Properties

Label 6034.2.a.o.1.3
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $1$
Dimension $25$
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: \(25\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.93664 q^{3} +1.00000 q^{4} +1.14962 q^{5} +2.93664 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.62386 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.93664 q^{3} +1.00000 q^{4} +1.14962 q^{5} +2.93664 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.62386 q^{9} -1.14962 q^{10} +1.78532 q^{11} -2.93664 q^{12} -1.58629 q^{13} +1.00000 q^{14} -3.37602 q^{15} +1.00000 q^{16} +4.75836 q^{17} -5.62386 q^{18} -8.25798 q^{19} +1.14962 q^{20} +2.93664 q^{21} -1.78532 q^{22} +5.21027 q^{23} +2.93664 q^{24} -3.67837 q^{25} +1.58629 q^{26} -7.70535 q^{27} -1.00000 q^{28} +5.51319 q^{29} +3.37602 q^{30} -4.05434 q^{31} -1.00000 q^{32} -5.24283 q^{33} -4.75836 q^{34} -1.14962 q^{35} +5.62386 q^{36} +9.55503 q^{37} +8.25798 q^{38} +4.65836 q^{39} -1.14962 q^{40} +3.24985 q^{41} -2.93664 q^{42} -9.79019 q^{43} +1.78532 q^{44} +6.46531 q^{45} -5.21027 q^{46} -2.57995 q^{47} -2.93664 q^{48} +1.00000 q^{49} +3.67837 q^{50} -13.9736 q^{51} -1.58629 q^{52} -2.33214 q^{53} +7.70535 q^{54} +2.05243 q^{55} +1.00000 q^{56} +24.2507 q^{57} -5.51319 q^{58} -5.81789 q^{59} -3.37602 q^{60} -11.6438 q^{61} +4.05434 q^{62} -5.62386 q^{63} +1.00000 q^{64} -1.82363 q^{65} +5.24283 q^{66} +8.12281 q^{67} +4.75836 q^{68} -15.3007 q^{69} +1.14962 q^{70} -3.84447 q^{71} -5.62386 q^{72} -8.13616 q^{73} -9.55503 q^{74} +10.8021 q^{75} -8.25798 q^{76} -1.78532 q^{77} -4.65836 q^{78} -2.39952 q^{79} +1.14962 q^{80} +5.75625 q^{81} -3.24985 q^{82} -1.26492 q^{83} +2.93664 q^{84} +5.47031 q^{85} +9.79019 q^{86} -16.1903 q^{87} -1.78532 q^{88} -0.725700 q^{89} -6.46531 q^{90} +1.58629 q^{91} +5.21027 q^{92} +11.9061 q^{93} +2.57995 q^{94} -9.49353 q^{95} +2.93664 q^{96} -8.02371 q^{97} -1.00000 q^{98} +10.0404 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 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
\(3\) −2.93664 −1.69547 −0.847735 0.530419i \(-0.822034\pi\)
−0.847735 + 0.530419i \(0.822034\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.14962 0.514126 0.257063 0.966395i \(-0.417245\pi\)
0.257063 + 0.966395i \(0.417245\pi\)
\(6\) 2.93664 1.19888
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 5.62386 1.87462
\(10\) −1.14962 −0.363542
\(11\) 1.78532 0.538293 0.269146 0.963099i \(-0.413258\pi\)
0.269146 + 0.963099i \(0.413258\pi\)
\(12\) −2.93664 −0.847735
\(13\) −1.58629 −0.439957 −0.219979 0.975505i \(-0.570599\pi\)
−0.219979 + 0.975505i \(0.570599\pi\)
\(14\) 1.00000 0.267261
\(15\) −3.37602 −0.871685
\(16\) 1.00000 0.250000
\(17\) 4.75836 1.15407 0.577036 0.816718i \(-0.304209\pi\)
0.577036 + 0.816718i \(0.304209\pi\)
\(18\) −5.62386 −1.32556
\(19\) −8.25798 −1.89451 −0.947255 0.320481i \(-0.896155\pi\)
−0.947255 + 0.320481i \(0.896155\pi\)
\(20\) 1.14962 0.257063
\(21\) 2.93664 0.640828
\(22\) −1.78532 −0.380631
\(23\) 5.21027 1.08642 0.543208 0.839598i \(-0.317209\pi\)
0.543208 + 0.839598i \(0.317209\pi\)
\(24\) 2.93664 0.599439
\(25\) −3.67837 −0.735675
\(26\) 1.58629 0.311097
\(27\) −7.70535 −1.48289
\(28\) −1.00000 −0.188982
\(29\) 5.51319 1.02377 0.511887 0.859053i \(-0.328947\pi\)
0.511887 + 0.859053i \(0.328947\pi\)
\(30\) 3.37602 0.616374
\(31\) −4.05434 −0.728181 −0.364090 0.931364i \(-0.618620\pi\)
−0.364090 + 0.931364i \(0.618620\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.24283 −0.912660
\(34\) −4.75836 −0.816053
\(35\) −1.14962 −0.194321
\(36\) 5.62386 0.937311
\(37\) 9.55503 1.57084 0.785419 0.618965i \(-0.212448\pi\)
0.785419 + 0.618965i \(0.212448\pi\)
\(38\) 8.25798 1.33962
\(39\) 4.65836 0.745935
\(40\) −1.14962 −0.181771
\(41\) 3.24985 0.507542 0.253771 0.967264i \(-0.418329\pi\)
0.253771 + 0.967264i \(0.418329\pi\)
\(42\) −2.93664 −0.453134
\(43\) −9.79019 −1.49299 −0.746495 0.665391i \(-0.768265\pi\)
−0.746495 + 0.665391i \(0.768265\pi\)
\(44\) 1.78532 0.269146
\(45\) 6.46531 0.963791
\(46\) −5.21027 −0.768212
\(47\) −2.57995 −0.376324 −0.188162 0.982138i \(-0.560253\pi\)
−0.188162 + 0.982138i \(0.560253\pi\)
\(48\) −2.93664 −0.423868
\(49\) 1.00000 0.142857
\(50\) 3.67837 0.520201
\(51\) −13.9736 −1.95670
\(52\) −1.58629 −0.219979
\(53\) −2.33214 −0.320344 −0.160172 0.987089i \(-0.551205\pi\)
−0.160172 + 0.987089i \(0.551205\pi\)
\(54\) 7.70535 1.04856
\(55\) 2.05243 0.276750
\(56\) 1.00000 0.133631
\(57\) 24.2507 3.21209
\(58\) −5.51319 −0.723917
\(59\) −5.81789 −0.757425 −0.378712 0.925514i \(-0.623633\pi\)
−0.378712 + 0.925514i \(0.623633\pi\)
\(60\) −3.37602 −0.435843
\(61\) −11.6438 −1.49083 −0.745415 0.666601i \(-0.767749\pi\)
−0.745415 + 0.666601i \(0.767749\pi\)
\(62\) 4.05434 0.514902
\(63\) −5.62386 −0.708540
\(64\) 1.00000 0.125000
\(65\) −1.82363 −0.226193
\(66\) 5.24283 0.645348
\(67\) 8.12281 0.992360 0.496180 0.868220i \(-0.334736\pi\)
0.496180 + 0.868220i \(0.334736\pi\)
\(68\) 4.75836 0.577036
\(69\) −15.3007 −1.84199
\(70\) 1.14962 0.137406
\(71\) −3.84447 −0.456255 −0.228128 0.973631i \(-0.573260\pi\)
−0.228128 + 0.973631i \(0.573260\pi\)
\(72\) −5.62386 −0.662779
\(73\) −8.13616 −0.952265 −0.476133 0.879373i \(-0.657962\pi\)
−0.476133 + 0.879373i \(0.657962\pi\)
\(74\) −9.55503 −1.11075
\(75\) 10.8021 1.24732
\(76\) −8.25798 −0.947255
\(77\) −1.78532 −0.203456
\(78\) −4.65836 −0.527456
\(79\) −2.39952 −0.269967 −0.134984 0.990848i \(-0.543098\pi\)
−0.134984 + 0.990848i \(0.543098\pi\)
\(80\) 1.14962 0.128531
\(81\) 5.75625 0.639584
\(82\) −3.24985 −0.358886
\(83\) −1.26492 −0.138843 −0.0694214 0.997587i \(-0.522115\pi\)
−0.0694214 + 0.997587i \(0.522115\pi\)
\(84\) 2.93664 0.320414
\(85\) 5.47031 0.593339
\(86\) 9.79019 1.05570
\(87\) −16.1903 −1.73578
\(88\) −1.78532 −0.190315
\(89\) −0.725700 −0.0769240 −0.0384620 0.999260i \(-0.512246\pi\)
−0.0384620 + 0.999260i \(0.512246\pi\)
\(90\) −6.46531 −0.681503
\(91\) 1.58629 0.166288
\(92\) 5.21027 0.543208
\(93\) 11.9061 1.23461
\(94\) 2.57995 0.266101
\(95\) −9.49353 −0.974016
\(96\) 2.93664 0.299720
\(97\) −8.02371 −0.814685 −0.407342 0.913276i \(-0.633544\pi\)
−0.407342 + 0.913276i \(0.633544\pi\)
\(98\) −1.00000 −0.101015
\(99\) 10.0404 1.00910
\(100\) −3.67837 −0.367837
\(101\) 9.51584 0.946862 0.473431 0.880831i \(-0.343015\pi\)
0.473431 + 0.880831i \(0.343015\pi\)
\(102\) 13.9736 1.38359
\(103\) 9.23894 0.910339 0.455170 0.890405i \(-0.349579\pi\)
0.455170 + 0.890405i \(0.349579\pi\)
\(104\) 1.58629 0.155548
\(105\) 3.37602 0.329466
\(106\) 2.33214 0.226517
\(107\) 18.3654 1.77545 0.887724 0.460376i \(-0.152285\pi\)
0.887724 + 0.460376i \(0.152285\pi\)
\(108\) −7.70535 −0.741447
\(109\) −1.35820 −0.130092 −0.0650458 0.997882i \(-0.520719\pi\)
−0.0650458 + 0.997882i \(0.520719\pi\)
\(110\) −2.05243 −0.195692
\(111\) −28.0597 −2.66331
\(112\) −1.00000 −0.0944911
\(113\) 15.4891 1.45709 0.728546 0.684997i \(-0.240196\pi\)
0.728546 + 0.684997i \(0.240196\pi\)
\(114\) −24.2507 −2.27129
\(115\) 5.98983 0.558555
\(116\) 5.51319 0.511887
\(117\) −8.92107 −0.824753
\(118\) 5.81789 0.535580
\(119\) −4.75836 −0.436199
\(120\) 3.37602 0.308187
\(121\) −7.81265 −0.710241
\(122\) 11.6438 1.05418
\(123\) −9.54365 −0.860522
\(124\) −4.05434 −0.364090
\(125\) −9.97683 −0.892355
\(126\) 5.62386 0.501014
\(127\) −14.3508 −1.27343 −0.636714 0.771100i \(-0.719707\pi\)
−0.636714 + 0.771100i \(0.719707\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 28.7503 2.53132
\(130\) 1.82363 0.159943
\(131\) 22.3860 1.95588 0.977939 0.208890i \(-0.0669852\pi\)
0.977939 + 0.208890i \(0.0669852\pi\)
\(132\) −5.24283 −0.456330
\(133\) 8.25798 0.716057
\(134\) −8.12281 −0.701704
\(135\) −8.85822 −0.762394
\(136\) −4.75836 −0.408026
\(137\) −1.74164 −0.148798 −0.0743990 0.997229i \(-0.523704\pi\)
−0.0743990 + 0.997229i \(0.523704\pi\)
\(138\) 15.3007 1.30248
\(139\) 12.4073 1.05237 0.526185 0.850370i \(-0.323622\pi\)
0.526185 + 0.850370i \(0.323622\pi\)
\(140\) −1.14962 −0.0971606
\(141\) 7.57638 0.638046
\(142\) 3.84447 0.322621
\(143\) −2.83203 −0.236826
\(144\) 5.62386 0.468655
\(145\) 6.33807 0.526348
\(146\) 8.13616 0.673353
\(147\) −2.93664 −0.242210
\(148\) 9.55503 0.785419
\(149\) 16.8812 1.38296 0.691480 0.722395i \(-0.256959\pi\)
0.691480 + 0.722395i \(0.256959\pi\)
\(150\) −10.8021 −0.881985
\(151\) −12.5442 −1.02083 −0.510416 0.859928i \(-0.670508\pi\)
−0.510416 + 0.859928i \(0.670508\pi\)
\(152\) 8.25798 0.669810
\(153\) 26.7604 2.16345
\(154\) 1.78532 0.143865
\(155\) −4.66095 −0.374376
\(156\) 4.65836 0.372967
\(157\) 24.5152 1.95652 0.978262 0.207371i \(-0.0664908\pi\)
0.978262 + 0.207371i \(0.0664908\pi\)
\(158\) 2.39952 0.190896
\(159\) 6.84866 0.543134
\(160\) −1.14962 −0.0908854
\(161\) −5.21027 −0.410627
\(162\) −5.75625 −0.452254
\(163\) −11.8060 −0.924720 −0.462360 0.886692i \(-0.652997\pi\)
−0.462360 + 0.886692i \(0.652997\pi\)
\(164\) 3.24985 0.253771
\(165\) −6.02726 −0.469222
\(166\) 1.26492 0.0981767
\(167\) −20.8750 −1.61536 −0.807679 0.589622i \(-0.799277\pi\)
−0.807679 + 0.589622i \(0.799277\pi\)
\(168\) −2.93664 −0.226567
\(169\) −10.4837 −0.806438
\(170\) −5.47031 −0.419554
\(171\) −46.4417 −3.55149
\(172\) −9.79019 −0.746495
\(173\) −6.10704 −0.464310 −0.232155 0.972679i \(-0.574578\pi\)
−0.232155 + 0.972679i \(0.574578\pi\)
\(174\) 16.1903 1.22738
\(175\) 3.67837 0.278059
\(176\) 1.78532 0.134573
\(177\) 17.0851 1.28419
\(178\) 0.725700 0.0543935
\(179\) 16.6851 1.24711 0.623553 0.781781i \(-0.285689\pi\)
0.623553 + 0.781781i \(0.285689\pi\)
\(180\) 6.46531 0.481895
\(181\) −11.4665 −0.852301 −0.426151 0.904652i \(-0.640131\pi\)
−0.426151 + 0.904652i \(0.640131\pi\)
\(182\) −1.58629 −0.117584
\(183\) 34.1935 2.52766
\(184\) −5.21027 −0.384106
\(185\) 10.9847 0.807608
\(186\) −11.9061 −0.873001
\(187\) 8.49518 0.621229
\(188\) −2.57995 −0.188162
\(189\) 7.70535 0.560482
\(190\) 9.49353 0.688733
\(191\) −16.0121 −1.15860 −0.579298 0.815116i \(-0.696673\pi\)
−0.579298 + 0.815116i \(0.696673\pi\)
\(192\) −2.93664 −0.211934
\(193\) 20.0663 1.44441 0.722203 0.691681i \(-0.243129\pi\)
0.722203 + 0.691681i \(0.243129\pi\)
\(194\) 8.02371 0.576069
\(195\) 5.35535 0.383504
\(196\) 1.00000 0.0714286
\(197\) 22.1819 1.58040 0.790198 0.612851i \(-0.209977\pi\)
0.790198 + 0.612851i \(0.209977\pi\)
\(198\) −10.0404 −0.713538
\(199\) −7.23178 −0.512647 −0.256324 0.966591i \(-0.582511\pi\)
−0.256324 + 0.966591i \(0.582511\pi\)
\(200\) 3.67837 0.260100
\(201\) −23.8538 −1.68252
\(202\) −9.51584 −0.669532
\(203\) −5.51319 −0.386950
\(204\) −13.9736 −0.978348
\(205\) 3.73610 0.260940
\(206\) −9.23894 −0.643707
\(207\) 29.3018 2.03662
\(208\) −1.58629 −0.109989
\(209\) −14.7431 −1.01980
\(210\) −3.37602 −0.232968
\(211\) −26.3059 −1.81097 −0.905485 0.424378i \(-0.860493\pi\)
−0.905485 + 0.424378i \(0.860493\pi\)
\(212\) −2.33214 −0.160172
\(213\) 11.2898 0.773567
\(214\) −18.3654 −1.25543
\(215\) −11.2550 −0.767585
\(216\) 7.70535 0.524282
\(217\) 4.05434 0.275226
\(218\) 1.35820 0.0919886
\(219\) 23.8930 1.61454
\(220\) 2.05243 0.138375
\(221\) −7.54814 −0.507743
\(222\) 28.0597 1.88324
\(223\) 9.15737 0.613223 0.306611 0.951835i \(-0.400805\pi\)
0.306611 + 0.951835i \(0.400805\pi\)
\(224\) 1.00000 0.0668153
\(225\) −20.6867 −1.37911
\(226\) −15.4891 −1.03032
\(227\) −10.2369 −0.679444 −0.339722 0.940526i \(-0.610333\pi\)
−0.339722 + 0.940526i \(0.610333\pi\)
\(228\) 24.2507 1.60604
\(229\) 0.0238752 0.00157772 0.000788859 1.00000i \(-0.499749\pi\)
0.000788859 1.00000i \(0.499749\pi\)
\(230\) −5.98983 −0.394958
\(231\) 5.24283 0.344953
\(232\) −5.51319 −0.361959
\(233\) 0.281238 0.0184245 0.00921226 0.999958i \(-0.497068\pi\)
0.00921226 + 0.999958i \(0.497068\pi\)
\(234\) 8.92107 0.583189
\(235\) −2.96596 −0.193478
\(236\) −5.81789 −0.378712
\(237\) 7.04654 0.457722
\(238\) 4.75836 0.308439
\(239\) 5.22424 0.337928 0.168964 0.985622i \(-0.445958\pi\)
0.168964 + 0.985622i \(0.445958\pi\)
\(240\) −3.37602 −0.217921
\(241\) −23.8541 −1.53658 −0.768290 0.640102i \(-0.778892\pi\)
−0.768290 + 0.640102i \(0.778892\pi\)
\(242\) 7.81265 0.502216
\(243\) 6.21199 0.398500
\(244\) −11.6438 −0.745415
\(245\) 1.14962 0.0734465
\(246\) 9.54365 0.608481
\(247\) 13.0995 0.833503
\(248\) 4.05434 0.257451
\(249\) 3.71461 0.235404
\(250\) 9.97683 0.630990
\(251\) 11.1379 0.703017 0.351508 0.936185i \(-0.385669\pi\)
0.351508 + 0.936185i \(0.385669\pi\)
\(252\) −5.62386 −0.354270
\(253\) 9.30198 0.584810
\(254\) 14.3508 0.900450
\(255\) −16.0643 −1.00599
\(256\) 1.00000 0.0625000
\(257\) −9.90011 −0.617552 −0.308776 0.951135i \(-0.599919\pi\)
−0.308776 + 0.951135i \(0.599919\pi\)
\(258\) −28.7503 −1.78991
\(259\) −9.55503 −0.593721
\(260\) −1.82363 −0.113097
\(261\) 31.0054 1.91919
\(262\) −22.3860 −1.38301
\(263\) 7.22031 0.445223 0.222612 0.974907i \(-0.428542\pi\)
0.222612 + 0.974907i \(0.428542\pi\)
\(264\) 5.24283 0.322674
\(265\) −2.68107 −0.164697
\(266\) −8.25798 −0.506329
\(267\) 2.13112 0.130422
\(268\) 8.12281 0.496180
\(269\) −1.70941 −0.104225 −0.0521123 0.998641i \(-0.516595\pi\)
−0.0521123 + 0.998641i \(0.516595\pi\)
\(270\) 8.85822 0.539094
\(271\) 16.5082 1.00280 0.501402 0.865214i \(-0.332818\pi\)
0.501402 + 0.865214i \(0.332818\pi\)
\(272\) 4.75836 0.288518
\(273\) −4.65836 −0.281937
\(274\) 1.74164 0.105216
\(275\) −6.56706 −0.396008
\(276\) −15.3007 −0.920994
\(277\) 18.1539 1.09076 0.545381 0.838188i \(-0.316385\pi\)
0.545381 + 0.838188i \(0.316385\pi\)
\(278\) −12.4073 −0.744138
\(279\) −22.8010 −1.36506
\(280\) 1.14962 0.0687029
\(281\) −22.0851 −1.31748 −0.658742 0.752369i \(-0.728911\pi\)
−0.658742 + 0.752369i \(0.728911\pi\)
\(282\) −7.57638 −0.451167
\(283\) 29.3599 1.74526 0.872631 0.488380i \(-0.162412\pi\)
0.872631 + 0.488380i \(0.162412\pi\)
\(284\) −3.84447 −0.228128
\(285\) 27.8791 1.65142
\(286\) 2.83203 0.167461
\(287\) −3.24985 −0.191833
\(288\) −5.62386 −0.331389
\(289\) 5.64203 0.331884
\(290\) −6.33807 −0.372184
\(291\) 23.5628 1.38127
\(292\) −8.13616 −0.476133
\(293\) 3.54694 0.207214 0.103607 0.994618i \(-0.466962\pi\)
0.103607 + 0.994618i \(0.466962\pi\)
\(294\) 2.93664 0.171268
\(295\) −6.68836 −0.389412
\(296\) −9.55503 −0.555375
\(297\) −13.7565 −0.798232
\(298\) −16.8812 −0.977901
\(299\) −8.26499 −0.477977
\(300\) 10.8021 0.623658
\(301\) 9.79019 0.564297
\(302\) 12.5442 0.721837
\(303\) −27.9446 −1.60538
\(304\) −8.25798 −0.473627
\(305\) −13.3859 −0.766474
\(306\) −26.7604 −1.52979
\(307\) 12.7006 0.724864 0.362432 0.932010i \(-0.381947\pi\)
0.362432 + 0.932010i \(0.381947\pi\)
\(308\) −1.78532 −0.101728
\(309\) −27.1314 −1.54345
\(310\) 4.66095 0.264724
\(311\) −10.0942 −0.572390 −0.286195 0.958171i \(-0.592391\pi\)
−0.286195 + 0.958171i \(0.592391\pi\)
\(312\) −4.65836 −0.263728
\(313\) −15.8054 −0.893376 −0.446688 0.894690i \(-0.647397\pi\)
−0.446688 + 0.894690i \(0.647397\pi\)
\(314\) −24.5152 −1.38347
\(315\) −6.46531 −0.364279
\(316\) −2.39952 −0.134984
\(317\) −34.7649 −1.95259 −0.976295 0.216443i \(-0.930554\pi\)
−0.976295 + 0.216443i \(0.930554\pi\)
\(318\) −6.84866 −0.384054
\(319\) 9.84278 0.551090
\(320\) 1.14962 0.0642657
\(321\) −53.9325 −3.01022
\(322\) 5.21027 0.290357
\(323\) −39.2945 −2.18640
\(324\) 5.75625 0.319792
\(325\) 5.83496 0.323666
\(326\) 11.8060 0.653876
\(327\) 3.98853 0.220566
\(328\) −3.24985 −0.179443
\(329\) 2.57995 0.142237
\(330\) 6.02726 0.331790
\(331\) −20.4265 −1.12274 −0.561372 0.827564i \(-0.689726\pi\)
−0.561372 + 0.827564i \(0.689726\pi\)
\(332\) −1.26492 −0.0694214
\(333\) 53.7362 2.94473
\(334\) 20.8750 1.14223
\(335\) 9.33815 0.510198
\(336\) 2.93664 0.160207
\(337\) −24.2917 −1.32325 −0.661626 0.749834i \(-0.730133\pi\)
−0.661626 + 0.749834i \(0.730133\pi\)
\(338\) 10.4837 0.570237
\(339\) −45.4859 −2.47046
\(340\) 5.47031 0.296669
\(341\) −7.23827 −0.391975
\(342\) 46.4417 2.51128
\(343\) −1.00000 −0.0539949
\(344\) 9.79019 0.527852
\(345\) −17.5900 −0.947013
\(346\) 6.10704 0.328317
\(347\) −4.05420 −0.217641 −0.108820 0.994061i \(-0.534707\pi\)
−0.108820 + 0.994061i \(0.534707\pi\)
\(348\) −16.1903 −0.867889
\(349\) 1.93402 0.103526 0.0517630 0.998659i \(-0.483516\pi\)
0.0517630 + 0.998659i \(0.483516\pi\)
\(350\) −3.67837 −0.196617
\(351\) 12.2229 0.652410
\(352\) −1.78532 −0.0951576
\(353\) −4.31153 −0.229480 −0.114740 0.993396i \(-0.536603\pi\)
−0.114740 + 0.993396i \(0.536603\pi\)
\(354\) −17.0851 −0.908061
\(355\) −4.41968 −0.234572
\(356\) −0.725700 −0.0384620
\(357\) 13.9736 0.739562
\(358\) −16.6851 −0.881837
\(359\) 24.5126 1.29373 0.646863 0.762606i \(-0.276081\pi\)
0.646863 + 0.762606i \(0.276081\pi\)
\(360\) −6.46531 −0.340752
\(361\) 49.1942 2.58917
\(362\) 11.4665 0.602668
\(363\) 22.9429 1.20419
\(364\) 1.58629 0.0831441
\(365\) −9.35349 −0.489584
\(366\) −34.1935 −1.78732
\(367\) 29.9890 1.56541 0.782707 0.622390i \(-0.213838\pi\)
0.782707 + 0.622390i \(0.213838\pi\)
\(368\) 5.21027 0.271604
\(369\) 18.2767 0.951448
\(370\) −10.9847 −0.571065
\(371\) 2.33214 0.121079
\(372\) 11.9061 0.617305
\(373\) −34.3875 −1.78052 −0.890259 0.455456i \(-0.849476\pi\)
−0.890259 + 0.455456i \(0.849476\pi\)
\(374\) −8.49518 −0.439275
\(375\) 29.2984 1.51296
\(376\) 2.57995 0.133051
\(377\) −8.74551 −0.450417
\(378\) −7.70535 −0.396320
\(379\) −31.3604 −1.61088 −0.805438 0.592680i \(-0.798070\pi\)
−0.805438 + 0.592680i \(0.798070\pi\)
\(380\) −9.49353 −0.487008
\(381\) 42.1432 2.15906
\(382\) 16.0121 0.819252
\(383\) −8.61714 −0.440315 −0.220158 0.975464i \(-0.570657\pi\)
−0.220158 + 0.975464i \(0.570657\pi\)
\(384\) 2.93664 0.149860
\(385\) −2.05243 −0.104602
\(386\) −20.0663 −1.02135
\(387\) −55.0587 −2.79879
\(388\) −8.02371 −0.407342
\(389\) 26.2878 1.33284 0.666421 0.745575i \(-0.267825\pi\)
0.666421 + 0.745575i \(0.267825\pi\)
\(390\) −5.35535 −0.271178
\(391\) 24.7924 1.25380
\(392\) −1.00000 −0.0505076
\(393\) −65.7398 −3.31613
\(394\) −22.1819 −1.11751
\(395\) −2.75854 −0.138797
\(396\) 10.0404 0.504548
\(397\) 2.36140 0.118515 0.0592576 0.998243i \(-0.481127\pi\)
0.0592576 + 0.998243i \(0.481127\pi\)
\(398\) 7.23178 0.362496
\(399\) −24.2507 −1.21405
\(400\) −3.67837 −0.183919
\(401\) 16.1640 0.807194 0.403597 0.914937i \(-0.367760\pi\)
0.403597 + 0.914937i \(0.367760\pi\)
\(402\) 23.8538 1.18972
\(403\) 6.43135 0.320368
\(404\) 9.51584 0.473431
\(405\) 6.61750 0.328826
\(406\) 5.51319 0.273615
\(407\) 17.0587 0.845571
\(408\) 13.9736 0.691797
\(409\) −25.5539 −1.26356 −0.631780 0.775148i \(-0.717676\pi\)
−0.631780 + 0.775148i \(0.717676\pi\)
\(410\) −3.73610 −0.184513
\(411\) 5.11456 0.252283
\(412\) 9.23894 0.455170
\(413\) 5.81789 0.286280
\(414\) −29.3018 −1.44011
\(415\) −1.45418 −0.0713827
\(416\) 1.58629 0.0777742
\(417\) −36.4357 −1.78426
\(418\) 14.7431 0.721108
\(419\) −35.7791 −1.74792 −0.873961 0.485996i \(-0.838457\pi\)
−0.873961 + 0.485996i \(0.838457\pi\)
\(420\) 3.37602 0.164733
\(421\) 29.7343 1.44916 0.724581 0.689190i \(-0.242033\pi\)
0.724581 + 0.689190i \(0.242033\pi\)
\(422\) 26.3059 1.28055
\(423\) −14.5093 −0.705465
\(424\) 2.33214 0.113259
\(425\) −17.5030 −0.849022
\(426\) −11.2898 −0.546995
\(427\) 11.6438 0.563481
\(428\) 18.3654 0.887724
\(429\) 8.31664 0.401531
\(430\) 11.2550 0.542764
\(431\) −1.00000 −0.0481683
\(432\) −7.70535 −0.370724
\(433\) −3.86209 −0.185600 −0.0928001 0.995685i \(-0.529582\pi\)
−0.0928001 + 0.995685i \(0.529582\pi\)
\(434\) −4.05434 −0.194615
\(435\) −18.6126 −0.892408
\(436\) −1.35820 −0.0650458
\(437\) −43.0263 −2.05823
\(438\) −23.8930 −1.14165
\(439\) −32.6481 −1.55821 −0.779105 0.626893i \(-0.784326\pi\)
−0.779105 + 0.626893i \(0.784326\pi\)
\(440\) −2.05243 −0.0978460
\(441\) 5.62386 0.267803
\(442\) 7.54814 0.359028
\(443\) −18.9858 −0.902043 −0.451022 0.892513i \(-0.648940\pi\)
−0.451022 + 0.892513i \(0.648940\pi\)
\(444\) −28.0597 −1.33165
\(445\) −0.834279 −0.0395486
\(446\) −9.15737 −0.433614
\(447\) −49.5740 −2.34477
\(448\) −1.00000 −0.0472456
\(449\) −32.1436 −1.51695 −0.758474 0.651703i \(-0.774055\pi\)
−0.758474 + 0.651703i \(0.774055\pi\)
\(450\) 20.6867 0.975179
\(451\) 5.80201 0.273206
\(452\) 15.4891 0.728546
\(453\) 36.8378 1.73079
\(454\) 10.2369 0.480440
\(455\) 1.82363 0.0854931
\(456\) −24.2507 −1.13564
\(457\) 27.0189 1.26389 0.631945 0.775013i \(-0.282257\pi\)
0.631945 + 0.775013i \(0.282257\pi\)
\(458\) −0.0238752 −0.00111561
\(459\) −36.6649 −1.71137
\(460\) 5.98983 0.279277
\(461\) −35.2448 −1.64151 −0.820756 0.571278i \(-0.806448\pi\)
−0.820756 + 0.571278i \(0.806448\pi\)
\(462\) −5.24283 −0.243919
\(463\) −41.8483 −1.94485 −0.972427 0.233208i \(-0.925078\pi\)
−0.972427 + 0.233208i \(0.925078\pi\)
\(464\) 5.51319 0.255943
\(465\) 13.6875 0.634744
\(466\) −0.281238 −0.0130281
\(467\) −34.5464 −1.59862 −0.799308 0.600921i \(-0.794800\pi\)
−0.799308 + 0.600921i \(0.794800\pi\)
\(468\) −8.92107 −0.412377
\(469\) −8.12281 −0.375077
\(470\) 2.96596 0.136809
\(471\) −71.9923 −3.31723
\(472\) 5.81789 0.267790
\(473\) −17.4786 −0.803666
\(474\) −7.04654 −0.323658
\(475\) 30.3759 1.39374
\(476\) −4.75836 −0.218099
\(477\) −13.1156 −0.600524
\(478\) −5.22424 −0.238951
\(479\) −30.6571 −1.40076 −0.700379 0.713771i \(-0.746986\pi\)
−0.700379 + 0.713771i \(0.746986\pi\)
\(480\) 3.37602 0.154094
\(481\) −15.1570 −0.691101
\(482\) 23.8541 1.08653
\(483\) 15.3007 0.696206
\(484\) −7.81265 −0.355120
\(485\) −9.22422 −0.418850
\(486\) −6.21199 −0.281782
\(487\) −3.75623 −0.170211 −0.0851056 0.996372i \(-0.527123\pi\)
−0.0851056 + 0.996372i \(0.527123\pi\)
\(488\) 11.6438 0.527088
\(489\) 34.6701 1.56784
\(490\) −1.14962 −0.0519345
\(491\) −9.39835 −0.424141 −0.212071 0.977254i \(-0.568021\pi\)
−0.212071 + 0.977254i \(0.568021\pi\)
\(492\) −9.54365 −0.430261
\(493\) 26.2338 1.18151
\(494\) −13.0995 −0.589376
\(495\) 11.5426 0.518802
\(496\) −4.05434 −0.182045
\(497\) 3.84447 0.172448
\(498\) −3.71461 −0.166456
\(499\) −7.39766 −0.331165 −0.165582 0.986196i \(-0.552950\pi\)
−0.165582 + 0.986196i \(0.552950\pi\)
\(500\) −9.97683 −0.446178
\(501\) 61.3025 2.73879
\(502\) −11.1379 −0.497108
\(503\) −37.2938 −1.66285 −0.831424 0.555639i \(-0.812474\pi\)
−0.831424 + 0.555639i \(0.812474\pi\)
\(504\) 5.62386 0.250507
\(505\) 10.9396 0.486806
\(506\) −9.30198 −0.413523
\(507\) 30.7868 1.36729
\(508\) −14.3508 −0.636714
\(509\) −17.4490 −0.773415 −0.386707 0.922203i \(-0.626388\pi\)
−0.386707 + 0.922203i \(0.626388\pi\)
\(510\) 16.0643 0.711341
\(511\) 8.13616 0.359922
\(512\) −1.00000 −0.0441942
\(513\) 63.6306 2.80936
\(514\) 9.90011 0.436675
\(515\) 10.6213 0.468029
\(516\) 28.7503 1.26566
\(517\) −4.60602 −0.202572
\(518\) 9.55503 0.419824
\(519\) 17.9342 0.787224
\(520\) 1.82363 0.0799714
\(521\) 16.4279 0.719721 0.359861 0.933006i \(-0.382824\pi\)
0.359861 + 0.933006i \(0.382824\pi\)
\(522\) −31.0054 −1.35707
\(523\) 27.1811 1.18855 0.594273 0.804263i \(-0.297440\pi\)
0.594273 + 0.804263i \(0.297440\pi\)
\(524\) 22.3860 0.977939
\(525\) −10.8021 −0.471441
\(526\) −7.22031 −0.314821
\(527\) −19.2920 −0.840374
\(528\) −5.24283 −0.228165
\(529\) 4.14691 0.180301
\(530\) 2.68107 0.116458
\(531\) −32.7190 −1.41988
\(532\) 8.25798 0.358029
\(533\) −5.15521 −0.223297
\(534\) −2.13112 −0.0922226
\(535\) 21.1132 0.912804
\(536\) −8.12281 −0.350852
\(537\) −48.9983 −2.11443
\(538\) 1.70941 0.0736979
\(539\) 1.78532 0.0768990
\(540\) −8.85822 −0.381197
\(541\) −29.4861 −1.26771 −0.633854 0.773453i \(-0.718528\pi\)
−0.633854 + 0.773453i \(0.718528\pi\)
\(542\) −16.5082 −0.709090
\(543\) 33.6731 1.44505
\(544\) −4.75836 −0.204013
\(545\) −1.56141 −0.0668834
\(546\) 4.65836 0.199359
\(547\) 32.1106 1.37295 0.686476 0.727152i \(-0.259157\pi\)
0.686476 + 0.727152i \(0.259157\pi\)
\(548\) −1.74164 −0.0743990
\(549\) −65.4829 −2.79474
\(550\) 6.56706 0.280020
\(551\) −45.5278 −1.93955
\(552\) 15.3007 0.651241
\(553\) 2.39952 0.102038
\(554\) −18.1539 −0.771285
\(555\) −32.2580 −1.36928
\(556\) 12.4073 0.526185
\(557\) 39.0697 1.65544 0.827719 0.561143i \(-0.189638\pi\)
0.827719 + 0.561143i \(0.189638\pi\)
\(558\) 22.8010 0.965245
\(559\) 15.5301 0.656852
\(560\) −1.14962 −0.0485803
\(561\) −24.9473 −1.05328
\(562\) 22.0851 0.931602
\(563\) 1.88705 0.0795298 0.0397649 0.999209i \(-0.487339\pi\)
0.0397649 + 0.999209i \(0.487339\pi\)
\(564\) 7.57638 0.319023
\(565\) 17.8066 0.749128
\(566\) −29.3599 −1.23409
\(567\) −5.75625 −0.241740
\(568\) 3.84447 0.161311
\(569\) 4.96763 0.208254 0.104127 0.994564i \(-0.466795\pi\)
0.104127 + 0.994564i \(0.466795\pi\)
\(570\) −27.8791 −1.16773
\(571\) −0.671131 −0.0280860 −0.0140430 0.999901i \(-0.504470\pi\)
−0.0140430 + 0.999901i \(0.504470\pi\)
\(572\) −2.83203 −0.118413
\(573\) 47.0219 1.96437
\(574\) 3.24985 0.135646
\(575\) −19.1653 −0.799249
\(576\) 5.62386 0.234328
\(577\) −43.8914 −1.82722 −0.913612 0.406586i \(-0.866719\pi\)
−0.913612 + 0.406586i \(0.866719\pi\)
\(578\) −5.64203 −0.234678
\(579\) −58.9276 −2.44895
\(580\) 6.33807 0.263174
\(581\) 1.26492 0.0524776
\(582\) −23.5628 −0.976708
\(583\) −4.16361 −0.172439
\(584\) 8.13616 0.336677
\(585\) −10.2558 −0.424027
\(586\) −3.54694 −0.146523
\(587\) −8.59868 −0.354905 −0.177453 0.984129i \(-0.556786\pi\)
−0.177453 + 0.984129i \(0.556786\pi\)
\(588\) −2.93664 −0.121105
\(589\) 33.4806 1.37955
\(590\) 6.68836 0.275356
\(591\) −65.1404 −2.67952
\(592\) 9.55503 0.392709
\(593\) 27.7616 1.14003 0.570015 0.821634i \(-0.306937\pi\)
0.570015 + 0.821634i \(0.306937\pi\)
\(594\) 13.7565 0.564435
\(595\) −5.47031 −0.224261
\(596\) 16.8812 0.691480
\(597\) 21.2371 0.869178
\(598\) 8.26499 0.337981
\(599\) −12.7583 −0.521292 −0.260646 0.965434i \(-0.583936\pi\)
−0.260646 + 0.965434i \(0.583936\pi\)
\(600\) −10.8021 −0.440992
\(601\) −17.0307 −0.694698 −0.347349 0.937736i \(-0.612918\pi\)
−0.347349 + 0.937736i \(0.612918\pi\)
\(602\) −9.79019 −0.399018
\(603\) 45.6816 1.86030
\(604\) −12.5442 −0.510416
\(605\) −8.98158 −0.365153
\(606\) 27.9446 1.13517
\(607\) 9.80151 0.397831 0.198916 0.980017i \(-0.436258\pi\)
0.198916 + 0.980017i \(0.436258\pi\)
\(608\) 8.25798 0.334905
\(609\) 16.1903 0.656062
\(610\) 13.3859 0.541979
\(611\) 4.09254 0.165566
\(612\) 26.7604 1.08172
\(613\) −2.61015 −0.105423 −0.0527116 0.998610i \(-0.516786\pi\)
−0.0527116 + 0.998610i \(0.516786\pi\)
\(614\) −12.7006 −0.512556
\(615\) −10.9716 −0.442417
\(616\) 1.78532 0.0719324
\(617\) −34.3615 −1.38334 −0.691670 0.722213i \(-0.743125\pi\)
−0.691670 + 0.722213i \(0.743125\pi\)
\(618\) 27.1314 1.09139
\(619\) −43.8047 −1.76066 −0.880329 0.474364i \(-0.842678\pi\)
−0.880329 + 0.474364i \(0.842678\pi\)
\(620\) −4.66095 −0.187188
\(621\) −40.1469 −1.61104
\(622\) 10.0942 0.404741
\(623\) 0.725700 0.0290745
\(624\) 4.65836 0.186484
\(625\) 6.92230 0.276892
\(626\) 15.8054 0.631712
\(627\) 43.2952 1.72904
\(628\) 24.5152 0.978262
\(629\) 45.4663 1.81286
\(630\) 6.46531 0.257584
\(631\) −10.9189 −0.434676 −0.217338 0.976096i \(-0.569737\pi\)
−0.217338 + 0.976096i \(0.569737\pi\)
\(632\) 2.39952 0.0954479
\(633\) 77.2509 3.07045
\(634\) 34.7649 1.38069
\(635\) −16.4980 −0.654702
\(636\) 6.84866 0.271567
\(637\) −1.58629 −0.0628511
\(638\) −9.84278 −0.389679
\(639\) −21.6208 −0.855306
\(640\) −1.14962 −0.0454427
\(641\) −32.6922 −1.29126 −0.645631 0.763649i \(-0.723406\pi\)
−0.645631 + 0.763649i \(0.723406\pi\)
\(642\) 53.9325 2.12855
\(643\) −49.7617 −1.96241 −0.981204 0.192972i \(-0.938187\pi\)
−0.981204 + 0.192972i \(0.938187\pi\)
\(644\) −5.21027 −0.205313
\(645\) 33.0519 1.30142
\(646\) 39.2945 1.54602
\(647\) 47.5690 1.87013 0.935065 0.354475i \(-0.115341\pi\)
0.935065 + 0.354475i \(0.115341\pi\)
\(648\) −5.75625 −0.226127
\(649\) −10.3868 −0.407716
\(650\) −5.83496 −0.228866
\(651\) −11.9061 −0.466638
\(652\) −11.8060 −0.462360
\(653\) −26.9639 −1.05518 −0.527589 0.849500i \(-0.676904\pi\)
−0.527589 + 0.849500i \(0.676904\pi\)
\(654\) −3.98853 −0.155964
\(655\) 25.7354 1.00557
\(656\) 3.24985 0.126885
\(657\) −45.7566 −1.78514
\(658\) −2.57995 −0.100577
\(659\) 29.0508 1.13166 0.565830 0.824522i \(-0.308556\pi\)
0.565830 + 0.824522i \(0.308556\pi\)
\(660\) −6.02726 −0.234611
\(661\) −9.87168 −0.383964 −0.191982 0.981398i \(-0.561492\pi\)
−0.191982 + 0.981398i \(0.561492\pi\)
\(662\) 20.4265 0.793899
\(663\) 22.1662 0.860863
\(664\) 1.26492 0.0490883
\(665\) 9.49353 0.368143
\(666\) −53.7362 −2.08224
\(667\) 28.7252 1.11224
\(668\) −20.8750 −0.807679
\(669\) −26.8919 −1.03970
\(670\) −9.33815 −0.360764
\(671\) −20.7878 −0.802503
\(672\) −2.93664 −0.113283
\(673\) 11.4677 0.442046 0.221023 0.975269i \(-0.429060\pi\)
0.221023 + 0.975269i \(0.429060\pi\)
\(674\) 24.2917 0.935681
\(675\) 28.3431 1.09093
\(676\) −10.4837 −0.403219
\(677\) −42.0191 −1.61493 −0.807463 0.589918i \(-0.799160\pi\)
−0.807463 + 0.589918i \(0.799160\pi\)
\(678\) 45.4859 1.74688
\(679\) 8.02371 0.307922
\(680\) −5.47031 −0.209777
\(681\) 30.0620 1.15198
\(682\) 7.23827 0.277168
\(683\) 36.7505 1.40622 0.703109 0.711082i \(-0.251795\pi\)
0.703109 + 0.711082i \(0.251795\pi\)
\(684\) −46.4417 −1.77574
\(685\) −2.00222 −0.0765009
\(686\) 1.00000 0.0381802
\(687\) −0.0701129 −0.00267497
\(688\) −9.79019 −0.373248
\(689\) 3.69945 0.140938
\(690\) 17.5900 0.669639
\(691\) −48.3547 −1.83950 −0.919750 0.392505i \(-0.871609\pi\)
−0.919750 + 0.392505i \(0.871609\pi\)
\(692\) −6.10704 −0.232155
\(693\) −10.0404 −0.381402
\(694\) 4.05420 0.153895
\(695\) 14.2636 0.541050
\(696\) 16.1903 0.613690
\(697\) 15.4640 0.585740
\(698\) −1.93402 −0.0732039
\(699\) −0.825896 −0.0312382
\(700\) 3.67837 0.139029
\(701\) 0.866545 0.0327290 0.0163645 0.999866i \(-0.494791\pi\)
0.0163645 + 0.999866i \(0.494791\pi\)
\(702\) −12.2229 −0.461324
\(703\) −78.9052 −2.97597
\(704\) 1.78532 0.0672866
\(705\) 8.70996 0.328036
\(706\) 4.31153 0.162267
\(707\) −9.51584 −0.357880
\(708\) 17.0851 0.642096
\(709\) −8.02004 −0.301199 −0.150599 0.988595i \(-0.548120\pi\)
−0.150599 + 0.988595i \(0.548120\pi\)
\(710\) 4.41968 0.165868
\(711\) −13.4946 −0.506087
\(712\) 0.725700 0.0271967
\(713\) −21.1242 −0.791108
\(714\) −13.9736 −0.522949
\(715\) −3.25575 −0.121758
\(716\) 16.6851 0.623553
\(717\) −15.3417 −0.572947
\(718\) −24.5126 −0.914802
\(719\) 23.6970 0.883747 0.441874 0.897077i \(-0.354314\pi\)
0.441874 + 0.897077i \(0.354314\pi\)
\(720\) 6.46531 0.240948
\(721\) −9.23894 −0.344076
\(722\) −49.1942 −1.83082
\(723\) 70.0511 2.60523
\(724\) −11.4665 −0.426151
\(725\) −20.2796 −0.753164
\(726\) −22.9429 −0.851493
\(727\) 9.88893 0.366760 0.183380 0.983042i \(-0.441296\pi\)
0.183380 + 0.983042i \(0.441296\pi\)
\(728\) −1.58629 −0.0587918
\(729\) −35.5112 −1.31523
\(730\) 9.35349 0.346188
\(731\) −46.5853 −1.72302
\(732\) 34.1935 1.26383
\(733\) 49.0859 1.81303 0.906515 0.422173i \(-0.138733\pi\)
0.906515 + 0.422173i \(0.138733\pi\)
\(734\) −29.9890 −1.10692
\(735\) −3.37602 −0.124526
\(736\) −5.21027 −0.192053
\(737\) 14.5018 0.534180
\(738\) −18.2767 −0.672776
\(739\) −22.2093 −0.816983 −0.408491 0.912762i \(-0.633945\pi\)
−0.408491 + 0.912762i \(0.633945\pi\)
\(740\) 10.9847 0.403804
\(741\) −38.4686 −1.41318
\(742\) −2.33214 −0.0856156
\(743\) 21.2031 0.777865 0.388933 0.921266i \(-0.372844\pi\)
0.388933 + 0.921266i \(0.372844\pi\)
\(744\) −11.9061 −0.436500
\(745\) 19.4069 0.711016
\(746\) 34.3875 1.25902
\(747\) −7.11373 −0.260278
\(748\) 8.49518 0.310615
\(749\) −18.3654 −0.671056
\(750\) −29.2984 −1.06983
\(751\) −27.0852 −0.988355 −0.494177 0.869361i \(-0.664531\pi\)
−0.494177 + 0.869361i \(0.664531\pi\)
\(752\) −2.57995 −0.0940810
\(753\) −32.7080 −1.19194
\(754\) 8.74551 0.318493
\(755\) −14.4211 −0.524836
\(756\) 7.70535 0.280241
\(757\) −13.1285 −0.477164 −0.238582 0.971122i \(-0.576683\pi\)
−0.238582 + 0.971122i \(0.576683\pi\)
\(758\) 31.3604 1.13906
\(759\) −27.3166 −0.991529
\(760\) 9.49353 0.344367
\(761\) 36.9079 1.33791 0.668955 0.743303i \(-0.266742\pi\)
0.668955 + 0.743303i \(0.266742\pi\)
\(762\) −42.1432 −1.52669
\(763\) 1.35820 0.0491700
\(764\) −16.0121 −0.579298
\(765\) 30.7643 1.11229
\(766\) 8.61714 0.311350
\(767\) 9.22885 0.333235
\(768\) −2.93664 −0.105967
\(769\) −22.0176 −0.793977 −0.396988 0.917824i \(-0.629945\pi\)
−0.396988 + 0.917824i \(0.629945\pi\)
\(770\) 2.05243 0.0739646
\(771\) 29.0731 1.04704
\(772\) 20.0663 0.722203
\(773\) 11.3044 0.406592 0.203296 0.979117i \(-0.434835\pi\)
0.203296 + 0.979117i \(0.434835\pi\)
\(774\) 55.0587 1.97904
\(775\) 14.9134 0.535704
\(776\) 8.02371 0.288035
\(777\) 28.0597 1.00664
\(778\) −26.2878 −0.942462
\(779\) −26.8372 −0.961543
\(780\) 5.35535 0.191752
\(781\) −6.86360 −0.245599
\(782\) −24.7924 −0.886573
\(783\) −42.4810 −1.51815
\(784\) 1.00000 0.0357143
\(785\) 28.1831 1.00590
\(786\) 65.7398 2.34486
\(787\) −40.7721 −1.45337 −0.726684 0.686972i \(-0.758940\pi\)
−0.726684 + 0.686972i \(0.758940\pi\)
\(788\) 22.1819 0.790198
\(789\) −21.2035 −0.754863
\(790\) 2.75854 0.0981444
\(791\) −15.4891 −0.550729
\(792\) −10.0404 −0.356769
\(793\) 18.4704 0.655901
\(794\) −2.36140 −0.0838029
\(795\) 7.87336 0.279239
\(796\) −7.23178 −0.256324
\(797\) −37.4043 −1.32493 −0.662464 0.749094i \(-0.730489\pi\)
−0.662464 + 0.749094i \(0.730489\pi\)
\(798\) 24.2507 0.858466
\(799\) −12.2763 −0.434305
\(800\) 3.67837 0.130050
\(801\) −4.08124 −0.144203
\(802\) −16.1640 −0.570772
\(803\) −14.5256 −0.512598
\(804\) −23.8538 −0.841258
\(805\) −5.98983 −0.211114
\(806\) −6.43135 −0.226535
\(807\) 5.01992 0.176710
\(808\) −9.51584 −0.334766
\(809\) 5.38580 0.189355 0.0946774 0.995508i \(-0.469818\pi\)
0.0946774 + 0.995508i \(0.469818\pi\)
\(810\) −6.61750 −0.232515
\(811\) 5.87662 0.206356 0.103178 0.994663i \(-0.467099\pi\)
0.103178 + 0.994663i \(0.467099\pi\)
\(812\) −5.51319 −0.193475
\(813\) −48.4788 −1.70023
\(814\) −17.0587 −0.597909
\(815\) −13.5724 −0.475422
\(816\) −13.9736 −0.489174
\(817\) 80.8472 2.82848
\(818\) 25.5539 0.893472
\(819\) 8.92107 0.311727
\(820\) 3.73610 0.130470
\(821\) −22.1183 −0.771932 −0.385966 0.922513i \(-0.626132\pi\)
−0.385966 + 0.922513i \(0.626132\pi\)
\(822\) −5.11456 −0.178391
\(823\) −10.5988 −0.369451 −0.184726 0.982790i \(-0.559140\pi\)
−0.184726 + 0.982790i \(0.559140\pi\)
\(824\) −9.23894 −0.321854
\(825\) 19.2851 0.671421
\(826\) −5.81789 −0.202430
\(827\) −23.2879 −0.809799 −0.404900 0.914361i \(-0.632694\pi\)
−0.404900 + 0.914361i \(0.632694\pi\)
\(828\) 29.3018 1.01831
\(829\) 40.1267 1.39366 0.696828 0.717238i \(-0.254594\pi\)
0.696828 + 0.717238i \(0.254594\pi\)
\(830\) 1.45418 0.0504752
\(831\) −53.3115 −1.84935
\(832\) −1.58629 −0.0549947
\(833\) 4.75836 0.164868
\(834\) 36.4357 1.26166
\(835\) −23.9983 −0.830497
\(836\) −14.7431 −0.509901
\(837\) 31.2401 1.07982
\(838\) 35.7791 1.23597
\(839\) 37.6068 1.29833 0.649166 0.760647i \(-0.275118\pi\)
0.649166 + 0.760647i \(0.275118\pi\)
\(840\) −3.37602 −0.116484
\(841\) 1.39525 0.0481121
\(842\) −29.7343 −1.02471
\(843\) 64.8559 2.23376
\(844\) −26.3059 −0.905485
\(845\) −12.0523 −0.414610
\(846\) 14.5093 0.498839
\(847\) 7.81265 0.268446
\(848\) −2.33214 −0.0800860
\(849\) −86.2194 −2.95904
\(850\) 17.5030 0.600349
\(851\) 49.7843 1.70658
\(852\) 11.2898 0.386784
\(853\) 33.2606 1.13882 0.569410 0.822054i \(-0.307172\pi\)
0.569410 + 0.822054i \(0.307172\pi\)
\(854\) −11.6438 −0.398441
\(855\) −53.3903 −1.82591
\(856\) −18.3654 −0.627716
\(857\) −8.69842 −0.297132 −0.148566 0.988902i \(-0.547466\pi\)
−0.148566 + 0.988902i \(0.547466\pi\)
\(858\) −8.31664 −0.283926
\(859\) 37.6302 1.28393 0.641963 0.766736i \(-0.278120\pi\)
0.641963 + 0.766736i \(0.278120\pi\)
\(860\) −11.2550 −0.383792
\(861\) 9.54365 0.325247
\(862\) 1.00000 0.0340601
\(863\) −43.5982 −1.48410 −0.742050 0.670345i \(-0.766146\pi\)
−0.742050 + 0.670345i \(0.766146\pi\)
\(864\) 7.70535 0.262141
\(865\) −7.02078 −0.238714
\(866\) 3.86209 0.131239
\(867\) −16.5686 −0.562700
\(868\) 4.05434 0.137613
\(869\) −4.28391 −0.145322
\(870\) 18.6126 0.631028
\(871\) −12.8851 −0.436596
\(872\) 1.35820 0.0459943
\(873\) −45.1243 −1.52723
\(874\) 43.0263 1.45539
\(875\) 9.97683 0.337278
\(876\) 23.8930 0.807269
\(877\) 6.13303 0.207098 0.103549 0.994624i \(-0.466980\pi\)
0.103549 + 0.994624i \(0.466980\pi\)
\(878\) 32.6481 1.10182
\(879\) −10.4161 −0.351326
\(880\) 2.05243 0.0691875
\(881\) 3.47957 0.117230 0.0586148 0.998281i \(-0.481332\pi\)
0.0586148 + 0.998281i \(0.481332\pi\)
\(882\) −5.62386 −0.189365
\(883\) −35.4174 −1.19189 −0.595946 0.803025i \(-0.703223\pi\)
−0.595946 + 0.803025i \(0.703223\pi\)
\(884\) −7.54814 −0.253871
\(885\) 19.6413 0.660236
\(886\) 18.9858 0.637841
\(887\) −17.2559 −0.579396 −0.289698 0.957118i \(-0.593555\pi\)
−0.289698 + 0.957118i \(0.593555\pi\)
\(888\) 28.0597 0.941622
\(889\) 14.3508 0.481311
\(890\) 0.834279 0.0279651
\(891\) 10.2767 0.344283
\(892\) 9.15737 0.306611
\(893\) 21.3051 0.712949
\(894\) 49.5740 1.65800
\(895\) 19.1816 0.641169
\(896\) 1.00000 0.0334077
\(897\) 24.2713 0.810396
\(898\) 32.1436 1.07264
\(899\) −22.3523 −0.745492
\(900\) −20.6867 −0.689556
\(901\) −11.0972 −0.369700
\(902\) −5.80201 −0.193186
\(903\) −28.7503 −0.956750
\(904\) −15.4891 −0.515160
\(905\) −13.1822 −0.438190
\(906\) −36.8378 −1.22385
\(907\) −30.6143 −1.01653 −0.508265 0.861201i \(-0.669713\pi\)
−0.508265 + 0.861201i \(0.669713\pi\)
\(908\) −10.2369 −0.339722
\(909\) 53.5158 1.77501
\(910\) −1.82363 −0.0604527
\(911\) −34.7533 −1.15143 −0.575715 0.817651i \(-0.695276\pi\)
−0.575715 + 0.817651i \(0.695276\pi\)
\(912\) 24.2507 0.803021
\(913\) −2.25828 −0.0747381
\(914\) −27.0189 −0.893705
\(915\) 39.3096 1.29953
\(916\) 0.0238752 0.000788859 0
\(917\) −22.3860 −0.739252
\(918\) 36.6649 1.21012
\(919\) 19.4075 0.640195 0.320097 0.947385i \(-0.396284\pi\)
0.320097 + 0.947385i \(0.396284\pi\)
\(920\) −5.98983 −0.197479
\(921\) −37.2972 −1.22899
\(922\) 35.2448 1.16072
\(923\) 6.09845 0.200733
\(924\) 5.24283 0.172476
\(925\) −35.1470 −1.15563
\(926\) 41.8483 1.37522
\(927\) 51.9585 1.70654
\(928\) −5.51319 −0.180979
\(929\) 10.9966 0.360785 0.180393 0.983595i \(-0.442263\pi\)
0.180393 + 0.983595i \(0.442263\pi\)
\(930\) −13.6875 −0.448832
\(931\) −8.25798 −0.270644
\(932\) 0.281238 0.00921226
\(933\) 29.6431 0.970471
\(934\) 34.5464 1.13039
\(935\) 9.76623 0.319390
\(936\) 8.92107 0.291594
\(937\) −34.4259 −1.12464 −0.562322 0.826918i \(-0.690092\pi\)
−0.562322 + 0.826918i \(0.690092\pi\)
\(938\) 8.12281 0.265219
\(939\) 46.4149 1.51469
\(940\) −2.96596 −0.0967389
\(941\) −32.9705 −1.07481 −0.537403 0.843325i \(-0.680595\pi\)
−0.537403 + 0.843325i \(0.680595\pi\)
\(942\) 71.9923 2.34564
\(943\) 16.9326 0.551402
\(944\) −5.81789 −0.189356
\(945\) 8.85822 0.288158
\(946\) 17.4786 0.568278
\(947\) 20.1854 0.655936 0.327968 0.944689i \(-0.393636\pi\)
0.327968 + 0.944689i \(0.393636\pi\)
\(948\) 7.04654 0.228861
\(949\) 12.9063 0.418956
\(950\) −30.3759 −0.985525
\(951\) 102.092 3.31056
\(952\) 4.75836 0.154219
\(953\) −2.27054 −0.0735501 −0.0367750 0.999324i \(-0.511708\pi\)
−0.0367750 + 0.999324i \(0.511708\pi\)
\(954\) 13.1156 0.424634
\(955\) −18.4079 −0.595664
\(956\) 5.22424 0.168964
\(957\) −28.9047 −0.934357
\(958\) 30.6571 0.990486
\(959\) 1.74164 0.0562404
\(960\) −3.37602 −0.108961
\(961\) −14.5623 −0.469753
\(962\) 15.1570 0.488683
\(963\) 103.284 3.32829
\(964\) −23.8541 −0.768290
\(965\) 23.0687 0.742607
\(966\) −15.3007 −0.492292
\(967\) 49.9533 1.60639 0.803195 0.595716i \(-0.203132\pi\)
0.803195 + 0.595716i \(0.203132\pi\)
\(968\) 7.81265 0.251108
\(969\) 115.394 3.70698
\(970\) 9.22422 0.296172
\(971\) −33.9991 −1.09108 −0.545542 0.838084i \(-0.683676\pi\)
−0.545542 + 0.838084i \(0.683676\pi\)
\(972\) 6.21199 0.199250
\(973\) −12.4073 −0.397758
\(974\) 3.75623 0.120357
\(975\) −17.1352 −0.548765
\(976\) −11.6438 −0.372707
\(977\) 27.3932 0.876386 0.438193 0.898881i \(-0.355619\pi\)
0.438193 + 0.898881i \(0.355619\pi\)
\(978\) −34.6701 −1.10863
\(979\) −1.29560 −0.0414076
\(980\) 1.14962 0.0367233
\(981\) −7.63831 −0.243872
\(982\) 9.39835 0.299913
\(983\) 35.4177 1.12965 0.564825 0.825210i \(-0.308944\pi\)
0.564825 + 0.825210i \(0.308944\pi\)
\(984\) 9.54365 0.304241
\(985\) 25.5008 0.812523
\(986\) −26.2338 −0.835453
\(987\) −7.57638 −0.241159
\(988\) 13.0995 0.416752
\(989\) −51.0095 −1.62201
\(990\) −11.5426 −0.366848
\(991\) 5.05835 0.160684 0.0803419 0.996767i \(-0.474399\pi\)
0.0803419 + 0.996767i \(0.474399\pi\)
\(992\) 4.05434 0.128725
\(993\) 59.9854 1.90358
\(994\) −3.84447 −0.121939
\(995\) −8.31380 −0.263565
\(996\) 3.71461 0.117702
\(997\) 37.8114 1.19750 0.598750 0.800936i \(-0.295664\pi\)
0.598750 + 0.800936i \(0.295664\pi\)
\(998\) 7.39766 0.234169
\(999\) −73.6248 −2.32939
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.o.1.3 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.o.1.3 25 1.1 even 1 trivial