Properties

Label 6019.2.a.b.1.10
Level $6019$
Weight $2$
Character 6019.1
Self dual yes
Analytic conductor $48.062$
Analytic rank $1$
Dimension $101$
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] = [6019,2,Mod(1,6019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6019, 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("6019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6019 = 13 \cdot 463 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6019.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: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(101\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.35123 q^{2} -2.62167 q^{3} +3.52828 q^{4} -1.32904 q^{5} +6.16416 q^{6} -2.62369 q^{7} -3.59334 q^{8} +3.87318 q^{9} +O(q^{10})\) \(q-2.35123 q^{2} -2.62167 q^{3} +3.52828 q^{4} -1.32904 q^{5} +6.16416 q^{6} -2.62369 q^{7} -3.59334 q^{8} +3.87318 q^{9} +3.12489 q^{10} +0.707561 q^{11} -9.25001 q^{12} +1.00000 q^{13} +6.16889 q^{14} +3.48432 q^{15} +1.39221 q^{16} +0.107924 q^{17} -9.10674 q^{18} -5.33371 q^{19} -4.68924 q^{20} +6.87846 q^{21} -1.66364 q^{22} +5.99504 q^{23} +9.42058 q^{24} -3.23364 q^{25} -2.35123 q^{26} -2.28919 q^{27} -9.25711 q^{28} -3.89189 q^{29} -8.19244 q^{30} +1.52075 q^{31} +3.91328 q^{32} -1.85499 q^{33} -0.253753 q^{34} +3.48700 q^{35} +13.6657 q^{36} +3.57394 q^{37} +12.5408 q^{38} -2.62167 q^{39} +4.77571 q^{40} -1.34958 q^{41} -16.1728 q^{42} +1.37913 q^{43} +2.49647 q^{44} -5.14763 q^{45} -14.0957 q^{46} -6.62813 q^{47} -3.64993 q^{48} -0.116260 q^{49} +7.60303 q^{50} -0.282941 q^{51} +3.52828 q^{52} -8.61589 q^{53} +5.38242 q^{54} -0.940380 q^{55} +9.42781 q^{56} +13.9833 q^{57} +9.15073 q^{58} -7.88656 q^{59} +12.2937 q^{60} +0.719770 q^{61} -3.57564 q^{62} -10.1620 q^{63} -11.9854 q^{64} -1.32904 q^{65} +4.36152 q^{66} +8.31103 q^{67} +0.380785 q^{68} -15.7170 q^{69} -8.19873 q^{70} +12.5153 q^{71} -13.9177 q^{72} +8.05783 q^{73} -8.40314 q^{74} +8.47756 q^{75} -18.8188 q^{76} -1.85642 q^{77} +6.16416 q^{78} -14.1205 q^{79} -1.85031 q^{80} -5.61802 q^{81} +3.17317 q^{82} +6.80636 q^{83} +24.2691 q^{84} -0.143435 q^{85} -3.24265 q^{86} +10.2033 q^{87} -2.54251 q^{88} -1.71630 q^{89} +12.1033 q^{90} -2.62369 q^{91} +21.1522 q^{92} -3.98692 q^{93} +15.5843 q^{94} +7.08874 q^{95} -10.2593 q^{96} -4.38469 q^{97} +0.273354 q^{98} +2.74051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35123 −1.66257 −0.831285 0.555846i \(-0.812394\pi\)
−0.831285 + 0.555846i \(0.812394\pi\)
\(3\) −2.62167 −1.51362 −0.756812 0.653632i \(-0.773244\pi\)
−0.756812 + 0.653632i \(0.773244\pi\)
\(4\) 3.52828 1.76414
\(5\) −1.32904 −0.594367 −0.297183 0.954820i \(-0.596047\pi\)
−0.297183 + 0.954820i \(0.596047\pi\)
\(6\) 6.16416 2.51651
\(7\) −2.62369 −0.991661 −0.495830 0.868419i \(-0.665136\pi\)
−0.495830 + 0.868419i \(0.665136\pi\)
\(8\) −3.59334 −1.27044
\(9\) 3.87318 1.29106
\(10\) 3.12489 0.988177
\(11\) 0.707561 0.213338 0.106669 0.994295i \(-0.465982\pi\)
0.106669 + 0.994295i \(0.465982\pi\)
\(12\) −9.25001 −2.67025
\(13\) 1.00000 0.277350
\(14\) 6.16889 1.64871
\(15\) 3.48432 0.899648
\(16\) 1.39221 0.348053
\(17\) 0.107924 0.0261753 0.0130877 0.999914i \(-0.495834\pi\)
0.0130877 + 0.999914i \(0.495834\pi\)
\(18\) −9.10674 −2.14648
\(19\) −5.33371 −1.22364 −0.611819 0.790998i \(-0.709562\pi\)
−0.611819 + 0.790998i \(0.709562\pi\)
\(20\) −4.68924 −1.04855
\(21\) 6.87846 1.50100
\(22\) −1.66364 −0.354689
\(23\) 5.99504 1.25005 0.625026 0.780604i \(-0.285088\pi\)
0.625026 + 0.780604i \(0.285088\pi\)
\(24\) 9.42058 1.92297
\(25\) −3.23364 −0.646728
\(26\) −2.35123 −0.461114
\(27\) −2.28919 −0.440555
\(28\) −9.25711 −1.74943
\(29\) −3.89189 −0.722706 −0.361353 0.932429i \(-0.617685\pi\)
−0.361353 + 0.932429i \(0.617685\pi\)
\(30\) −8.19244 −1.49573
\(31\) 1.52075 0.273135 0.136568 0.990631i \(-0.456393\pi\)
0.136568 + 0.990631i \(0.456393\pi\)
\(32\) 3.91328 0.691776
\(33\) −1.85499 −0.322913
\(34\) −0.253753 −0.0435183
\(35\) 3.48700 0.589410
\(36\) 13.6657 2.27761
\(37\) 3.57394 0.587551 0.293776 0.955874i \(-0.405088\pi\)
0.293776 + 0.955874i \(0.405088\pi\)
\(38\) 12.5408 2.03438
\(39\) −2.62167 −0.419804
\(40\) 4.77571 0.755107
\(41\) −1.34958 −0.210769 −0.105385 0.994432i \(-0.533607\pi\)
−0.105385 + 0.994432i \(0.533607\pi\)
\(42\) −16.1728 −2.49552
\(43\) 1.37913 0.210315 0.105158 0.994456i \(-0.466465\pi\)
0.105158 + 0.994456i \(0.466465\pi\)
\(44\) 2.49647 0.376358
\(45\) −5.14763 −0.767363
\(46\) −14.0957 −2.07830
\(47\) −6.62813 −0.966813 −0.483406 0.875396i \(-0.660601\pi\)
−0.483406 + 0.875396i \(0.660601\pi\)
\(48\) −3.64993 −0.526822
\(49\) −0.116260 −0.0166086
\(50\) 7.60303 1.07523
\(51\) −0.282941 −0.0396196
\(52\) 3.52828 0.489285
\(53\) −8.61589 −1.18348 −0.591742 0.806128i \(-0.701560\pi\)
−0.591742 + 0.806128i \(0.701560\pi\)
\(54\) 5.38242 0.732454
\(55\) −0.940380 −0.126801
\(56\) 9.42781 1.25984
\(57\) 13.9833 1.85213
\(58\) 9.15073 1.20155
\(59\) −7.88656 −1.02674 −0.513372 0.858166i \(-0.671604\pi\)
−0.513372 + 0.858166i \(0.671604\pi\)
\(60\) 12.2937 1.58711
\(61\) 0.719770 0.0921572 0.0460786 0.998938i \(-0.485328\pi\)
0.0460786 + 0.998938i \(0.485328\pi\)
\(62\) −3.57564 −0.454106
\(63\) −10.1620 −1.28029
\(64\) −11.9854 −1.49818
\(65\) −1.32904 −0.164848
\(66\) 4.36152 0.536866
\(67\) 8.31103 1.01535 0.507677 0.861547i \(-0.330504\pi\)
0.507677 + 0.861547i \(0.330504\pi\)
\(68\) 0.380785 0.0461770
\(69\) −15.7170 −1.89211
\(70\) −8.19873 −0.979936
\(71\) 12.5153 1.48530 0.742649 0.669681i \(-0.233569\pi\)
0.742649 + 0.669681i \(0.233569\pi\)
\(72\) −13.9177 −1.64021
\(73\) 8.05783 0.943098 0.471549 0.881840i \(-0.343695\pi\)
0.471549 + 0.881840i \(0.343695\pi\)
\(74\) −8.40314 −0.976846
\(75\) 8.47756 0.978904
\(76\) −18.8188 −2.15867
\(77\) −1.85642 −0.211559
\(78\) 6.16416 0.697954
\(79\) −14.1205 −1.58868 −0.794340 0.607474i \(-0.792183\pi\)
−0.794340 + 0.607474i \(0.792183\pi\)
\(80\) −1.85031 −0.206871
\(81\) −5.61802 −0.624224
\(82\) 3.17317 0.350418
\(83\) 6.80636 0.747095 0.373547 0.927611i \(-0.378141\pi\)
0.373547 + 0.927611i \(0.378141\pi\)
\(84\) 24.2691 2.64798
\(85\) −0.143435 −0.0155577
\(86\) −3.24265 −0.349664
\(87\) 10.2033 1.09391
\(88\) −2.54251 −0.271032
\(89\) −1.71630 −0.181928 −0.0909639 0.995854i \(-0.528995\pi\)
−0.0909639 + 0.995854i \(0.528995\pi\)
\(90\) 12.1033 1.27580
\(91\) −2.62369 −0.275037
\(92\) 21.1522 2.20527
\(93\) −3.98692 −0.413424
\(94\) 15.5843 1.60739
\(95\) 7.08874 0.727289
\(96\) −10.2593 −1.04709
\(97\) −4.38469 −0.445197 −0.222599 0.974910i \(-0.571454\pi\)
−0.222599 + 0.974910i \(0.571454\pi\)
\(98\) 0.273354 0.0276130
\(99\) 2.74051 0.275432
\(100\) −11.4092 −1.14092
\(101\) 6.80213 0.676837 0.338419 0.940996i \(-0.390108\pi\)
0.338419 + 0.940996i \(0.390108\pi\)
\(102\) 0.665258 0.0658704
\(103\) 18.1665 1.79000 0.895001 0.446065i \(-0.147175\pi\)
0.895001 + 0.446065i \(0.147175\pi\)
\(104\) −3.59334 −0.352356
\(105\) −9.14178 −0.892146
\(106\) 20.2579 1.96763
\(107\) −15.3751 −1.48637 −0.743183 0.669088i \(-0.766685\pi\)
−0.743183 + 0.669088i \(0.766685\pi\)
\(108\) −8.07692 −0.777202
\(109\) 0.344652 0.0330117 0.0165058 0.999864i \(-0.494746\pi\)
0.0165058 + 0.999864i \(0.494746\pi\)
\(110\) 2.21105 0.210815
\(111\) −9.36970 −0.889332
\(112\) −3.65273 −0.345151
\(113\) −2.04628 −0.192498 −0.0962489 0.995357i \(-0.530684\pi\)
−0.0962489 + 0.995357i \(0.530684\pi\)
\(114\) −32.8779 −3.07929
\(115\) −7.96767 −0.742989
\(116\) −13.7317 −1.27496
\(117\) 3.87318 0.358076
\(118\) 18.5431 1.70703
\(119\) −0.283158 −0.0259570
\(120\) −12.5204 −1.14295
\(121\) −10.4994 −0.954487
\(122\) −1.69235 −0.153218
\(123\) 3.53816 0.319025
\(124\) 5.36564 0.481849
\(125\) 10.9429 0.978760
\(126\) 23.8932 2.12858
\(127\) 14.0584 1.24749 0.623743 0.781630i \(-0.285611\pi\)
0.623743 + 0.781630i \(0.285611\pi\)
\(128\) 20.3540 1.79905
\(129\) −3.61563 −0.318338
\(130\) 3.12489 0.274071
\(131\) −15.5706 −1.36041 −0.680205 0.733022i \(-0.738109\pi\)
−0.680205 + 0.733022i \(0.738109\pi\)
\(132\) −6.54494 −0.569664
\(133\) 13.9940 1.21343
\(134\) −19.5412 −1.68810
\(135\) 3.04244 0.261851
\(136\) −0.387807 −0.0332541
\(137\) −9.60707 −0.820787 −0.410394 0.911908i \(-0.634609\pi\)
−0.410394 + 0.911908i \(0.634609\pi\)
\(138\) 36.9544 3.14577
\(139\) −3.70004 −0.313833 −0.156917 0.987612i \(-0.550155\pi\)
−0.156917 + 0.987612i \(0.550155\pi\)
\(140\) 12.3031 1.03980
\(141\) 17.3768 1.46339
\(142\) −29.4264 −2.46941
\(143\) 0.707561 0.0591692
\(144\) 5.39229 0.449357
\(145\) 5.17250 0.429553
\(146\) −18.9458 −1.56797
\(147\) 0.304796 0.0251392
\(148\) 12.6099 1.03652
\(149\) 6.95047 0.569405 0.284703 0.958616i \(-0.408105\pi\)
0.284703 + 0.958616i \(0.408105\pi\)
\(150\) −19.9327 −1.62750
\(151\) 24.5043 1.99413 0.997064 0.0765743i \(-0.0243982\pi\)
0.997064 + 0.0765743i \(0.0243982\pi\)
\(152\) 19.1659 1.55456
\(153\) 0.418007 0.0337939
\(154\) 4.36487 0.351731
\(155\) −2.02115 −0.162342
\(156\) −9.25001 −0.740593
\(157\) 21.4347 1.71067 0.855336 0.518073i \(-0.173351\pi\)
0.855336 + 0.518073i \(0.173351\pi\)
\(158\) 33.2005 2.64129
\(159\) 22.5881 1.79135
\(160\) −5.20092 −0.411169
\(161\) −15.7291 −1.23963
\(162\) 13.2093 1.03782
\(163\) 19.2620 1.50872 0.754360 0.656461i \(-0.227948\pi\)
0.754360 + 0.656461i \(0.227948\pi\)
\(164\) −4.76170 −0.371826
\(165\) 2.46537 0.191929
\(166\) −16.0033 −1.24210
\(167\) 8.10339 0.627059 0.313529 0.949578i \(-0.398489\pi\)
0.313529 + 0.949578i \(0.398489\pi\)
\(168\) −24.7167 −1.90693
\(169\) 1.00000 0.0769231
\(170\) 0.337249 0.0258658
\(171\) −20.6584 −1.57979
\(172\) 4.86596 0.371026
\(173\) 20.7994 1.58135 0.790676 0.612234i \(-0.209729\pi\)
0.790676 + 0.612234i \(0.209729\pi\)
\(174\) −23.9902 −1.81870
\(175\) 8.48407 0.641335
\(176\) 0.985074 0.0742528
\(177\) 20.6760 1.55410
\(178\) 4.03543 0.302468
\(179\) −19.5198 −1.45898 −0.729488 0.683994i \(-0.760242\pi\)
−0.729488 + 0.683994i \(0.760242\pi\)
\(180\) −18.1623 −1.35374
\(181\) 5.32245 0.395615 0.197807 0.980241i \(-0.436618\pi\)
0.197807 + 0.980241i \(0.436618\pi\)
\(182\) 6.16889 0.457269
\(183\) −1.88700 −0.139491
\(184\) −21.5422 −1.58811
\(185\) −4.74992 −0.349221
\(186\) 9.37416 0.687347
\(187\) 0.0763625 0.00558418
\(188\) −23.3859 −1.70559
\(189\) 6.00613 0.436882
\(190\) −16.6673 −1.20917
\(191\) 2.86695 0.207445 0.103723 0.994606i \(-0.466925\pi\)
0.103723 + 0.994606i \(0.466925\pi\)
\(192\) 31.4219 2.26768
\(193\) 3.14768 0.226575 0.113288 0.993562i \(-0.463862\pi\)
0.113288 + 0.993562i \(0.463862\pi\)
\(194\) 10.3094 0.740172
\(195\) 3.48432 0.249518
\(196\) −0.410199 −0.0292999
\(197\) −21.4159 −1.52582 −0.762911 0.646504i \(-0.776230\pi\)
−0.762911 + 0.646504i \(0.776230\pi\)
\(198\) −6.44357 −0.457924
\(199\) −0.754636 −0.0534948 −0.0267474 0.999642i \(-0.508515\pi\)
−0.0267474 + 0.999642i \(0.508515\pi\)
\(200\) 11.6196 0.821629
\(201\) −21.7888 −1.53687
\(202\) −15.9934 −1.12529
\(203\) 10.2111 0.716679
\(204\) −0.998294 −0.0698946
\(205\) 1.79365 0.125274
\(206\) −42.7137 −2.97600
\(207\) 23.2199 1.61389
\(208\) 1.39221 0.0965325
\(209\) −3.77393 −0.261048
\(210\) 21.4944 1.48326
\(211\) −26.1617 −1.80104 −0.900522 0.434811i \(-0.856815\pi\)
−0.900522 + 0.434811i \(0.856815\pi\)
\(212\) −30.3993 −2.08783
\(213\) −32.8111 −2.24818
\(214\) 36.1504 2.47119
\(215\) −1.83292 −0.125004
\(216\) 8.22586 0.559699
\(217\) −3.98998 −0.270857
\(218\) −0.810356 −0.0548842
\(219\) −21.1250 −1.42750
\(220\) −3.31792 −0.223694
\(221\) 0.107924 0.00725973
\(222\) 22.0303 1.47858
\(223\) 0.967801 0.0648087 0.0324044 0.999475i \(-0.489684\pi\)
0.0324044 + 0.999475i \(0.489684\pi\)
\(224\) −10.2672 −0.686007
\(225\) −12.5245 −0.834965
\(226\) 4.81127 0.320041
\(227\) 14.5384 0.964950 0.482475 0.875910i \(-0.339738\pi\)
0.482475 + 0.875910i \(0.339738\pi\)
\(228\) 49.3369 3.26742
\(229\) 26.0378 1.72063 0.860315 0.509763i \(-0.170267\pi\)
0.860315 + 0.509763i \(0.170267\pi\)
\(230\) 18.7338 1.23527
\(231\) 4.86693 0.320220
\(232\) 13.9849 0.918154
\(233\) −4.89033 −0.320376 −0.160188 0.987086i \(-0.551210\pi\)
−0.160188 + 0.987086i \(0.551210\pi\)
\(234\) −9.10674 −0.595326
\(235\) 8.80908 0.574641
\(236\) −27.8260 −1.81132
\(237\) 37.0193 2.40466
\(238\) 0.665769 0.0431554
\(239\) 24.9185 1.61184 0.805921 0.592024i \(-0.201671\pi\)
0.805921 + 0.592024i \(0.201671\pi\)
\(240\) 4.85091 0.313125
\(241\) 13.6432 0.878833 0.439416 0.898284i \(-0.355185\pi\)
0.439416 + 0.898284i \(0.355185\pi\)
\(242\) 24.6864 1.58690
\(243\) 21.5962 1.38540
\(244\) 2.53955 0.162578
\(245\) 0.154515 0.00987160
\(246\) −8.31903 −0.530402
\(247\) −5.33371 −0.339376
\(248\) −5.46458 −0.347001
\(249\) −17.8441 −1.13082
\(250\) −25.7292 −1.62726
\(251\) 16.5467 1.04442 0.522208 0.852818i \(-0.325108\pi\)
0.522208 + 0.852818i \(0.325108\pi\)
\(252\) −35.8545 −2.25862
\(253\) 4.24185 0.266683
\(254\) −33.0546 −2.07403
\(255\) 0.376041 0.0235486
\(256\) −23.8860 −1.49287
\(257\) −14.4629 −0.902170 −0.451085 0.892481i \(-0.648963\pi\)
−0.451085 + 0.892481i \(0.648963\pi\)
\(258\) 8.50117 0.529260
\(259\) −9.37689 −0.582652
\(260\) −4.68924 −0.290815
\(261\) −15.0740 −0.933057
\(262\) 36.6101 2.26178
\(263\) 2.67360 0.164862 0.0824308 0.996597i \(-0.473732\pi\)
0.0824308 + 0.996597i \(0.473732\pi\)
\(264\) 6.66563 0.410241
\(265\) 11.4509 0.703423
\(266\) −32.9031 −2.01742
\(267\) 4.49959 0.275371
\(268\) 29.3237 1.79123
\(269\) −10.5165 −0.641203 −0.320601 0.947214i \(-0.603885\pi\)
−0.320601 + 0.947214i \(0.603885\pi\)
\(270\) −7.15347 −0.435347
\(271\) 15.3528 0.932617 0.466308 0.884622i \(-0.345584\pi\)
0.466308 + 0.884622i \(0.345584\pi\)
\(272\) 0.150253 0.00911040
\(273\) 6.87846 0.416303
\(274\) 22.5884 1.36462
\(275\) −2.28800 −0.137971
\(276\) −55.4542 −3.33795
\(277\) 24.8770 1.49471 0.747356 0.664424i \(-0.231323\pi\)
0.747356 + 0.664424i \(0.231323\pi\)
\(278\) 8.69964 0.521770
\(279\) 5.89015 0.352634
\(280\) −12.5300 −0.748810
\(281\) 26.6898 1.59218 0.796090 0.605178i \(-0.206898\pi\)
0.796090 + 0.605178i \(0.206898\pi\)
\(282\) −40.8569 −2.43299
\(283\) −0.347485 −0.0206559 −0.0103279 0.999947i \(-0.503288\pi\)
−0.0103279 + 0.999947i \(0.503288\pi\)
\(284\) 44.1576 2.62027
\(285\) −18.5844 −1.10084
\(286\) −1.66364 −0.0983730
\(287\) 3.54088 0.209011
\(288\) 15.1568 0.893124
\(289\) −16.9884 −0.999315
\(290\) −12.1617 −0.714161
\(291\) 11.4952 0.673862
\(292\) 28.4303 1.66376
\(293\) −3.60994 −0.210895 −0.105447 0.994425i \(-0.533627\pi\)
−0.105447 + 0.994425i \(0.533627\pi\)
\(294\) −0.716647 −0.0417957
\(295\) 10.4816 0.610262
\(296\) −12.8424 −0.746448
\(297\) −1.61974 −0.0939870
\(298\) −16.3422 −0.946676
\(299\) 5.99504 0.346702
\(300\) 29.9112 1.72692
\(301\) −3.61840 −0.208561
\(302\) −57.6151 −3.31538
\(303\) −17.8330 −1.02448
\(304\) −7.42566 −0.425891
\(305\) −0.956607 −0.0547751
\(306\) −0.982832 −0.0561847
\(307\) 8.68582 0.495726 0.247863 0.968795i \(-0.420272\pi\)
0.247863 + 0.968795i \(0.420272\pi\)
\(308\) −6.54997 −0.373219
\(309\) −47.6267 −2.70939
\(310\) 4.75218 0.269906
\(311\) 24.5052 1.38956 0.694781 0.719221i \(-0.255501\pi\)
0.694781 + 0.719221i \(0.255501\pi\)
\(312\) 9.42058 0.533335
\(313\) −2.14430 −0.121203 −0.0606014 0.998162i \(-0.519302\pi\)
−0.0606014 + 0.998162i \(0.519302\pi\)
\(314\) −50.3978 −2.84411
\(315\) 13.5058 0.760964
\(316\) −49.8211 −2.80265
\(317\) −30.3704 −1.70577 −0.852886 0.522097i \(-0.825150\pi\)
−0.852886 + 0.522097i \(0.825150\pi\)
\(318\) −53.1097 −2.97825
\(319\) −2.75375 −0.154180
\(320\) 15.9292 0.890468
\(321\) 40.3085 2.24980
\(322\) 36.9828 2.06097
\(323\) −0.575633 −0.0320291
\(324\) −19.8220 −1.10122
\(325\) −3.23364 −0.179370
\(326\) −45.2895 −2.50835
\(327\) −0.903565 −0.0499673
\(328\) 4.84951 0.267769
\(329\) 17.3902 0.958750
\(330\) −5.79665 −0.319095
\(331\) 19.5857 1.07653 0.538265 0.842776i \(-0.319080\pi\)
0.538265 + 0.842776i \(0.319080\pi\)
\(332\) 24.0148 1.31798
\(333\) 13.8425 0.758564
\(334\) −19.0529 −1.04253
\(335\) −11.0457 −0.603493
\(336\) 9.57627 0.522428
\(337\) 5.43680 0.296161 0.148081 0.988975i \(-0.452690\pi\)
0.148081 + 0.988975i \(0.452690\pi\)
\(338\) −2.35123 −0.127890
\(339\) 5.36468 0.291369
\(340\) −0.506080 −0.0274460
\(341\) 1.07602 0.0582700
\(342\) 48.5727 2.62651
\(343\) 18.6708 1.00813
\(344\) −4.95568 −0.267193
\(345\) 20.8886 1.12461
\(346\) −48.9043 −2.62911
\(347\) 19.9788 1.07252 0.536258 0.844054i \(-0.319837\pi\)
0.536258 + 0.844054i \(0.319837\pi\)
\(348\) 36.0000 1.92980
\(349\) −31.9403 −1.70972 −0.854861 0.518857i \(-0.826358\pi\)
−0.854861 + 0.518857i \(0.826358\pi\)
\(350\) −19.9480 −1.06626
\(351\) −2.28919 −0.122188
\(352\) 2.76888 0.147582
\(353\) −32.1803 −1.71279 −0.856393 0.516325i \(-0.827300\pi\)
−0.856393 + 0.516325i \(0.827300\pi\)
\(354\) −48.6140 −2.58381
\(355\) −16.6334 −0.882811
\(356\) −6.05561 −0.320946
\(357\) 0.742348 0.0392892
\(358\) 45.8955 2.42565
\(359\) 13.7843 0.727508 0.363754 0.931495i \(-0.381495\pi\)
0.363754 + 0.931495i \(0.381495\pi\)
\(360\) 18.4972 0.974888
\(361\) 9.44848 0.497289
\(362\) −12.5143 −0.657738
\(363\) 27.5259 1.44474
\(364\) −9.25711 −0.485205
\(365\) −10.7092 −0.560546
\(366\) 4.43678 0.231914
\(367\) 23.0347 1.20240 0.601202 0.799097i \(-0.294689\pi\)
0.601202 + 0.799097i \(0.294689\pi\)
\(368\) 8.34636 0.435084
\(369\) −5.22717 −0.272115
\(370\) 11.1682 0.580604
\(371\) 22.6054 1.17361
\(372\) −14.0670 −0.729338
\(373\) −8.73331 −0.452194 −0.226097 0.974105i \(-0.572597\pi\)
−0.226097 + 0.974105i \(0.572597\pi\)
\(374\) −0.179546 −0.00928409
\(375\) −28.6887 −1.48148
\(376\) 23.8172 1.22828
\(377\) −3.89189 −0.200443
\(378\) −14.1218 −0.726346
\(379\) −5.20921 −0.267579 −0.133789 0.991010i \(-0.542715\pi\)
−0.133789 + 0.991010i \(0.542715\pi\)
\(380\) 25.0111 1.28304
\(381\) −36.8567 −1.88822
\(382\) −6.74087 −0.344893
\(383\) −16.9776 −0.867517 −0.433758 0.901029i \(-0.642813\pi\)
−0.433758 + 0.901029i \(0.642813\pi\)
\(384\) −53.3615 −2.72309
\(385\) 2.46726 0.125743
\(386\) −7.40092 −0.376697
\(387\) 5.34161 0.271529
\(388\) −15.4704 −0.785391
\(389\) 1.03217 0.0523330 0.0261665 0.999658i \(-0.491670\pi\)
0.0261665 + 0.999658i \(0.491670\pi\)
\(390\) −8.19244 −0.414840
\(391\) 0.647006 0.0327205
\(392\) 0.417763 0.0211002
\(393\) 40.8210 2.05915
\(394\) 50.3538 2.53679
\(395\) 18.7668 0.944258
\(396\) 9.66929 0.485900
\(397\) 4.58914 0.230322 0.115161 0.993347i \(-0.463262\pi\)
0.115161 + 0.993347i \(0.463262\pi\)
\(398\) 1.77432 0.0889388
\(399\) −36.6877 −1.83668
\(400\) −4.50191 −0.225096
\(401\) −10.4623 −0.522461 −0.261231 0.965276i \(-0.584128\pi\)
−0.261231 + 0.965276i \(0.584128\pi\)
\(402\) 51.2305 2.55515
\(403\) 1.52075 0.0757541
\(404\) 23.9998 1.19404
\(405\) 7.46660 0.371018
\(406\) −24.0087 −1.19153
\(407\) 2.52878 0.125347
\(408\) 1.01670 0.0503343
\(409\) 5.84104 0.288821 0.144411 0.989518i \(-0.453871\pi\)
0.144411 + 0.989518i \(0.453871\pi\)
\(410\) −4.21729 −0.208277
\(411\) 25.1866 1.24236
\(412\) 64.0966 3.15782
\(413\) 20.6919 1.01818
\(414\) −54.5952 −2.68321
\(415\) −9.04595 −0.444048
\(416\) 3.91328 0.191864
\(417\) 9.70030 0.475026
\(418\) 8.87337 0.434011
\(419\) 3.37716 0.164985 0.0824926 0.996592i \(-0.473712\pi\)
0.0824926 + 0.996592i \(0.473712\pi\)
\(420\) −32.2548 −1.57387
\(421\) −3.42403 −0.166877 −0.0834384 0.996513i \(-0.526590\pi\)
−0.0834384 + 0.996513i \(0.526590\pi\)
\(422\) 61.5121 2.99436
\(423\) −25.6719 −1.24821
\(424\) 30.9599 1.50354
\(425\) −0.348986 −0.0169283
\(426\) 77.1466 3.73776
\(427\) −1.88845 −0.0913887
\(428\) −54.2477 −2.62216
\(429\) −1.85499 −0.0895600
\(430\) 4.30962 0.207829
\(431\) −19.8333 −0.955337 −0.477669 0.878540i \(-0.658518\pi\)
−0.477669 + 0.878540i \(0.658518\pi\)
\(432\) −3.18704 −0.153337
\(433\) −1.21486 −0.0583827 −0.0291913 0.999574i \(-0.509293\pi\)
−0.0291913 + 0.999574i \(0.509293\pi\)
\(434\) 9.38136 0.450320
\(435\) −13.5606 −0.650181
\(436\) 1.21603 0.0582372
\(437\) −31.9758 −1.52961
\(438\) 49.6698 2.37331
\(439\) 10.5353 0.502824 0.251412 0.967880i \(-0.419105\pi\)
0.251412 + 0.967880i \(0.419105\pi\)
\(440\) 3.37911 0.161093
\(441\) −0.450297 −0.0214427
\(442\) −0.253753 −0.0120698
\(443\) −2.53327 −0.120359 −0.0601796 0.998188i \(-0.519167\pi\)
−0.0601796 + 0.998188i \(0.519167\pi\)
\(444\) −33.0589 −1.56891
\(445\) 2.28104 0.108132
\(446\) −2.27552 −0.107749
\(447\) −18.2219 −0.861866
\(448\) 31.4460 1.48569
\(449\) 11.6762 0.551032 0.275516 0.961297i \(-0.411151\pi\)
0.275516 + 0.961297i \(0.411151\pi\)
\(450\) 29.4479 1.38819
\(451\) −0.954910 −0.0449650
\(452\) −7.21985 −0.339593
\(453\) −64.2422 −3.01836
\(454\) −34.1832 −1.60430
\(455\) 3.48700 0.163473
\(456\) −50.2467 −2.35301
\(457\) −4.01990 −0.188043 −0.0940214 0.995570i \(-0.529972\pi\)
−0.0940214 + 0.995570i \(0.529972\pi\)
\(458\) −61.2210 −2.86067
\(459\) −0.247058 −0.0115317
\(460\) −28.1122 −1.31074
\(461\) 13.9221 0.648415 0.324208 0.945986i \(-0.394902\pi\)
0.324208 + 0.945986i \(0.394902\pi\)
\(462\) −11.4433 −0.532389
\(463\) 1.00000 0.0464739
\(464\) −5.41834 −0.251540
\(465\) 5.29879 0.245726
\(466\) 11.4983 0.532648
\(467\) −32.3287 −1.49599 −0.747997 0.663702i \(-0.768985\pi\)
−0.747997 + 0.663702i \(0.768985\pi\)
\(468\) 13.6657 0.631696
\(469\) −21.8056 −1.00689
\(470\) −20.7122 −0.955382
\(471\) −56.1947 −2.58932
\(472\) 28.3391 1.30441
\(473\) 0.975817 0.0448681
\(474\) −87.0410 −3.99792
\(475\) 17.2473 0.791361
\(476\) −0.999061 −0.0457919
\(477\) −33.3709 −1.52795
\(478\) −58.5890 −2.67980
\(479\) −15.2818 −0.698244 −0.349122 0.937077i \(-0.613520\pi\)
−0.349122 + 0.937077i \(0.613520\pi\)
\(480\) 13.6351 0.622355
\(481\) 3.57394 0.162957
\(482\) −32.0782 −1.46112
\(483\) 41.2366 1.87633
\(484\) −37.0447 −1.68385
\(485\) 5.82744 0.264610
\(486\) −50.7776 −2.30332
\(487\) −29.7596 −1.34854 −0.674268 0.738487i \(-0.735541\pi\)
−0.674268 + 0.738487i \(0.735541\pi\)
\(488\) −2.58638 −0.117080
\(489\) −50.4988 −2.28363
\(490\) −0.363300 −0.0164122
\(491\) 0.814690 0.0367665 0.0183832 0.999831i \(-0.494148\pi\)
0.0183832 + 0.999831i \(0.494148\pi\)
\(492\) 12.4836 0.562806
\(493\) −0.420027 −0.0189171
\(494\) 12.5408 0.564237
\(495\) −3.64226 −0.163707
\(496\) 2.11721 0.0950655
\(497\) −32.8363 −1.47291
\(498\) 41.9555 1.88007
\(499\) 13.8712 0.620962 0.310481 0.950580i \(-0.399510\pi\)
0.310481 + 0.950580i \(0.399510\pi\)
\(500\) 38.6096 1.72667
\(501\) −21.2444 −0.949132
\(502\) −38.9050 −1.73642
\(503\) −11.4522 −0.510627 −0.255313 0.966858i \(-0.582179\pi\)
−0.255313 + 0.966858i \(0.582179\pi\)
\(504\) 36.5156 1.62653
\(505\) −9.04034 −0.402290
\(506\) −9.97357 −0.443379
\(507\) −2.62167 −0.116433
\(508\) 49.6022 2.20074
\(509\) 14.5997 0.647120 0.323560 0.946208i \(-0.395120\pi\)
0.323560 + 0.946208i \(0.395120\pi\)
\(510\) −0.884158 −0.0391512
\(511\) −21.1412 −0.935233
\(512\) 15.4535 0.682955
\(513\) 12.2099 0.539080
\(514\) 34.0056 1.49992
\(515\) −24.1441 −1.06392
\(516\) −12.7570 −0.561594
\(517\) −4.68981 −0.206257
\(518\) 22.0472 0.968700
\(519\) −54.5294 −2.39357
\(520\) 4.77571 0.209429
\(521\) −20.0474 −0.878293 −0.439147 0.898415i \(-0.644719\pi\)
−0.439147 + 0.898415i \(0.644719\pi\)
\(522\) 35.4424 1.55127
\(523\) −6.94031 −0.303479 −0.151739 0.988421i \(-0.548487\pi\)
−0.151739 + 0.988421i \(0.548487\pi\)
\(524\) −54.9375 −2.39995
\(525\) −22.2425 −0.970741
\(526\) −6.28626 −0.274094
\(527\) 0.164125 0.00714940
\(528\) −2.58254 −0.112391
\(529\) 12.9405 0.562630
\(530\) −26.9237 −1.16949
\(531\) −30.5461 −1.32559
\(532\) 49.3748 2.14067
\(533\) −1.34958 −0.0584568
\(534\) −10.5796 −0.457823
\(535\) 20.4342 0.883447
\(536\) −29.8644 −1.28995
\(537\) 51.1745 2.20834
\(538\) 24.7267 1.06604
\(539\) −0.0822612 −0.00354324
\(540\) 10.7346 0.461943
\(541\) −45.4324 −1.95329 −0.976645 0.214858i \(-0.931071\pi\)
−0.976645 + 0.214858i \(0.931071\pi\)
\(542\) −36.0980 −1.55054
\(543\) −13.9537 −0.598812
\(544\) 0.422335 0.0181075
\(545\) −0.458058 −0.0196210
\(546\) −16.1728 −0.692133
\(547\) −24.8677 −1.06327 −0.531633 0.846975i \(-0.678421\pi\)
−0.531633 + 0.846975i \(0.678421\pi\)
\(548\) −33.8965 −1.44798
\(549\) 2.78780 0.118980
\(550\) 5.37961 0.229387
\(551\) 20.7582 0.884330
\(552\) 56.4767 2.40381
\(553\) 37.0478 1.57543
\(554\) −58.4914 −2.48506
\(555\) 12.4527 0.528589
\(556\) −13.0548 −0.553646
\(557\) −41.3128 −1.75048 −0.875239 0.483691i \(-0.839296\pi\)
−0.875239 + 0.483691i \(0.839296\pi\)
\(558\) −13.8491 −0.586279
\(559\) 1.37913 0.0583309
\(560\) 4.85464 0.205146
\(561\) −0.200198 −0.00845235
\(562\) −62.7539 −2.64711
\(563\) −1.83339 −0.0772683 −0.0386342 0.999253i \(-0.512301\pi\)
−0.0386342 + 0.999253i \(0.512301\pi\)
\(564\) 61.3103 2.58163
\(565\) 2.71960 0.114414
\(566\) 0.817018 0.0343418
\(567\) 14.7399 0.619019
\(568\) −44.9719 −1.88698
\(569\) 9.05523 0.379615 0.189807 0.981821i \(-0.439214\pi\)
0.189807 + 0.981821i \(0.439214\pi\)
\(570\) 43.6961 1.83023
\(571\) 42.9181 1.79607 0.898033 0.439929i \(-0.144996\pi\)
0.898033 + 0.439929i \(0.144996\pi\)
\(572\) 2.49647 0.104383
\(573\) −7.51622 −0.313995
\(574\) −8.32542 −0.347496
\(575\) −19.3858 −0.808444
\(576\) −46.4217 −1.93424
\(577\) 27.9436 1.16331 0.581654 0.813436i \(-0.302406\pi\)
0.581654 + 0.813436i \(0.302406\pi\)
\(578\) 39.9435 1.66143
\(579\) −8.25220 −0.342950
\(580\) 18.2500 0.757791
\(581\) −17.8578 −0.740865
\(582\) −27.0279 −1.12034
\(583\) −6.09627 −0.252482
\(584\) −28.9545 −1.19815
\(585\) −5.14763 −0.212828
\(586\) 8.48780 0.350628
\(587\) −1.21353 −0.0500876 −0.0250438 0.999686i \(-0.507973\pi\)
−0.0250438 + 0.999686i \(0.507973\pi\)
\(588\) 1.07541 0.0443491
\(589\) −8.11125 −0.334218
\(590\) −24.6446 −1.01460
\(591\) 56.1456 2.30952
\(592\) 4.97567 0.204499
\(593\) −22.0297 −0.904652 −0.452326 0.891853i \(-0.649406\pi\)
−0.452326 + 0.891853i \(0.649406\pi\)
\(594\) 3.80839 0.156260
\(595\) 0.376329 0.0154280
\(596\) 24.5232 1.00451
\(597\) 1.97841 0.0809710
\(598\) −14.0957 −0.576417
\(599\) −0.369341 −0.0150909 −0.00754543 0.999972i \(-0.502402\pi\)
−0.00754543 + 0.999972i \(0.502402\pi\)
\(600\) −30.4628 −1.24364
\(601\) −17.7828 −0.725375 −0.362688 0.931911i \(-0.618141\pi\)
−0.362688 + 0.931911i \(0.618141\pi\)
\(602\) 8.50770 0.346748
\(603\) 32.1901 1.31088
\(604\) 86.4579 3.51792
\(605\) 13.9541 0.567315
\(606\) 41.9294 1.70327
\(607\) −2.58727 −0.105014 −0.0525071 0.998621i \(-0.516721\pi\)
−0.0525071 + 0.998621i \(0.516721\pi\)
\(608\) −20.8723 −0.846483
\(609\) −26.7702 −1.08478
\(610\) 2.24920 0.0910676
\(611\) −6.62813 −0.268146
\(612\) 1.47485 0.0596172
\(613\) −25.0800 −1.01297 −0.506486 0.862248i \(-0.669056\pi\)
−0.506486 + 0.862248i \(0.669056\pi\)
\(614\) −20.4224 −0.824179
\(615\) −4.70237 −0.189618
\(616\) 6.67075 0.268772
\(617\) 29.7439 1.19745 0.598723 0.800956i \(-0.295675\pi\)
0.598723 + 0.800956i \(0.295675\pi\)
\(618\) 111.981 4.50455
\(619\) −46.6537 −1.87517 −0.937585 0.347757i \(-0.886943\pi\)
−0.937585 + 0.347757i \(0.886943\pi\)
\(620\) −7.13118 −0.286395
\(621\) −13.7238 −0.550717
\(622\) −57.6173 −2.31025
\(623\) 4.50305 0.180411
\(624\) −3.64993 −0.146114
\(625\) 1.62464 0.0649855
\(626\) 5.04174 0.201508
\(627\) 9.89401 0.395129
\(628\) 75.6275 3.01787
\(629\) 0.385712 0.0153793
\(630\) −31.7552 −1.26516
\(631\) 11.4475 0.455720 0.227860 0.973694i \(-0.426827\pi\)
0.227860 + 0.973694i \(0.426827\pi\)
\(632\) 50.7398 2.01832
\(633\) 68.5874 2.72610
\(634\) 71.4078 2.83597
\(635\) −18.6843 −0.741464
\(636\) 79.6971 3.16019
\(637\) −0.116260 −0.00460640
\(638\) 6.47470 0.256336
\(639\) 48.4742 1.91761
\(640\) −27.0513 −1.06930
\(641\) −29.4859 −1.16462 −0.582311 0.812966i \(-0.697851\pi\)
−0.582311 + 0.812966i \(0.697851\pi\)
\(642\) −94.7746 −3.74045
\(643\) 14.7596 0.582061 0.291031 0.956714i \(-0.406002\pi\)
0.291031 + 0.956714i \(0.406002\pi\)
\(644\) −55.4967 −2.18688
\(645\) 4.80533 0.189210
\(646\) 1.35345 0.0532506
\(647\) 2.91165 0.114469 0.0572344 0.998361i \(-0.481772\pi\)
0.0572344 + 0.998361i \(0.481772\pi\)
\(648\) 20.1875 0.793039
\(649\) −5.58022 −0.219043
\(650\) 7.60303 0.298216
\(651\) 10.4604 0.409977
\(652\) 67.9619 2.66159
\(653\) −49.8023 −1.94891 −0.974457 0.224575i \(-0.927901\pi\)
−0.974457 + 0.224575i \(0.927901\pi\)
\(654\) 2.12449 0.0830741
\(655\) 20.6940 0.808582
\(656\) −1.87890 −0.0733588
\(657\) 31.2094 1.21760
\(658\) −40.8883 −1.59399
\(659\) −23.8814 −0.930288 −0.465144 0.885235i \(-0.653998\pi\)
−0.465144 + 0.885235i \(0.653998\pi\)
\(660\) 8.69852 0.338589
\(661\) 29.0768 1.13096 0.565479 0.824763i \(-0.308691\pi\)
0.565479 + 0.824763i \(0.308691\pi\)
\(662\) −46.0506 −1.78981
\(663\) −0.282941 −0.0109885
\(664\) −24.4576 −0.949138
\(665\) −18.5986 −0.721224
\(666\) −32.5469 −1.26117
\(667\) −23.3320 −0.903420
\(668\) 28.5910 1.10622
\(669\) −2.53726 −0.0980961
\(670\) 25.9711 1.00335
\(671\) 0.509281 0.0196606
\(672\) 26.9173 1.03836
\(673\) −21.5051 −0.828963 −0.414481 0.910058i \(-0.636037\pi\)
−0.414481 + 0.910058i \(0.636037\pi\)
\(674\) −12.7832 −0.492389
\(675\) 7.40243 0.284920
\(676\) 3.52828 0.135703
\(677\) 16.2930 0.626190 0.313095 0.949722i \(-0.398634\pi\)
0.313095 + 0.949722i \(0.398634\pi\)
\(678\) −12.6136 −0.484422
\(679\) 11.5040 0.441485
\(680\) 0.515412 0.0197652
\(681\) −38.1151 −1.46057
\(682\) −2.52998 −0.0968780
\(683\) −49.2052 −1.88279 −0.941393 0.337312i \(-0.890482\pi\)
−0.941393 + 0.337312i \(0.890482\pi\)
\(684\) −72.8888 −2.78697
\(685\) 12.7682 0.487849
\(686\) −43.8995 −1.67609
\(687\) −68.2628 −2.60439
\(688\) 1.92004 0.0732008
\(689\) −8.61589 −0.328239
\(690\) −49.1140 −1.86974
\(691\) 36.5844 1.39174 0.695868 0.718169i \(-0.255020\pi\)
0.695868 + 0.718169i \(0.255020\pi\)
\(692\) 73.3863 2.78973
\(693\) −7.19024 −0.273135
\(694\) −46.9746 −1.78313
\(695\) 4.91752 0.186532
\(696\) −36.6639 −1.38974
\(697\) −0.145652 −0.00551695
\(698\) 75.0989 2.84253
\(699\) 12.8209 0.484930
\(700\) 29.9342 1.13141
\(701\) −38.2776 −1.44573 −0.722863 0.690991i \(-0.757174\pi\)
−0.722863 + 0.690991i \(0.757174\pi\)
\(702\) 5.38242 0.203146
\(703\) −19.0623 −0.718950
\(704\) −8.48042 −0.319618
\(705\) −23.0946 −0.869791
\(706\) 75.6633 2.84763
\(707\) −17.8467 −0.671193
\(708\) 72.9508 2.74166
\(709\) −26.1524 −0.982174 −0.491087 0.871111i \(-0.663400\pi\)
−0.491087 + 0.871111i \(0.663400\pi\)
\(710\) 39.1090 1.46774
\(711\) −54.6912 −2.05108
\(712\) 6.16727 0.231128
\(713\) 9.11697 0.341433
\(714\) −1.74543 −0.0653211
\(715\) −0.940380 −0.0351682
\(716\) −68.8713 −2.57384
\(717\) −65.3281 −2.43972
\(718\) −32.4101 −1.20953
\(719\) −13.1714 −0.491211 −0.245606 0.969370i \(-0.578987\pi\)
−0.245606 + 0.969370i \(0.578987\pi\)
\(720\) −7.16659 −0.267083
\(721\) −47.6633 −1.77507
\(722\) −22.2156 −0.826777
\(723\) −35.7679 −1.33022
\(724\) 18.7791 0.697921
\(725\) 12.5850 0.467394
\(726\) −64.7197 −2.40197
\(727\) 42.1627 1.56373 0.781863 0.623450i \(-0.214269\pi\)
0.781863 + 0.623450i \(0.214269\pi\)
\(728\) 9.42781 0.349418
\(729\) −39.7642 −1.47275
\(730\) 25.1798 0.931947
\(731\) 0.148841 0.00550507
\(732\) −6.65788 −0.246082
\(733\) −22.4940 −0.830836 −0.415418 0.909631i \(-0.636365\pi\)
−0.415418 + 0.909631i \(0.636365\pi\)
\(734\) −54.1600 −1.99908
\(735\) −0.405088 −0.0149419
\(736\) 23.4602 0.864756
\(737\) 5.88056 0.216613
\(738\) 12.2903 0.452411
\(739\) −16.8143 −0.618525 −0.309263 0.950977i \(-0.600082\pi\)
−0.309263 + 0.950977i \(0.600082\pi\)
\(740\) −16.7591 −0.616075
\(741\) 13.9833 0.513688
\(742\) −53.1505 −1.95122
\(743\) 18.4612 0.677277 0.338638 0.940917i \(-0.390034\pi\)
0.338638 + 0.940917i \(0.390034\pi\)
\(744\) 14.3264 0.525230
\(745\) −9.23749 −0.338435
\(746\) 20.5340 0.751804
\(747\) 26.3622 0.964544
\(748\) 0.269428 0.00985128
\(749\) 40.3395 1.47397
\(750\) 67.4536 2.46306
\(751\) −28.9175 −1.05521 −0.527607 0.849489i \(-0.676910\pi\)
−0.527607 + 0.849489i \(0.676910\pi\)
\(752\) −9.22776 −0.336502
\(753\) −43.3800 −1.58085
\(754\) 9.15073 0.333250
\(755\) −32.5672 −1.18524
\(756\) 21.1913 0.770721
\(757\) 34.6847 1.26064 0.630319 0.776336i \(-0.282924\pi\)
0.630319 + 0.776336i \(0.282924\pi\)
\(758\) 12.2480 0.444869
\(759\) −11.1208 −0.403658
\(760\) −25.4723 −0.923977
\(761\) 0.409172 0.0148325 0.00741623 0.999972i \(-0.497639\pi\)
0.00741623 + 0.999972i \(0.497639\pi\)
\(762\) 86.6585 3.13931
\(763\) −0.904259 −0.0327364
\(764\) 10.1154 0.365963
\(765\) −0.555551 −0.0200860
\(766\) 39.9183 1.44231
\(767\) −7.88656 −0.284767
\(768\) 62.6213 2.25965
\(769\) 10.0799 0.363490 0.181745 0.983346i \(-0.441825\pi\)
0.181745 + 0.983346i \(0.441825\pi\)
\(770\) −5.80110 −0.209057
\(771\) 37.9170 1.36555
\(772\) 11.1059 0.399710
\(773\) −10.3448 −0.372076 −0.186038 0.982543i \(-0.559565\pi\)
−0.186038 + 0.982543i \(0.559565\pi\)
\(774\) −12.5594 −0.451437
\(775\) −4.91757 −0.176644
\(776\) 15.7557 0.565596
\(777\) 24.5832 0.881916
\(778\) −2.42686 −0.0870073
\(779\) 7.19827 0.257905
\(780\) 12.2937 0.440184
\(781\) 8.85536 0.316870
\(782\) −1.52126 −0.0544002
\(783\) 8.90929 0.318392
\(784\) −0.161859 −0.00578067
\(785\) −28.4876 −1.01677
\(786\) −95.9797 −3.42348
\(787\) −29.8489 −1.06400 −0.531998 0.846745i \(-0.678559\pi\)
−0.531998 + 0.846745i \(0.678559\pi\)
\(788\) −75.5614 −2.69176
\(789\) −7.00932 −0.249538
\(790\) −44.1250 −1.56990
\(791\) 5.36880 0.190893
\(792\) −9.84759 −0.349919
\(793\) 0.719770 0.0255598
\(794\) −10.7901 −0.382927
\(795\) −30.0205 −1.06472
\(796\) −2.66257 −0.0943723
\(797\) −34.9895 −1.23939 −0.619697 0.784842i \(-0.712744\pi\)
−0.619697 + 0.784842i \(0.712744\pi\)
\(798\) 86.2612 3.05362
\(799\) −0.715332 −0.0253066
\(800\) −12.6541 −0.447391
\(801\) −6.64755 −0.234880
\(802\) 24.5992 0.868628
\(803\) 5.70140 0.201198
\(804\) −76.8771 −2.71125
\(805\) 20.9047 0.736793
\(806\) −3.57564 −0.125946
\(807\) 27.5709 0.970540
\(808\) −24.4424 −0.859881
\(809\) −32.6961 −1.14953 −0.574766 0.818318i \(-0.694907\pi\)
−0.574766 + 0.818318i \(0.694907\pi\)
\(810\) −17.5557 −0.616844
\(811\) 4.92204 0.172836 0.0864181 0.996259i \(-0.472458\pi\)
0.0864181 + 0.996259i \(0.472458\pi\)
\(812\) 36.0277 1.26432
\(813\) −40.2501 −1.41163
\(814\) −5.94573 −0.208398
\(815\) −25.6001 −0.896732
\(816\) −0.393913 −0.0137897
\(817\) −7.35588 −0.257349
\(818\) −13.7336 −0.480185
\(819\) −10.1620 −0.355090
\(820\) 6.32851 0.221001
\(821\) −23.2833 −0.812593 −0.406296 0.913741i \(-0.633180\pi\)
−0.406296 + 0.913741i \(0.633180\pi\)
\(822\) −59.2195 −2.06552
\(823\) −31.9014 −1.11201 −0.556006 0.831178i \(-0.687667\pi\)
−0.556006 + 0.831178i \(0.687667\pi\)
\(824\) −65.2786 −2.27409
\(825\) 5.99839 0.208837
\(826\) −48.6514 −1.69280
\(827\) 52.8324 1.83716 0.918582 0.395231i \(-0.129335\pi\)
0.918582 + 0.395231i \(0.129335\pi\)
\(828\) 81.9262 2.84713
\(829\) −27.2027 −0.944789 −0.472394 0.881387i \(-0.656610\pi\)
−0.472394 + 0.881387i \(0.656610\pi\)
\(830\) 21.2691 0.738262
\(831\) −65.2193 −2.26243
\(832\) −11.9854 −0.415520
\(833\) −0.0125472 −0.000434735 0
\(834\) −22.8076 −0.789764
\(835\) −10.7698 −0.372703
\(836\) −13.3155 −0.460525
\(837\) −3.48129 −0.120331
\(838\) −7.94049 −0.274300
\(839\) 13.4158 0.463165 0.231583 0.972815i \(-0.425610\pi\)
0.231583 + 0.972815i \(0.425610\pi\)
\(840\) 32.8495 1.13342
\(841\) −13.8532 −0.477696
\(842\) 8.05067 0.277445
\(843\) −69.9720 −2.40996
\(844\) −92.3058 −3.17729
\(845\) −1.32904 −0.0457205
\(846\) 60.3607 2.07524
\(847\) 27.5470 0.946528
\(848\) −11.9951 −0.411915
\(849\) 0.910994 0.0312652
\(850\) 0.820547 0.0281445
\(851\) 21.4259 0.734470
\(852\) −115.767 −3.96611
\(853\) 19.9257 0.682243 0.341122 0.940019i \(-0.389193\pi\)
0.341122 + 0.940019i \(0.389193\pi\)
\(854\) 4.44019 0.151940
\(855\) 27.4560 0.938974
\(856\) 55.2480 1.88834
\(857\) 15.0050 0.512560 0.256280 0.966603i \(-0.417503\pi\)
0.256280 + 0.966603i \(0.417503\pi\)
\(858\) 4.36152 0.148900
\(859\) −35.5168 −1.21182 −0.605909 0.795534i \(-0.707190\pi\)
−0.605909 + 0.795534i \(0.707190\pi\)
\(860\) −6.46707 −0.220525
\(861\) −9.28303 −0.316365
\(862\) 46.6327 1.58832
\(863\) 28.8239 0.981177 0.490589 0.871391i \(-0.336782\pi\)
0.490589 + 0.871391i \(0.336782\pi\)
\(864\) −8.95825 −0.304766
\(865\) −27.6434 −0.939903
\(866\) 2.85643 0.0970653
\(867\) 44.5379 1.51259
\(868\) −14.0778 −0.477831
\(869\) −9.99110 −0.338925
\(870\) 31.8841 1.08097
\(871\) 8.31103 0.281609
\(872\) −1.23845 −0.0419393
\(873\) −16.9827 −0.574776
\(874\) 75.1825 2.54309
\(875\) −28.7107 −0.970598
\(876\) −74.5350 −2.51830
\(877\) 18.5733 0.627174 0.313587 0.949559i \(-0.398469\pi\)
0.313587 + 0.949559i \(0.398469\pi\)
\(878\) −24.7710 −0.835981
\(879\) 9.46409 0.319216
\(880\) −1.30921 −0.0441334
\(881\) 17.5796 0.592273 0.296137 0.955146i \(-0.404302\pi\)
0.296137 + 0.955146i \(0.404302\pi\)
\(882\) 1.05875 0.0356500
\(883\) 17.5269 0.589826 0.294913 0.955524i \(-0.404709\pi\)
0.294913 + 0.955524i \(0.404709\pi\)
\(884\) 0.380785 0.0128072
\(885\) −27.4793 −0.923708
\(886\) 5.95630 0.200106
\(887\) 35.8634 1.20417 0.602087 0.798431i \(-0.294336\pi\)
0.602087 + 0.798431i \(0.294336\pi\)
\(888\) 33.6685 1.12984
\(889\) −36.8850 −1.23708
\(890\) −5.36326 −0.179777
\(891\) −3.97509 −0.133171
\(892\) 3.41467 0.114332
\(893\) 35.3526 1.18303
\(894\) 42.8438 1.43291
\(895\) 25.9426 0.867167
\(896\) −53.4025 −1.78405
\(897\) −15.7170 −0.524777
\(898\) −27.4533 −0.916129
\(899\) −5.91860 −0.197396
\(900\) −44.1899 −1.47300
\(901\) −0.929858 −0.0309781
\(902\) 2.24521 0.0747574
\(903\) 9.48628 0.315684
\(904\) 7.35299 0.244557
\(905\) −7.07378 −0.235140
\(906\) 151.048 5.01824
\(907\) 28.5273 0.947235 0.473617 0.880731i \(-0.342948\pi\)
0.473617 + 0.880731i \(0.342948\pi\)
\(908\) 51.2957 1.70231
\(909\) 26.3459 0.873838
\(910\) −8.19873 −0.271785
\(911\) −29.6322 −0.981760 −0.490880 0.871227i \(-0.663325\pi\)
−0.490880 + 0.871227i \(0.663325\pi\)
\(912\) 19.4677 0.644639
\(913\) 4.81591 0.159383
\(914\) 9.45170 0.312635
\(915\) 2.50791 0.0829090
\(916\) 91.8689 3.03543
\(917\) 40.8524 1.34906
\(918\) 0.580890 0.0191722
\(919\) −10.6593 −0.351619 −0.175810 0.984424i \(-0.556254\pi\)
−0.175810 + 0.984424i \(0.556254\pi\)
\(920\) 28.6306 0.943922
\(921\) −22.7714 −0.750343
\(922\) −32.7340 −1.07804
\(923\) 12.5153 0.411947
\(924\) 17.1719 0.564914
\(925\) −11.5568 −0.379986
\(926\) −2.35123 −0.0772662
\(927\) 70.3622 2.31100
\(928\) −15.2300 −0.499951
\(929\) −51.3170 −1.68366 −0.841828 0.539747i \(-0.818520\pi\)
−0.841828 + 0.539747i \(0.818520\pi\)
\(930\) −12.4587 −0.408536
\(931\) 0.620098 0.0203229
\(932\) −17.2545 −0.565189
\(933\) −64.2447 −2.10328
\(934\) 76.0123 2.48720
\(935\) −0.101489 −0.00331905
\(936\) −13.9177 −0.454913
\(937\) 54.0810 1.76675 0.883374 0.468668i \(-0.155266\pi\)
0.883374 + 0.468668i \(0.155266\pi\)
\(938\) 51.2699 1.67402
\(939\) 5.62165 0.183456
\(940\) 31.0809 1.01375
\(941\) 48.0503 1.56640 0.783198 0.621772i \(-0.213587\pi\)
0.783198 + 0.621772i \(0.213587\pi\)
\(942\) 132.127 4.30492
\(943\) −8.09079 −0.263472
\(944\) −10.9798 −0.357361
\(945\) −7.98241 −0.259668
\(946\) −2.29437 −0.0745964
\(947\) −8.03466 −0.261091 −0.130546 0.991442i \(-0.541673\pi\)
−0.130546 + 0.991442i \(0.541673\pi\)
\(948\) 130.615 4.24217
\(949\) 8.05783 0.261568
\(950\) −40.5524 −1.31569
\(951\) 79.6213 2.58190
\(952\) 1.01748 0.0329768
\(953\) 52.2712 1.69323 0.846615 0.532206i \(-0.178637\pi\)
0.846615 + 0.532206i \(0.178637\pi\)
\(954\) 78.4626 2.54032
\(955\) −3.81031 −0.123299
\(956\) 87.9194 2.84352
\(957\) 7.21944 0.233371
\(958\) 35.9311 1.16088
\(959\) 25.2060 0.813943
\(960\) −41.7611 −1.34783
\(961\) −28.6873 −0.925397
\(962\) −8.40314 −0.270928
\(963\) −59.5505 −1.91899
\(964\) 48.1369 1.55038
\(965\) −4.18341 −0.134669
\(966\) −96.9568 −3.11953
\(967\) −56.0172 −1.80139 −0.900695 0.434451i \(-0.856942\pi\)
−0.900695 + 0.434451i \(0.856942\pi\)
\(968\) 37.7278 1.21262
\(969\) 1.50912 0.0484800
\(970\) −13.7017 −0.439934
\(971\) −16.4988 −0.529472 −0.264736 0.964321i \(-0.585285\pi\)
−0.264736 + 0.964321i \(0.585285\pi\)
\(972\) 76.1975 2.44404
\(973\) 9.70775 0.311216
\(974\) 69.9716 2.24204
\(975\) 8.47756 0.271499
\(976\) 1.00207 0.0320756
\(977\) 5.29964 0.169550 0.0847752 0.996400i \(-0.472983\pi\)
0.0847752 + 0.996400i \(0.472983\pi\)
\(978\) 118.734 3.79670
\(979\) −1.21439 −0.0388121
\(980\) 0.545172 0.0174149
\(981\) 1.33490 0.0426200
\(982\) −1.91552 −0.0611268
\(983\) 27.6712 0.882575 0.441288 0.897366i \(-0.354522\pi\)
0.441288 + 0.897366i \(0.354522\pi\)
\(984\) −12.7138 −0.405302
\(985\) 28.4627 0.906897
\(986\) 0.987580 0.0314510
\(987\) −45.5913 −1.45119
\(988\) −18.8188 −0.598707
\(989\) 8.26793 0.262905
\(990\) 8.56379 0.272175
\(991\) 24.6785 0.783938 0.391969 0.919978i \(-0.371794\pi\)
0.391969 + 0.919978i \(0.371794\pi\)
\(992\) 5.95112 0.188948
\(993\) −51.3474 −1.62946
\(994\) 77.2058 2.44882
\(995\) 1.00295 0.0317955
\(996\) −62.9589 −1.99493
\(997\) −53.6541 −1.69924 −0.849621 0.527393i \(-0.823170\pi\)
−0.849621 + 0.527393i \(0.823170\pi\)
\(998\) −32.6145 −1.03239
\(999\) −8.18143 −0.258849
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 6019.2.a.b.1.10 101
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6019.2.a.b.1.10 101 1.1 even 1 trivial