Properties

Label 6034.2.a.j.1.1
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $1$
Dimension $4$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.10273.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 5x^{2} + x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.38266\) of defining polynomial
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.38266 q^{3} +1.00000 q^{4} -2.61326 q^{5} +2.38266 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.67708 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.38266 q^{3} +1.00000 q^{4} -2.61326 q^{5} +2.38266 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.67708 q^{9} +2.61326 q^{10} -3.93618 q^{11} -2.38266 q^{12} +1.76940 q^{13} -1.00000 q^{14} +6.22653 q^{15} +1.00000 q^{16} -2.61734 q^{17} -2.67708 q^{18} -0.510304 q^{19} -2.61326 q^{20} -2.38266 q^{21} +3.93618 q^{22} -6.44241 q^{23} +2.38266 q^{24} +1.82915 q^{25} -1.76940 q^{26} +0.769400 q^{27} +1.00000 q^{28} +4.06382 q^{29} -6.22653 q^{30} +4.60919 q^{31} -1.00000 q^{32} +9.37859 q^{33} +2.61734 q^{34} -2.61326 q^{35} +2.67708 q^{36} +4.31884 q^{37} +0.510304 q^{38} -4.21588 q^{39} +2.61326 q^{40} -11.8751 q^{41} +2.38266 q^{42} +8.97125 q^{43} -3.93618 q^{44} -6.99593 q^{45} +6.44241 q^{46} +11.4571 q^{47} -2.38266 q^{48} +1.00000 q^{49} -1.82915 q^{50} +6.23623 q^{51} +1.76940 q^{52} -8.70151 q^{53} -0.769400 q^{54} +10.2863 q^{55} -1.00000 q^{56} +1.21588 q^{57} -4.06382 q^{58} -9.05975 q^{59} +6.22653 q^{60} +6.05975 q^{61} -4.60919 q^{62} +2.67708 q^{63} +1.00000 q^{64} -4.62391 q^{65} -9.37859 q^{66} -9.84386 q^{67} -2.61734 q^{68} +15.3501 q^{69} +2.61326 q^{70} -7.39920 q^{71} -2.67708 q^{72} -0.662367 q^{73} -4.31884 q^{74} -4.35824 q^{75} -0.510304 q^{76} -3.93618 q^{77} +4.21588 q^{78} +14.1195 q^{79} -2.61326 q^{80} -9.86447 q^{81} +11.8751 q^{82} -8.90768 q^{83} -2.38266 q^{84} +6.83979 q^{85} -8.97125 q^{86} -9.68272 q^{87} +3.93618 q^{88} +16.3272 q^{89} +6.99593 q^{90} +1.76940 q^{91} -6.44241 q^{92} -10.9821 q^{93} -11.4571 q^{94} +1.33356 q^{95} +2.38266 q^{96} +4.26593 q^{97} -1.00000 q^{98} -10.5375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - q^{10} - 13 q^{11} - 2 q^{12} + 11 q^{13} - 4 q^{14} + 2 q^{15} + 4 q^{16} - 18 q^{17} - 2 q^{18} + q^{20} - 2 q^{21} + 13 q^{22} - 2 q^{23} + 2 q^{24} - 5 q^{25} - 11 q^{26} + 7 q^{27} + 4 q^{28} + 19 q^{29} - 2 q^{30} - 12 q^{31} - 4 q^{32} + 11 q^{33} + 18 q^{34} + q^{35} + 2 q^{36} + 7 q^{37} - 16 q^{39} - q^{40} - 6 q^{41} + 2 q^{42} + 2 q^{43} - 13 q^{44} - 9 q^{45} + 2 q^{46} + 19 q^{47} - 2 q^{48} + 4 q^{49} + 5 q^{50} - 4 q^{51} + 11 q^{52} - 17 q^{53} - 7 q^{54} + 2 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 20 q^{59} + 2 q^{60} + 8 q^{61} + 12 q^{62} + 2 q^{63} + 4 q^{64} + 15 q^{65} - 11 q^{66} - 24 q^{67} - 18 q^{68} + 25 q^{69} - q^{70} + q^{71} - 2 q^{72} + 3 q^{73} - 7 q^{74} - 19 q^{75} - 13 q^{77} + 16 q^{78} + 24 q^{79} + q^{80} - 20 q^{81} + 6 q^{82} - 23 q^{83} - 2 q^{84} - 7 q^{85} - 2 q^{86} - 5 q^{87} + 13 q^{88} - 6 q^{89} + 9 q^{90} + 11 q^{91} - 2 q^{92} - 12 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} + 6 q^{97} - 4 q^{98} + 5 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.38266 −1.37563 −0.687816 0.725885i \(-0.741430\pi\)
−0.687816 + 0.725885i \(0.741430\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.61326 −1.16869 −0.584344 0.811506i \(-0.698648\pi\)
−0.584344 + 0.811506i \(0.698648\pi\)
\(6\) 2.38266 0.972718
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 2.67708 0.892361
\(10\) 2.61326 0.826387
\(11\) −3.93618 −1.18680 −0.593401 0.804907i \(-0.702215\pi\)
−0.593401 + 0.804907i \(0.702215\pi\)
\(12\) −2.38266 −0.687816
\(13\) 1.76940 0.490743 0.245372 0.969429i \(-0.421090\pi\)
0.245372 + 0.969429i \(0.421090\pi\)
\(14\) −1.00000 −0.267261
\(15\) 6.22653 1.60768
\(16\) 1.00000 0.250000
\(17\) −2.61734 −0.634797 −0.317399 0.948292i \(-0.602809\pi\)
−0.317399 + 0.948292i \(0.602809\pi\)
\(18\) −2.67708 −0.630995
\(19\) −0.510304 −0.117072 −0.0585359 0.998285i \(-0.518643\pi\)
−0.0585359 + 0.998285i \(0.518643\pi\)
\(20\) −2.61326 −0.584344
\(21\) −2.38266 −0.519940
\(22\) 3.93618 0.839196
\(23\) −6.44241 −1.34334 −0.671668 0.740853i \(-0.734422\pi\)
−0.671668 + 0.740853i \(0.734422\pi\)
\(24\) 2.38266 0.486359
\(25\) 1.82915 0.365829
\(26\) −1.76940 −0.347008
\(27\) 0.769400 0.148071
\(28\) 1.00000 0.188982
\(29\) 4.06382 0.754633 0.377316 0.926084i \(-0.376847\pi\)
0.377316 + 0.926084i \(0.376847\pi\)
\(30\) −6.22653 −1.13680
\(31\) 4.60919 0.827835 0.413918 0.910314i \(-0.364160\pi\)
0.413918 + 0.910314i \(0.364160\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.37859 1.63260
\(34\) 2.61734 0.448870
\(35\) −2.61326 −0.441722
\(36\) 2.67708 0.446181
\(37\) 4.31884 0.710013 0.355007 0.934864i \(-0.384479\pi\)
0.355007 + 0.934864i \(0.384479\pi\)
\(38\) 0.510304 0.0827823
\(39\) −4.21588 −0.675082
\(40\) 2.61326 0.413193
\(41\) −11.8751 −1.85458 −0.927291 0.374342i \(-0.877869\pi\)
−0.927291 + 0.374342i \(0.877869\pi\)
\(42\) 2.38266 0.367653
\(43\) 8.97125 1.36810 0.684051 0.729434i \(-0.260217\pi\)
0.684051 + 0.729434i \(0.260217\pi\)
\(44\) −3.93618 −0.593401
\(45\) −6.99593 −1.04289
\(46\) 6.44241 0.949882
\(47\) 11.4571 1.67119 0.835597 0.549343i \(-0.185122\pi\)
0.835597 + 0.549343i \(0.185122\pi\)
\(48\) −2.38266 −0.343908
\(49\) 1.00000 0.142857
\(50\) −1.82915 −0.258680
\(51\) 6.23623 0.873247
\(52\) 1.76940 0.245372
\(53\) −8.70151 −1.19524 −0.597622 0.801778i \(-0.703888\pi\)
−0.597622 + 0.801778i \(0.703888\pi\)
\(54\) −0.769400 −0.104702
\(55\) 10.2863 1.38700
\(56\) −1.00000 −0.133631
\(57\) 1.21588 0.161048
\(58\) −4.06382 −0.533606
\(59\) −9.05975 −1.17948 −0.589739 0.807594i \(-0.700770\pi\)
−0.589739 + 0.807594i \(0.700770\pi\)
\(60\) 6.22653 0.803841
\(61\) 6.05975 0.775871 0.387936 0.921686i \(-0.373188\pi\)
0.387936 + 0.921686i \(0.373188\pi\)
\(62\) −4.60919 −0.585368
\(63\) 2.67708 0.337281
\(64\) 1.00000 0.125000
\(65\) −4.62391 −0.573525
\(66\) −9.37859 −1.15442
\(67\) −9.84386 −1.20262 −0.601310 0.799016i \(-0.705354\pi\)
−0.601310 + 0.799016i \(0.705354\pi\)
\(68\) −2.61734 −0.317399
\(69\) 15.3501 1.84793
\(70\) 2.61326 0.312345
\(71\) −7.39920 −0.878123 −0.439062 0.898457i \(-0.644689\pi\)
−0.439062 + 0.898457i \(0.644689\pi\)
\(72\) −2.67708 −0.315497
\(73\) −0.662367 −0.0775242 −0.0387621 0.999248i \(-0.512341\pi\)
−0.0387621 + 0.999248i \(0.512341\pi\)
\(74\) −4.31884 −0.502055
\(75\) −4.35824 −0.503246
\(76\) −0.510304 −0.0585359
\(77\) −3.93618 −0.448569
\(78\) 4.21588 0.477355
\(79\) 14.1195 1.58857 0.794284 0.607547i \(-0.207846\pi\)
0.794284 + 0.607547i \(0.207846\pi\)
\(80\) −2.61326 −0.292172
\(81\) −9.86447 −1.09605
\(82\) 11.8751 1.31139
\(83\) −8.90768 −0.977745 −0.488873 0.872355i \(-0.662592\pi\)
−0.488873 + 0.872355i \(0.662592\pi\)
\(84\) −2.38266 −0.259970
\(85\) 6.83979 0.741880
\(86\) −8.97125 −0.967394
\(87\) −9.68272 −1.03810
\(88\) 3.93618 0.419598
\(89\) 16.3272 1.73068 0.865342 0.501183i \(-0.167101\pi\)
0.865342 + 0.501183i \(0.167101\pi\)
\(90\) 6.99593 0.737435
\(91\) 1.76940 0.185483
\(92\) −6.44241 −0.671668
\(93\) −10.9821 −1.13880
\(94\) −11.4571 −1.18171
\(95\) 1.33356 0.136820
\(96\) 2.38266 0.243180
\(97\) 4.26593 0.433139 0.216570 0.976267i \(-0.430513\pi\)
0.216570 + 0.976267i \(0.430513\pi\)
\(98\) −1.00000 −0.101015
\(99\) −10.5375 −1.05906
\(100\) 1.82915 0.182915
\(101\) 12.9593 1.28950 0.644749 0.764395i \(-0.276962\pi\)
0.644749 + 0.764395i \(0.276962\pi\)
\(102\) −6.23623 −0.617479
\(103\) −11.1668 −1.10030 −0.550148 0.835067i \(-0.685429\pi\)
−0.550148 + 0.835067i \(0.685429\pi\)
\(104\) −1.76940 −0.173504
\(105\) 6.22653 0.607647
\(106\) 8.70151 0.845165
\(107\) 11.7925 1.14002 0.570012 0.821636i \(-0.306938\pi\)
0.570012 + 0.821636i \(0.306938\pi\)
\(108\) 0.769400 0.0740355
\(109\) 6.73683 0.645271 0.322636 0.946523i \(-0.395431\pi\)
0.322636 + 0.946523i \(0.395431\pi\)
\(110\) −10.2863 −0.980758
\(111\) −10.2903 −0.976717
\(112\) 1.00000 0.0944911
\(113\) 9.77779 0.919817 0.459909 0.887966i \(-0.347882\pi\)
0.459909 + 0.887966i \(0.347882\pi\)
\(114\) −1.21588 −0.113878
\(115\) 16.8357 1.56994
\(116\) 4.06382 0.377316
\(117\) 4.73683 0.437920
\(118\) 9.05975 0.834017
\(119\) −2.61734 −0.239931
\(120\) −6.22653 −0.568402
\(121\) 4.49351 0.408501
\(122\) −6.05975 −0.548624
\(123\) 28.2944 2.55122
\(124\) 4.60919 0.413918
\(125\) 8.28627 0.741147
\(126\) −2.67708 −0.238494
\(127\) 2.61734 0.232251 0.116126 0.993235i \(-0.462953\pi\)
0.116126 + 0.993235i \(0.462953\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −21.3755 −1.88200
\(130\) 4.62391 0.405544
\(131\) 20.0378 1.75071 0.875356 0.483478i \(-0.160627\pi\)
0.875356 + 0.483478i \(0.160627\pi\)
\(132\) 9.37859 0.816301
\(133\) −0.510304 −0.0442490
\(134\) 9.84386 0.850380
\(135\) −2.01064 −0.173049
\(136\) 2.61734 0.224435
\(137\) 9.50216 0.811824 0.405912 0.913912i \(-0.366954\pi\)
0.405912 + 0.913912i \(0.366954\pi\)
\(138\) −15.3501 −1.30669
\(139\) −3.92528 −0.332938 −0.166469 0.986047i \(-0.553236\pi\)
−0.166469 + 0.986047i \(0.553236\pi\)
\(140\) −2.61326 −0.220861
\(141\) −27.2985 −2.29895
\(142\) 7.39920 0.620927
\(143\) −6.96467 −0.582415
\(144\) 2.67708 0.223090
\(145\) −10.6198 −0.881929
\(146\) 0.662367 0.0548179
\(147\) −2.38266 −0.196519
\(148\) 4.31884 0.355007
\(149\) 5.29416 0.433715 0.216857 0.976203i \(-0.430419\pi\)
0.216857 + 0.976203i \(0.430419\pi\)
\(150\) 4.35824 0.355849
\(151\) −7.84360 −0.638303 −0.319152 0.947704i \(-0.603398\pi\)
−0.319152 + 0.947704i \(0.603398\pi\)
\(152\) 0.510304 0.0413911
\(153\) −7.00683 −0.566469
\(154\) 3.93618 0.317186
\(155\) −12.0450 −0.967480
\(156\) −4.21588 −0.337541
\(157\) 17.0066 1.35727 0.678636 0.734475i \(-0.262571\pi\)
0.678636 + 0.734475i \(0.262571\pi\)
\(158\) −14.1195 −1.12329
\(159\) 20.7328 1.64421
\(160\) 2.61326 0.206597
\(161\) −6.44241 −0.507733
\(162\) 9.86447 0.775026
\(163\) 0.495587 0.0388174 0.0194087 0.999812i \(-0.493822\pi\)
0.0194087 + 0.999812i \(0.493822\pi\)
\(164\) −11.8751 −0.927291
\(165\) −24.5087 −1.90800
\(166\) 8.90768 0.691370
\(167\) 7.55627 0.584722 0.292361 0.956308i \(-0.405559\pi\)
0.292361 + 0.956308i \(0.405559\pi\)
\(168\) 2.38266 0.183826
\(169\) −9.86923 −0.759171
\(170\) −6.83979 −0.524588
\(171\) −1.36613 −0.104470
\(172\) 8.97125 0.684051
\(173\) 12.1410 0.923066 0.461533 0.887123i \(-0.347300\pi\)
0.461533 + 0.887123i \(0.347300\pi\)
\(174\) 9.68272 0.734045
\(175\) 1.82915 0.138271
\(176\) −3.93618 −0.296701
\(177\) 21.5863 1.62253
\(178\) −16.3272 −1.22378
\(179\) −10.2509 −0.766192 −0.383096 0.923709i \(-0.625142\pi\)
−0.383096 + 0.923709i \(0.625142\pi\)
\(180\) −6.99593 −0.521446
\(181\) 21.8045 1.62071 0.810357 0.585937i \(-0.199273\pi\)
0.810357 + 0.585937i \(0.199273\pi\)
\(182\) −1.76940 −0.131157
\(183\) −14.4383 −1.06731
\(184\) 6.44241 0.474941
\(185\) −11.2863 −0.829783
\(186\) 10.9821 0.805250
\(187\) 10.3023 0.753379
\(188\) 11.4571 0.835597
\(189\) 0.769400 0.0559656
\(190\) −1.33356 −0.0967466
\(191\) −0.944326 −0.0683290 −0.0341645 0.999416i \(-0.510877\pi\)
−0.0341645 + 0.999416i \(0.510877\pi\)
\(192\) −2.38266 −0.171954
\(193\) −20.6651 −1.48751 −0.743754 0.668453i \(-0.766957\pi\)
−0.743754 + 0.668453i \(0.766957\pi\)
\(194\) −4.26593 −0.306276
\(195\) 11.0172 0.788959
\(196\) 1.00000 0.0714286
\(197\) 5.81036 0.413971 0.206985 0.978344i \(-0.433635\pi\)
0.206985 + 0.978344i \(0.433635\pi\)
\(198\) 10.5375 0.748866
\(199\) −1.59949 −0.113385 −0.0566923 0.998392i \(-0.518055\pi\)
−0.0566923 + 0.998392i \(0.518055\pi\)
\(200\) −1.82915 −0.129340
\(201\) 23.4546 1.65436
\(202\) −12.9593 −0.911812
\(203\) 4.06382 0.285224
\(204\) 6.23623 0.436624
\(205\) 31.0328 2.16743
\(206\) 11.1668 0.778026
\(207\) −17.2469 −1.19874
\(208\) 1.76940 0.122686
\(209\) 2.00865 0.138941
\(210\) −6.22653 −0.429671
\(211\) −11.0145 −0.758266 −0.379133 0.925342i \(-0.623778\pi\)
−0.379133 + 0.925342i \(0.623778\pi\)
\(212\) −8.70151 −0.597622
\(213\) 17.6298 1.20797
\(214\) −11.7925 −0.806119
\(215\) −23.4442 −1.59888
\(216\) −0.769400 −0.0523510
\(217\) 4.60919 0.312892
\(218\) −6.73683 −0.456276
\(219\) 1.57820 0.106645
\(220\) 10.2863 0.693501
\(221\) −4.63111 −0.311522
\(222\) 10.2903 0.690643
\(223\) 2.20524 0.147674 0.0738369 0.997270i \(-0.476476\pi\)
0.0738369 + 0.997270i \(0.476476\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 4.89678 0.326452
\(226\) −9.77779 −0.650409
\(227\) 10.7465 0.713273 0.356636 0.934243i \(-0.383924\pi\)
0.356636 + 0.934243i \(0.383924\pi\)
\(228\) 1.21588 0.0805238
\(229\) −21.9052 −1.44753 −0.723767 0.690044i \(-0.757591\pi\)
−0.723767 + 0.690044i \(0.757591\pi\)
\(230\) −16.8357 −1.11011
\(231\) 9.37859 0.617066
\(232\) −4.06382 −0.266803
\(233\) −14.1342 −0.925963 −0.462982 0.886368i \(-0.653220\pi\)
−0.462982 + 0.886368i \(0.653220\pi\)
\(234\) −4.73683 −0.309656
\(235\) −29.9405 −1.95310
\(236\) −9.05975 −0.589739
\(237\) −33.6420 −2.18528
\(238\) 2.61734 0.169657
\(239\) −17.0234 −1.10115 −0.550575 0.834786i \(-0.685592\pi\)
−0.550575 + 0.834786i \(0.685592\pi\)
\(240\) 6.22653 0.401921
\(241\) −18.1722 −1.17057 −0.585286 0.810827i \(-0.699018\pi\)
−0.585286 + 0.810827i \(0.699018\pi\)
\(242\) −4.49351 −0.288854
\(243\) 21.1955 1.35969
\(244\) 6.05975 0.387936
\(245\) −2.61326 −0.166955
\(246\) −28.2944 −1.80399
\(247\) −0.902932 −0.0574522
\(248\) −4.60919 −0.292684
\(249\) 21.2240 1.34502
\(250\) −8.28627 −0.524070
\(251\) 20.5716 1.29847 0.649234 0.760588i \(-0.275089\pi\)
0.649234 + 0.760588i \(0.275089\pi\)
\(252\) 2.67708 0.168640
\(253\) 25.3585 1.59427
\(254\) −2.61734 −0.164226
\(255\) −16.2969 −1.02055
\(256\) 1.00000 0.0625000
\(257\) −4.29035 −0.267625 −0.133812 0.991007i \(-0.542722\pi\)
−0.133812 + 0.991007i \(0.542722\pi\)
\(258\) 21.3755 1.33078
\(259\) 4.31884 0.268360
\(260\) −4.62391 −0.286763
\(261\) 10.8792 0.673405
\(262\) −20.0378 −1.23794
\(263\) 21.4345 1.32171 0.660855 0.750514i \(-0.270194\pi\)
0.660855 + 0.750514i \(0.270194\pi\)
\(264\) −9.37859 −0.577212
\(265\) 22.7393 1.39687
\(266\) 0.510304 0.0312888
\(267\) −38.9023 −2.38078
\(268\) −9.84386 −0.601310
\(269\) 5.98095 0.364665 0.182332 0.983237i \(-0.441635\pi\)
0.182332 + 0.983237i \(0.441635\pi\)
\(270\) 2.01064 0.122364
\(271\) −23.0641 −1.40104 −0.700521 0.713632i \(-0.747049\pi\)
−0.700521 + 0.713632i \(0.747049\pi\)
\(272\) −2.61734 −0.158699
\(273\) −4.21588 −0.255157
\(274\) −9.50216 −0.574046
\(275\) −7.19985 −0.434167
\(276\) 15.3501 0.923967
\(277\) 9.54762 0.573661 0.286831 0.957981i \(-0.407398\pi\)
0.286831 + 0.957981i \(0.407398\pi\)
\(278\) 3.92528 0.235422
\(279\) 12.3392 0.738728
\(280\) 2.61326 0.156172
\(281\) −6.01272 −0.358689 −0.179344 0.983786i \(-0.557398\pi\)
−0.179344 + 0.983786i \(0.557398\pi\)
\(282\) 27.2985 1.62560
\(283\) −29.7178 −1.76654 −0.883269 0.468866i \(-0.844663\pi\)
−0.883269 + 0.468866i \(0.844663\pi\)
\(284\) −7.39920 −0.439062
\(285\) −3.17742 −0.188214
\(286\) 6.96467 0.411830
\(287\) −11.8751 −0.700966
\(288\) −2.67708 −0.157749
\(289\) −10.1495 −0.597032
\(290\) 10.6198 0.623618
\(291\) −10.1643 −0.595840
\(292\) −0.662367 −0.0387621
\(293\) 2.20956 0.129084 0.0645418 0.997915i \(-0.479441\pi\)
0.0645418 + 0.997915i \(0.479441\pi\)
\(294\) 2.38266 0.138960
\(295\) 23.6755 1.37844
\(296\) −4.31884 −0.251028
\(297\) −3.02849 −0.175731
\(298\) −5.29416 −0.306683
\(299\) −11.3992 −0.659233
\(300\) −4.35824 −0.251623
\(301\) 8.97125 0.517094
\(302\) 7.84360 0.451349
\(303\) −30.8776 −1.77387
\(304\) −0.510304 −0.0292680
\(305\) −15.8357 −0.906751
\(306\) 7.00683 0.400554
\(307\) −5.01222 −0.286062 −0.143031 0.989718i \(-0.545685\pi\)
−0.143031 + 0.989718i \(0.545685\pi\)
\(308\) −3.93618 −0.224285
\(309\) 26.6067 1.51360
\(310\) 12.0450 0.684112
\(311\) −5.93920 −0.336781 −0.168390 0.985720i \(-0.553857\pi\)
−0.168390 + 0.985720i \(0.553857\pi\)
\(312\) 4.21588 0.238677
\(313\) −17.9396 −1.01400 −0.507002 0.861945i \(-0.669246\pi\)
−0.507002 + 0.861945i \(0.669246\pi\)
\(314\) −17.0066 −0.959736
\(315\) −6.99593 −0.394176
\(316\) 14.1195 0.794284
\(317\) 25.9572 1.45790 0.728951 0.684566i \(-0.240008\pi\)
0.728951 + 0.684566i \(0.240008\pi\)
\(318\) −20.7328 −1.16264
\(319\) −15.9959 −0.895600
\(320\) −2.61326 −0.146086
\(321\) −28.0976 −1.56825
\(322\) 6.44241 0.359022
\(323\) 1.33564 0.0743169
\(324\) −9.86447 −0.548026
\(325\) 3.23649 0.179528
\(326\) −0.495587 −0.0274480
\(327\) −16.0516 −0.887656
\(328\) 11.8751 0.655694
\(329\) 11.4571 0.631652
\(330\) 24.5087 1.34916
\(331\) −15.8973 −0.873794 −0.436897 0.899512i \(-0.643923\pi\)
−0.436897 + 0.899512i \(0.643923\pi\)
\(332\) −8.90768 −0.488873
\(333\) 11.5619 0.633589
\(334\) −7.55627 −0.413461
\(335\) 25.7246 1.40549
\(336\) −2.38266 −0.129985
\(337\) −27.5044 −1.49826 −0.749130 0.662423i \(-0.769528\pi\)
−0.749130 + 0.662423i \(0.769528\pi\)
\(338\) 9.86923 0.536815
\(339\) −23.2972 −1.26533
\(340\) 6.83979 0.370940
\(341\) −18.1426 −0.982477
\(342\) 1.36613 0.0738717
\(343\) 1.00000 0.0539949
\(344\) −8.97125 −0.483697
\(345\) −40.1138 −2.15966
\(346\) −12.1410 −0.652707
\(347\) −13.8129 −0.741513 −0.370756 0.928730i \(-0.620902\pi\)
−0.370756 + 0.928730i \(0.620902\pi\)
\(348\) −9.68272 −0.519048
\(349\) 27.5712 1.47585 0.737927 0.674880i \(-0.235805\pi\)
0.737927 + 0.674880i \(0.235805\pi\)
\(350\) −1.82915 −0.0977720
\(351\) 1.36138 0.0726648
\(352\) 3.93618 0.209799
\(353\) 15.4180 0.820617 0.410308 0.911947i \(-0.365421\pi\)
0.410308 + 0.911947i \(0.365421\pi\)
\(354\) −21.5863 −1.14730
\(355\) 19.3361 1.02625
\(356\) 16.3272 0.865342
\(357\) 6.23623 0.330056
\(358\) 10.2509 0.541779
\(359\) −13.2973 −0.701804 −0.350902 0.936412i \(-0.614125\pi\)
−0.350902 + 0.936412i \(0.614125\pi\)
\(360\) 6.99593 0.368718
\(361\) −18.7396 −0.986294
\(362\) −21.8045 −1.14602
\(363\) −10.7065 −0.561946
\(364\) 1.76940 0.0927417
\(365\) 1.73094 0.0906015
\(366\) 14.4383 0.754704
\(367\) 28.7975 1.50322 0.751609 0.659609i \(-0.229278\pi\)
0.751609 + 0.659609i \(0.229278\pi\)
\(368\) −6.44241 −0.335834
\(369\) −31.7907 −1.65496
\(370\) 11.2863 0.586745
\(371\) −8.70151 −0.451760
\(372\) −10.9821 −0.569398
\(373\) 3.49940 0.181192 0.0905960 0.995888i \(-0.471123\pi\)
0.0905960 + 0.995888i \(0.471123\pi\)
\(374\) −10.3023 −0.532720
\(375\) −19.7434 −1.01954
\(376\) −11.4571 −0.590856
\(377\) 7.19052 0.370331
\(378\) −0.769400 −0.0395736
\(379\) −5.91921 −0.304049 −0.152025 0.988377i \(-0.548579\pi\)
−0.152025 + 0.988377i \(0.548579\pi\)
\(380\) 1.33356 0.0684102
\(381\) −6.23623 −0.319492
\(382\) 0.944326 0.0483159
\(383\) −2.97031 −0.151776 −0.0758878 0.997116i \(-0.524179\pi\)
−0.0758878 + 0.997116i \(0.524179\pi\)
\(384\) 2.38266 0.121590
\(385\) 10.2863 0.524237
\(386\) 20.6651 1.05183
\(387\) 24.0168 1.22084
\(388\) 4.26593 0.216570
\(389\) 6.70990 0.340205 0.170103 0.985426i \(-0.445590\pi\)
0.170103 + 0.985426i \(0.445590\pi\)
\(390\) −11.0172 −0.557878
\(391\) 16.8620 0.852746
\(392\) −1.00000 −0.0505076
\(393\) −47.7434 −2.40834
\(394\) −5.81036 −0.292722
\(395\) −36.8980 −1.85654
\(396\) −10.5375 −0.529528
\(397\) 13.5622 0.680666 0.340333 0.940305i \(-0.389460\pi\)
0.340333 + 0.940305i \(0.389460\pi\)
\(398\) 1.59949 0.0801750
\(399\) 1.21588 0.0608703
\(400\) 1.82915 0.0914574
\(401\) −13.1430 −0.656332 −0.328166 0.944620i \(-0.606431\pi\)
−0.328166 + 0.944620i \(0.606431\pi\)
\(402\) −23.4546 −1.16981
\(403\) 8.15550 0.406254
\(404\) 12.9593 0.644749
\(405\) 25.7785 1.28094
\(406\) −4.06382 −0.201684
\(407\) −16.9997 −0.842646
\(408\) −6.23623 −0.308739
\(409\) 18.8416 0.931658 0.465829 0.884875i \(-0.345756\pi\)
0.465829 + 0.884875i \(0.345756\pi\)
\(410\) −31.0328 −1.53260
\(411\) −22.6404 −1.11677
\(412\) −11.1668 −0.550148
\(413\) −9.05975 −0.445801
\(414\) 17.2469 0.847638
\(415\) 23.2781 1.14268
\(416\) −1.76940 −0.0867520
\(417\) 9.35261 0.457999
\(418\) −2.00865 −0.0982463
\(419\) −12.8973 −0.630074 −0.315037 0.949079i \(-0.602017\pi\)
−0.315037 + 0.949079i \(0.602017\pi\)
\(420\) 6.22653 0.303823
\(421\) −16.5184 −0.805059 −0.402530 0.915407i \(-0.631869\pi\)
−0.402530 + 0.915407i \(0.631869\pi\)
\(422\) 11.0145 0.536175
\(423\) 30.6717 1.49131
\(424\) 8.70151 0.422582
\(425\) −4.78749 −0.232228
\(426\) −17.6298 −0.854167
\(427\) 6.05975 0.293252
\(428\) 11.7925 0.570012
\(429\) 16.5945 0.801189
\(430\) 23.4442 1.13058
\(431\) 1.00000 0.0481683
\(432\) 0.769400 0.0370178
\(433\) 8.93592 0.429433 0.214716 0.976676i \(-0.431117\pi\)
0.214716 + 0.976676i \(0.431117\pi\)
\(434\) −4.60919 −0.221248
\(435\) 25.3035 1.21321
\(436\) 6.73683 0.322636
\(437\) 3.28759 0.157267
\(438\) −1.57820 −0.0754092
\(439\) −10.6669 −0.509101 −0.254551 0.967059i \(-0.581928\pi\)
−0.254551 + 0.967059i \(0.581928\pi\)
\(440\) −10.2863 −0.490379
\(441\) 2.67708 0.127480
\(442\) 4.63111 0.220280
\(443\) −29.5100 −1.40206 −0.701032 0.713130i \(-0.747277\pi\)
−0.701032 + 0.713130i \(0.747277\pi\)
\(444\) −10.2903 −0.488358
\(445\) −42.6674 −2.02263
\(446\) −2.20524 −0.104421
\(447\) −12.6142 −0.596631
\(448\) 1.00000 0.0472456
\(449\) −8.80065 −0.415328 −0.207664 0.978200i \(-0.566586\pi\)
−0.207664 + 0.978200i \(0.566586\pi\)
\(450\) −4.89678 −0.230836
\(451\) 46.7426 2.20102
\(452\) 9.77779 0.459909
\(453\) 18.6887 0.878070
\(454\) −10.7465 −0.504360
\(455\) −4.62391 −0.216772
\(456\) −1.21588 −0.0569390
\(457\) −2.87643 −0.134554 −0.0672769 0.997734i \(-0.521431\pi\)
−0.0672769 + 0.997734i \(0.521431\pi\)
\(458\) 21.9052 1.02356
\(459\) −2.01378 −0.0939951
\(460\) 16.8357 0.784969
\(461\) −31.0928 −1.44814 −0.724068 0.689728i \(-0.757730\pi\)
−0.724068 + 0.689728i \(0.757730\pi\)
\(462\) −9.37859 −0.436332
\(463\) 11.3344 0.526756 0.263378 0.964693i \(-0.415163\pi\)
0.263378 + 0.964693i \(0.415163\pi\)
\(464\) 4.06382 0.188658
\(465\) 28.6993 1.33090
\(466\) 14.1342 0.654755
\(467\) 37.9010 1.75385 0.876924 0.480629i \(-0.159592\pi\)
0.876924 + 0.480629i \(0.159592\pi\)
\(468\) 4.73683 0.218960
\(469\) −9.84386 −0.454547
\(470\) 29.9405 1.38105
\(471\) −40.5209 −1.86711
\(472\) 9.05975 0.417009
\(473\) −35.3124 −1.62367
\(474\) 33.6420 1.54523
\(475\) −0.933422 −0.0428283
\(476\) −2.61734 −0.119965
\(477\) −23.2947 −1.06659
\(478\) 17.0234 0.778631
\(479\) −21.0034 −0.959669 −0.479834 0.877359i \(-0.659303\pi\)
−0.479834 + 0.877359i \(0.659303\pi\)
\(480\) −6.22653 −0.284201
\(481\) 7.64176 0.348434
\(482\) 18.1722 0.827719
\(483\) 15.3501 0.698454
\(484\) 4.49351 0.204250
\(485\) −11.1480 −0.506204
\(486\) −21.1955 −0.961448
\(487\) −30.1820 −1.36768 −0.683838 0.729633i \(-0.739691\pi\)
−0.683838 + 0.729633i \(0.739691\pi\)
\(488\) −6.05975 −0.274312
\(489\) −1.18082 −0.0533984
\(490\) 2.61326 0.118055
\(491\) −1.49758 −0.0675849 −0.0337925 0.999429i \(-0.510759\pi\)
−0.0337925 + 0.999429i \(0.510759\pi\)
\(492\) 28.2944 1.27561
\(493\) −10.6364 −0.479039
\(494\) 0.902932 0.0406248
\(495\) 27.5372 1.23771
\(496\) 4.60919 0.206959
\(497\) −7.39920 −0.331899
\(498\) −21.2240 −0.951071
\(499\) 13.6529 0.611188 0.305594 0.952162i \(-0.401145\pi\)
0.305594 + 0.952162i \(0.401145\pi\)
\(500\) 8.28627 0.370573
\(501\) −18.0041 −0.804362
\(502\) −20.5716 −0.918156
\(503\) −44.0099 −1.96231 −0.981153 0.193231i \(-0.938103\pi\)
−0.981153 + 0.193231i \(0.938103\pi\)
\(504\) −2.67708 −0.119247
\(505\) −33.8660 −1.50702
\(506\) −25.3585 −1.12732
\(507\) 23.5150 1.04434
\(508\) 2.61734 0.116126
\(509\) −40.4846 −1.79445 −0.897223 0.441578i \(-0.854419\pi\)
−0.897223 + 0.441578i \(0.854419\pi\)
\(510\) 16.2969 0.721640
\(511\) −0.662367 −0.0293014
\(512\) −1.00000 −0.0441942
\(513\) −0.392628 −0.0173349
\(514\) 4.29035 0.189239
\(515\) 29.1817 1.28590
\(516\) −21.3755 −0.941002
\(517\) −45.0973 −1.98338
\(518\) −4.31884 −0.189759
\(519\) −28.9280 −1.26980
\(520\) 4.62391 0.202772
\(521\) 29.5814 1.29598 0.647992 0.761647i \(-0.275609\pi\)
0.647992 + 0.761647i \(0.275609\pi\)
\(522\) −10.8792 −0.476169
\(523\) −19.0348 −0.832334 −0.416167 0.909288i \(-0.636627\pi\)
−0.416167 + 0.909288i \(0.636627\pi\)
\(524\) 20.0378 0.875356
\(525\) −4.35824 −0.190209
\(526\) −21.4345 −0.934590
\(527\) −12.0638 −0.525508
\(528\) 9.37859 0.408151
\(529\) 18.5047 0.804550
\(530\) −22.7393 −0.987733
\(531\) −24.2537 −1.05252
\(532\) −0.510304 −0.0221245
\(533\) −21.0118 −0.910123
\(534\) 38.9023 1.68347
\(535\) −30.8169 −1.33233
\(536\) 9.84386 0.425190
\(537\) 24.4246 1.05400
\(538\) −5.98095 −0.257857
\(539\) −3.93618 −0.169543
\(540\) −2.01064 −0.0865243
\(541\) −36.1532 −1.55435 −0.777175 0.629285i \(-0.783348\pi\)
−0.777175 + 0.629285i \(0.783348\pi\)
\(542\) 23.0641 0.990686
\(543\) −51.9527 −2.22950
\(544\) 2.61734 0.112217
\(545\) −17.6051 −0.754120
\(546\) 4.21588 0.180423
\(547\) 31.6407 1.35286 0.676429 0.736508i \(-0.263527\pi\)
0.676429 + 0.736508i \(0.263527\pi\)
\(548\) 9.50216 0.405912
\(549\) 16.2225 0.692357
\(550\) 7.19985 0.307003
\(551\) −2.07379 −0.0883462
\(552\) −15.3501 −0.653343
\(553\) 14.1195 0.600422
\(554\) −9.54762 −0.405640
\(555\) 26.8914 1.14148
\(556\) −3.92528 −0.166469
\(557\) −6.23987 −0.264392 −0.132196 0.991224i \(-0.542203\pi\)
−0.132196 + 0.991224i \(0.542203\pi\)
\(558\) −12.3392 −0.522360
\(559\) 15.8737 0.671387
\(560\) −2.61326 −0.110431
\(561\) −24.5469 −1.03637
\(562\) 6.01272 0.253631
\(563\) −35.8441 −1.51065 −0.755325 0.655351i \(-0.772521\pi\)
−0.755325 + 0.655351i \(0.772521\pi\)
\(564\) −27.2985 −1.14947
\(565\) −25.5519 −1.07498
\(566\) 29.7178 1.24913
\(567\) −9.86447 −0.414269
\(568\) 7.39920 0.310463
\(569\) −34.6952 −1.45450 −0.727249 0.686374i \(-0.759201\pi\)
−0.727249 + 0.686374i \(0.759201\pi\)
\(570\) 3.17742 0.133088
\(571\) −12.0991 −0.506334 −0.253167 0.967423i \(-0.581472\pi\)
−0.253167 + 0.967423i \(0.581472\pi\)
\(572\) −6.96467 −0.291208
\(573\) 2.25001 0.0939955
\(574\) 11.8751 0.495658
\(575\) −11.7841 −0.491432
\(576\) 2.67708 0.111545
\(577\) −9.42049 −0.392180 −0.196090 0.980586i \(-0.562824\pi\)
−0.196090 + 0.980586i \(0.562824\pi\)
\(578\) 10.1495 0.422166
\(579\) 49.2380 2.04626
\(580\) −10.6198 −0.440965
\(581\) −8.90768 −0.369553
\(582\) 10.1643 0.421322
\(583\) 34.2507 1.41852
\(584\) 0.662367 0.0274089
\(585\) −12.3786 −0.511792
\(586\) −2.20956 −0.0912759
\(587\) 20.1188 0.830392 0.415196 0.909732i \(-0.363713\pi\)
0.415196 + 0.909732i \(0.363713\pi\)
\(588\) −2.38266 −0.0982594
\(589\) −2.35209 −0.0969162
\(590\) −23.6755 −0.974705
\(591\) −13.8441 −0.569471
\(592\) 4.31884 0.177503
\(593\) 40.6217 1.66813 0.834066 0.551665i \(-0.186007\pi\)
0.834066 + 0.551665i \(0.186007\pi\)
\(594\) 3.02849 0.124261
\(595\) 6.83979 0.280404
\(596\) 5.29416 0.216857
\(597\) 3.81104 0.155975
\(598\) 11.3992 0.466148
\(599\) 23.0043 0.939931 0.469965 0.882685i \(-0.344266\pi\)
0.469965 + 0.882685i \(0.344266\pi\)
\(600\) 4.35824 0.177924
\(601\) −4.46226 −0.182019 −0.0910096 0.995850i \(-0.529009\pi\)
−0.0910096 + 0.995850i \(0.529009\pi\)
\(602\) −8.97125 −0.365641
\(603\) −26.3529 −1.07317
\(604\) −7.84360 −0.319152
\(605\) −11.7427 −0.477410
\(606\) 30.8776 1.25432
\(607\) 25.6061 1.03932 0.519659 0.854374i \(-0.326059\pi\)
0.519659 + 0.854374i \(0.326059\pi\)
\(608\) 0.510304 0.0206956
\(609\) −9.68272 −0.392363
\(610\) 15.8357 0.641169
\(611\) 20.2722 0.820127
\(612\) −7.00683 −0.283234
\(613\) 4.35667 0.175964 0.0879820 0.996122i \(-0.471958\pi\)
0.0879820 + 0.996122i \(0.471958\pi\)
\(614\) 5.01222 0.202277
\(615\) −73.9407 −2.98158
\(616\) 3.93618 0.158593
\(617\) −41.7099 −1.67918 −0.839589 0.543223i \(-0.817204\pi\)
−0.839589 + 0.543223i \(0.817204\pi\)
\(618\) −26.6067 −1.07028
\(619\) −15.6482 −0.628952 −0.314476 0.949265i \(-0.601829\pi\)
−0.314476 + 0.949265i \(0.601829\pi\)
\(620\) −12.0450 −0.483740
\(621\) −4.95679 −0.198909
\(622\) 5.93920 0.238140
\(623\) 16.3272 0.654137
\(624\) −4.21588 −0.168770
\(625\) −30.8000 −1.23200
\(626\) 17.9396 0.717009
\(627\) −4.78594 −0.191132
\(628\) 17.0066 0.678636
\(629\) −11.3039 −0.450715
\(630\) 6.99593 0.278724
\(631\) 41.2127 1.64065 0.820326 0.571895i \(-0.193792\pi\)
0.820326 + 0.571895i \(0.193792\pi\)
\(632\) −14.1195 −0.561643
\(633\) 26.2437 1.04310
\(634\) −25.9572 −1.03089
\(635\) −6.83979 −0.271429
\(636\) 20.7328 0.822107
\(637\) 1.76940 0.0701062
\(638\) 15.9959 0.633285
\(639\) −19.8083 −0.783603
\(640\) 2.61326 0.103298
\(641\) −28.6468 −1.13148 −0.565740 0.824584i \(-0.691409\pi\)
−0.565740 + 0.824584i \(0.691409\pi\)
\(642\) 28.0976 1.10892
\(643\) −38.1967 −1.50633 −0.753166 0.657831i \(-0.771474\pi\)
−0.753166 + 0.657831i \(0.771474\pi\)
\(644\) −6.44241 −0.253867
\(645\) 55.8597 2.19947
\(646\) −1.33564 −0.0525500
\(647\) −34.5209 −1.35716 −0.678579 0.734527i \(-0.737404\pi\)
−0.678579 + 0.734527i \(0.737404\pi\)
\(648\) 9.86447 0.387513
\(649\) 35.6608 1.39981
\(650\) −3.23649 −0.126946
\(651\) −10.9821 −0.430424
\(652\) 0.495587 0.0194087
\(653\) 20.0758 0.785625 0.392813 0.919619i \(-0.371502\pi\)
0.392813 + 0.919619i \(0.371502\pi\)
\(654\) 16.0516 0.627667
\(655\) −52.3641 −2.04604
\(656\) −11.8751 −0.463645
\(657\) −1.77321 −0.0691796
\(658\) −11.4571 −0.446645
\(659\) 2.19621 0.0855523 0.0427762 0.999085i \(-0.486380\pi\)
0.0427762 + 0.999085i \(0.486380\pi\)
\(660\) −24.5087 −0.954001
\(661\) −6.40958 −0.249304 −0.124652 0.992201i \(-0.539781\pi\)
−0.124652 + 0.992201i \(0.539781\pi\)
\(662\) 15.8973 0.617865
\(663\) 11.0344 0.428540
\(664\) 8.90768 0.345685
\(665\) 1.33356 0.0517132
\(666\) −11.5619 −0.448015
\(667\) −26.1808 −1.01372
\(668\) 7.55627 0.292361
\(669\) −5.25434 −0.203145
\(670\) −25.7246 −0.993828
\(671\) −23.8523 −0.920806
\(672\) 2.38266 0.0919132
\(673\) 24.3145 0.937255 0.468628 0.883396i \(-0.344749\pi\)
0.468628 + 0.883396i \(0.344749\pi\)
\(674\) 27.5044 1.05943
\(675\) 1.40734 0.0541687
\(676\) −9.86923 −0.379586
\(677\) 8.27719 0.318118 0.159059 0.987269i \(-0.449154\pi\)
0.159059 + 0.987269i \(0.449154\pi\)
\(678\) 23.2972 0.894723
\(679\) 4.26593 0.163711
\(680\) −6.83979 −0.262294
\(681\) −25.6054 −0.981200
\(682\) 18.1426 0.694716
\(683\) −21.5950 −0.826309 −0.413154 0.910661i \(-0.635573\pi\)
−0.413154 + 0.910661i \(0.635573\pi\)
\(684\) −1.36613 −0.0522352
\(685\) −24.8316 −0.948768
\(686\) −1.00000 −0.0381802
\(687\) 52.1926 1.99127
\(688\) 8.97125 0.342026
\(689\) −15.3964 −0.586558
\(690\) 40.1138 1.52711
\(691\) −32.9106 −1.25198 −0.625988 0.779832i \(-0.715304\pi\)
−0.625988 + 0.779832i \(0.715304\pi\)
\(692\) 12.1410 0.461533
\(693\) −10.5375 −0.400286
\(694\) 13.8129 0.524329
\(695\) 10.2578 0.389100
\(696\) 9.68272 0.367022
\(697\) 31.0812 1.17728
\(698\) −27.5712 −1.04359
\(699\) 33.6771 1.27378
\(700\) 1.82915 0.0691353
\(701\) 28.4402 1.07417 0.537085 0.843528i \(-0.319525\pi\)
0.537085 + 0.843528i \(0.319525\pi\)
\(702\) −1.36138 −0.0513818
\(703\) −2.20392 −0.0831226
\(704\) −3.93618 −0.148350
\(705\) 71.3381 2.68675
\(706\) −15.4180 −0.580264
\(707\) 12.9593 0.487384
\(708\) 21.5863 0.811264
\(709\) −37.4596 −1.40683 −0.703413 0.710781i \(-0.748341\pi\)
−0.703413 + 0.710781i \(0.748341\pi\)
\(710\) −19.3361 −0.725669
\(711\) 37.7991 1.41758
\(712\) −16.3272 −0.611889
\(713\) −29.6943 −1.11206
\(714\) −6.23623 −0.233385
\(715\) 18.2005 0.680661
\(716\) −10.2509 −0.383096
\(717\) 40.5609 1.51478
\(718\) 13.2973 0.496251
\(719\) −17.6605 −0.658627 −0.329313 0.944221i \(-0.606817\pi\)
−0.329313 + 0.944221i \(0.606817\pi\)
\(720\) −6.99593 −0.260723
\(721\) −11.1668 −0.415873
\(722\) 18.7396 0.697415
\(723\) 43.2981 1.61027
\(724\) 21.8045 0.810357
\(725\) 7.43333 0.276067
\(726\) 10.7065 0.397356
\(727\) −29.8960 −1.10878 −0.554390 0.832257i \(-0.687049\pi\)
−0.554390 + 0.832257i \(0.687049\pi\)
\(728\) −1.76940 −0.0655783
\(729\) −20.9084 −0.774384
\(730\) −1.73094 −0.0640650
\(731\) −23.4808 −0.868468
\(732\) −14.4383 −0.533656
\(733\) 41.4747 1.53190 0.765952 0.642898i \(-0.222268\pi\)
0.765952 + 0.642898i \(0.222268\pi\)
\(734\) −28.7975 −1.06294
\(735\) 6.22653 0.229669
\(736\) 6.44241 0.237470
\(737\) 38.7472 1.42727
\(738\) 31.7907 1.17023
\(739\) −44.7271 −1.64531 −0.822657 0.568538i \(-0.807509\pi\)
−0.822657 + 0.568538i \(0.807509\pi\)
\(740\) −11.2863 −0.414892
\(741\) 2.15138 0.0790330
\(742\) 8.70151 0.319442
\(743\) 2.97600 0.109179 0.0545894 0.998509i \(-0.482615\pi\)
0.0545894 + 0.998509i \(0.482615\pi\)
\(744\) 10.9821 0.402625
\(745\) −13.8350 −0.506877
\(746\) −3.49940 −0.128122
\(747\) −23.8466 −0.872502
\(748\) 10.3023 0.376690
\(749\) 11.7925 0.430889
\(750\) 19.7434 0.720927
\(751\) 7.18212 0.262079 0.131040 0.991377i \(-0.458169\pi\)
0.131040 + 0.991377i \(0.458169\pi\)
\(752\) 11.4571 0.417798
\(753\) −49.0152 −1.78621
\(754\) −7.19052 −0.261863
\(755\) 20.4974 0.745977
\(756\) 0.769400 0.0279828
\(757\) 11.2660 0.409471 0.204736 0.978817i \(-0.434367\pi\)
0.204736 + 0.978817i \(0.434367\pi\)
\(758\) 5.91921 0.214995
\(759\) −60.4207 −2.19313
\(760\) −1.33356 −0.0483733
\(761\) 48.7344 1.76662 0.883310 0.468790i \(-0.155310\pi\)
0.883310 + 0.468790i \(0.155310\pi\)
\(762\) 6.23623 0.225915
\(763\) 6.73683 0.243890
\(764\) −0.944326 −0.0341645
\(765\) 18.3107 0.662025
\(766\) 2.97031 0.107322
\(767\) −16.0303 −0.578821
\(768\) −2.38266 −0.0859770
\(769\) 45.5354 1.64205 0.821024 0.570894i \(-0.193403\pi\)
0.821024 + 0.570894i \(0.193403\pi\)
\(770\) −10.2863 −0.370692
\(771\) 10.2225 0.368153
\(772\) −20.6651 −0.743754
\(773\) 24.1468 0.868500 0.434250 0.900792i \(-0.357013\pi\)
0.434250 + 0.900792i \(0.357013\pi\)
\(774\) −24.0168 −0.863265
\(775\) 8.43089 0.302846
\(776\) −4.26593 −0.153138
\(777\) −10.2903 −0.369164
\(778\) −6.70990 −0.240561
\(779\) 6.05992 0.217119
\(780\) 11.0172 0.394480
\(781\) 29.1246 1.04216
\(782\) −16.8620 −0.602982
\(783\) 3.12670 0.111739
\(784\) 1.00000 0.0357143
\(785\) −44.4427 −1.58623
\(786\) 47.7434 1.70295
\(787\) −15.1832 −0.541223 −0.270611 0.962689i \(-0.587226\pi\)
−0.270611 + 0.962689i \(0.587226\pi\)
\(788\) 5.81036 0.206985
\(789\) −51.0713 −1.81818
\(790\) 36.8980 1.31277
\(791\) 9.77779 0.347658
\(792\) 10.5375 0.374433
\(793\) 10.7221 0.380753
\(794\) −13.5622 −0.481303
\(795\) −54.1802 −1.92157
\(796\) −1.59949 −0.0566923
\(797\) 38.3843 1.35964 0.679821 0.733379i \(-0.262058\pi\)
0.679821 + 0.733379i \(0.262058\pi\)
\(798\) −1.21588 −0.0430418
\(799\) −29.9872 −1.06087
\(800\) −1.82915 −0.0646701
\(801\) 43.7094 1.54439
\(802\) 13.1430 0.464097
\(803\) 2.60720 0.0920060
\(804\) 23.4546 0.827180
\(805\) 16.8357 0.593381
\(806\) −8.15550 −0.287265
\(807\) −14.2506 −0.501645
\(808\) −12.9593 −0.455906
\(809\) 29.7430 1.04571 0.522855 0.852422i \(-0.324867\pi\)
0.522855 + 0.852422i \(0.324867\pi\)
\(810\) −25.7785 −0.905763
\(811\) −52.4383 −1.84136 −0.920679 0.390320i \(-0.872364\pi\)
−0.920679 + 0.390320i \(0.872364\pi\)
\(812\) 4.06382 0.142612
\(813\) 54.9539 1.92732
\(814\) 16.9997 0.595841
\(815\) −1.29510 −0.0453654
\(816\) 6.23623 0.218312
\(817\) −4.57807 −0.160166
\(818\) −18.8416 −0.658781
\(819\) 4.73683 0.165518
\(820\) 31.0328 1.08371
\(821\) 9.03281 0.315247 0.157624 0.987499i \(-0.449617\pi\)
0.157624 + 0.987499i \(0.449617\pi\)
\(822\) 22.6404 0.789676
\(823\) 13.7443 0.479096 0.239548 0.970885i \(-0.423001\pi\)
0.239548 + 0.970885i \(0.423001\pi\)
\(824\) 11.1668 0.389013
\(825\) 17.1548 0.597254
\(826\) 9.05975 0.315229
\(827\) 46.6119 1.62086 0.810428 0.585838i \(-0.199235\pi\)
0.810428 + 0.585838i \(0.199235\pi\)
\(828\) −17.2469 −0.599370
\(829\) 25.9939 0.902806 0.451403 0.892320i \(-0.350924\pi\)
0.451403 + 0.892320i \(0.350924\pi\)
\(830\) −23.2781 −0.807996
\(831\) −22.7488 −0.789146
\(832\) 1.76940 0.0613429
\(833\) −2.61734 −0.0906853
\(834\) −9.35261 −0.323854
\(835\) −19.7465 −0.683357
\(836\) 2.00865 0.0694706
\(837\) 3.54631 0.122578
\(838\) 12.8973 0.445530
\(839\) −23.6709 −0.817211 −0.408605 0.912711i \(-0.633985\pi\)
−0.408605 + 0.912711i \(0.633985\pi\)
\(840\) −6.22653 −0.214836
\(841\) −12.4854 −0.430530
\(842\) 16.5184 0.569263
\(843\) 14.3263 0.493424
\(844\) −11.0145 −0.379133
\(845\) 25.7909 0.887234
\(846\) −30.6717 −1.05451
\(847\) 4.49351 0.154399
\(848\) −8.70151 −0.298811
\(849\) 70.8075 2.43011
\(850\) 4.78749 0.164210
\(851\) −27.8238 −0.953786
\(852\) 17.6298 0.603987
\(853\) −0.141838 −0.00485645 −0.00242822 0.999997i \(-0.500773\pi\)
−0.00242822 + 0.999997i \(0.500773\pi\)
\(854\) −6.05975 −0.207360
\(855\) 3.57005 0.122093
\(856\) −11.7925 −0.403060
\(857\) 36.4607 1.24548 0.622738 0.782431i \(-0.286020\pi\)
0.622738 + 0.782431i \(0.286020\pi\)
\(858\) −16.5945 −0.566526
\(859\) −32.1398 −1.09660 −0.548299 0.836283i \(-0.684724\pi\)
−0.548299 + 0.836283i \(0.684724\pi\)
\(860\) −23.4442 −0.799442
\(861\) 28.2944 0.964271
\(862\) −1.00000 −0.0340601
\(863\) 47.2395 1.60805 0.804026 0.594595i \(-0.202688\pi\)
0.804026 + 0.594595i \(0.202688\pi\)
\(864\) −0.769400 −0.0261755
\(865\) −31.7277 −1.07878
\(866\) −8.93592 −0.303655
\(867\) 24.1830 0.821296
\(868\) 4.60919 0.156446
\(869\) −55.5769 −1.88532
\(870\) −25.3035 −0.857869
\(871\) −17.4177 −0.590177
\(872\) −6.73683 −0.228138
\(873\) 11.4202 0.386517
\(874\) −3.28759 −0.111204
\(875\) 8.28627 0.280127
\(876\) 1.57820 0.0533224
\(877\) 44.6371 1.50729 0.753644 0.657282i \(-0.228294\pi\)
0.753644 + 0.657282i \(0.228294\pi\)
\(878\) 10.6669 0.359989
\(879\) −5.26463 −0.177571
\(880\) 10.2863 0.346750
\(881\) −22.0713 −0.743602 −0.371801 0.928312i \(-0.621260\pi\)
−0.371801 + 0.928312i \(0.621260\pi\)
\(882\) −2.67708 −0.0901421
\(883\) −31.9181 −1.07413 −0.537064 0.843542i \(-0.680467\pi\)
−0.537064 + 0.843542i \(0.680467\pi\)
\(884\) −4.63111 −0.155761
\(885\) −56.4108 −1.89623
\(886\) 29.5100 0.991409
\(887\) 53.8899 1.80945 0.904723 0.425999i \(-0.140077\pi\)
0.904723 + 0.425999i \(0.140077\pi\)
\(888\) 10.2903 0.345321
\(889\) 2.61734 0.0877827
\(890\) 42.6674 1.43021
\(891\) 38.8283 1.30080
\(892\) 2.20524 0.0738369
\(893\) −5.84662 −0.195650
\(894\) 12.6142 0.421882
\(895\) 26.7884 0.895439
\(896\) −1.00000 −0.0334077
\(897\) 27.1605 0.906861
\(898\) 8.80065 0.293682
\(899\) 18.7309 0.624711
\(900\) 4.89678 0.163226
\(901\) 22.7748 0.758738
\(902\) −46.7426 −1.55636
\(903\) −21.3755 −0.711331
\(904\) −9.77779 −0.325204
\(905\) −56.9808 −1.89411
\(906\) −18.6887 −0.620889
\(907\) −47.7372 −1.58509 −0.792544 0.609815i \(-0.791244\pi\)
−0.792544 + 0.609815i \(0.791244\pi\)
\(908\) 10.7465 0.356636
\(909\) 34.6931 1.15070
\(910\) 4.62391 0.153281
\(911\) 23.6674 0.784135 0.392067 0.919937i \(-0.371760\pi\)
0.392067 + 0.919937i \(0.371760\pi\)
\(912\) 1.21588 0.0402619
\(913\) 35.0622 1.16039
\(914\) 2.87643 0.0951439
\(915\) 37.7312 1.24735
\(916\) −21.9052 −0.723767
\(917\) 20.0378 0.661707
\(918\) 2.01378 0.0664646
\(919\) −12.1321 −0.400202 −0.200101 0.979775i \(-0.564127\pi\)
−0.200101 + 0.979775i \(0.564127\pi\)
\(920\) −16.8357 −0.555057
\(921\) 11.9424 0.393516
\(922\) 31.0928 1.02399
\(923\) −13.0921 −0.430933
\(924\) 9.37859 0.308533
\(925\) 7.89980 0.259744
\(926\) −11.3344 −0.372473
\(927\) −29.8944 −0.981861
\(928\) −4.06382 −0.133401
\(929\) −17.7527 −0.582449 −0.291224 0.956655i \(-0.594063\pi\)
−0.291224 + 0.956655i \(0.594063\pi\)
\(930\) −28.6993 −0.941086
\(931\) −0.510304 −0.0167245
\(932\) −14.1342 −0.462982
\(933\) 14.1511 0.463286
\(934\) −37.9010 −1.24016
\(935\) −26.9226 −0.880465
\(936\) −4.73683 −0.154828
\(937\) 8.44423 0.275861 0.137930 0.990442i \(-0.455955\pi\)
0.137930 + 0.990442i \(0.455955\pi\)
\(938\) 9.84386 0.321414
\(939\) 42.7439 1.39490
\(940\) −29.9405 −0.976551
\(941\) 18.8649 0.614978 0.307489 0.951552i \(-0.400511\pi\)
0.307489 + 0.951552i \(0.400511\pi\)
\(942\) 40.5209 1.32024
\(943\) 76.5044 2.49133
\(944\) −9.05975 −0.294870
\(945\) −2.01064 −0.0654063
\(946\) 35.3124 1.14811
\(947\) −25.1991 −0.818860 −0.409430 0.912341i \(-0.634272\pi\)
−0.409430 + 0.912341i \(0.634272\pi\)
\(948\) −33.6420 −1.09264
\(949\) −1.17199 −0.0380445
\(950\) 0.933422 0.0302842
\(951\) −61.8473 −2.00554
\(952\) 2.61734 0.0848284
\(953\) −12.6032 −0.408259 −0.204129 0.978944i \(-0.565436\pi\)
−0.204129 + 0.978944i \(0.565436\pi\)
\(954\) 23.2947 0.754193
\(955\) 2.46777 0.0798552
\(956\) −17.0234 −0.550575
\(957\) 38.1129 1.23202
\(958\) 21.0034 0.678588
\(959\) 9.50216 0.306841
\(960\) 6.22653 0.200960
\(961\) −9.75536 −0.314689
\(962\) −7.64176 −0.246380
\(963\) 31.5695 1.01731
\(964\) −18.1722 −0.585286
\(965\) 54.0034 1.73843
\(966\) −15.3501 −0.493881
\(967\) −6.30646 −0.202802 −0.101401 0.994846i \(-0.532333\pi\)
−0.101401 + 0.994846i \(0.532333\pi\)
\(968\) −4.49351 −0.144427
\(969\) −3.18238 −0.102233
\(970\) 11.1480 0.357940
\(971\) −20.1034 −0.645148 −0.322574 0.946544i \(-0.604548\pi\)
−0.322574 + 0.946544i \(0.604548\pi\)
\(972\) 21.1955 0.679847
\(973\) −3.92528 −0.125839
\(974\) 30.1820 0.967094
\(975\) −7.71147 −0.246965
\(976\) 6.05975 0.193968
\(977\) −40.0374 −1.28091 −0.640455 0.767996i \(-0.721254\pi\)
−0.640455 + 0.767996i \(0.721254\pi\)
\(978\) 1.18082 0.0377584
\(979\) −64.2669 −2.05398
\(980\) −2.61326 −0.0834776
\(981\) 18.0351 0.575815
\(982\) 1.49758 0.0477898
\(983\) 20.4105 0.650993 0.325496 0.945543i \(-0.394469\pi\)
0.325496 + 0.945543i \(0.394469\pi\)
\(984\) −28.2944 −0.901993
\(985\) −15.1840 −0.483802
\(986\) 10.6364 0.338732
\(987\) −27.2985 −0.868920
\(988\) −0.902932 −0.0287261
\(989\) −57.7964 −1.83782
\(990\) −27.5372 −0.875190
\(991\) 44.8529 1.42480 0.712400 0.701773i \(-0.247608\pi\)
0.712400 + 0.701773i \(0.247608\pi\)
\(992\) −4.60919 −0.146342
\(993\) 37.8779 1.20202
\(994\) 7.39920 0.234688
\(995\) 4.17988 0.132511
\(996\) 21.2240 0.672509
\(997\) 50.7816 1.60827 0.804135 0.594447i \(-0.202629\pi\)
0.804135 + 0.594447i \(0.202629\pi\)
\(998\) −13.6529 −0.432175
\(999\) 3.32292 0.105132
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 6034.2.a.j.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.j.1.1 4 1.1 even 1 trivial