Properties

Label 4022.2.a.f.1.11
Level $4022$
Weight $2$
Character 4022.1
Self dual yes
Analytic conductor $32.116$
Analytic rank $0$
Dimension $50$
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] = [4022,2,Mod(1,4022)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4022.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4022 = 2 \cdot 2011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4022.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: \(32.1158316930\)
Analytic rank: \(0\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 4022.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.60405 q^{3} +1.00000 q^{4} +1.46390 q^{5} -1.60405 q^{6} +4.50208 q^{7} +1.00000 q^{8} -0.427040 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.60405 q^{3} +1.00000 q^{4} +1.46390 q^{5} -1.60405 q^{6} +4.50208 q^{7} +1.00000 q^{8} -0.427040 q^{9} +1.46390 q^{10} +0.640800 q^{11} -1.60405 q^{12} -0.795145 q^{13} +4.50208 q^{14} -2.34817 q^{15} +1.00000 q^{16} +3.01845 q^{17} -0.427040 q^{18} -4.80731 q^{19} +1.46390 q^{20} -7.22154 q^{21} +0.640800 q^{22} +4.47690 q^{23} -1.60405 q^{24} -2.85699 q^{25} -0.795145 q^{26} +5.49713 q^{27} +4.50208 q^{28} +4.51886 q^{29} -2.34817 q^{30} +3.84587 q^{31} +1.00000 q^{32} -1.02787 q^{33} +3.01845 q^{34} +6.59061 q^{35} -0.427040 q^{36} +10.3793 q^{37} -4.80731 q^{38} +1.27545 q^{39} +1.46390 q^{40} +4.31664 q^{41} -7.22154 q^{42} -5.08727 q^{43} +0.640800 q^{44} -0.625145 q^{45} +4.47690 q^{46} -9.95370 q^{47} -1.60405 q^{48} +13.2687 q^{49} -2.85699 q^{50} -4.84174 q^{51} -0.795145 q^{52} -11.6932 q^{53} +5.49713 q^{54} +0.938070 q^{55} +4.50208 q^{56} +7.71114 q^{57} +4.51886 q^{58} +0.0329516 q^{59} -2.34817 q^{60} -10.2099 q^{61} +3.84587 q^{62} -1.92257 q^{63} +1.00000 q^{64} -1.16402 q^{65} -1.02787 q^{66} +13.1604 q^{67} +3.01845 q^{68} -7.18115 q^{69} +6.59061 q^{70} -7.70461 q^{71} -0.427040 q^{72} +12.6960 q^{73} +10.3793 q^{74} +4.58273 q^{75} -4.80731 q^{76} +2.88493 q^{77} +1.27545 q^{78} +14.2214 q^{79} +1.46390 q^{80} -7.53652 q^{81} +4.31664 q^{82} +14.5419 q^{83} -7.22154 q^{84} +4.41873 q^{85} -5.08727 q^{86} -7.24845 q^{87} +0.640800 q^{88} +6.30123 q^{89} -0.625145 q^{90} -3.57981 q^{91} +4.47690 q^{92} -6.16895 q^{93} -9.95370 q^{94} -7.03744 q^{95} -1.60405 q^{96} -7.18050 q^{97} +13.2687 q^{98} -0.273647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 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
\(3\) −1.60405 −0.926096 −0.463048 0.886333i \(-0.653244\pi\)
−0.463048 + 0.886333i \(0.653244\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.46390 0.654678 0.327339 0.944907i \(-0.393848\pi\)
0.327339 + 0.944907i \(0.393848\pi\)
\(6\) −1.60405 −0.654849
\(7\) 4.50208 1.70163 0.850813 0.525468i \(-0.176110\pi\)
0.850813 + 0.525468i \(0.176110\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.427040 −0.142347
\(10\) 1.46390 0.462927
\(11\) 0.640800 0.193209 0.0966043 0.995323i \(-0.469202\pi\)
0.0966043 + 0.995323i \(0.469202\pi\)
\(12\) −1.60405 −0.463048
\(13\) −0.795145 −0.220533 −0.110267 0.993902i \(-0.535171\pi\)
−0.110267 + 0.993902i \(0.535171\pi\)
\(14\) 4.50208 1.20323
\(15\) −2.34817 −0.606294
\(16\) 1.00000 0.250000
\(17\) 3.01845 0.732083 0.366041 0.930599i \(-0.380713\pi\)
0.366041 + 0.930599i \(0.380713\pi\)
\(18\) −0.427040 −0.100654
\(19\) −4.80731 −1.10287 −0.551436 0.834217i \(-0.685920\pi\)
−0.551436 + 0.834217i \(0.685920\pi\)
\(20\) 1.46390 0.327339
\(21\) −7.22154 −1.57587
\(22\) 0.640800 0.136619
\(23\) 4.47690 0.933498 0.466749 0.884390i \(-0.345425\pi\)
0.466749 + 0.884390i \(0.345425\pi\)
\(24\) −1.60405 −0.327424
\(25\) −2.85699 −0.571397
\(26\) −0.795145 −0.155941
\(27\) 5.49713 1.05792
\(28\) 4.50208 0.850813
\(29\) 4.51886 0.839131 0.419565 0.907725i \(-0.362183\pi\)
0.419565 + 0.907725i \(0.362183\pi\)
\(30\) −2.34817 −0.428715
\(31\) 3.84587 0.690738 0.345369 0.938467i \(-0.387754\pi\)
0.345369 + 0.938467i \(0.387754\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.02787 −0.178930
\(34\) 3.01845 0.517661
\(35\) 6.59061 1.11402
\(36\) −0.427040 −0.0711733
\(37\) 10.3793 1.70635 0.853177 0.521622i \(-0.174673\pi\)
0.853177 + 0.521622i \(0.174673\pi\)
\(38\) −4.80731 −0.779849
\(39\) 1.27545 0.204235
\(40\) 1.46390 0.231464
\(41\) 4.31664 0.674146 0.337073 0.941478i \(-0.390563\pi\)
0.337073 + 0.941478i \(0.390563\pi\)
\(42\) −7.22154 −1.11431
\(43\) −5.08727 −0.775802 −0.387901 0.921701i \(-0.626800\pi\)
−0.387901 + 0.921701i \(0.626800\pi\)
\(44\) 0.640800 0.0966043
\(45\) −0.625145 −0.0931911
\(46\) 4.47690 0.660083
\(47\) −9.95370 −1.45190 −0.725948 0.687750i \(-0.758599\pi\)
−0.725948 + 0.687750i \(0.758599\pi\)
\(48\) −1.60405 −0.231524
\(49\) 13.2687 1.89553
\(50\) −2.85699 −0.404039
\(51\) −4.84174 −0.677979
\(52\) −0.795145 −0.110267
\(53\) −11.6932 −1.60618 −0.803092 0.595855i \(-0.796813\pi\)
−0.803092 + 0.595855i \(0.796813\pi\)
\(54\) 5.49713 0.748064
\(55\) 0.938070 0.126489
\(56\) 4.50208 0.601616
\(57\) 7.71114 1.02137
\(58\) 4.51886 0.593355
\(59\) 0.0329516 0.00428994 0.00214497 0.999998i \(-0.499317\pi\)
0.00214497 + 0.999998i \(0.499317\pi\)
\(60\) −2.34817 −0.303147
\(61\) −10.2099 −1.30724 −0.653620 0.756823i \(-0.726750\pi\)
−0.653620 + 0.756823i \(0.726750\pi\)
\(62\) 3.84587 0.488426
\(63\) −1.92257 −0.242221
\(64\) 1.00000 0.125000
\(65\) −1.16402 −0.144378
\(66\) −1.02787 −0.126522
\(67\) 13.1604 1.60780 0.803899 0.594765i \(-0.202755\pi\)
0.803899 + 0.594765i \(0.202755\pi\)
\(68\) 3.01845 0.366041
\(69\) −7.18115 −0.864508
\(70\) 6.59061 0.787729
\(71\) −7.70461 −0.914368 −0.457184 0.889372i \(-0.651142\pi\)
−0.457184 + 0.889372i \(0.651142\pi\)
\(72\) −0.427040 −0.0503271
\(73\) 12.6960 1.48595 0.742975 0.669319i \(-0.233414\pi\)
0.742975 + 0.669319i \(0.233414\pi\)
\(74\) 10.3793 1.20657
\(75\) 4.58273 0.529168
\(76\) −4.80731 −0.551436
\(77\) 2.88493 0.328769
\(78\) 1.27545 0.144416
\(79\) 14.2214 1.60004 0.800019 0.599975i \(-0.204823\pi\)
0.800019 + 0.599975i \(0.204823\pi\)
\(80\) 1.46390 0.163669
\(81\) −7.53652 −0.837391
\(82\) 4.31664 0.476693
\(83\) 14.5419 1.59618 0.798089 0.602540i \(-0.205845\pi\)
0.798089 + 0.602540i \(0.205845\pi\)
\(84\) −7.22154 −0.787935
\(85\) 4.41873 0.479278
\(86\) −5.08727 −0.548575
\(87\) −7.24845 −0.777115
\(88\) 0.640800 0.0683095
\(89\) 6.30123 0.667929 0.333965 0.942586i \(-0.391613\pi\)
0.333965 + 0.942586i \(0.391613\pi\)
\(90\) −0.625145 −0.0658961
\(91\) −3.57981 −0.375266
\(92\) 4.47690 0.466749
\(93\) −6.16895 −0.639690
\(94\) −9.95370 −1.02665
\(95\) −7.03744 −0.722026
\(96\) −1.60405 −0.163712
\(97\) −7.18050 −0.729069 −0.364535 0.931190i \(-0.618772\pi\)
−0.364535 + 0.931190i \(0.618772\pi\)
\(98\) 13.2687 1.34034
\(99\) −0.273647 −0.0275026
\(100\) −2.85699 −0.285699
\(101\) 11.0254 1.09707 0.548534 0.836128i \(-0.315186\pi\)
0.548534 + 0.836128i \(0.315186\pi\)
\(102\) −4.84174 −0.479403
\(103\) −7.91711 −0.780096 −0.390048 0.920795i \(-0.627542\pi\)
−0.390048 + 0.920795i \(0.627542\pi\)
\(104\) −0.795145 −0.0779703
\(105\) −10.5716 −1.03169
\(106\) −11.6932 −1.13574
\(107\) −12.0099 −1.16104 −0.580520 0.814246i \(-0.697151\pi\)
−0.580520 + 0.814246i \(0.697151\pi\)
\(108\) 5.49713 0.528961
\(109\) −9.78046 −0.936798 −0.468399 0.883517i \(-0.655169\pi\)
−0.468399 + 0.883517i \(0.655169\pi\)
\(110\) 0.938070 0.0894415
\(111\) −16.6489 −1.58025
\(112\) 4.50208 0.425407
\(113\) 4.63963 0.436460 0.218230 0.975897i \(-0.429972\pi\)
0.218230 + 0.975897i \(0.429972\pi\)
\(114\) 7.71114 0.722215
\(115\) 6.55375 0.611140
\(116\) 4.51886 0.419565
\(117\) 0.339558 0.0313922
\(118\) 0.0329516 0.00303344
\(119\) 13.5893 1.24573
\(120\) −2.34817 −0.214357
\(121\) −10.5894 −0.962670
\(122\) −10.2099 −0.924358
\(123\) −6.92409 −0.624324
\(124\) 3.84587 0.345369
\(125\) −11.5019 −1.02876
\(126\) −1.92257 −0.171276
\(127\) −14.9796 −1.32922 −0.664612 0.747189i \(-0.731403\pi\)
−0.664612 + 0.747189i \(0.731403\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.16022 0.718467
\(130\) −1.16402 −0.102091
\(131\) −2.72944 −0.238472 −0.119236 0.992866i \(-0.538044\pi\)
−0.119236 + 0.992866i \(0.538044\pi\)
\(132\) −1.02787 −0.0894648
\(133\) −21.6429 −1.87668
\(134\) 13.1604 1.13689
\(135\) 8.04726 0.692598
\(136\) 3.01845 0.258830
\(137\) −0.510043 −0.0435759 −0.0217880 0.999763i \(-0.506936\pi\)
−0.0217880 + 0.999763i \(0.506936\pi\)
\(138\) −7.18115 −0.611300
\(139\) 7.39069 0.626870 0.313435 0.949610i \(-0.398520\pi\)
0.313435 + 0.949610i \(0.398520\pi\)
\(140\) 6.59061 0.557008
\(141\) 15.9662 1.34459
\(142\) −7.70461 −0.646556
\(143\) −0.509529 −0.0426090
\(144\) −0.427040 −0.0355866
\(145\) 6.61517 0.549360
\(146\) 12.6960 1.05073
\(147\) −21.2836 −1.75544
\(148\) 10.3793 0.853177
\(149\) 14.0030 1.14717 0.573583 0.819147i \(-0.305553\pi\)
0.573583 + 0.819147i \(0.305553\pi\)
\(150\) 4.58273 0.374179
\(151\) 0.167706 0.0136477 0.00682387 0.999977i \(-0.497828\pi\)
0.00682387 + 0.999977i \(0.497828\pi\)
\(152\) −4.80731 −0.389924
\(153\) −1.28900 −0.104209
\(154\) 2.88493 0.232475
\(155\) 5.62998 0.452211
\(156\) 1.27545 0.102118
\(157\) −10.7916 −0.861267 −0.430634 0.902527i \(-0.641710\pi\)
−0.430634 + 0.902527i \(0.641710\pi\)
\(158\) 14.2214 1.13140
\(159\) 18.7564 1.48748
\(160\) 1.46390 0.115732
\(161\) 20.1554 1.58846
\(162\) −7.53652 −0.592125
\(163\) −16.6289 −1.30247 −0.651237 0.758875i \(-0.725749\pi\)
−0.651237 + 0.758875i \(0.725749\pi\)
\(164\) 4.31664 0.337073
\(165\) −1.50471 −0.117141
\(166\) 14.5419 1.12867
\(167\) 20.7414 1.60502 0.802510 0.596638i \(-0.203497\pi\)
0.802510 + 0.596638i \(0.203497\pi\)
\(168\) −7.22154 −0.557154
\(169\) −12.3677 −0.951365
\(170\) 4.41873 0.338901
\(171\) 2.05291 0.156990
\(172\) −5.08727 −0.387901
\(173\) −0.856747 −0.0651373 −0.0325686 0.999470i \(-0.510369\pi\)
−0.0325686 + 0.999470i \(0.510369\pi\)
\(174\) −7.24845 −0.549504
\(175\) −12.8624 −0.972304
\(176\) 0.640800 0.0483021
\(177\) −0.0528559 −0.00397289
\(178\) 6.30123 0.472297
\(179\) −3.22266 −0.240873 −0.120436 0.992721i \(-0.538429\pi\)
−0.120436 + 0.992721i \(0.538429\pi\)
\(180\) −0.625145 −0.0465955
\(181\) 14.1885 1.05463 0.527313 0.849671i \(-0.323199\pi\)
0.527313 + 0.849671i \(0.323199\pi\)
\(182\) −3.57981 −0.265353
\(183\) 16.3771 1.21063
\(184\) 4.47690 0.330041
\(185\) 15.1944 1.11711
\(186\) −6.16895 −0.452329
\(187\) 1.93423 0.141445
\(188\) −9.95370 −0.725948
\(189\) 24.7485 1.80019
\(190\) −7.03744 −0.510550
\(191\) 14.2218 1.02906 0.514528 0.857473i \(-0.327967\pi\)
0.514528 + 0.857473i \(0.327967\pi\)
\(192\) −1.60405 −0.115762
\(193\) 19.0874 1.37394 0.686971 0.726685i \(-0.258940\pi\)
0.686971 + 0.726685i \(0.258940\pi\)
\(194\) −7.18050 −0.515530
\(195\) 1.86713 0.133708
\(196\) 13.2687 0.947766
\(197\) −21.5889 −1.53815 −0.769074 0.639159i \(-0.779283\pi\)
−0.769074 + 0.639159i \(0.779283\pi\)
\(198\) −0.273647 −0.0194473
\(199\) 15.4251 1.09346 0.546728 0.837310i \(-0.315873\pi\)
0.546728 + 0.837310i \(0.315873\pi\)
\(200\) −2.85699 −0.202019
\(201\) −21.1099 −1.48898
\(202\) 11.0254 0.775745
\(203\) 20.3443 1.42789
\(204\) −4.84174 −0.338989
\(205\) 6.31915 0.441348
\(206\) −7.91711 −0.551611
\(207\) −1.91181 −0.132880
\(208\) −0.795145 −0.0551334
\(209\) −3.08053 −0.213084
\(210\) −10.5716 −0.729512
\(211\) 17.9469 1.23552 0.617758 0.786369i \(-0.288041\pi\)
0.617758 + 0.786369i \(0.288041\pi\)
\(212\) −11.6932 −0.803092
\(213\) 12.3585 0.846793
\(214\) −12.0099 −0.820980
\(215\) −7.44728 −0.507900
\(216\) 5.49713 0.374032
\(217\) 17.3144 1.17538
\(218\) −9.78046 −0.662416
\(219\) −20.3649 −1.37613
\(220\) 0.938070 0.0632447
\(221\) −2.40011 −0.161449
\(222\) −16.6489 −1.11740
\(223\) 1.95762 0.131092 0.0655460 0.997850i \(-0.479121\pi\)
0.0655460 + 0.997850i \(0.479121\pi\)
\(224\) 4.50208 0.300808
\(225\) 1.22005 0.0813364
\(226\) 4.63963 0.308624
\(227\) 20.7135 1.37480 0.687401 0.726278i \(-0.258752\pi\)
0.687401 + 0.726278i \(0.258752\pi\)
\(228\) 7.71114 0.510683
\(229\) 14.1741 0.936650 0.468325 0.883556i \(-0.344858\pi\)
0.468325 + 0.883556i \(0.344858\pi\)
\(230\) 6.55375 0.432141
\(231\) −4.62757 −0.304471
\(232\) 4.51886 0.296677
\(233\) 13.5610 0.888414 0.444207 0.895924i \(-0.353485\pi\)
0.444207 + 0.895924i \(0.353485\pi\)
\(234\) 0.339558 0.0221976
\(235\) −14.5713 −0.950524
\(236\) 0.0329516 0.00214497
\(237\) −22.8118 −1.48179
\(238\) 13.5893 0.880865
\(239\) 19.1300 1.23742 0.618708 0.785621i \(-0.287656\pi\)
0.618708 + 0.785621i \(0.287656\pi\)
\(240\) −2.34817 −0.151574
\(241\) 8.68193 0.559252 0.279626 0.960109i \(-0.409789\pi\)
0.279626 + 0.960109i \(0.409789\pi\)
\(242\) −10.5894 −0.680711
\(243\) −4.40246 −0.282418
\(244\) −10.2099 −0.653620
\(245\) 19.4241 1.24096
\(246\) −6.92409 −0.441464
\(247\) 3.82251 0.243220
\(248\) 3.84587 0.244213
\(249\) −23.3258 −1.47821
\(250\) −11.5019 −0.727442
\(251\) −8.13314 −0.513359 −0.256680 0.966497i \(-0.582629\pi\)
−0.256680 + 0.966497i \(0.582629\pi\)
\(252\) −1.92257 −0.121110
\(253\) 2.86880 0.180360
\(254\) −14.9796 −0.939903
\(255\) −7.08784 −0.443858
\(256\) 1.00000 0.0625000
\(257\) 14.6400 0.913216 0.456608 0.889668i \(-0.349064\pi\)
0.456608 + 0.889668i \(0.349064\pi\)
\(258\) 8.16022 0.508033
\(259\) 46.7286 2.90358
\(260\) −1.16402 −0.0721892
\(261\) −1.92973 −0.119447
\(262\) −2.72944 −0.168625
\(263\) 0.227959 0.0140566 0.00702829 0.999975i \(-0.497763\pi\)
0.00702829 + 0.999975i \(0.497763\pi\)
\(264\) −1.02787 −0.0632612
\(265\) −17.1177 −1.05153
\(266\) −21.6429 −1.32701
\(267\) −10.1075 −0.618566
\(268\) 13.1604 0.803899
\(269\) −8.67065 −0.528659 −0.264330 0.964432i \(-0.585151\pi\)
−0.264330 + 0.964432i \(0.585151\pi\)
\(270\) 8.04726 0.489741
\(271\) 2.31008 0.140327 0.0701636 0.997535i \(-0.477648\pi\)
0.0701636 + 0.997535i \(0.477648\pi\)
\(272\) 3.01845 0.183021
\(273\) 5.74217 0.347532
\(274\) −0.510043 −0.0308128
\(275\) −1.83076 −0.110399
\(276\) −7.18115 −0.432254
\(277\) 0.538739 0.0323697 0.0161848 0.999869i \(-0.494848\pi\)
0.0161848 + 0.999869i \(0.494848\pi\)
\(278\) 7.39069 0.443264
\(279\) −1.64234 −0.0983242
\(280\) 6.59061 0.393864
\(281\) −0.972148 −0.0579935 −0.0289967 0.999580i \(-0.509231\pi\)
−0.0289967 + 0.999580i \(0.509231\pi\)
\(282\) 15.9662 0.950772
\(283\) 1.76080 0.104669 0.0523344 0.998630i \(-0.483334\pi\)
0.0523344 + 0.998630i \(0.483334\pi\)
\(284\) −7.70461 −0.457184
\(285\) 11.2884 0.668665
\(286\) −0.509529 −0.0301291
\(287\) 19.4339 1.14714
\(288\) −0.427040 −0.0251635
\(289\) −7.88893 −0.464055
\(290\) 6.61517 0.388456
\(291\) 11.5178 0.675188
\(292\) 12.6960 0.742975
\(293\) −24.4340 −1.42745 −0.713724 0.700427i \(-0.752993\pi\)
−0.713724 + 0.700427i \(0.752993\pi\)
\(294\) −21.2836 −1.24129
\(295\) 0.0482380 0.00280853
\(296\) 10.3793 0.603287
\(297\) 3.52256 0.204400
\(298\) 14.0030 0.811169
\(299\) −3.55978 −0.205867
\(300\) 4.58273 0.264584
\(301\) −22.9033 −1.32013
\(302\) 0.167706 0.00965041
\(303\) −17.6852 −1.01599
\(304\) −4.80731 −0.275718
\(305\) −14.9463 −0.855820
\(306\) −1.28900 −0.0736872
\(307\) −5.25863 −0.300126 −0.150063 0.988676i \(-0.547948\pi\)
−0.150063 + 0.988676i \(0.547948\pi\)
\(308\) 2.88493 0.164384
\(309\) 12.6994 0.722443
\(310\) 5.62998 0.319762
\(311\) −16.1067 −0.913328 −0.456664 0.889639i \(-0.650956\pi\)
−0.456664 + 0.889639i \(0.650956\pi\)
\(312\) 1.27545 0.0722080
\(313\) −21.9897 −1.24293 −0.621466 0.783441i \(-0.713463\pi\)
−0.621466 + 0.783441i \(0.713463\pi\)
\(314\) −10.7916 −0.609008
\(315\) −2.81445 −0.158576
\(316\) 14.2214 0.800019
\(317\) −17.3222 −0.972911 −0.486455 0.873705i \(-0.661710\pi\)
−0.486455 + 0.873705i \(0.661710\pi\)
\(318\) 18.7564 1.05181
\(319\) 2.89569 0.162127
\(320\) 1.46390 0.0818347
\(321\) 19.2644 1.07523
\(322\) 20.1554 1.12321
\(323\) −14.5106 −0.807394
\(324\) −7.53652 −0.418695
\(325\) 2.27172 0.126012
\(326\) −16.6289 −0.920988
\(327\) 15.6883 0.867564
\(328\) 4.31664 0.238347
\(329\) −44.8123 −2.47058
\(330\) −1.50471 −0.0828314
\(331\) 27.3324 1.50233 0.751163 0.660117i \(-0.229493\pi\)
0.751163 + 0.660117i \(0.229493\pi\)
\(332\) 14.5419 0.798089
\(333\) −4.43239 −0.242894
\(334\) 20.7414 1.13492
\(335\) 19.2656 1.05259
\(336\) −7.22154 −0.393967
\(337\) 27.7097 1.50944 0.754722 0.656044i \(-0.227772\pi\)
0.754722 + 0.656044i \(0.227772\pi\)
\(338\) −12.3677 −0.672717
\(339\) −7.44218 −0.404204
\(340\) 4.41873 0.239639
\(341\) 2.46443 0.133457
\(342\) 2.05291 0.111009
\(343\) 28.2223 1.52386
\(344\) −5.08727 −0.274287
\(345\) −10.5125 −0.565974
\(346\) −0.856747 −0.0460590
\(347\) −11.7509 −0.630820 −0.315410 0.948955i \(-0.602142\pi\)
−0.315410 + 0.948955i \(0.602142\pi\)
\(348\) −7.24845 −0.388558
\(349\) 18.2275 0.975695 0.487847 0.872929i \(-0.337782\pi\)
0.487847 + 0.872929i \(0.337782\pi\)
\(350\) −12.8624 −0.687523
\(351\) −4.37101 −0.233307
\(352\) 0.640800 0.0341548
\(353\) 0.110514 0.00588207 0.00294103 0.999996i \(-0.499064\pi\)
0.00294103 + 0.999996i \(0.499064\pi\)
\(354\) −0.0528559 −0.00280926
\(355\) −11.2788 −0.598617
\(356\) 6.30123 0.333965
\(357\) −21.7979 −1.15367
\(358\) −3.22266 −0.170323
\(359\) −7.27872 −0.384156 −0.192078 0.981380i \(-0.561523\pi\)
−0.192078 + 0.981380i \(0.561523\pi\)
\(360\) −0.625145 −0.0329480
\(361\) 4.11024 0.216328
\(362\) 14.1885 0.745733
\(363\) 16.9858 0.891525
\(364\) −3.57981 −0.187633
\(365\) 18.5857 0.972819
\(366\) 16.3771 0.856044
\(367\) 34.8926 1.82138 0.910690 0.413090i \(-0.135550\pi\)
0.910690 + 0.413090i \(0.135550\pi\)
\(368\) 4.47690 0.233374
\(369\) −1.84338 −0.0959624
\(370\) 15.1944 0.789917
\(371\) −52.6437 −2.73313
\(372\) −6.16895 −0.319845
\(373\) −14.7398 −0.763197 −0.381598 0.924328i \(-0.624626\pi\)
−0.381598 + 0.924328i \(0.624626\pi\)
\(374\) 1.93423 0.100016
\(375\) 18.4495 0.952729
\(376\) −9.95370 −0.513323
\(377\) −3.59315 −0.185056
\(378\) 24.7485 1.27293
\(379\) −5.57572 −0.286405 −0.143203 0.989693i \(-0.545740\pi\)
−0.143203 + 0.989693i \(0.545740\pi\)
\(380\) −7.03744 −0.361013
\(381\) 24.0279 1.23099
\(382\) 14.2218 0.727653
\(383\) 19.9811 1.02099 0.510493 0.859882i \(-0.329463\pi\)
0.510493 + 0.859882i \(0.329463\pi\)
\(384\) −1.60405 −0.0818561
\(385\) 4.22327 0.215238
\(386\) 19.0874 0.971523
\(387\) 2.17247 0.110433
\(388\) −7.18050 −0.364535
\(389\) 19.3642 0.981803 0.490902 0.871215i \(-0.336667\pi\)
0.490902 + 0.871215i \(0.336667\pi\)
\(390\) 1.86713 0.0945460
\(391\) 13.5133 0.683397
\(392\) 13.2687 0.670172
\(393\) 4.37814 0.220848
\(394\) −21.5889 −1.08764
\(395\) 20.8188 1.04751
\(396\) −0.273647 −0.0137513
\(397\) −28.4011 −1.42541 −0.712706 0.701463i \(-0.752530\pi\)
−0.712706 + 0.701463i \(0.752530\pi\)
\(398\) 15.4251 0.773190
\(399\) 34.7162 1.73798
\(400\) −2.85699 −0.142849
\(401\) −21.5763 −1.07747 −0.538734 0.842476i \(-0.681097\pi\)
−0.538734 + 0.842476i \(0.681097\pi\)
\(402\) −21.1099 −1.05286
\(403\) −3.05802 −0.152331
\(404\) 11.0254 0.548534
\(405\) −11.0327 −0.548221
\(406\) 20.3443 1.00967
\(407\) 6.65109 0.329682
\(408\) −4.84174 −0.239702
\(409\) −9.91465 −0.490248 −0.245124 0.969492i \(-0.578829\pi\)
−0.245124 + 0.969492i \(0.578829\pi\)
\(410\) 6.31915 0.312080
\(411\) 0.818132 0.0403555
\(412\) −7.91711 −0.390048
\(413\) 0.148351 0.00729987
\(414\) −1.91181 −0.0939605
\(415\) 21.2879 1.04498
\(416\) −0.795145 −0.0389852
\(417\) −11.8550 −0.580542
\(418\) −3.08053 −0.150673
\(419\) −30.1952 −1.47513 −0.737567 0.675274i \(-0.764026\pi\)
−0.737567 + 0.675274i \(0.764026\pi\)
\(420\) −10.5716 −0.515843
\(421\) −18.5652 −0.904813 −0.452407 0.891812i \(-0.649434\pi\)
−0.452407 + 0.891812i \(0.649434\pi\)
\(422\) 17.9469 0.873641
\(423\) 4.25062 0.206672
\(424\) −11.6932 −0.567872
\(425\) −8.62368 −0.418310
\(426\) 12.3585 0.598773
\(427\) −45.9656 −2.22443
\(428\) −12.0099 −0.580520
\(429\) 0.817307 0.0394600
\(430\) −7.44728 −0.359140
\(431\) −29.5691 −1.42429 −0.712147 0.702030i \(-0.752277\pi\)
−0.712147 + 0.702030i \(0.752277\pi\)
\(432\) 5.49713 0.264481
\(433\) −37.6270 −1.80824 −0.904119 0.427280i \(-0.859472\pi\)
−0.904119 + 0.427280i \(0.859472\pi\)
\(434\) 17.3144 0.831118
\(435\) −10.6110 −0.508760
\(436\) −9.78046 −0.468399
\(437\) −21.5218 −1.02953
\(438\) −20.3649 −0.973073
\(439\) 22.4696 1.07242 0.536209 0.844085i \(-0.319856\pi\)
0.536209 + 0.844085i \(0.319856\pi\)
\(440\) 0.938070 0.0447207
\(441\) −5.66627 −0.269823
\(442\) −2.40011 −0.114161
\(443\) 36.7579 1.74642 0.873211 0.487342i \(-0.162034\pi\)
0.873211 + 0.487342i \(0.162034\pi\)
\(444\) −16.6489 −0.790124
\(445\) 9.22440 0.437278
\(446\) 1.95762 0.0926961
\(447\) −22.4614 −1.06239
\(448\) 4.50208 0.212703
\(449\) −4.29656 −0.202767 −0.101384 0.994847i \(-0.532327\pi\)
−0.101384 + 0.994847i \(0.532327\pi\)
\(450\) 1.22005 0.0575135
\(451\) 2.76611 0.130251
\(452\) 4.63963 0.218230
\(453\) −0.269008 −0.0126391
\(454\) 20.7135 0.972132
\(455\) −5.24049 −0.245678
\(456\) 7.71114 0.361107
\(457\) −4.32456 −0.202295 −0.101147 0.994871i \(-0.532251\pi\)
−0.101147 + 0.994871i \(0.532251\pi\)
\(458\) 14.1741 0.662311
\(459\) 16.5928 0.774487
\(460\) 6.55375 0.305570
\(461\) −30.6666 −1.42829 −0.714143 0.700000i \(-0.753183\pi\)
−0.714143 + 0.700000i \(0.753183\pi\)
\(462\) −4.62757 −0.215294
\(463\) 0.252334 0.0117270 0.00586349 0.999983i \(-0.498134\pi\)
0.00586349 + 0.999983i \(0.498134\pi\)
\(464\) 4.51886 0.209783
\(465\) −9.03075 −0.418791
\(466\) 13.5610 0.628203
\(467\) −11.7911 −0.545628 −0.272814 0.962067i \(-0.587954\pi\)
−0.272814 + 0.962067i \(0.587954\pi\)
\(468\) 0.339558 0.0156961
\(469\) 59.2492 2.73587
\(470\) −14.5713 −0.672122
\(471\) 17.3103 0.797616
\(472\) 0.0329516 0.00151672
\(473\) −3.25993 −0.149892
\(474\) −22.8118 −1.04778
\(475\) 13.7344 0.630178
\(476\) 13.5893 0.622866
\(477\) 4.99346 0.228635
\(478\) 19.1300 0.874985
\(479\) 18.7333 0.855945 0.427973 0.903792i \(-0.359228\pi\)
0.427973 + 0.903792i \(0.359228\pi\)
\(480\) −2.34817 −0.107179
\(481\) −8.25308 −0.376308
\(482\) 8.68193 0.395451
\(483\) −32.3301 −1.47107
\(484\) −10.5894 −0.481335
\(485\) −10.5116 −0.477306
\(486\) −4.40246 −0.199700
\(487\) −35.2519 −1.59742 −0.798708 0.601719i \(-0.794483\pi\)
−0.798708 + 0.601719i \(0.794483\pi\)
\(488\) −10.2099 −0.462179
\(489\) 26.6734 1.20621
\(490\) 19.4241 0.877493
\(491\) −40.3227 −1.81974 −0.909869 0.414895i \(-0.863818\pi\)
−0.909869 + 0.414895i \(0.863818\pi\)
\(492\) −6.92409 −0.312162
\(493\) 13.6400 0.614313
\(494\) 3.82251 0.171983
\(495\) −0.400593 −0.0180053
\(496\) 3.84587 0.172685
\(497\) −34.6868 −1.55591
\(498\) −23.3258 −1.04525
\(499\) −8.63150 −0.386399 −0.193199 0.981160i \(-0.561886\pi\)
−0.193199 + 0.981160i \(0.561886\pi\)
\(500\) −11.5019 −0.514379
\(501\) −33.2702 −1.48640
\(502\) −8.13314 −0.363000
\(503\) 7.23331 0.322517 0.161259 0.986912i \(-0.448445\pi\)
0.161259 + 0.986912i \(0.448445\pi\)
\(504\) −1.92257 −0.0856379
\(505\) 16.1401 0.718226
\(506\) 2.86880 0.127534
\(507\) 19.8384 0.881055
\(508\) −14.9796 −0.664612
\(509\) −42.0142 −1.86225 −0.931124 0.364704i \(-0.881170\pi\)
−0.931124 + 0.364704i \(0.881170\pi\)
\(510\) −7.08784 −0.313855
\(511\) 57.1583 2.52853
\(512\) 1.00000 0.0441942
\(513\) −26.4264 −1.16675
\(514\) 14.6400 0.645741
\(515\) −11.5899 −0.510711
\(516\) 8.16022 0.359233
\(517\) −6.37833 −0.280519
\(518\) 46.7286 2.05314
\(519\) 1.37426 0.0603234
\(520\) −1.16402 −0.0510454
\(521\) −25.1221 −1.10062 −0.550310 0.834960i \(-0.685491\pi\)
−0.550310 + 0.834960i \(0.685491\pi\)
\(522\) −1.92973 −0.0844620
\(523\) −33.6186 −1.47004 −0.735018 0.678047i \(-0.762826\pi\)
−0.735018 + 0.678047i \(0.762826\pi\)
\(524\) −2.72944 −0.119236
\(525\) 20.6318 0.900447
\(526\) 0.227959 0.00993950
\(527\) 11.6086 0.505678
\(528\) −1.02787 −0.0447324
\(529\) −2.95739 −0.128582
\(530\) −17.1177 −0.743546
\(531\) −0.0140716 −0.000610658 0
\(532\) −21.6429 −0.938339
\(533\) −3.43235 −0.148672
\(534\) −10.1075 −0.437393
\(535\) −17.5813 −0.760107
\(536\) 13.1604 0.568443
\(537\) 5.16929 0.223071
\(538\) −8.67065 −0.373818
\(539\) 8.50261 0.366233
\(540\) 8.04726 0.346299
\(541\) −13.2826 −0.571064 −0.285532 0.958369i \(-0.592170\pi\)
−0.285532 + 0.958369i \(0.592170\pi\)
\(542\) 2.31008 0.0992263
\(543\) −22.7591 −0.976685
\(544\) 3.01845 0.129415
\(545\) −14.3176 −0.613301
\(546\) 5.74217 0.245742
\(547\) 7.91845 0.338569 0.169284 0.985567i \(-0.445854\pi\)
0.169284 + 0.985567i \(0.445854\pi\)
\(548\) −0.510043 −0.0217880
\(549\) 4.36002 0.186081
\(550\) −1.83076 −0.0780638
\(551\) −21.7235 −0.925454
\(552\) −7.18115 −0.305650
\(553\) 64.0261 2.72267
\(554\) 0.538739 0.0228888
\(555\) −24.3724 −1.03455
\(556\) 7.39069 0.313435
\(557\) −11.0239 −0.467099 −0.233549 0.972345i \(-0.575034\pi\)
−0.233549 + 0.972345i \(0.575034\pi\)
\(558\) −1.64234 −0.0695257
\(559\) 4.04512 0.171090
\(560\) 6.59061 0.278504
\(561\) −3.10259 −0.130991
\(562\) −0.972148 −0.0410076
\(563\) −37.2641 −1.57049 −0.785247 0.619182i \(-0.787464\pi\)
−0.785247 + 0.619182i \(0.787464\pi\)
\(564\) 15.9662 0.672297
\(565\) 6.79198 0.285741
\(566\) 1.76080 0.0740120
\(567\) −33.9300 −1.42493
\(568\) −7.70461 −0.323278
\(569\) 10.0406 0.420926 0.210463 0.977602i \(-0.432503\pi\)
0.210463 + 0.977602i \(0.432503\pi\)
\(570\) 11.2884 0.472818
\(571\) 3.63429 0.152090 0.0760452 0.997104i \(-0.475771\pi\)
0.0760452 + 0.997104i \(0.475771\pi\)
\(572\) −0.509529 −0.0213045
\(573\) −22.8125 −0.953005
\(574\) 19.4339 0.811154
\(575\) −12.7904 −0.533398
\(576\) −0.427040 −0.0177933
\(577\) 0.717085 0.0298526 0.0149263 0.999889i \(-0.495249\pi\)
0.0149263 + 0.999889i \(0.495249\pi\)
\(578\) −7.88893 −0.328136
\(579\) −30.6171 −1.27240
\(580\) 6.61517 0.274680
\(581\) 65.4687 2.71610
\(582\) 11.5178 0.477430
\(583\) −7.49301 −0.310329
\(584\) 12.6960 0.525363
\(585\) 0.497081 0.0205518
\(586\) −24.4340 −1.00936
\(587\) −11.3283 −0.467570 −0.233785 0.972288i \(-0.575111\pi\)
−0.233785 + 0.972288i \(0.575111\pi\)
\(588\) −21.2836 −0.877722
\(589\) −18.4883 −0.761797
\(590\) 0.0482380 0.00198593
\(591\) 34.6296 1.42447
\(592\) 10.3793 0.426588
\(593\) −11.3351 −0.465478 −0.232739 0.972539i \(-0.574769\pi\)
−0.232739 + 0.972539i \(0.574769\pi\)
\(594\) 3.52256 0.144532
\(595\) 19.8935 0.815552
\(596\) 14.0030 0.573583
\(597\) −24.7425 −1.01265
\(598\) −3.55978 −0.145570
\(599\) 2.45449 0.100288 0.0501439 0.998742i \(-0.484032\pi\)
0.0501439 + 0.998742i \(0.484032\pi\)
\(600\) 4.58273 0.187089
\(601\) −18.2791 −0.745621 −0.372811 0.927907i \(-0.621606\pi\)
−0.372811 + 0.927907i \(0.621606\pi\)
\(602\) −22.9033 −0.933469
\(603\) −5.62001 −0.228865
\(604\) 0.167706 0.00682387
\(605\) −15.5018 −0.630239
\(606\) −17.6852 −0.718414
\(607\) 2.74297 0.111334 0.0556669 0.998449i \(-0.482272\pi\)
0.0556669 + 0.998449i \(0.482272\pi\)
\(608\) −4.80731 −0.194962
\(609\) −32.6331 −1.32236
\(610\) −14.9463 −0.605156
\(611\) 7.91463 0.320192
\(612\) −1.28900 −0.0521047
\(613\) −43.8834 −1.77243 −0.886217 0.463270i \(-0.846676\pi\)
−0.886217 + 0.463270i \(0.846676\pi\)
\(614\) −5.25863 −0.212221
\(615\) −10.1362 −0.408731
\(616\) 2.88493 0.116237
\(617\) 5.42811 0.218528 0.109264 0.994013i \(-0.465151\pi\)
0.109264 + 0.994013i \(0.465151\pi\)
\(618\) 12.6994 0.510845
\(619\) 34.3814 1.38191 0.690953 0.722899i \(-0.257191\pi\)
0.690953 + 0.722899i \(0.257191\pi\)
\(620\) 5.62998 0.226106
\(621\) 24.6101 0.987568
\(622\) −16.1067 −0.645821
\(623\) 28.3687 1.13657
\(624\) 1.27545 0.0510588
\(625\) −2.55271 −0.102108
\(626\) −21.9897 −0.878886
\(627\) 4.94130 0.197337
\(628\) −10.7916 −0.430634
\(629\) 31.3296 1.24919
\(630\) −2.81445 −0.112130
\(631\) −30.5592 −1.21654 −0.608271 0.793730i \(-0.708136\pi\)
−0.608271 + 0.793730i \(0.708136\pi\)
\(632\) 14.2214 0.565699
\(633\) −28.7876 −1.14421
\(634\) −17.3222 −0.687952
\(635\) −21.9287 −0.870213
\(636\) 18.7564 0.743740
\(637\) −10.5506 −0.418028
\(638\) 2.89569 0.114641
\(639\) 3.29017 0.130157
\(640\) 1.46390 0.0578659
\(641\) −26.6530 −1.05273 −0.526364 0.850259i \(-0.676445\pi\)
−0.526364 + 0.850259i \(0.676445\pi\)
\(642\) 19.2644 0.760306
\(643\) −21.5247 −0.848850 −0.424425 0.905463i \(-0.639524\pi\)
−0.424425 + 0.905463i \(0.639524\pi\)
\(644\) 20.1554 0.794232
\(645\) 11.9458 0.470364
\(646\) −14.5106 −0.570914
\(647\) −35.4030 −1.39183 −0.695917 0.718122i \(-0.745002\pi\)
−0.695917 + 0.718122i \(0.745002\pi\)
\(648\) −7.53652 −0.296062
\(649\) 0.0211154 0.000828852 0
\(650\) 2.27172 0.0891041
\(651\) −27.7731 −1.08851
\(652\) −16.6289 −0.651237
\(653\) −6.97559 −0.272976 −0.136488 0.990642i \(-0.543582\pi\)
−0.136488 + 0.990642i \(0.543582\pi\)
\(654\) 15.6883 0.613461
\(655\) −3.99563 −0.156122
\(656\) 4.31664 0.168537
\(657\) −5.42168 −0.211520
\(658\) −44.8123 −1.74697
\(659\) 29.9221 1.16560 0.582800 0.812616i \(-0.301957\pi\)
0.582800 + 0.812616i \(0.301957\pi\)
\(660\) −1.50471 −0.0585706
\(661\) 39.0608 1.51929 0.759644 0.650339i \(-0.225373\pi\)
0.759644 + 0.650339i \(0.225373\pi\)
\(662\) 27.3324 1.06230
\(663\) 3.84988 0.149517
\(664\) 14.5419 0.564334
\(665\) −31.6831 −1.22862
\(666\) −4.43239 −0.171752
\(667\) 20.2305 0.783327
\(668\) 20.7414 0.802510
\(669\) −3.14011 −0.121404
\(670\) 19.2656 0.744294
\(671\) −6.54248 −0.252570
\(672\) −7.22154 −0.278577
\(673\) 3.43410 0.132375 0.0661875 0.997807i \(-0.478916\pi\)
0.0661875 + 0.997807i \(0.478916\pi\)
\(674\) 27.7097 1.06734
\(675\) −15.7052 −0.604494
\(676\) −12.3677 −0.475682
\(677\) −12.5494 −0.482315 −0.241157 0.970486i \(-0.577527\pi\)
−0.241157 + 0.970486i \(0.577527\pi\)
\(678\) −7.44218 −0.285815
\(679\) −32.3272 −1.24060
\(680\) 4.41873 0.169450
\(681\) −33.2254 −1.27320
\(682\) 2.46443 0.0943681
\(683\) −2.68799 −0.102853 −0.0514266 0.998677i \(-0.516377\pi\)
−0.0514266 + 0.998677i \(0.516377\pi\)
\(684\) 2.05291 0.0784951
\(685\) −0.746654 −0.0285282
\(686\) 28.2223 1.07753
\(687\) −22.7359 −0.867427
\(688\) −5.08727 −0.193950
\(689\) 9.29778 0.354217
\(690\) −10.5125 −0.400204
\(691\) 9.26446 0.352437 0.176218 0.984351i \(-0.443614\pi\)
0.176218 + 0.984351i \(0.443614\pi\)
\(692\) −0.856747 −0.0325686
\(693\) −1.23198 −0.0467991
\(694\) −11.7509 −0.446057
\(695\) 10.8193 0.410398
\(696\) −7.24845 −0.274752
\(697\) 13.0296 0.493531
\(698\) 18.2275 0.689921
\(699\) −21.7525 −0.822756
\(700\) −12.8624 −0.486152
\(701\) 31.7970 1.20096 0.600479 0.799641i \(-0.294977\pi\)
0.600479 + 0.799641i \(0.294977\pi\)
\(702\) −4.37101 −0.164973
\(703\) −49.8967 −1.88189
\(704\) 0.640800 0.0241511
\(705\) 23.3730 0.880276
\(706\) 0.110514 0.00415925
\(707\) 49.6373 1.86680
\(708\) −0.0528559 −0.00198645
\(709\) −30.6649 −1.15165 −0.575823 0.817574i \(-0.695318\pi\)
−0.575823 + 0.817574i \(0.695318\pi\)
\(710\) −11.2788 −0.423286
\(711\) −6.07312 −0.227760
\(712\) 6.30123 0.236149
\(713\) 17.2176 0.644803
\(714\) −21.7979 −0.815765
\(715\) −0.745901 −0.0278951
\(716\) −3.22266 −0.120436
\(717\) −30.6854 −1.14597
\(718\) −7.27872 −0.271640
\(719\) 21.1623 0.789222 0.394611 0.918848i \(-0.370879\pi\)
0.394611 + 0.918848i \(0.370879\pi\)
\(720\) −0.625145 −0.0232978
\(721\) −35.6434 −1.32743
\(722\) 4.11024 0.152967
\(723\) −13.9262 −0.517921
\(724\) 14.1885 0.527313
\(725\) −12.9103 −0.479477
\(726\) 16.9858 0.630403
\(727\) 15.0442 0.557960 0.278980 0.960297i \(-0.410004\pi\)
0.278980 + 0.960297i \(0.410004\pi\)
\(728\) −3.57981 −0.132676
\(729\) 29.6713 1.09894
\(730\) 18.5857 0.687887
\(731\) −15.3557 −0.567951
\(732\) 16.3771 0.605314
\(733\) 49.2290 1.81831 0.909157 0.416453i \(-0.136727\pi\)
0.909157 + 0.416453i \(0.136727\pi\)
\(734\) 34.8926 1.28791
\(735\) −31.1572 −1.14925
\(736\) 4.47690 0.165021
\(737\) 8.43319 0.310641
\(738\) −1.84338 −0.0678556
\(739\) 38.1345 1.40280 0.701400 0.712768i \(-0.252559\pi\)
0.701400 + 0.712768i \(0.252559\pi\)
\(740\) 15.1944 0.558556
\(741\) −6.13147 −0.225245
\(742\) −52.6437 −1.93261
\(743\) 31.7699 1.16552 0.582762 0.812643i \(-0.301972\pi\)
0.582762 + 0.812643i \(0.301972\pi\)
\(744\) −6.16895 −0.226165
\(745\) 20.4990 0.751024
\(746\) −14.7398 −0.539661
\(747\) −6.20995 −0.227210
\(748\) 1.93423 0.0707223
\(749\) −54.0695 −1.97566
\(750\) 18.4495 0.673681
\(751\) −13.1318 −0.479187 −0.239594 0.970873i \(-0.577014\pi\)
−0.239594 + 0.970873i \(0.577014\pi\)
\(752\) −9.95370 −0.362974
\(753\) 13.0459 0.475420
\(754\) −3.59315 −0.130855
\(755\) 0.245506 0.00893487
\(756\) 24.7485 0.900094
\(757\) 1.10834 0.0402833 0.0201416 0.999797i \(-0.493588\pi\)
0.0201416 + 0.999797i \(0.493588\pi\)
\(758\) −5.57572 −0.202519
\(759\) −4.60168 −0.167030
\(760\) −7.03744 −0.255275
\(761\) 13.5311 0.490501 0.245251 0.969460i \(-0.421130\pi\)
0.245251 + 0.969460i \(0.421130\pi\)
\(762\) 24.0279 0.870441
\(763\) −44.0324 −1.59408
\(764\) 14.2218 0.514528
\(765\) −1.88697 −0.0682236
\(766\) 19.9811 0.721946
\(767\) −0.0262013 −0.000946074 0
\(768\) −1.60405 −0.0578810
\(769\) 32.4517 1.17024 0.585118 0.810948i \(-0.301048\pi\)
0.585118 + 0.810948i \(0.301048\pi\)
\(770\) 4.22327 0.152196
\(771\) −23.4832 −0.845725
\(772\) 19.0874 0.686971
\(773\) −0.220654 −0.00793639 −0.00396819 0.999992i \(-0.501263\pi\)
−0.00396819 + 0.999992i \(0.501263\pi\)
\(774\) 2.17247 0.0780877
\(775\) −10.9876 −0.394686
\(776\) −7.18050 −0.257765
\(777\) −74.9548 −2.68899
\(778\) 19.3642 0.694240
\(779\) −20.7514 −0.743497
\(780\) 1.86713 0.0668541
\(781\) −4.93711 −0.176664
\(782\) 13.5133 0.483235
\(783\) 24.8407 0.887735
\(784\) 13.2687 0.473883
\(785\) −15.7979 −0.563852
\(786\) 4.37814 0.156163
\(787\) 42.3311 1.50894 0.754470 0.656335i \(-0.227894\pi\)
0.754470 + 0.656335i \(0.227894\pi\)
\(788\) −21.5889 −0.769074
\(789\) −0.365657 −0.0130177
\(790\) 20.8188 0.740701
\(791\) 20.8880 0.742692
\(792\) −0.273647 −0.00972363
\(793\) 8.11832 0.288290
\(794\) −28.4011 −1.00792
\(795\) 27.4576 0.973820
\(796\) 15.4251 0.546728
\(797\) −47.2639 −1.67417 −0.837086 0.547071i \(-0.815743\pi\)
−0.837086 + 0.547071i \(0.815743\pi\)
\(798\) 34.7162 1.22894
\(799\) −30.0448 −1.06291
\(800\) −2.85699 −0.101010
\(801\) −2.69088 −0.0950774
\(802\) −21.5763 −0.761886
\(803\) 8.13558 0.287098
\(804\) −21.1099 −0.744488
\(805\) 29.5055 1.03993
\(806\) −3.05802 −0.107714
\(807\) 13.9081 0.489589
\(808\) 11.0254 0.387872
\(809\) 31.5230 1.10829 0.554144 0.832421i \(-0.313046\pi\)
0.554144 + 0.832421i \(0.313046\pi\)
\(810\) −11.0327 −0.387651
\(811\) 32.8236 1.15259 0.576296 0.817241i \(-0.304498\pi\)
0.576296 + 0.817241i \(0.304498\pi\)
\(812\) 20.3443 0.713943
\(813\) −3.70547 −0.129956
\(814\) 6.65109 0.233120
\(815\) −24.3431 −0.852700
\(816\) −4.84174 −0.169495
\(817\) 24.4561 0.855611
\(818\) −9.91465 −0.346658
\(819\) 1.52872 0.0534178
\(820\) 6.31915 0.220674
\(821\) −30.5298 −1.06550 −0.532749 0.846273i \(-0.678841\pi\)
−0.532749 + 0.846273i \(0.678841\pi\)
\(822\) 0.818132 0.0285356
\(823\) 31.5870 1.10106 0.550528 0.834817i \(-0.314427\pi\)
0.550528 + 0.834817i \(0.314427\pi\)
\(824\) −7.91711 −0.275805
\(825\) 2.93662 0.102240
\(826\) 0.148351 0.00516179
\(827\) −35.1242 −1.22139 −0.610693 0.791867i \(-0.709109\pi\)
−0.610693 + 0.791867i \(0.709109\pi\)
\(828\) −1.91181 −0.0664401
\(829\) −20.6724 −0.717982 −0.358991 0.933341i \(-0.616879\pi\)
−0.358991 + 0.933341i \(0.616879\pi\)
\(830\) 21.2879 0.738914
\(831\) −0.864161 −0.0299774
\(832\) −0.795145 −0.0275667
\(833\) 40.0511 1.38769
\(834\) −11.8550 −0.410505
\(835\) 30.3635 1.05077
\(836\) −3.08053 −0.106542
\(837\) 21.1412 0.730748
\(838\) −30.1952 −1.04308
\(839\) −14.4932 −0.500362 −0.250181 0.968199i \(-0.580490\pi\)
−0.250181 + 0.968199i \(0.580490\pi\)
\(840\) −10.5716 −0.364756
\(841\) −8.57993 −0.295860
\(842\) −18.5652 −0.639800
\(843\) 1.55937 0.0537075
\(844\) 17.9469 0.617758
\(845\) −18.1052 −0.622837
\(846\) 4.25062 0.146139
\(847\) −47.6742 −1.63811
\(848\) −11.6932 −0.401546
\(849\) −2.82441 −0.0969334
\(850\) −8.62368 −0.295790
\(851\) 46.4673 1.59288
\(852\) 12.3585 0.423396
\(853\) 2.25368 0.0771645 0.0385823 0.999255i \(-0.487716\pi\)
0.0385823 + 0.999255i \(0.487716\pi\)
\(854\) −45.9656 −1.57291
\(855\) 3.00527 0.102778
\(856\) −12.0099 −0.410490
\(857\) −34.4017 −1.17514 −0.587570 0.809173i \(-0.699916\pi\)
−0.587570 + 0.809173i \(0.699916\pi\)
\(858\) 0.817307 0.0279024
\(859\) −0.744390 −0.0253982 −0.0126991 0.999919i \(-0.504042\pi\)
−0.0126991 + 0.999919i \(0.504042\pi\)
\(860\) −7.44728 −0.253950
\(861\) −31.1728 −1.06237
\(862\) −29.5691 −1.00713
\(863\) 39.1580 1.33295 0.666476 0.745526i \(-0.267802\pi\)
0.666476 + 0.745526i \(0.267802\pi\)
\(864\) 5.49713 0.187016
\(865\) −1.25420 −0.0426439
\(866\) −37.6270 −1.27862
\(867\) 12.6542 0.429759
\(868\) 17.3144 0.587689
\(869\) 9.11311 0.309141
\(870\) −10.6110 −0.359748
\(871\) −10.4644 −0.354573
\(872\) −9.78046 −0.331208
\(873\) 3.06636 0.103781
\(874\) −21.5218 −0.727987
\(875\) −51.7824 −1.75056
\(876\) −20.3649 −0.688066
\(877\) −19.0938 −0.644751 −0.322376 0.946612i \(-0.604481\pi\)
−0.322376 + 0.946612i \(0.604481\pi\)
\(878\) 22.4696 0.758314
\(879\) 39.1932 1.32195
\(880\) 0.938070 0.0316223
\(881\) −1.04628 −0.0352500 −0.0176250 0.999845i \(-0.505611\pi\)
−0.0176250 + 0.999845i \(0.505611\pi\)
\(882\) −5.66627 −0.190793
\(883\) −26.0847 −0.877820 −0.438910 0.898531i \(-0.644635\pi\)
−0.438910 + 0.898531i \(0.644635\pi\)
\(884\) −2.40011 −0.0807244
\(885\) −0.0773759 −0.00260096
\(886\) 36.7579 1.23491
\(887\) −11.1024 −0.372783 −0.186392 0.982476i \(-0.559679\pi\)
−0.186392 + 0.982476i \(0.559679\pi\)
\(888\) −16.6489 −0.558702
\(889\) −67.4394 −2.26184
\(890\) 9.22440 0.309203
\(891\) −4.82940 −0.161791
\(892\) 1.95762 0.0655460
\(893\) 47.8505 1.60126
\(894\) −22.4614 −0.751220
\(895\) −4.71766 −0.157694
\(896\) 4.50208 0.150404
\(897\) 5.71005 0.190653
\(898\) −4.29656 −0.143378
\(899\) 17.3789 0.579620
\(900\) 1.22005 0.0406682
\(901\) −35.2954 −1.17586
\(902\) 2.76611 0.0921012
\(903\) 36.7379 1.22256
\(904\) 4.63963 0.154312
\(905\) 20.7707 0.690440
\(906\) −0.269008 −0.00893721
\(907\) 41.9498 1.39292 0.696460 0.717595i \(-0.254757\pi\)
0.696460 + 0.717595i \(0.254757\pi\)
\(908\) 20.7135 0.687401
\(909\) −4.70828 −0.156164
\(910\) −5.24049 −0.173721
\(911\) −42.8803 −1.42069 −0.710344 0.703855i \(-0.751461\pi\)
−0.710344 + 0.703855i \(0.751461\pi\)
\(912\) 7.71114 0.255341
\(913\) 9.31844 0.308395
\(914\) −4.32456 −0.143044
\(915\) 23.9745 0.792572
\(916\) 14.1741 0.468325
\(917\) −12.2881 −0.405790
\(918\) 16.5928 0.547645
\(919\) 5.70909 0.188325 0.0941627 0.995557i \(-0.469983\pi\)
0.0941627 + 0.995557i \(0.469983\pi\)
\(920\) 6.55375 0.216071
\(921\) 8.43508 0.277945
\(922\) −30.6666 −1.00995
\(923\) 6.12628 0.201649
\(924\) −4.62757 −0.152236
\(925\) −29.6536 −0.975006
\(926\) 0.252334 0.00829222
\(927\) 3.38092 0.111044
\(928\) 4.51886 0.148339
\(929\) −19.3802 −0.635844 −0.317922 0.948117i \(-0.602985\pi\)
−0.317922 + 0.948117i \(0.602985\pi\)
\(930\) −9.03075 −0.296130
\(931\) −63.7869 −2.09053
\(932\) 13.5610 0.444207
\(933\) 25.8359 0.845830
\(934\) −11.7911 −0.385817
\(935\) 2.83152 0.0926007
\(936\) 0.339558 0.0110988
\(937\) −36.1143 −1.17980 −0.589901 0.807475i \(-0.700833\pi\)
−0.589901 + 0.807475i \(0.700833\pi\)
\(938\) 59.2492 1.93455
\(939\) 35.2725 1.15107
\(940\) −14.5713 −0.475262
\(941\) −30.1657 −0.983374 −0.491687 0.870772i \(-0.663620\pi\)
−0.491687 + 0.870772i \(0.663620\pi\)
\(942\) 17.3103 0.564000
\(943\) 19.3252 0.629314
\(944\) 0.0329516 0.00107248
\(945\) 36.2294 1.17854
\(946\) −3.25993 −0.105989
\(947\) −5.83660 −0.189664 −0.0948319 0.995493i \(-0.530231\pi\)
−0.0948319 + 0.995493i \(0.530231\pi\)
\(948\) −22.8118 −0.740894
\(949\) −10.0951 −0.327702
\(950\) 13.7344 0.445603
\(951\) 27.7856 0.901009
\(952\) 13.5893 0.440433
\(953\) −42.4375 −1.37469 −0.687343 0.726333i \(-0.741223\pi\)
−0.687343 + 0.726333i \(0.741223\pi\)
\(954\) 4.99346 0.161669
\(955\) 20.8194 0.673700
\(956\) 19.1300 0.618708
\(957\) −4.64481 −0.150145
\(958\) 18.7333 0.605245
\(959\) −2.29626 −0.0741500
\(960\) −2.34817 −0.0757868
\(961\) −16.2093 −0.522880
\(962\) −8.25308 −0.266090
\(963\) 5.12870 0.165270
\(964\) 8.68193 0.279626
\(965\) 27.9421 0.899489
\(966\) −32.3301 −1.04020
\(967\) 34.3625 1.10502 0.552512 0.833505i \(-0.313669\pi\)
0.552512 + 0.833505i \(0.313669\pi\)
\(968\) −10.5894 −0.340355
\(969\) 23.2757 0.747724
\(970\) −10.5116 −0.337506
\(971\) −21.1595 −0.679042 −0.339521 0.940599i \(-0.610265\pi\)
−0.339521 + 0.940599i \(0.610265\pi\)
\(972\) −4.40246 −0.141209
\(973\) 33.2735 1.06670
\(974\) −35.2519 −1.12954
\(975\) −3.64394 −0.116699
\(976\) −10.2099 −0.326810
\(977\) −53.7924 −1.72097 −0.860486 0.509474i \(-0.829840\pi\)
−0.860486 + 0.509474i \(0.829840\pi\)
\(978\) 26.6734 0.852923
\(979\) 4.03783 0.129050
\(980\) 19.4241 0.620481
\(981\) 4.17664 0.133350
\(982\) −40.3227 −1.28675
\(983\) 17.3371 0.552969 0.276484 0.961018i \(-0.410831\pi\)
0.276484 + 0.961018i \(0.410831\pi\)
\(984\) −6.92409 −0.220732
\(985\) −31.6041 −1.00699
\(986\) 13.6400 0.434385
\(987\) 71.8810 2.28800
\(988\) 3.82251 0.121610
\(989\) −22.7752 −0.724209
\(990\) −0.400593 −0.0127317
\(991\) −3.87627 −0.123134 −0.0615668 0.998103i \(-0.519610\pi\)
−0.0615668 + 0.998103i \(0.519610\pi\)
\(992\) 3.84587 0.122106
\(993\) −43.8424 −1.39130
\(994\) −34.6868 −1.10020
\(995\) 22.5809 0.715861
\(996\) −23.3258 −0.739107
\(997\) −53.5674 −1.69650 −0.848248 0.529600i \(-0.822342\pi\)
−0.848248 + 0.529600i \(0.822342\pi\)
\(998\) −8.63150 −0.273225
\(999\) 57.0566 1.80519
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 4022.2.a.f.1.11 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4022.2.a.f.1.11 50 1.1 even 1 trivial