Properties

Label 6026.2.a.j.1.16
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $33$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(0\)
Dimension: \(33\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.0820624 q^{3} +1.00000 q^{4} -3.26458 q^{5} +0.0820624 q^{6} -0.430136 q^{7} -1.00000 q^{8} -2.99327 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.0820624 q^{3} +1.00000 q^{4} -3.26458 q^{5} +0.0820624 q^{6} -0.430136 q^{7} -1.00000 q^{8} -2.99327 q^{9} +3.26458 q^{10} +4.69415 q^{11} -0.0820624 q^{12} +7.01292 q^{13} +0.430136 q^{14} +0.267899 q^{15} +1.00000 q^{16} +0.392111 q^{17} +2.99327 q^{18} +8.43997 q^{19} -3.26458 q^{20} +0.0352980 q^{21} -4.69415 q^{22} +1.00000 q^{23} +0.0820624 q^{24} +5.65746 q^{25} -7.01292 q^{26} +0.491822 q^{27} -0.430136 q^{28} +0.423629 q^{29} -0.267899 q^{30} +8.04433 q^{31} -1.00000 q^{32} -0.385213 q^{33} -0.392111 q^{34} +1.40421 q^{35} -2.99327 q^{36} -3.06092 q^{37} -8.43997 q^{38} -0.575497 q^{39} +3.26458 q^{40} +6.59524 q^{41} -0.0352980 q^{42} -2.90818 q^{43} +4.69415 q^{44} +9.77175 q^{45} -1.00000 q^{46} -8.57331 q^{47} -0.0820624 q^{48} -6.81498 q^{49} -5.65746 q^{50} -0.0321776 q^{51} +7.01292 q^{52} -10.7899 q^{53} -0.491822 q^{54} -15.3244 q^{55} +0.430136 q^{56} -0.692604 q^{57} -0.423629 q^{58} -1.19489 q^{59} +0.267899 q^{60} +7.80797 q^{61} -8.04433 q^{62} +1.28751 q^{63} +1.00000 q^{64} -22.8942 q^{65} +0.385213 q^{66} -4.56048 q^{67} +0.392111 q^{68} -0.0820624 q^{69} -1.40421 q^{70} -2.37416 q^{71} +2.99327 q^{72} +10.1037 q^{73} +3.06092 q^{74} -0.464265 q^{75} +8.43997 q^{76} -2.01912 q^{77} +0.575497 q^{78} +2.93297 q^{79} -3.26458 q^{80} +8.93944 q^{81} -6.59524 q^{82} -5.21951 q^{83} +0.0352980 q^{84} -1.28008 q^{85} +2.90818 q^{86} -0.0347640 q^{87} -4.69415 q^{88} +1.31862 q^{89} -9.77175 q^{90} -3.01651 q^{91} +1.00000 q^{92} -0.660137 q^{93} +8.57331 q^{94} -27.5529 q^{95} +0.0820624 q^{96} -8.70998 q^{97} +6.81498 q^{98} -14.0508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 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
\(3\) −0.0820624 −0.0473788 −0.0236894 0.999719i \(-0.507541\pi\)
−0.0236894 + 0.999719i \(0.507541\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.26458 −1.45996 −0.729982 0.683467i \(-0.760471\pi\)
−0.729982 + 0.683467i \(0.760471\pi\)
\(6\) 0.0820624 0.0335018
\(7\) −0.430136 −0.162576 −0.0812880 0.996691i \(-0.525903\pi\)
−0.0812880 + 0.996691i \(0.525903\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.99327 −0.997755
\(10\) 3.26458 1.03235
\(11\) 4.69415 1.41534 0.707669 0.706544i \(-0.249747\pi\)
0.707669 + 0.706544i \(0.249747\pi\)
\(12\) −0.0820624 −0.0236894
\(13\) 7.01292 1.94503 0.972517 0.232830i \(-0.0747987\pi\)
0.972517 + 0.232830i \(0.0747987\pi\)
\(14\) 0.430136 0.114959
\(15\) 0.267899 0.0691713
\(16\) 1.00000 0.250000
\(17\) 0.392111 0.0951009 0.0475504 0.998869i \(-0.484859\pi\)
0.0475504 + 0.998869i \(0.484859\pi\)
\(18\) 2.99327 0.705520
\(19\) 8.43997 1.93626 0.968131 0.250446i \(-0.0805772\pi\)
0.968131 + 0.250446i \(0.0805772\pi\)
\(20\) −3.26458 −0.729982
\(21\) 0.0352980 0.00770265
\(22\) −4.69415 −1.00080
\(23\) 1.00000 0.208514
\(24\) 0.0820624 0.0167509
\(25\) 5.65746 1.13149
\(26\) −7.01292 −1.37535
\(27\) 0.491822 0.0946512
\(28\) −0.430136 −0.0812880
\(29\) 0.423629 0.0786659 0.0393330 0.999226i \(-0.487477\pi\)
0.0393330 + 0.999226i \(0.487477\pi\)
\(30\) −0.267899 −0.0489115
\(31\) 8.04433 1.44480 0.722402 0.691473i \(-0.243038\pi\)
0.722402 + 0.691473i \(0.243038\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.385213 −0.0670570
\(34\) −0.392111 −0.0672465
\(35\) 1.40421 0.237355
\(36\) −2.99327 −0.498878
\(37\) −3.06092 −0.503212 −0.251606 0.967830i \(-0.580959\pi\)
−0.251606 + 0.967830i \(0.580959\pi\)
\(38\) −8.43997 −1.36914
\(39\) −0.575497 −0.0921533
\(40\) 3.26458 0.516175
\(41\) 6.59524 1.03000 0.515002 0.857189i \(-0.327791\pi\)
0.515002 + 0.857189i \(0.327791\pi\)
\(42\) −0.0352980 −0.00544660
\(43\) −2.90818 −0.443494 −0.221747 0.975104i \(-0.571176\pi\)
−0.221747 + 0.975104i \(0.571176\pi\)
\(44\) 4.69415 0.707669
\(45\) 9.77175 1.45669
\(46\) −1.00000 −0.147442
\(47\) −8.57331 −1.25055 −0.625273 0.780406i \(-0.715012\pi\)
−0.625273 + 0.780406i \(0.715012\pi\)
\(48\) −0.0820624 −0.0118447
\(49\) −6.81498 −0.973569
\(50\) −5.65746 −0.800086
\(51\) −0.0321776 −0.00450576
\(52\) 7.01292 0.972517
\(53\) −10.7899 −1.48211 −0.741055 0.671444i \(-0.765674\pi\)
−0.741055 + 0.671444i \(0.765674\pi\)
\(54\) −0.491822 −0.0669285
\(55\) −15.3244 −2.06634
\(56\) 0.430136 0.0574793
\(57\) −0.692604 −0.0917377
\(58\) −0.423629 −0.0556252
\(59\) −1.19489 −0.155561 −0.0777806 0.996971i \(-0.524783\pi\)
−0.0777806 + 0.996971i \(0.524783\pi\)
\(60\) 0.267899 0.0345856
\(61\) 7.80797 0.999709 0.499854 0.866110i \(-0.333387\pi\)
0.499854 + 0.866110i \(0.333387\pi\)
\(62\) −8.04433 −1.02163
\(63\) 1.28751 0.162211
\(64\) 1.00000 0.125000
\(65\) −22.8942 −2.83968
\(66\) 0.385213 0.0474165
\(67\) −4.56048 −0.557152 −0.278576 0.960414i \(-0.589862\pi\)
−0.278576 + 0.960414i \(0.589862\pi\)
\(68\) 0.392111 0.0475504
\(69\) −0.0820624 −0.00987916
\(70\) −1.40421 −0.167835
\(71\) −2.37416 −0.281761 −0.140880 0.990027i \(-0.544993\pi\)
−0.140880 + 0.990027i \(0.544993\pi\)
\(72\) 2.99327 0.352760
\(73\) 10.1037 1.18255 0.591273 0.806472i \(-0.298626\pi\)
0.591273 + 0.806472i \(0.298626\pi\)
\(74\) 3.06092 0.355824
\(75\) −0.464265 −0.0536087
\(76\) 8.43997 0.968131
\(77\) −2.01912 −0.230100
\(78\) 0.575497 0.0651623
\(79\) 2.93297 0.329985 0.164993 0.986295i \(-0.447240\pi\)
0.164993 + 0.986295i \(0.447240\pi\)
\(80\) −3.26458 −0.364991
\(81\) 8.93944 0.993271
\(82\) −6.59524 −0.728323
\(83\) −5.21951 −0.572916 −0.286458 0.958093i \(-0.592478\pi\)
−0.286458 + 0.958093i \(0.592478\pi\)
\(84\) 0.0352980 0.00385133
\(85\) −1.28008 −0.138844
\(86\) 2.90818 0.313597
\(87\) −0.0347640 −0.00372709
\(88\) −4.69415 −0.500398
\(89\) 1.31862 0.139774 0.0698869 0.997555i \(-0.477736\pi\)
0.0698869 + 0.997555i \(0.477736\pi\)
\(90\) −9.77175 −1.03003
\(91\) −3.01651 −0.316216
\(92\) 1.00000 0.104257
\(93\) −0.660137 −0.0684530
\(94\) 8.57331 0.884269
\(95\) −27.5529 −2.82687
\(96\) 0.0820624 0.00837546
\(97\) −8.70998 −0.884365 −0.442182 0.896925i \(-0.645796\pi\)
−0.442182 + 0.896925i \(0.645796\pi\)
\(98\) 6.81498 0.688417
\(99\) −14.0508 −1.41216
\(100\) 5.65746 0.565746
\(101\) 14.4610 1.43892 0.719460 0.694534i \(-0.244389\pi\)
0.719460 + 0.694534i \(0.244389\pi\)
\(102\) 0.0321776 0.00318605
\(103\) 5.41642 0.533696 0.266848 0.963739i \(-0.414018\pi\)
0.266848 + 0.963739i \(0.414018\pi\)
\(104\) −7.01292 −0.687674
\(105\) −0.115233 −0.0112456
\(106\) 10.7899 1.04801
\(107\) 7.98644 0.772079 0.386039 0.922482i \(-0.373843\pi\)
0.386039 + 0.922482i \(0.373843\pi\)
\(108\) 0.491822 0.0473256
\(109\) −4.86800 −0.466269 −0.233135 0.972444i \(-0.574898\pi\)
−0.233135 + 0.972444i \(0.574898\pi\)
\(110\) 15.3244 1.46112
\(111\) 0.251186 0.0238416
\(112\) −0.430136 −0.0406440
\(113\) −10.6438 −1.00128 −0.500640 0.865656i \(-0.666902\pi\)
−0.500640 + 0.865656i \(0.666902\pi\)
\(114\) 0.692604 0.0648683
\(115\) −3.26458 −0.304423
\(116\) 0.423629 0.0393330
\(117\) −20.9915 −1.94067
\(118\) 1.19489 0.109998
\(119\) −0.168661 −0.0154611
\(120\) −0.267899 −0.0244557
\(121\) 11.0350 1.00318
\(122\) −7.80797 −0.706901
\(123\) −0.541222 −0.0488003
\(124\) 8.04433 0.722402
\(125\) −2.14634 −0.191975
\(126\) −1.28751 −0.114701
\(127\) −9.85596 −0.874575 −0.437287 0.899322i \(-0.644061\pi\)
−0.437287 + 0.899322i \(0.644061\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.238653 0.0210122
\(130\) 22.8942 2.00796
\(131\) −1.00000 −0.0873704
\(132\) −0.385213 −0.0335285
\(133\) −3.63033 −0.314790
\(134\) 4.56048 0.393966
\(135\) −1.60559 −0.138187
\(136\) −0.392111 −0.0336232
\(137\) 9.24072 0.789488 0.394744 0.918791i \(-0.370833\pi\)
0.394744 + 0.918791i \(0.370833\pi\)
\(138\) 0.0820624 0.00698562
\(139\) 8.94770 0.758934 0.379467 0.925205i \(-0.376107\pi\)
0.379467 + 0.925205i \(0.376107\pi\)
\(140\) 1.40421 0.118678
\(141\) 0.703546 0.0592493
\(142\) 2.37416 0.199235
\(143\) 32.9197 2.75288
\(144\) −2.99327 −0.249439
\(145\) −1.38297 −0.114849
\(146\) −10.1037 −0.836186
\(147\) 0.559254 0.0461265
\(148\) −3.06092 −0.251606
\(149\) −15.0343 −1.23166 −0.615830 0.787879i \(-0.711179\pi\)
−0.615830 + 0.787879i \(0.711179\pi\)
\(150\) 0.464265 0.0379071
\(151\) −6.88891 −0.560612 −0.280306 0.959911i \(-0.590436\pi\)
−0.280306 + 0.959911i \(0.590436\pi\)
\(152\) −8.43997 −0.684572
\(153\) −1.17369 −0.0948874
\(154\) 2.01912 0.162705
\(155\) −26.2613 −2.10936
\(156\) −0.575497 −0.0460767
\(157\) 1.52244 0.121504 0.0607519 0.998153i \(-0.480650\pi\)
0.0607519 + 0.998153i \(0.480650\pi\)
\(158\) −2.93297 −0.233335
\(159\) 0.885448 0.0702206
\(160\) 3.26458 0.258087
\(161\) −0.430136 −0.0338995
\(162\) −8.93944 −0.702349
\(163\) −9.15878 −0.717371 −0.358685 0.933459i \(-0.616775\pi\)
−0.358685 + 0.933459i \(0.616775\pi\)
\(164\) 6.59524 0.515002
\(165\) 1.25756 0.0979007
\(166\) 5.21951 0.405113
\(167\) 17.4206 1.34805 0.674023 0.738711i \(-0.264565\pi\)
0.674023 + 0.738711i \(0.264565\pi\)
\(168\) −0.0352980 −0.00272330
\(169\) 36.1811 2.78316
\(170\) 1.28008 0.0981774
\(171\) −25.2631 −1.93191
\(172\) −2.90818 −0.221747
\(173\) 20.3398 1.54641 0.773203 0.634159i \(-0.218654\pi\)
0.773203 + 0.634159i \(0.218654\pi\)
\(174\) 0.0347640 0.00263545
\(175\) −2.43348 −0.183954
\(176\) 4.69415 0.353835
\(177\) 0.0980554 0.00737030
\(178\) −1.31862 −0.0988349
\(179\) −16.5115 −1.23412 −0.617062 0.786914i \(-0.711677\pi\)
−0.617062 + 0.786914i \(0.711677\pi\)
\(180\) 9.77175 0.728343
\(181\) 16.1923 1.20357 0.601784 0.798659i \(-0.294457\pi\)
0.601784 + 0.798659i \(0.294457\pi\)
\(182\) 3.01651 0.223599
\(183\) −0.640741 −0.0473650
\(184\) −1.00000 −0.0737210
\(185\) 9.99260 0.734671
\(186\) 0.660137 0.0484036
\(187\) 1.84063 0.134600
\(188\) −8.57331 −0.625273
\(189\) −0.211550 −0.0153880
\(190\) 27.5529 1.99890
\(191\) 3.52330 0.254937 0.127469 0.991843i \(-0.459315\pi\)
0.127469 + 0.991843i \(0.459315\pi\)
\(192\) −0.0820624 −0.00592235
\(193\) 11.1232 0.800666 0.400333 0.916370i \(-0.368895\pi\)
0.400333 + 0.916370i \(0.368895\pi\)
\(194\) 8.70998 0.625340
\(195\) 1.87876 0.134541
\(196\) −6.81498 −0.486785
\(197\) −12.4197 −0.884869 −0.442435 0.896801i \(-0.645885\pi\)
−0.442435 + 0.896801i \(0.645885\pi\)
\(198\) 14.0508 0.998549
\(199\) 18.0071 1.27649 0.638244 0.769834i \(-0.279661\pi\)
0.638244 + 0.769834i \(0.279661\pi\)
\(200\) −5.65746 −0.400043
\(201\) 0.374244 0.0263972
\(202\) −14.4610 −1.01747
\(203\) −0.182218 −0.0127892
\(204\) −0.0321776 −0.00225288
\(205\) −21.5307 −1.50377
\(206\) −5.41642 −0.377380
\(207\) −2.99327 −0.208046
\(208\) 7.01292 0.486259
\(209\) 39.6184 2.74046
\(210\) 0.115233 0.00795184
\(211\) 11.1671 0.768774 0.384387 0.923172i \(-0.374413\pi\)
0.384387 + 0.923172i \(0.374413\pi\)
\(212\) −10.7899 −0.741055
\(213\) 0.194829 0.0133495
\(214\) −7.98644 −0.545942
\(215\) 9.49399 0.647484
\(216\) −0.491822 −0.0334642
\(217\) −3.46015 −0.234891
\(218\) 4.86800 0.329702
\(219\) −0.829132 −0.0560276
\(220\) −15.3244 −1.03317
\(221\) 2.74984 0.184974
\(222\) −0.251186 −0.0168585
\(223\) 3.20050 0.214322 0.107161 0.994242i \(-0.465824\pi\)
0.107161 + 0.994242i \(0.465824\pi\)
\(224\) 0.430136 0.0287397
\(225\) −16.9343 −1.12895
\(226\) 10.6438 0.708012
\(227\) 23.5821 1.56520 0.782598 0.622527i \(-0.213894\pi\)
0.782598 + 0.622527i \(0.213894\pi\)
\(228\) −0.692604 −0.0458688
\(229\) 12.0256 0.794673 0.397336 0.917673i \(-0.369935\pi\)
0.397336 + 0.917673i \(0.369935\pi\)
\(230\) 3.26458 0.215260
\(231\) 0.165694 0.0109019
\(232\) −0.423629 −0.0278126
\(233\) 23.4503 1.53628 0.768140 0.640282i \(-0.221183\pi\)
0.768140 + 0.640282i \(0.221183\pi\)
\(234\) 20.9915 1.37226
\(235\) 27.9882 1.82575
\(236\) −1.19489 −0.0777806
\(237\) −0.240687 −0.0156343
\(238\) 0.168661 0.0109327
\(239\) −26.3555 −1.70480 −0.852398 0.522894i \(-0.824852\pi\)
−0.852398 + 0.522894i \(0.824852\pi\)
\(240\) 0.267899 0.0172928
\(241\) 20.2788 1.30627 0.653135 0.757241i \(-0.273453\pi\)
0.653135 + 0.757241i \(0.273453\pi\)
\(242\) −11.0350 −0.709357
\(243\) −2.20906 −0.141711
\(244\) 7.80797 0.499854
\(245\) 22.2480 1.42138
\(246\) 0.541222 0.0345070
\(247\) 59.1888 3.76610
\(248\) −8.04433 −0.510815
\(249\) 0.428326 0.0271440
\(250\) 2.14634 0.135747
\(251\) 9.30325 0.587216 0.293608 0.955926i \(-0.405144\pi\)
0.293608 + 0.955926i \(0.405144\pi\)
\(252\) 1.28751 0.0811056
\(253\) 4.69415 0.295118
\(254\) 9.85596 0.618418
\(255\) 0.105046 0.00657825
\(256\) 1.00000 0.0625000
\(257\) 11.0778 0.691016 0.345508 0.938416i \(-0.387707\pi\)
0.345508 + 0.938416i \(0.387707\pi\)
\(258\) −0.238653 −0.0148579
\(259\) 1.31661 0.0818102
\(260\) −22.8942 −1.41984
\(261\) −1.26803 −0.0784893
\(262\) 1.00000 0.0617802
\(263\) 6.39419 0.394282 0.197141 0.980375i \(-0.436834\pi\)
0.197141 + 0.980375i \(0.436834\pi\)
\(264\) 0.385213 0.0237082
\(265\) 35.2245 2.16383
\(266\) 3.63033 0.222590
\(267\) −0.108209 −0.00662231
\(268\) −4.56048 −0.278576
\(269\) −3.13554 −0.191177 −0.0955885 0.995421i \(-0.530473\pi\)
−0.0955885 + 0.995421i \(0.530473\pi\)
\(270\) 1.60559 0.0977131
\(271\) −4.59049 −0.278852 −0.139426 0.990232i \(-0.544526\pi\)
−0.139426 + 0.990232i \(0.544526\pi\)
\(272\) 0.392111 0.0237752
\(273\) 0.247542 0.0149819
\(274\) −9.24072 −0.558252
\(275\) 26.5570 1.60145
\(276\) −0.0820624 −0.00493958
\(277\) 10.2904 0.618291 0.309146 0.951015i \(-0.399957\pi\)
0.309146 + 0.951015i \(0.399957\pi\)
\(278\) −8.94770 −0.536648
\(279\) −24.0788 −1.44156
\(280\) −1.40421 −0.0839177
\(281\) −3.94747 −0.235487 −0.117743 0.993044i \(-0.537566\pi\)
−0.117743 + 0.993044i \(0.537566\pi\)
\(282\) −0.703546 −0.0418956
\(283\) −32.5566 −1.93529 −0.967643 0.252322i \(-0.918806\pi\)
−0.967643 + 0.252322i \(0.918806\pi\)
\(284\) −2.37416 −0.140880
\(285\) 2.26106 0.133934
\(286\) −32.9197 −1.94658
\(287\) −2.83685 −0.167454
\(288\) 2.99327 0.176380
\(289\) −16.8462 −0.990956
\(290\) 1.38297 0.0812107
\(291\) 0.714763 0.0419001
\(292\) 10.1037 0.591273
\(293\) −32.9645 −1.92580 −0.962902 0.269851i \(-0.913025\pi\)
−0.962902 + 0.269851i \(0.913025\pi\)
\(294\) −0.559254 −0.0326164
\(295\) 3.90080 0.227114
\(296\) 3.06092 0.177912
\(297\) 2.30868 0.133963
\(298\) 15.0343 0.870915
\(299\) 7.01292 0.405568
\(300\) −0.464265 −0.0268044
\(301\) 1.25091 0.0721015
\(302\) 6.88891 0.396412
\(303\) −1.18670 −0.0681742
\(304\) 8.43997 0.484065
\(305\) −25.4897 −1.45954
\(306\) 1.17369 0.0670955
\(307\) −25.9169 −1.47916 −0.739578 0.673070i \(-0.764975\pi\)
−0.739578 + 0.673070i \(0.764975\pi\)
\(308\) −2.01912 −0.115050
\(309\) −0.444485 −0.0252859
\(310\) 26.2613 1.49154
\(311\) −3.83774 −0.217618 −0.108809 0.994063i \(-0.534704\pi\)
−0.108809 + 0.994063i \(0.534704\pi\)
\(312\) 0.575497 0.0325811
\(313\) −6.24693 −0.353097 −0.176549 0.984292i \(-0.556493\pi\)
−0.176549 + 0.984292i \(0.556493\pi\)
\(314\) −1.52244 −0.0859162
\(315\) −4.20318 −0.236822
\(316\) 2.93297 0.164993
\(317\) −25.3907 −1.42609 −0.713043 0.701120i \(-0.752684\pi\)
−0.713043 + 0.701120i \(0.752684\pi\)
\(318\) −0.885448 −0.0496534
\(319\) 1.98858 0.111339
\(320\) −3.26458 −0.182495
\(321\) −0.655387 −0.0365801
\(322\) 0.430136 0.0239705
\(323\) 3.30940 0.184140
\(324\) 8.93944 0.496635
\(325\) 39.6754 2.20079
\(326\) 9.15878 0.507258
\(327\) 0.399480 0.0220913
\(328\) −6.59524 −0.364161
\(329\) 3.68769 0.203309
\(330\) −1.25756 −0.0692263
\(331\) −7.53905 −0.414384 −0.207192 0.978300i \(-0.566432\pi\)
−0.207192 + 0.978300i \(0.566432\pi\)
\(332\) −5.21951 −0.286458
\(333\) 9.16214 0.502082
\(334\) −17.4206 −0.953212
\(335\) 14.8880 0.813421
\(336\) 0.0352980 0.00192566
\(337\) 11.9190 0.649271 0.324636 0.945839i \(-0.394758\pi\)
0.324636 + 0.945839i \(0.394758\pi\)
\(338\) −36.1811 −1.96799
\(339\) 0.873452 0.0474394
\(340\) −1.28008 −0.0694219
\(341\) 37.7613 2.04489
\(342\) 25.2631 1.36607
\(343\) 5.94232 0.320855
\(344\) 2.90818 0.156799
\(345\) 0.267899 0.0144232
\(346\) −20.3398 −1.09347
\(347\) 7.36904 0.395591 0.197795 0.980243i \(-0.436622\pi\)
0.197795 + 0.980243i \(0.436622\pi\)
\(348\) −0.0347640 −0.00186355
\(349\) −21.0168 −1.12501 −0.562503 0.826796i \(-0.690161\pi\)
−0.562503 + 0.826796i \(0.690161\pi\)
\(350\) 2.43348 0.130075
\(351\) 3.44911 0.184100
\(352\) −4.69415 −0.250199
\(353\) 15.1586 0.806812 0.403406 0.915021i \(-0.367826\pi\)
0.403406 + 0.915021i \(0.367826\pi\)
\(354\) −0.0980554 −0.00521159
\(355\) 7.75062 0.411360
\(356\) 1.31862 0.0698869
\(357\) 0.0138407 0.000732529 0
\(358\) 16.5115 0.872658
\(359\) −2.44671 −0.129132 −0.0645662 0.997913i \(-0.520566\pi\)
−0.0645662 + 0.997913i \(0.520566\pi\)
\(360\) −9.77175 −0.515016
\(361\) 52.2330 2.74911
\(362\) −16.1923 −0.851051
\(363\) −0.905560 −0.0475296
\(364\) −3.01651 −0.158108
\(365\) −32.9842 −1.72647
\(366\) 0.640741 0.0334921
\(367\) −24.1705 −1.26169 −0.630844 0.775910i \(-0.717291\pi\)
−0.630844 + 0.775910i \(0.717291\pi\)
\(368\) 1.00000 0.0521286
\(369\) −19.7413 −1.02769
\(370\) −9.99260 −0.519491
\(371\) 4.64113 0.240956
\(372\) −0.660137 −0.0342265
\(373\) −26.0960 −1.35120 −0.675599 0.737269i \(-0.736115\pi\)
−0.675599 + 0.737269i \(0.736115\pi\)
\(374\) −1.84063 −0.0951765
\(375\) 0.176134 0.00909553
\(376\) 8.57331 0.442135
\(377\) 2.97088 0.153008
\(378\) 0.211550 0.0108810
\(379\) −14.3027 −0.734682 −0.367341 0.930086i \(-0.619732\pi\)
−0.367341 + 0.930086i \(0.619732\pi\)
\(380\) −27.5529 −1.41344
\(381\) 0.808804 0.0414363
\(382\) −3.52330 −0.180268
\(383\) 24.4379 1.24872 0.624360 0.781136i \(-0.285360\pi\)
0.624360 + 0.781136i \(0.285360\pi\)
\(384\) 0.0820624 0.00418773
\(385\) 6.59158 0.335938
\(386\) −11.1232 −0.566156
\(387\) 8.70496 0.442498
\(388\) −8.70998 −0.442182
\(389\) −27.4047 −1.38947 −0.694736 0.719265i \(-0.744479\pi\)
−0.694736 + 0.719265i \(0.744479\pi\)
\(390\) −1.87876 −0.0951345
\(391\) 0.392111 0.0198299
\(392\) 6.81498 0.344209
\(393\) 0.0820624 0.00413950
\(394\) 12.4197 0.625697
\(395\) −9.57491 −0.481766
\(396\) −14.0508 −0.706081
\(397\) 31.6805 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(398\) −18.0071 −0.902614
\(399\) 0.297914 0.0149144
\(400\) 5.65746 0.282873
\(401\) 7.56755 0.377905 0.188953 0.981986i \(-0.439491\pi\)
0.188953 + 0.981986i \(0.439491\pi\)
\(402\) −0.374244 −0.0186656
\(403\) 56.4143 2.81019
\(404\) 14.4610 0.719460
\(405\) −29.1835 −1.45014
\(406\) 0.182218 0.00904333
\(407\) −14.3684 −0.712215
\(408\) 0.0321776 0.00159303
\(409\) 5.13400 0.253860 0.126930 0.991912i \(-0.459488\pi\)
0.126930 + 0.991912i \(0.459488\pi\)
\(410\) 21.5307 1.06332
\(411\) −0.758316 −0.0374050
\(412\) 5.41642 0.266848
\(413\) 0.513964 0.0252905
\(414\) 2.99327 0.147111
\(415\) 17.0395 0.836436
\(416\) −7.01292 −0.343837
\(417\) −0.734270 −0.0359574
\(418\) −39.6184 −1.93780
\(419\) 8.27791 0.404402 0.202201 0.979344i \(-0.435191\pi\)
0.202201 + 0.979344i \(0.435191\pi\)
\(420\) −0.115233 −0.00562280
\(421\) −5.80953 −0.283139 −0.141570 0.989928i \(-0.545215\pi\)
−0.141570 + 0.989928i \(0.545215\pi\)
\(422\) −11.1671 −0.543605
\(423\) 25.6622 1.24774
\(424\) 10.7899 0.524005
\(425\) 2.21835 0.107606
\(426\) −0.194829 −0.00943950
\(427\) −3.35849 −0.162529
\(428\) 7.98644 0.386039
\(429\) −2.70147 −0.130428
\(430\) −9.49399 −0.457841
\(431\) −5.55309 −0.267483 −0.133741 0.991016i \(-0.542699\pi\)
−0.133741 + 0.991016i \(0.542699\pi\)
\(432\) 0.491822 0.0236628
\(433\) −33.3320 −1.60183 −0.800916 0.598776i \(-0.795654\pi\)
−0.800916 + 0.598776i \(0.795654\pi\)
\(434\) 3.46015 0.166093
\(435\) 0.113490 0.00544142
\(436\) −4.86800 −0.233135
\(437\) 8.43997 0.403738
\(438\) 0.829132 0.0396175
\(439\) −19.1564 −0.914287 −0.457144 0.889393i \(-0.651127\pi\)
−0.457144 + 0.889393i \(0.651127\pi\)
\(440\) 15.3244 0.730562
\(441\) 20.3991 0.971384
\(442\) −2.74984 −0.130797
\(443\) 16.5825 0.787856 0.393928 0.919141i \(-0.371116\pi\)
0.393928 + 0.919141i \(0.371116\pi\)
\(444\) 0.251186 0.0119208
\(445\) −4.30475 −0.204064
\(446\) −3.20050 −0.151548
\(447\) 1.23375 0.0583545
\(448\) −0.430136 −0.0203220
\(449\) −25.5612 −1.20631 −0.603153 0.797626i \(-0.706089\pi\)
−0.603153 + 0.797626i \(0.706089\pi\)
\(450\) 16.9343 0.798290
\(451\) 30.9590 1.45780
\(452\) −10.6438 −0.500640
\(453\) 0.565321 0.0265611
\(454\) −23.5821 −1.10676
\(455\) 9.84763 0.461664
\(456\) 0.692604 0.0324342
\(457\) 37.4064 1.74980 0.874898 0.484307i \(-0.160928\pi\)
0.874898 + 0.484307i \(0.160928\pi\)
\(458\) −12.0256 −0.561918
\(459\) 0.192849 0.00900141
\(460\) −3.26458 −0.152212
\(461\) −14.4246 −0.671823 −0.335911 0.941894i \(-0.609044\pi\)
−0.335911 + 0.941894i \(0.609044\pi\)
\(462\) −0.165694 −0.00770878
\(463\) 2.35074 0.109248 0.0546241 0.998507i \(-0.482604\pi\)
0.0546241 + 0.998507i \(0.482604\pi\)
\(464\) 0.423629 0.0196665
\(465\) 2.15507 0.0999389
\(466\) −23.4503 −1.08631
\(467\) −18.1238 −0.838671 −0.419335 0.907831i \(-0.637737\pi\)
−0.419335 + 0.907831i \(0.637737\pi\)
\(468\) −20.9915 −0.970334
\(469\) 1.96163 0.0905795
\(470\) −27.9882 −1.29100
\(471\) −0.124935 −0.00575670
\(472\) 1.19489 0.0549992
\(473\) −13.6514 −0.627694
\(474\) 0.240687 0.0110551
\(475\) 47.7488 2.19087
\(476\) −0.168661 −0.00773056
\(477\) 32.2971 1.47878
\(478\) 26.3555 1.20547
\(479\) 12.6937 0.579988 0.289994 0.957028i \(-0.406347\pi\)
0.289994 + 0.957028i \(0.406347\pi\)
\(480\) −0.267899 −0.0122279
\(481\) −21.4660 −0.978764
\(482\) −20.2788 −0.923672
\(483\) 0.0352980 0.00160611
\(484\) 11.0350 0.501591
\(485\) 28.4344 1.29114
\(486\) 2.20906 0.100205
\(487\) −10.0632 −0.456008 −0.228004 0.973660i \(-0.573220\pi\)
−0.228004 + 0.973660i \(0.573220\pi\)
\(488\) −7.80797 −0.353450
\(489\) 0.751591 0.0339881
\(490\) −22.2480 −1.00506
\(491\) −1.30028 −0.0586808 −0.0293404 0.999569i \(-0.509341\pi\)
−0.0293404 + 0.999569i \(0.509341\pi\)
\(492\) −0.541222 −0.0244002
\(493\) 0.166109 0.00748120
\(494\) −59.1888 −2.66303
\(495\) 45.8700 2.06170
\(496\) 8.04433 0.361201
\(497\) 1.02121 0.0458075
\(498\) −0.428326 −0.0191937
\(499\) −27.0515 −1.21099 −0.605496 0.795848i \(-0.707025\pi\)
−0.605496 + 0.795848i \(0.707025\pi\)
\(500\) −2.14634 −0.0959874
\(501\) −1.42958 −0.0638687
\(502\) −9.30325 −0.415224
\(503\) −27.1135 −1.20893 −0.604465 0.796632i \(-0.706613\pi\)
−0.604465 + 0.796632i \(0.706613\pi\)
\(504\) −1.28751 −0.0573503
\(505\) −47.2089 −2.10077
\(506\) −4.69415 −0.208680
\(507\) −2.96911 −0.131863
\(508\) −9.85596 −0.437287
\(509\) 9.56850 0.424116 0.212058 0.977257i \(-0.431983\pi\)
0.212058 + 0.977257i \(0.431983\pi\)
\(510\) −0.105046 −0.00465152
\(511\) −4.34595 −0.192254
\(512\) −1.00000 −0.0441942
\(513\) 4.15096 0.183269
\(514\) −11.0778 −0.488622
\(515\) −17.6823 −0.779176
\(516\) 0.238653 0.0105061
\(517\) −40.2444 −1.76994
\(518\) −1.31661 −0.0578486
\(519\) −1.66913 −0.0732668
\(520\) 22.8942 1.00398
\(521\) 20.1657 0.883476 0.441738 0.897144i \(-0.354362\pi\)
0.441738 + 0.897144i \(0.354362\pi\)
\(522\) 1.26803 0.0555003
\(523\) 28.4827 1.24546 0.622730 0.782437i \(-0.286023\pi\)
0.622730 + 0.782437i \(0.286023\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0.199697 0.00871550
\(526\) −6.39419 −0.278800
\(527\) 3.15427 0.137402
\(528\) −0.385213 −0.0167642
\(529\) 1.00000 0.0434783
\(530\) −35.2245 −1.53006
\(531\) 3.57662 0.155212
\(532\) −3.63033 −0.157395
\(533\) 46.2519 2.00339
\(534\) 0.108209 0.00468268
\(535\) −26.0724 −1.12721
\(536\) 4.56048 0.196983
\(537\) 1.35497 0.0584713
\(538\) 3.13554 0.135183
\(539\) −31.9905 −1.37793
\(540\) −1.60559 −0.0690936
\(541\) 28.2408 1.21417 0.607084 0.794638i \(-0.292339\pi\)
0.607084 + 0.794638i \(0.292339\pi\)
\(542\) 4.59049 0.197178
\(543\) −1.32878 −0.0570235
\(544\) −0.392111 −0.0168116
\(545\) 15.8919 0.680736
\(546\) −0.247542 −0.0105938
\(547\) −37.5444 −1.60528 −0.802642 0.596461i \(-0.796573\pi\)
−0.802642 + 0.596461i \(0.796573\pi\)
\(548\) 9.24072 0.394744
\(549\) −23.3713 −0.997464
\(550\) −26.5570 −1.13239
\(551\) 3.57541 0.152318
\(552\) 0.0820624 0.00349281
\(553\) −1.26158 −0.0536477
\(554\) −10.2904 −0.437198
\(555\) −0.820017 −0.0348078
\(556\) 8.94770 0.379467
\(557\) 10.6696 0.452085 0.226042 0.974117i \(-0.427421\pi\)
0.226042 + 0.974117i \(0.427421\pi\)
\(558\) 24.0788 1.01934
\(559\) −20.3949 −0.862611
\(560\) 1.40421 0.0593388
\(561\) −0.151046 −0.00637718
\(562\) 3.94747 0.166514
\(563\) −16.5551 −0.697713 −0.348857 0.937176i \(-0.613430\pi\)
−0.348857 + 0.937176i \(0.613430\pi\)
\(564\) 0.703546 0.0296246
\(565\) 34.7474 1.46183
\(566\) 32.5566 1.36845
\(567\) −3.84517 −0.161482
\(568\) 2.37416 0.0996174
\(569\) −21.4970 −0.901199 −0.450600 0.892726i \(-0.648790\pi\)
−0.450600 + 0.892726i \(0.648790\pi\)
\(570\) −2.26106 −0.0947054
\(571\) 14.8688 0.622241 0.311120 0.950371i \(-0.399296\pi\)
0.311120 + 0.950371i \(0.399296\pi\)
\(572\) 32.9197 1.37644
\(573\) −0.289131 −0.0120786
\(574\) 2.83685 0.118408
\(575\) 5.65746 0.235933
\(576\) −2.99327 −0.124719
\(577\) −9.89497 −0.411933 −0.205966 0.978559i \(-0.566034\pi\)
−0.205966 + 0.978559i \(0.566034\pi\)
\(578\) 16.8462 0.700712
\(579\) −0.912797 −0.0379346
\(580\) −1.38297 −0.0574247
\(581\) 2.24510 0.0931424
\(582\) −0.714763 −0.0296279
\(583\) −50.6495 −2.09769
\(584\) −10.1037 −0.418093
\(585\) 68.5285 2.83331
\(586\) 32.9645 1.36175
\(587\) 20.1117 0.830099 0.415049 0.909799i \(-0.363764\pi\)
0.415049 + 0.909799i \(0.363764\pi\)
\(588\) 0.559254 0.0230632
\(589\) 67.8939 2.79752
\(590\) −3.90080 −0.160594
\(591\) 1.01919 0.0419240
\(592\) −3.06092 −0.125803
\(593\) −5.05075 −0.207409 −0.103705 0.994608i \(-0.533070\pi\)
−0.103705 + 0.994608i \(0.533070\pi\)
\(594\) −2.30868 −0.0947265
\(595\) 0.550607 0.0225727
\(596\) −15.0343 −0.615830
\(597\) −1.47770 −0.0604784
\(598\) −7.01292 −0.286780
\(599\) 15.7237 0.642453 0.321227 0.947002i \(-0.395905\pi\)
0.321227 + 0.947002i \(0.395905\pi\)
\(600\) 0.464265 0.0189536
\(601\) 25.1582 1.02622 0.513112 0.858321i \(-0.328492\pi\)
0.513112 + 0.858321i \(0.328492\pi\)
\(602\) −1.25091 −0.0509834
\(603\) 13.6507 0.555901
\(604\) −6.88891 −0.280306
\(605\) −36.0246 −1.46461
\(606\) 1.18670 0.0482065
\(607\) 49.1008 1.99294 0.996470 0.0839514i \(-0.0267541\pi\)
0.996470 + 0.0839514i \(0.0267541\pi\)
\(608\) −8.43997 −0.342286
\(609\) 0.0149533 0.000605936 0
\(610\) 25.4897 1.03205
\(611\) −60.1239 −2.43235
\(612\) −1.17369 −0.0474437
\(613\) 27.2840 1.10199 0.550996 0.834508i \(-0.314248\pi\)
0.550996 + 0.834508i \(0.314248\pi\)
\(614\) 25.9169 1.04592
\(615\) 1.76686 0.0712467
\(616\) 2.01912 0.0813527
\(617\) 20.0601 0.807589 0.403794 0.914850i \(-0.367691\pi\)
0.403794 + 0.914850i \(0.367691\pi\)
\(618\) 0.444485 0.0178798
\(619\) 27.2731 1.09620 0.548099 0.836414i \(-0.315352\pi\)
0.548099 + 0.836414i \(0.315352\pi\)
\(620\) −26.2613 −1.05468
\(621\) 0.491822 0.0197361
\(622\) 3.83774 0.153879
\(623\) −0.567187 −0.0227239
\(624\) −0.575497 −0.0230383
\(625\) −21.2804 −0.851217
\(626\) 6.24693 0.249677
\(627\) −3.25119 −0.129840
\(628\) 1.52244 0.0607519
\(629\) −1.20022 −0.0478559
\(630\) 4.20318 0.167459
\(631\) −12.0792 −0.480867 −0.240434 0.970666i \(-0.577290\pi\)
−0.240434 + 0.970666i \(0.577290\pi\)
\(632\) −2.93297 −0.116667
\(633\) −0.916398 −0.0364236
\(634\) 25.3907 1.00840
\(635\) 32.1755 1.27685
\(636\) 0.885448 0.0351103
\(637\) −47.7929 −1.89363
\(638\) −1.98858 −0.0787285
\(639\) 7.10648 0.281128
\(640\) 3.26458 0.129044
\(641\) 9.73303 0.384432 0.192216 0.981353i \(-0.438433\pi\)
0.192216 + 0.981353i \(0.438433\pi\)
\(642\) 0.655387 0.0258661
\(643\) 42.3437 1.66987 0.834935 0.550348i \(-0.185505\pi\)
0.834935 + 0.550348i \(0.185505\pi\)
\(644\) −0.430136 −0.0169497
\(645\) −0.779100 −0.0306770
\(646\) −3.30940 −0.130207
\(647\) −9.99405 −0.392907 −0.196453 0.980513i \(-0.562942\pi\)
−0.196453 + 0.980513i \(0.562942\pi\)
\(648\) −8.93944 −0.351174
\(649\) −5.60898 −0.220172
\(650\) −39.6754 −1.55620
\(651\) 0.283949 0.0111288
\(652\) −9.15878 −0.358685
\(653\) −2.21195 −0.0865604 −0.0432802 0.999063i \(-0.513781\pi\)
−0.0432802 + 0.999063i \(0.513781\pi\)
\(654\) −0.399480 −0.0156209
\(655\) 3.26458 0.127558
\(656\) 6.59524 0.257501
\(657\) −30.2430 −1.17989
\(658\) −3.68769 −0.143761
\(659\) 47.8327 1.86330 0.931648 0.363362i \(-0.118371\pi\)
0.931648 + 0.363362i \(0.118371\pi\)
\(660\) 1.25756 0.0489504
\(661\) −33.3845 −1.29851 −0.649254 0.760572i \(-0.724919\pi\)
−0.649254 + 0.760572i \(0.724919\pi\)
\(662\) 7.53905 0.293014
\(663\) −0.225659 −0.00876386
\(664\) 5.21951 0.202556
\(665\) 11.8515 0.459582
\(666\) −9.16214 −0.355026
\(667\) 0.423629 0.0164030
\(668\) 17.4206 0.674023
\(669\) −0.262641 −0.0101543
\(670\) −14.8880 −0.575175
\(671\) 36.6518 1.41493
\(672\) −0.0352980 −0.00136165
\(673\) 26.7251 1.03018 0.515088 0.857137i \(-0.327759\pi\)
0.515088 + 0.857137i \(0.327759\pi\)
\(674\) −11.9190 −0.459104
\(675\) 2.78247 0.107097
\(676\) 36.1811 1.39158
\(677\) −7.53143 −0.289457 −0.144728 0.989471i \(-0.546231\pi\)
−0.144728 + 0.989471i \(0.546231\pi\)
\(678\) −0.873452 −0.0335447
\(679\) 3.74648 0.143777
\(680\) 1.28008 0.0490887
\(681\) −1.93520 −0.0741571
\(682\) −37.7613 −1.44595
\(683\) 49.0461 1.87670 0.938348 0.345693i \(-0.112356\pi\)
0.938348 + 0.345693i \(0.112356\pi\)
\(684\) −25.2631 −0.965957
\(685\) −30.1670 −1.15262
\(686\) −5.94232 −0.226879
\(687\) −0.986848 −0.0376506
\(688\) −2.90818 −0.110873
\(689\) −75.6689 −2.88276
\(690\) −0.267899 −0.0101987
\(691\) 44.6339 1.69795 0.848977 0.528430i \(-0.177219\pi\)
0.848977 + 0.528430i \(0.177219\pi\)
\(692\) 20.3398 0.773203
\(693\) 6.04377 0.229584
\(694\) −7.36904 −0.279725
\(695\) −29.2105 −1.10802
\(696\) 0.0347640 0.00131773
\(697\) 2.58607 0.0979543
\(698\) 21.0168 0.795499
\(699\) −1.92439 −0.0727870
\(700\) −2.43348 −0.0919768
\(701\) 24.2366 0.915404 0.457702 0.889106i \(-0.348673\pi\)
0.457702 + 0.889106i \(0.348673\pi\)
\(702\) −3.44911 −0.130178
\(703\) −25.8340 −0.974349
\(704\) 4.69415 0.176917
\(705\) −2.29678 −0.0865018
\(706\) −15.1586 −0.570502
\(707\) −6.22018 −0.233934
\(708\) 0.0980554 0.00368515
\(709\) −5.50590 −0.206778 −0.103389 0.994641i \(-0.532969\pi\)
−0.103389 + 0.994641i \(0.532969\pi\)
\(710\) −7.75062 −0.290876
\(711\) −8.77916 −0.329244
\(712\) −1.31862 −0.0494175
\(713\) 8.04433 0.301262
\(714\) −0.0138407 −0.000517976 0
\(715\) −107.469 −4.01911
\(716\) −16.5115 −0.617062
\(717\) 2.16280 0.0807711
\(718\) 2.44671 0.0913104
\(719\) 45.7831 1.70742 0.853711 0.520747i \(-0.174347\pi\)
0.853711 + 0.520747i \(0.174347\pi\)
\(720\) 9.77175 0.364172
\(721\) −2.32980 −0.0867662
\(722\) −52.2330 −1.94391
\(723\) −1.66412 −0.0618895
\(724\) 16.1923 0.601784
\(725\) 2.39667 0.0890099
\(726\) 0.905560 0.0336085
\(727\) 0.748945 0.0277768 0.0138884 0.999904i \(-0.495579\pi\)
0.0138884 + 0.999904i \(0.495579\pi\)
\(728\) 3.01651 0.111799
\(729\) −26.6370 −0.986557
\(730\) 32.9842 1.22080
\(731\) −1.14033 −0.0421766
\(732\) −0.640741 −0.0236825
\(733\) −3.00665 −0.111053 −0.0555266 0.998457i \(-0.517684\pi\)
−0.0555266 + 0.998457i \(0.517684\pi\)
\(734\) 24.1705 0.892148
\(735\) −1.82573 −0.0673430
\(736\) −1.00000 −0.0368605
\(737\) −21.4076 −0.788558
\(738\) 19.7413 0.726688
\(739\) −6.88295 −0.253193 −0.126597 0.991954i \(-0.540405\pi\)
−0.126597 + 0.991954i \(0.540405\pi\)
\(740\) 9.99260 0.367335
\(741\) −4.85718 −0.178433
\(742\) −4.64113 −0.170381
\(743\) −37.5100 −1.37611 −0.688054 0.725660i \(-0.741535\pi\)
−0.688054 + 0.725660i \(0.741535\pi\)
\(744\) 0.660137 0.0242018
\(745\) 49.0807 1.79818
\(746\) 26.0960 0.955441
\(747\) 15.6234 0.571630
\(748\) 1.84063 0.0673000
\(749\) −3.43526 −0.125522
\(750\) −0.176134 −0.00643151
\(751\) −19.5694 −0.714096 −0.357048 0.934086i \(-0.616217\pi\)
−0.357048 + 0.934086i \(0.616217\pi\)
\(752\) −8.57331 −0.312636
\(753\) −0.763447 −0.0278216
\(754\) −2.97088 −0.108193
\(755\) 22.4894 0.818473
\(756\) −0.211550 −0.00769401
\(757\) 44.6420 1.62254 0.811271 0.584670i \(-0.198776\pi\)
0.811271 + 0.584670i \(0.198776\pi\)
\(758\) 14.3027 0.519499
\(759\) −0.385213 −0.0139823
\(760\) 27.5529 0.999450
\(761\) −13.3607 −0.484327 −0.242163 0.970236i \(-0.577857\pi\)
−0.242163 + 0.970236i \(0.577857\pi\)
\(762\) −0.808804 −0.0292999
\(763\) 2.09390 0.0758043
\(764\) 3.52330 0.127469
\(765\) 3.83161 0.138532
\(766\) −24.4379 −0.882979
\(767\) −8.37966 −0.302572
\(768\) −0.0820624 −0.00296117
\(769\) 19.8318 0.715152 0.357576 0.933884i \(-0.383603\pi\)
0.357576 + 0.933884i \(0.383603\pi\)
\(770\) −6.59158 −0.237544
\(771\) −0.909074 −0.0327395
\(772\) 11.1232 0.400333
\(773\) 13.0489 0.469338 0.234669 0.972075i \(-0.424599\pi\)
0.234669 + 0.972075i \(0.424599\pi\)
\(774\) −8.70496 −0.312893
\(775\) 45.5105 1.63479
\(776\) 8.70998 0.312670
\(777\) −0.108044 −0.00387607
\(778\) 27.4047 0.982505
\(779\) 55.6636 1.99436
\(780\) 1.87876 0.0672703
\(781\) −11.1446 −0.398787
\(782\) −0.392111 −0.0140219
\(783\) 0.208350 0.00744582
\(784\) −6.81498 −0.243392
\(785\) −4.97012 −0.177391
\(786\) −0.0820624 −0.00292707
\(787\) −42.2986 −1.50778 −0.753892 0.656999i \(-0.771826\pi\)
−0.753892 + 0.656999i \(0.771826\pi\)
\(788\) −12.4197 −0.442435
\(789\) −0.524722 −0.0186806
\(790\) 9.57491 0.340660
\(791\) 4.57826 0.162784
\(792\) 14.0508 0.499274
\(793\) 54.7567 1.94447
\(794\) −31.6805 −1.12430
\(795\) −2.89061 −0.102519
\(796\) 18.0071 0.638244
\(797\) 21.2221 0.751725 0.375862 0.926676i \(-0.377347\pi\)
0.375862 + 0.926676i \(0.377347\pi\)
\(798\) −0.297914 −0.0105460
\(799\) −3.36169 −0.118928
\(800\) −5.65746 −0.200022
\(801\) −3.94699 −0.139460
\(802\) −7.56755 −0.267219
\(803\) 47.4281 1.67370
\(804\) 0.374244 0.0131986
\(805\) 1.40421 0.0494920
\(806\) −56.4143 −1.98711
\(807\) 0.257310 0.00905773
\(808\) −14.4610 −0.508735
\(809\) 25.8723 0.909620 0.454810 0.890588i \(-0.349707\pi\)
0.454810 + 0.890588i \(0.349707\pi\)
\(810\) 29.1835 1.02540
\(811\) 15.1785 0.532989 0.266494 0.963836i \(-0.414135\pi\)
0.266494 + 0.963836i \(0.414135\pi\)
\(812\) −0.182218 −0.00639460
\(813\) 0.376706 0.0132117
\(814\) 14.3684 0.503612
\(815\) 29.8995 1.04734
\(816\) −0.0321776 −0.00112644
\(817\) −24.5450 −0.858720
\(818\) −5.13400 −0.179506
\(819\) 9.02922 0.315506
\(820\) −21.5307 −0.751884
\(821\) 11.3213 0.395115 0.197557 0.980291i \(-0.436699\pi\)
0.197557 + 0.980291i \(0.436699\pi\)
\(822\) 0.758316 0.0264493
\(823\) −26.6435 −0.928736 −0.464368 0.885642i \(-0.653718\pi\)
−0.464368 + 0.885642i \(0.653718\pi\)
\(824\) −5.41642 −0.188690
\(825\) −2.17933 −0.0758745
\(826\) −0.513964 −0.0178831
\(827\) 21.0126 0.730681 0.365341 0.930874i \(-0.380953\pi\)
0.365341 + 0.930874i \(0.380953\pi\)
\(828\) −2.99327 −0.104023
\(829\) 22.5989 0.784891 0.392446 0.919775i \(-0.371629\pi\)
0.392446 + 0.919775i \(0.371629\pi\)
\(830\) −17.0395 −0.591450
\(831\) −0.844457 −0.0292939
\(832\) 7.01292 0.243129
\(833\) −2.67223 −0.0925873
\(834\) 0.734270 0.0254257
\(835\) −56.8709 −1.96810
\(836\) 39.6184 1.37023
\(837\) 3.95638 0.136752
\(838\) −8.27791 −0.285956
\(839\) −19.1141 −0.659892 −0.329946 0.944000i \(-0.607030\pi\)
−0.329946 + 0.944000i \(0.607030\pi\)
\(840\) 0.115233 0.00397592
\(841\) −28.8205 −0.993812
\(842\) 5.80953 0.200210
\(843\) 0.323939 0.0111571
\(844\) 11.1671 0.384387
\(845\) −118.116 −4.06331
\(846\) −25.6622 −0.882284
\(847\) −4.74655 −0.163094
\(848\) −10.7899 −0.370528
\(849\) 2.67167 0.0916915
\(850\) −2.21835 −0.0760889
\(851\) −3.06092 −0.104927
\(852\) 0.194829 0.00667474
\(853\) −7.28828 −0.249546 −0.124773 0.992185i \(-0.539820\pi\)
−0.124773 + 0.992185i \(0.539820\pi\)
\(854\) 3.35849 0.114925
\(855\) 82.4732 2.82052
\(856\) −7.98644 −0.272971
\(857\) −21.7676 −0.743568 −0.371784 0.928319i \(-0.621254\pi\)
−0.371784 + 0.928319i \(0.621254\pi\)
\(858\) 2.70147 0.0922266
\(859\) 39.7270 1.35547 0.677734 0.735307i \(-0.262962\pi\)
0.677734 + 0.735307i \(0.262962\pi\)
\(860\) 9.49399 0.323742
\(861\) 0.232799 0.00793376
\(862\) 5.55309 0.189139
\(863\) 23.1937 0.789522 0.394761 0.918784i \(-0.370827\pi\)
0.394761 + 0.918784i \(0.370827\pi\)
\(864\) −0.491822 −0.0167321
\(865\) −66.4008 −2.25769
\(866\) 33.3320 1.13267
\(867\) 1.38244 0.0469503
\(868\) −3.46015 −0.117445
\(869\) 13.7678 0.467041
\(870\) −0.113490 −0.00384766
\(871\) −31.9823 −1.08368
\(872\) 4.86800 0.164851
\(873\) 26.0713 0.882380
\(874\) −8.43997 −0.285486
\(875\) 0.923219 0.0312105
\(876\) −0.829132 −0.0280138
\(877\) −35.2424 −1.19005 −0.595025 0.803707i \(-0.702858\pi\)
−0.595025 + 0.803707i \(0.702858\pi\)
\(878\) 19.1564 0.646499
\(879\) 2.70514 0.0912422
\(880\) −15.3244 −0.516586
\(881\) −0.0754909 −0.00254335 −0.00127168 0.999999i \(-0.500405\pi\)
−0.00127168 + 0.999999i \(0.500405\pi\)
\(882\) −20.3991 −0.686872
\(883\) 14.1303 0.475523 0.237762 0.971324i \(-0.423586\pi\)
0.237762 + 0.971324i \(0.423586\pi\)
\(884\) 2.74984 0.0924872
\(885\) −0.320109 −0.0107604
\(886\) −16.5825 −0.557099
\(887\) −24.3394 −0.817238 −0.408619 0.912705i \(-0.633990\pi\)
−0.408619 + 0.912705i \(0.633990\pi\)
\(888\) −0.251186 −0.00842926
\(889\) 4.23940 0.142185
\(890\) 4.30475 0.144295
\(891\) 41.9630 1.40581
\(892\) 3.20050 0.107161
\(893\) −72.3584 −2.42138
\(894\) −1.23375 −0.0412629
\(895\) 53.9029 1.80178
\(896\) 0.430136 0.0143698
\(897\) −0.575497 −0.0192153
\(898\) 25.5612 0.852987
\(899\) 3.40781 0.113657
\(900\) −16.9343 −0.564476
\(901\) −4.23085 −0.140950
\(902\) −30.9590 −1.03082
\(903\) −0.102653 −0.00341608
\(904\) 10.6438 0.354006
\(905\) −52.8611 −1.75716
\(906\) −0.565321 −0.0187815
\(907\) −19.1072 −0.634445 −0.317223 0.948351i \(-0.602750\pi\)
−0.317223 + 0.948351i \(0.602750\pi\)
\(908\) 23.5821 0.782598
\(909\) −43.2855 −1.43569
\(910\) −9.84763 −0.326446
\(911\) 5.66835 0.187801 0.0939004 0.995582i \(-0.470066\pi\)
0.0939004 + 0.995582i \(0.470066\pi\)
\(912\) −0.692604 −0.0229344
\(913\) −24.5012 −0.810870
\(914\) −37.4064 −1.23729
\(915\) 2.09175 0.0691511
\(916\) 12.0256 0.397336
\(917\) 0.430136 0.0142043
\(918\) −0.192849 −0.00636496
\(919\) −16.5208 −0.544971 −0.272486 0.962160i \(-0.587846\pi\)
−0.272486 + 0.962160i \(0.587846\pi\)
\(920\) 3.26458 0.107630
\(921\) 2.12681 0.0700806
\(922\) 14.4246 0.475050
\(923\) −16.6498 −0.548034
\(924\) 0.165694 0.00545093
\(925\) −17.3170 −0.569381
\(926\) −2.35074 −0.0772501
\(927\) −16.2128 −0.532498
\(928\) −0.423629 −0.0139063
\(929\) −8.32030 −0.272980 −0.136490 0.990641i \(-0.543582\pi\)
−0.136490 + 0.990641i \(0.543582\pi\)
\(930\) −2.15507 −0.0706675
\(931\) −57.5182 −1.88508
\(932\) 23.4503 0.768140
\(933\) 0.314934 0.0103105
\(934\) 18.1238 0.593030
\(935\) −6.00887 −0.196511
\(936\) 20.9915 0.686130
\(937\) 17.6298 0.575941 0.287970 0.957639i \(-0.407020\pi\)
0.287970 + 0.957639i \(0.407020\pi\)
\(938\) −1.96163 −0.0640494
\(939\) 0.512638 0.0167293
\(940\) 27.9882 0.912875
\(941\) 20.4441 0.666459 0.333229 0.942846i \(-0.391862\pi\)
0.333229 + 0.942846i \(0.391862\pi\)
\(942\) 0.124935 0.00407060
\(943\) 6.59524 0.214771
\(944\) −1.19489 −0.0388903
\(945\) 0.690622 0.0224659
\(946\) 13.6514 0.443846
\(947\) 40.4257 1.31366 0.656830 0.754039i \(-0.271897\pi\)
0.656830 + 0.754039i \(0.271897\pi\)
\(948\) −0.240687 −0.00781714
\(949\) 70.8563 2.30009
\(950\) −47.7488 −1.54918
\(951\) 2.08363 0.0675662
\(952\) 0.168661 0.00546633
\(953\) 61.6500 1.99704 0.998520 0.0543781i \(-0.0173176\pi\)
0.998520 + 0.0543781i \(0.0173176\pi\)
\(954\) −32.2971 −1.04566
\(955\) −11.5021 −0.372199
\(956\) −26.3555 −0.852398
\(957\) −0.163187 −0.00527510
\(958\) −12.6937 −0.410113
\(959\) −3.97477 −0.128352
\(960\) 0.267899 0.00864641
\(961\) 33.7112 1.08746
\(962\) 21.4660 0.692091
\(963\) −23.9055 −0.770345
\(964\) 20.2788 0.653135
\(965\) −36.3126 −1.16894
\(966\) −0.0352980 −0.00113569
\(967\) 24.1797 0.777565 0.388783 0.921330i \(-0.372896\pi\)
0.388783 + 0.921330i \(0.372896\pi\)
\(968\) −11.0350 −0.354679
\(969\) −0.271578 −0.00872433
\(970\) −28.4344 −0.912974
\(971\) −21.4891 −0.689617 −0.344808 0.938673i \(-0.612056\pi\)
−0.344808 + 0.938673i \(0.612056\pi\)
\(972\) −2.20906 −0.0708556
\(973\) −3.84873 −0.123385
\(974\) 10.0632 0.322447
\(975\) −3.25586 −0.104271
\(976\) 7.80797 0.249927
\(977\) −6.93961 −0.222018 −0.111009 0.993819i \(-0.535408\pi\)
−0.111009 + 0.993819i \(0.535408\pi\)
\(978\) −0.751591 −0.0240332
\(979\) 6.18981 0.197827
\(980\) 22.2480 0.710688
\(981\) 14.5712 0.465223
\(982\) 1.30028 0.0414936
\(983\) −16.7848 −0.535352 −0.267676 0.963509i \(-0.586256\pi\)
−0.267676 + 0.963509i \(0.586256\pi\)
\(984\) 0.541222 0.0172535
\(985\) 40.5452 1.29188
\(986\) −0.166109 −0.00529000
\(987\) −0.302621 −0.00963252
\(988\) 59.1888 1.88305
\(989\) −2.90818 −0.0924748
\(990\) −45.8700 −1.45784
\(991\) 19.0338 0.604629 0.302314 0.953208i \(-0.402241\pi\)
0.302314 + 0.953208i \(0.402241\pi\)
\(992\) −8.04433 −0.255408
\(993\) 0.618673 0.0196330
\(994\) −1.02121 −0.0323908
\(995\) −58.7855 −1.86363
\(996\) 0.428326 0.0135720
\(997\) 38.5516 1.22094 0.610471 0.792038i \(-0.290980\pi\)
0.610471 + 0.792038i \(0.290980\pi\)
\(998\) 27.0515 0.856300
\(999\) −1.50543 −0.0476296
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 6026.2.a.j.1.16 33
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.j.1.16 33 1.1 even 1 trivial