.89445 0.378048
\(686\) 0.961590 0.0367137
\(687\) 14.3310i 0.546762i
\(688\) −6.17389 −0.235377
\(689\) 0 0
\(690\) −26.2264 −0.998422
\(691\) 26.1768i 0.995813i 0.867231 + 0.497906i \(0.165898\pi\)
−0.867231 + 0.497906i \(0.834102\pi\)
\(692\) −0.581623 −0.0221100
\(693\) −4.36108 −0.165664
\(694\) − 26.4399i − 1.00365i
\(695\) 25.0598i 0.950572i
\(696\) − 18.8590i − 0.714847i
\(697\) 22.0122i 0.833772i
\(698\) 21.1820 0.801752
\(699\) 26.2200 0.991731
\(700\) 7.00459i 0.264749i
\(701\) 2.16383 0.0817267 0.0408634 0.999165i \(-0.486989\pi\)
0.0408634 + 0.999165i \(0.486989\pi\)
\(702\) 0 0
\(703\) 45.8850 1.73059
\(704\) 29.5401i 1.11334i
\(705\) 36.2573 1.36553
\(706\) 1.54288 0.0580670
\(707\) 6.10247i 0.229507i
\(708\) 22.4707i 0.844500i
\(709\) − 34.7042i − 1.30334i −0.758501 0.651672i \(-0.774068\pi\)
0.758501 0.651672i \(-0.225932\pi\)
\(710\) − 27.8256i − 1.04427i
\(711\) −7.57849 −0.284215
\(712\) −53.5279 −2.00604
\(713\) − 19.5416i − 0.731840i
\(714\) −4.67725 −0.175042
\(715\) 0 0
\(716\) −14.6748 −0.548424
\(717\) − 31.7647i − 1.18627i
\(718\) −20.5809 −0.768074
\(719\) −0.969723 −0.0361646 −0.0180823 0.999837i \(-0.505756\pi\)
−0.0180823 + 0.999837i \(0.505756\pi\)
\(720\) − 2.23289i − 0.0832149i
\(721\) − 3.66700i − 0.136566i
\(722\) 3.64621i 0.135698i
\(723\) − 49.9509i − 1.85769i
\(724\) −1.97400 −0.0733632
\(725\) 20.9021 0.776286
\(726\) − 19.2822i − 0.715628i
\(727\) 17.0417 0.632040 0.316020 0.948752i \(-0.397653\pi\)
0.316020 + 0.948752i \(0.397653\pi\)
\(728\) 0 0
\(729\) 13.8988 0.514771
\(730\) − 21.6270i − 0.800452i
\(731\) −21.8062 −0.806531
\(732\) −11.3209 −0.418433
\(733\) 13.5638i 0.500989i 0.968118 + 0.250494i \(0.0805932\pi\)
−0.968118 + 0.250494i \(0.919407\pi\)
\(734\) 17.1477i 0.632933i
\(735\) 6.74354i 0.248739i
\(736\) − 21.2258i − 0.782392i
\(737\) 64.4173 2.37284
\(738\) −8.21276 −0.302316
\(739\) 25.5091i 0.938366i 0.883101 + 0.469183i \(0.155452\pi\)
−0.883101 + 0.469183i \(0.844548\pi\)
\(740\) 35.0702 1.28921
\(741\) 0 0
\(742\) −9.59411 −0.352211
\(743\) 20.1185i 0.738078i 0.929414 + 0.369039i \(0.120313\pi\)
−0.929414 + 0.369039i \(0.879687\pi\)
\(744\) 28.3964 1.04106
\(745\) 19.0831 0.699150
\(746\) − 24.9996i − 0.915299i
\(747\) − 6.93391i − 0.253698i
\(748\) 12.0867i 0.441932i
\(749\) − 9.82398i − 0.358960i
\(750\) 9.81638 0.358444
\(751\) 50.7696 1.85261 0.926305 0.376774i \(-0.122967\pi\)
0.926305 + 0.376774i \(0.122967\pi\)
\(752\) − 3.72570i − 0.135862i
\(753\) −5.84360 −0.212953
\(754\) 0 0
\(755\) −30.1077 −1.09573
\(756\) − 4.38184i − 0.159366i
\(757\) 5.42838 0.197298 0.0986490 0.995122i \(-0.468548\pi\)
0.0986490 + 0.995122i \(0.468548\pi\)
\(758\) −22.1854 −0.805808
\(759\) 36.9127i 1.33985i
\(760\) 47.9053i 1.73771i
\(761\) 29.3194i 1.06283i 0.847112 + 0.531414i \(0.178339\pi\)
−0.847112 + 0.531414i \(0.821661\pi\)
\(762\) 21.0278i 0.761757i
\(763\) 1.51609 0.0548860
\(764\) −10.9137 −0.394843
\(765\) − 7.88657i − 0.285139i
\(766\) −7.60786 −0.274883
\(767\) 0 0
\(768\) 33.8054 1.21985
\(769\) − 46.5006i − 1.67686i −0.545013 0.838428i \(-0.683475\pi\)
0.545013 0.838428i \(-0.316525\pi\)
\(770\) −14.9843 −0.539997
\(771\) 36.8731 1.32795
\(772\) 5.01679i 0.180558i
\(773\) − 15.5317i − 0.558637i −0.960198 0.279319i \(-0.909891\pi\)
0.960198 0.279319i \(-0.0901085\pi\)
\(774\) − 8.13590i − 0.292439i
\(775\) 31.4729i 1.13054i
\(776\) 20.4292 0.733366
\(777\) 19.1011 0.685250
\(778\) − 6.43810i − 0.230817i
\(779\) 42.9370 1.53838
\(780\) 0 0
\(781\) −39.1635 −1.40138
\(782\) 9.51857i 0.340384i
\(783\) −13.0757 −0.467287
\(784\) 0.692948 0.0247481
\(785\) − 49.9936i − 1.78435i
\(786\) − 14.7078i − 0.524611i
\(787\) − 33.9561i − 1.21040i −0.796072 0.605202i \(-0.793092\pi\)
0.796072 0.605202i \(-0.206908\pi\)
\(788\) 9.78603i 0.348613i
\(789\) 20.6679 0.735797
\(790\) −26.0391 −0.926428
\(791\) − 10.7558i − 0.382430i
\(792\) −12.8967 −0.458264
\(793\) 0 0
\(794\) 37.3392 1.32512
\(795\) − 67.2826i − 2.38627i
\(796\) 14.4592 0.512492
\(797\) −5.90891 −0.209304 −0.104652 0.994509i \(-0.533373\pi\)
−0.104652 + 0.994509i \(0.533373\pi\)
\(798\) 9.12344i 0.322966i
\(799\) − 13.1592i − 0.465539i
\(800\) 34.1852i 1.20863i
\(801\) − 17.1891i − 0.607347i
\(802\) 24.5485 0.866838
\(803\) −30.4393 −1.07418
\(804\) − 29.9772i − 1.05722i
\(805\) 13.7237 0.483695
\(806\) 0 0
\(807\) −5.44552 −0.191691
\(808\) 18.0464i 0.634868i
\(809\) −30.4401 −1.07022 −0.535109 0.844783i \(-0.679730\pi\)
−0.535109 + 0.844783i \(0.679730\pi\)
\(810\) −35.7190 −1.25504
\(811\) − 21.9976i − 0.772442i −0.922406 0.386221i \(-0.873780\pi\)
0.922406 0.386221i \(-0.126220\pi\)
\(812\) 3.45066i 0.121095i
\(813\) − 22.0334i − 0.772744i
\(814\) 42.4432i 1.48763i
\(815\) 59.2001 2.07369
\(816\) −3.37055 −0.117993
\(817\) 42.5352i 1.48812i
\(818\) 10.6648 0.372885
\(819\) 0 0
\(820\) 32.8170 1.14602
\(821\) − 0.557598i − 0.0194603i −0.999953 0.00973015i \(-0.996903\pi\)
0.999953 0.00973015i \(-0.00309725\pi\)
\(822\) 5.57251 0.194364
\(823\) −9.50436 −0.331301 −0.165651 0.986185i \(-0.552972\pi\)
−0.165651 + 0.986185i \(0.552972\pi\)
\(824\) − 10.8441i − 0.377773i
\(825\) − 59.4499i − 2.06978i
\(826\) 10.1107i 0.351796i
\(827\) − 40.7855i − 1.41825i −0.705083 0.709125i \(-0.749090\pi\)
0.705083 0.709125i \(-0.250910\pi\)
\(828\) 4.13014 0.143532
\(829\) −2.74011 −0.0951679 −0.0475839 0.998867i \(-0.515152\pi\)
−0.0475839 + 0.998867i \(0.515152\pi\)
\(830\) − 23.8243i − 0.826955i
\(831\) 18.1701 0.630313
\(832\) 0 0
\(833\) 2.44749 0.0848006
\(834\) 14.1136i 0.488712i
\(835\) −41.8074 −1.44680
\(836\) 23.5762 0.815401
\(837\) − 19.6884i − 0.680530i
\(838\) 14.4090i 0.497751i
\(839\) − 4.66572i − 0.161078i −0.996751 0.0805392i \(-0.974336\pi\)
0.996751 0.0805392i \(-0.0256642\pi\)
\(840\) 19.9421i 0.688070i
\(841\) −18.7030 −0.644931
\(842\) 12.5911 0.433919
\(843\) 1.13567i 0.0391145i
\(844\) 12.8944 0.443843
\(845\) 0 0
\(846\) 4.90970 0.168799
\(847\) 10.0899i 0.346693i
\(848\) −6.91377 −0.237420
\(849\) 37.3448 1.28167
\(850\) − 15.3302i − 0.525821i
\(851\) − 38.8724i − 1.33253i
\(852\) 18.2251i 0.624382i
\(853\) 25.2886i 0.865864i 0.901427 + 0.432932i \(0.142521\pi\)
−0.901427 + 0.432932i \(0.857479\pi\)
\(854\) −5.09385 −0.174308
\(855\) −15.3835 −0.526106
\(856\) − 29.0517i − 0.992966i
\(857\) −9.30340 −0.317798 −0.158899 0.987295i \(-0.550794\pi\)
−0.158899 + 0.987295i \(0.550794\pi\)
\(858\) 0 0
\(859\) 42.4360 1.44790 0.723949 0.689854i \(-0.242325\pi\)
0.723949 + 0.689854i \(0.242325\pi\)
\(860\) 32.5099i 1.10858i
\(861\) 17.8739 0.609142
\(862\) 24.2284 0.825223
\(863\) 17.0172i 0.579273i 0.957137 + 0.289636i \(0.0935344\pi\)
−0.957137 + 0.289636i \(0.906466\pi\)
\(864\) − 21.3852i − 0.727538i
\(865\) − 1.83529i − 0.0624016i
\(866\) − 19.3165i − 0.656400i
\(867\) 21.8805 0.743100
\(868\) −5.19575 −0.176355
\(869\) 36.6491i 1.24323i
\(870\) 20.8082 0.705462
\(871\) 0 0
\(872\) 4.48340 0.151827
\(873\) 6.56032i 0.222033i
\(874\) 18.5669 0.628036
\(875\) −5.13668 −0.173652
\(876\) 14.1652i 0.478598i
\(877\) − 39.3974i − 1.33035i −0.746685 0.665177i \(-0.768356\pi\)
0.746685 0.665177i \(-0.231644\pi\)
\(878\) − 28.6006i − 0.965225i
\(879\) 18.6670i 0.629623i
\(880\) −10.7981 −0.364004
\(881\) −9.92005 −0.334215 −0.167107 0.985939i \(-0.553443\pi\)
−0.167107 + 0.985939i \(0.553443\pi\)
\(882\) 0.913160i 0.0307477i
\(883\) 18.9158 0.636568 0.318284 0.947995i \(-0.396894\pi\)
0.318284 + 0.947995i \(0.396894\pi\)
\(884\) 0 0
\(885\) −70.9053 −2.38345
\(886\) 4.62586i 0.155409i
\(887\) 24.2260 0.813431 0.406715 0.913555i \(-0.366674\pi\)
0.406715 + 0.913555i \(0.366674\pi\)
\(888\) 56.4863 1.89556
\(889\) − 11.0034i − 0.369041i
\(890\) − 59.0603i − 1.97971i
\(891\) 50.2732i 1.68421i
\(892\) − 2.74157i − 0.0917945i
\(893\) −25.6683 −0.858958
\(894\) 10.7475 0.359450
\(895\) − 46.3058i − 1.54783i
\(896\) −4.31086 −0.144016
\(897\) 0 0
\(898\) −18.7633 −0.626140
\(899\) 15.5044i 0.517102i
\(900\) −6.65181 −0.221727
\(901\) −24.4195 −0.813530
\(902\) 39.7164i 1.32241i
\(903\) 17.7067i 0.589241i
\(904\) − 31.8071i − 1.05789i
\(905\) − 6.22888i − 0.207055i
\(906\) −16.9565 −0.563343
\(907\) 20.0403 0.665427 0.332714 0.943028i \(-0.392036\pi\)
0.332714 + 0.943028i \(0.392036\pi\)
\(908\) − 9.67539i − 0.321089i
\(909\) −5.79512 −0.192212
\(910\) 0 0
\(911\) 32.5680 1.07903 0.539514 0.841977i \(-0.318608\pi\)
0.539514 + 0.841977i \(0.318608\pi\)
\(912\) 6.57459i 0.217707i
\(913\) −33.5319 −1.10974
\(914\) 4.77892 0.158073
\(915\) − 35.7227i − 1.18095i
\(916\) − 7.75435i − 0.256211i
\(917\) 7.69627i 0.254153i
\(918\) 9.59006i 0.316519i
\(919\) −43.7858 −1.44436 −0.722181 0.691705i \(-0.756860\pi\)
−0.722181 + 0.691705i \(0.756860\pi\)
\(920\) 40.5839 1.33801
\(921\) − 2.77037i − 0.0912868i
\(922\) −3.97430 −0.130887
\(923\) 0 0
\(924\) 9.81439 0.322870
\(925\) 62.6061i 2.05848i
\(926\) 23.4418 0.770346
\(927\) 3.48231 0.114374
\(928\) 16.8406i 0.552821i
\(929\) − 47.7826i − 1.56770i −0.620953 0.783848i \(-0.713254\pi\)
0.620953 0.783848i \(-0.286746\pi\)
\(930\) 31.3313i 1.02740i
\(931\) − 4.77408i − 0.156464i
\(932\) −14.1874 −0.464722
\(933\) −19.9591 −0.653433
\(934\) 15.5649i 0.509299i
\(935\) −38.1389 −1.24728
\(936\) 0 0
\(937\) −18.7762 −0.613393 −0.306696 0.951807i \(-0.599224\pi\)
−0.306696 + 0.951807i \(0.599224\pi\)
\(938\) − 13.4883i − 0.440407i
\(939\) −57.8073 −1.88647
\(940\) −19.6184 −0.639883
\(941\) − 41.5379i − 1.35410i −0.735938 0.677049i \(-0.763259\pi\)
0.735938 0.677049i \(-0.236741\pi\)
\(942\) − 28.1561i − 0.917377i
\(943\) − 36.3749i − 1.18453i
\(944\) 7.28603i 0.237140i
\(945\) 13.8267 0.449783
\(946\) −39.3447 −1.27921
\(947\) 33.6878i 1.09471i 0.836902 + 0.547353i \(0.184364\pi\)
−0.836902 + 0.547353i \(0.815636\pi\)
\(948\) 17.0550 0.553920
\(949\) 0 0
\(950\) −29.9030 −0.970183
\(951\) − 8.95167i − 0.290278i
\(952\) 7.23778 0.234578
\(953\) 30.0769 0.974286 0.487143 0.873322i \(-0.338039\pi\)
0.487143 + 0.873322i \(0.338039\pi\)
\(954\) − 9.11090i − 0.294976i
\(955\) − 34.4376i − 1.11438i
\(956\) 17.1875i 0.555884i
\(957\) − 29.2867i − 0.946706i
\(958\) 3.74490 0.120992
\(959\) −2.91596 −0.0941614
\(960\) 43.3774i 1.40000i
\(961\) 7.65460 0.246922
\(962\) 0 0
\(963\) 9.32919 0.300629
\(964\) 27.0279i 0.870510i
\(965\) −15.8303 −0.509595
\(966\) 7.72910 0.248680
\(967\) − 0.586833i − 0.0188713i −0.999955 0.00943564i \(-0.996996\pi\)
0.999955 0.00943564i \(-0.00300350\pi\)
\(968\) 29.8381i 0.959032i
\(969\) 23.2215i 0.745981i
\(970\) 22.5407i 0.723739i
\(971\) 6.42217 0.206097 0.103049 0.994676i \(-0.467140\pi\)
0.103049 + 0.994676i \(0.467140\pi\)
\(972\) 10.2496 0.328755
\(973\) − 7.38529i − 0.236762i
\(974\) 17.4107 0.557876
\(975\) 0 0
\(976\) −3.67076 −0.117498
\(977\) − 29.2836i − 0.936867i −0.883499 0.468433i \(-0.844819\pi\)
0.883499 0.468433i \(-0.155181\pi\)
\(978\) 33.3412 1.06614
\(979\) −83.1253 −2.65670
\(980\) − 3.64886i − 0.116559i
\(981\) 1.43973i 0.0459670i
\(982\) − 14.9690i − 0.477679i
\(983\) 39.4156i 1.25716i 0.777745 + 0.628581i \(0.216364\pi\)
−0.777745 + 0.628581i \(0.783636\pi\)
\(984\) 52.8572 1.68503
\(985\) −30.8794 −0.983899
\(986\) − 7.55209i − 0.240507i
\(987\) −10.6853 −0.340116
\(988\) 0 0
\(989\) 36.0345 1.14583
\(990\) − 14.2296i − 0.452248i
\(991\) 24.3027 0.772000 0.386000 0.922499i \(-0.373856\pi\)
0.386000 + 0.922499i \(0.373856\pi\)
\(992\) −25.3573 −0.805096
\(993\) − 28.4177i − 0.901809i
\(994\) 8.20039i 0.260100i
\(995\) 45.6253i 1.44642i
\(996\) 15.6044i 0.494444i
\(997\) −46.4460 −1.47096 −0.735479 0.677547i \(-0.763043\pi\)
−0.735479 + 0.677547i \(0.763043\pi\)
\(998\) −22.5870 −0.714980
\(999\) − 39.1643i − 1.23910i
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 1183.2.c.j.337.10 24
13.5 odd 4 1183.2.a.r.1.5 yes 12
13.8 odd 4 1183.2.a.q.1.8 12
13.12 even 2 inner 1183.2.c.j.337.15 24
91.34 even 4 8281.2.a.cn.1.8 12
91.83 even 4 8281.2.a.cq.1.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1183.2.a.q.1.8 12 13.8 odd 4
1183.2.a.r.1.5 yes 12 13.5 odd 4
1183.2.c.j.337.10 24 1.1 even 1 trivial
1183.2.c.j.337.15 24 13.12 even 2 inner
8281.2.a.cn.1.8 12 91.34 even 4
8281.2.a.cq.1.5 12 91.83 even 4