Properties

Label 4034.2.a.c.1.12
Level $4034$
Weight $2$
Character 4034.1
Self dual yes
Analytic conductor $32.212$
Analytic rank $0$
Dimension $49$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(0\)
Dimension: \(49\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.80649 q^{3} +1.00000 q^{4} +0.991336 q^{5} +1.80649 q^{6} +3.46798 q^{7} -1.00000 q^{8} +0.263400 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.80649 q^{3} +1.00000 q^{4} +0.991336 q^{5} +1.80649 q^{6} +3.46798 q^{7} -1.00000 q^{8} +0.263400 q^{9} -0.991336 q^{10} -4.83823 q^{11} -1.80649 q^{12} +4.44127 q^{13} -3.46798 q^{14} -1.79084 q^{15} +1.00000 q^{16} +4.57513 q^{17} -0.263400 q^{18} +5.87465 q^{19} +0.991336 q^{20} -6.26487 q^{21} +4.83823 q^{22} +0.390058 q^{23} +1.80649 q^{24} -4.01725 q^{25} -4.44127 q^{26} +4.94364 q^{27} +3.46798 q^{28} -5.36675 q^{29} +1.79084 q^{30} -3.85804 q^{31} -1.00000 q^{32} +8.74020 q^{33} -4.57513 q^{34} +3.43794 q^{35} +0.263400 q^{36} +1.64933 q^{37} -5.87465 q^{38} -8.02311 q^{39} -0.991336 q^{40} +0.615159 q^{41} +6.26487 q^{42} +3.89233 q^{43} -4.83823 q^{44} +0.261118 q^{45} -0.390058 q^{46} +9.56451 q^{47} -1.80649 q^{48} +5.02690 q^{49} +4.01725 q^{50} -8.26492 q^{51} +4.44127 q^{52} +5.41601 q^{53} -4.94364 q^{54} -4.79631 q^{55} -3.46798 q^{56} -10.6125 q^{57} +5.36675 q^{58} +2.15882 q^{59} -1.79084 q^{60} -0.659535 q^{61} +3.85804 q^{62} +0.913467 q^{63} +1.00000 q^{64} +4.40280 q^{65} -8.74020 q^{66} -3.75828 q^{67} +4.57513 q^{68} -0.704636 q^{69} -3.43794 q^{70} +7.60582 q^{71} -0.263400 q^{72} +7.96823 q^{73} -1.64933 q^{74} +7.25712 q^{75} +5.87465 q^{76} -16.7789 q^{77} +8.02311 q^{78} +7.32579 q^{79} +0.991336 q^{80} -9.72082 q^{81} -0.615159 q^{82} -4.60880 q^{83} -6.26487 q^{84} +4.53549 q^{85} -3.89233 q^{86} +9.69496 q^{87} +4.83823 q^{88} -17.5829 q^{89} -0.261118 q^{90} +15.4023 q^{91} +0.390058 q^{92} +6.96950 q^{93} -9.56451 q^{94} +5.82376 q^{95} +1.80649 q^{96} -0.900577 q^{97} -5.02690 q^{98} -1.27439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 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
\(3\) −1.80649 −1.04298 −0.521488 0.853258i \(-0.674623\pi\)
−0.521488 + 0.853258i \(0.674623\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.991336 0.443339 0.221670 0.975122i \(-0.428849\pi\)
0.221670 + 0.975122i \(0.428849\pi\)
\(6\) 1.80649 0.737496
\(7\) 3.46798 1.31077 0.655387 0.755293i \(-0.272506\pi\)
0.655387 + 0.755293i \(0.272506\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.263400 0.0878000
\(10\) −0.991336 −0.313488
\(11\) −4.83823 −1.45878 −0.729390 0.684098i \(-0.760196\pi\)
−0.729390 + 0.684098i \(0.760196\pi\)
\(12\) −1.80649 −0.521488
\(13\) 4.44127 1.23179 0.615894 0.787829i \(-0.288795\pi\)
0.615894 + 0.787829i \(0.288795\pi\)
\(14\) −3.46798 −0.926857
\(15\) −1.79084 −0.462392
\(16\) 1.00000 0.250000
\(17\) 4.57513 1.10963 0.554816 0.831973i \(-0.312789\pi\)
0.554816 + 0.831973i \(0.312789\pi\)
\(18\) −0.263400 −0.0620840
\(19\) 5.87465 1.34774 0.673869 0.738851i \(-0.264631\pi\)
0.673869 + 0.738851i \(0.264631\pi\)
\(20\) 0.991336 0.221670
\(21\) −6.26487 −1.36711
\(22\) 4.83823 1.03151
\(23\) 0.390058 0.0813328 0.0406664 0.999173i \(-0.487052\pi\)
0.0406664 + 0.999173i \(0.487052\pi\)
\(24\) 1.80649 0.368748
\(25\) −4.01725 −0.803450
\(26\) −4.44127 −0.871005
\(27\) 4.94364 0.951403
\(28\) 3.46798 0.655387
\(29\) −5.36675 −0.996580 −0.498290 0.867011i \(-0.666038\pi\)
−0.498290 + 0.867011i \(0.666038\pi\)
\(30\) 1.79084 0.326961
\(31\) −3.85804 −0.692924 −0.346462 0.938064i \(-0.612617\pi\)
−0.346462 + 0.938064i \(0.612617\pi\)
\(32\) −1.00000 −0.176777
\(33\) 8.74020 1.52147
\(34\) −4.57513 −0.784628
\(35\) 3.43794 0.581117
\(36\) 0.263400 0.0439000
\(37\) 1.64933 0.271149 0.135574 0.990767i \(-0.456712\pi\)
0.135574 + 0.990767i \(0.456712\pi\)
\(38\) −5.87465 −0.952995
\(39\) −8.02311 −1.28473
\(40\) −0.991336 −0.156744
\(41\) 0.615159 0.0960717 0.0480359 0.998846i \(-0.484704\pi\)
0.0480359 + 0.998846i \(0.484704\pi\)
\(42\) 6.26487 0.966690
\(43\) 3.89233 0.593575 0.296787 0.954944i \(-0.404085\pi\)
0.296787 + 0.954944i \(0.404085\pi\)
\(44\) −4.83823 −0.729390
\(45\) 0.261118 0.0389252
\(46\) −0.390058 −0.0575110
\(47\) 9.56451 1.39513 0.697564 0.716523i \(-0.254268\pi\)
0.697564 + 0.716523i \(0.254268\pi\)
\(48\) −1.80649 −0.260744
\(49\) 5.02690 0.718128
\(50\) 4.01725 0.568125
\(51\) −8.26492 −1.15732
\(52\) 4.44127 0.615894
\(53\) 5.41601 0.743947 0.371973 0.928243i \(-0.378681\pi\)
0.371973 + 0.928243i \(0.378681\pi\)
\(54\) −4.94364 −0.672744
\(55\) −4.79631 −0.646735
\(56\) −3.46798 −0.463429
\(57\) −10.6125 −1.40566
\(58\) 5.36675 0.704688
\(59\) 2.15882 0.281055 0.140527 0.990077i \(-0.455120\pi\)
0.140527 + 0.990077i \(0.455120\pi\)
\(60\) −1.79084 −0.231196
\(61\) −0.659535 −0.0844448 −0.0422224 0.999108i \(-0.513444\pi\)
−0.0422224 + 0.999108i \(0.513444\pi\)
\(62\) 3.85804 0.489972
\(63\) 0.913467 0.115086
\(64\) 1.00000 0.125000
\(65\) 4.40280 0.546100
\(66\) −8.74020 −1.07584
\(67\) −3.75828 −0.459147 −0.229574 0.973291i \(-0.573733\pi\)
−0.229574 + 0.973291i \(0.573733\pi\)
\(68\) 4.57513 0.554816
\(69\) −0.704636 −0.0848282
\(70\) −3.43794 −0.410912
\(71\) 7.60582 0.902644 0.451322 0.892361i \(-0.350953\pi\)
0.451322 + 0.892361i \(0.350953\pi\)
\(72\) −0.263400 −0.0310420
\(73\) 7.96823 0.932610 0.466305 0.884624i \(-0.345585\pi\)
0.466305 + 0.884624i \(0.345585\pi\)
\(74\) −1.64933 −0.191731
\(75\) 7.25712 0.837980
\(76\) 5.87465 0.673869
\(77\) −16.7789 −1.91213
\(78\) 8.02311 0.908438
\(79\) 7.32579 0.824216 0.412108 0.911135i \(-0.364793\pi\)
0.412108 + 0.911135i \(0.364793\pi\)
\(80\) 0.991336 0.110835
\(81\) −9.72082 −1.08009
\(82\) −0.615159 −0.0679330
\(83\) −4.60880 −0.505881 −0.252941 0.967482i \(-0.581398\pi\)
−0.252941 + 0.967482i \(0.581398\pi\)
\(84\) −6.26487 −0.683553
\(85\) 4.53549 0.491943
\(86\) −3.89233 −0.419721
\(87\) 9.69496 1.03941
\(88\) 4.83823 0.515757
\(89\) −17.5829 −1.86378 −0.931892 0.362736i \(-0.881843\pi\)
−0.931892 + 0.362736i \(0.881843\pi\)
\(90\) −0.261118 −0.0275243
\(91\) 15.4023 1.61459
\(92\) 0.390058 0.0406664
\(93\) 6.96950 0.722704
\(94\) −9.56451 −0.986504
\(95\) 5.82376 0.597505
\(96\) 1.80649 0.184374
\(97\) −0.900577 −0.0914397 −0.0457199 0.998954i \(-0.514558\pi\)
−0.0457199 + 0.998954i \(0.514558\pi\)
\(98\) −5.02690 −0.507793
\(99\) −1.27439 −0.128081
\(100\) −4.01725 −0.401725
\(101\) −12.6829 −1.26200 −0.630999 0.775784i \(-0.717355\pi\)
−0.630999 + 0.775784i \(0.717355\pi\)
\(102\) 8.26492 0.818349
\(103\) 5.27874 0.520130 0.260065 0.965591i \(-0.416256\pi\)
0.260065 + 0.965591i \(0.416256\pi\)
\(104\) −4.44127 −0.435503
\(105\) −6.21059 −0.606092
\(106\) −5.41601 −0.526050
\(107\) 3.15234 0.304748 0.152374 0.988323i \(-0.451308\pi\)
0.152374 + 0.988323i \(0.451308\pi\)
\(108\) 4.94364 0.475702
\(109\) 2.14772 0.205715 0.102857 0.994696i \(-0.467201\pi\)
0.102857 + 0.994696i \(0.467201\pi\)
\(110\) 4.79631 0.457310
\(111\) −2.97950 −0.282802
\(112\) 3.46798 0.327693
\(113\) −4.18617 −0.393802 −0.196901 0.980423i \(-0.563088\pi\)
−0.196901 + 0.980423i \(0.563088\pi\)
\(114\) 10.6125 0.993951
\(115\) 0.386679 0.0360580
\(116\) −5.36675 −0.498290
\(117\) 1.16983 0.108151
\(118\) −2.15882 −0.198736
\(119\) 15.8665 1.45448
\(120\) 1.79084 0.163480
\(121\) 12.4085 1.12804
\(122\) 0.659535 0.0597115
\(123\) −1.11128 −0.100201
\(124\) −3.85804 −0.346462
\(125\) −8.93913 −0.799540
\(126\) −0.913467 −0.0813781
\(127\) −1.41613 −0.125661 −0.0628306 0.998024i \(-0.520013\pi\)
−0.0628306 + 0.998024i \(0.520013\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.03145 −0.619085
\(130\) −4.40280 −0.386151
\(131\) −6.01277 −0.525338 −0.262669 0.964886i \(-0.584603\pi\)
−0.262669 + 0.964886i \(0.584603\pi\)
\(132\) 8.74020 0.760737
\(133\) 20.3732 1.76658
\(134\) 3.75828 0.324666
\(135\) 4.90081 0.421794
\(136\) −4.57513 −0.392314
\(137\) −2.75774 −0.235610 −0.117805 0.993037i \(-0.537586\pi\)
−0.117805 + 0.993037i \(0.537586\pi\)
\(138\) 0.704636 0.0599826
\(139\) −10.1459 −0.860564 −0.430282 0.902695i \(-0.641586\pi\)
−0.430282 + 0.902695i \(0.641586\pi\)
\(140\) 3.43794 0.290559
\(141\) −17.2782 −1.45508
\(142\) −7.60582 −0.638266
\(143\) −21.4879 −1.79691
\(144\) 0.263400 0.0219500
\(145\) −5.32025 −0.441823
\(146\) −7.96823 −0.659455
\(147\) −9.08103 −0.748991
\(148\) 1.64933 0.135574
\(149\) −8.07347 −0.661405 −0.330702 0.943735i \(-0.607286\pi\)
−0.330702 + 0.943735i \(0.607286\pi\)
\(150\) −7.25712 −0.592541
\(151\) 13.3238 1.08427 0.542136 0.840290i \(-0.317616\pi\)
0.542136 + 0.840290i \(0.317616\pi\)
\(152\) −5.87465 −0.476497
\(153\) 1.20509 0.0974257
\(154\) 16.7789 1.35208
\(155\) −3.82462 −0.307200
\(156\) −8.02311 −0.642363
\(157\) 13.5492 1.08135 0.540673 0.841233i \(-0.318170\pi\)
0.540673 + 0.841233i \(0.318170\pi\)
\(158\) −7.32579 −0.582809
\(159\) −9.78396 −0.775919
\(160\) −0.991336 −0.0783720
\(161\) 1.35272 0.106609
\(162\) 9.72082 0.763740
\(163\) 23.3382 1.82799 0.913996 0.405724i \(-0.132981\pi\)
0.913996 + 0.405724i \(0.132981\pi\)
\(164\) 0.615159 0.0480359
\(165\) 8.66448 0.674529
\(166\) 4.60880 0.357712
\(167\) 1.63790 0.126744 0.0633722 0.997990i \(-0.479814\pi\)
0.0633722 + 0.997990i \(0.479814\pi\)
\(168\) 6.26487 0.483345
\(169\) 6.72490 0.517300
\(170\) −4.53549 −0.347856
\(171\) 1.54738 0.118331
\(172\) 3.89233 0.296787
\(173\) 16.1710 1.22946 0.614729 0.788739i \(-0.289265\pi\)
0.614729 + 0.788739i \(0.289265\pi\)
\(174\) −9.69496 −0.734973
\(175\) −13.9318 −1.05314
\(176\) −4.83823 −0.364695
\(177\) −3.89989 −0.293133
\(178\) 17.5829 1.31789
\(179\) −20.3815 −1.52339 −0.761694 0.647937i \(-0.775632\pi\)
−0.761694 + 0.647937i \(0.775632\pi\)
\(180\) 0.261118 0.0194626
\(181\) −9.22723 −0.685855 −0.342927 0.939362i \(-0.611418\pi\)
−0.342927 + 0.939362i \(0.611418\pi\)
\(182\) −15.4023 −1.14169
\(183\) 1.19144 0.0880740
\(184\) −0.390058 −0.0287555
\(185\) 1.63505 0.120211
\(186\) −6.96950 −0.511029
\(187\) −22.1355 −1.61871
\(188\) 9.56451 0.697564
\(189\) 17.1444 1.24707
\(190\) −5.82376 −0.422500
\(191\) −0.252623 −0.0182792 −0.00913958 0.999958i \(-0.502909\pi\)
−0.00913958 + 0.999958i \(0.502909\pi\)
\(192\) −1.80649 −0.130372
\(193\) −1.91294 −0.137696 −0.0688481 0.997627i \(-0.521932\pi\)
−0.0688481 + 0.997627i \(0.521932\pi\)
\(194\) 0.900577 0.0646576
\(195\) −7.95360 −0.569569
\(196\) 5.02690 0.359064
\(197\) −4.73274 −0.337193 −0.168597 0.985685i \(-0.553924\pi\)
−0.168597 + 0.985685i \(0.553924\pi\)
\(198\) 1.27439 0.0905670
\(199\) −4.27859 −0.303301 −0.151651 0.988434i \(-0.548459\pi\)
−0.151651 + 0.988434i \(0.548459\pi\)
\(200\) 4.01725 0.284063
\(201\) 6.78930 0.478880
\(202\) 12.6829 0.892367
\(203\) −18.6118 −1.30629
\(204\) −8.26492 −0.578660
\(205\) 0.609830 0.0425924
\(206\) −5.27874 −0.367787
\(207\) 0.102741 0.00714102
\(208\) 4.44127 0.307947
\(209\) −28.4229 −1.96605
\(210\) 6.21059 0.428572
\(211\) 11.5068 0.792159 0.396079 0.918216i \(-0.370371\pi\)
0.396079 + 0.918216i \(0.370371\pi\)
\(212\) 5.41601 0.371973
\(213\) −13.7398 −0.941437
\(214\) −3.15234 −0.215489
\(215\) 3.85861 0.263155
\(216\) −4.94364 −0.336372
\(217\) −13.3796 −0.908267
\(218\) −2.14772 −0.145462
\(219\) −14.3945 −0.972691
\(220\) −4.79631 −0.323367
\(221\) 20.3194 1.36683
\(222\) 2.97950 0.199971
\(223\) −3.74371 −0.250697 −0.125349 0.992113i \(-0.540005\pi\)
−0.125349 + 0.992113i \(0.540005\pi\)
\(224\) −3.46798 −0.231714
\(225\) −1.05814 −0.0705430
\(226\) 4.18617 0.278460
\(227\) −2.29245 −0.152156 −0.0760778 0.997102i \(-0.524240\pi\)
−0.0760778 + 0.997102i \(0.524240\pi\)
\(228\) −10.6125 −0.702830
\(229\) −7.69231 −0.508322 −0.254161 0.967162i \(-0.581799\pi\)
−0.254161 + 0.967162i \(0.581799\pi\)
\(230\) −0.386679 −0.0254969
\(231\) 30.3109 1.99431
\(232\) 5.36675 0.352344
\(233\) 16.1219 1.05618 0.528090 0.849188i \(-0.322908\pi\)
0.528090 + 0.849188i \(0.322908\pi\)
\(234\) −1.16983 −0.0764743
\(235\) 9.48165 0.618514
\(236\) 2.15882 0.140527
\(237\) −13.2340 −0.859638
\(238\) −15.8665 −1.02847
\(239\) 20.9409 1.35456 0.677278 0.735727i \(-0.263159\pi\)
0.677278 + 0.735727i \(0.263159\pi\)
\(240\) −1.79084 −0.115598
\(241\) 22.1655 1.42781 0.713904 0.700244i \(-0.246925\pi\)
0.713904 + 0.700244i \(0.246925\pi\)
\(242\) −12.4085 −0.797646
\(243\) 2.72964 0.175107
\(244\) −0.659535 −0.0422224
\(245\) 4.98335 0.318374
\(246\) 1.11128 0.0708525
\(247\) 26.0909 1.66013
\(248\) 3.85804 0.244986
\(249\) 8.32574 0.527622
\(250\) 8.93913 0.565360
\(251\) 23.1640 1.46210 0.731049 0.682324i \(-0.239031\pi\)
0.731049 + 0.682324i \(0.239031\pi\)
\(252\) 0.913467 0.0575430
\(253\) −1.88719 −0.118647
\(254\) 1.41613 0.0888558
\(255\) −8.19332 −0.513085
\(256\) 1.00000 0.0625000
\(257\) 10.7051 0.667766 0.333883 0.942614i \(-0.391641\pi\)
0.333883 + 0.942614i \(0.391641\pi\)
\(258\) 7.03145 0.437759
\(259\) 5.71986 0.355415
\(260\) 4.40280 0.273050
\(261\) −1.41360 −0.0874997
\(262\) 6.01277 0.371470
\(263\) 24.7435 1.52575 0.762875 0.646546i \(-0.223787\pi\)
0.762875 + 0.646546i \(0.223787\pi\)
\(264\) −8.74020 −0.537922
\(265\) 5.36909 0.329821
\(266\) −20.3732 −1.24916
\(267\) 31.7633 1.94388
\(268\) −3.75828 −0.229574
\(269\) −5.46180 −0.333012 −0.166506 0.986040i \(-0.553248\pi\)
−0.166506 + 0.986040i \(0.553248\pi\)
\(270\) −4.90081 −0.298254
\(271\) 17.0311 1.03457 0.517283 0.855814i \(-0.326943\pi\)
0.517283 + 0.855814i \(0.326943\pi\)
\(272\) 4.57513 0.277408
\(273\) −27.8240 −1.68398
\(274\) 2.75774 0.166601
\(275\) 19.4364 1.17206
\(276\) −0.704636 −0.0424141
\(277\) −13.9848 −0.840267 −0.420134 0.907462i \(-0.638017\pi\)
−0.420134 + 0.907462i \(0.638017\pi\)
\(278\) 10.1459 0.608511
\(279\) −1.01621 −0.0608388
\(280\) −3.43794 −0.205456
\(281\) −27.4034 −1.63475 −0.817375 0.576106i \(-0.804571\pi\)
−0.817375 + 0.576106i \(0.804571\pi\)
\(282\) 17.2782 1.02890
\(283\) 1.39969 0.0832027 0.0416013 0.999134i \(-0.486754\pi\)
0.0416013 + 0.999134i \(0.486754\pi\)
\(284\) 7.60582 0.451322
\(285\) −10.5206 −0.623184
\(286\) 21.4879 1.27061
\(287\) 2.13336 0.125928
\(288\) −0.263400 −0.0155210
\(289\) 3.93182 0.231284
\(290\) 5.32025 0.312416
\(291\) 1.62688 0.0953695
\(292\) 7.96823 0.466305
\(293\) 16.6471 0.972535 0.486267 0.873810i \(-0.338358\pi\)
0.486267 + 0.873810i \(0.338358\pi\)
\(294\) 9.08103 0.529616
\(295\) 2.14012 0.124603
\(296\) −1.64933 −0.0958656
\(297\) −23.9184 −1.38789
\(298\) 8.07347 0.467684
\(299\) 1.73236 0.100185
\(300\) 7.25712 0.418990
\(301\) 13.4985 0.778042
\(302\) −13.3238 −0.766697
\(303\) 22.9115 1.31623
\(304\) 5.87465 0.336935
\(305\) −0.653821 −0.0374377
\(306\) −1.20509 −0.0688904
\(307\) 4.66626 0.266317 0.133159 0.991095i \(-0.457488\pi\)
0.133159 + 0.991095i \(0.457488\pi\)
\(308\) −16.7789 −0.956066
\(309\) −9.53598 −0.542483
\(310\) 3.82462 0.217224
\(311\) −7.36031 −0.417365 −0.208682 0.977983i \(-0.566918\pi\)
−0.208682 + 0.977983i \(0.566918\pi\)
\(312\) 8.02311 0.454219
\(313\) 17.9361 1.01381 0.506906 0.862002i \(-0.330789\pi\)
0.506906 + 0.862002i \(0.330789\pi\)
\(314\) −13.5492 −0.764627
\(315\) 0.905553 0.0510221
\(316\) 7.32579 0.412108
\(317\) 22.6279 1.27091 0.635456 0.772137i \(-0.280812\pi\)
0.635456 + 0.772137i \(0.280812\pi\)
\(318\) 9.78396 0.548657
\(319\) 25.9655 1.45379
\(320\) 0.991336 0.0554174
\(321\) −5.69466 −0.317845
\(322\) −1.35272 −0.0753839
\(323\) 26.8773 1.49549
\(324\) −9.72082 −0.540046
\(325\) −17.8417 −0.989680
\(326\) −23.3382 −1.29259
\(327\) −3.87984 −0.214556
\(328\) −0.615159 −0.0339665
\(329\) 33.1695 1.82870
\(330\) −8.66448 −0.476964
\(331\) 13.1505 0.722815 0.361408 0.932408i \(-0.382296\pi\)
0.361408 + 0.932408i \(0.382296\pi\)
\(332\) −4.60880 −0.252941
\(333\) 0.434435 0.0238069
\(334\) −1.63790 −0.0896219
\(335\) −3.72572 −0.203558
\(336\) −6.26487 −0.341777
\(337\) 8.66798 0.472175 0.236088 0.971732i \(-0.424135\pi\)
0.236088 + 0.971732i \(0.424135\pi\)
\(338\) −6.72490 −0.365786
\(339\) 7.56226 0.410726
\(340\) 4.53549 0.245972
\(341\) 18.6661 1.01082
\(342\) −1.54738 −0.0836730
\(343\) −6.84268 −0.369470
\(344\) −3.89233 −0.209860
\(345\) −0.698531 −0.0376076
\(346\) −16.1710 −0.869358
\(347\) 30.4882 1.63669 0.818346 0.574726i \(-0.194891\pi\)
0.818346 + 0.574726i \(0.194891\pi\)
\(348\) 9.69496 0.519705
\(349\) 10.3172 0.552268 0.276134 0.961119i \(-0.410947\pi\)
0.276134 + 0.961119i \(0.410947\pi\)
\(350\) 13.9318 0.744684
\(351\) 21.9560 1.17193
\(352\) 4.83823 0.257878
\(353\) 21.7091 1.15546 0.577728 0.816229i \(-0.303939\pi\)
0.577728 + 0.816229i \(0.303939\pi\)
\(354\) 3.89989 0.207277
\(355\) 7.53992 0.400177
\(356\) −17.5829 −0.931892
\(357\) −28.6626 −1.51699
\(358\) 20.3815 1.07720
\(359\) 24.3223 1.28368 0.641842 0.766837i \(-0.278171\pi\)
0.641842 + 0.766837i \(0.278171\pi\)
\(360\) −0.261118 −0.0137621
\(361\) 15.5116 0.816398
\(362\) 9.22723 0.484973
\(363\) −22.4157 −1.17652
\(364\) 15.4023 0.807297
\(365\) 7.89919 0.413463
\(366\) −1.19144 −0.0622777
\(367\) −5.77669 −0.301541 −0.150770 0.988569i \(-0.548175\pi\)
−0.150770 + 0.988569i \(0.548175\pi\)
\(368\) 0.390058 0.0203332
\(369\) 0.162033 0.00843510
\(370\) −1.63505 −0.0850020
\(371\) 18.7826 0.975146
\(372\) 6.96950 0.361352
\(373\) 26.6727 1.38106 0.690529 0.723304i \(-0.257378\pi\)
0.690529 + 0.723304i \(0.257378\pi\)
\(374\) 22.1355 1.14460
\(375\) 16.1484 0.833902
\(376\) −9.56451 −0.493252
\(377\) −23.8352 −1.22757
\(378\) −17.1444 −0.881815
\(379\) −7.02665 −0.360935 −0.180467 0.983581i \(-0.557761\pi\)
−0.180467 + 0.983581i \(0.557761\pi\)
\(380\) 5.82376 0.298753
\(381\) 2.55822 0.131062
\(382\) 0.252623 0.0129253
\(383\) −5.62613 −0.287482 −0.143741 0.989615i \(-0.545913\pi\)
−0.143741 + 0.989615i \(0.545913\pi\)
\(384\) 1.80649 0.0921870
\(385\) −16.6335 −0.847723
\(386\) 1.91294 0.0973659
\(387\) 1.02524 0.0521159
\(388\) −0.900577 −0.0457199
\(389\) −16.1901 −0.820872 −0.410436 0.911889i \(-0.634624\pi\)
−0.410436 + 0.911889i \(0.634624\pi\)
\(390\) 7.95360 0.402746
\(391\) 1.78457 0.0902495
\(392\) −5.02690 −0.253897
\(393\) 10.8620 0.547916
\(394\) 4.73274 0.238432
\(395\) 7.26232 0.365407
\(396\) −1.27439 −0.0640405
\(397\) −25.5830 −1.28398 −0.641988 0.766715i \(-0.721890\pi\)
−0.641988 + 0.766715i \(0.721890\pi\)
\(398\) 4.27859 0.214466
\(399\) −36.8039 −1.84250
\(400\) −4.01725 −0.200863
\(401\) 19.0673 0.952175 0.476088 0.879398i \(-0.342054\pi\)
0.476088 + 0.879398i \(0.342054\pi\)
\(402\) −6.78930 −0.338619
\(403\) −17.1346 −0.853536
\(404\) −12.6829 −0.630999
\(405\) −9.63660 −0.478847
\(406\) 18.6118 0.923687
\(407\) −7.97986 −0.395547
\(408\) 8.26492 0.409175
\(409\) 20.2004 0.998844 0.499422 0.866359i \(-0.333546\pi\)
0.499422 + 0.866359i \(0.333546\pi\)
\(410\) −0.609830 −0.0301173
\(411\) 4.98182 0.245735
\(412\) 5.27874 0.260065
\(413\) 7.48676 0.368399
\(414\) −0.102741 −0.00504946
\(415\) −4.56887 −0.224277
\(416\) −4.44127 −0.217751
\(417\) 18.3284 0.897548
\(418\) 28.4229 1.39021
\(419\) 8.13037 0.397195 0.198597 0.980081i \(-0.436361\pi\)
0.198597 + 0.980081i \(0.436361\pi\)
\(420\) −6.21059 −0.303046
\(421\) −21.7269 −1.05891 −0.529453 0.848339i \(-0.677603\pi\)
−0.529453 + 0.848339i \(0.677603\pi\)
\(422\) −11.5068 −0.560141
\(423\) 2.51929 0.122492
\(424\) −5.41601 −0.263025
\(425\) −18.3795 −0.891534
\(426\) 13.7398 0.665696
\(427\) −2.28726 −0.110688
\(428\) 3.15234 0.152374
\(429\) 38.8176 1.87413
\(430\) −3.85861 −0.186079
\(431\) 24.8566 1.19730 0.598650 0.801011i \(-0.295704\pi\)
0.598650 + 0.801011i \(0.295704\pi\)
\(432\) 4.94364 0.237851
\(433\) 21.4707 1.03182 0.515908 0.856644i \(-0.327455\pi\)
0.515908 + 0.856644i \(0.327455\pi\)
\(434\) 13.3796 0.642242
\(435\) 9.61097 0.460811
\(436\) 2.14772 0.102857
\(437\) 2.29146 0.109615
\(438\) 14.3945 0.687796
\(439\) 20.6508 0.985609 0.492804 0.870140i \(-0.335972\pi\)
0.492804 + 0.870140i \(0.335972\pi\)
\(440\) 4.79631 0.228655
\(441\) 1.32409 0.0630517
\(442\) −20.3194 −0.966495
\(443\) −13.9285 −0.661764 −0.330882 0.943672i \(-0.607346\pi\)
−0.330882 + 0.943672i \(0.607346\pi\)
\(444\) −2.97950 −0.141401
\(445\) −17.4306 −0.826288
\(446\) 3.74371 0.177270
\(447\) 14.5846 0.689830
\(448\) 3.46798 0.163847
\(449\) 3.56271 0.168135 0.0840675 0.996460i \(-0.473209\pi\)
0.0840675 + 0.996460i \(0.473209\pi\)
\(450\) 1.05814 0.0498814
\(451\) −2.97628 −0.140148
\(452\) −4.18617 −0.196901
\(453\) −24.0692 −1.13087
\(454\) 2.29245 0.107590
\(455\) 15.2688 0.715813
\(456\) 10.6125 0.496976
\(457\) −20.6838 −0.967549 −0.483775 0.875193i \(-0.660735\pi\)
−0.483775 + 0.875193i \(0.660735\pi\)
\(458\) 7.69231 0.359438
\(459\) 22.6178 1.05571
\(460\) 0.386679 0.0180290
\(461\) −1.39819 −0.0651201 −0.0325600 0.999470i \(-0.510366\pi\)
−0.0325600 + 0.999470i \(0.510366\pi\)
\(462\) −30.3109 −1.41019
\(463\) 18.4190 0.856003 0.428002 0.903778i \(-0.359218\pi\)
0.428002 + 0.903778i \(0.359218\pi\)
\(464\) −5.36675 −0.249145
\(465\) 6.90912 0.320403
\(466\) −16.1219 −0.746832
\(467\) 17.8825 0.827504 0.413752 0.910390i \(-0.364218\pi\)
0.413752 + 0.910390i \(0.364218\pi\)
\(468\) 1.16983 0.0540755
\(469\) −13.0337 −0.601838
\(470\) −9.48165 −0.437356
\(471\) −24.4765 −1.12782
\(472\) −2.15882 −0.0993678
\(473\) −18.8320 −0.865896
\(474\) 13.2340 0.607856
\(475\) −23.6000 −1.08284
\(476\) 15.8665 0.727238
\(477\) 1.42658 0.0653185
\(478\) −20.9409 −0.957816
\(479\) −22.2536 −1.01679 −0.508396 0.861123i \(-0.669762\pi\)
−0.508396 + 0.861123i \(0.669762\pi\)
\(480\) 1.79084 0.0817402
\(481\) 7.32514 0.333998
\(482\) −22.1655 −1.00961
\(483\) −2.44366 −0.111191
\(484\) 12.4085 0.564021
\(485\) −0.892775 −0.0405388
\(486\) −2.72964 −0.123819
\(487\) 8.74071 0.396079 0.198040 0.980194i \(-0.436543\pi\)
0.198040 + 0.980194i \(0.436543\pi\)
\(488\) 0.659535 0.0298557
\(489\) −42.1602 −1.90655
\(490\) −4.98335 −0.225125
\(491\) −7.08110 −0.319566 −0.159783 0.987152i \(-0.551079\pi\)
−0.159783 + 0.987152i \(0.551079\pi\)
\(492\) −1.11128 −0.0501003
\(493\) −24.5536 −1.10584
\(494\) −26.0909 −1.17389
\(495\) −1.26335 −0.0567833
\(496\) −3.85804 −0.173231
\(497\) 26.3768 1.18316
\(498\) −8.32574 −0.373085
\(499\) 5.27856 0.236301 0.118150 0.992996i \(-0.462303\pi\)
0.118150 + 0.992996i \(0.462303\pi\)
\(500\) −8.93913 −0.399770
\(501\) −2.95885 −0.132192
\(502\) −23.1640 −1.03386
\(503\) −21.5204 −0.959546 −0.479773 0.877393i \(-0.659281\pi\)
−0.479773 + 0.877393i \(0.659281\pi\)
\(504\) −0.913467 −0.0406890
\(505\) −12.5730 −0.559493
\(506\) 1.88719 0.0838959
\(507\) −12.1485 −0.539532
\(508\) −1.41613 −0.0628306
\(509\) 29.2034 1.29442 0.647210 0.762312i \(-0.275936\pi\)
0.647210 + 0.762312i \(0.275936\pi\)
\(510\) 8.19332 0.362806
\(511\) 27.6337 1.22244
\(512\) −1.00000 −0.0441942
\(513\) 29.0422 1.28224
\(514\) −10.7051 −0.472182
\(515\) 5.23301 0.230594
\(516\) −7.03145 −0.309542
\(517\) −46.2753 −2.03518
\(518\) −5.71986 −0.251316
\(519\) −29.2127 −1.28230
\(520\) −4.40280 −0.193075
\(521\) −30.3033 −1.32761 −0.663805 0.747905i \(-0.731060\pi\)
−0.663805 + 0.747905i \(0.731060\pi\)
\(522\) 1.41360 0.0618717
\(523\) −32.9269 −1.43979 −0.719896 0.694082i \(-0.755811\pi\)
−0.719896 + 0.694082i \(0.755811\pi\)
\(524\) −6.01277 −0.262669
\(525\) 25.1676 1.09840
\(526\) −24.7435 −1.07887
\(527\) −17.6510 −0.768891
\(528\) 8.74020 0.380369
\(529\) −22.8479 −0.993385
\(530\) −5.36909 −0.233218
\(531\) 0.568634 0.0246766
\(532\) 20.3732 0.883290
\(533\) 2.73209 0.118340
\(534\) −31.7633 −1.37453
\(535\) 3.12503 0.135107
\(536\) 3.75828 0.162333
\(537\) 36.8190 1.58886
\(538\) 5.46180 0.235475
\(539\) −24.3213 −1.04759
\(540\) 4.90081 0.210897
\(541\) 6.11490 0.262900 0.131450 0.991323i \(-0.458037\pi\)
0.131450 + 0.991323i \(0.458037\pi\)
\(542\) −17.0311 −0.731549
\(543\) 16.6689 0.715330
\(544\) −4.57513 −0.196157
\(545\) 2.12912 0.0912013
\(546\) 27.8240 1.19076
\(547\) −46.1801 −1.97452 −0.987258 0.159126i \(-0.949133\pi\)
−0.987258 + 0.159126i \(0.949133\pi\)
\(548\) −2.75774 −0.117805
\(549\) −0.173722 −0.00741426
\(550\) −19.4364 −0.828770
\(551\) −31.5278 −1.34313
\(552\) 0.704636 0.0299913
\(553\) 25.4057 1.08036
\(554\) 13.9848 0.594159
\(555\) −2.95369 −0.125377
\(556\) −10.1459 −0.430282
\(557\) 34.3387 1.45498 0.727488 0.686120i \(-0.240688\pi\)
0.727488 + 0.686120i \(0.240688\pi\)
\(558\) 1.01621 0.0430195
\(559\) 17.2869 0.731158
\(560\) 3.43794 0.145279
\(561\) 39.9876 1.68828
\(562\) 27.4034 1.15594
\(563\) −12.7013 −0.535296 −0.267648 0.963517i \(-0.586246\pi\)
−0.267648 + 0.963517i \(0.586246\pi\)
\(564\) −17.2782 −0.727542
\(565\) −4.14990 −0.174588
\(566\) −1.39969 −0.0588332
\(567\) −33.7116 −1.41576
\(568\) −7.60582 −0.319133
\(569\) 12.6056 0.528456 0.264228 0.964460i \(-0.414883\pi\)
0.264228 + 0.964460i \(0.414883\pi\)
\(570\) 10.5206 0.440657
\(571\) 39.7015 1.66146 0.830728 0.556679i \(-0.187925\pi\)
0.830728 + 0.556679i \(0.187925\pi\)
\(572\) −21.4879 −0.898454
\(573\) 0.456361 0.0190647
\(574\) −2.13336 −0.0890448
\(575\) −1.56696 −0.0653469
\(576\) 0.263400 0.0109750
\(577\) 18.2349 0.759130 0.379565 0.925165i \(-0.376074\pi\)
0.379565 + 0.925165i \(0.376074\pi\)
\(578\) −3.93182 −0.163542
\(579\) 3.45570 0.143614
\(580\) −5.32025 −0.220911
\(581\) −15.9832 −0.663096
\(582\) −1.62688 −0.0674364
\(583\) −26.2039 −1.08525
\(584\) −7.96823 −0.329728
\(585\) 1.15970 0.0479476
\(586\) −16.6471 −0.687686
\(587\) −46.2844 −1.91036 −0.955182 0.296020i \(-0.904340\pi\)
−0.955182 + 0.296020i \(0.904340\pi\)
\(588\) −9.08103 −0.374495
\(589\) −22.6647 −0.933881
\(590\) −2.14012 −0.0881073
\(591\) 8.54963 0.351685
\(592\) 1.64933 0.0677872
\(593\) −39.2941 −1.61362 −0.806808 0.590813i \(-0.798807\pi\)
−0.806808 + 0.590813i \(0.798807\pi\)
\(594\) 23.9184 0.981386
\(595\) 15.7290 0.644826
\(596\) −8.07347 −0.330702
\(597\) 7.72922 0.316336
\(598\) −1.73236 −0.0708413
\(599\) 18.9396 0.773850 0.386925 0.922111i \(-0.373537\pi\)
0.386925 + 0.922111i \(0.373537\pi\)
\(600\) −7.25712 −0.296271
\(601\) 1.18833 0.0484730 0.0242365 0.999706i \(-0.492285\pi\)
0.0242365 + 0.999706i \(0.492285\pi\)
\(602\) −13.4985 −0.550159
\(603\) −0.989932 −0.0403132
\(604\) 13.3238 0.542136
\(605\) 12.3010 0.500105
\(606\) −22.9115 −0.930718
\(607\) 22.5047 0.913439 0.456719 0.889611i \(-0.349024\pi\)
0.456719 + 0.889611i \(0.349024\pi\)
\(608\) −5.87465 −0.238249
\(609\) 33.6220 1.36243
\(610\) 0.653821 0.0264724
\(611\) 42.4786 1.71850
\(612\) 1.20509 0.0487129
\(613\) −35.1216 −1.41855 −0.709274 0.704933i \(-0.750977\pi\)
−0.709274 + 0.704933i \(0.750977\pi\)
\(614\) −4.66626 −0.188315
\(615\) −1.10165 −0.0444228
\(616\) 16.7789 0.676041
\(617\) −45.6860 −1.83925 −0.919624 0.392799i \(-0.871507\pi\)
−0.919624 + 0.392799i \(0.871507\pi\)
\(618\) 9.53598 0.383593
\(619\) −5.56332 −0.223609 −0.111804 0.993730i \(-0.535663\pi\)
−0.111804 + 0.993730i \(0.535663\pi\)
\(620\) −3.82462 −0.153600
\(621\) 1.92831 0.0773803
\(622\) 7.36031 0.295122
\(623\) −60.9772 −2.44300
\(624\) −8.02311 −0.321181
\(625\) 11.2246 0.448983
\(626\) −17.9361 −0.716873
\(627\) 51.3457 2.05055
\(628\) 13.5492 0.540673
\(629\) 7.54592 0.300876
\(630\) −0.905553 −0.0360781
\(631\) 40.7240 1.62120 0.810598 0.585603i \(-0.199142\pi\)
0.810598 + 0.585603i \(0.199142\pi\)
\(632\) −7.32579 −0.291404
\(633\) −20.7868 −0.826203
\(634\) −22.6279 −0.898670
\(635\) −1.40386 −0.0557105
\(636\) −9.78396 −0.387959
\(637\) 22.3258 0.884581
\(638\) −25.9655 −1.02799
\(639\) 2.00337 0.0792522
\(640\) −0.991336 −0.0391860
\(641\) 5.93815 0.234543 0.117271 0.993100i \(-0.462585\pi\)
0.117271 + 0.993100i \(0.462585\pi\)
\(642\) 5.69466 0.224750
\(643\) 22.7412 0.896827 0.448414 0.893826i \(-0.351989\pi\)
0.448414 + 0.893826i \(0.351989\pi\)
\(644\) 1.35272 0.0533044
\(645\) −6.97053 −0.274464
\(646\) −26.8773 −1.05747
\(647\) −37.4156 −1.47096 −0.735479 0.677548i \(-0.763043\pi\)
−0.735479 + 0.677548i \(0.763043\pi\)
\(648\) 9.72082 0.381870
\(649\) −10.4449 −0.409997
\(650\) 17.8417 0.699810
\(651\) 24.1701 0.947301
\(652\) 23.3382 0.913996
\(653\) −44.6646 −1.74786 −0.873930 0.486052i \(-0.838437\pi\)
−0.873930 + 0.486052i \(0.838437\pi\)
\(654\) 3.87984 0.151714
\(655\) −5.96068 −0.232903
\(656\) 0.615159 0.0240179
\(657\) 2.09883 0.0818832
\(658\) −33.1695 −1.29308
\(659\) 17.9391 0.698809 0.349405 0.936972i \(-0.386384\pi\)
0.349405 + 0.936972i \(0.386384\pi\)
\(660\) 8.66448 0.337265
\(661\) 20.0545 0.780028 0.390014 0.920809i \(-0.372470\pi\)
0.390014 + 0.920809i \(0.372470\pi\)
\(662\) −13.1505 −0.511108
\(663\) −36.7068 −1.42557
\(664\) 4.60880 0.178856
\(665\) 20.1967 0.783194
\(666\) −0.434435 −0.0168340
\(667\) −2.09334 −0.0810546
\(668\) 1.63790 0.0633722
\(669\) 6.76297 0.261471
\(670\) 3.72572 0.143937
\(671\) 3.19098 0.123186
\(672\) 6.26487 0.241673
\(673\) 39.2695 1.51373 0.756863 0.653573i \(-0.226731\pi\)
0.756863 + 0.653573i \(0.226731\pi\)
\(674\) −8.66798 −0.333878
\(675\) −19.8598 −0.764405
\(676\) 6.72490 0.258650
\(677\) 22.2291 0.854333 0.427166 0.904173i \(-0.359512\pi\)
0.427166 + 0.904173i \(0.359512\pi\)
\(678\) −7.56226 −0.290427
\(679\) −3.12318 −0.119857
\(680\) −4.53549 −0.173928
\(681\) 4.14129 0.158695
\(682\) −18.6661 −0.714761
\(683\) 18.1134 0.693091 0.346546 0.938033i \(-0.387355\pi\)
0.346546 + 0.938033i \(0.387355\pi\)
\(684\) 1.54738 0.0591657
\(685\) −2.73385 −0.104455
\(686\) 6.84268 0.261255
\(687\) 13.8961 0.530168
\(688\) 3.89233 0.148394
\(689\) 24.0540 0.916384
\(690\) 0.698531 0.0265926
\(691\) 7.91737 0.301191 0.150596 0.988595i \(-0.451881\pi\)
0.150596 + 0.988595i \(0.451881\pi\)
\(692\) 16.1710 0.614729
\(693\) −4.41956 −0.167885
\(694\) −30.4882 −1.15732
\(695\) −10.0580 −0.381522
\(696\) −9.69496 −0.367487
\(697\) 2.81443 0.106604
\(698\) −10.3172 −0.390512
\(699\) −29.1240 −1.10157
\(700\) −13.9318 −0.526571
\(701\) 22.7900 0.860766 0.430383 0.902646i \(-0.358379\pi\)
0.430383 + 0.902646i \(0.358379\pi\)
\(702\) −21.9560 −0.828677
\(703\) 9.68927 0.365438
\(704\) −4.83823 −0.182348
\(705\) −17.1285 −0.645096
\(706\) −21.7091 −0.817031
\(707\) −43.9841 −1.65419
\(708\) −3.89989 −0.146567
\(709\) 11.1318 0.418063 0.209032 0.977909i \(-0.432969\pi\)
0.209032 + 0.977909i \(0.432969\pi\)
\(710\) −7.53992 −0.282968
\(711\) 1.92961 0.0723662
\(712\) 17.5829 0.658947
\(713\) −1.50486 −0.0563575
\(714\) 28.6626 1.07267
\(715\) −21.3017 −0.796640
\(716\) −20.3815 −0.761694
\(717\) −37.8296 −1.41277
\(718\) −24.3223 −0.907701
\(719\) −26.7265 −0.996730 −0.498365 0.866967i \(-0.666066\pi\)
−0.498365 + 0.866967i \(0.666066\pi\)
\(720\) 0.261118 0.00973130
\(721\) 18.3066 0.681772
\(722\) −15.5116 −0.577281
\(723\) −40.0418 −1.48917
\(724\) −9.22723 −0.342927
\(725\) 21.5596 0.800702
\(726\) 22.4157 0.831926
\(727\) 5.91475 0.219366 0.109683 0.993967i \(-0.465016\pi\)
0.109683 + 0.993967i \(0.465016\pi\)
\(728\) −15.4023 −0.570845
\(729\) 24.2314 0.897459
\(730\) −7.89919 −0.292362
\(731\) 17.8079 0.658650
\(732\) 1.19144 0.0440370
\(733\) −16.1525 −0.596606 −0.298303 0.954471i \(-0.596421\pi\)
−0.298303 + 0.954471i \(0.596421\pi\)
\(734\) 5.77669 0.213222
\(735\) −9.00236 −0.332057
\(736\) −0.390058 −0.0143777
\(737\) 18.1834 0.669796
\(738\) −0.162033 −0.00596452
\(739\) 4.56505 0.167928 0.0839640 0.996469i \(-0.473242\pi\)
0.0839640 + 0.996469i \(0.473242\pi\)
\(740\) 1.63505 0.0601055
\(741\) −47.1330 −1.73147
\(742\) −18.7826 −0.689532
\(743\) −1.10692 −0.0406089 −0.0203045 0.999794i \(-0.506464\pi\)
−0.0203045 + 0.999794i \(0.506464\pi\)
\(744\) −6.96950 −0.255514
\(745\) −8.00353 −0.293227
\(746\) −26.6727 −0.976556
\(747\) −1.21396 −0.0444164
\(748\) −22.1355 −0.809355
\(749\) 10.9322 0.399456
\(750\) −16.1484 −0.589657
\(751\) −4.06957 −0.148501 −0.0742504 0.997240i \(-0.523656\pi\)
−0.0742504 + 0.997240i \(0.523656\pi\)
\(752\) 9.56451 0.348782
\(753\) −41.8455 −1.52493
\(754\) 23.8352 0.868026
\(755\) 13.2083 0.480701
\(756\) 17.1444 0.623537
\(757\) −31.9015 −1.15948 −0.579740 0.814801i \(-0.696846\pi\)
−0.579740 + 0.814801i \(0.696846\pi\)
\(758\) 7.02665 0.255219
\(759\) 3.40919 0.123746
\(760\) −5.82376 −0.211250
\(761\) 41.5648 1.50672 0.753361 0.657607i \(-0.228431\pi\)
0.753361 + 0.657607i \(0.228431\pi\)
\(762\) −2.55822 −0.0926745
\(763\) 7.44827 0.269645
\(764\) −0.252623 −0.00913958
\(765\) 1.19465 0.0431926
\(766\) 5.62613 0.203280
\(767\) 9.58792 0.346200
\(768\) −1.80649 −0.0651860
\(769\) 1.47872 0.0533241 0.0266620 0.999645i \(-0.491512\pi\)
0.0266620 + 0.999645i \(0.491512\pi\)
\(770\) 16.6335 0.599431
\(771\) −19.3387 −0.696465
\(772\) −1.91294 −0.0688481
\(773\) −37.2985 −1.34154 −0.670768 0.741668i \(-0.734035\pi\)
−0.670768 + 0.741668i \(0.734035\pi\)
\(774\) −1.02524 −0.0368515
\(775\) 15.4987 0.556730
\(776\) 0.900577 0.0323288
\(777\) −10.3329 −0.370689
\(778\) 16.1901 0.580444
\(779\) 3.61385 0.129480
\(780\) −7.95360 −0.284784
\(781\) −36.7987 −1.31676
\(782\) −1.78457 −0.0638160
\(783\) −26.5312 −0.948149
\(784\) 5.02690 0.179532
\(785\) 13.4318 0.479403
\(786\) −10.8620 −0.387435
\(787\) 36.3902 1.29717 0.648585 0.761142i \(-0.275361\pi\)
0.648585 + 0.761142i \(0.275361\pi\)
\(788\) −4.73274 −0.168597
\(789\) −44.6989 −1.59132
\(790\) −7.26232 −0.258382
\(791\) −14.5176 −0.516185
\(792\) 1.27439 0.0452835
\(793\) −2.92917 −0.104018
\(794\) 25.5830 0.907908
\(795\) −9.69920 −0.343995
\(796\) −4.27859 −0.151651
\(797\) −22.1309 −0.783917 −0.391959 0.919983i \(-0.628202\pi\)
−0.391959 + 0.919983i \(0.628202\pi\)
\(798\) 36.8039 1.30285
\(799\) 43.7589 1.54808
\(800\) 4.01725 0.142031
\(801\) −4.63134 −0.163640
\(802\) −19.0673 −0.673290
\(803\) −38.5521 −1.36047
\(804\) 6.78930 0.239440
\(805\) 1.34100 0.0472639
\(806\) 17.1346 0.603541
\(807\) 9.86668 0.347323
\(808\) 12.6829 0.446184
\(809\) 50.9644 1.79181 0.895906 0.444243i \(-0.146527\pi\)
0.895906 + 0.444243i \(0.146527\pi\)
\(810\) 9.63660 0.338596
\(811\) 29.8202 1.04713 0.523564 0.851986i \(-0.324602\pi\)
0.523564 + 0.851986i \(0.324602\pi\)
\(812\) −18.6118 −0.653145
\(813\) −30.7665 −1.07903
\(814\) 7.97986 0.279694
\(815\) 23.1360 0.810420
\(816\) −8.26492 −0.289330
\(817\) 22.8661 0.799984
\(818\) −20.2004 −0.706289
\(819\) 4.05695 0.141761
\(820\) 0.609830 0.0212962
\(821\) −31.0815 −1.08475 −0.542376 0.840136i \(-0.682475\pi\)
−0.542376 + 0.840136i \(0.682475\pi\)
\(822\) −4.98182 −0.173761
\(823\) 9.16996 0.319645 0.159822 0.987146i \(-0.448908\pi\)
0.159822 + 0.987146i \(0.448908\pi\)
\(824\) −5.27874 −0.183894
\(825\) −35.1116 −1.22243
\(826\) −7.48676 −0.260498
\(827\) 2.37504 0.0825881 0.0412941 0.999147i \(-0.486852\pi\)
0.0412941 + 0.999147i \(0.486852\pi\)
\(828\) 0.102741 0.00357051
\(829\) −31.1481 −1.08182 −0.540909 0.841081i \(-0.681920\pi\)
−0.540909 + 0.841081i \(0.681920\pi\)
\(830\) 4.56887 0.158588
\(831\) 25.2634 0.876379
\(832\) 4.44127 0.153973
\(833\) 22.9987 0.796858
\(834\) −18.3284 −0.634662
\(835\) 1.62371 0.0561908
\(836\) −28.4229 −0.983027
\(837\) −19.0727 −0.659250
\(838\) −8.13037 −0.280859
\(839\) 29.8781 1.03151 0.515754 0.856737i \(-0.327512\pi\)
0.515754 + 0.856737i \(0.327512\pi\)
\(840\) 6.21059 0.214286
\(841\) −0.198037 −0.00682887
\(842\) 21.7269 0.748760
\(843\) 49.5039 1.70501
\(844\) 11.5068 0.396079
\(845\) 6.66664 0.229339
\(846\) −2.51929 −0.0866151
\(847\) 43.0323 1.47861
\(848\) 5.41601 0.185987
\(849\) −2.52852 −0.0867785
\(850\) 18.3795 0.630410
\(851\) 0.643337 0.0220533
\(852\) −13.7398 −0.470718
\(853\) −39.1255 −1.33963 −0.669816 0.742527i \(-0.733627\pi\)
−0.669816 + 0.742527i \(0.733627\pi\)
\(854\) 2.28726 0.0782683
\(855\) 1.53398 0.0524610
\(856\) −3.15234 −0.107745
\(857\) −5.63162 −0.192372 −0.0961862 0.995363i \(-0.530664\pi\)
−0.0961862 + 0.995363i \(0.530664\pi\)
\(858\) −38.8176 −1.32521
\(859\) −13.3591 −0.455806 −0.227903 0.973684i \(-0.573187\pi\)
−0.227903 + 0.973684i \(0.573187\pi\)
\(860\) 3.85861 0.131577
\(861\) −3.85389 −0.131340
\(862\) −24.8566 −0.846619
\(863\) −38.7837 −1.32021 −0.660106 0.751172i \(-0.729489\pi\)
−0.660106 + 0.751172i \(0.729489\pi\)
\(864\) −4.94364 −0.168186
\(865\) 16.0309 0.545067
\(866\) −21.4707 −0.729604
\(867\) −7.10279 −0.241223
\(868\) −13.3796 −0.454134
\(869\) −35.4438 −1.20235
\(870\) −9.61097 −0.325842
\(871\) −16.6916 −0.565572
\(872\) −2.14772 −0.0727311
\(873\) −0.237212 −0.00802841
\(874\) −2.29146 −0.0775097
\(875\) −31.0007 −1.04802
\(876\) −14.3945 −0.486345
\(877\) −17.6039 −0.594441 −0.297220 0.954809i \(-0.596060\pi\)
−0.297220 + 0.954809i \(0.596060\pi\)
\(878\) −20.6508 −0.696931
\(879\) −30.0728 −1.01433
\(880\) −4.79631 −0.161684
\(881\) 37.3148 1.25717 0.628583 0.777742i \(-0.283635\pi\)
0.628583 + 0.777742i \(0.283635\pi\)
\(882\) −1.32409 −0.0445843
\(883\) −44.9842 −1.51384 −0.756920 0.653508i \(-0.773297\pi\)
−0.756920 + 0.653508i \(0.773297\pi\)
\(884\) 20.3194 0.683415
\(885\) −3.86610 −0.129958
\(886\) 13.9285 0.467938
\(887\) 57.1469 1.91881 0.959403 0.282040i \(-0.0910111\pi\)
0.959403 + 0.282040i \(0.0910111\pi\)
\(888\) 2.97950 0.0999856
\(889\) −4.91111 −0.164713
\(890\) 17.4306 0.584274
\(891\) 47.0316 1.57562
\(892\) −3.74371 −0.125349
\(893\) 56.1882 1.88027
\(894\) −14.5846 −0.487783
\(895\) −20.2050 −0.675377
\(896\) −3.46798 −0.115857
\(897\) −3.12948 −0.104490
\(898\) −3.56271 −0.118889
\(899\) 20.7051 0.690554
\(900\) −1.05814 −0.0352715
\(901\) 24.7790 0.825507
\(902\) 2.97628 0.0990993
\(903\) −24.3849 −0.811480
\(904\) 4.18617 0.139230
\(905\) −9.14729 −0.304066
\(906\) 24.0692 0.799647
\(907\) −5.87490 −0.195073 −0.0975364 0.995232i \(-0.531096\pi\)
−0.0975364 + 0.995232i \(0.531096\pi\)
\(908\) −2.29245 −0.0760778
\(909\) −3.34068 −0.110803
\(910\) −15.2688 −0.506156
\(911\) −56.7383 −1.87982 −0.939912 0.341416i \(-0.889093\pi\)
−0.939912 + 0.341416i \(0.889093\pi\)
\(912\) −10.6125 −0.351415
\(913\) 22.2984 0.737970
\(914\) 20.6838 0.684161
\(915\) 1.18112 0.0390466
\(916\) −7.69231 −0.254161
\(917\) −20.8522 −0.688600
\(918\) −22.6178 −0.746498
\(919\) −30.4436 −1.00424 −0.502121 0.864797i \(-0.667447\pi\)
−0.502121 + 0.864797i \(0.667447\pi\)
\(920\) −0.386679 −0.0127484
\(921\) −8.42954 −0.277763
\(922\) 1.39819 0.0460469
\(923\) 33.7795 1.11187
\(924\) 30.3109 0.997154
\(925\) −6.62579 −0.217855
\(926\) −18.4190 −0.605286
\(927\) 1.39042 0.0456674
\(928\) 5.36675 0.176172
\(929\) 43.8675 1.43925 0.719623 0.694365i \(-0.244315\pi\)
0.719623 + 0.694365i \(0.244315\pi\)
\(930\) −6.90912 −0.226559
\(931\) 29.5313 0.967849
\(932\) 16.1219 0.528090
\(933\) 13.2963 0.435302
\(934\) −17.8825 −0.585134
\(935\) −21.9438 −0.717638
\(936\) −1.16983 −0.0382371
\(937\) 17.4667 0.570612 0.285306 0.958437i \(-0.407905\pi\)
0.285306 + 0.958437i \(0.407905\pi\)
\(938\) 13.0337 0.425564
\(939\) −32.4014 −1.05738
\(940\) 9.48165 0.309257
\(941\) −15.0431 −0.490392 −0.245196 0.969474i \(-0.578852\pi\)
−0.245196 + 0.969474i \(0.578852\pi\)
\(942\) 24.4765 0.797488
\(943\) 0.239948 0.00781378
\(944\) 2.15882 0.0702637
\(945\) 16.9959 0.552877
\(946\) 18.8320 0.612281
\(947\) −10.9124 −0.354604 −0.177302 0.984156i \(-0.556737\pi\)
−0.177302 + 0.984156i \(0.556737\pi\)
\(948\) −13.2340 −0.429819
\(949\) 35.3891 1.14878
\(950\) 23.6000 0.765684
\(951\) −40.8771 −1.32553
\(952\) −15.8665 −0.514235
\(953\) 54.7022 1.77198 0.885990 0.463705i \(-0.153480\pi\)
0.885990 + 0.463705i \(0.153480\pi\)
\(954\) −1.42658 −0.0461872
\(955\) −0.250434 −0.00810387
\(956\) 20.9409 0.677278
\(957\) −46.9065 −1.51627
\(958\) 22.2536 0.718981
\(959\) −9.56379 −0.308831
\(960\) −1.79084 −0.0577990
\(961\) −16.1155 −0.519856
\(962\) −7.32514 −0.236172
\(963\) 0.830326 0.0267569
\(964\) 22.1655 0.713904
\(965\) −1.89636 −0.0610461
\(966\) 2.44366 0.0786236
\(967\) −14.7095 −0.473025 −0.236513 0.971628i \(-0.576004\pi\)
−0.236513 + 0.971628i \(0.576004\pi\)
\(968\) −12.4085 −0.398823
\(969\) −48.5536 −1.55976
\(970\) 0.892775 0.0286653
\(971\) 32.4180 1.04034 0.520171 0.854062i \(-0.325868\pi\)
0.520171 + 0.854062i \(0.325868\pi\)
\(972\) 2.72964 0.0875533
\(973\) −35.1858 −1.12800
\(974\) −8.74071 −0.280070
\(975\) 32.2308 1.03221
\(976\) −0.659535 −0.0211112
\(977\) −26.1555 −0.836790 −0.418395 0.908265i \(-0.637407\pi\)
−0.418395 + 0.908265i \(0.637407\pi\)
\(978\) 42.1602 1.34814
\(979\) 85.0701 2.71885
\(980\) 4.98335 0.159187
\(981\) 0.565711 0.0180618
\(982\) 7.08110 0.225967
\(983\) 3.91663 0.124921 0.0624605 0.998047i \(-0.480105\pi\)
0.0624605 + 0.998047i \(0.480105\pi\)
\(984\) 1.11128 0.0354262
\(985\) −4.69173 −0.149491
\(986\) 24.5536 0.781945
\(987\) −59.9204 −1.90729
\(988\) 26.0909 0.830064
\(989\) 1.51824 0.0482771
\(990\) 1.26335 0.0401519
\(991\) 52.1499 1.65660 0.828298 0.560288i \(-0.189310\pi\)
0.828298 + 0.560288i \(0.189310\pi\)
\(992\) 3.85804 0.122493
\(993\) −23.7562 −0.753880
\(994\) −26.3768 −0.836622
\(995\) −4.24152 −0.134465
\(996\) 8.32574 0.263811
\(997\) −43.4143 −1.37494 −0.687472 0.726211i \(-0.741279\pi\)
−0.687472 + 0.726211i \(0.741279\pi\)
\(998\) −5.27856 −0.167090
\(999\) 8.15371 0.257972
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.c.1.12 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.c.1.12 49 1.1 even 1 trivial