Properties

Label 6033.2.a.c.1.3
Level $6033$
Weight $2$
Character 6033.1
Self dual yes
Analytic conductor $48.174$
Analytic rank $0$
Dimension $82$
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] = [6033,2,Mod(1,6033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6033, 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("6033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6033 = 3 \cdot 2011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6033.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: \(48.1737475394\)
Analytic rank: \(0\)
Dimension: \(82\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 6033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.60707 q^{2} -1.00000 q^{3} +4.79682 q^{4} +3.79845 q^{5} +2.60707 q^{6} +0.267933 q^{7} -7.29150 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.60707 q^{2} -1.00000 q^{3} +4.79682 q^{4} +3.79845 q^{5} +2.60707 q^{6} +0.267933 q^{7} -7.29150 q^{8} +1.00000 q^{9} -9.90282 q^{10} -3.59805 q^{11} -4.79682 q^{12} -2.40460 q^{13} -0.698520 q^{14} -3.79845 q^{15} +9.41582 q^{16} +4.06799 q^{17} -2.60707 q^{18} +5.75949 q^{19} +18.2205 q^{20} -0.267933 q^{21} +9.38038 q^{22} +8.77446 q^{23} +7.29150 q^{24} +9.42821 q^{25} +6.26897 q^{26} -1.00000 q^{27} +1.28523 q^{28} +3.95909 q^{29} +9.90282 q^{30} +9.31418 q^{31} -9.96472 q^{32} +3.59805 q^{33} -10.6055 q^{34} +1.01773 q^{35} +4.79682 q^{36} -5.99166 q^{37} -15.0154 q^{38} +2.40460 q^{39} -27.6964 q^{40} +7.35835 q^{41} +0.698520 q^{42} +6.70189 q^{43} -17.2592 q^{44} +3.79845 q^{45} -22.8756 q^{46} +2.54569 q^{47} -9.41582 q^{48} -6.92821 q^{49} -24.5800 q^{50} -4.06799 q^{51} -11.5344 q^{52} +12.1009 q^{53} +2.60707 q^{54} -13.6670 q^{55} -1.95363 q^{56} -5.75949 q^{57} -10.3216 q^{58} -3.20680 q^{59} -18.2205 q^{60} -10.5338 q^{61} -24.2827 q^{62} +0.267933 q^{63} +7.14707 q^{64} -9.13376 q^{65} -9.38038 q^{66} +8.82801 q^{67} +19.5134 q^{68} -8.77446 q^{69} -2.65329 q^{70} -11.4169 q^{71} -7.29150 q^{72} +13.4256 q^{73} +15.6207 q^{74} -9.42821 q^{75} +27.6272 q^{76} -0.964036 q^{77} -6.26897 q^{78} -12.8664 q^{79} +35.7655 q^{80} +1.00000 q^{81} -19.1837 q^{82} +5.32736 q^{83} -1.28523 q^{84} +15.4520 q^{85} -17.4723 q^{86} -3.95909 q^{87} +26.2352 q^{88} -3.00869 q^{89} -9.90282 q^{90} -0.644272 q^{91} +42.0895 q^{92} -9.31418 q^{93} -6.63678 q^{94} +21.8771 q^{95} +9.96472 q^{96} -9.03564 q^{97} +18.0623 q^{98} -3.59805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60707 −1.84348 −0.921739 0.387812i \(-0.873231\pi\)
−0.921739 + 0.387812i \(0.873231\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.79682 2.39841
\(5\) 3.79845 1.69872 0.849359 0.527816i \(-0.176989\pi\)
0.849359 + 0.527816i \(0.176989\pi\)
\(6\) 2.60707 1.06433
\(7\) 0.267933 0.101269 0.0506346 0.998717i \(-0.483876\pi\)
0.0506346 + 0.998717i \(0.483876\pi\)
\(8\) −7.29150 −2.57794
\(9\) 1.00000 0.333333
\(10\) −9.90282 −3.13155
\(11\) −3.59805 −1.08485 −0.542427 0.840103i \(-0.682494\pi\)
−0.542427 + 0.840103i \(0.682494\pi\)
\(12\) −4.79682 −1.38472
\(13\) −2.40460 −0.666917 −0.333458 0.942765i \(-0.608216\pi\)
−0.333458 + 0.942765i \(0.608216\pi\)
\(14\) −0.698520 −0.186687
\(15\) −3.79845 −0.980755
\(16\) 9.41582 2.35396
\(17\) 4.06799 0.986632 0.493316 0.869850i \(-0.335785\pi\)
0.493316 + 0.869850i \(0.335785\pi\)
\(18\) −2.60707 −0.614492
\(19\) 5.75949 1.32132 0.660659 0.750686i \(-0.270277\pi\)
0.660659 + 0.750686i \(0.270277\pi\)
\(20\) 18.2205 4.07422
\(21\) −0.267933 −0.0584677
\(22\) 9.38038 1.99990
\(23\) 8.77446 1.82960 0.914800 0.403906i \(-0.132348\pi\)
0.914800 + 0.403906i \(0.132348\pi\)
\(24\) 7.29150 1.48837
\(25\) 9.42821 1.88564
\(26\) 6.26897 1.22945
\(27\) −1.00000 −0.192450
\(28\) 1.28523 0.242885
\(29\) 3.95909 0.735185 0.367592 0.929987i \(-0.380182\pi\)
0.367592 + 0.929987i \(0.380182\pi\)
\(30\) 9.90282 1.80800
\(31\) 9.31418 1.67288 0.836438 0.548061i \(-0.184634\pi\)
0.836438 + 0.548061i \(0.184634\pi\)
\(32\) −9.96472 −1.76153
\(33\) 3.59805 0.626340
\(34\) −10.6055 −1.81883
\(35\) 1.01773 0.172028
\(36\) 4.79682 0.799470
\(37\) −5.99166 −0.985024 −0.492512 0.870306i \(-0.663921\pi\)
−0.492512 + 0.870306i \(0.663921\pi\)
\(38\) −15.0154 −2.43582
\(39\) 2.40460 0.385045
\(40\) −27.6964 −4.37918
\(41\) 7.35835 1.14918 0.574591 0.818441i \(-0.305161\pi\)
0.574591 + 0.818441i \(0.305161\pi\)
\(42\) 0.698520 0.107784
\(43\) 6.70189 1.02203 0.511015 0.859572i \(-0.329270\pi\)
0.511015 + 0.859572i \(0.329270\pi\)
\(44\) −17.2592 −2.60192
\(45\) 3.79845 0.566239
\(46\) −22.8756 −3.37283
\(47\) 2.54569 0.371326 0.185663 0.982613i \(-0.440557\pi\)
0.185663 + 0.982613i \(0.440557\pi\)
\(48\) −9.41582 −1.35906
\(49\) −6.92821 −0.989745
\(50\) −24.5800 −3.47614
\(51\) −4.06799 −0.569632
\(52\) −11.5344 −1.59954
\(53\) 12.1009 1.66219 0.831095 0.556130i \(-0.187714\pi\)
0.831095 + 0.556130i \(0.187714\pi\)
\(54\) 2.60707 0.354777
\(55\) −13.6670 −1.84286
\(56\) −1.95363 −0.261065
\(57\) −5.75949 −0.762863
\(58\) −10.3216 −1.35530
\(59\) −3.20680 −0.417490 −0.208745 0.977970i \(-0.566938\pi\)
−0.208745 + 0.977970i \(0.566938\pi\)
\(60\) −18.2205 −2.35225
\(61\) −10.5338 −1.34871 −0.674356 0.738406i \(-0.735579\pi\)
−0.674356 + 0.738406i \(0.735579\pi\)
\(62\) −24.2827 −3.08391
\(63\) 0.267933 0.0337564
\(64\) 7.14707 0.893384
\(65\) −9.13376 −1.13290
\(66\) −9.38038 −1.15464
\(67\) 8.82801 1.07851 0.539257 0.842141i \(-0.318705\pi\)
0.539257 + 0.842141i \(0.318705\pi\)
\(68\) 19.5134 2.36635
\(69\) −8.77446 −1.05632
\(70\) −2.65329 −0.317129
\(71\) −11.4169 −1.35494 −0.677469 0.735551i \(-0.736923\pi\)
−0.677469 + 0.735551i \(0.736923\pi\)
\(72\) −7.29150 −0.859312
\(73\) 13.4256 1.57135 0.785673 0.618642i \(-0.212317\pi\)
0.785673 + 0.618642i \(0.212317\pi\)
\(74\) 15.6207 1.81587
\(75\) −9.42821 −1.08868
\(76\) 27.6272 3.16906
\(77\) −0.964036 −0.109862
\(78\) −6.26897 −0.709821
\(79\) −12.8664 −1.44759 −0.723793 0.690017i \(-0.757603\pi\)
−0.723793 + 0.690017i \(0.757603\pi\)
\(80\) 35.7655 3.99871
\(81\) 1.00000 0.111111
\(82\) −19.1837 −2.11849
\(83\) 5.32736 0.584754 0.292377 0.956303i \(-0.405554\pi\)
0.292377 + 0.956303i \(0.405554\pi\)
\(84\) −1.28523 −0.140230
\(85\) 15.4520 1.67601
\(86\) −17.4723 −1.88409
\(87\) −3.95909 −0.424459
\(88\) 26.2352 2.79668
\(89\) −3.00869 −0.318920 −0.159460 0.987204i \(-0.550975\pi\)
−0.159460 + 0.987204i \(0.550975\pi\)
\(90\) −9.90282 −1.04385
\(91\) −0.644272 −0.0675381
\(92\) 42.0895 4.38813
\(93\) −9.31418 −0.965836
\(94\) −6.63678 −0.684532
\(95\) 21.8771 2.24454
\(96\) 9.96472 1.01702
\(97\) −9.03564 −0.917430 −0.458715 0.888583i \(-0.651690\pi\)
−0.458715 + 0.888583i \(0.651690\pi\)
\(98\) 18.0623 1.82457
\(99\) −3.59805 −0.361618
\(100\) 45.2254 4.52254
\(101\) 4.46532 0.444316 0.222158 0.975011i \(-0.428690\pi\)
0.222158 + 0.975011i \(0.428690\pi\)
\(102\) 10.6055 1.05010
\(103\) −4.48598 −0.442017 −0.221008 0.975272i \(-0.570935\pi\)
−0.221008 + 0.975272i \(0.570935\pi\)
\(104\) 17.5332 1.71927
\(105\) −1.01773 −0.0993202
\(106\) −31.5480 −3.06421
\(107\) −3.59497 −0.347539 −0.173769 0.984786i \(-0.555595\pi\)
−0.173769 + 0.984786i \(0.555595\pi\)
\(108\) −4.79682 −0.461574
\(109\) −11.9929 −1.14871 −0.574355 0.818607i \(-0.694747\pi\)
−0.574355 + 0.818607i \(0.694747\pi\)
\(110\) 35.6309 3.39727
\(111\) 5.99166 0.568704
\(112\) 2.52281 0.238383
\(113\) −15.7023 −1.47715 −0.738573 0.674173i \(-0.764500\pi\)
−0.738573 + 0.674173i \(0.764500\pi\)
\(114\) 15.0154 1.40632
\(115\) 33.3293 3.10798
\(116\) 18.9910 1.76327
\(117\) −2.40460 −0.222306
\(118\) 8.36036 0.769634
\(119\) 1.08995 0.0999154
\(120\) 27.6964 2.52832
\(121\) 1.94598 0.176907
\(122\) 27.4623 2.48632
\(123\) −7.35835 −0.663480
\(124\) 44.6784 4.01224
\(125\) 16.8203 1.50446
\(126\) −0.698520 −0.0622291
\(127\) 2.24302 0.199036 0.0995180 0.995036i \(-0.468270\pi\)
0.0995180 + 0.995036i \(0.468270\pi\)
\(128\) 1.29651 0.114596
\(129\) −6.70189 −0.590069
\(130\) 23.8124 2.08848
\(131\) 18.5651 1.62204 0.811022 0.585016i \(-0.198912\pi\)
0.811022 + 0.585016i \(0.198912\pi\)
\(132\) 17.2592 1.50222
\(133\) 1.54316 0.133809
\(134\) −23.0153 −1.98822
\(135\) −3.79845 −0.326918
\(136\) −29.6617 −2.54347
\(137\) −21.4624 −1.83366 −0.916830 0.399278i \(-0.869261\pi\)
−0.916830 + 0.399278i \(0.869261\pi\)
\(138\) 22.8756 1.94730
\(139\) −3.50028 −0.296890 −0.148445 0.988921i \(-0.547427\pi\)
−0.148445 + 0.988921i \(0.547427\pi\)
\(140\) 4.88186 0.412593
\(141\) −2.54569 −0.214385
\(142\) 29.7647 2.49780
\(143\) 8.65188 0.723507
\(144\) 9.41582 0.784652
\(145\) 15.0384 1.24887
\(146\) −35.0014 −2.89674
\(147\) 6.92821 0.571429
\(148\) −28.7409 −2.36249
\(149\) 13.5304 1.10845 0.554227 0.832366i \(-0.313014\pi\)
0.554227 + 0.832366i \(0.313014\pi\)
\(150\) 24.5800 2.00695
\(151\) 2.21669 0.180392 0.0901959 0.995924i \(-0.471251\pi\)
0.0901959 + 0.995924i \(0.471251\pi\)
\(152\) −41.9953 −3.40627
\(153\) 4.06799 0.328877
\(154\) 2.51331 0.202528
\(155\) 35.3794 2.84175
\(156\) 11.5344 0.923494
\(157\) −12.7142 −1.01470 −0.507350 0.861740i \(-0.669375\pi\)
−0.507350 + 0.861740i \(0.669375\pi\)
\(158\) 33.5437 2.66859
\(159\) −12.1009 −0.959666
\(160\) −37.8505 −2.99234
\(161\) 2.35097 0.185282
\(162\) −2.60707 −0.204831
\(163\) 6.00276 0.470172 0.235086 0.971975i \(-0.424463\pi\)
0.235086 + 0.971975i \(0.424463\pi\)
\(164\) 35.2967 2.75621
\(165\) 13.6670 1.06398
\(166\) −13.8888 −1.07798
\(167\) 20.8557 1.61386 0.806931 0.590646i \(-0.201127\pi\)
0.806931 + 0.590646i \(0.201127\pi\)
\(168\) 1.95363 0.150726
\(169\) −7.21789 −0.555222
\(170\) −40.2846 −3.08969
\(171\) 5.75949 0.440439
\(172\) 32.1478 2.45124
\(173\) 2.72129 0.206896 0.103448 0.994635i \(-0.467012\pi\)
0.103448 + 0.994635i \(0.467012\pi\)
\(174\) 10.3216 0.782481
\(175\) 2.52613 0.190957
\(176\) −33.8786 −2.55370
\(177\) 3.20680 0.241038
\(178\) 7.84387 0.587923
\(179\) −18.9231 −1.41438 −0.707190 0.707024i \(-0.750037\pi\)
−0.707190 + 0.707024i \(0.750037\pi\)
\(180\) 18.2205 1.35807
\(181\) −14.5059 −1.07821 −0.539107 0.842237i \(-0.681238\pi\)
−0.539107 + 0.842237i \(0.681238\pi\)
\(182\) 1.67966 0.124505
\(183\) 10.5338 0.778679
\(184\) −63.9790 −4.71659
\(185\) −22.7590 −1.67328
\(186\) 24.2827 1.78050
\(187\) −14.6368 −1.07035
\(188\) 12.2112 0.890593
\(189\) −0.267933 −0.0194892
\(190\) −57.0352 −4.13777
\(191\) −12.5931 −0.911208 −0.455604 0.890183i \(-0.650577\pi\)
−0.455604 + 0.890183i \(0.650577\pi\)
\(192\) −7.14707 −0.515796
\(193\) −15.3829 −1.10729 −0.553643 0.832754i \(-0.686763\pi\)
−0.553643 + 0.832754i \(0.686763\pi\)
\(194\) 23.5565 1.69126
\(195\) 9.13376 0.654082
\(196\) −33.2334 −2.37381
\(197\) −3.62152 −0.258023 −0.129011 0.991643i \(-0.541180\pi\)
−0.129011 + 0.991643i \(0.541180\pi\)
\(198\) 9.38038 0.666634
\(199\) −10.1713 −0.721023 −0.360512 0.932755i \(-0.617398\pi\)
−0.360512 + 0.932755i \(0.617398\pi\)
\(200\) −68.7458 −4.86106
\(201\) −8.82801 −0.622680
\(202\) −11.6414 −0.819087
\(203\) 1.06077 0.0744515
\(204\) −19.5134 −1.36621
\(205\) 27.9503 1.95213
\(206\) 11.6953 0.814848
\(207\) 8.77446 0.609867
\(208\) −22.6413 −1.56989
\(209\) −20.7229 −1.43344
\(210\) 2.65329 0.183095
\(211\) −4.30673 −0.296488 −0.148244 0.988951i \(-0.547362\pi\)
−0.148244 + 0.988951i \(0.547362\pi\)
\(212\) 58.0459 3.98661
\(213\) 11.4169 0.782274
\(214\) 9.37234 0.640680
\(215\) 25.4568 1.73614
\(216\) 7.29150 0.496124
\(217\) 2.49558 0.169411
\(218\) 31.2663 2.11762
\(219\) −13.4256 −0.907217
\(220\) −65.5582 −4.41993
\(221\) −9.78189 −0.658001
\(222\) −15.6207 −1.04839
\(223\) 21.8837 1.46544 0.732721 0.680529i \(-0.238250\pi\)
0.732721 + 0.680529i \(0.238250\pi\)
\(224\) −2.66988 −0.178389
\(225\) 9.42821 0.628547
\(226\) 40.9370 2.72309
\(227\) 6.65746 0.441871 0.220935 0.975288i \(-0.429089\pi\)
0.220935 + 0.975288i \(0.429089\pi\)
\(228\) −27.6272 −1.82966
\(229\) 12.3710 0.817497 0.408748 0.912647i \(-0.365965\pi\)
0.408748 + 0.912647i \(0.365965\pi\)
\(230\) −86.8919 −5.72948
\(231\) 0.964036 0.0634289
\(232\) −28.8677 −1.89526
\(233\) −0.436822 −0.0286172 −0.0143086 0.999898i \(-0.504555\pi\)
−0.0143086 + 0.999898i \(0.504555\pi\)
\(234\) 6.26897 0.409815
\(235\) 9.66965 0.630779
\(236\) −15.3825 −1.00131
\(237\) 12.8664 0.835765
\(238\) −2.84157 −0.184192
\(239\) 22.6043 1.46215 0.731075 0.682298i \(-0.239019\pi\)
0.731075 + 0.682298i \(0.239019\pi\)
\(240\) −35.7655 −2.30865
\(241\) −6.62056 −0.426468 −0.213234 0.977001i \(-0.568400\pi\)
−0.213234 + 0.977001i \(0.568400\pi\)
\(242\) −5.07330 −0.326124
\(243\) −1.00000 −0.0641500
\(244\) −50.5286 −3.23476
\(245\) −26.3165 −1.68130
\(246\) 19.1837 1.22311
\(247\) −13.8493 −0.881209
\(248\) −67.9144 −4.31257
\(249\) −5.32736 −0.337608
\(250\) −43.8518 −2.77343
\(251\) 8.28948 0.523227 0.261614 0.965173i \(-0.415745\pi\)
0.261614 + 0.965173i \(0.415745\pi\)
\(252\) 1.28523 0.0809616
\(253\) −31.5710 −1.98485
\(254\) −5.84771 −0.366918
\(255\) −15.4520 −0.967644
\(256\) −17.6742 −1.10464
\(257\) 28.5492 1.78085 0.890424 0.455132i \(-0.150408\pi\)
0.890424 + 0.455132i \(0.150408\pi\)
\(258\) 17.4723 1.08778
\(259\) −1.60536 −0.0997525
\(260\) −43.8130 −2.71717
\(261\) 3.95909 0.245062
\(262\) −48.4006 −2.99020
\(263\) −22.4246 −1.38276 −0.691379 0.722493i \(-0.742996\pi\)
−0.691379 + 0.722493i \(0.742996\pi\)
\(264\) −26.2352 −1.61466
\(265\) 45.9647 2.82359
\(266\) −4.02312 −0.246673
\(267\) 3.00869 0.184129
\(268\) 42.3464 2.58672
\(269\) 19.4430 1.18546 0.592732 0.805400i \(-0.298049\pi\)
0.592732 + 0.805400i \(0.298049\pi\)
\(270\) 9.90282 0.602667
\(271\) −18.4821 −1.12271 −0.561353 0.827577i \(-0.689719\pi\)
−0.561353 + 0.827577i \(0.689719\pi\)
\(272\) 38.3035 2.32249
\(273\) 0.644272 0.0389931
\(274\) 55.9541 3.38031
\(275\) −33.9232 −2.04564
\(276\) −42.0895 −2.53349
\(277\) 14.3715 0.863498 0.431749 0.901994i \(-0.357897\pi\)
0.431749 + 0.901994i \(0.357897\pi\)
\(278\) 9.12548 0.547310
\(279\) 9.31418 0.557626
\(280\) −7.42077 −0.443476
\(281\) 26.1043 1.55725 0.778626 0.627488i \(-0.215917\pi\)
0.778626 + 0.627488i \(0.215917\pi\)
\(282\) 6.63678 0.395215
\(283\) 11.6766 0.694105 0.347052 0.937846i \(-0.387183\pi\)
0.347052 + 0.937846i \(0.387183\pi\)
\(284\) −54.7648 −3.24970
\(285\) −21.8771 −1.29589
\(286\) −22.5561 −1.33377
\(287\) 1.97154 0.116377
\(288\) −9.96472 −0.587177
\(289\) −0.451471 −0.0265571
\(290\) −39.2062 −2.30227
\(291\) 9.03564 0.529678
\(292\) 64.4001 3.76873
\(293\) −7.43455 −0.434331 −0.217166 0.976135i \(-0.569681\pi\)
−0.217166 + 0.976135i \(0.569681\pi\)
\(294\) −18.0623 −1.05342
\(295\) −12.1809 −0.709198
\(296\) 43.6882 2.53933
\(297\) 3.59805 0.208780
\(298\) −35.2747 −2.04341
\(299\) −21.0991 −1.22019
\(300\) −45.2254 −2.61109
\(301\) 1.79566 0.103500
\(302\) −5.77907 −0.332548
\(303\) −4.46532 −0.256526
\(304\) 54.2303 3.11032
\(305\) −40.0120 −2.29108
\(306\) −10.6055 −0.606278
\(307\) −7.28317 −0.415672 −0.207836 0.978164i \(-0.566642\pi\)
−0.207836 + 0.978164i \(0.566642\pi\)
\(308\) −4.62431 −0.263494
\(309\) 4.48598 0.255198
\(310\) −92.2367 −5.23869
\(311\) 29.4235 1.66846 0.834228 0.551420i \(-0.185914\pi\)
0.834228 + 0.551420i \(0.185914\pi\)
\(312\) −17.5332 −0.992620
\(313\) 5.41969 0.306339 0.153170 0.988200i \(-0.451052\pi\)
0.153170 + 0.988200i \(0.451052\pi\)
\(314\) 33.1467 1.87058
\(315\) 1.01773 0.0573425
\(316\) −61.7179 −3.47190
\(317\) −17.7986 −0.999668 −0.499834 0.866121i \(-0.666606\pi\)
−0.499834 + 0.866121i \(0.666606\pi\)
\(318\) 31.5480 1.76912
\(319\) −14.2450 −0.797568
\(320\) 27.1478 1.51761
\(321\) 3.59497 0.200652
\(322\) −6.12913 −0.341563
\(323\) 23.4295 1.30365
\(324\) 4.79682 0.266490
\(325\) −22.6711 −1.25757
\(326\) −15.6496 −0.866752
\(327\) 11.9929 0.663208
\(328\) −53.6534 −2.96251
\(329\) 0.682073 0.0376039
\(330\) −35.6309 −1.96141
\(331\) −15.2761 −0.839648 −0.419824 0.907605i \(-0.637908\pi\)
−0.419824 + 0.907605i \(0.637908\pi\)
\(332\) 25.5544 1.40248
\(333\) −5.99166 −0.328341
\(334\) −54.3722 −2.97512
\(335\) 33.5328 1.83209
\(336\) −2.52281 −0.137631
\(337\) 11.5829 0.630962 0.315481 0.948932i \(-0.397834\pi\)
0.315481 + 0.948932i \(0.397834\pi\)
\(338\) 18.8175 1.02354
\(339\) 15.7023 0.852831
\(340\) 74.1206 4.01976
\(341\) −33.5129 −1.81483
\(342\) −15.0154 −0.811939
\(343\) −3.73183 −0.201500
\(344\) −48.8669 −2.63472
\(345\) −33.3293 −1.79439
\(346\) −7.09460 −0.381408
\(347\) 34.6954 1.86255 0.931273 0.364323i \(-0.118700\pi\)
0.931273 + 0.364323i \(0.118700\pi\)
\(348\) −18.9910 −1.01803
\(349\) −3.01573 −0.161428 −0.0807141 0.996737i \(-0.525720\pi\)
−0.0807141 + 0.996737i \(0.525720\pi\)
\(350\) −6.58579 −0.352025
\(351\) 2.40460 0.128348
\(352\) 35.8536 1.91100
\(353\) 16.4090 0.873364 0.436682 0.899616i \(-0.356153\pi\)
0.436682 + 0.899616i \(0.356153\pi\)
\(354\) −8.36036 −0.444348
\(355\) −43.3666 −2.30166
\(356\) −14.4321 −0.764901
\(357\) −1.08995 −0.0576862
\(358\) 49.3339 2.60738
\(359\) −20.2348 −1.06795 −0.533975 0.845500i \(-0.679302\pi\)
−0.533975 + 0.845500i \(0.679302\pi\)
\(360\) −27.6964 −1.45973
\(361\) 14.1717 0.745879
\(362\) 37.8179 1.98766
\(363\) −1.94598 −0.102137
\(364\) −3.09046 −0.161984
\(365\) 50.9964 2.66927
\(366\) −27.4623 −1.43548
\(367\) −3.71559 −0.193952 −0.0969760 0.995287i \(-0.530917\pi\)
−0.0969760 + 0.995287i \(0.530917\pi\)
\(368\) 82.6188 4.30680
\(369\) 7.35835 0.383060
\(370\) 59.3344 3.08465
\(371\) 3.24224 0.168329
\(372\) −44.6784 −2.31647
\(373\) −8.11999 −0.420437 −0.210219 0.977654i \(-0.567418\pi\)
−0.210219 + 0.977654i \(0.567418\pi\)
\(374\) 38.1593 1.97317
\(375\) −16.8203 −0.868598
\(376\) −18.5619 −0.957255
\(377\) −9.52004 −0.490307
\(378\) 0.698520 0.0359280
\(379\) 25.9500 1.33296 0.666482 0.745521i \(-0.267799\pi\)
0.666482 + 0.745521i \(0.267799\pi\)
\(380\) 104.941 5.38334
\(381\) −2.24302 −0.114913
\(382\) 32.8312 1.67979
\(383\) −0.169806 −0.00867666 −0.00433833 0.999991i \(-0.501381\pi\)
−0.00433833 + 0.999991i \(0.501381\pi\)
\(384\) −1.29651 −0.0661622
\(385\) −3.66184 −0.186625
\(386\) 40.1043 2.04126
\(387\) 6.70189 0.340676
\(388\) −43.3423 −2.20037
\(389\) 19.0406 0.965397 0.482698 0.875787i \(-0.339657\pi\)
0.482698 + 0.875787i \(0.339657\pi\)
\(390\) −23.8124 −1.20579
\(391\) 35.6944 1.80514
\(392\) 50.5171 2.55150
\(393\) −18.5651 −0.936488
\(394\) 9.44156 0.475659
\(395\) −48.8725 −2.45904
\(396\) −17.2592 −0.867307
\(397\) 24.6932 1.23931 0.619657 0.784872i \(-0.287272\pi\)
0.619657 + 0.784872i \(0.287272\pi\)
\(398\) 26.5173 1.32919
\(399\) −1.54316 −0.0772544
\(400\) 88.7744 4.43872
\(401\) −6.38350 −0.318777 −0.159388 0.987216i \(-0.550952\pi\)
−0.159388 + 0.987216i \(0.550952\pi\)
\(402\) 23.0153 1.14790
\(403\) −22.3969 −1.11567
\(404\) 21.4193 1.06565
\(405\) 3.79845 0.188746
\(406\) −2.76550 −0.137250
\(407\) 21.5583 1.06861
\(408\) 29.6617 1.46848
\(409\) −7.73191 −0.382318 −0.191159 0.981559i \(-0.561225\pi\)
−0.191159 + 0.981559i \(0.561225\pi\)
\(410\) −72.8684 −3.59872
\(411\) 21.4624 1.05866
\(412\) −21.5184 −1.06014
\(413\) −0.859208 −0.0422789
\(414\) −22.8756 −1.12428
\(415\) 20.2357 0.993332
\(416\) 23.9612 1.17479
\(417\) 3.50028 0.171410
\(418\) 54.0262 2.64251
\(419\) −10.7078 −0.523112 −0.261556 0.965188i \(-0.584236\pi\)
−0.261556 + 0.965188i \(0.584236\pi\)
\(420\) −4.88186 −0.238210
\(421\) −7.22015 −0.351889 −0.175944 0.984400i \(-0.556298\pi\)
−0.175944 + 0.984400i \(0.556298\pi\)
\(422\) 11.2280 0.546569
\(423\) 2.54569 0.123775
\(424\) −88.2339 −4.28502
\(425\) 38.3538 1.86043
\(426\) −29.7647 −1.44210
\(427\) −2.82235 −0.136583
\(428\) −17.2444 −0.833540
\(429\) −8.65188 −0.417717
\(430\) −66.3677 −3.20053
\(431\) 22.6822 1.09256 0.546282 0.837601i \(-0.316043\pi\)
0.546282 + 0.837601i \(0.316043\pi\)
\(432\) −9.41582 −0.453019
\(433\) −30.7398 −1.47726 −0.738630 0.674111i \(-0.764527\pi\)
−0.738630 + 0.674111i \(0.764527\pi\)
\(434\) −6.50614 −0.312305
\(435\) −15.0384 −0.721036
\(436\) −57.5276 −2.75507
\(437\) 50.5364 2.41748
\(438\) 35.0014 1.67243
\(439\) −18.8919 −0.901662 −0.450831 0.892609i \(-0.648872\pi\)
−0.450831 + 0.892609i \(0.648872\pi\)
\(440\) 99.6530 4.75077
\(441\) −6.92821 −0.329915
\(442\) 25.5021 1.21301
\(443\) 12.2912 0.583973 0.291986 0.956422i \(-0.405684\pi\)
0.291986 + 0.956422i \(0.405684\pi\)
\(444\) 28.7409 1.36398
\(445\) −11.4283 −0.541756
\(446\) −57.0524 −2.70151
\(447\) −13.5304 −0.639966
\(448\) 1.91494 0.0904722
\(449\) −1.87592 −0.0885303 −0.0442651 0.999020i \(-0.514095\pi\)
−0.0442651 + 0.999020i \(0.514095\pi\)
\(450\) −24.5800 −1.15871
\(451\) −26.4757 −1.24669
\(452\) −75.3210 −3.54280
\(453\) −2.21669 −0.104149
\(454\) −17.3565 −0.814579
\(455\) −2.44723 −0.114728
\(456\) 41.9953 1.96661
\(457\) 41.9744 1.96348 0.981739 0.190232i \(-0.0609241\pi\)
0.981739 + 0.190232i \(0.0609241\pi\)
\(458\) −32.2520 −1.50704
\(459\) −4.06799 −0.189877
\(460\) 159.875 7.45420
\(461\) −6.42824 −0.299393 −0.149696 0.988732i \(-0.547830\pi\)
−0.149696 + 0.988732i \(0.547830\pi\)
\(462\) −2.51331 −0.116930
\(463\) 28.0027 1.30140 0.650699 0.759336i \(-0.274476\pi\)
0.650699 + 0.759336i \(0.274476\pi\)
\(464\) 37.2781 1.73059
\(465\) −35.3794 −1.64068
\(466\) 1.13883 0.0527551
\(467\) 5.52032 0.255450 0.127725 0.991810i \(-0.459233\pi\)
0.127725 + 0.991810i \(0.459233\pi\)
\(468\) −11.5344 −0.533180
\(469\) 2.36531 0.109220
\(470\) −25.2095 −1.16283
\(471\) 12.7142 0.585837
\(472\) 23.3824 1.07626
\(473\) −24.1138 −1.10875
\(474\) −33.5437 −1.54071
\(475\) 54.3017 2.49153
\(476\) 5.22828 0.239638
\(477\) 12.1009 0.554063
\(478\) −58.9310 −2.69544
\(479\) 17.1502 0.783615 0.391807 0.920047i \(-0.371850\pi\)
0.391807 + 0.920047i \(0.371850\pi\)
\(480\) 37.8505 1.72763
\(481\) 14.4076 0.656929
\(482\) 17.2603 0.786184
\(483\) −2.35097 −0.106973
\(484\) 9.33449 0.424295
\(485\) −34.3214 −1.55845
\(486\) 2.60707 0.118259
\(487\) −31.6438 −1.43392 −0.716959 0.697116i \(-0.754466\pi\)
−0.716959 + 0.697116i \(0.754466\pi\)
\(488\) 76.8071 3.47689
\(489\) −6.00276 −0.271454
\(490\) 68.6089 3.09943
\(491\) −9.26008 −0.417901 −0.208951 0.977926i \(-0.567005\pi\)
−0.208951 + 0.977926i \(0.567005\pi\)
\(492\) −35.2967 −1.59130
\(493\) 16.1055 0.725357
\(494\) 36.1061 1.62449
\(495\) −13.6670 −0.614287
\(496\) 87.7007 3.93788
\(497\) −3.05897 −0.137213
\(498\) 13.8888 0.622372
\(499\) −19.1263 −0.856212 −0.428106 0.903729i \(-0.640819\pi\)
−0.428106 + 0.903729i \(0.640819\pi\)
\(500\) 80.6840 3.60830
\(501\) −20.8557 −0.931763
\(502\) −21.6113 −0.964557
\(503\) 41.0482 1.83025 0.915125 0.403171i \(-0.132092\pi\)
0.915125 + 0.403171i \(0.132092\pi\)
\(504\) −1.95363 −0.0870217
\(505\) 16.9613 0.754768
\(506\) 82.3077 3.65902
\(507\) 7.21789 0.320558
\(508\) 10.7594 0.477369
\(509\) −18.8554 −0.835752 −0.417876 0.908504i \(-0.637225\pi\)
−0.417876 + 0.908504i \(0.637225\pi\)
\(510\) 40.2846 1.78383
\(511\) 3.59716 0.159129
\(512\) 43.4850 1.92178
\(513\) −5.75949 −0.254288
\(514\) −74.4297 −3.28295
\(515\) −17.0398 −0.750861
\(516\) −32.1478 −1.41523
\(517\) −9.15951 −0.402835
\(518\) 4.18530 0.183891
\(519\) −2.72129 −0.119451
\(520\) 66.5988 2.92055
\(521\) 18.0923 0.792638 0.396319 0.918113i \(-0.370287\pi\)
0.396319 + 0.918113i \(0.370287\pi\)
\(522\) −10.3216 −0.451765
\(523\) −4.96337 −0.217033 −0.108517 0.994095i \(-0.534610\pi\)
−0.108517 + 0.994095i \(0.534610\pi\)
\(524\) 89.0536 3.89032
\(525\) −2.52613 −0.110249
\(526\) 58.4624 2.54908
\(527\) 37.8900 1.65051
\(528\) 33.8786 1.47438
\(529\) 53.9911 2.34744
\(530\) −119.833 −5.20523
\(531\) −3.20680 −0.139163
\(532\) 7.40224 0.320928
\(533\) −17.6939 −0.766408
\(534\) −7.84387 −0.339437
\(535\) −13.6553 −0.590370
\(536\) −64.3695 −2.78034
\(537\) 18.9231 0.816592
\(538\) −50.6894 −2.18538
\(539\) 24.9281 1.07373
\(540\) −18.2205 −0.784084
\(541\) −1.21030 −0.0520350 −0.0260175 0.999661i \(-0.508283\pi\)
−0.0260175 + 0.999661i \(0.508283\pi\)
\(542\) 48.1841 2.06968
\(543\) 14.5059 0.622507
\(544\) −40.5364 −1.73798
\(545\) −45.5543 −1.95133
\(546\) −1.67966 −0.0718829
\(547\) 36.3222 1.55303 0.776513 0.630102i \(-0.216987\pi\)
0.776513 + 0.630102i \(0.216987\pi\)
\(548\) −102.951 −4.39787
\(549\) −10.5338 −0.449571
\(550\) 88.4401 3.77110
\(551\) 22.8023 0.971412
\(552\) 63.9790 2.72313
\(553\) −3.44734 −0.146596
\(554\) −37.4674 −1.59184
\(555\) 22.7590 0.966067
\(556\) −16.7902 −0.712064
\(557\) −33.6971 −1.42779 −0.713896 0.700252i \(-0.753071\pi\)
−0.713896 + 0.700252i \(0.753071\pi\)
\(558\) −24.2827 −1.02797
\(559\) −16.1154 −0.681608
\(560\) 9.58276 0.404945
\(561\) 14.6368 0.617968
\(562\) −68.0558 −2.87076
\(563\) −2.14572 −0.0904314 −0.0452157 0.998977i \(-0.514398\pi\)
−0.0452157 + 0.998977i \(0.514398\pi\)
\(564\) −12.2112 −0.514184
\(565\) −59.6443 −2.50926
\(566\) −30.4418 −1.27957
\(567\) 0.267933 0.0112521
\(568\) 83.2464 3.49294
\(569\) −43.5427 −1.82541 −0.912703 0.408624i \(-0.866009\pi\)
−0.912703 + 0.408624i \(0.866009\pi\)
\(570\) 57.0352 2.38894
\(571\) −20.2154 −0.845990 −0.422995 0.906132i \(-0.639021\pi\)
−0.422995 + 0.906132i \(0.639021\pi\)
\(572\) 41.5015 1.73527
\(573\) 12.5931 0.526086
\(574\) −5.13995 −0.214538
\(575\) 82.7274 3.44997
\(576\) 7.14707 0.297795
\(577\) −32.6414 −1.35888 −0.679440 0.733731i \(-0.737777\pi\)
−0.679440 + 0.733731i \(0.737777\pi\)
\(578\) 1.17702 0.0489575
\(579\) 15.3829 0.639292
\(580\) 72.1365 2.99530
\(581\) 1.42738 0.0592175
\(582\) −23.5565 −0.976450
\(583\) −43.5398 −1.80323
\(584\) −97.8927 −4.05083
\(585\) −9.13376 −0.377634
\(586\) 19.3824 0.800680
\(587\) −41.0021 −1.69234 −0.846169 0.532914i \(-0.821097\pi\)
−0.846169 + 0.532914i \(0.821097\pi\)
\(588\) 33.2334 1.37052
\(589\) 53.6449 2.21040
\(590\) 31.7564 1.30739
\(591\) 3.62152 0.148970
\(592\) −56.4165 −2.31870
\(593\) −0.790839 −0.0324759 −0.0162379 0.999868i \(-0.505169\pi\)
−0.0162379 + 0.999868i \(0.505169\pi\)
\(594\) −9.38038 −0.384881
\(595\) 4.14011 0.169728
\(596\) 64.9028 2.65852
\(597\) 10.1713 0.416283
\(598\) 55.0068 2.24940
\(599\) −16.9417 −0.692221 −0.346110 0.938194i \(-0.612498\pi\)
−0.346110 + 0.938194i \(0.612498\pi\)
\(600\) 68.7458 2.80654
\(601\) 18.6504 0.760764 0.380382 0.924829i \(-0.375793\pi\)
0.380382 + 0.924829i \(0.375793\pi\)
\(602\) −4.68141 −0.190800
\(603\) 8.82801 0.359504
\(604\) 10.6331 0.432653
\(605\) 7.39169 0.300515
\(606\) 11.6414 0.472900
\(607\) 45.2381 1.83616 0.918079 0.396396i \(-0.129739\pi\)
0.918079 + 0.396396i \(0.129739\pi\)
\(608\) −57.3917 −2.32754
\(609\) −1.06077 −0.0429846
\(610\) 104.314 4.22356
\(611\) −6.12136 −0.247644
\(612\) 19.5134 0.788782
\(613\) 29.4103 1.18787 0.593936 0.804513i \(-0.297573\pi\)
0.593936 + 0.804513i \(0.297573\pi\)
\(614\) 18.9877 0.766282
\(615\) −27.9503 −1.12707
\(616\) 7.02927 0.283217
\(617\) −39.0511 −1.57214 −0.786069 0.618139i \(-0.787887\pi\)
−0.786069 + 0.618139i \(0.787887\pi\)
\(618\) −11.6953 −0.470452
\(619\) −3.76517 −0.151335 −0.0756674 0.997133i \(-0.524109\pi\)
−0.0756674 + 0.997133i \(0.524109\pi\)
\(620\) 169.709 6.81567
\(621\) −8.77446 −0.352107
\(622\) −76.7092 −3.07576
\(623\) −0.806127 −0.0322968
\(624\) 22.6413 0.906378
\(625\) 16.7501 0.670003
\(626\) −14.1295 −0.564729
\(627\) 20.7229 0.827594
\(628\) −60.9875 −2.43366
\(629\) −24.3740 −0.971856
\(630\) −2.65329 −0.105710
\(631\) 44.9735 1.79037 0.895183 0.445699i \(-0.147045\pi\)
0.895183 + 0.445699i \(0.147045\pi\)
\(632\) 93.8156 3.73178
\(633\) 4.30673 0.171177
\(634\) 46.4021 1.84286
\(635\) 8.52000 0.338106
\(636\) −58.0459 −2.30167
\(637\) 16.6596 0.660077
\(638\) 37.1378 1.47030
\(639\) −11.4169 −0.451646
\(640\) 4.92472 0.194667
\(641\) 13.5355 0.534620 0.267310 0.963611i \(-0.413865\pi\)
0.267310 + 0.963611i \(0.413865\pi\)
\(642\) −9.37234 −0.369897
\(643\) −16.9111 −0.666909 −0.333454 0.942766i \(-0.608214\pi\)
−0.333454 + 0.942766i \(0.608214\pi\)
\(644\) 11.2772 0.444382
\(645\) −25.4568 −1.00236
\(646\) −61.0824 −2.40326
\(647\) −28.3162 −1.11322 −0.556612 0.830773i \(-0.687899\pi\)
−0.556612 + 0.830773i \(0.687899\pi\)
\(648\) −7.29150 −0.286437
\(649\) 11.5382 0.452916
\(650\) 59.1051 2.31829
\(651\) −2.49558 −0.0978093
\(652\) 28.7941 1.12767
\(653\) −34.1458 −1.33623 −0.668114 0.744059i \(-0.732898\pi\)
−0.668114 + 0.744059i \(0.732898\pi\)
\(654\) −31.2663 −1.22261
\(655\) 70.5187 2.75540
\(656\) 69.2849 2.70512
\(657\) 13.4256 0.523782
\(658\) −1.77821 −0.0693219
\(659\) −26.7867 −1.04346 −0.521730 0.853111i \(-0.674713\pi\)
−0.521730 + 0.853111i \(0.674713\pi\)
\(660\) 65.5582 2.55185
\(661\) −43.3935 −1.68781 −0.843906 0.536491i \(-0.819750\pi\)
−0.843906 + 0.536491i \(0.819750\pi\)
\(662\) 39.8258 1.54787
\(663\) 9.78189 0.379897
\(664\) −38.8445 −1.50746
\(665\) 5.86160 0.227303
\(666\) 15.6207 0.605290
\(667\) 34.7389 1.34509
\(668\) 100.041 3.87070
\(669\) −21.8837 −0.846074
\(670\) −87.4223 −3.37742
\(671\) 37.9011 1.46316
\(672\) 2.66988 0.102993
\(673\) −9.08056 −0.350030 −0.175015 0.984566i \(-0.555997\pi\)
−0.175015 + 0.984566i \(0.555997\pi\)
\(674\) −30.1975 −1.16316
\(675\) −9.42821 −0.362892
\(676\) −34.6229 −1.33165
\(677\) −20.3909 −0.783685 −0.391843 0.920032i \(-0.628162\pi\)
−0.391843 + 0.920032i \(0.628162\pi\)
\(678\) −40.9370 −1.57217
\(679\) −2.42094 −0.0929073
\(680\) −112.669 −4.32064
\(681\) −6.65746 −0.255114
\(682\) 87.3705 3.34559
\(683\) −11.7185 −0.448395 −0.224198 0.974544i \(-0.571976\pi\)
−0.224198 + 0.974544i \(0.571976\pi\)
\(684\) 27.6272 1.05635
\(685\) −81.5239 −3.11487
\(686\) 9.72913 0.371460
\(687\) −12.3710 −0.471982
\(688\) 63.1038 2.40581
\(689\) −29.0979 −1.10854
\(690\) 86.8919 3.30792
\(691\) 40.7391 1.54979 0.774893 0.632092i \(-0.217803\pi\)
0.774893 + 0.632092i \(0.217803\pi\)
\(692\) 13.0535 0.496221
\(693\) −0.964036 −0.0366207
\(694\) −90.4533 −3.43356
\(695\) −13.2956 −0.504332
\(696\) 28.8677 1.09423
\(697\) 29.9337 1.13382
\(698\) 7.86222 0.297589
\(699\) 0.436822 0.0165221
\(700\) 12.1174 0.457994
\(701\) 37.7045 1.42408 0.712040 0.702139i \(-0.247771\pi\)
0.712040 + 0.702139i \(0.247771\pi\)
\(702\) −6.26897 −0.236607
\(703\) −34.5089 −1.30153
\(704\) −25.7155 −0.969191
\(705\) −9.66965 −0.364180
\(706\) −42.7795 −1.61003
\(707\) 1.19641 0.0449955
\(708\) 15.3825 0.578108
\(709\) 1.18775 0.0446071 0.0223035 0.999751i \(-0.492900\pi\)
0.0223035 + 0.999751i \(0.492900\pi\)
\(710\) 113.060 4.24305
\(711\) −12.8664 −0.482529
\(712\) 21.9379 0.822156
\(713\) 81.7269 3.06070
\(714\) 2.84157 0.106343
\(715\) 32.8637 1.22903
\(716\) −90.7707 −3.39226
\(717\) −22.6043 −0.844172
\(718\) 52.7535 1.96874
\(719\) 6.66302 0.248489 0.124244 0.992252i \(-0.460349\pi\)
0.124244 + 0.992252i \(0.460349\pi\)
\(720\) 35.7655 1.33290
\(721\) −1.20194 −0.0447626
\(722\) −36.9466 −1.37501
\(723\) 6.62056 0.246221
\(724\) −69.5821 −2.58600
\(725\) 37.3271 1.38629
\(726\) 5.07330 0.188288
\(727\) 51.3143 1.90314 0.951572 0.307427i \(-0.0994680\pi\)
0.951572 + 0.307427i \(0.0994680\pi\)
\(728\) 4.69771 0.174109
\(729\) 1.00000 0.0370370
\(730\) −132.951 −4.92074
\(731\) 27.2632 1.00837
\(732\) 50.5286 1.86759
\(733\) −16.4742 −0.608489 −0.304244 0.952594i \(-0.598404\pi\)
−0.304244 + 0.952594i \(0.598404\pi\)
\(734\) 9.68679 0.357546
\(735\) 26.3165 0.970697
\(736\) −87.4350 −3.22290
\(737\) −31.7636 −1.17003
\(738\) −19.1837 −0.706163
\(739\) −28.6876 −1.05529 −0.527646 0.849464i \(-0.676925\pi\)
−0.527646 + 0.849464i \(0.676925\pi\)
\(740\) −109.171 −4.01320
\(741\) 13.8493 0.508766
\(742\) −8.45274 −0.310310
\(743\) 19.5452 0.717046 0.358523 0.933521i \(-0.383281\pi\)
0.358523 + 0.933521i \(0.383281\pi\)
\(744\) 67.9144 2.48986
\(745\) 51.3945 1.88295
\(746\) 21.1694 0.775066
\(747\) 5.32736 0.194918
\(748\) −70.2102 −2.56714
\(749\) −0.963211 −0.0351950
\(750\) 43.8518 1.60124
\(751\) 52.6114 1.91982 0.959908 0.280316i \(-0.0904393\pi\)
0.959908 + 0.280316i \(0.0904393\pi\)
\(752\) 23.9697 0.874086
\(753\) −8.28948 −0.302085
\(754\) 24.8194 0.903870
\(755\) 8.41999 0.306435
\(756\) −1.28523 −0.0467432
\(757\) −10.0850 −0.366546 −0.183273 0.983062i \(-0.558669\pi\)
−0.183273 + 0.983062i \(0.558669\pi\)
\(758\) −67.6536 −2.45729
\(759\) 31.5710 1.14595
\(760\) −159.517 −5.78629
\(761\) −15.3482 −0.556372 −0.278186 0.960527i \(-0.589733\pi\)
−0.278186 + 0.960527i \(0.589733\pi\)
\(762\) 5.84771 0.211840
\(763\) −3.21329 −0.116329
\(764\) −60.4070 −2.18545
\(765\) 15.4520 0.558670
\(766\) 0.442695 0.0159952
\(767\) 7.71109 0.278431
\(768\) 17.6742 0.637764
\(769\) 24.1991 0.872643 0.436322 0.899791i \(-0.356281\pi\)
0.436322 + 0.899791i \(0.356281\pi\)
\(770\) 9.54668 0.344039
\(771\) −28.5492 −1.02817
\(772\) −73.7890 −2.65572
\(773\) 10.6841 0.384279 0.192140 0.981368i \(-0.438457\pi\)
0.192140 + 0.981368i \(0.438457\pi\)
\(774\) −17.4723 −0.628029
\(775\) 87.8161 3.15445
\(776\) 65.8834 2.36507
\(777\) 1.60536 0.0575921
\(778\) −49.6402 −1.77969
\(779\) 42.3803 1.51843
\(780\) 43.8130 1.56876
\(781\) 41.0786 1.46991
\(782\) −93.0578 −3.32774
\(783\) −3.95909 −0.141486
\(784\) −65.2348 −2.32982
\(785\) −48.2940 −1.72369
\(786\) 48.4006 1.72639
\(787\) 20.7417 0.739363 0.369682 0.929158i \(-0.379467\pi\)
0.369682 + 0.929158i \(0.379467\pi\)
\(788\) −17.3718 −0.618844
\(789\) 22.4246 0.798335
\(790\) 127.414 4.53319
\(791\) −4.20716 −0.149589
\(792\) 26.2352 0.932227
\(793\) 25.3296 0.899479
\(794\) −64.3768 −2.28465
\(795\) −45.9647 −1.63020
\(796\) −48.7898 −1.72931
\(797\) 4.81693 0.170624 0.0853122 0.996354i \(-0.472811\pi\)
0.0853122 + 0.996354i \(0.472811\pi\)
\(798\) 4.02312 0.142417
\(799\) 10.3558 0.366363
\(800\) −93.9494 −3.32161
\(801\) −3.00869 −0.106307
\(802\) 16.6422 0.587658
\(803\) −48.3059 −1.70468
\(804\) −42.3464 −1.49344
\(805\) 8.93002 0.314742
\(806\) 58.3903 2.05671
\(807\) −19.4430 −0.684428
\(808\) −32.5589 −1.14542
\(809\) 5.68949 0.200032 0.100016 0.994986i \(-0.468111\pi\)
0.100016 + 0.994986i \(0.468111\pi\)
\(810\) −9.90282 −0.347950
\(811\) −31.3160 −1.09965 −0.549827 0.835279i \(-0.685306\pi\)
−0.549827 + 0.835279i \(0.685306\pi\)
\(812\) 5.08832 0.178565
\(813\) 18.4821 0.648194
\(814\) −56.2041 −1.96995
\(815\) 22.8012 0.798690
\(816\) −38.3035 −1.34089
\(817\) 38.5995 1.35042
\(818\) 20.1576 0.704795
\(819\) −0.644272 −0.0225127
\(820\) 134.073 4.68202
\(821\) −12.6840 −0.442675 −0.221338 0.975197i \(-0.571042\pi\)
−0.221338 + 0.975197i \(0.571042\pi\)
\(822\) −55.9541 −1.95162
\(823\) 33.1041 1.15394 0.576968 0.816767i \(-0.304236\pi\)
0.576968 + 0.816767i \(0.304236\pi\)
\(824\) 32.7095 1.13949
\(825\) 33.9232 1.18105
\(826\) 2.24002 0.0779401
\(827\) 41.8492 1.45524 0.727620 0.685980i \(-0.240626\pi\)
0.727620 + 0.685980i \(0.240626\pi\)
\(828\) 42.0895 1.46271
\(829\) 0.0492245 0.00170964 0.000854819 1.00000i \(-0.499728\pi\)
0.000854819 1.00000i \(0.499728\pi\)
\(830\) −52.7559 −1.83118
\(831\) −14.3715 −0.498541
\(832\) −17.1859 −0.595813
\(833\) −28.1839 −0.976514
\(834\) −9.12548 −0.315990
\(835\) 79.2192 2.74149
\(836\) −99.4041 −3.43796
\(837\) −9.31418 −0.321945
\(838\) 27.9161 0.964344
\(839\) −3.31470 −0.114436 −0.0572181 0.998362i \(-0.518223\pi\)
−0.0572181 + 0.998362i \(0.518223\pi\)
\(840\) 7.42077 0.256041
\(841\) −13.3256 −0.459504
\(842\) 18.8234 0.648699
\(843\) −26.1043 −0.899080
\(844\) −20.6586 −0.711099
\(845\) −27.4168 −0.943166
\(846\) −6.63678 −0.228177
\(847\) 0.521391 0.0179152
\(848\) 113.940 3.91272
\(849\) −11.6766 −0.400741
\(850\) −99.9912 −3.42967
\(851\) −52.5736 −1.80220
\(852\) 54.7648 1.87621
\(853\) −30.4858 −1.04381 −0.521907 0.853002i \(-0.674779\pi\)
−0.521907 + 0.853002i \(0.674779\pi\)
\(854\) 7.35806 0.251787
\(855\) 21.8771 0.748182
\(856\) 26.2127 0.895933
\(857\) 30.6216 1.04602 0.523008 0.852328i \(-0.324810\pi\)
0.523008 + 0.852328i \(0.324810\pi\)
\(858\) 22.5561 0.770052
\(859\) 9.02237 0.307839 0.153920 0.988083i \(-0.450810\pi\)
0.153920 + 0.988083i \(0.450810\pi\)
\(860\) 122.112 4.16397
\(861\) −1.97154 −0.0671900
\(862\) −59.1342 −2.01412
\(863\) −5.08874 −0.173223 −0.0866113 0.996242i \(-0.527604\pi\)
−0.0866113 + 0.996242i \(0.527604\pi\)
\(864\) 9.96472 0.339007
\(865\) 10.3367 0.351458
\(866\) 80.1408 2.72330
\(867\) 0.451471 0.0153328
\(868\) 11.9708 0.406316
\(869\) 46.2941 1.57042
\(870\) 39.2062 1.32921
\(871\) −21.2279 −0.719279
\(872\) 87.4461 2.96130
\(873\) −9.03564 −0.305810
\(874\) −131.752 −4.45658
\(875\) 4.50672 0.152355
\(876\) −64.4001 −2.17588
\(877\) −17.0757 −0.576607 −0.288304 0.957539i \(-0.593091\pi\)
−0.288304 + 0.957539i \(0.593091\pi\)
\(878\) 49.2526 1.66219
\(879\) 7.43455 0.250761
\(880\) −128.686 −4.33801
\(881\) −15.4514 −0.520572 −0.260286 0.965532i \(-0.583817\pi\)
−0.260286 + 0.965532i \(0.583817\pi\)
\(882\) 18.0623 0.608191
\(883\) 12.5842 0.423493 0.211746 0.977325i \(-0.432085\pi\)
0.211746 + 0.977325i \(0.432085\pi\)
\(884\) −46.9220 −1.57816
\(885\) 12.1809 0.409456
\(886\) −32.0440 −1.07654
\(887\) 46.3542 1.55642 0.778212 0.628002i \(-0.216127\pi\)
0.778212 + 0.628002i \(0.216127\pi\)
\(888\) −43.6882 −1.46608
\(889\) 0.600979 0.0201562
\(890\) 29.7945 0.998714
\(891\) −3.59805 −0.120539
\(892\) 104.972 3.51473
\(893\) 14.6618 0.490640
\(894\) 35.2747 1.17976
\(895\) −71.8784 −2.40263
\(896\) 0.347378 0.0116051
\(897\) 21.0991 0.704478
\(898\) 4.89066 0.163204
\(899\) 36.8757 1.22987
\(900\) 45.2254 1.50751
\(901\) 49.2264 1.63997
\(902\) 69.0241 2.29825
\(903\) −1.79566 −0.0597557
\(904\) 114.493 3.80799
\(905\) −55.0998 −1.83158
\(906\) 5.77907 0.191997
\(907\) 13.1600 0.436970 0.218485 0.975840i \(-0.429889\pi\)
0.218485 + 0.975840i \(0.429889\pi\)
\(908\) 31.9346 1.05979
\(909\) 4.46532 0.148105
\(910\) 6.38011 0.211499
\(911\) 1.05810 0.0350566 0.0175283 0.999846i \(-0.494420\pi\)
0.0175283 + 0.999846i \(0.494420\pi\)
\(912\) −54.2303 −1.79575
\(913\) −19.1681 −0.634372
\(914\) −109.430 −3.61963
\(915\) 40.0120 1.32276
\(916\) 59.3413 1.96069
\(917\) 4.97421 0.164263
\(918\) 10.6055 0.350035
\(919\) −20.6586 −0.681465 −0.340733 0.940160i \(-0.610675\pi\)
−0.340733 + 0.940160i \(0.610675\pi\)
\(920\) −243.021 −8.01216
\(921\) 7.28317 0.239988
\(922\) 16.7589 0.551924
\(923\) 27.4531 0.903631
\(924\) 4.62431 0.152129
\(925\) −56.4907 −1.85740
\(926\) −73.0051 −2.39910
\(927\) −4.48598 −0.147339
\(928\) −39.4512 −1.29505
\(929\) 7.81780 0.256494 0.128247 0.991742i \(-0.459065\pi\)
0.128247 + 0.991742i \(0.459065\pi\)
\(930\) 92.2367 3.02456
\(931\) −39.9030 −1.30777
\(932\) −2.09536 −0.0686356
\(933\) −29.4235 −0.963283
\(934\) −14.3919 −0.470916
\(935\) −55.5972 −1.81822
\(936\) 17.5332 0.573089
\(937\) 13.1949 0.431057 0.215529 0.976498i \(-0.430853\pi\)
0.215529 + 0.976498i \(0.430853\pi\)
\(938\) −6.16654 −0.201345
\(939\) −5.41969 −0.176865
\(940\) 46.3836 1.51287
\(941\) −30.0295 −0.978933 −0.489467 0.872022i \(-0.662808\pi\)
−0.489467 + 0.872022i \(0.662808\pi\)
\(942\) −33.1467 −1.07998
\(943\) 64.5655 2.10254
\(944\) −30.1947 −0.982754
\(945\) −1.01773 −0.0331067
\(946\) 62.8663 2.04396
\(947\) −30.5887 −0.994000 −0.497000 0.867751i \(-0.665565\pi\)
−0.497000 + 0.867751i \(0.665565\pi\)
\(948\) 61.7179 2.00451
\(949\) −32.2832 −1.04796
\(950\) −141.568 −4.59308
\(951\) 17.7986 0.577158
\(952\) −7.94736 −0.257575
\(953\) 11.6434 0.377168 0.188584 0.982057i \(-0.439610\pi\)
0.188584 + 0.982057i \(0.439610\pi\)
\(954\) −31.5480 −1.02140
\(955\) −47.8344 −1.54788
\(956\) 108.429 3.50683
\(957\) 14.2450 0.460476
\(958\) −44.7119 −1.44458
\(959\) −5.75049 −0.185693
\(960\) −27.1478 −0.876191
\(961\) 55.7540 1.79852
\(962\) −37.5616 −1.21103
\(963\) −3.59497 −0.115846
\(964\) −31.7576 −1.02284
\(965\) −58.4312 −1.88097
\(966\) 6.12913 0.197202
\(967\) 7.65412 0.246140 0.123070 0.992398i \(-0.460726\pi\)
0.123070 + 0.992398i \(0.460726\pi\)
\(968\) −14.1891 −0.456055
\(969\) −23.4295 −0.752665
\(970\) 89.4783 2.87298
\(971\) −30.5790 −0.981327 −0.490664 0.871349i \(-0.663246\pi\)
−0.490664 + 0.871349i \(0.663246\pi\)
\(972\) −4.79682 −0.153858
\(973\) −0.937841 −0.0300658
\(974\) 82.4976 2.64339
\(975\) 22.6711 0.726056
\(976\) −99.1842 −3.17481
\(977\) −50.2007 −1.60606 −0.803031 0.595937i \(-0.796781\pi\)
−0.803031 + 0.595937i \(0.796781\pi\)
\(978\) 15.6496 0.500420
\(979\) 10.8254 0.345982
\(980\) −126.235 −4.03244
\(981\) −11.9929 −0.382903
\(982\) 24.1417 0.770392
\(983\) 13.9497 0.444925 0.222463 0.974941i \(-0.428590\pi\)
0.222463 + 0.974941i \(0.428590\pi\)
\(984\) 53.6534 1.71041
\(985\) −13.7562 −0.438308
\(986\) −41.9883 −1.33718
\(987\) −0.682073 −0.0217106
\(988\) −66.4325 −2.11350
\(989\) 58.8055 1.86991
\(990\) 35.6309 1.13242
\(991\) −27.3164 −0.867733 −0.433866 0.900977i \(-0.642851\pi\)
−0.433866 + 0.900977i \(0.642851\pi\)
\(992\) −92.8132 −2.94682
\(993\) 15.2761 0.484771
\(994\) 7.97494 0.252950
\(995\) −38.6351 −1.22482
\(996\) −25.5544 −0.809722
\(997\) 45.8837 1.45315 0.726576 0.687087i \(-0.241111\pi\)
0.726576 + 0.687087i \(0.241111\pi\)
\(998\) 49.8637 1.57841
\(999\) 5.99166 0.189568
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 6033.2.a.c.1.3 82
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6033.2.a.c.1.3 82 1.1 even 1 trivial