Properties

Label 6031.2.a.e.1.1
Level $6031$
Weight $2$
Character 6031.1
Self dual yes
Analytic conductor $48.158$
Analytic rank $0$
Dimension $134$
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] = [6031,2,Mod(1,6031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6031, 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("6031.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6031 = 37 \cdot 163 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6031.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: \(48.1577774590\)
Analytic rank: \(0\)
Dimension: \(134\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6031.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.78315 q^{2} -1.65667 q^{3} +5.74594 q^{4} +3.71472 q^{5} +4.61077 q^{6} +4.59606 q^{7} -10.4255 q^{8} -0.255436 q^{9} +O(q^{10})\) \(q-2.78315 q^{2} -1.65667 q^{3} +5.74594 q^{4} +3.71472 q^{5} +4.61077 q^{6} +4.59606 q^{7} -10.4255 q^{8} -0.255436 q^{9} -10.3386 q^{10} -1.10295 q^{11} -9.51915 q^{12} -2.71799 q^{13} -12.7915 q^{14} -6.15408 q^{15} +17.5240 q^{16} +6.21211 q^{17} +0.710918 q^{18} +5.35804 q^{19} +21.3446 q^{20} -7.61416 q^{21} +3.06968 q^{22} +5.61663 q^{23} +17.2717 q^{24} +8.79915 q^{25} +7.56460 q^{26} +5.39319 q^{27} +26.4087 q^{28} -5.18366 q^{29} +17.1277 q^{30} -7.32311 q^{31} -27.9208 q^{32} +1.82723 q^{33} -17.2893 q^{34} +17.0731 q^{35} -1.46772 q^{36} +1.00000 q^{37} -14.9122 q^{38} +4.50283 q^{39} -38.7280 q^{40} +10.9705 q^{41} +21.1914 q^{42} -9.15768 q^{43} -6.33750 q^{44} -0.948873 q^{45} -15.6320 q^{46} +3.92533 q^{47} -29.0315 q^{48} +14.1237 q^{49} -24.4894 q^{50} -10.2914 q^{51} -15.6174 q^{52} +6.94608 q^{53} -15.0101 q^{54} -4.09716 q^{55} -47.9163 q^{56} -8.87652 q^{57} +14.4269 q^{58} +7.51309 q^{59} -35.3610 q^{60} -3.73546 q^{61} +20.3813 q^{62} -1.17400 q^{63} +42.6600 q^{64} -10.0966 q^{65} -5.08546 q^{66} -7.82975 q^{67} +35.6945 q^{68} -9.30492 q^{69} -47.5170 q^{70} +4.16909 q^{71} +2.66306 q^{72} -13.3367 q^{73} -2.78315 q^{74} -14.5773 q^{75} +30.7870 q^{76} -5.06923 q^{77} -12.5321 q^{78} +0.552624 q^{79} +65.0967 q^{80} -8.16844 q^{81} -30.5326 q^{82} +10.1877 q^{83} -43.7505 q^{84} +23.0763 q^{85} +25.4872 q^{86} +8.58763 q^{87} +11.4989 q^{88} -1.31198 q^{89} +2.64086 q^{90} -12.4921 q^{91} +32.2729 q^{92} +12.1320 q^{93} -10.9248 q^{94} +19.9036 q^{95} +46.2557 q^{96} +1.24177 q^{97} -39.3085 q^{98} +0.281734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78315 −1.96799 −0.983993 0.178205i \(-0.942971\pi\)
−0.983993 + 0.178205i \(0.942971\pi\)
\(3\) −1.65667 −0.956480 −0.478240 0.878229i \(-0.658725\pi\)
−0.478240 + 0.878229i \(0.658725\pi\)
\(4\) 5.74594 2.87297
\(5\) 3.71472 1.66127 0.830637 0.556814i \(-0.187977\pi\)
0.830637 + 0.556814i \(0.187977\pi\)
\(6\) 4.61077 1.88234
\(7\) 4.59606 1.73715 0.868573 0.495561i \(-0.165038\pi\)
0.868573 + 0.495561i \(0.165038\pi\)
\(8\) −10.4255 −3.68598
\(9\) −0.255436 −0.0851453
\(10\) −10.3386 −3.26936
\(11\) −1.10295 −0.332552 −0.166276 0.986079i \(-0.553174\pi\)
−0.166276 + 0.986079i \(0.553174\pi\)
\(12\) −9.51915 −2.74794
\(13\) −2.71799 −0.753836 −0.376918 0.926247i \(-0.623016\pi\)
−0.376918 + 0.926247i \(0.623016\pi\)
\(14\) −12.7915 −3.41868
\(15\) −6.15408 −1.58898
\(16\) 17.5240 4.38099
\(17\) 6.21211 1.50666 0.753329 0.657643i \(-0.228447\pi\)
0.753329 + 0.657643i \(0.228447\pi\)
\(18\) 0.710918 0.167565
\(19\) 5.35804 1.22922 0.614609 0.788832i \(-0.289314\pi\)
0.614609 + 0.788832i \(0.289314\pi\)
\(20\) 21.3446 4.77279
\(21\) −7.61416 −1.66155
\(22\) 3.06968 0.654459
\(23\) 5.61663 1.17115 0.585575 0.810618i \(-0.300869\pi\)
0.585575 + 0.810618i \(0.300869\pi\)
\(24\) 17.2717 3.52557
\(25\) 8.79915 1.75983
\(26\) 7.56460 1.48354
\(27\) 5.39319 1.03792
\(28\) 26.4087 4.99077
\(29\) −5.18366 −0.962581 −0.481291 0.876561i \(-0.659832\pi\)
−0.481291 + 0.876561i \(0.659832\pi\)
\(30\) 17.1277 3.12708
\(31\) −7.32311 −1.31527 −0.657635 0.753337i \(-0.728443\pi\)
−0.657635 + 0.753337i \(0.728443\pi\)
\(32\) −27.9208 −4.93575
\(33\) 1.82723 0.318080
\(34\) −17.2893 −2.96508
\(35\) 17.0731 2.88587
\(36\) −1.46772 −0.244620
\(37\) 1.00000 0.164399
\(38\) −14.9122 −2.41909
\(39\) 4.50283 0.721029
\(40\) −38.7280 −6.12343
\(41\) 10.9705 1.71331 0.856653 0.515893i \(-0.172540\pi\)
0.856653 + 0.515893i \(0.172540\pi\)
\(42\) 21.1914 3.26990
\(43\) −9.15768 −1.39653 −0.698266 0.715838i \(-0.746045\pi\)
−0.698266 + 0.715838i \(0.746045\pi\)
\(44\) −6.33750 −0.955414
\(45\) −0.948873 −0.141450
\(46\) −15.6320 −2.30481
\(47\) 3.92533 0.572569 0.286284 0.958145i \(-0.407580\pi\)
0.286284 + 0.958145i \(0.407580\pi\)
\(48\) −29.0315 −4.19033
\(49\) 14.1237 2.01768
\(50\) −24.4894 −3.46332
\(51\) −10.2914 −1.44109
\(52\) −15.6174 −2.16575
\(53\) 6.94608 0.954118 0.477059 0.878871i \(-0.341703\pi\)
0.477059 + 0.878871i \(0.341703\pi\)
\(54\) −15.0101 −2.04261
\(55\) −4.09716 −0.552461
\(56\) −47.9163 −6.40309
\(57\) −8.87652 −1.17572
\(58\) 14.4269 1.89435
\(59\) 7.51309 0.978120 0.489060 0.872250i \(-0.337340\pi\)
0.489060 + 0.872250i \(0.337340\pi\)
\(60\) −35.3610 −4.56508
\(61\) −3.73546 −0.478277 −0.239138 0.970985i \(-0.576865\pi\)
−0.239138 + 0.970985i \(0.576865\pi\)
\(62\) 20.3813 2.58843
\(63\) −1.17400 −0.147910
\(64\) 42.6600 5.33251
\(65\) −10.0966 −1.25233
\(66\) −5.08546 −0.625977
\(67\) −7.82975 −0.956557 −0.478278 0.878208i \(-0.658739\pi\)
−0.478278 + 0.878208i \(0.658739\pi\)
\(68\) 35.6945 4.32859
\(69\) −9.30492 −1.12018
\(70\) −47.5170 −5.67936
\(71\) 4.16909 0.494780 0.247390 0.968916i \(-0.420427\pi\)
0.247390 + 0.968916i \(0.420427\pi\)
\(72\) 2.66306 0.313844
\(73\) −13.3367 −1.56095 −0.780473 0.625189i \(-0.785022\pi\)
−0.780473 + 0.625189i \(0.785022\pi\)
\(74\) −2.78315 −0.323535
\(75\) −14.5773 −1.68324
\(76\) 30.7870 3.53151
\(77\) −5.06923 −0.577692
\(78\) −12.5321 −1.41898
\(79\) 0.552624 0.0621751 0.0310876 0.999517i \(-0.490103\pi\)
0.0310876 + 0.999517i \(0.490103\pi\)
\(80\) 65.0967 7.27803
\(81\) −8.16844 −0.907605
\(82\) −30.5326 −3.37176
\(83\) 10.1877 1.11824 0.559122 0.829086i \(-0.311138\pi\)
0.559122 + 0.829086i \(0.311138\pi\)
\(84\) −43.7505 −4.77357
\(85\) 23.0763 2.50297
\(86\) 25.4872 2.74836
\(87\) 8.58763 0.920690
\(88\) 11.4989 1.22578
\(89\) −1.31198 −0.139070 −0.0695349 0.997580i \(-0.522152\pi\)
−0.0695349 + 0.997580i \(0.522152\pi\)
\(90\) 2.64086 0.278371
\(91\) −12.4921 −1.30952
\(92\) 32.2729 3.36468
\(93\) 12.1320 1.25803
\(94\) −10.9248 −1.12681
\(95\) 19.9036 2.04207
\(96\) 46.2557 4.72095
\(97\) 1.24177 0.126083 0.0630415 0.998011i \(-0.479920\pi\)
0.0630415 + 0.998011i \(0.479920\pi\)
\(98\) −39.3085 −3.97076
\(99\) 0.281734 0.0283153
\(100\) 50.5594 5.05594
\(101\) 13.7793 1.37110 0.685548 0.728028i \(-0.259563\pi\)
0.685548 + 0.728028i \(0.259563\pi\)
\(102\) 28.6427 2.83605
\(103\) −11.8949 −1.17204 −0.586021 0.810296i \(-0.699306\pi\)
−0.586021 + 0.810296i \(0.699306\pi\)
\(104\) 28.3365 2.77863
\(105\) −28.2845 −2.76028
\(106\) −19.3320 −1.87769
\(107\) 2.12286 0.205224 0.102612 0.994721i \(-0.467280\pi\)
0.102612 + 0.994721i \(0.467280\pi\)
\(108\) 30.9890 2.98192
\(109\) 6.57732 0.629993 0.314997 0.949093i \(-0.397997\pi\)
0.314997 + 0.949093i \(0.397997\pi\)
\(110\) 11.4030 1.08724
\(111\) −1.65667 −0.157244
\(112\) 80.5412 7.61043
\(113\) −15.3313 −1.44225 −0.721126 0.692804i \(-0.756375\pi\)
−0.721126 + 0.692804i \(0.756375\pi\)
\(114\) 24.7047 2.31381
\(115\) 20.8642 1.94560
\(116\) −29.7850 −2.76547
\(117\) 0.694274 0.0641856
\(118\) −20.9101 −1.92493
\(119\) 28.5512 2.61729
\(120\) 64.1595 5.85694
\(121\) −9.78350 −0.889409
\(122\) 10.3964 0.941243
\(123\) −18.1745 −1.63874
\(124\) −42.0782 −3.77873
\(125\) 14.1128 1.26229
\(126\) 3.26742 0.291085
\(127\) 4.49641 0.398991 0.199496 0.979899i \(-0.436070\pi\)
0.199496 + 0.979899i \(0.436070\pi\)
\(128\) −62.8878 −5.55855
\(129\) 15.1713 1.33576
\(130\) 28.1004 2.46457
\(131\) 5.97529 0.522064 0.261032 0.965330i \(-0.415937\pi\)
0.261032 + 0.965330i \(0.415937\pi\)
\(132\) 10.4992 0.913834
\(133\) 24.6259 2.13533
\(134\) 21.7914 1.88249
\(135\) 20.0342 1.72427
\(136\) −64.7646 −5.55352
\(137\) −5.20287 −0.444511 −0.222256 0.974988i \(-0.571342\pi\)
−0.222256 + 0.974988i \(0.571342\pi\)
\(138\) 25.8970 2.20450
\(139\) 13.3120 1.12911 0.564557 0.825394i \(-0.309047\pi\)
0.564557 + 0.825394i \(0.309047\pi\)
\(140\) 98.1009 8.29104
\(141\) −6.50299 −0.547651
\(142\) −11.6032 −0.973721
\(143\) 2.99782 0.250690
\(144\) −4.47625 −0.373021
\(145\) −19.2558 −1.59911
\(146\) 37.1182 3.07192
\(147\) −23.3984 −1.92987
\(148\) 5.74594 0.472314
\(149\) −6.24671 −0.511751 −0.255875 0.966710i \(-0.582364\pi\)
−0.255875 + 0.966710i \(0.582364\pi\)
\(150\) 40.5709 3.31260
\(151\) 16.3668 1.33191 0.665957 0.745990i \(-0.268023\pi\)
0.665957 + 0.745990i \(0.268023\pi\)
\(152\) −55.8604 −4.53088
\(153\) −1.58680 −0.128285
\(154\) 14.1084 1.13689
\(155\) −27.2033 −2.18502
\(156\) 25.8730 2.07150
\(157\) 3.38381 0.270057 0.135029 0.990842i \(-0.456887\pi\)
0.135029 + 0.990842i \(0.456887\pi\)
\(158\) −1.53804 −0.122360
\(159\) −11.5074 −0.912595
\(160\) −103.718 −8.19964
\(161\) 25.8144 2.03446
\(162\) 22.7340 1.78615
\(163\) −1.00000 −0.0783260
\(164\) 63.0359 4.92228
\(165\) 6.78765 0.528418
\(166\) −28.3539 −2.20069
\(167\) −2.19759 −0.170055 −0.0850274 0.996379i \(-0.527098\pi\)
−0.0850274 + 0.996379i \(0.527098\pi\)
\(168\) 79.3817 6.12443
\(169\) −5.61251 −0.431731
\(170\) −64.2248 −4.92582
\(171\) −1.36864 −0.104662
\(172\) −52.6195 −4.01220
\(173\) 20.1207 1.52975 0.764873 0.644181i \(-0.222802\pi\)
0.764873 + 0.644181i \(0.222802\pi\)
\(174\) −23.9007 −1.81191
\(175\) 40.4414 3.05708
\(176\) −19.3281 −1.45691
\(177\) −12.4467 −0.935553
\(178\) 3.65145 0.273688
\(179\) 20.3025 1.51748 0.758738 0.651395i \(-0.225816\pi\)
0.758738 + 0.651395i \(0.225816\pi\)
\(180\) −5.45217 −0.406381
\(181\) −1.25951 −0.0936190 −0.0468095 0.998904i \(-0.514905\pi\)
−0.0468095 + 0.998904i \(0.514905\pi\)
\(182\) 34.7673 2.57712
\(183\) 6.18844 0.457462
\(184\) −58.5564 −4.31684
\(185\) 3.71472 0.273112
\(186\) −33.7652 −2.47579
\(187\) −6.85166 −0.501043
\(188\) 22.5547 1.64497
\(189\) 24.7874 1.80302
\(190\) −55.3948 −4.01876
\(191\) 7.25715 0.525109 0.262554 0.964917i \(-0.415435\pi\)
0.262554 + 0.964917i \(0.415435\pi\)
\(192\) −70.6737 −5.10044
\(193\) 24.6473 1.77416 0.887078 0.461621i \(-0.152732\pi\)
0.887078 + 0.461621i \(0.152732\pi\)
\(194\) −3.45605 −0.248130
\(195\) 16.7267 1.19783
\(196\) 81.1541 5.79672
\(197\) −3.80347 −0.270986 −0.135493 0.990778i \(-0.543262\pi\)
−0.135493 + 0.990778i \(0.543262\pi\)
\(198\) −0.784108 −0.0557241
\(199\) −13.7326 −0.973481 −0.486741 0.873547i \(-0.661814\pi\)
−0.486741 + 0.873547i \(0.661814\pi\)
\(200\) −91.7359 −6.48671
\(201\) 12.9713 0.914928
\(202\) −38.3500 −2.69830
\(203\) −23.8244 −1.67214
\(204\) −59.1340 −4.14021
\(205\) 40.7524 2.84627
\(206\) 33.1054 2.30656
\(207\) −1.43469 −0.0997179
\(208\) −47.6301 −3.30255
\(209\) −5.90966 −0.408780
\(210\) 78.7200 5.43220
\(211\) −18.3345 −1.26220 −0.631099 0.775702i \(-0.717396\pi\)
−0.631099 + 0.775702i \(0.717396\pi\)
\(212\) 39.9118 2.74115
\(213\) −6.90682 −0.473247
\(214\) −5.90824 −0.403879
\(215\) −34.0182 −2.32002
\(216\) −56.2269 −3.82576
\(217\) −33.6574 −2.28482
\(218\) −18.3057 −1.23982
\(219\) 22.0946 1.49301
\(220\) −23.5420 −1.58720
\(221\) −16.8845 −1.13577
\(222\) 4.61077 0.309455
\(223\) −14.8830 −0.996637 −0.498319 0.866994i \(-0.666049\pi\)
−0.498319 + 0.866994i \(0.666049\pi\)
\(224\) −128.326 −8.57413
\(225\) −2.24762 −0.149841
\(226\) 42.6695 2.83833
\(227\) −22.2425 −1.47629 −0.738143 0.674644i \(-0.764297\pi\)
−0.738143 + 0.674644i \(0.764297\pi\)
\(228\) −51.0040 −3.37782
\(229\) −3.57791 −0.236435 −0.118217 0.992988i \(-0.537718\pi\)
−0.118217 + 0.992988i \(0.537718\pi\)
\(230\) −58.0684 −3.82891
\(231\) 8.39805 0.552551
\(232\) 54.0424 3.54806
\(233\) 1.56507 0.102531 0.0512655 0.998685i \(-0.483675\pi\)
0.0512655 + 0.998685i \(0.483675\pi\)
\(234\) −1.93227 −0.126316
\(235\) 14.5815 0.951193
\(236\) 43.1698 2.81011
\(237\) −0.915518 −0.0594693
\(238\) −79.4624 −5.15078
\(239\) −15.3179 −0.990830 −0.495415 0.868656i \(-0.664984\pi\)
−0.495415 + 0.868656i \(0.664984\pi\)
\(240\) −107.844 −6.96129
\(241\) 27.0631 1.74329 0.871645 0.490138i \(-0.163054\pi\)
0.871645 + 0.490138i \(0.163054\pi\)
\(242\) 27.2290 1.75034
\(243\) −2.64714 −0.169814
\(244\) −21.4638 −1.37408
\(245\) 52.4657 3.35191
\(246\) 50.5826 3.22503
\(247\) −14.5631 −0.926630
\(248\) 76.3474 4.84806
\(249\) −16.8777 −1.06958
\(250\) −39.2781 −2.48416
\(251\) −28.5112 −1.79961 −0.899806 0.436290i \(-0.856292\pi\)
−0.899806 + 0.436290i \(0.856292\pi\)
\(252\) −6.74573 −0.424941
\(253\) −6.19488 −0.389469
\(254\) −12.5142 −0.785210
\(255\) −38.2298 −2.39404
\(256\) 89.7062 5.60664
\(257\) −3.33751 −0.208188 −0.104094 0.994567i \(-0.533194\pi\)
−0.104094 + 0.994567i \(0.533194\pi\)
\(258\) −42.2240 −2.62875
\(259\) 4.59606 0.285585
\(260\) −58.0144 −3.59790
\(261\) 1.32409 0.0819593
\(262\) −16.6302 −1.02741
\(263\) −13.9384 −0.859480 −0.429740 0.902953i \(-0.641395\pi\)
−0.429740 + 0.902953i \(0.641395\pi\)
\(264\) −19.0498 −1.17244
\(265\) 25.8028 1.58505
\(266\) −68.5375 −4.20231
\(267\) 2.17352 0.133018
\(268\) −44.9893 −2.74816
\(269\) 7.90192 0.481788 0.240894 0.970551i \(-0.422559\pi\)
0.240894 + 0.970551i \(0.422559\pi\)
\(270\) −55.7583 −3.39334
\(271\) 13.8091 0.838845 0.419422 0.907791i \(-0.362233\pi\)
0.419422 + 0.907791i \(0.362233\pi\)
\(272\) 108.861 6.60066
\(273\) 20.6952 1.25253
\(274\) 14.4804 0.874792
\(275\) −9.70504 −0.585236
\(276\) −53.4656 −3.21825
\(277\) 12.4308 0.746894 0.373447 0.927652i \(-0.378176\pi\)
0.373447 + 0.927652i \(0.378176\pi\)
\(278\) −37.0495 −2.22208
\(279\) 1.87059 0.111989
\(280\) −177.996 −10.6373
\(281\) 0.422354 0.0251955 0.0125978 0.999921i \(-0.495990\pi\)
0.0125978 + 0.999921i \(0.495990\pi\)
\(282\) 18.0988 1.07777
\(283\) 4.48772 0.266767 0.133384 0.991064i \(-0.457416\pi\)
0.133384 + 0.991064i \(0.457416\pi\)
\(284\) 23.9554 1.42149
\(285\) −32.9738 −1.95320
\(286\) −8.34338 −0.493355
\(287\) 50.4211 2.97626
\(288\) 7.13199 0.420256
\(289\) 21.5904 1.27002
\(290\) 53.5920 3.14703
\(291\) −2.05721 −0.120596
\(292\) −76.6321 −4.48455
\(293\) 2.60823 0.152374 0.0761871 0.997094i \(-0.475725\pi\)
0.0761871 + 0.997094i \(0.475725\pi\)
\(294\) 65.1213 3.79795
\(295\) 27.9090 1.62493
\(296\) −10.4255 −0.605972
\(297\) −5.94843 −0.345163
\(298\) 17.3856 1.00712
\(299\) −15.2660 −0.882855
\(300\) −83.7604 −4.83591
\(301\) −42.0892 −2.42598
\(302\) −45.5514 −2.62119
\(303\) −22.8278 −1.31143
\(304\) 93.8942 5.38520
\(305\) −13.8762 −0.794549
\(306\) 4.41630 0.252463
\(307\) −34.7728 −1.98459 −0.992295 0.123894i \(-0.960462\pi\)
−0.992295 + 0.123894i \(0.960462\pi\)
\(308\) −29.1275 −1.65969
\(309\) 19.7060 1.12104
\(310\) 75.7110 4.30010
\(311\) −11.7094 −0.663980 −0.331990 0.943283i \(-0.607720\pi\)
−0.331990 + 0.943283i \(0.607720\pi\)
\(312\) −46.9444 −2.65770
\(313\) 31.8928 1.80269 0.901345 0.433103i \(-0.142581\pi\)
0.901345 + 0.433103i \(0.142581\pi\)
\(314\) −9.41766 −0.531469
\(315\) −4.36108 −0.245719
\(316\) 3.17535 0.178627
\(317\) −13.3177 −0.747998 −0.373999 0.927429i \(-0.622014\pi\)
−0.373999 + 0.927429i \(0.622014\pi\)
\(318\) 32.0268 1.79598
\(319\) 5.71733 0.320109
\(320\) 158.470 8.85875
\(321\) −3.51688 −0.196293
\(322\) −71.8453 −4.00378
\(323\) 33.2848 1.85201
\(324\) −46.9354 −2.60752
\(325\) −23.9160 −1.32662
\(326\) 2.78315 0.154145
\(327\) −10.8965 −0.602576
\(328\) −114.373 −6.31522
\(329\) 18.0410 0.994635
\(330\) −18.8911 −1.03992
\(331\) 19.9617 1.09720 0.548598 0.836086i \(-0.315162\pi\)
0.548598 + 0.836086i \(0.315162\pi\)
\(332\) 58.5378 3.21268
\(333\) −0.255436 −0.0139978
\(334\) 6.11623 0.334665
\(335\) −29.0854 −1.58910
\(336\) −133.430 −7.27922
\(337\) −21.4557 −1.16877 −0.584383 0.811478i \(-0.698663\pi\)
−0.584383 + 0.811478i \(0.698663\pi\)
\(338\) 15.6205 0.849641
\(339\) 25.3990 1.37949
\(340\) 132.595 7.19097
\(341\) 8.07704 0.437396
\(342\) 3.80913 0.205974
\(343\) 32.7411 1.76785
\(344\) 95.4737 5.14760
\(345\) −34.5652 −1.86093
\(346\) −55.9989 −3.01052
\(347\) −11.4970 −0.617190 −0.308595 0.951194i \(-0.599859\pi\)
−0.308595 + 0.951194i \(0.599859\pi\)
\(348\) 49.3440 2.64512
\(349\) 1.04098 0.0557225 0.0278613 0.999612i \(-0.491130\pi\)
0.0278613 + 0.999612i \(0.491130\pi\)
\(350\) −112.555 −6.01630
\(351\) −14.6587 −0.782422
\(352\) 30.7953 1.64140
\(353\) 15.3784 0.818508 0.409254 0.912420i \(-0.365789\pi\)
0.409254 + 0.912420i \(0.365789\pi\)
\(354\) 34.6411 1.84116
\(355\) 15.4870 0.821965
\(356\) −7.53857 −0.399544
\(357\) −47.3000 −2.50338
\(358\) −56.5048 −2.98637
\(359\) 9.50535 0.501673 0.250836 0.968029i \(-0.419294\pi\)
0.250836 + 0.968029i \(0.419294\pi\)
\(360\) 9.89251 0.521381
\(361\) 9.70860 0.510979
\(362\) 3.50542 0.184241
\(363\) 16.2081 0.850702
\(364\) −71.7786 −3.76222
\(365\) −49.5422 −2.59316
\(366\) −17.2234 −0.900280
\(367\) 25.9002 1.35198 0.675990 0.736911i \(-0.263716\pi\)
0.675990 + 0.736911i \(0.263716\pi\)
\(368\) 98.4258 5.13080
\(369\) −2.80226 −0.145880
\(370\) −10.3386 −0.537480
\(371\) 31.9246 1.65744
\(372\) 69.7098 3.61428
\(373\) −4.34848 −0.225156 −0.112578 0.993643i \(-0.535911\pi\)
−0.112578 + 0.993643i \(0.535911\pi\)
\(374\) 19.0692 0.986046
\(375\) −23.3803 −1.20735
\(376\) −40.9237 −2.11048
\(377\) 14.0892 0.725629
\(378\) −68.9872 −3.54832
\(379\) 3.73722 0.191968 0.0959839 0.995383i \(-0.469400\pi\)
0.0959839 + 0.995383i \(0.469400\pi\)
\(380\) 114.365 5.86681
\(381\) −7.44907 −0.381628
\(382\) −20.1978 −1.03341
\(383\) −3.61440 −0.184687 −0.0923437 0.995727i \(-0.529436\pi\)
−0.0923437 + 0.995727i \(0.529436\pi\)
\(384\) 104.184 5.31664
\(385\) −18.8308 −0.959705
\(386\) −68.5974 −3.49151
\(387\) 2.33920 0.118908
\(388\) 7.13516 0.362233
\(389\) 19.6635 0.996980 0.498490 0.866895i \(-0.333888\pi\)
0.498490 + 0.866895i \(0.333888\pi\)
\(390\) −46.5531 −2.35731
\(391\) 34.8912 1.76452
\(392\) −147.247 −7.43712
\(393\) −9.89910 −0.499344
\(394\) 10.5856 0.533297
\(395\) 2.05285 0.103290
\(396\) 1.61882 0.0813490
\(397\) −36.3959 −1.82666 −0.913328 0.407225i \(-0.866497\pi\)
−0.913328 + 0.407225i \(0.866497\pi\)
\(398\) 38.2200 1.91580
\(399\) −40.7970 −2.04240
\(400\) 154.196 7.70981
\(401\) 35.1406 1.75484 0.877418 0.479726i \(-0.159264\pi\)
0.877418 + 0.479726i \(0.159264\pi\)
\(402\) −36.1012 −1.80057
\(403\) 19.9042 0.991498
\(404\) 79.1753 3.93912
\(405\) −30.3435 −1.50778
\(406\) 66.3069 3.29076
\(407\) −1.10295 −0.0546713
\(408\) 107.294 5.31183
\(409\) 15.3877 0.760875 0.380438 0.924807i \(-0.375773\pi\)
0.380438 + 0.924807i \(0.375773\pi\)
\(410\) −113.420 −5.60142
\(411\) 8.61945 0.425166
\(412\) −68.3476 −3.36724
\(413\) 34.5306 1.69914
\(414\) 3.99296 0.196243
\(415\) 37.8444 1.85771
\(416\) 75.8887 3.72075
\(417\) −22.0537 −1.07997
\(418\) 16.4475 0.804473
\(419\) 20.8875 1.02042 0.510210 0.860050i \(-0.329568\pi\)
0.510210 + 0.860050i \(0.329568\pi\)
\(420\) −162.521 −7.93021
\(421\) −10.1900 −0.496630 −0.248315 0.968679i \(-0.579877\pi\)
−0.248315 + 0.968679i \(0.579877\pi\)
\(422\) 51.0277 2.48399
\(423\) −1.00267 −0.0487515
\(424\) −72.4166 −3.51686
\(425\) 54.6613 2.65146
\(426\) 19.2227 0.931345
\(427\) −17.1684 −0.830837
\(428\) 12.1978 0.589604
\(429\) −4.96640 −0.239780
\(430\) 94.6779 4.56578
\(431\) 19.0243 0.916367 0.458183 0.888858i \(-0.348500\pi\)
0.458183 + 0.888858i \(0.348500\pi\)
\(432\) 94.5102 4.54712
\(433\) −15.3699 −0.738628 −0.369314 0.929305i \(-0.620407\pi\)
−0.369314 + 0.929305i \(0.620407\pi\)
\(434\) 93.6738 4.49649
\(435\) 31.9006 1.52952
\(436\) 37.7929 1.80995
\(437\) 30.0942 1.43960
\(438\) −61.4926 −2.93823
\(439\) −12.3834 −0.591026 −0.295513 0.955339i \(-0.595491\pi\)
−0.295513 + 0.955339i \(0.595491\pi\)
\(440\) 42.7151 2.03636
\(441\) −3.60771 −0.171796
\(442\) 46.9921 2.23519
\(443\) −38.2137 −1.81559 −0.907795 0.419414i \(-0.862235\pi\)
−0.907795 + 0.419414i \(0.862235\pi\)
\(444\) −9.51915 −0.451759
\(445\) −4.87365 −0.231033
\(446\) 41.4216 1.96137
\(447\) 10.3488 0.489479
\(448\) 196.068 9.26334
\(449\) 2.35482 0.111131 0.0555654 0.998455i \(-0.482304\pi\)
0.0555654 + 0.998455i \(0.482304\pi\)
\(450\) 6.25547 0.294886
\(451\) −12.0999 −0.569764
\(452\) −88.0930 −4.14355
\(453\) −27.1145 −1.27395
\(454\) 61.9043 2.90531
\(455\) −46.4045 −2.17548
\(456\) 92.5425 4.33370
\(457\) −28.2696 −1.32240 −0.661198 0.750211i \(-0.729952\pi\)
−0.661198 + 0.750211i \(0.729952\pi\)
\(458\) 9.95787 0.465301
\(459\) 33.5031 1.56379
\(460\) 119.885 5.58965
\(461\) −29.3839 −1.36854 −0.684272 0.729227i \(-0.739880\pi\)
−0.684272 + 0.729227i \(0.739880\pi\)
\(462\) −23.3731 −1.08741
\(463\) 34.8385 1.61908 0.809542 0.587062i \(-0.199715\pi\)
0.809542 + 0.587062i \(0.199715\pi\)
\(464\) −90.8383 −4.21706
\(465\) 45.0670 2.08993
\(466\) −4.35583 −0.201780
\(467\) −18.6112 −0.861224 −0.430612 0.902537i \(-0.641702\pi\)
−0.430612 + 0.902537i \(0.641702\pi\)
\(468\) 3.98926 0.184403
\(469\) −35.9860 −1.66168
\(470\) −40.5826 −1.87194
\(471\) −5.60587 −0.258305
\(472\) −78.3279 −3.60534
\(473\) 10.1005 0.464420
\(474\) 2.54803 0.117035
\(475\) 47.1462 2.16322
\(476\) 164.054 7.51939
\(477\) −1.77428 −0.0812387
\(478\) 42.6320 1.94994
\(479\) −20.9626 −0.957807 −0.478904 0.877867i \(-0.658966\pi\)
−0.478904 + 0.877867i \(0.658966\pi\)
\(480\) 171.827 7.84279
\(481\) −2.71799 −0.123930
\(482\) −75.3208 −3.43077
\(483\) −42.7660 −1.94592
\(484\) −56.2154 −2.55525
\(485\) 4.61285 0.209459
\(486\) 7.36739 0.334191
\(487\) −22.7736 −1.03197 −0.515985 0.856598i \(-0.672574\pi\)
−0.515985 + 0.856598i \(0.672574\pi\)
\(488\) 38.9442 1.76292
\(489\) 1.65667 0.0749173
\(490\) −146.020 −6.59652
\(491\) −4.39156 −0.198188 −0.0990941 0.995078i \(-0.531594\pi\)
−0.0990941 + 0.995078i \(0.531594\pi\)
\(492\) −104.430 −4.70806
\(493\) −32.2015 −1.45028
\(494\) 40.5314 1.82359
\(495\) 1.04656 0.0470394
\(496\) −128.330 −5.76219
\(497\) 19.1614 0.859505
\(498\) 46.9731 2.10492
\(499\) 16.2976 0.729579 0.364789 0.931090i \(-0.381141\pi\)
0.364789 + 0.931090i \(0.381141\pi\)
\(500\) 81.0913 3.62651
\(501\) 3.64069 0.162654
\(502\) 79.3511 3.54161
\(503\) −9.85567 −0.439442 −0.219721 0.975563i \(-0.570515\pi\)
−0.219721 + 0.975563i \(0.570515\pi\)
\(504\) 12.2396 0.545193
\(505\) 51.1864 2.27776
\(506\) 17.2413 0.766469
\(507\) 9.29808 0.412942
\(508\) 25.8361 1.14629
\(509\) −40.5627 −1.79791 −0.898956 0.438039i \(-0.855673\pi\)
−0.898956 + 0.438039i \(0.855673\pi\)
\(510\) 106.399 4.71145
\(511\) −61.2964 −2.71159
\(512\) −123.891 −5.47524
\(513\) 28.8969 1.27583
\(514\) 9.28881 0.409712
\(515\) −44.1863 −1.94708
\(516\) 87.1733 3.83759
\(517\) −4.32945 −0.190409
\(518\) −12.7915 −0.562028
\(519\) −33.3334 −1.46317
\(520\) 105.262 4.61606
\(521\) 7.83018 0.343046 0.171523 0.985180i \(-0.445131\pi\)
0.171523 + 0.985180i \(0.445131\pi\)
\(522\) −3.68515 −0.161295
\(523\) 8.73951 0.382152 0.191076 0.981575i \(-0.438802\pi\)
0.191076 + 0.981575i \(0.438802\pi\)
\(524\) 34.3337 1.49987
\(525\) −66.9982 −2.92404
\(526\) 38.7928 1.69144
\(527\) −45.4920 −1.98166
\(528\) 32.0203 1.39351
\(529\) 8.54659 0.371591
\(530\) −71.8131 −3.11936
\(531\) −1.91911 −0.0832824
\(532\) 141.499 6.13475
\(533\) −29.8178 −1.29155
\(534\) −6.04925 −0.261777
\(535\) 7.88582 0.340934
\(536\) 81.6294 3.52585
\(537\) −33.6345 −1.45144
\(538\) −21.9922 −0.948153
\(539\) −15.5778 −0.670983
\(540\) 115.115 4.95378
\(541\) 19.7353 0.848488 0.424244 0.905548i \(-0.360540\pi\)
0.424244 + 0.905548i \(0.360540\pi\)
\(542\) −38.4329 −1.65084
\(543\) 2.08660 0.0895447
\(544\) −173.447 −7.43650
\(545\) 24.4329 1.04659
\(546\) −57.5980 −2.46497
\(547\) −11.0721 −0.473409 −0.236705 0.971582i \(-0.576067\pi\)
−0.236705 + 0.971582i \(0.576067\pi\)
\(548\) −29.8954 −1.27707
\(549\) 0.954171 0.0407230
\(550\) 27.0106 1.15174
\(551\) −27.7743 −1.18322
\(552\) 97.0088 4.12897
\(553\) 2.53989 0.108007
\(554\) −34.5968 −1.46988
\(555\) −6.15408 −0.261226
\(556\) 76.4903 3.24391
\(557\) −20.4802 −0.867773 −0.433887 0.900967i \(-0.642858\pi\)
−0.433887 + 0.900967i \(0.642858\pi\)
\(558\) −5.20613 −0.220393
\(559\) 24.8905 1.05276
\(560\) 299.188 12.6430
\(561\) 11.3510 0.479238
\(562\) −1.17548 −0.0495845
\(563\) −22.8590 −0.963392 −0.481696 0.876338i \(-0.659979\pi\)
−0.481696 + 0.876338i \(0.659979\pi\)
\(564\) −37.3658 −1.57338
\(565\) −56.9517 −2.39597
\(566\) −12.4900 −0.524995
\(567\) −37.5426 −1.57664
\(568\) −43.4650 −1.82375
\(569\) 35.1365 1.47300 0.736499 0.676438i \(-0.236477\pi\)
0.736499 + 0.676438i \(0.236477\pi\)
\(570\) 91.7711 3.84387
\(571\) −31.8750 −1.33393 −0.666965 0.745089i \(-0.732407\pi\)
−0.666965 + 0.745089i \(0.732407\pi\)
\(572\) 17.2253 0.720225
\(573\) −12.0227 −0.502256
\(574\) −140.330 −5.85725
\(575\) 49.4216 2.06102
\(576\) −10.8969 −0.454038
\(577\) −6.06522 −0.252499 −0.126249 0.991999i \(-0.540294\pi\)
−0.126249 + 0.991999i \(0.540294\pi\)
\(578\) −60.0893 −2.49938
\(579\) −40.8326 −1.69694
\(580\) −110.643 −4.59420
\(581\) 46.8232 1.94255
\(582\) 5.72554 0.237331
\(583\) −7.66120 −0.317294
\(584\) 139.043 5.75362
\(585\) 2.57903 0.106630
\(586\) −7.25910 −0.299871
\(587\) −40.4724 −1.67047 −0.835236 0.549891i \(-0.814669\pi\)
−0.835236 + 0.549891i \(0.814669\pi\)
\(588\) −134.446 −5.54445
\(589\) −39.2375 −1.61675
\(590\) −77.6751 −3.19783
\(591\) 6.30111 0.259193
\(592\) 17.5240 0.720231
\(593\) 8.81828 0.362123 0.181062 0.983472i \(-0.442047\pi\)
0.181062 + 0.983472i \(0.442047\pi\)
\(594\) 16.5554 0.679276
\(595\) 106.060 4.34803
\(596\) −35.8933 −1.47025
\(597\) 22.7505 0.931116
\(598\) 42.4876 1.73745
\(599\) 17.4213 0.711815 0.355907 0.934521i \(-0.384172\pi\)
0.355907 + 0.934521i \(0.384172\pi\)
\(600\) 151.976 6.20441
\(601\) 30.6270 1.24930 0.624651 0.780904i \(-0.285241\pi\)
0.624651 + 0.780904i \(0.285241\pi\)
\(602\) 117.141 4.77430
\(603\) 2.00000 0.0814463
\(604\) 94.0429 3.82655
\(605\) −36.3430 −1.47755
\(606\) 63.5334 2.58087
\(607\) 12.4350 0.504720 0.252360 0.967633i \(-0.418793\pi\)
0.252360 + 0.967633i \(0.418793\pi\)
\(608\) −149.601 −6.06712
\(609\) 39.4692 1.59937
\(610\) 38.6196 1.56366
\(611\) −10.6690 −0.431623
\(612\) −9.11765 −0.368559
\(613\) −8.84033 −0.357057 −0.178529 0.983935i \(-0.557134\pi\)
−0.178529 + 0.983935i \(0.557134\pi\)
\(614\) 96.7782 3.90565
\(615\) −67.5134 −2.72240
\(616\) 52.8494 2.12936
\(617\) 19.7128 0.793609 0.396805 0.917903i \(-0.370119\pi\)
0.396805 + 0.917903i \(0.370119\pi\)
\(618\) −54.8448 −2.20618
\(619\) −4.42275 −0.177765 −0.0888827 0.996042i \(-0.528330\pi\)
−0.0888827 + 0.996042i \(0.528330\pi\)
\(620\) −156.309 −6.27751
\(621\) 30.2916 1.21556
\(622\) 32.5891 1.30670
\(623\) −6.02994 −0.241585
\(624\) 78.9074 3.15883
\(625\) 8.42932 0.337173
\(626\) −88.7626 −3.54767
\(627\) 9.79037 0.390990
\(628\) 19.4432 0.775867
\(629\) 6.21211 0.247693
\(630\) 12.1375 0.483571
\(631\) −48.3101 −1.92319 −0.961597 0.274466i \(-0.911499\pi\)
−0.961597 + 0.274466i \(0.911499\pi\)
\(632\) −5.76141 −0.229176
\(633\) 30.3743 1.20727
\(634\) 37.0653 1.47205
\(635\) 16.7029 0.662834
\(636\) −66.1208 −2.62186
\(637\) −38.3882 −1.52100
\(638\) −15.9122 −0.629970
\(639\) −1.06494 −0.0421282
\(640\) −233.610 −9.23427
\(641\) 6.08065 0.240171 0.120086 0.992764i \(-0.461683\pi\)
0.120086 + 0.992764i \(0.461683\pi\)
\(642\) 9.78801 0.386302
\(643\) −25.5937 −1.00932 −0.504659 0.863319i \(-0.668382\pi\)
−0.504659 + 0.863319i \(0.668382\pi\)
\(644\) 148.328 5.84494
\(645\) 56.3571 2.21906
\(646\) −92.6366 −3.64474
\(647\) −14.4522 −0.568175 −0.284088 0.958798i \(-0.591691\pi\)
−0.284088 + 0.958798i \(0.591691\pi\)
\(648\) 85.1604 3.34542
\(649\) −8.28657 −0.325276
\(650\) 66.5620 2.61078
\(651\) 55.7593 2.18538
\(652\) −5.74594 −0.225028
\(653\) 19.9622 0.781183 0.390591 0.920564i \(-0.372271\pi\)
0.390591 + 0.920564i \(0.372271\pi\)
\(654\) 30.3265 1.18586
\(655\) 22.1965 0.867291
\(656\) 192.247 7.50598
\(657\) 3.40668 0.132907
\(658\) −50.2110 −1.95743
\(659\) 39.3158 1.53153 0.765764 0.643122i \(-0.222361\pi\)
0.765764 + 0.643122i \(0.222361\pi\)
\(660\) 39.0014 1.51813
\(661\) 16.6710 0.648429 0.324214 0.945984i \(-0.394900\pi\)
0.324214 + 0.945984i \(0.394900\pi\)
\(662\) −55.5565 −2.15927
\(663\) 27.9721 1.08635
\(664\) −106.212 −4.12183
\(665\) 91.4782 3.54737
\(666\) 0.710918 0.0275475
\(667\) −29.1147 −1.12733
\(668\) −12.6272 −0.488562
\(669\) 24.6562 0.953264
\(670\) 80.9490 3.12733
\(671\) 4.12003 0.159052
\(672\) 212.594 8.20098
\(673\) 13.5098 0.520766 0.260383 0.965505i \(-0.416151\pi\)
0.260383 + 0.965505i \(0.416151\pi\)
\(674\) 59.7145 2.30012
\(675\) 47.4555 1.82656
\(676\) −32.2491 −1.24035
\(677\) 0.844641 0.0324622 0.0162311 0.999868i \(-0.494833\pi\)
0.0162311 + 0.999868i \(0.494833\pi\)
\(678\) −70.6894 −2.71481
\(679\) 5.70726 0.219025
\(680\) −240.582 −9.22592
\(681\) 36.8485 1.41204
\(682\) −22.4796 −0.860790
\(683\) −14.4323 −0.552238 −0.276119 0.961123i \(-0.589048\pi\)
−0.276119 + 0.961123i \(0.589048\pi\)
\(684\) −7.86411 −0.300692
\(685\) −19.3272 −0.738455
\(686\) −91.1234 −3.47911
\(687\) 5.92742 0.226145
\(688\) −160.479 −6.11820
\(689\) −18.8794 −0.719249
\(690\) 96.2003 3.66228
\(691\) 9.69410 0.368781 0.184390 0.982853i \(-0.440969\pi\)
0.184390 + 0.982853i \(0.440969\pi\)
\(692\) 115.612 4.39492
\(693\) 1.29486 0.0491878
\(694\) 31.9978 1.21462
\(695\) 49.4506 1.87577
\(696\) −89.5306 −3.39365
\(697\) 68.1501 2.58137
\(698\) −2.89722 −0.109661
\(699\) −2.59281 −0.0980690
\(700\) 232.374 8.78291
\(701\) 24.0594 0.908709 0.454355 0.890821i \(-0.349870\pi\)
0.454355 + 0.890821i \(0.349870\pi\)
\(702\) 40.7973 1.53980
\(703\) 5.35804 0.202082
\(704\) −47.0520 −1.77334
\(705\) −24.1568 −0.909798
\(706\) −42.8004 −1.61081
\(707\) 63.3306 2.38179
\(708\) −71.5182 −2.68782
\(709\) −27.6717 −1.03923 −0.519617 0.854399i \(-0.673925\pi\)
−0.519617 + 0.854399i \(0.673925\pi\)
\(710\) −43.1027 −1.61762
\(711\) −0.141160 −0.00529392
\(712\) 13.6781 0.512609
\(713\) −41.1312 −1.54038
\(714\) 131.643 4.92662
\(715\) 11.1361 0.416465
\(716\) 116.657 4.35967
\(717\) 25.3767 0.947710
\(718\) −26.4548 −0.987286
\(719\) 34.0154 1.26856 0.634280 0.773104i \(-0.281297\pi\)
0.634280 + 0.773104i \(0.281297\pi\)
\(720\) −16.6280 −0.619690
\(721\) −54.6697 −2.03601
\(722\) −27.0205 −1.00560
\(723\) −44.8347 −1.66742
\(724\) −7.23710 −0.268965
\(725\) −45.6118 −1.69398
\(726\) −45.1095 −1.67417
\(727\) 21.5273 0.798405 0.399202 0.916863i \(-0.369287\pi\)
0.399202 + 0.916863i \(0.369287\pi\)
\(728\) 130.236 4.82688
\(729\) 28.8908 1.07003
\(730\) 137.884 5.10330
\(731\) −56.8885 −2.10410
\(732\) 35.5584 1.31428
\(733\) 40.3845 1.49164 0.745818 0.666149i \(-0.232059\pi\)
0.745818 + 0.666149i \(0.232059\pi\)
\(734\) −72.0842 −2.66068
\(735\) −86.9185 −3.20604
\(736\) −156.821 −5.78051
\(737\) 8.63584 0.318105
\(738\) 7.79913 0.287090
\(739\) −20.2544 −0.745069 −0.372535 0.928018i \(-0.621511\pi\)
−0.372535 + 0.928018i \(0.621511\pi\)
\(740\) 21.3446 0.784642
\(741\) 24.1263 0.886303
\(742\) −88.8510 −3.26182
\(743\) 21.0539 0.772393 0.386197 0.922417i \(-0.373789\pi\)
0.386197 + 0.922417i \(0.373789\pi\)
\(744\) −126.483 −4.63708
\(745\) −23.2048 −0.850158
\(746\) 12.1025 0.443104
\(747\) −2.60230 −0.0952132
\(748\) −39.3693 −1.43948
\(749\) 9.75677 0.356505
\(750\) 65.0709 2.37605
\(751\) 20.0221 0.730618 0.365309 0.930886i \(-0.380963\pi\)
0.365309 + 0.930886i \(0.380963\pi\)
\(752\) 68.7874 2.50842
\(753\) 47.2337 1.72129
\(754\) −39.2123 −1.42803
\(755\) 60.7982 2.21267
\(756\) 142.427 5.18002
\(757\) 22.6342 0.822653 0.411327 0.911488i \(-0.365066\pi\)
0.411327 + 0.911488i \(0.365066\pi\)
\(758\) −10.4012 −0.377790
\(759\) 10.2629 0.372519
\(760\) −207.506 −7.52703
\(761\) −9.07442 −0.328948 −0.164474 0.986381i \(-0.552593\pi\)
−0.164474 + 0.986381i \(0.552593\pi\)
\(762\) 20.7319 0.751038
\(763\) 30.2297 1.09439
\(764\) 41.6992 1.50862
\(765\) −5.89451 −0.213116
\(766\) 10.0594 0.363462
\(767\) −20.4205 −0.737343
\(768\) −148.614 −5.36264
\(769\) −38.1413 −1.37541 −0.687706 0.725989i \(-0.741382\pi\)
−0.687706 + 0.725989i \(0.741382\pi\)
\(770\) 52.4089 1.88869
\(771\) 5.52916 0.199128
\(772\) 141.622 5.09710
\(773\) 42.4191 1.52571 0.762854 0.646570i \(-0.223797\pi\)
0.762854 + 0.646570i \(0.223797\pi\)
\(774\) −6.51035 −0.234010
\(775\) −64.4372 −2.31465
\(776\) −12.9462 −0.464740
\(777\) −7.61416 −0.273156
\(778\) −54.7266 −1.96204
\(779\) 58.7805 2.10603
\(780\) 96.1109 3.44132
\(781\) −4.59831 −0.164540
\(782\) −97.1075 −3.47256
\(783\) −27.9565 −0.999083
\(784\) 247.504 8.83942
\(785\) 12.5699 0.448639
\(786\) 27.5507 0.982702
\(787\) 24.9380 0.888943 0.444472 0.895793i \(-0.353391\pi\)
0.444472 + 0.895793i \(0.353391\pi\)
\(788\) −21.8545 −0.778536
\(789\) 23.0914 0.822076
\(790\) −5.71338 −0.203273
\(791\) −70.4637 −2.50540
\(792\) −2.93722 −0.104370
\(793\) 10.1530 0.360542
\(794\) 101.295 3.59483
\(795\) −42.7467 −1.51607
\(796\) −78.9070 −2.79678
\(797\) −39.9954 −1.41671 −0.708355 0.705857i \(-0.750562\pi\)
−0.708355 + 0.705857i \(0.750562\pi\)
\(798\) 113.544 4.01942
\(799\) 24.3846 0.862666
\(800\) −245.680 −8.68609
\(801\) 0.335127 0.0118411
\(802\) −97.8016 −3.45349
\(803\) 14.7098 0.519096
\(804\) 74.5326 2.62856
\(805\) 95.8932 3.37979
\(806\) −55.3964 −1.95125
\(807\) −13.0909 −0.460821
\(808\) −143.657 −5.05383
\(809\) −21.9738 −0.772559 −0.386280 0.922382i \(-0.626240\pi\)
−0.386280 + 0.922382i \(0.626240\pi\)
\(810\) 84.4506 2.96729
\(811\) 14.4954 0.509004 0.254502 0.967072i \(-0.418088\pi\)
0.254502 + 0.967072i \(0.418088\pi\)
\(812\) −136.894 −4.80402
\(813\) −22.8772 −0.802339
\(814\) 3.06968 0.107592
\(815\) −3.71472 −0.130121
\(816\) −180.347 −6.31340
\(817\) −49.0672 −1.71664
\(818\) −42.8265 −1.49739
\(819\) 3.19092 0.111500
\(820\) 234.161 8.17725
\(821\) −35.2799 −1.23128 −0.615638 0.788029i \(-0.711102\pi\)
−0.615638 + 0.788029i \(0.711102\pi\)
\(822\) −23.9893 −0.836721
\(823\) −22.3090 −0.777644 −0.388822 0.921313i \(-0.627118\pi\)
−0.388822 + 0.921313i \(0.627118\pi\)
\(824\) 124.011 4.32013
\(825\) 16.0781 0.559767
\(826\) −96.1039 −3.34388
\(827\) −12.4067 −0.431424 −0.215712 0.976457i \(-0.569207\pi\)
−0.215712 + 0.976457i \(0.569207\pi\)
\(828\) −8.24365 −0.286487
\(829\) 1.80212 0.0625902 0.0312951 0.999510i \(-0.490037\pi\)
0.0312951 + 0.999510i \(0.490037\pi\)
\(830\) −105.327 −3.65595
\(831\) −20.5937 −0.714389
\(832\) −115.950 −4.01984
\(833\) 87.7382 3.03995
\(834\) 61.3789 2.12538
\(835\) −8.16344 −0.282507
\(836\) −33.9566 −1.17441
\(837\) −39.4949 −1.36515
\(838\) −58.1330 −2.00817
\(839\) 12.2814 0.424003 0.212001 0.977269i \(-0.432002\pi\)
0.212001 + 0.977269i \(0.432002\pi\)
\(840\) 294.881 10.1744
\(841\) −2.12968 −0.0734371
\(842\) 28.3603 0.977362
\(843\) −0.699703 −0.0240990
\(844\) −105.349 −3.62626
\(845\) −20.8489 −0.717224
\(846\) 2.79059 0.0959424
\(847\) −44.9655 −1.54503
\(848\) 121.723 4.17999
\(849\) −7.43469 −0.255158
\(850\) −152.131 −5.21805
\(851\) 5.61663 0.192536
\(852\) −39.6862 −1.35963
\(853\) −11.0752 −0.379209 −0.189605 0.981861i \(-0.560721\pi\)
−0.189605 + 0.981861i \(0.560721\pi\)
\(854\) 47.7823 1.63508
\(855\) −5.08410 −0.173873
\(856\) −22.1319 −0.756453
\(857\) −9.86369 −0.336937 −0.168469 0.985707i \(-0.553882\pi\)
−0.168469 + 0.985707i \(0.553882\pi\)
\(858\) 13.8223 0.471884
\(859\) 5.01395 0.171074 0.0855368 0.996335i \(-0.472739\pi\)
0.0855368 + 0.996335i \(0.472739\pi\)
\(860\) −195.467 −6.66536
\(861\) −83.5312 −2.84674
\(862\) −52.9474 −1.80340
\(863\) −13.4895 −0.459188 −0.229594 0.973286i \(-0.573740\pi\)
−0.229594 + 0.973286i \(0.573740\pi\)
\(864\) −150.582 −5.12292
\(865\) 74.7427 2.54133
\(866\) 42.7767 1.45361
\(867\) −35.7681 −1.21475
\(868\) −193.394 −6.56421
\(869\) −0.609518 −0.0206765
\(870\) −88.7844 −3.01007
\(871\) 21.2812 0.721087
\(872\) −68.5721 −2.32214
\(873\) −0.317194 −0.0107354
\(874\) −83.7567 −2.83311
\(875\) 64.8632 2.19278
\(876\) 126.954 4.28939
\(877\) −24.8006 −0.837457 −0.418728 0.908112i \(-0.637524\pi\)
−0.418728 + 0.908112i \(0.637524\pi\)
\(878\) 34.4648 1.16313
\(879\) −4.32098 −0.145743
\(880\) −71.7985 −2.42033
\(881\) −19.3182 −0.650846 −0.325423 0.945569i \(-0.605507\pi\)
−0.325423 + 0.945569i \(0.605507\pi\)
\(882\) 10.0408 0.338092
\(883\) 9.84949 0.331462 0.165731 0.986171i \(-0.447002\pi\)
0.165731 + 0.986171i \(0.447002\pi\)
\(884\) −97.0173 −3.26305
\(885\) −46.2361 −1.55421
\(886\) 106.355 3.57306
\(887\) 14.6169 0.490786 0.245393 0.969424i \(-0.421083\pi\)
0.245393 + 0.969424i \(0.421083\pi\)
\(888\) 17.2717 0.579600
\(889\) 20.6657 0.693106
\(890\) 13.5641 0.454670
\(891\) 9.00940 0.301826
\(892\) −85.5167 −2.86331
\(893\) 21.0321 0.703812
\(894\) −28.8022 −0.963289
\(895\) 75.4180 2.52094
\(896\) −289.036 −9.65600
\(897\) 25.2907 0.844433
\(898\) −6.55382 −0.218704
\(899\) 37.9605 1.26605
\(900\) −12.9147 −0.430490
\(901\) 43.1499 1.43753
\(902\) 33.6760 1.12129
\(903\) 69.7280 2.32040
\(904\) 159.837 5.31611
\(905\) −4.67875 −0.155527
\(906\) 75.4638 2.50712
\(907\) −28.6113 −0.950021 −0.475011 0.879980i \(-0.657556\pi\)
−0.475011 + 0.879980i \(0.657556\pi\)
\(908\) −127.804 −4.24133
\(909\) −3.51974 −0.116742
\(910\) 129.151 4.28131
\(911\) −31.3655 −1.03919 −0.519593 0.854414i \(-0.673916\pi\)
−0.519593 + 0.854414i \(0.673916\pi\)
\(912\) −155.552 −5.15084
\(913\) −11.2365 −0.371875
\(914\) 78.6786 2.60246
\(915\) 22.9883 0.759970
\(916\) −20.5585 −0.679271
\(917\) 27.4628 0.906901
\(918\) −93.2443 −3.07752
\(919\) 2.89897 0.0956282 0.0478141 0.998856i \(-0.484775\pi\)
0.0478141 + 0.998856i \(0.484775\pi\)
\(920\) −217.521 −7.17145
\(921\) 57.6072 1.89822
\(922\) 81.7799 2.69328
\(923\) −11.3316 −0.372983
\(924\) 48.2547 1.58746
\(925\) 8.79915 0.289314
\(926\) −96.9610 −3.18634
\(927\) 3.03839 0.0997939
\(928\) 144.732 4.75107
\(929\) −30.2605 −0.992816 −0.496408 0.868089i \(-0.665348\pi\)
−0.496408 + 0.868089i \(0.665348\pi\)
\(930\) −125.428 −4.11296
\(931\) 75.6755 2.48017
\(932\) 8.99280 0.294569
\(933\) 19.3987 0.635084
\(934\) 51.7978 1.69488
\(935\) −25.4520 −0.832370
\(936\) −7.23817 −0.236587
\(937\) 35.2479 1.15150 0.575749 0.817627i \(-0.304711\pi\)
0.575749 + 0.817627i \(0.304711\pi\)
\(938\) 100.155 3.27016
\(939\) −52.8360 −1.72424
\(940\) 83.7846 2.73275
\(941\) 47.7928 1.55800 0.779000 0.627024i \(-0.215727\pi\)
0.779000 + 0.627024i \(0.215727\pi\)
\(942\) 15.6020 0.508340
\(943\) 61.6174 2.00654
\(944\) 131.659 4.28514
\(945\) 92.0783 2.99531
\(946\) −28.1112 −0.913973
\(947\) 7.37722 0.239728 0.119864 0.992790i \(-0.461754\pi\)
0.119864 + 0.992790i \(0.461754\pi\)
\(948\) −5.26051 −0.170854
\(949\) 36.2492 1.17670
\(950\) −131.215 −4.25718
\(951\) 22.0631 0.715446
\(952\) −297.662 −9.64727
\(953\) 51.8927 1.68097 0.840484 0.541836i \(-0.182271\pi\)
0.840484 + 0.541836i \(0.182271\pi\)
\(954\) 4.93809 0.159877
\(955\) 26.9583 0.872349
\(956\) −88.0156 −2.84663
\(957\) −9.47174 −0.306178
\(958\) 58.3422 1.88495
\(959\) −23.9127 −0.772181
\(960\) −262.533 −8.47322
\(961\) 22.6280 0.729935
\(962\) 7.56460 0.243892
\(963\) −0.542254 −0.0174739
\(964\) 155.503 5.00842
\(965\) 91.5580 2.94736
\(966\) 119.024 3.82954
\(967\) 11.6437 0.374436 0.187218 0.982318i \(-0.440053\pi\)
0.187218 + 0.982318i \(0.440053\pi\)
\(968\) 101.998 3.27835
\(969\) −55.1419 −1.77141
\(970\) −12.8383 −0.412212
\(971\) −40.9212 −1.31322 −0.656611 0.754229i \(-0.728011\pi\)
−0.656611 + 0.754229i \(0.728011\pi\)
\(972\) −15.2103 −0.487870
\(973\) 61.1829 1.96143
\(974\) 63.3824 2.03090
\(975\) 39.6211 1.26889
\(976\) −65.4601 −2.09533
\(977\) 33.5888 1.07460 0.537300 0.843391i \(-0.319444\pi\)
0.537300 + 0.843391i \(0.319444\pi\)
\(978\) −4.61077 −0.147436
\(979\) 1.44705 0.0462480
\(980\) 301.465 9.62995
\(981\) −1.68008 −0.0536410
\(982\) 12.2224 0.390032
\(983\) −6.19480 −0.197583 −0.0987917 0.995108i \(-0.531498\pi\)
−0.0987917 + 0.995108i \(0.531498\pi\)
\(984\) 189.479 6.04038
\(985\) −14.1288 −0.450182
\(986\) 89.6217 2.85414
\(987\) −29.8881 −0.951349
\(988\) −83.6789 −2.66218
\(989\) −51.4353 −1.63555
\(990\) −2.91274 −0.0925730
\(991\) −40.8533 −1.29775 −0.648873 0.760897i \(-0.724759\pi\)
−0.648873 + 0.760897i \(0.724759\pi\)
\(992\) 204.467 6.49185
\(993\) −33.0700 −1.04945
\(994\) −53.3291 −1.69149
\(995\) −51.0129 −1.61722
\(996\) −96.9780 −3.07287
\(997\) −55.9686 −1.77254 −0.886272 0.463164i \(-0.846714\pi\)
−0.886272 + 0.463164i \(0.846714\pi\)
\(998\) −45.3586 −1.43580
\(999\) 5.39319 0.170633
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 6031.2.a.e.1.1 134
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6031.2.a.e.1.1 134 1.1 even 1 trivial