Properties

Label 4022.2.a.f.1.14
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 1.14
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.45431 q^{3} +1.00000 q^{4} -2.49956 q^{5} -1.45431 q^{6} -3.69872 q^{7} +1.00000 q^{8} -0.884987 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.45431 q^{3} +1.00000 q^{4} -2.49956 q^{5} -1.45431 q^{6} -3.69872 q^{7} +1.00000 q^{8} -0.884987 q^{9} -2.49956 q^{10} -3.95977 q^{11} -1.45431 q^{12} -4.27037 q^{13} -3.69872 q^{14} +3.63513 q^{15} +1.00000 q^{16} +2.57289 q^{17} -0.884987 q^{18} -6.17964 q^{19} -2.49956 q^{20} +5.37908 q^{21} -3.95977 q^{22} +2.01625 q^{23} -1.45431 q^{24} +1.24781 q^{25} -4.27037 q^{26} +5.64997 q^{27} -3.69872 q^{28} +0.563494 q^{29} +3.63513 q^{30} -6.95868 q^{31} +1.00000 q^{32} +5.75872 q^{33} +2.57289 q^{34} +9.24519 q^{35} -0.884987 q^{36} -7.95922 q^{37} -6.17964 q^{38} +6.21043 q^{39} -2.49956 q^{40} -5.61346 q^{41} +5.37908 q^{42} -7.70471 q^{43} -3.95977 q^{44} +2.21208 q^{45} +2.01625 q^{46} +3.56019 q^{47} -1.45431 q^{48} +6.68055 q^{49} +1.24781 q^{50} -3.74177 q^{51} -4.27037 q^{52} -14.2373 q^{53} +5.64997 q^{54} +9.89769 q^{55} -3.69872 q^{56} +8.98710 q^{57} +0.563494 q^{58} +10.6070 q^{59} +3.63513 q^{60} -9.71533 q^{61} -6.95868 q^{62} +3.27332 q^{63} +1.00000 q^{64} +10.6740 q^{65} +5.75872 q^{66} -0.780231 q^{67} +2.57289 q^{68} -2.93225 q^{69} +9.24519 q^{70} +7.96118 q^{71} -0.884987 q^{72} +15.9875 q^{73} -7.95922 q^{74} -1.81470 q^{75} -6.17964 q^{76} +14.6461 q^{77} +6.21043 q^{78} +13.5629 q^{79} -2.49956 q^{80} -5.56184 q^{81} -5.61346 q^{82} -5.77362 q^{83} +5.37908 q^{84} -6.43110 q^{85} -7.70471 q^{86} -0.819494 q^{87} -3.95977 q^{88} +16.5453 q^{89} +2.21208 q^{90} +15.7949 q^{91} +2.01625 q^{92} +10.1201 q^{93} +3.56019 q^{94} +15.4464 q^{95} -1.45431 q^{96} +8.78153 q^{97} +6.68055 q^{98} +3.50434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 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
\(3\) −1.45431 −0.839645 −0.419823 0.907606i \(-0.637908\pi\)
−0.419823 + 0.907606i \(0.637908\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.49956 −1.11784 −0.558919 0.829222i \(-0.688784\pi\)
−0.558919 + 0.829222i \(0.688784\pi\)
\(6\) −1.45431 −0.593719
\(7\) −3.69872 −1.39799 −0.698993 0.715129i \(-0.746368\pi\)
−0.698993 + 0.715129i \(0.746368\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.884987 −0.294996
\(10\) −2.49956 −0.790431
\(11\) −3.95977 −1.19392 −0.596958 0.802273i \(-0.703624\pi\)
−0.596958 + 0.802273i \(0.703624\pi\)
\(12\) −1.45431 −0.419823
\(13\) −4.27037 −1.18439 −0.592193 0.805796i \(-0.701738\pi\)
−0.592193 + 0.805796i \(0.701738\pi\)
\(14\) −3.69872 −0.988525
\(15\) 3.63513 0.938588
\(16\) 1.00000 0.250000
\(17\) 2.57289 0.624017 0.312009 0.950079i \(-0.398998\pi\)
0.312009 + 0.950079i \(0.398998\pi\)
\(18\) −0.884987 −0.208593
\(19\) −6.17964 −1.41771 −0.708853 0.705356i \(-0.750787\pi\)
−0.708853 + 0.705356i \(0.750787\pi\)
\(20\) −2.49956 −0.558919
\(21\) 5.37908 1.17381
\(22\) −3.95977 −0.844225
\(23\) 2.01625 0.420417 0.210208 0.977657i \(-0.432586\pi\)
0.210208 + 0.977657i \(0.432586\pi\)
\(24\) −1.45431 −0.296859
\(25\) 1.24781 0.249563
\(26\) −4.27037 −0.837488
\(27\) 5.64997 1.08734
\(28\) −3.69872 −0.698993
\(29\) 0.563494 0.104638 0.0523191 0.998630i \(-0.483339\pi\)
0.0523191 + 0.998630i \(0.483339\pi\)
\(30\) 3.63513 0.663682
\(31\) −6.95868 −1.24982 −0.624908 0.780699i \(-0.714863\pi\)
−0.624908 + 0.780699i \(0.714863\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.75872 1.00247
\(34\) 2.57289 0.441247
\(35\) 9.24519 1.56272
\(36\) −0.884987 −0.147498
\(37\) −7.95922 −1.30849 −0.654244 0.756283i \(-0.727013\pi\)
−0.654244 + 0.756283i \(0.727013\pi\)
\(38\) −6.17964 −1.00247
\(39\) 6.21043 0.994465
\(40\) −2.49956 −0.395216
\(41\) −5.61346 −0.876675 −0.438337 0.898811i \(-0.644432\pi\)
−0.438337 + 0.898811i \(0.644432\pi\)
\(42\) 5.37908 0.830010
\(43\) −7.70471 −1.17496 −0.587479 0.809240i \(-0.699879\pi\)
−0.587479 + 0.809240i \(0.699879\pi\)
\(44\) −3.95977 −0.596958
\(45\) 2.21208 0.329757
\(46\) 2.01625 0.297280
\(47\) 3.56019 0.519307 0.259654 0.965702i \(-0.416392\pi\)
0.259654 + 0.965702i \(0.416392\pi\)
\(48\) −1.45431 −0.209911
\(49\) 6.68055 0.954364
\(50\) 1.24781 0.176467
\(51\) −3.74177 −0.523953
\(52\) −4.27037 −0.592193
\(53\) −14.2373 −1.95564 −0.977821 0.209444i \(-0.932835\pi\)
−0.977821 + 0.209444i \(0.932835\pi\)
\(54\) 5.64997 0.768863
\(55\) 9.89769 1.33460
\(56\) −3.69872 −0.494263
\(57\) 8.98710 1.19037
\(58\) 0.563494 0.0739903
\(59\) 10.6070 1.38091 0.690456 0.723374i \(-0.257410\pi\)
0.690456 + 0.723374i \(0.257410\pi\)
\(60\) 3.63513 0.469294
\(61\) −9.71533 −1.24392 −0.621960 0.783049i \(-0.713663\pi\)
−0.621960 + 0.783049i \(0.713663\pi\)
\(62\) −6.95868 −0.883753
\(63\) 3.27332 0.412400
\(64\) 1.00000 0.125000
\(65\) 10.6740 1.32395
\(66\) 5.75872 0.708850
\(67\) −0.780231 −0.0953204 −0.0476602 0.998864i \(-0.515176\pi\)
−0.0476602 + 0.998864i \(0.515176\pi\)
\(68\) 2.57289 0.312009
\(69\) −2.93225 −0.353001
\(70\) 9.24519 1.10501
\(71\) 7.96118 0.944818 0.472409 0.881379i \(-0.343385\pi\)
0.472409 + 0.881379i \(0.343385\pi\)
\(72\) −0.884987 −0.104297
\(73\) 15.9875 1.87120 0.935599 0.353066i \(-0.114861\pi\)
0.935599 + 0.353066i \(0.114861\pi\)
\(74\) −7.95922 −0.925241
\(75\) −1.81470 −0.209544
\(76\) −6.17964 −0.708853
\(77\) 14.6461 1.66908
\(78\) 6.21043 0.703193
\(79\) 13.5629 1.52594 0.762971 0.646433i \(-0.223740\pi\)
0.762971 + 0.646433i \(0.223740\pi\)
\(80\) −2.49956 −0.279460
\(81\) −5.56184 −0.617982
\(82\) −5.61346 −0.619903
\(83\) −5.77362 −0.633737 −0.316869 0.948469i \(-0.602631\pi\)
−0.316869 + 0.948469i \(0.602631\pi\)
\(84\) 5.37908 0.586906
\(85\) −6.43110 −0.697550
\(86\) −7.70471 −0.830820
\(87\) −0.819494 −0.0878589
\(88\) −3.95977 −0.422113
\(89\) 16.5453 1.75380 0.876901 0.480672i \(-0.159607\pi\)
0.876901 + 0.480672i \(0.159607\pi\)
\(90\) 2.21208 0.233174
\(91\) 15.7949 1.65576
\(92\) 2.01625 0.210208
\(93\) 10.1201 1.04940
\(94\) 3.56019 0.367206
\(95\) 15.4464 1.58477
\(96\) −1.45431 −0.148430
\(97\) 8.78153 0.891629 0.445815 0.895125i \(-0.352914\pi\)
0.445815 + 0.895125i \(0.352914\pi\)
\(98\) 6.68055 0.674837
\(99\) 3.50434 0.352200
\(100\) 1.24781 0.124781
\(101\) 1.36973 0.136294 0.0681469 0.997675i \(-0.478291\pi\)
0.0681469 + 0.997675i \(0.478291\pi\)
\(102\) −3.74177 −0.370491
\(103\) −5.63186 −0.554924 −0.277462 0.960737i \(-0.589493\pi\)
−0.277462 + 0.960737i \(0.589493\pi\)
\(104\) −4.27037 −0.418744
\(105\) −13.4454 −1.31213
\(106\) −14.2373 −1.38285
\(107\) 18.2872 1.76789 0.883945 0.467590i \(-0.154878\pi\)
0.883945 + 0.467590i \(0.154878\pi\)
\(108\) 5.64997 0.543669
\(109\) −14.6610 −1.40427 −0.702135 0.712044i \(-0.747770\pi\)
−0.702135 + 0.712044i \(0.747770\pi\)
\(110\) 9.89769 0.943708
\(111\) 11.5752 1.09867
\(112\) −3.69872 −0.349496
\(113\) −17.0292 −1.60197 −0.800987 0.598682i \(-0.795691\pi\)
−0.800987 + 0.598682i \(0.795691\pi\)
\(114\) 8.98710 0.841719
\(115\) −5.03974 −0.469958
\(116\) 0.563494 0.0523191
\(117\) 3.77922 0.349389
\(118\) 10.6070 0.976452
\(119\) −9.51640 −0.872367
\(120\) 3.63513 0.331841
\(121\) 4.67976 0.425433
\(122\) −9.71533 −0.879584
\(123\) 8.16370 0.736096
\(124\) −6.95868 −0.624908
\(125\) 9.37883 0.838868
\(126\) 3.27332 0.291611
\(127\) −12.2429 −1.08638 −0.543191 0.839609i \(-0.682784\pi\)
−0.543191 + 0.839609i \(0.682784\pi\)
\(128\) 1.00000 0.0883883
\(129\) 11.2050 0.986547
\(130\) 10.6740 0.936176
\(131\) −3.81360 −0.333195 −0.166598 0.986025i \(-0.553278\pi\)
−0.166598 + 0.986025i \(0.553278\pi\)
\(132\) 5.75872 0.501233
\(133\) 22.8568 1.98193
\(134\) −0.780231 −0.0674017
\(135\) −14.1225 −1.21547
\(136\) 2.57289 0.220623
\(137\) −15.8322 −1.35264 −0.676320 0.736608i \(-0.736426\pi\)
−0.676320 + 0.736608i \(0.736426\pi\)
\(138\) −2.93225 −0.249609
\(139\) −10.2425 −0.868759 −0.434380 0.900730i \(-0.643032\pi\)
−0.434380 + 0.900730i \(0.643032\pi\)
\(140\) 9.24519 0.781361
\(141\) −5.17762 −0.436034
\(142\) 7.96118 0.668087
\(143\) 16.9097 1.41406
\(144\) −0.884987 −0.0737489
\(145\) −1.40849 −0.116969
\(146\) 15.9875 1.32314
\(147\) −9.71557 −0.801327
\(148\) −7.95922 −0.654244
\(149\) −11.7499 −0.962593 −0.481296 0.876558i \(-0.659834\pi\)
−0.481296 + 0.876558i \(0.659834\pi\)
\(150\) −1.81470 −0.148170
\(151\) 5.76900 0.469474 0.234737 0.972059i \(-0.424577\pi\)
0.234737 + 0.972059i \(0.424577\pi\)
\(152\) −6.17964 −0.501235
\(153\) −2.27697 −0.184082
\(154\) 14.6461 1.18021
\(155\) 17.3937 1.39709
\(156\) 6.21043 0.497232
\(157\) −5.17265 −0.412823 −0.206411 0.978465i \(-0.566179\pi\)
−0.206411 + 0.978465i \(0.566179\pi\)
\(158\) 13.5629 1.07900
\(159\) 20.7054 1.64205
\(160\) −2.49956 −0.197608
\(161\) −7.45754 −0.587737
\(162\) −5.56184 −0.436979
\(163\) −4.43532 −0.347401 −0.173700 0.984799i \(-0.555572\pi\)
−0.173700 + 0.984799i \(0.555572\pi\)
\(164\) −5.61346 −0.438337
\(165\) −14.3943 −1.12059
\(166\) −5.77362 −0.448120
\(167\) −2.90902 −0.225107 −0.112554 0.993646i \(-0.535903\pi\)
−0.112554 + 0.993646i \(0.535903\pi\)
\(168\) 5.37908 0.415005
\(169\) 5.23603 0.402771
\(170\) −6.43110 −0.493243
\(171\) 5.46890 0.418217
\(172\) −7.70471 −0.587479
\(173\) −12.1386 −0.922882 −0.461441 0.887171i \(-0.652667\pi\)
−0.461441 + 0.887171i \(0.652667\pi\)
\(174\) −0.819494 −0.0621257
\(175\) −4.61531 −0.348885
\(176\) −3.95977 −0.298479
\(177\) −15.4258 −1.15948
\(178\) 16.5453 1.24012
\(179\) 22.6815 1.69530 0.847648 0.530560i \(-0.178018\pi\)
0.847648 + 0.530560i \(0.178018\pi\)
\(180\) 2.21208 0.164879
\(181\) −5.22540 −0.388401 −0.194201 0.980962i \(-0.562211\pi\)
−0.194201 + 0.980962i \(0.562211\pi\)
\(182\) 15.7949 1.17080
\(183\) 14.1291 1.04445
\(184\) 2.01625 0.148640
\(185\) 19.8946 1.46268
\(186\) 10.1201 0.742039
\(187\) −10.1880 −0.745023
\(188\) 3.56019 0.259654
\(189\) −20.8977 −1.52008
\(190\) 15.4464 1.12060
\(191\) −8.67170 −0.627462 −0.313731 0.949512i \(-0.601579\pi\)
−0.313731 + 0.949512i \(0.601579\pi\)
\(192\) −1.45431 −0.104956
\(193\) −3.45130 −0.248430 −0.124215 0.992255i \(-0.539641\pi\)
−0.124215 + 0.992255i \(0.539641\pi\)
\(194\) 8.78153 0.630477
\(195\) −15.5234 −1.11165
\(196\) 6.68055 0.477182
\(197\) 2.83509 0.201992 0.100996 0.994887i \(-0.467797\pi\)
0.100996 + 0.994887i \(0.467797\pi\)
\(198\) 3.50434 0.249043
\(199\) −11.0882 −0.786024 −0.393012 0.919533i \(-0.628567\pi\)
−0.393012 + 0.919533i \(0.628567\pi\)
\(200\) 1.24781 0.0882337
\(201\) 1.13470 0.0800353
\(202\) 1.36973 0.0963742
\(203\) −2.08421 −0.146283
\(204\) −3.74177 −0.261977
\(205\) 14.0312 0.979980
\(206\) −5.63186 −0.392391
\(207\) −1.78435 −0.124021
\(208\) −4.27037 −0.296097
\(209\) 24.4699 1.69262
\(210\) −13.4454 −0.927818
\(211\) 6.12946 0.421970 0.210985 0.977489i \(-0.432333\pi\)
0.210985 + 0.977489i \(0.432333\pi\)
\(212\) −14.2373 −0.977821
\(213\) −11.5780 −0.793312
\(214\) 18.2872 1.25009
\(215\) 19.2584 1.31341
\(216\) 5.64997 0.384432
\(217\) 25.7382 1.74722
\(218\) −14.6610 −0.992969
\(219\) −23.2508 −1.57114
\(220\) 9.89769 0.667302
\(221\) −10.9872 −0.739077
\(222\) 11.5752 0.776874
\(223\) 24.4239 1.63554 0.817772 0.575542i \(-0.195209\pi\)
0.817772 + 0.575542i \(0.195209\pi\)
\(224\) −3.69872 −0.247131
\(225\) −1.10430 −0.0736199
\(226\) −17.0292 −1.13277
\(227\) 18.8628 1.25197 0.625985 0.779835i \(-0.284697\pi\)
0.625985 + 0.779835i \(0.284697\pi\)
\(228\) 8.98710 0.595185
\(229\) 5.51478 0.364427 0.182213 0.983259i \(-0.441674\pi\)
0.182213 + 0.983259i \(0.441674\pi\)
\(230\) −5.03974 −0.332311
\(231\) −21.2999 −1.40143
\(232\) 0.563494 0.0369952
\(233\) 3.77347 0.247209 0.123604 0.992332i \(-0.460555\pi\)
0.123604 + 0.992332i \(0.460555\pi\)
\(234\) 3.77922 0.247055
\(235\) −8.89892 −0.580502
\(236\) 10.6070 0.690456
\(237\) −19.7246 −1.28125
\(238\) −9.51640 −0.616857
\(239\) −13.1769 −0.852345 −0.426172 0.904642i \(-0.640138\pi\)
−0.426172 + 0.904642i \(0.640138\pi\)
\(240\) 3.63513 0.234647
\(241\) −16.5754 −1.06771 −0.533856 0.845575i \(-0.679258\pi\)
−0.533856 + 0.845575i \(0.679258\pi\)
\(242\) 4.67976 0.300827
\(243\) −8.86128 −0.568451
\(244\) −9.71533 −0.621960
\(245\) −16.6984 −1.06682
\(246\) 8.16370 0.520498
\(247\) 26.3893 1.67911
\(248\) −6.95868 −0.441877
\(249\) 8.39663 0.532115
\(250\) 9.37883 0.593169
\(251\) −29.1200 −1.83804 −0.919018 0.394215i \(-0.871017\pi\)
−0.919018 + 0.394215i \(0.871017\pi\)
\(252\) 3.27332 0.206200
\(253\) −7.98388 −0.501942
\(254\) −12.2429 −0.768188
\(255\) 9.35280 0.585695
\(256\) 1.00000 0.0625000
\(257\) −20.7742 −1.29586 −0.647931 0.761699i \(-0.724365\pi\)
−0.647931 + 0.761699i \(0.724365\pi\)
\(258\) 11.2050 0.697594
\(259\) 29.4390 1.82925
\(260\) 10.6740 0.661976
\(261\) −0.498685 −0.0308678
\(262\) −3.81360 −0.235605
\(263\) −20.9500 −1.29183 −0.645915 0.763410i \(-0.723524\pi\)
−0.645915 + 0.763410i \(0.723524\pi\)
\(264\) 5.75872 0.354425
\(265\) 35.5870 2.18609
\(266\) 22.8568 1.40144
\(267\) −24.0620 −1.47257
\(268\) −0.780231 −0.0476602
\(269\) −5.65226 −0.344624 −0.172312 0.985042i \(-0.555124\pi\)
−0.172312 + 0.985042i \(0.555124\pi\)
\(270\) −14.1225 −0.859465
\(271\) −11.9929 −0.728518 −0.364259 0.931298i \(-0.618678\pi\)
−0.364259 + 0.931298i \(0.618678\pi\)
\(272\) 2.57289 0.156004
\(273\) −22.9707 −1.39025
\(274\) −15.8322 −0.956461
\(275\) −4.94105 −0.297957
\(276\) −2.93225 −0.176501
\(277\) −1.12905 −0.0678379 −0.0339190 0.999425i \(-0.510799\pi\)
−0.0339190 + 0.999425i \(0.510799\pi\)
\(278\) −10.2425 −0.614306
\(279\) 6.15834 0.368690
\(280\) 9.24519 0.552506
\(281\) 21.8794 1.30522 0.652608 0.757695i \(-0.273675\pi\)
0.652608 + 0.757695i \(0.273675\pi\)
\(282\) −5.17762 −0.308323
\(283\) 25.2573 1.50139 0.750695 0.660649i \(-0.229719\pi\)
0.750695 + 0.660649i \(0.229719\pi\)
\(284\) 7.96118 0.472409
\(285\) −22.4638 −1.33064
\(286\) 16.9097 0.999889
\(287\) 20.7626 1.22558
\(288\) −0.884987 −0.0521484
\(289\) −10.3802 −0.610603
\(290\) −1.40849 −0.0827092
\(291\) −12.7711 −0.748652
\(292\) 15.9875 0.935599
\(293\) −5.94045 −0.347045 −0.173522 0.984830i \(-0.555515\pi\)
−0.173522 + 0.984830i \(0.555515\pi\)
\(294\) −9.71557 −0.566624
\(295\) −26.5128 −1.54364
\(296\) −7.95922 −0.462621
\(297\) −22.3726 −1.29819
\(298\) −11.7499 −0.680656
\(299\) −8.61012 −0.497936
\(300\) −1.81470 −0.104772
\(301\) 28.4976 1.64257
\(302\) 5.76900 0.331968
\(303\) −1.99202 −0.114438
\(304\) −6.17964 −0.354427
\(305\) 24.2841 1.39050
\(306\) −2.27697 −0.130166
\(307\) 10.4116 0.594224 0.297112 0.954843i \(-0.403977\pi\)
0.297112 + 0.954843i \(0.403977\pi\)
\(308\) 14.6461 0.834538
\(309\) 8.19047 0.465939
\(310\) 17.3937 0.987893
\(311\) 33.2987 1.88820 0.944098 0.329665i \(-0.106936\pi\)
0.944098 + 0.329665i \(0.106936\pi\)
\(312\) 6.21043 0.351596
\(313\) 6.47296 0.365873 0.182937 0.983125i \(-0.441440\pi\)
0.182937 + 0.983125i \(0.441440\pi\)
\(314\) −5.17265 −0.291910
\(315\) −8.18187 −0.460996
\(316\) 13.5629 0.762971
\(317\) 19.4944 1.09491 0.547457 0.836834i \(-0.315596\pi\)
0.547457 + 0.836834i \(0.315596\pi\)
\(318\) 20.7054 1.16110
\(319\) −2.23130 −0.124929
\(320\) −2.49956 −0.139730
\(321\) −26.5952 −1.48440
\(322\) −7.45754 −0.415593
\(323\) −15.8995 −0.884673
\(324\) −5.56184 −0.308991
\(325\) −5.32862 −0.295579
\(326\) −4.43532 −0.245650
\(327\) 21.3216 1.17909
\(328\) −5.61346 −0.309951
\(329\) −13.1682 −0.725984
\(330\) −14.3943 −0.792380
\(331\) 3.65322 0.200799 0.100400 0.994947i \(-0.467988\pi\)
0.100400 + 0.994947i \(0.467988\pi\)
\(332\) −5.77362 −0.316869
\(333\) 7.04381 0.385998
\(334\) −2.90902 −0.159175
\(335\) 1.95024 0.106553
\(336\) 5.37908 0.293453
\(337\) −19.3565 −1.05442 −0.527208 0.849736i \(-0.676761\pi\)
−0.527208 + 0.849736i \(0.676761\pi\)
\(338\) 5.23603 0.284802
\(339\) 24.7657 1.34509
\(340\) −6.43110 −0.348775
\(341\) 27.5548 1.49217
\(342\) 5.46890 0.295724
\(343\) 1.18157 0.0637990
\(344\) −7.70471 −0.415410
\(345\) 7.32934 0.394598
\(346\) −12.1386 −0.652576
\(347\) −32.2125 −1.72926 −0.864628 0.502413i \(-0.832446\pi\)
−0.864628 + 0.502413i \(0.832446\pi\)
\(348\) −0.819494 −0.0439295
\(349\) 6.54921 0.350571 0.175286 0.984518i \(-0.443915\pi\)
0.175286 + 0.984518i \(0.443915\pi\)
\(350\) −4.61531 −0.246699
\(351\) −24.1274 −1.28783
\(352\) −3.95977 −0.211056
\(353\) 25.0982 1.33584 0.667922 0.744231i \(-0.267184\pi\)
0.667922 + 0.744231i \(0.267184\pi\)
\(354\) −15.4258 −0.819874
\(355\) −19.8995 −1.05615
\(356\) 16.5453 0.876901
\(357\) 13.8398 0.732479
\(358\) 22.6815 1.19875
\(359\) −7.88624 −0.416220 −0.208110 0.978105i \(-0.566731\pi\)
−0.208110 + 0.978105i \(0.566731\pi\)
\(360\) 2.21208 0.116587
\(361\) 19.1880 1.00989
\(362\) −5.22540 −0.274641
\(363\) −6.80582 −0.357213
\(364\) 15.7949 0.827878
\(365\) −39.9618 −2.09170
\(366\) 14.1291 0.738539
\(367\) −10.9855 −0.573440 −0.286720 0.958014i \(-0.592565\pi\)
−0.286720 + 0.958014i \(0.592565\pi\)
\(368\) 2.01625 0.105104
\(369\) 4.96784 0.258615
\(370\) 19.8946 1.03427
\(371\) 52.6598 2.73396
\(372\) 10.1201 0.524701
\(373\) −2.84154 −0.147130 −0.0735648 0.997290i \(-0.523438\pi\)
−0.0735648 + 0.997290i \(0.523438\pi\)
\(374\) −10.1880 −0.526811
\(375\) −13.6397 −0.704351
\(376\) 3.56019 0.183603
\(377\) −2.40632 −0.123932
\(378\) −20.8977 −1.07486
\(379\) −21.7288 −1.11613 −0.558066 0.829797i \(-0.688456\pi\)
−0.558066 + 0.829797i \(0.688456\pi\)
\(380\) 15.4464 0.792384
\(381\) 17.8050 0.912176
\(382\) −8.67170 −0.443683
\(383\) −22.9149 −1.17090 −0.585448 0.810710i \(-0.699081\pi\)
−0.585448 + 0.810710i \(0.699081\pi\)
\(384\) −1.45431 −0.0742149
\(385\) −36.6088 −1.86576
\(386\) −3.45130 −0.175666
\(387\) 6.81857 0.346607
\(388\) 8.78153 0.445815
\(389\) −31.2393 −1.58390 −0.791948 0.610589i \(-0.790933\pi\)
−0.791948 + 0.610589i \(0.790933\pi\)
\(390\) −15.5234 −0.786056
\(391\) 5.18758 0.262347
\(392\) 6.68055 0.337418
\(393\) 5.54614 0.279766
\(394\) 2.83509 0.142830
\(395\) −33.9012 −1.70576
\(396\) 3.50434 0.176100
\(397\) 20.5339 1.03057 0.515283 0.857020i \(-0.327687\pi\)
0.515283 + 0.857020i \(0.327687\pi\)
\(398\) −11.0882 −0.555803
\(399\) −33.2408 −1.66412
\(400\) 1.24781 0.0623907
\(401\) −25.4113 −1.26898 −0.634489 0.772932i \(-0.718789\pi\)
−0.634489 + 0.772932i \(0.718789\pi\)
\(402\) 1.13470 0.0565935
\(403\) 29.7161 1.48026
\(404\) 1.36973 0.0681469
\(405\) 13.9022 0.690804
\(406\) −2.08421 −0.103437
\(407\) 31.5167 1.56222
\(408\) −3.74177 −0.185245
\(409\) −2.49880 −0.123558 −0.0617790 0.998090i \(-0.519677\pi\)
−0.0617790 + 0.998090i \(0.519677\pi\)
\(410\) 14.0312 0.692951
\(411\) 23.0250 1.13574
\(412\) −5.63186 −0.277462
\(413\) −39.2323 −1.93050
\(414\) −1.78435 −0.0876962
\(415\) 14.4315 0.708416
\(416\) −4.27037 −0.209372
\(417\) 14.8958 0.729450
\(418\) 24.4699 1.19686
\(419\) −22.0519 −1.07730 −0.538652 0.842528i \(-0.681066\pi\)
−0.538652 + 0.842528i \(0.681066\pi\)
\(420\) −13.4454 −0.656066
\(421\) 37.9420 1.84918 0.924589 0.380966i \(-0.124408\pi\)
0.924589 + 0.380966i \(0.124408\pi\)
\(422\) 6.12946 0.298378
\(423\) −3.15072 −0.153193
\(424\) −14.2373 −0.691424
\(425\) 3.21048 0.155731
\(426\) −11.5780 −0.560956
\(427\) 35.9343 1.73898
\(428\) 18.2872 0.883945
\(429\) −24.5919 −1.18731
\(430\) 19.2584 0.928723
\(431\) 15.8101 0.761544 0.380772 0.924669i \(-0.375658\pi\)
0.380772 + 0.924669i \(0.375658\pi\)
\(432\) 5.64997 0.271834
\(433\) 23.1500 1.11252 0.556258 0.831010i \(-0.312237\pi\)
0.556258 + 0.831010i \(0.312237\pi\)
\(434\) 25.7382 1.23547
\(435\) 2.04838 0.0982121
\(436\) −14.6610 −0.702135
\(437\) −12.4597 −0.596028
\(438\) −23.2508 −1.11097
\(439\) −10.3378 −0.493398 −0.246699 0.969092i \(-0.579346\pi\)
−0.246699 + 0.969092i \(0.579346\pi\)
\(440\) 9.89769 0.471854
\(441\) −5.91220 −0.281533
\(442\) −10.9872 −0.522607
\(443\) −31.8458 −1.51304 −0.756520 0.653971i \(-0.773102\pi\)
−0.756520 + 0.653971i \(0.773102\pi\)
\(444\) 11.5752 0.549333
\(445\) −41.3561 −1.96047
\(446\) 24.4239 1.15650
\(447\) 17.0880 0.808236
\(448\) −3.69872 −0.174748
\(449\) −8.92406 −0.421153 −0.210576 0.977577i \(-0.567534\pi\)
−0.210576 + 0.977577i \(0.567534\pi\)
\(450\) −1.10430 −0.0520571
\(451\) 22.2280 1.04667
\(452\) −17.0292 −0.800987
\(453\) −8.38990 −0.394192
\(454\) 18.8628 0.885277
\(455\) −39.4803 −1.85087
\(456\) 8.98710 0.420860
\(457\) −35.3746 −1.65475 −0.827376 0.561648i \(-0.810168\pi\)
−0.827376 + 0.561648i \(0.810168\pi\)
\(458\) 5.51478 0.257689
\(459\) 14.5367 0.678517
\(460\) −5.03974 −0.234979
\(461\) −16.7319 −0.779281 −0.389640 0.920967i \(-0.627401\pi\)
−0.389640 + 0.920967i \(0.627401\pi\)
\(462\) −21.2999 −0.990962
\(463\) 5.46233 0.253856 0.126928 0.991912i \(-0.459488\pi\)
0.126928 + 0.991912i \(0.459488\pi\)
\(464\) 0.563494 0.0261595
\(465\) −25.2957 −1.17306
\(466\) 3.77347 0.174803
\(467\) −22.9179 −1.06051 −0.530257 0.847837i \(-0.677905\pi\)
−0.530257 + 0.847837i \(0.677905\pi\)
\(468\) 3.77922 0.174694
\(469\) 2.88586 0.133257
\(470\) −8.89892 −0.410477
\(471\) 7.52263 0.346625
\(472\) 10.6070 0.488226
\(473\) 30.5089 1.40280
\(474\) −19.7246 −0.905980
\(475\) −7.71104 −0.353807
\(476\) −9.51640 −0.436183
\(477\) 12.5998 0.576906
\(478\) −13.1769 −0.602699
\(479\) −27.0543 −1.23614 −0.618070 0.786123i \(-0.712085\pi\)
−0.618070 + 0.786123i \(0.712085\pi\)
\(480\) 3.63513 0.165920
\(481\) 33.9888 1.54976
\(482\) −16.5754 −0.754987
\(483\) 10.8456 0.493490
\(484\) 4.67976 0.212717
\(485\) −21.9500 −0.996697
\(486\) −8.86128 −0.401956
\(487\) 25.6673 1.16310 0.581548 0.813512i \(-0.302447\pi\)
0.581548 + 0.813512i \(0.302447\pi\)
\(488\) −9.71533 −0.439792
\(489\) 6.45032 0.291694
\(490\) −16.6984 −0.754359
\(491\) 22.4322 1.01235 0.506176 0.862430i \(-0.331059\pi\)
0.506176 + 0.862430i \(0.331059\pi\)
\(492\) 8.16370 0.368048
\(493\) 1.44981 0.0652960
\(494\) 26.3893 1.18731
\(495\) −8.75933 −0.393702
\(496\) −6.95868 −0.312454
\(497\) −29.4462 −1.32084
\(498\) 8.39663 0.376262
\(499\) −11.9870 −0.536612 −0.268306 0.963334i \(-0.586464\pi\)
−0.268306 + 0.963334i \(0.586464\pi\)
\(500\) 9.37883 0.419434
\(501\) 4.23062 0.189010
\(502\) −29.1200 −1.29969
\(503\) 10.7759 0.480473 0.240237 0.970714i \(-0.422775\pi\)
0.240237 + 0.970714i \(0.422775\pi\)
\(504\) 3.27332 0.145805
\(505\) −3.42374 −0.152354
\(506\) −7.98388 −0.354927
\(507\) −7.61480 −0.338185
\(508\) −12.2429 −0.543191
\(509\) 10.6066 0.470131 0.235065 0.971980i \(-0.424470\pi\)
0.235065 + 0.971980i \(0.424470\pi\)
\(510\) 9.35280 0.414149
\(511\) −59.1334 −2.61591
\(512\) 1.00000 0.0441942
\(513\) −34.9148 −1.54153
\(514\) −20.7742 −0.916312
\(515\) 14.0772 0.620315
\(516\) 11.2050 0.493274
\(517\) −14.0975 −0.620009
\(518\) 29.4390 1.29347
\(519\) 17.6533 0.774894
\(520\) 10.6740 0.468088
\(521\) −9.89862 −0.433666 −0.216833 0.976209i \(-0.569573\pi\)
−0.216833 + 0.976209i \(0.569573\pi\)
\(522\) −0.498685 −0.0218268
\(523\) −32.0225 −1.40025 −0.700124 0.714022i \(-0.746872\pi\)
−0.700124 + 0.714022i \(0.746872\pi\)
\(524\) −3.81360 −0.166598
\(525\) 6.71209 0.292940
\(526\) −20.9500 −0.913461
\(527\) −17.9039 −0.779906
\(528\) 5.75872 0.250616
\(529\) −18.9347 −0.823250
\(530\) 35.5870 1.54580
\(531\) −9.38704 −0.407363
\(532\) 22.8568 0.990967
\(533\) 23.9715 1.03832
\(534\) −24.0620 −1.04126
\(535\) −45.7100 −1.97622
\(536\) −0.780231 −0.0337009
\(537\) −32.9859 −1.42345
\(538\) −5.65226 −0.243686
\(539\) −26.4534 −1.13943
\(540\) −14.1225 −0.607734
\(541\) −17.6071 −0.756987 −0.378494 0.925604i \(-0.623558\pi\)
−0.378494 + 0.925604i \(0.623558\pi\)
\(542\) −11.9929 −0.515140
\(543\) 7.59935 0.326119
\(544\) 2.57289 0.110312
\(545\) 36.6461 1.56975
\(546\) −22.9707 −0.983053
\(547\) −39.6926 −1.69713 −0.848567 0.529088i \(-0.822534\pi\)
−0.848567 + 0.529088i \(0.822534\pi\)
\(548\) −15.8322 −0.676320
\(549\) 8.59794 0.366951
\(550\) −4.94105 −0.210687
\(551\) −3.48219 −0.148346
\(552\) −2.93225 −0.124805
\(553\) −50.1653 −2.13324
\(554\) −1.12905 −0.0479687
\(555\) −28.9329 −1.22813
\(556\) −10.2425 −0.434380
\(557\) 10.6074 0.449450 0.224725 0.974422i \(-0.427852\pi\)
0.224725 + 0.974422i \(0.427852\pi\)
\(558\) 6.15834 0.260703
\(559\) 32.9019 1.39160
\(560\) 9.24519 0.390680
\(561\) 14.8166 0.625555
\(562\) 21.8794 0.922927
\(563\) 39.8934 1.68131 0.840653 0.541574i \(-0.182171\pi\)
0.840653 + 0.541574i \(0.182171\pi\)
\(564\) −5.17762 −0.218017
\(565\) 42.5656 1.79075
\(566\) 25.2573 1.06164
\(567\) 20.5717 0.863930
\(568\) 7.96118 0.334044
\(569\) 2.62368 0.109990 0.0549951 0.998487i \(-0.482486\pi\)
0.0549951 + 0.998487i \(0.482486\pi\)
\(570\) −22.4638 −0.940906
\(571\) −17.7392 −0.742362 −0.371181 0.928560i \(-0.621047\pi\)
−0.371181 + 0.928560i \(0.621047\pi\)
\(572\) 16.9097 0.707028
\(573\) 12.6113 0.526845
\(574\) 20.7626 0.866615
\(575\) 2.51590 0.104920
\(576\) −0.884987 −0.0368745
\(577\) 1.88691 0.0785531 0.0392766 0.999228i \(-0.487495\pi\)
0.0392766 + 0.999228i \(0.487495\pi\)
\(578\) −10.3802 −0.431761
\(579\) 5.01925 0.208593
\(580\) −1.40849 −0.0584843
\(581\) 21.3550 0.885956
\(582\) −12.7711 −0.529377
\(583\) 56.3763 2.33487
\(584\) 15.9875 0.661568
\(585\) −9.44639 −0.390560
\(586\) −5.94045 −0.245398
\(587\) 45.8692 1.89323 0.946613 0.322373i \(-0.104481\pi\)
0.946613 + 0.322373i \(0.104481\pi\)
\(588\) −9.71557 −0.400663
\(589\) 43.0021 1.77187
\(590\) −26.5128 −1.09152
\(591\) −4.12309 −0.169601
\(592\) −7.95922 −0.327122
\(593\) −22.7125 −0.932691 −0.466346 0.884603i \(-0.654430\pi\)
−0.466346 + 0.884603i \(0.654430\pi\)
\(594\) −22.3726 −0.917958
\(595\) 23.7868 0.975165
\(596\) −11.7499 −0.481296
\(597\) 16.1257 0.659982
\(598\) −8.61012 −0.352094
\(599\) −1.39791 −0.0571172 −0.0285586 0.999592i \(-0.509092\pi\)
−0.0285586 + 0.999592i \(0.509092\pi\)
\(600\) −1.81470 −0.0740850
\(601\) 1.32460 0.0540316 0.0270158 0.999635i \(-0.491400\pi\)
0.0270158 + 0.999635i \(0.491400\pi\)
\(602\) 28.4976 1.16147
\(603\) 0.690494 0.0281191
\(604\) 5.76900 0.234737
\(605\) −11.6974 −0.475566
\(606\) −1.99202 −0.0809202
\(607\) 16.0726 0.652367 0.326183 0.945306i \(-0.394237\pi\)
0.326183 + 0.945306i \(0.394237\pi\)
\(608\) −6.17964 −0.250618
\(609\) 3.03108 0.122826
\(610\) 24.2841 0.983233
\(611\) −15.2033 −0.615061
\(612\) −2.27697 −0.0920412
\(613\) 10.4160 0.420698 0.210349 0.977626i \(-0.432540\pi\)
0.210349 + 0.977626i \(0.432540\pi\)
\(614\) 10.4116 0.420180
\(615\) −20.4057 −0.822836
\(616\) 14.6461 0.590107
\(617\) −15.1751 −0.610927 −0.305463 0.952204i \(-0.598811\pi\)
−0.305463 + 0.952204i \(0.598811\pi\)
\(618\) 8.19047 0.329469
\(619\) 44.0206 1.76934 0.884668 0.466221i \(-0.154385\pi\)
0.884668 + 0.466221i \(0.154385\pi\)
\(620\) 17.3937 0.698546
\(621\) 11.3917 0.457135
\(622\) 33.2987 1.33516
\(623\) −61.1966 −2.45179
\(624\) 6.21043 0.248616
\(625\) −29.6820 −1.18728
\(626\) 6.47296 0.258711
\(627\) −35.5868 −1.42120
\(628\) −5.17265 −0.206411
\(629\) −20.4782 −0.816519
\(630\) −8.18187 −0.325974
\(631\) −35.4807 −1.41247 −0.706233 0.707980i \(-0.749607\pi\)
−0.706233 + 0.707980i \(0.749607\pi\)
\(632\) 13.5629 0.539502
\(633\) −8.91413 −0.354305
\(634\) 19.4944 0.774221
\(635\) 30.6019 1.21440
\(636\) 20.7054 0.821023
\(637\) −28.5284 −1.13034
\(638\) −2.23130 −0.0883382
\(639\) −7.04554 −0.278717
\(640\) −2.49956 −0.0988039
\(641\) −0.285736 −0.0112859 −0.00564295 0.999984i \(-0.501796\pi\)
−0.00564295 + 0.999984i \(0.501796\pi\)
\(642\) −26.5952 −1.04963
\(643\) 29.4910 1.16301 0.581505 0.813543i \(-0.302464\pi\)
0.581505 + 0.813543i \(0.302464\pi\)
\(644\) −7.45754 −0.293868
\(645\) −28.0077 −1.10280
\(646\) −15.8995 −0.625558
\(647\) 16.8892 0.663984 0.331992 0.943282i \(-0.392279\pi\)
0.331992 + 0.943282i \(0.392279\pi\)
\(648\) −5.56184 −0.218490
\(649\) −42.0012 −1.64869
\(650\) −5.32862 −0.209006
\(651\) −37.4313 −1.46705
\(652\) −4.43532 −0.173700
\(653\) −17.5616 −0.687237 −0.343618 0.939109i \(-0.611653\pi\)
−0.343618 + 0.939109i \(0.611653\pi\)
\(654\) 21.3216 0.833741
\(655\) 9.53232 0.372459
\(656\) −5.61346 −0.219169
\(657\) −14.1487 −0.551995
\(658\) −13.1682 −0.513348
\(659\) 43.8588 1.70850 0.854248 0.519865i \(-0.174018\pi\)
0.854248 + 0.519865i \(0.174018\pi\)
\(660\) −14.3943 −0.560297
\(661\) 14.8547 0.577780 0.288890 0.957362i \(-0.406714\pi\)
0.288890 + 0.957362i \(0.406714\pi\)
\(662\) 3.65322 0.141986
\(663\) 15.9787 0.620563
\(664\) −5.77362 −0.224060
\(665\) −57.1319 −2.21548
\(666\) 7.04381 0.272942
\(667\) 1.13614 0.0439916
\(668\) −2.90902 −0.112554
\(669\) −35.5199 −1.37328
\(670\) 1.95024 0.0753442
\(671\) 38.4704 1.48513
\(672\) 5.37908 0.207503
\(673\) −17.1289 −0.660269 −0.330134 0.943934i \(-0.607094\pi\)
−0.330134 + 0.943934i \(0.607094\pi\)
\(674\) −19.3565 −0.745584
\(675\) 7.05011 0.271359
\(676\) 5.23603 0.201386
\(677\) 3.11713 0.119801 0.0599005 0.998204i \(-0.480922\pi\)
0.0599005 + 0.998204i \(0.480922\pi\)
\(678\) 24.7657 0.951122
\(679\) −32.4804 −1.24648
\(680\) −6.43110 −0.246621
\(681\) −27.4324 −1.05121
\(682\) 27.5548 1.05513
\(683\) 3.47425 0.132939 0.0664693 0.997788i \(-0.478827\pi\)
0.0664693 + 0.997788i \(0.478827\pi\)
\(684\) 5.46890 0.209109
\(685\) 39.5737 1.51203
\(686\) 1.18157 0.0451127
\(687\) −8.02019 −0.305989
\(688\) −7.70471 −0.293739
\(689\) 60.7984 2.31624
\(690\) 7.32934 0.279023
\(691\) −16.6611 −0.633819 −0.316910 0.948456i \(-0.602645\pi\)
−0.316910 + 0.948456i \(0.602645\pi\)
\(692\) −12.1386 −0.461441
\(693\) −12.9616 −0.492370
\(694\) −32.2125 −1.22277
\(695\) 25.6018 0.971133
\(696\) −0.819494 −0.0310628
\(697\) −14.4428 −0.547060
\(698\) 6.54921 0.247891
\(699\) −5.48780 −0.207568
\(700\) −4.61531 −0.174442
\(701\) −30.9722 −1.16980 −0.584902 0.811104i \(-0.698867\pi\)
−0.584902 + 0.811104i \(0.698867\pi\)
\(702\) −24.1274 −0.910631
\(703\) 49.1852 1.85505
\(704\) −3.95977 −0.149239
\(705\) 12.9418 0.487416
\(706\) 25.0982 0.944584
\(707\) −5.06627 −0.190537
\(708\) −15.4258 −0.579738
\(709\) −13.6250 −0.511698 −0.255849 0.966717i \(-0.582355\pi\)
−0.255849 + 0.966717i \(0.582355\pi\)
\(710\) −19.8995 −0.746813
\(711\) −12.0030 −0.450146
\(712\) 16.5453 0.620062
\(713\) −14.0304 −0.525444
\(714\) 13.8398 0.517941
\(715\) −42.2668 −1.58069
\(716\) 22.6815 0.847648
\(717\) 19.1633 0.715667
\(718\) −7.88624 −0.294312
\(719\) 27.5495 1.02742 0.513711 0.857963i \(-0.328270\pi\)
0.513711 + 0.857963i \(0.328270\pi\)
\(720\) 2.21208 0.0824394
\(721\) 20.8307 0.775776
\(722\) 19.1880 0.714102
\(723\) 24.1057 0.896500
\(724\) −5.22540 −0.194201
\(725\) 0.703135 0.0261138
\(726\) −6.80582 −0.252588
\(727\) −17.7917 −0.659856 −0.329928 0.944006i \(-0.607025\pi\)
−0.329928 + 0.944006i \(0.607025\pi\)
\(728\) 15.7949 0.585398
\(729\) 29.5725 1.09528
\(730\) −39.9618 −1.47905
\(731\) −19.8234 −0.733193
\(732\) 14.1291 0.522226
\(733\) 24.5244 0.905830 0.452915 0.891554i \(-0.350384\pi\)
0.452915 + 0.891554i \(0.350384\pi\)
\(734\) −10.9855 −0.405483
\(735\) 24.2847 0.895754
\(736\) 2.01625 0.0743199
\(737\) 3.08953 0.113804
\(738\) 4.96784 0.182869
\(739\) 14.0201 0.515737 0.257869 0.966180i \(-0.416980\pi\)
0.257869 + 0.966180i \(0.416980\pi\)
\(740\) 19.8946 0.731339
\(741\) −38.3782 −1.40986
\(742\) 52.6598 1.93320
\(743\) 47.0278 1.72528 0.862641 0.505817i \(-0.168809\pi\)
0.862641 + 0.505817i \(0.168809\pi\)
\(744\) 10.1201 0.371020
\(745\) 29.3697 1.07602
\(746\) −2.84154 −0.104036
\(747\) 5.10958 0.186950
\(748\) −10.1880 −0.372512
\(749\) −67.6393 −2.47149
\(750\) −13.6397 −0.498052
\(751\) 39.6133 1.44551 0.722755 0.691105i \(-0.242876\pi\)
0.722755 + 0.691105i \(0.242876\pi\)
\(752\) 3.56019 0.129827
\(753\) 42.3494 1.54330
\(754\) −2.40632 −0.0876332
\(755\) −14.4200 −0.524796
\(756\) −20.8977 −0.760041
\(757\) −10.9455 −0.397820 −0.198910 0.980018i \(-0.563740\pi\)
−0.198910 + 0.980018i \(0.563740\pi\)
\(758\) −21.7288 −0.789225
\(759\) 11.6110 0.421453
\(760\) 15.4464 0.560300
\(761\) −27.4110 −0.993650 −0.496825 0.867851i \(-0.665501\pi\)
−0.496825 + 0.867851i \(0.665501\pi\)
\(762\) 17.8050 0.645006
\(763\) 54.2270 1.96315
\(764\) −8.67170 −0.313731
\(765\) 5.69144 0.205774
\(766\) −22.9149 −0.827949
\(767\) −45.2957 −1.63553
\(768\) −1.45431 −0.0524778
\(769\) −0.681540 −0.0245770 −0.0122885 0.999924i \(-0.503912\pi\)
−0.0122885 + 0.999924i \(0.503912\pi\)
\(770\) −36.6088 −1.31929
\(771\) 30.2121 1.08806
\(772\) −3.45130 −0.124215
\(773\) −48.1630 −1.73230 −0.866152 0.499781i \(-0.833414\pi\)
−0.866152 + 0.499781i \(0.833414\pi\)
\(774\) 6.81857 0.245088
\(775\) −8.68313 −0.311907
\(776\) 8.78153 0.315239
\(777\) −42.8133 −1.53592
\(778\) −31.2393 −1.11998
\(779\) 34.6891 1.24287
\(780\) −15.5234 −0.555825
\(781\) −31.5244 −1.12803
\(782\) 5.18758 0.185508
\(783\) 3.18372 0.113777
\(784\) 6.68055 0.238591
\(785\) 12.9294 0.461469
\(786\) 5.54614 0.197824
\(787\) −9.07799 −0.323595 −0.161798 0.986824i \(-0.551729\pi\)
−0.161798 + 0.986824i \(0.551729\pi\)
\(788\) 2.83509 0.100996
\(789\) 30.4677 1.08468
\(790\) −33.9012 −1.20615
\(791\) 62.9863 2.23954
\(792\) 3.50434 0.124521
\(793\) 41.4880 1.47328
\(794\) 20.5339 0.728720
\(795\) −51.7545 −1.83554
\(796\) −11.0882 −0.393012
\(797\) −18.1718 −0.643677 −0.321838 0.946795i \(-0.604301\pi\)
−0.321838 + 0.946795i \(0.604301\pi\)
\(798\) −33.2408 −1.17671
\(799\) 9.15998 0.324057
\(800\) 1.24781 0.0441169
\(801\) −14.6424 −0.517364
\(802\) −25.4113 −0.897303
\(803\) −63.3069 −2.23405
\(804\) 1.13470 0.0400177
\(805\) 18.6406 0.656995
\(806\) 29.7161 1.04671
\(807\) 8.22012 0.289362
\(808\) 1.36973 0.0481871
\(809\) 16.3207 0.573806 0.286903 0.957960i \(-0.407374\pi\)
0.286903 + 0.957960i \(0.407374\pi\)
\(810\) 13.9022 0.488472
\(811\) 15.8896 0.557958 0.278979 0.960297i \(-0.410004\pi\)
0.278979 + 0.960297i \(0.410004\pi\)
\(812\) −2.08421 −0.0731413
\(813\) 17.4414 0.611697
\(814\) 31.5167 1.10466
\(815\) 11.0864 0.388338
\(816\) −3.74177 −0.130988
\(817\) 47.6123 1.66574
\(818\) −2.49880 −0.0873686
\(819\) −13.9783 −0.488441
\(820\) 14.0312 0.489990
\(821\) −32.8837 −1.14765 −0.573825 0.818978i \(-0.694541\pi\)
−0.573825 + 0.818978i \(0.694541\pi\)
\(822\) 23.0250 0.803088
\(823\) 46.1868 1.60997 0.804986 0.593294i \(-0.202173\pi\)
0.804986 + 0.593294i \(0.202173\pi\)
\(824\) −5.63186 −0.196195
\(825\) 7.18581 0.250178
\(826\) −39.2323 −1.36507
\(827\) −7.83901 −0.272589 −0.136294 0.990668i \(-0.543519\pi\)
−0.136294 + 0.990668i \(0.543519\pi\)
\(828\) −1.78435 −0.0620106
\(829\) −25.7021 −0.892670 −0.446335 0.894866i \(-0.647271\pi\)
−0.446335 + 0.894866i \(0.647271\pi\)
\(830\) 14.4315 0.500926
\(831\) 1.64198 0.0569598
\(832\) −4.27037 −0.148048
\(833\) 17.1883 0.595539
\(834\) 14.8958 0.515799
\(835\) 7.27129 0.251633
\(836\) 24.4699 0.846311
\(837\) −39.3163 −1.35897
\(838\) −22.0519 −0.761770
\(839\) −49.8165 −1.71986 −0.859929 0.510414i \(-0.829492\pi\)
−0.859929 + 0.510414i \(0.829492\pi\)
\(840\) −13.4454 −0.463909
\(841\) −28.6825 −0.989051
\(842\) 37.9420 1.30757
\(843\) −31.8194 −1.09592
\(844\) 6.12946 0.210985
\(845\) −13.0878 −0.450233
\(846\) −3.15072 −0.108324
\(847\) −17.3092 −0.594749
\(848\) −14.2373 −0.488910
\(849\) −36.7319 −1.26064
\(850\) 3.21048 0.110119
\(851\) −16.0478 −0.550111
\(852\) −11.5780 −0.396656
\(853\) 9.85602 0.337464 0.168732 0.985662i \(-0.446033\pi\)
0.168732 + 0.985662i \(0.446033\pi\)
\(854\) 35.9343 1.22965
\(855\) −13.6699 −0.467499
\(856\) 18.2872 0.625044
\(857\) 26.1024 0.891641 0.445821 0.895122i \(-0.352912\pi\)
0.445821 + 0.895122i \(0.352912\pi\)
\(858\) −24.5919 −0.839552
\(859\) 8.02377 0.273768 0.136884 0.990587i \(-0.456291\pi\)
0.136884 + 0.990587i \(0.456291\pi\)
\(860\) 19.2584 0.656706
\(861\) −30.1952 −1.02905
\(862\) 15.8101 0.538493
\(863\) 31.7409 1.08047 0.540236 0.841514i \(-0.318335\pi\)
0.540236 + 0.841514i \(0.318335\pi\)
\(864\) 5.64997 0.192216
\(865\) 30.3412 1.03163
\(866\) 23.1500 0.786668
\(867\) 15.0961 0.512690
\(868\) 25.7382 0.873612
\(869\) −53.7058 −1.82184
\(870\) 2.04838 0.0694464
\(871\) 3.33187 0.112896
\(872\) −14.6610 −0.496484
\(873\) −7.77154 −0.263027
\(874\) −12.4597 −0.421455
\(875\) −34.6897 −1.17272
\(876\) −23.2508 −0.785571
\(877\) 19.8898 0.671630 0.335815 0.941928i \(-0.390988\pi\)
0.335815 + 0.941928i \(0.390988\pi\)
\(878\) −10.3378 −0.348885
\(879\) 8.63925 0.291395
\(880\) 9.89769 0.333651
\(881\) −20.3517 −0.685667 −0.342833 0.939396i \(-0.611387\pi\)
−0.342833 + 0.939396i \(0.611387\pi\)
\(882\) −5.91220 −0.199074
\(883\) 16.2450 0.546689 0.273344 0.961916i \(-0.411870\pi\)
0.273344 + 0.961916i \(0.411870\pi\)
\(884\) −10.9872 −0.369539
\(885\) 38.5578 1.29611
\(886\) −31.8458 −1.06988
\(887\) −24.0745 −0.808343 −0.404172 0.914683i \(-0.632440\pi\)
−0.404172 + 0.914683i \(0.632440\pi\)
\(888\) 11.5752 0.388437
\(889\) 45.2831 1.51875
\(890\) −41.3561 −1.38626
\(891\) 22.0236 0.737818
\(892\) 24.4239 0.817772
\(893\) −22.0007 −0.736226
\(894\) 17.0880 0.571509
\(895\) −56.6938 −1.89507
\(896\) −3.69872 −0.123566
\(897\) 12.5218 0.418090
\(898\) −8.92406 −0.297800
\(899\) −3.92117 −0.130778
\(900\) −1.10430 −0.0368099
\(901\) −36.6309 −1.22035
\(902\) 22.2280 0.740111
\(903\) −41.4443 −1.37918
\(904\) −17.0292 −0.566383
\(905\) 13.0612 0.434170
\(906\) −8.38990 −0.278736
\(907\) 49.6591 1.64890 0.824452 0.565932i \(-0.191484\pi\)
0.824452 + 0.565932i \(0.191484\pi\)
\(908\) 18.8628 0.625985
\(909\) −1.21220 −0.0402061
\(910\) −39.4803 −1.30876
\(911\) −45.4012 −1.50421 −0.752105 0.659044i \(-0.770961\pi\)
−0.752105 + 0.659044i \(0.770961\pi\)
\(912\) 8.98710 0.297593
\(913\) 22.8622 0.756629
\(914\) −35.3746 −1.17009
\(915\) −35.3165 −1.16753
\(916\) 5.51478 0.182213
\(917\) 14.1054 0.465802
\(918\) 14.5367 0.479784
\(919\) 47.1125 1.55410 0.777050 0.629439i \(-0.216715\pi\)
0.777050 + 0.629439i \(0.216715\pi\)
\(920\) −5.03974 −0.166155
\(921\) −15.1417 −0.498937
\(922\) −16.7319 −0.551035
\(923\) −33.9971 −1.11903
\(924\) −21.2999 −0.700716
\(925\) −9.93162 −0.326550
\(926\) 5.46233 0.179503
\(927\) 4.98413 0.163700
\(928\) 0.563494 0.0184976
\(929\) 24.1684 0.792940 0.396470 0.918048i \(-0.370235\pi\)
0.396470 + 0.918048i \(0.370235\pi\)
\(930\) −25.2957 −0.829480
\(931\) −41.2834 −1.35301
\(932\) 3.77347 0.123604
\(933\) −48.4266 −1.58542
\(934\) −22.9179 −0.749897
\(935\) 25.4656 0.832816
\(936\) 3.77922 0.123528
\(937\) 41.6540 1.36078 0.680388 0.732852i \(-0.261811\pi\)
0.680388 + 0.732852i \(0.261811\pi\)
\(938\) 2.88586 0.0942266
\(939\) −9.41367 −0.307204
\(940\) −8.89892 −0.290251
\(941\) 15.3158 0.499282 0.249641 0.968339i \(-0.419687\pi\)
0.249641 + 0.968339i \(0.419687\pi\)
\(942\) 7.52263 0.245101
\(943\) −11.3181 −0.368569
\(944\) 10.6070 0.345228
\(945\) 52.2350 1.69921
\(946\) 30.5089 0.991929
\(947\) 38.8651 1.26295 0.631473 0.775398i \(-0.282451\pi\)
0.631473 + 0.775398i \(0.282451\pi\)
\(948\) −19.7246 −0.640625
\(949\) −68.2725 −2.21622
\(950\) −7.71104 −0.250179
\(951\) −28.3508 −0.919339
\(952\) −9.51640 −0.308428
\(953\) 47.0994 1.52570 0.762849 0.646577i \(-0.223800\pi\)
0.762849 + 0.646577i \(0.223800\pi\)
\(954\) 12.5998 0.407934
\(955\) 21.6754 0.701401
\(956\) −13.1769 −0.426172
\(957\) 3.24500 0.104896
\(958\) −27.0543 −0.874084
\(959\) 58.5591 1.89097
\(960\) 3.63513 0.117323
\(961\) 17.4232 0.562039
\(962\) 33.9888 1.09584
\(963\) −16.1839 −0.521520
\(964\) −16.5754 −0.533856
\(965\) 8.62673 0.277704
\(966\) 10.8456 0.348950
\(967\) −33.7240 −1.08449 −0.542245 0.840221i \(-0.682425\pi\)
−0.542245 + 0.840221i \(0.682425\pi\)
\(968\) 4.67976 0.150413
\(969\) 23.1228 0.742812
\(970\) −21.9500 −0.704771
\(971\) −32.4877 −1.04258 −0.521290 0.853380i \(-0.674549\pi\)
−0.521290 + 0.853380i \(0.674549\pi\)
\(972\) −8.86128 −0.284226
\(973\) 37.8842 1.21451
\(974\) 25.6673 0.822432
\(975\) 7.74946 0.248181
\(976\) −9.71533 −0.310980
\(977\) 12.5170 0.400454 0.200227 0.979750i \(-0.435832\pi\)
0.200227 + 0.979750i \(0.435832\pi\)
\(978\) 6.45032 0.206259
\(979\) −65.5157 −2.09389
\(980\) −16.6984 −0.533412
\(981\) 12.9748 0.414253
\(982\) 22.4322 0.715841
\(983\) −10.1862 −0.324888 −0.162444 0.986718i \(-0.551938\pi\)
−0.162444 + 0.986718i \(0.551938\pi\)
\(984\) 8.16370 0.260249
\(985\) −7.08648 −0.225794
\(986\) 1.44981 0.0461712
\(987\) 19.1506 0.609569
\(988\) 26.3893 0.839556
\(989\) −15.5346 −0.493972
\(990\) −8.75933 −0.278390
\(991\) −2.41835 −0.0768215 −0.0384108 0.999262i \(-0.512230\pi\)
−0.0384108 + 0.999262i \(0.512230\pi\)
\(992\) −6.95868 −0.220938
\(993\) −5.31291 −0.168600
\(994\) −29.4462 −0.933976
\(995\) 27.7157 0.878648
\(996\) 8.39663 0.266057
\(997\) 44.8902 1.42169 0.710844 0.703350i \(-0.248313\pi\)
0.710844 + 0.703350i \(0.248313\pi\)
\(998\) −11.9870 −0.379442
\(999\) −44.9694 −1.42277
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.1.14 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4022.2.a.f.1.14 50 1.1 even 1 trivial