Properties

Label 4034.2.a.b.1.6
Level $4034$
Weight $2$
Character 4034.1
Self dual yes
Analytic conductor $32.212$
Analytic rank $1$
Dimension $35$
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] = [4034,2,Mod(1,4034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4034, 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("4034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4034.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: \(32.2116521754\)
Analytic rank: \(1\)
Dimension: \(35\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 4034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.23091 q^{3} +1.00000 q^{4} +1.94904 q^{5} +2.23091 q^{6} +1.55699 q^{7} -1.00000 q^{8} +1.97697 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.23091 q^{3} +1.00000 q^{4} +1.94904 q^{5} +2.23091 q^{6} +1.55699 q^{7} -1.00000 q^{8} +1.97697 q^{9} -1.94904 q^{10} -0.440224 q^{11} -2.23091 q^{12} -5.73346 q^{13} -1.55699 q^{14} -4.34813 q^{15} +1.00000 q^{16} -0.734051 q^{17} -1.97697 q^{18} +6.42751 q^{19} +1.94904 q^{20} -3.47351 q^{21} +0.440224 q^{22} +7.59175 q^{23} +2.23091 q^{24} -1.20126 q^{25} +5.73346 q^{26} +2.28228 q^{27} +1.55699 q^{28} -8.95243 q^{29} +4.34813 q^{30} -4.51395 q^{31} -1.00000 q^{32} +0.982102 q^{33} +0.734051 q^{34} +3.03463 q^{35} +1.97697 q^{36} +3.37500 q^{37} -6.42751 q^{38} +12.7908 q^{39} -1.94904 q^{40} +10.4996 q^{41} +3.47351 q^{42} -7.09790 q^{43} -0.440224 q^{44} +3.85319 q^{45} -7.59175 q^{46} -10.1456 q^{47} -2.23091 q^{48} -4.57578 q^{49} +1.20126 q^{50} +1.63760 q^{51} -5.73346 q^{52} -0.00409262 q^{53} -2.28228 q^{54} -0.858013 q^{55} -1.55699 q^{56} -14.3392 q^{57} +8.95243 q^{58} -9.64546 q^{59} -4.34813 q^{60} +3.38658 q^{61} +4.51395 q^{62} +3.07813 q^{63} +1.00000 q^{64} -11.1747 q^{65} -0.982102 q^{66} +5.65852 q^{67} -0.734051 q^{68} -16.9365 q^{69} -3.03463 q^{70} -16.3890 q^{71} -1.97697 q^{72} +12.4924 q^{73} -3.37500 q^{74} +2.67991 q^{75} +6.42751 q^{76} -0.685425 q^{77} -12.7908 q^{78} -8.36805 q^{79} +1.94904 q^{80} -11.0225 q^{81} -10.4996 q^{82} +8.50361 q^{83} -3.47351 q^{84} -1.43069 q^{85} +7.09790 q^{86} +19.9721 q^{87} +0.440224 q^{88} -3.03215 q^{89} -3.85319 q^{90} -8.92694 q^{91} +7.59175 q^{92} +10.0702 q^{93} +10.1456 q^{94} +12.5274 q^{95} +2.23091 q^{96} +16.7782 q^{97} +4.57578 q^{98} -0.870312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 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
\(3\) −2.23091 −1.28802 −0.644009 0.765018i \(-0.722730\pi\)
−0.644009 + 0.765018i \(0.722730\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.94904 0.871635 0.435817 0.900035i \(-0.356459\pi\)
0.435817 + 0.900035i \(0.356459\pi\)
\(6\) 2.23091 0.910766
\(7\) 1.55699 0.588487 0.294244 0.955730i \(-0.404932\pi\)
0.294244 + 0.955730i \(0.404932\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.97697 0.658991
\(10\) −1.94904 −0.616339
\(11\) −0.440224 −0.132733 −0.0663663 0.997795i \(-0.521141\pi\)
−0.0663663 + 0.997795i \(0.521141\pi\)
\(12\) −2.23091 −0.644009
\(13\) −5.73346 −1.59017 −0.795087 0.606495i \(-0.792575\pi\)
−0.795087 + 0.606495i \(0.792575\pi\)
\(14\) −1.55699 −0.416123
\(15\) −4.34813 −1.12268
\(16\) 1.00000 0.250000
\(17\) −0.734051 −0.178034 −0.0890168 0.996030i \(-0.528372\pi\)
−0.0890168 + 0.996030i \(0.528372\pi\)
\(18\) −1.97697 −0.465977
\(19\) 6.42751 1.47457 0.737285 0.675581i \(-0.236107\pi\)
0.737285 + 0.675581i \(0.236107\pi\)
\(20\) 1.94904 0.435817
\(21\) −3.47351 −0.757982
\(22\) 0.440224 0.0938562
\(23\) 7.59175 1.58299 0.791495 0.611176i \(-0.209303\pi\)
0.791495 + 0.611176i \(0.209303\pi\)
\(24\) 2.23091 0.455383
\(25\) −1.20126 −0.240253
\(26\) 5.73346 1.12442
\(27\) 2.28228 0.439226
\(28\) 1.55699 0.294244
\(29\) −8.95243 −1.66242 −0.831212 0.555955i \(-0.812353\pi\)
−0.831212 + 0.555955i \(0.812353\pi\)
\(30\) 4.34813 0.793856
\(31\) −4.51395 −0.810729 −0.405365 0.914155i \(-0.632855\pi\)
−0.405365 + 0.914155i \(0.632855\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.982102 0.170962
\(34\) 0.734051 0.125889
\(35\) 3.03463 0.512946
\(36\) 1.97697 0.329496
\(37\) 3.37500 0.554846 0.277423 0.960748i \(-0.410520\pi\)
0.277423 + 0.960748i \(0.410520\pi\)
\(38\) −6.42751 −1.04268
\(39\) 12.7908 2.04817
\(40\) −1.94904 −0.308169
\(41\) 10.4996 1.63977 0.819883 0.572531i \(-0.194038\pi\)
0.819883 + 0.572531i \(0.194038\pi\)
\(42\) 3.47351 0.535974
\(43\) −7.09790 −1.08242 −0.541210 0.840888i \(-0.682033\pi\)
−0.541210 + 0.840888i \(0.682033\pi\)
\(44\) −0.440224 −0.0663663
\(45\) 3.85319 0.574400
\(46\) −7.59175 −1.11934
\(47\) −10.1456 −1.47989 −0.739947 0.672666i \(-0.765149\pi\)
−0.739947 + 0.672666i \(0.765149\pi\)
\(48\) −2.23091 −0.322005
\(49\) −4.57578 −0.653683
\(50\) 1.20126 0.169884
\(51\) 1.63760 0.229310
\(52\) −5.73346 −0.795087
\(53\) −0.00409262 −0.000562165 0 −0.000281082 1.00000i \(-0.500089\pi\)
−0.000281082 1.00000i \(0.500089\pi\)
\(54\) −2.28228 −0.310579
\(55\) −0.858013 −0.115694
\(56\) −1.55699 −0.208062
\(57\) −14.3392 −1.89927
\(58\) 8.95243 1.17551
\(59\) −9.64546 −1.25573 −0.627866 0.778321i \(-0.716072\pi\)
−0.627866 + 0.778321i \(0.716072\pi\)
\(60\) −4.34813 −0.561341
\(61\) 3.38658 0.433607 0.216803 0.976215i \(-0.430437\pi\)
0.216803 + 0.976215i \(0.430437\pi\)
\(62\) 4.51395 0.573272
\(63\) 3.07813 0.387808
\(64\) 1.00000 0.125000
\(65\) −11.1747 −1.38605
\(66\) −0.982102 −0.120888
\(67\) 5.65852 0.691298 0.345649 0.938364i \(-0.387659\pi\)
0.345649 + 0.938364i \(0.387659\pi\)
\(68\) −0.734051 −0.0890168
\(69\) −16.9365 −2.03892
\(70\) −3.03463 −0.362708
\(71\) −16.3890 −1.94502 −0.972511 0.232859i \(-0.925192\pi\)
−0.972511 + 0.232859i \(0.925192\pi\)
\(72\) −1.97697 −0.232989
\(73\) 12.4924 1.46213 0.731064 0.682309i \(-0.239024\pi\)
0.731064 + 0.682309i \(0.239024\pi\)
\(74\) −3.37500 −0.392336
\(75\) 2.67991 0.309450
\(76\) 6.42751 0.737285
\(77\) −0.685425 −0.0781115
\(78\) −12.7908 −1.44828
\(79\) −8.36805 −0.941479 −0.470739 0.882272i \(-0.656013\pi\)
−0.470739 + 0.882272i \(0.656013\pi\)
\(80\) 1.94904 0.217909
\(81\) −11.0225 −1.22472
\(82\) −10.4996 −1.15949
\(83\) 8.50361 0.933392 0.466696 0.884418i \(-0.345444\pi\)
0.466696 + 0.884418i \(0.345444\pi\)
\(84\) −3.47351 −0.378991
\(85\) −1.43069 −0.155180
\(86\) 7.09790 0.765386
\(87\) 19.9721 2.14123
\(88\) 0.440224 0.0469281
\(89\) −3.03215 −0.321407 −0.160703 0.987003i \(-0.551376\pi\)
−0.160703 + 0.987003i \(0.551376\pi\)
\(90\) −3.85319 −0.406162
\(91\) −8.92694 −0.935798
\(92\) 7.59175 0.791495
\(93\) 10.0702 1.04423
\(94\) 10.1456 1.04644
\(95\) 12.5274 1.28529
\(96\) 2.23091 0.227692
\(97\) 16.7782 1.70357 0.851784 0.523894i \(-0.175521\pi\)
0.851784 + 0.523894i \(0.175521\pi\)
\(98\) 4.57578 0.462224
\(99\) −0.870312 −0.0874696
\(100\) −1.20126 −0.120126
\(101\) 17.6493 1.75617 0.878087 0.478500i \(-0.158819\pi\)
0.878087 + 0.478500i \(0.158819\pi\)
\(102\) −1.63760 −0.162147
\(103\) −0.540281 −0.0532355 −0.0266178 0.999646i \(-0.508474\pi\)
−0.0266178 + 0.999646i \(0.508474\pi\)
\(104\) 5.73346 0.562212
\(105\) −6.77000 −0.660684
\(106\) 0.00409262 0.000397511 0
\(107\) −4.36318 −0.421804 −0.210902 0.977507i \(-0.567640\pi\)
−0.210902 + 0.977507i \(0.567640\pi\)
\(108\) 2.28228 0.219613
\(109\) −2.93220 −0.280854 −0.140427 0.990091i \(-0.544847\pi\)
−0.140427 + 0.990091i \(0.544847\pi\)
\(110\) 0.858013 0.0818083
\(111\) −7.52933 −0.714652
\(112\) 1.55699 0.147122
\(113\) −4.52487 −0.425664 −0.212832 0.977089i \(-0.568269\pi\)
−0.212832 + 0.977089i \(0.568269\pi\)
\(114\) 14.3392 1.34299
\(115\) 14.7966 1.37979
\(116\) −8.95243 −0.831212
\(117\) −11.3349 −1.04791
\(118\) 9.64546 0.887937
\(119\) −1.14291 −0.104770
\(120\) 4.34813 0.396928
\(121\) −10.8062 −0.982382
\(122\) −3.38658 −0.306606
\(123\) −23.4237 −2.11205
\(124\) −4.51395 −0.405365
\(125\) −12.0865 −1.08105
\(126\) −3.07813 −0.274222
\(127\) −16.3837 −1.45382 −0.726911 0.686732i \(-0.759045\pi\)
−0.726911 + 0.686732i \(0.759045\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 15.8348 1.39418
\(130\) 11.1747 0.980087
\(131\) −1.43967 −0.125784 −0.0628921 0.998020i \(-0.520032\pi\)
−0.0628921 + 0.998020i \(0.520032\pi\)
\(132\) 0.982102 0.0854810
\(133\) 10.0076 0.867766
\(134\) −5.65852 −0.488822
\(135\) 4.44825 0.382844
\(136\) 0.734051 0.0629444
\(137\) 9.63273 0.822980 0.411490 0.911414i \(-0.365009\pi\)
0.411490 + 0.911414i \(0.365009\pi\)
\(138\) 16.9365 1.44173
\(139\) −3.04315 −0.258117 −0.129059 0.991637i \(-0.541196\pi\)
−0.129059 + 0.991637i \(0.541196\pi\)
\(140\) 3.03463 0.256473
\(141\) 22.6340 1.90613
\(142\) 16.3890 1.37534
\(143\) 2.52401 0.211068
\(144\) 1.97697 0.164748
\(145\) −17.4486 −1.44903
\(146\) −12.4924 −1.03388
\(147\) 10.2082 0.841955
\(148\) 3.37500 0.277423
\(149\) 5.79400 0.474663 0.237331 0.971429i \(-0.423727\pi\)
0.237331 + 0.971429i \(0.423727\pi\)
\(150\) −2.67991 −0.218814
\(151\) −9.39394 −0.764468 −0.382234 0.924066i \(-0.624845\pi\)
−0.382234 + 0.924066i \(0.624845\pi\)
\(152\) −6.42751 −0.521340
\(153\) −1.45120 −0.117323
\(154\) 0.685425 0.0552332
\(155\) −8.79785 −0.706660
\(156\) 12.7908 1.02409
\(157\) −0.880167 −0.0702450 −0.0351225 0.999383i \(-0.511182\pi\)
−0.0351225 + 0.999383i \(0.511182\pi\)
\(158\) 8.36805 0.665726
\(159\) 0.00913028 0.000724079 0
\(160\) −1.94904 −0.154085
\(161\) 11.8203 0.931569
\(162\) 11.0225 0.866009
\(163\) 22.9288 1.79592 0.897960 0.440076i \(-0.145049\pi\)
0.897960 + 0.440076i \(0.145049\pi\)
\(164\) 10.4996 0.819883
\(165\) 1.91415 0.149017
\(166\) −8.50361 −0.660008
\(167\) −3.44539 −0.266613 −0.133306 0.991075i \(-0.542559\pi\)
−0.133306 + 0.991075i \(0.542559\pi\)
\(168\) 3.47351 0.267987
\(169\) 19.8725 1.52866
\(170\) 1.43069 0.109729
\(171\) 12.7070 0.971729
\(172\) −7.09790 −0.541210
\(173\) 10.7624 0.818249 0.409125 0.912479i \(-0.365834\pi\)
0.409125 + 0.912479i \(0.365834\pi\)
\(174\) −19.9721 −1.51408
\(175\) −1.87035 −0.141386
\(176\) −0.440224 −0.0331832
\(177\) 21.5182 1.61741
\(178\) 3.03215 0.227269
\(179\) 25.1072 1.87660 0.938300 0.345823i \(-0.112400\pi\)
0.938300 + 0.345823i \(0.112400\pi\)
\(180\) 3.85319 0.287200
\(181\) −21.5432 −1.60129 −0.800645 0.599139i \(-0.795510\pi\)
−0.800645 + 0.599139i \(0.795510\pi\)
\(182\) 8.92694 0.661709
\(183\) −7.55516 −0.558494
\(184\) −7.59175 −0.559671
\(185\) 6.57799 0.483624
\(186\) −10.0702 −0.738385
\(187\) 0.323147 0.0236309
\(188\) −10.1456 −0.739947
\(189\) 3.55350 0.258479
\(190\) −12.5274 −0.908836
\(191\) −17.7850 −1.28688 −0.643440 0.765497i \(-0.722493\pi\)
−0.643440 + 0.765497i \(0.722493\pi\)
\(192\) −2.23091 −0.161002
\(193\) −20.1608 −1.45121 −0.725603 0.688114i \(-0.758439\pi\)
−0.725603 + 0.688114i \(0.758439\pi\)
\(194\) −16.7782 −1.20460
\(195\) 24.9298 1.78526
\(196\) −4.57578 −0.326841
\(197\) −2.10006 −0.149623 −0.0748114 0.997198i \(-0.523835\pi\)
−0.0748114 + 0.997198i \(0.523835\pi\)
\(198\) 0.870312 0.0618504
\(199\) 2.62596 0.186149 0.0930747 0.995659i \(-0.470330\pi\)
0.0930747 + 0.995659i \(0.470330\pi\)
\(200\) 1.20126 0.0849421
\(201\) −12.6237 −0.890405
\(202\) −17.6493 −1.24180
\(203\) −13.9389 −0.978316
\(204\) 1.63760 0.114655
\(205\) 20.4641 1.42928
\(206\) 0.540281 0.0376432
\(207\) 15.0087 1.04318
\(208\) −5.73346 −0.397544
\(209\) −2.82955 −0.195724
\(210\) 6.77000 0.467174
\(211\) −3.83782 −0.264206 −0.132103 0.991236i \(-0.542173\pi\)
−0.132103 + 0.991236i \(0.542173\pi\)
\(212\) −0.00409262 −0.000281082 0
\(213\) 36.5625 2.50522
\(214\) 4.36318 0.298261
\(215\) −13.8341 −0.943474
\(216\) −2.28228 −0.155290
\(217\) −7.02818 −0.477104
\(218\) 2.93220 0.198594
\(219\) −27.8695 −1.88325
\(220\) −0.858013 −0.0578472
\(221\) 4.20865 0.283104
\(222\) 7.52933 0.505336
\(223\) −14.2152 −0.951922 −0.475961 0.879466i \(-0.657900\pi\)
−0.475961 + 0.879466i \(0.657900\pi\)
\(224\) −1.55699 −0.104031
\(225\) −2.37486 −0.158324
\(226\) 4.52487 0.300990
\(227\) 7.70742 0.511559 0.255780 0.966735i \(-0.417668\pi\)
0.255780 + 0.966735i \(0.417668\pi\)
\(228\) −14.3392 −0.949637
\(229\) −12.7734 −0.844090 −0.422045 0.906575i \(-0.638688\pi\)
−0.422045 + 0.906575i \(0.638688\pi\)
\(230\) −14.7966 −0.975658
\(231\) 1.52912 0.100609
\(232\) 8.95243 0.587756
\(233\) −7.97890 −0.522715 −0.261358 0.965242i \(-0.584170\pi\)
−0.261358 + 0.965242i \(0.584170\pi\)
\(234\) 11.3349 0.740985
\(235\) −19.7742 −1.28993
\(236\) −9.64546 −0.627866
\(237\) 18.6684 1.21264
\(238\) 1.14291 0.0740839
\(239\) −8.65986 −0.560160 −0.280080 0.959977i \(-0.590361\pi\)
−0.280080 + 0.959977i \(0.590361\pi\)
\(240\) −4.34813 −0.280670
\(241\) −13.0891 −0.843144 −0.421572 0.906795i \(-0.638521\pi\)
−0.421572 + 0.906795i \(0.638521\pi\)
\(242\) 10.8062 0.694649
\(243\) 17.7434 1.13824
\(244\) 3.38658 0.216803
\(245\) −8.91835 −0.569773
\(246\) 23.4237 1.49344
\(247\) −36.8518 −2.34483
\(248\) 4.51395 0.286636
\(249\) −18.9708 −1.20223
\(250\) 12.0865 0.764416
\(251\) −0.752494 −0.0474970 −0.0237485 0.999718i \(-0.507560\pi\)
−0.0237485 + 0.999718i \(0.507560\pi\)
\(252\) 3.07813 0.193904
\(253\) −3.34207 −0.210114
\(254\) 16.3837 1.02801
\(255\) 3.19175 0.199875
\(256\) 1.00000 0.0625000
\(257\) 16.8740 1.05257 0.526287 0.850307i \(-0.323584\pi\)
0.526287 + 0.850307i \(0.323584\pi\)
\(258\) −15.8348 −0.985831
\(259\) 5.25484 0.326520
\(260\) −11.1747 −0.693026
\(261\) −17.6987 −1.09552
\(262\) 1.43967 0.0889429
\(263\) −7.34698 −0.453034 −0.226517 0.974007i \(-0.572734\pi\)
−0.226517 + 0.974007i \(0.572734\pi\)
\(264\) −0.982102 −0.0604442
\(265\) −0.00797666 −0.000490002 0
\(266\) −10.0076 −0.613603
\(267\) 6.76446 0.413978
\(268\) 5.65852 0.345649
\(269\) −10.0737 −0.614202 −0.307101 0.951677i \(-0.599359\pi\)
−0.307101 + 0.951677i \(0.599359\pi\)
\(270\) −4.44825 −0.270712
\(271\) −28.5181 −1.73235 −0.866175 0.499740i \(-0.833429\pi\)
−0.866175 + 0.499740i \(0.833429\pi\)
\(272\) −0.734051 −0.0445084
\(273\) 19.9152 1.20532
\(274\) −9.63273 −0.581935
\(275\) 0.528825 0.0318894
\(276\) −16.9365 −1.01946
\(277\) 13.4506 0.808166 0.404083 0.914722i \(-0.367591\pi\)
0.404083 + 0.914722i \(0.367591\pi\)
\(278\) 3.04315 0.182516
\(279\) −8.92396 −0.534263
\(280\) −3.03463 −0.181354
\(281\) 20.3270 1.21261 0.606305 0.795232i \(-0.292651\pi\)
0.606305 + 0.795232i \(0.292651\pi\)
\(282\) −22.6340 −1.34784
\(283\) −13.6527 −0.811568 −0.405784 0.913969i \(-0.633001\pi\)
−0.405784 + 0.913969i \(0.633001\pi\)
\(284\) −16.3890 −0.972511
\(285\) −27.9476 −1.65547
\(286\) −2.52401 −0.149248
\(287\) 16.3478 0.964981
\(288\) −1.97697 −0.116494
\(289\) −16.4612 −0.968304
\(290\) 17.4486 1.02462
\(291\) −37.4307 −2.19423
\(292\) 12.4924 0.731064
\(293\) −29.9923 −1.75217 −0.876084 0.482158i \(-0.839853\pi\)
−0.876084 + 0.482158i \(0.839853\pi\)
\(294\) −10.2082 −0.595352
\(295\) −18.7993 −1.09454
\(296\) −3.37500 −0.196168
\(297\) −1.00472 −0.0582996
\(298\) −5.79400 −0.335637
\(299\) −43.5270 −2.51723
\(300\) 2.67991 0.154725
\(301\) −11.0514 −0.636990
\(302\) 9.39394 0.540561
\(303\) −39.3741 −2.26199
\(304\) 6.42751 0.368643
\(305\) 6.60056 0.377947
\(306\) 1.45120 0.0829596
\(307\) −21.1556 −1.20741 −0.603707 0.797206i \(-0.706310\pi\)
−0.603707 + 0.797206i \(0.706310\pi\)
\(308\) −0.685425 −0.0390557
\(309\) 1.20532 0.0685683
\(310\) 8.79785 0.499684
\(311\) −10.5951 −0.600794 −0.300397 0.953814i \(-0.597119\pi\)
−0.300397 + 0.953814i \(0.597119\pi\)
\(312\) −12.7908 −0.724139
\(313\) 16.6891 0.943324 0.471662 0.881779i \(-0.343654\pi\)
0.471662 + 0.881779i \(0.343654\pi\)
\(314\) 0.880167 0.0496707
\(315\) 5.99938 0.338027
\(316\) −8.36805 −0.470739
\(317\) −21.1420 −1.18745 −0.593725 0.804668i \(-0.702343\pi\)
−0.593725 + 0.804668i \(0.702343\pi\)
\(318\) −0.00913028 −0.000512001 0
\(319\) 3.94108 0.220658
\(320\) 1.94904 0.108954
\(321\) 9.73387 0.543292
\(322\) −11.8203 −0.658719
\(323\) −4.71812 −0.262523
\(324\) −11.0225 −0.612361
\(325\) 6.88739 0.382044
\(326\) −22.9288 −1.26991
\(327\) 6.54148 0.361745
\(328\) −10.4996 −0.579745
\(329\) −15.7967 −0.870898
\(330\) −1.91415 −0.105371
\(331\) −33.7844 −1.85696 −0.928478 0.371388i \(-0.878882\pi\)
−0.928478 + 0.371388i \(0.878882\pi\)
\(332\) 8.50361 0.466696
\(333\) 6.67228 0.365639
\(334\) 3.44539 0.188524
\(335\) 11.0287 0.602560
\(336\) −3.47351 −0.189496
\(337\) −5.38261 −0.293210 −0.146605 0.989195i \(-0.546835\pi\)
−0.146605 + 0.989195i \(0.546835\pi\)
\(338\) −19.8725 −1.08092
\(339\) 10.0946 0.548263
\(340\) −1.43069 −0.0775901
\(341\) 1.98715 0.107610
\(342\) −12.7070 −0.687116
\(343\) −18.0234 −0.973171
\(344\) 7.09790 0.382693
\(345\) −33.0099 −1.77719
\(346\) −10.7624 −0.578589
\(347\) −1.75005 −0.0939474 −0.0469737 0.998896i \(-0.514958\pi\)
−0.0469737 + 0.998896i \(0.514958\pi\)
\(348\) 19.9721 1.07062
\(349\) 18.3326 0.981320 0.490660 0.871351i \(-0.336756\pi\)
0.490660 + 0.871351i \(0.336756\pi\)
\(350\) 1.87035 0.0999747
\(351\) −13.0854 −0.698446
\(352\) 0.440224 0.0234640
\(353\) 26.0465 1.38632 0.693159 0.720785i \(-0.256219\pi\)
0.693159 + 0.720785i \(0.256219\pi\)
\(354\) −21.5182 −1.14368
\(355\) −31.9428 −1.69535
\(356\) −3.03215 −0.160703
\(357\) 2.54973 0.134946
\(358\) −25.1072 −1.32696
\(359\) 0.941185 0.0496739 0.0248369 0.999692i \(-0.492093\pi\)
0.0248369 + 0.999692i \(0.492093\pi\)
\(360\) −3.85319 −0.203081
\(361\) 22.3128 1.17436
\(362\) 21.5432 1.13228
\(363\) 24.1077 1.26533
\(364\) −8.92694 −0.467899
\(365\) 24.3482 1.27444
\(366\) 7.55516 0.394915
\(367\) −23.6295 −1.23345 −0.616725 0.787178i \(-0.711541\pi\)
−0.616725 + 0.787178i \(0.711541\pi\)
\(368\) 7.59175 0.395747
\(369\) 20.7575 1.08059
\(370\) −6.57799 −0.341974
\(371\) −0.00637217 −0.000330827 0
\(372\) 10.0702 0.522117
\(373\) −5.77445 −0.298990 −0.149495 0.988762i \(-0.547765\pi\)
−0.149495 + 0.988762i \(0.547765\pi\)
\(374\) −0.323147 −0.0167095
\(375\) 26.9639 1.39241
\(376\) 10.1456 0.523221
\(377\) 51.3284 2.64355
\(378\) −3.55350 −0.182772
\(379\) 27.9068 1.43347 0.716737 0.697343i \(-0.245635\pi\)
0.716737 + 0.697343i \(0.245635\pi\)
\(380\) 12.5274 0.642644
\(381\) 36.5507 1.87255
\(382\) 17.7850 0.909961
\(383\) −17.7600 −0.907496 −0.453748 0.891130i \(-0.649913\pi\)
−0.453748 + 0.891130i \(0.649913\pi\)
\(384\) 2.23091 0.113846
\(385\) −1.33592 −0.0680847
\(386\) 20.1608 1.02616
\(387\) −14.0324 −0.713305
\(388\) 16.7782 0.851784
\(389\) 7.81152 0.396060 0.198030 0.980196i \(-0.436546\pi\)
0.198030 + 0.980196i \(0.436546\pi\)
\(390\) −24.9298 −1.26237
\(391\) −5.57273 −0.281825
\(392\) 4.57578 0.231112
\(393\) 3.21177 0.162012
\(394\) 2.10006 0.105799
\(395\) −16.3096 −0.820626
\(396\) −0.870312 −0.0437348
\(397\) −2.81916 −0.141490 −0.0707449 0.997494i \(-0.522538\pi\)
−0.0707449 + 0.997494i \(0.522538\pi\)
\(398\) −2.62596 −0.131627
\(399\) −22.3260 −1.11770
\(400\) −1.20126 −0.0600631
\(401\) −3.65545 −0.182545 −0.0912723 0.995826i \(-0.529093\pi\)
−0.0912723 + 0.995826i \(0.529093\pi\)
\(402\) 12.6237 0.629611
\(403\) 25.8805 1.28920
\(404\) 17.6493 0.878087
\(405\) −21.4832 −1.06751
\(406\) 13.9389 0.691774
\(407\) −1.48576 −0.0736462
\(408\) −1.63760 −0.0810735
\(409\) −23.6464 −1.16924 −0.584619 0.811308i \(-0.698756\pi\)
−0.584619 + 0.811308i \(0.698756\pi\)
\(410\) −20.4641 −1.01065
\(411\) −21.4898 −1.06001
\(412\) −0.540281 −0.0266178
\(413\) −15.0179 −0.738983
\(414\) −15.0087 −0.737637
\(415\) 16.5738 0.813577
\(416\) 5.73346 0.281106
\(417\) 6.78901 0.332459
\(418\) 2.82955 0.138398
\(419\) −20.9633 −1.02412 −0.512061 0.858949i \(-0.671118\pi\)
−0.512061 + 0.858949i \(0.671118\pi\)
\(420\) −6.77000 −0.330342
\(421\) 4.81889 0.234859 0.117429 0.993081i \(-0.462535\pi\)
0.117429 + 0.993081i \(0.462535\pi\)
\(422\) 3.83782 0.186822
\(423\) −20.0577 −0.975236
\(424\) 0.00409262 0.000198755 0
\(425\) 0.881788 0.0427730
\(426\) −36.5625 −1.77146
\(427\) 5.27287 0.255172
\(428\) −4.36318 −0.210902
\(429\) −5.63084 −0.271860
\(430\) 13.8341 0.667137
\(431\) −37.9963 −1.83022 −0.915109 0.403207i \(-0.867896\pi\)
−0.915109 + 0.403207i \(0.867896\pi\)
\(432\) 2.28228 0.109806
\(433\) −8.67778 −0.417027 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(434\) 7.02818 0.337363
\(435\) 38.9263 1.86637
\(436\) −2.93220 −0.140427
\(437\) 48.7960 2.33423
\(438\) 27.8695 1.33166
\(439\) −18.2631 −0.871651 −0.435826 0.900031i \(-0.643544\pi\)
−0.435826 + 0.900031i \(0.643544\pi\)
\(440\) 0.858013 0.0409042
\(441\) −9.04619 −0.430771
\(442\) −4.20865 −0.200185
\(443\) 23.0656 1.09588 0.547941 0.836517i \(-0.315412\pi\)
0.547941 + 0.836517i \(0.315412\pi\)
\(444\) −7.52933 −0.357326
\(445\) −5.90976 −0.280149
\(446\) 14.2152 0.673111
\(447\) −12.9259 −0.611374
\(448\) 1.55699 0.0735609
\(449\) 23.0115 1.08598 0.542990 0.839739i \(-0.317292\pi\)
0.542990 + 0.839739i \(0.317292\pi\)
\(450\) 2.37486 0.111952
\(451\) −4.62219 −0.217650
\(452\) −4.52487 −0.212832
\(453\) 20.9571 0.984649
\(454\) −7.70742 −0.361727
\(455\) −17.3989 −0.815674
\(456\) 14.3392 0.671495
\(457\) 11.0924 0.518879 0.259439 0.965759i \(-0.416462\pi\)
0.259439 + 0.965759i \(0.416462\pi\)
\(458\) 12.7734 0.596862
\(459\) −1.67531 −0.0781969
\(460\) 14.7966 0.689894
\(461\) −35.2780 −1.64306 −0.821530 0.570166i \(-0.806879\pi\)
−0.821530 + 0.570166i \(0.806879\pi\)
\(462\) −1.52912 −0.0711413
\(463\) −18.6447 −0.866491 −0.433245 0.901276i \(-0.642632\pi\)
−0.433245 + 0.901276i \(0.642632\pi\)
\(464\) −8.95243 −0.415606
\(465\) 19.6272 0.910191
\(466\) 7.97890 0.369616
\(467\) 19.8755 0.919731 0.459865 0.887989i \(-0.347898\pi\)
0.459865 + 0.887989i \(0.347898\pi\)
\(468\) −11.3349 −0.523956
\(469\) 8.81026 0.406820
\(470\) 19.7742 0.912116
\(471\) 1.96358 0.0904768
\(472\) 9.64546 0.443968
\(473\) 3.12467 0.143672
\(474\) −18.6684 −0.857467
\(475\) −7.72112 −0.354269
\(476\) −1.14291 −0.0523852
\(477\) −0.00809100 −0.000370462 0
\(478\) 8.65986 0.396093
\(479\) 33.1663 1.51541 0.757703 0.652599i \(-0.226321\pi\)
0.757703 + 0.652599i \(0.226321\pi\)
\(480\) 4.34813 0.198464
\(481\) −19.3504 −0.882303
\(482\) 13.0891 0.596193
\(483\) −26.3700 −1.19988
\(484\) −10.8062 −0.491191
\(485\) 32.7013 1.48489
\(486\) −17.7434 −0.804856
\(487\) 9.28333 0.420668 0.210334 0.977630i \(-0.432545\pi\)
0.210334 + 0.977630i \(0.432545\pi\)
\(488\) −3.38658 −0.153303
\(489\) −51.1521 −2.31318
\(490\) 8.91835 0.402890
\(491\) −6.84627 −0.308968 −0.154484 0.987995i \(-0.549372\pi\)
−0.154484 + 0.987995i \(0.549372\pi\)
\(492\) −23.4237 −1.05602
\(493\) 6.57154 0.295967
\(494\) 36.8518 1.65804
\(495\) −1.69627 −0.0762416
\(496\) −4.51395 −0.202682
\(497\) −25.5176 −1.14462
\(498\) 18.9708 0.850102
\(499\) 9.43753 0.422482 0.211241 0.977434i \(-0.432250\pi\)
0.211241 + 0.977434i \(0.432250\pi\)
\(500\) −12.0865 −0.540524
\(501\) 7.68638 0.343402
\(502\) 0.752494 0.0335854
\(503\) −17.3061 −0.771641 −0.385820 0.922574i \(-0.626082\pi\)
−0.385820 + 0.922574i \(0.626082\pi\)
\(504\) −3.07813 −0.137111
\(505\) 34.3992 1.53074
\(506\) 3.34207 0.148573
\(507\) −44.3339 −1.96894
\(508\) −16.3837 −0.726911
\(509\) −31.5887 −1.40015 −0.700073 0.714071i \(-0.746849\pi\)
−0.700073 + 0.714071i \(0.746849\pi\)
\(510\) −3.19175 −0.141333
\(511\) 19.4506 0.860444
\(512\) −1.00000 −0.0441942
\(513\) 14.6694 0.647670
\(514\) −16.8740 −0.744282
\(515\) −1.05303 −0.0464019
\(516\) 15.8348 0.697088
\(517\) 4.46636 0.196430
\(518\) −5.25484 −0.230885
\(519\) −24.0099 −1.05392
\(520\) 11.1747 0.490043
\(521\) 8.00837 0.350853 0.175427 0.984493i \(-0.443870\pi\)
0.175427 + 0.984493i \(0.443870\pi\)
\(522\) 17.6987 0.774652
\(523\) −38.2521 −1.67265 −0.836325 0.548235i \(-0.815300\pi\)
−0.836325 + 0.548235i \(0.815300\pi\)
\(524\) −1.43967 −0.0628921
\(525\) 4.17260 0.182107
\(526\) 7.34698 0.320344
\(527\) 3.31347 0.144337
\(528\) 0.982102 0.0427405
\(529\) 34.6346 1.50585
\(530\) 0.00797666 0.000346484 0
\(531\) −19.0688 −0.827517
\(532\) 10.0076 0.433883
\(533\) −60.1991 −2.60751
\(534\) −6.76446 −0.292727
\(535\) −8.50399 −0.367660
\(536\) −5.65852 −0.244411
\(537\) −56.0120 −2.41709
\(538\) 10.0737 0.434306
\(539\) 2.01437 0.0867651
\(540\) 4.44825 0.191422
\(541\) 5.77632 0.248343 0.124172 0.992261i \(-0.460373\pi\)
0.124172 + 0.992261i \(0.460373\pi\)
\(542\) 28.5181 1.22496
\(543\) 48.0609 2.06249
\(544\) 0.734051 0.0314722
\(545\) −5.71496 −0.244802
\(546\) −19.9152 −0.852293
\(547\) 21.4907 0.918878 0.459439 0.888209i \(-0.348051\pi\)
0.459439 + 0.888209i \(0.348051\pi\)
\(548\) 9.63273 0.411490
\(549\) 6.69517 0.285743
\(550\) −0.528825 −0.0225492
\(551\) −57.5418 −2.45136
\(552\) 16.9365 0.720867
\(553\) −13.0290 −0.554048
\(554\) −13.4506 −0.571460
\(555\) −14.6749 −0.622916
\(556\) −3.04315 −0.129059
\(557\) −2.53863 −0.107565 −0.0537827 0.998553i \(-0.517128\pi\)
−0.0537827 + 0.998553i \(0.517128\pi\)
\(558\) 8.92396 0.377781
\(559\) 40.6955 1.72124
\(560\) 3.03463 0.128237
\(561\) −0.720913 −0.0304370
\(562\) −20.3270 −0.857445
\(563\) −16.4735 −0.694274 −0.347137 0.937814i \(-0.612846\pi\)
−0.347137 + 0.937814i \(0.612846\pi\)
\(564\) 22.6340 0.953065
\(565\) −8.81913 −0.371023
\(566\) 13.6527 0.573865
\(567\) −17.1619 −0.720733
\(568\) 16.3890 0.687669
\(569\) 30.6335 1.28422 0.642112 0.766611i \(-0.278058\pi\)
0.642112 + 0.766611i \(0.278058\pi\)
\(570\) 27.9476 1.17060
\(571\) −7.84295 −0.328217 −0.164109 0.986442i \(-0.552475\pi\)
−0.164109 + 0.986442i \(0.552475\pi\)
\(572\) 2.52401 0.105534
\(573\) 39.6769 1.65752
\(574\) −16.3478 −0.682345
\(575\) −9.11968 −0.380317
\(576\) 1.97697 0.0823739
\(577\) −22.6644 −0.943532 −0.471766 0.881724i \(-0.656383\pi\)
−0.471766 + 0.881724i \(0.656383\pi\)
\(578\) 16.4612 0.684694
\(579\) 44.9770 1.86918
\(580\) −17.4486 −0.724514
\(581\) 13.2400 0.549289
\(582\) 37.4307 1.55155
\(583\) 0.00180167 7.46176e−5 0
\(584\) −12.4924 −0.516941
\(585\) −22.0921 −0.913396
\(586\) 29.9923 1.23897
\(587\) 26.0059 1.07338 0.536690 0.843780i \(-0.319675\pi\)
0.536690 + 0.843780i \(0.319675\pi\)
\(588\) 10.2082 0.420978
\(589\) −29.0134 −1.19548
\(590\) 18.7993 0.773957
\(591\) 4.68504 0.192717
\(592\) 3.37500 0.138712
\(593\) −15.6415 −0.642321 −0.321160 0.947025i \(-0.604073\pi\)
−0.321160 + 0.947025i \(0.604073\pi\)
\(594\) 1.00472 0.0412240
\(595\) −2.22757 −0.0913216
\(596\) 5.79400 0.237331
\(597\) −5.85829 −0.239764
\(598\) 43.5270 1.77995
\(599\) 40.7617 1.66548 0.832739 0.553665i \(-0.186771\pi\)
0.832739 + 0.553665i \(0.186771\pi\)
\(600\) −2.67991 −0.109407
\(601\) −19.6906 −0.803197 −0.401598 0.915816i \(-0.631545\pi\)
−0.401598 + 0.915816i \(0.631545\pi\)
\(602\) 11.0514 0.450420
\(603\) 11.1867 0.455559
\(604\) −9.39394 −0.382234
\(605\) −21.0617 −0.856279
\(606\) 39.3741 1.59947
\(607\) 12.1307 0.492371 0.246185 0.969223i \(-0.420823\pi\)
0.246185 + 0.969223i \(0.420823\pi\)
\(608\) −6.42751 −0.260670
\(609\) 31.0964 1.26009
\(610\) −6.60056 −0.267249
\(611\) 58.1696 2.35329
\(612\) −1.45120 −0.0586613
\(613\) −19.5832 −0.790958 −0.395479 0.918475i \(-0.629421\pi\)
−0.395479 + 0.918475i \(0.629421\pi\)
\(614\) 21.1556 0.853770
\(615\) −45.6537 −1.84094
\(616\) 0.685425 0.0276166
\(617\) −47.2394 −1.90179 −0.950893 0.309519i \(-0.899832\pi\)
−0.950893 + 0.309519i \(0.899832\pi\)
\(618\) −1.20532 −0.0484851
\(619\) 41.9874 1.68762 0.843809 0.536644i \(-0.180308\pi\)
0.843809 + 0.536644i \(0.180308\pi\)
\(620\) −8.79785 −0.353330
\(621\) 17.3265 0.695290
\(622\) 10.5951 0.424825
\(623\) −4.72102 −0.189144
\(624\) 12.7908 0.512044
\(625\) −17.5507 −0.702026
\(626\) −16.6891 −0.667031
\(627\) 6.31247 0.252096
\(628\) −0.880167 −0.0351225
\(629\) −2.47742 −0.0987813
\(630\) −5.99938 −0.239021
\(631\) −23.8201 −0.948265 −0.474132 0.880454i \(-0.657238\pi\)
−0.474132 + 0.880454i \(0.657238\pi\)
\(632\) 8.36805 0.332863
\(633\) 8.56184 0.340302
\(634\) 21.1420 0.839654
\(635\) −31.9325 −1.26720
\(636\) 0.00913028 0.000362039 0
\(637\) 26.2350 1.03947
\(638\) −3.94108 −0.156029
\(639\) −32.4007 −1.28175
\(640\) −1.94904 −0.0770424
\(641\) −32.3939 −1.27948 −0.639742 0.768590i \(-0.720959\pi\)
−0.639742 + 0.768590i \(0.720959\pi\)
\(642\) −9.73387 −0.384165
\(643\) −7.72057 −0.304470 −0.152235 0.988344i \(-0.548647\pi\)
−0.152235 + 0.988344i \(0.548647\pi\)
\(644\) 11.8203 0.465784
\(645\) 30.8626 1.21521
\(646\) 4.71812 0.185632
\(647\) −46.7724 −1.83881 −0.919406 0.393309i \(-0.871330\pi\)
−0.919406 + 0.393309i \(0.871330\pi\)
\(648\) 11.0225 0.433005
\(649\) 4.24617 0.166677
\(650\) −6.88739 −0.270146
\(651\) 15.6793 0.614519
\(652\) 22.9288 0.897960
\(653\) 35.5160 1.38985 0.694924 0.719083i \(-0.255438\pi\)
0.694924 + 0.719083i \(0.255438\pi\)
\(654\) −6.54148 −0.255792
\(655\) −2.80596 −0.109638
\(656\) 10.4996 0.409941
\(657\) 24.6972 0.963530
\(658\) 15.7967 0.615818
\(659\) −12.7899 −0.498224 −0.249112 0.968475i \(-0.580139\pi\)
−0.249112 + 0.968475i \(0.580139\pi\)
\(660\) 1.91415 0.0745083
\(661\) −44.0998 −1.71529 −0.857643 0.514246i \(-0.828072\pi\)
−0.857643 + 0.514246i \(0.828072\pi\)
\(662\) 33.7844 1.31307
\(663\) −9.38913 −0.364644
\(664\) −8.50361 −0.330004
\(665\) 19.5051 0.756375
\(666\) −6.67228 −0.258546
\(667\) −67.9646 −2.63160
\(668\) −3.44539 −0.133306
\(669\) 31.7129 1.22609
\(670\) −11.0287 −0.426074
\(671\) −1.49085 −0.0575538
\(672\) 3.47351 0.133994
\(673\) 21.5334 0.830050 0.415025 0.909810i \(-0.363773\pi\)
0.415025 + 0.909810i \(0.363773\pi\)
\(674\) 5.38261 0.207330
\(675\) −2.74162 −0.105525
\(676\) 19.8725 0.764328
\(677\) 12.2531 0.470924 0.235462 0.971884i \(-0.424340\pi\)
0.235462 + 0.971884i \(0.424340\pi\)
\(678\) −10.0946 −0.387680
\(679\) 26.1235 1.00253
\(680\) 1.43069 0.0548645
\(681\) −17.1946 −0.658897
\(682\) −1.98715 −0.0760920
\(683\) 34.1387 1.30628 0.653141 0.757237i \(-0.273451\pi\)
0.653141 + 0.757237i \(0.273451\pi\)
\(684\) 12.7070 0.485865
\(685\) 18.7745 0.717338
\(686\) 18.0234 0.688136
\(687\) 28.4964 1.08720
\(688\) −7.09790 −0.270605
\(689\) 0.0234649 0.000893940 0
\(690\) 33.0099 1.25667
\(691\) 29.0781 1.10618 0.553091 0.833121i \(-0.313448\pi\)
0.553091 + 0.833121i \(0.313448\pi\)
\(692\) 10.7624 0.409125
\(693\) −1.35507 −0.0514748
\(694\) 1.75005 0.0664309
\(695\) −5.93122 −0.224984
\(696\) −19.9721 −0.757040
\(697\) −7.70726 −0.291933
\(698\) −18.3326 −0.693898
\(699\) 17.8002 0.673267
\(700\) −1.87035 −0.0706928
\(701\) −28.4110 −1.07307 −0.536533 0.843879i \(-0.680266\pi\)
−0.536533 + 0.843879i \(0.680266\pi\)
\(702\) 13.0854 0.493876
\(703\) 21.6928 0.818161
\(704\) −0.440224 −0.0165916
\(705\) 44.1145 1.66145
\(706\) −26.0465 −0.980274
\(707\) 27.4799 1.03349
\(708\) 21.5182 0.808703
\(709\) 13.0845 0.491400 0.245700 0.969346i \(-0.420982\pi\)
0.245700 + 0.969346i \(0.420982\pi\)
\(710\) 31.9428 1.19879
\(711\) −16.5434 −0.620426
\(712\) 3.03215 0.113635
\(713\) −34.2688 −1.28338
\(714\) −2.54973 −0.0954214
\(715\) 4.91938 0.183974
\(716\) 25.1072 0.938300
\(717\) 19.3194 0.721496
\(718\) −0.941185 −0.0351247
\(719\) −8.91601 −0.332511 −0.166256 0.986083i \(-0.553168\pi\)
−0.166256 + 0.986083i \(0.553168\pi\)
\(720\) 3.85319 0.143600
\(721\) −0.841213 −0.0313284
\(722\) −22.3128 −0.830398
\(723\) 29.2007 1.08598
\(724\) −21.5432 −0.800645
\(725\) 10.7542 0.399402
\(726\) −24.1077 −0.894721
\(727\) −19.8521 −0.736274 −0.368137 0.929771i \(-0.620004\pi\)
−0.368137 + 0.929771i \(0.620004\pi\)
\(728\) 8.92694 0.330854
\(729\) −6.51645 −0.241350
\(730\) −24.3482 −0.901167
\(731\) 5.21022 0.192707
\(732\) −7.55516 −0.279247
\(733\) −16.3650 −0.604454 −0.302227 0.953236i \(-0.597730\pi\)
−0.302227 + 0.953236i \(0.597730\pi\)
\(734\) 23.6295 0.872181
\(735\) 19.8961 0.733878
\(736\) −7.59175 −0.279836
\(737\) −2.49102 −0.0917578
\(738\) −20.7575 −0.764093
\(739\) 7.64397 0.281188 0.140594 0.990067i \(-0.455099\pi\)
0.140594 + 0.990067i \(0.455099\pi\)
\(740\) 6.57799 0.241812
\(741\) 82.2132 3.02018
\(742\) 0.00637217 0.000233930 0
\(743\) 43.7311 1.60434 0.802169 0.597097i \(-0.203679\pi\)
0.802169 + 0.597097i \(0.203679\pi\)
\(744\) −10.0702 −0.369193
\(745\) 11.2927 0.413733
\(746\) 5.77445 0.211418
\(747\) 16.8114 0.615097
\(748\) 0.323147 0.0118154
\(749\) −6.79343 −0.248227
\(750\) −26.9639 −0.984582
\(751\) 19.5508 0.713418 0.356709 0.934216i \(-0.383899\pi\)
0.356709 + 0.934216i \(0.383899\pi\)
\(752\) −10.1456 −0.369973
\(753\) 1.67875 0.0611770
\(754\) −51.3284 −1.86927
\(755\) −18.3091 −0.666337
\(756\) 3.55350 0.129239
\(757\) −43.6472 −1.58638 −0.793192 0.608972i \(-0.791582\pi\)
−0.793192 + 0.608972i \(0.791582\pi\)
\(758\) −27.9068 −1.01362
\(759\) 7.45587 0.270631
\(760\) −12.5274 −0.454418
\(761\) −15.4617 −0.560487 −0.280243 0.959929i \(-0.590415\pi\)
−0.280243 + 0.959929i \(0.590415\pi\)
\(762\) −36.5507 −1.32409
\(763\) −4.56541 −0.165279
\(764\) −17.7850 −0.643440
\(765\) −2.82844 −0.102262
\(766\) 17.7600 0.641696
\(767\) 55.3019 1.99683
\(768\) −2.23091 −0.0805011
\(769\) −29.3228 −1.05741 −0.528704 0.848806i \(-0.677322\pi\)
−0.528704 + 0.848806i \(0.677322\pi\)
\(770\) 1.33592 0.0481431
\(771\) −37.6445 −1.35573
\(772\) −20.1608 −0.725603
\(773\) 53.2951 1.91689 0.958446 0.285275i \(-0.0920848\pi\)
0.958446 + 0.285275i \(0.0920848\pi\)
\(774\) 14.0324 0.504383
\(775\) 5.42244 0.194780
\(776\) −16.7782 −0.602302
\(777\) −11.7231 −0.420564
\(778\) −7.81152 −0.280057
\(779\) 67.4864 2.41795
\(780\) 24.9298 0.892630
\(781\) 7.21486 0.258168
\(782\) 5.57273 0.199280
\(783\) −20.4320 −0.730180
\(784\) −4.57578 −0.163421
\(785\) −1.71548 −0.0612280
\(786\) −3.21177 −0.114560
\(787\) −32.5507 −1.16031 −0.580153 0.814507i \(-0.697007\pi\)
−0.580153 + 0.814507i \(0.697007\pi\)
\(788\) −2.10006 −0.0748114
\(789\) 16.3905 0.583517
\(790\) 16.3096 0.580270
\(791\) −7.04518 −0.250498
\(792\) 0.870312 0.0309252
\(793\) −19.4168 −0.689511
\(794\) 2.81916 0.100048
\(795\) 0.0177952 0.000631132 0
\(796\) 2.62596 0.0930747
\(797\) −30.4445 −1.07840 −0.539200 0.842178i \(-0.681273\pi\)
−0.539200 + 0.842178i \(0.681273\pi\)
\(798\) 22.3260 0.790332
\(799\) 7.44742 0.263471
\(800\) 1.20126 0.0424710
\(801\) −5.99447 −0.211804
\(802\) 3.65545 0.129079
\(803\) −5.49947 −0.194072
\(804\) −12.6237 −0.445202
\(805\) 23.0381 0.811988
\(806\) −25.8805 −0.911603
\(807\) 22.4735 0.791103
\(808\) −17.6493 −0.620902
\(809\) −15.4266 −0.542371 −0.271186 0.962527i \(-0.587416\pi\)
−0.271186 + 0.962527i \(0.587416\pi\)
\(810\) 21.4832 0.754844
\(811\) −10.0002 −0.351154 −0.175577 0.984466i \(-0.556179\pi\)
−0.175577 + 0.984466i \(0.556179\pi\)
\(812\) −13.9389 −0.489158
\(813\) 63.6214 2.23130
\(814\) 1.48576 0.0520758
\(815\) 44.6890 1.56539
\(816\) 1.63760 0.0573276
\(817\) −45.6218 −1.59610
\(818\) 23.6464 0.826775
\(819\) −17.6483 −0.616682
\(820\) 20.4641 0.714639
\(821\) 5.43781 0.189781 0.0948904 0.995488i \(-0.469750\pi\)
0.0948904 + 0.995488i \(0.469750\pi\)
\(822\) 21.4898 0.749542
\(823\) −28.8032 −1.00402 −0.502008 0.864863i \(-0.667405\pi\)
−0.502008 + 0.864863i \(0.667405\pi\)
\(824\) 0.540281 0.0188216
\(825\) −1.17976 −0.0410741
\(826\) 15.0179 0.522540
\(827\) 26.4130 0.918468 0.459234 0.888315i \(-0.348124\pi\)
0.459234 + 0.888315i \(0.348124\pi\)
\(828\) 15.0087 0.521588
\(829\) −12.4596 −0.432738 −0.216369 0.976312i \(-0.569421\pi\)
−0.216369 + 0.976312i \(0.569421\pi\)
\(830\) −16.5738 −0.575286
\(831\) −30.0071 −1.04093
\(832\) −5.73346 −0.198772
\(833\) 3.35886 0.116377
\(834\) −6.78901 −0.235084
\(835\) −6.71519 −0.232389
\(836\) −2.82955 −0.0978619
\(837\) −10.3021 −0.356093
\(838\) 20.9633 0.724164
\(839\) 45.5511 1.57260 0.786299 0.617846i \(-0.211995\pi\)
0.786299 + 0.617846i \(0.211995\pi\)
\(840\) 6.77000 0.233587
\(841\) 51.1460 1.76366
\(842\) −4.81889 −0.166070
\(843\) −45.3479 −1.56186
\(844\) −3.83782 −0.132103
\(845\) 38.7323 1.33243
\(846\) 20.0577 0.689596
\(847\) −16.8252 −0.578119
\(848\) −0.00409262 −0.000140541 0
\(849\) 30.4579 1.04531
\(850\) −0.881788 −0.0302451
\(851\) 25.6221 0.878316
\(852\) 36.5625 1.25261
\(853\) 24.1539 0.827014 0.413507 0.910501i \(-0.364304\pi\)
0.413507 + 0.910501i \(0.364304\pi\)
\(854\) −5.27287 −0.180434
\(855\) 24.7664 0.846993
\(856\) 4.36318 0.149130
\(857\) 15.6571 0.534836 0.267418 0.963581i \(-0.413830\pi\)
0.267418 + 0.963581i \(0.413830\pi\)
\(858\) 5.63084 0.192234
\(859\) −36.3757 −1.24112 −0.620562 0.784158i \(-0.713095\pi\)
−0.620562 + 0.784158i \(0.713095\pi\)
\(860\) −13.8341 −0.471737
\(861\) −36.4706 −1.24291
\(862\) 37.9963 1.29416
\(863\) 27.9874 0.952703 0.476352 0.879255i \(-0.341959\pi\)
0.476352 + 0.879255i \(0.341959\pi\)
\(864\) −2.28228 −0.0776449
\(865\) 20.9763 0.713214
\(866\) 8.67778 0.294883
\(867\) 36.7234 1.24719
\(868\) −7.02818 −0.238552
\(869\) 3.68382 0.124965
\(870\) −38.9263 −1.31973
\(871\) −32.4429 −1.09928
\(872\) 2.93220 0.0992968
\(873\) 33.1700 1.12264
\(874\) −48.7960 −1.65055
\(875\) −18.8185 −0.636183
\(876\) −27.8695 −0.941624
\(877\) −0.0316773 −0.00106967 −0.000534834 1.00000i \(-0.500170\pi\)
−0.000534834 1.00000i \(0.500170\pi\)
\(878\) 18.2631 0.616350
\(879\) 66.9102 2.25682
\(880\) −0.858013 −0.0289236
\(881\) 29.5166 0.994440 0.497220 0.867625i \(-0.334354\pi\)
0.497220 + 0.867625i \(0.334354\pi\)
\(882\) 9.04619 0.304601
\(883\) −21.2466 −0.715004 −0.357502 0.933912i \(-0.616372\pi\)
−0.357502 + 0.933912i \(0.616372\pi\)
\(884\) 4.20865 0.141552
\(885\) 41.9397 1.40979
\(886\) −23.0656 −0.774906
\(887\) 55.9524 1.87870 0.939349 0.342963i \(-0.111431\pi\)
0.939349 + 0.342963i \(0.111431\pi\)
\(888\) 7.52933 0.252668
\(889\) −25.5093 −0.855556
\(890\) 5.90976 0.198096
\(891\) 4.85237 0.162561
\(892\) −14.2152 −0.475961
\(893\) −65.2111 −2.18221
\(894\) 12.9259 0.432307
\(895\) 48.9348 1.63571
\(896\) −1.55699 −0.0520154
\(897\) 97.1049 3.24224
\(898\) −23.0115 −0.767904
\(899\) 40.4108 1.34778
\(900\) −2.37486 −0.0791621
\(901\) 0.00300419 0.000100084 0
\(902\) 4.62219 0.153902
\(903\) 24.6546 0.820455
\(904\) 4.52487 0.150495
\(905\) −41.9884 −1.39574
\(906\) −20.9571 −0.696252
\(907\) −16.7072 −0.554754 −0.277377 0.960761i \(-0.589465\pi\)
−0.277377 + 0.960761i \(0.589465\pi\)
\(908\) 7.70742 0.255780
\(909\) 34.8923 1.15730
\(910\) 17.3989 0.576769
\(911\) −5.37099 −0.177949 −0.0889745 0.996034i \(-0.528359\pi\)
−0.0889745 + 0.996034i \(0.528359\pi\)
\(912\) −14.3392 −0.474819
\(913\) −3.74349 −0.123892
\(914\) −11.0924 −0.366903
\(915\) −14.7253 −0.486803
\(916\) −12.7734 −0.422045
\(917\) −2.24155 −0.0740224
\(918\) 1.67531 0.0552936
\(919\) −42.9358 −1.41632 −0.708161 0.706051i \(-0.750475\pi\)
−0.708161 + 0.706051i \(0.750475\pi\)
\(920\) −14.7966 −0.487829
\(921\) 47.1963 1.55517
\(922\) 35.2780 1.16182
\(923\) 93.9659 3.09292
\(924\) 1.52912 0.0503045
\(925\) −4.05426 −0.133303
\(926\) 18.6447 0.612701
\(927\) −1.06812 −0.0350817
\(928\) 8.95243 0.293878
\(929\) 9.93544 0.325971 0.162986 0.986628i \(-0.447888\pi\)
0.162986 + 0.986628i \(0.447888\pi\)
\(930\) −19.6272 −0.643602
\(931\) −29.4108 −0.963902
\(932\) −7.97890 −0.261358
\(933\) 23.6368 0.773833
\(934\) −19.8755 −0.650348
\(935\) 0.629825 0.0205975
\(936\) 11.3349 0.370493
\(937\) −4.70578 −0.153731 −0.0768655 0.997041i \(-0.524491\pi\)
−0.0768655 + 0.997041i \(0.524491\pi\)
\(938\) −8.81026 −0.287665
\(939\) −37.2319 −1.21502
\(940\) −19.7742 −0.644963
\(941\) 25.6757 0.837005 0.418503 0.908216i \(-0.362555\pi\)
0.418503 + 0.908216i \(0.362555\pi\)
\(942\) −1.96358 −0.0639768
\(943\) 79.7105 2.59573
\(944\) −9.64546 −0.313933
\(945\) 6.92589 0.225299
\(946\) −3.12467 −0.101592
\(947\) −11.2389 −0.365215 −0.182607 0.983186i \(-0.558454\pi\)
−0.182607 + 0.983186i \(0.558454\pi\)
\(948\) 18.6684 0.606321
\(949\) −71.6248 −2.32504
\(950\) 7.72112 0.250506
\(951\) 47.1659 1.52946
\(952\) 1.14291 0.0370420
\(953\) 36.7864 1.19163 0.595814 0.803123i \(-0.296830\pi\)
0.595814 + 0.803123i \(0.296830\pi\)
\(954\) 0.00809100 0.000261956 0
\(955\) −34.6636 −1.12169
\(956\) −8.65986 −0.280080
\(957\) −8.79221 −0.284212
\(958\) −33.1663 −1.07155
\(959\) 14.9981 0.484313
\(960\) −4.34813 −0.140335
\(961\) −10.6242 −0.342718
\(962\) 19.3504 0.623882
\(963\) −8.62589 −0.277965
\(964\) −13.0891 −0.421572
\(965\) −39.2941 −1.26492
\(966\) 26.3700 0.848442
\(967\) −36.4809 −1.17315 −0.586574 0.809896i \(-0.699524\pi\)
−0.586574 + 0.809896i \(0.699524\pi\)
\(968\) 10.8062 0.347325
\(969\) 10.5257 0.338135
\(970\) −32.7013 −1.04997
\(971\) −53.8830 −1.72919 −0.864594 0.502471i \(-0.832424\pi\)
−0.864594 + 0.502471i \(0.832424\pi\)
\(972\) 17.7434 0.569119
\(973\) −4.73816 −0.151899
\(974\) −9.28333 −0.297457
\(975\) −15.3652 −0.492079
\(976\) 3.38658 0.108402
\(977\) 7.10952 0.227454 0.113727 0.993512i \(-0.463721\pi\)
0.113727 + 0.993512i \(0.463721\pi\)
\(978\) 51.1521 1.63566
\(979\) 1.33483 0.0426612
\(980\) −8.91835 −0.284886
\(981\) −5.79688 −0.185080
\(982\) 6.84627 0.218473
\(983\) −41.6492 −1.32840 −0.664202 0.747553i \(-0.731228\pi\)
−0.664202 + 0.747553i \(0.731228\pi\)
\(984\) 23.4237 0.746722
\(985\) −4.09308 −0.130417
\(986\) −6.57154 −0.209281
\(987\) 35.2410 1.12173
\(988\) −36.8518 −1.17241
\(989\) −53.8855 −1.71346
\(990\) 1.69627 0.0539109
\(991\) −21.4172 −0.680339 −0.340169 0.940364i \(-0.610484\pi\)
−0.340169 + 0.940364i \(0.610484\pi\)
\(992\) 4.51395 0.143318
\(993\) 75.3700 2.39179
\(994\) 25.5176 0.809369
\(995\) 5.11809 0.162254
\(996\) −18.9708 −0.601113
\(997\) 14.7933 0.468510 0.234255 0.972175i \(-0.424735\pi\)
0.234255 + 0.972175i \(0.424735\pi\)
\(998\) −9.43753 −0.298740
\(999\) 7.70271 0.243703
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 4034.2.a.b.1.6 35
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.b.1.6 35 1.1 even 1 trivial