Properties

Label 6031.2.a.b.1.16
Level $6031$
Weight $2$
Character 6031.1
Self dual yes
Analytic conductor $48.158$
Analytic rank $1$
Dimension $109$
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] = [6031,2,Mod(1,6031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6031, 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("6031.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6031 = 37 \cdot 163 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6031.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: \(48.1577774590\)
Analytic rank: \(1\)
Dimension: \(109\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 6031.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.18825 q^{2} +1.71398 q^{3} +2.78846 q^{4} +0.914186 q^{5} -3.75063 q^{6} +0.835020 q^{7} -1.72535 q^{8} -0.0622604 q^{9} +O(q^{10})\) \(q-2.18825 q^{2} +1.71398 q^{3} +2.78846 q^{4} +0.914186 q^{5} -3.75063 q^{6} +0.835020 q^{7} -1.72535 q^{8} -0.0622604 q^{9} -2.00047 q^{10} +2.33428 q^{11} +4.77937 q^{12} +3.32438 q^{13} -1.82724 q^{14} +1.56690 q^{15} -1.80142 q^{16} -7.84946 q^{17} +0.136242 q^{18} -5.24808 q^{19} +2.54917 q^{20} +1.43121 q^{21} -5.10800 q^{22} -2.29348 q^{23} -2.95722 q^{24} -4.16426 q^{25} -7.27460 q^{26} -5.24866 q^{27} +2.32842 q^{28} +5.13859 q^{29} -3.42878 q^{30} +3.95083 q^{31} +7.39265 q^{32} +4.00092 q^{33} +17.1766 q^{34} +0.763364 q^{35} -0.173611 q^{36} +1.00000 q^{37} +11.4841 q^{38} +5.69794 q^{39} -1.57729 q^{40} +6.86656 q^{41} -3.13185 q^{42} +3.74030 q^{43} +6.50905 q^{44} -0.0569176 q^{45} +5.01872 q^{46} -10.9703 q^{47} -3.08760 q^{48} -6.30274 q^{49} +9.11247 q^{50} -13.4538 q^{51} +9.26990 q^{52} +6.38689 q^{53} +11.4854 q^{54} +2.13397 q^{55} -1.44070 q^{56} -8.99512 q^{57} -11.2445 q^{58} -8.21573 q^{59} +4.36924 q^{60} -4.46938 q^{61} -8.64542 q^{62} -0.0519887 q^{63} -12.5742 q^{64} +3.03911 q^{65} -8.75503 q^{66} +4.37459 q^{67} -21.8879 q^{68} -3.93099 q^{69} -1.67043 q^{70} -6.40629 q^{71} +0.107421 q^{72} -4.99899 q^{73} -2.18825 q^{74} -7.13748 q^{75} -14.6340 q^{76} +1.94917 q^{77} -12.4685 q^{78} -4.86798 q^{79} -1.64683 q^{80} -8.80934 q^{81} -15.0258 q^{82} +4.72671 q^{83} +3.99087 q^{84} -7.17587 q^{85} -8.18473 q^{86} +8.80746 q^{87} -4.02745 q^{88} -13.5605 q^{89} +0.124550 q^{90} +2.77592 q^{91} -6.39528 q^{92} +6.77166 q^{93} +24.0058 q^{94} -4.79772 q^{95} +12.6709 q^{96} -3.59979 q^{97} +13.7920 q^{98} -0.145333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18825 −1.54733 −0.773665 0.633595i \(-0.781579\pi\)
−0.773665 + 0.633595i \(0.781579\pi\)
\(3\) 1.71398 0.989569 0.494784 0.869016i \(-0.335247\pi\)
0.494784 + 0.869016i \(0.335247\pi\)
\(4\) 2.78846 1.39423
\(5\) 0.914186 0.408837 0.204418 0.978884i \(-0.434470\pi\)
0.204418 + 0.978884i \(0.434470\pi\)
\(6\) −3.75063 −1.53119
\(7\) 0.835020 0.315608 0.157804 0.987470i \(-0.449559\pi\)
0.157804 + 0.987470i \(0.449559\pi\)
\(8\) −1.72535 −0.610003
\(9\) −0.0622604 −0.0207535
\(10\) −2.00047 −0.632605
\(11\) 2.33428 0.703812 0.351906 0.936035i \(-0.385534\pi\)
0.351906 + 0.936035i \(0.385534\pi\)
\(12\) 4.77937 1.37969
\(13\) 3.32438 0.922018 0.461009 0.887395i \(-0.347488\pi\)
0.461009 + 0.887395i \(0.347488\pi\)
\(14\) −1.82724 −0.488349
\(15\) 1.56690 0.404572
\(16\) −1.80142 −0.450354
\(17\) −7.84946 −1.90377 −0.951887 0.306450i \(-0.900859\pi\)
−0.951887 + 0.306450i \(0.900859\pi\)
\(18\) 0.136242 0.0321125
\(19\) −5.24808 −1.20399 −0.601996 0.798499i \(-0.705628\pi\)
−0.601996 + 0.798499i \(0.705628\pi\)
\(20\) 2.54917 0.570012
\(21\) 1.43121 0.312316
\(22\) −5.10800 −1.08903
\(23\) −2.29348 −0.478224 −0.239112 0.970992i \(-0.576856\pi\)
−0.239112 + 0.970992i \(0.576856\pi\)
\(24\) −2.95722 −0.603640
\(25\) −4.16426 −0.832853
\(26\) −7.27460 −1.42667
\(27\) −5.24866 −1.01011
\(28\) 2.32842 0.440030
\(29\) 5.13859 0.954212 0.477106 0.878846i \(-0.341686\pi\)
0.477106 + 0.878846i \(0.341686\pi\)
\(30\) −3.42878 −0.626006
\(31\) 3.95083 0.709590 0.354795 0.934944i \(-0.384551\pi\)
0.354795 + 0.934944i \(0.384551\pi\)
\(32\) 7.39265 1.30685
\(33\) 4.00092 0.696471
\(34\) 17.1766 2.94577
\(35\) 0.763364 0.129032
\(36\) −0.173611 −0.0289351
\(37\) 1.00000 0.164399
\(38\) 11.4841 1.86297
\(39\) 5.69794 0.912400
\(40\) −1.57729 −0.249391
\(41\) 6.86656 1.07238 0.536189 0.844098i \(-0.319864\pi\)
0.536189 + 0.844098i \(0.319864\pi\)
\(42\) −3.13185 −0.483255
\(43\) 3.74030 0.570391 0.285195 0.958469i \(-0.407942\pi\)
0.285195 + 0.958469i \(0.407942\pi\)
\(44\) 6.50905 0.981276
\(45\) −0.0569176 −0.00848478
\(46\) 5.01872 0.739970
\(47\) −10.9703 −1.60018 −0.800091 0.599879i \(-0.795216\pi\)
−0.800091 + 0.599879i \(0.795216\pi\)
\(48\) −3.08760 −0.445656
\(49\) −6.30274 −0.900392
\(50\) 9.11247 1.28870
\(51\) −13.4538 −1.88392
\(52\) 9.26990 1.28550
\(53\) 6.38689 0.877307 0.438653 0.898656i \(-0.355456\pi\)
0.438653 + 0.898656i \(0.355456\pi\)
\(54\) 11.4854 1.56297
\(55\) 2.13397 0.287744
\(56\) −1.44070 −0.192522
\(57\) −8.99512 −1.19143
\(58\) −11.2445 −1.47648
\(59\) −8.21573 −1.06960 −0.534798 0.844980i \(-0.679612\pi\)
−0.534798 + 0.844980i \(0.679612\pi\)
\(60\) 4.36924 0.564066
\(61\) −4.46938 −0.572246 −0.286123 0.958193i \(-0.592367\pi\)
−0.286123 + 0.958193i \(0.592367\pi\)
\(62\) −8.64542 −1.09797
\(63\) −0.0519887 −0.00654995
\(64\) −12.5742 −1.57177
\(65\) 3.03911 0.376955
\(66\) −8.75503 −1.07767
\(67\) 4.37459 0.534441 0.267220 0.963635i \(-0.413895\pi\)
0.267220 + 0.963635i \(0.413895\pi\)
\(68\) −21.8879 −2.65430
\(69\) −3.93099 −0.473236
\(70\) −1.67043 −0.199655
\(71\) −6.40629 −0.760287 −0.380143 0.924928i \(-0.624125\pi\)
−0.380143 + 0.924928i \(0.624125\pi\)
\(72\) 0.107421 0.0126597
\(73\) −4.99899 −0.585087 −0.292544 0.956252i \(-0.594502\pi\)
−0.292544 + 0.956252i \(0.594502\pi\)
\(74\) −2.18825 −0.254379
\(75\) −7.13748 −0.824165
\(76\) −14.6340 −1.67864
\(77\) 1.94917 0.222129
\(78\) −12.4685 −1.41178
\(79\) −4.86798 −0.547691 −0.273845 0.961774i \(-0.588296\pi\)
−0.273845 + 0.961774i \(0.588296\pi\)
\(80\) −1.64683 −0.184121
\(81\) −8.80934 −0.978816
\(82\) −15.0258 −1.65932
\(83\) 4.72671 0.518823 0.259412 0.965767i \(-0.416471\pi\)
0.259412 + 0.965767i \(0.416471\pi\)
\(84\) 3.99087 0.435440
\(85\) −7.17587 −0.778332
\(86\) −8.18473 −0.882582
\(87\) 8.80746 0.944259
\(88\) −4.02745 −0.429327
\(89\) −13.5605 −1.43741 −0.718704 0.695317i \(-0.755264\pi\)
−0.718704 + 0.695317i \(0.755264\pi\)
\(90\) 0.124550 0.0131287
\(91\) 2.77592 0.290996
\(92\) −6.39528 −0.666754
\(93\) 6.77166 0.702188
\(94\) 24.0058 2.47601
\(95\) −4.79772 −0.492236
\(96\) 12.6709 1.29322
\(97\) −3.59979 −0.365503 −0.182752 0.983159i \(-0.558500\pi\)
−0.182752 + 0.983159i \(0.558500\pi\)
\(98\) 13.7920 1.39320
\(99\) −0.145333 −0.0146065
\(100\) −11.6119 −1.16119
\(101\) −6.65567 −0.662264 −0.331132 0.943585i \(-0.607430\pi\)
−0.331132 + 0.943585i \(0.607430\pi\)
\(102\) 29.4404 2.91504
\(103\) 1.12889 0.111232 0.0556162 0.998452i \(-0.482288\pi\)
0.0556162 + 0.998452i \(0.482288\pi\)
\(104\) −5.73572 −0.562433
\(105\) 1.30839 0.127686
\(106\) −13.9761 −1.35748
\(107\) −7.70706 −0.745070 −0.372535 0.928018i \(-0.621511\pi\)
−0.372535 + 0.928018i \(0.621511\pi\)
\(108\) −14.6357 −1.40832
\(109\) 13.2167 1.26593 0.632967 0.774178i \(-0.281837\pi\)
0.632967 + 0.774178i \(0.281837\pi\)
\(110\) −4.66967 −0.445235
\(111\) 1.71398 0.162684
\(112\) −1.50422 −0.142135
\(113\) −0.630461 −0.0593088 −0.0296544 0.999560i \(-0.509441\pi\)
−0.0296544 + 0.999560i \(0.509441\pi\)
\(114\) 19.6836 1.84354
\(115\) −2.09667 −0.195516
\(116\) 14.3287 1.33039
\(117\) −0.206977 −0.0191351
\(118\) 17.9781 1.65502
\(119\) −6.55445 −0.600846
\(120\) −2.70345 −0.246790
\(121\) −5.55113 −0.504648
\(122\) 9.78015 0.885453
\(123\) 11.7692 1.06119
\(124\) 11.0167 0.989331
\(125\) −8.37785 −0.749337
\(126\) 0.113764 0.0101349
\(127\) −3.79018 −0.336324 −0.168162 0.985759i \(-0.553783\pi\)
−0.168162 + 0.985759i \(0.553783\pi\)
\(128\) 12.7302 1.12520
\(129\) 6.41082 0.564441
\(130\) −6.65034 −0.583273
\(131\) 14.2847 1.24806 0.624030 0.781400i \(-0.285494\pi\)
0.624030 + 0.781400i \(0.285494\pi\)
\(132\) 11.1564 0.971040
\(133\) −4.38225 −0.379989
\(134\) −9.57271 −0.826956
\(135\) −4.79826 −0.412968
\(136\) 13.5430 1.16131
\(137\) −6.88594 −0.588306 −0.294153 0.955758i \(-0.595037\pi\)
−0.294153 + 0.955758i \(0.595037\pi\)
\(138\) 8.60201 0.732252
\(139\) 19.4321 1.64821 0.824106 0.566436i \(-0.191678\pi\)
0.824106 + 0.566436i \(0.191678\pi\)
\(140\) 2.12861 0.179900
\(141\) −18.8029 −1.58349
\(142\) 14.0186 1.17641
\(143\) 7.76004 0.648927
\(144\) 0.112157 0.00934641
\(145\) 4.69763 0.390117
\(146\) 10.9391 0.905323
\(147\) −10.8028 −0.891000
\(148\) 2.78846 0.229210
\(149\) −18.3192 −1.50076 −0.750382 0.661005i \(-0.770130\pi\)
−0.750382 + 0.661005i \(0.770130\pi\)
\(150\) 15.6186 1.27526
\(151\) 2.98919 0.243256 0.121628 0.992576i \(-0.461188\pi\)
0.121628 + 0.992576i \(0.461188\pi\)
\(152\) 9.05476 0.734438
\(153\) 0.488710 0.0395099
\(154\) −4.26528 −0.343706
\(155\) 3.61180 0.290106
\(156\) 15.8885 1.27210
\(157\) −2.72784 −0.217705 −0.108853 0.994058i \(-0.534718\pi\)
−0.108853 + 0.994058i \(0.534718\pi\)
\(158\) 10.6524 0.847458
\(159\) 10.9470 0.868155
\(160\) 6.75826 0.534288
\(161\) −1.91510 −0.150931
\(162\) 19.2771 1.51455
\(163\) 1.00000 0.0783260
\(164\) 19.1471 1.49514
\(165\) 3.65759 0.284743
\(166\) −10.3432 −0.802791
\(167\) −20.8505 −1.61346 −0.806728 0.590922i \(-0.798764\pi\)
−0.806728 + 0.590922i \(0.798764\pi\)
\(168\) −2.46934 −0.190513
\(169\) −1.94848 −0.149883
\(170\) 15.7026 1.20434
\(171\) 0.326747 0.0249870
\(172\) 10.4297 0.795255
\(173\) 0.640619 0.0487054 0.0243527 0.999703i \(-0.492248\pi\)
0.0243527 + 0.999703i \(0.492248\pi\)
\(174\) −19.2730 −1.46108
\(175\) −3.47724 −0.262855
\(176\) −4.20501 −0.316965
\(177\) −14.0816 −1.05844
\(178\) 29.6738 2.22414
\(179\) −19.8446 −1.48326 −0.741628 0.670812i \(-0.765946\pi\)
−0.741628 + 0.670812i \(0.765946\pi\)
\(180\) −0.158712 −0.0118297
\(181\) −9.96944 −0.741023 −0.370511 0.928828i \(-0.620818\pi\)
−0.370511 + 0.928828i \(0.620818\pi\)
\(182\) −6.07443 −0.450267
\(183\) −7.66045 −0.566277
\(184\) 3.95705 0.291718
\(185\) 0.914186 0.0672123
\(186\) −14.8181 −1.08652
\(187\) −18.3228 −1.33990
\(188\) −30.5902 −2.23102
\(189\) −4.38274 −0.318797
\(190\) 10.4986 0.761651
\(191\) −12.1566 −0.879620 −0.439810 0.898091i \(-0.644954\pi\)
−0.439810 + 0.898091i \(0.644954\pi\)
\(192\) −21.5519 −1.55538
\(193\) 5.19084 0.373645 0.186823 0.982394i \(-0.440181\pi\)
0.186823 + 0.982394i \(0.440181\pi\)
\(194\) 7.87725 0.565554
\(195\) 5.20898 0.373023
\(196\) −17.5749 −1.25535
\(197\) −22.8147 −1.62548 −0.812741 0.582625i \(-0.802026\pi\)
−0.812741 + 0.582625i \(0.802026\pi\)
\(198\) 0.318026 0.0226011
\(199\) 14.1877 1.00574 0.502871 0.864361i \(-0.332277\pi\)
0.502871 + 0.864361i \(0.332277\pi\)
\(200\) 7.18480 0.508042
\(201\) 7.49797 0.528866
\(202\) 14.5643 1.02474
\(203\) 4.29082 0.301157
\(204\) −37.5155 −2.62661
\(205\) 6.27732 0.438427
\(206\) −2.47029 −0.172113
\(207\) 0.142793 0.00992481
\(208\) −5.98860 −0.415235
\(209\) −12.2505 −0.847384
\(210\) −2.86310 −0.197572
\(211\) 0.554700 0.0381871 0.0190936 0.999818i \(-0.493922\pi\)
0.0190936 + 0.999818i \(0.493922\pi\)
\(212\) 17.8096 1.22317
\(213\) −10.9803 −0.752356
\(214\) 16.8650 1.15287
\(215\) 3.41933 0.233197
\(216\) 9.05577 0.616167
\(217\) 3.29902 0.223952
\(218\) −28.9216 −1.95882
\(219\) −8.56819 −0.578984
\(220\) 5.95048 0.401181
\(221\) −26.0946 −1.75531
\(222\) −3.75063 −0.251726
\(223\) 6.75719 0.452495 0.226247 0.974070i \(-0.427354\pi\)
0.226247 + 0.974070i \(0.427354\pi\)
\(224\) 6.17301 0.412452
\(225\) 0.259269 0.0172846
\(226\) 1.37961 0.0917703
\(227\) 11.4761 0.761696 0.380848 0.924638i \(-0.375632\pi\)
0.380848 + 0.924638i \(0.375632\pi\)
\(228\) −25.0825 −1.66113
\(229\) 7.75773 0.512645 0.256323 0.966591i \(-0.417489\pi\)
0.256323 + 0.966591i \(0.417489\pi\)
\(230\) 4.58805 0.302527
\(231\) 3.34085 0.219812
\(232\) −8.86585 −0.582072
\(233\) 30.3130 1.98587 0.992935 0.118661i \(-0.0378602\pi\)
0.992935 + 0.118661i \(0.0378602\pi\)
\(234\) 0.452919 0.0296083
\(235\) −10.0289 −0.654213
\(236\) −22.9092 −1.49126
\(237\) −8.34364 −0.541977
\(238\) 14.3428 0.929706
\(239\) −18.1701 −1.17532 −0.587662 0.809106i \(-0.699952\pi\)
−0.587662 + 0.809106i \(0.699952\pi\)
\(240\) −2.82264 −0.182201
\(241\) 17.4502 1.12407 0.562034 0.827114i \(-0.310019\pi\)
0.562034 + 0.827114i \(0.310019\pi\)
\(242\) 12.1473 0.780857
\(243\) 0.646924 0.0415002
\(244\) −12.4627 −0.797842
\(245\) −5.76188 −0.368113
\(246\) −25.7540 −1.64201
\(247\) −17.4466 −1.11010
\(248\) −6.81656 −0.432852
\(249\) 8.10150 0.513412
\(250\) 18.3329 1.15947
\(251\) 29.2719 1.84763 0.923814 0.382841i \(-0.125054\pi\)
0.923814 + 0.382841i \(0.125054\pi\)
\(252\) −0.144968 −0.00913214
\(253\) −5.35363 −0.336580
\(254\) 8.29389 0.520405
\(255\) −12.2993 −0.770213
\(256\) −2.70855 −0.169284
\(257\) 11.2034 0.698846 0.349423 0.936965i \(-0.386378\pi\)
0.349423 + 0.936965i \(0.386378\pi\)
\(258\) −14.0285 −0.873376
\(259\) 0.835020 0.0518856
\(260\) 8.47442 0.525561
\(261\) −0.319931 −0.0198032
\(262\) −31.2586 −1.93116
\(263\) 8.47911 0.522844 0.261422 0.965225i \(-0.415809\pi\)
0.261422 + 0.965225i \(0.415809\pi\)
\(264\) −6.90298 −0.424849
\(265\) 5.83881 0.358675
\(266\) 9.58947 0.587968
\(267\) −23.2424 −1.42241
\(268\) 12.1984 0.745133
\(269\) −17.3014 −1.05488 −0.527441 0.849591i \(-0.676849\pi\)
−0.527441 + 0.849591i \(0.676849\pi\)
\(270\) 10.4998 0.638998
\(271\) −30.9441 −1.87972 −0.939859 0.341562i \(-0.889044\pi\)
−0.939859 + 0.341562i \(0.889044\pi\)
\(272\) 14.1401 0.857372
\(273\) 4.75789 0.287961
\(274\) 15.0682 0.910303
\(275\) −9.72056 −0.586172
\(276\) −10.9614 −0.659799
\(277\) −30.9477 −1.85947 −0.929733 0.368235i \(-0.879962\pi\)
−0.929733 + 0.368235i \(0.879962\pi\)
\(278\) −42.5224 −2.55033
\(279\) −0.245980 −0.0147265
\(280\) −1.31707 −0.0787099
\(281\) 3.89759 0.232511 0.116255 0.993219i \(-0.462911\pi\)
0.116255 + 0.993219i \(0.462911\pi\)
\(282\) 41.1455 2.45018
\(283\) −9.62865 −0.572364 −0.286182 0.958175i \(-0.592386\pi\)
−0.286182 + 0.958175i \(0.592386\pi\)
\(284\) −17.8637 −1.06001
\(285\) −8.22322 −0.487101
\(286\) −16.9810 −1.00410
\(287\) 5.73372 0.338451
\(288\) −0.460270 −0.0271216
\(289\) 44.6140 2.62435
\(290\) −10.2796 −0.603639
\(291\) −6.16998 −0.361691
\(292\) −13.9395 −0.815746
\(293\) −25.3379 −1.48026 −0.740128 0.672466i \(-0.765235\pi\)
−0.740128 + 0.672466i \(0.765235\pi\)
\(294\) 23.6393 1.37867
\(295\) −7.51071 −0.437290
\(296\) −1.72535 −0.100284
\(297\) −12.2519 −0.710925
\(298\) 40.0870 2.32218
\(299\) −7.62441 −0.440931
\(300\) −19.9026 −1.14907
\(301\) 3.12323 0.180020
\(302\) −6.54110 −0.376398
\(303\) −11.4077 −0.655355
\(304\) 9.45397 0.542223
\(305\) −4.08585 −0.233955
\(306\) −1.06942 −0.0611348
\(307\) −8.05311 −0.459615 −0.229808 0.973236i \(-0.573810\pi\)
−0.229808 + 0.973236i \(0.573810\pi\)
\(308\) 5.43518 0.309698
\(309\) 1.93489 0.110072
\(310\) −7.90353 −0.448890
\(311\) 31.3906 1.78000 0.889998 0.455965i \(-0.150706\pi\)
0.889998 + 0.455965i \(0.150706\pi\)
\(312\) −9.83092 −0.556567
\(313\) 12.9650 0.732828 0.366414 0.930452i \(-0.380585\pi\)
0.366414 + 0.930452i \(0.380585\pi\)
\(314\) 5.96920 0.336861
\(315\) −0.0475273 −0.00267786
\(316\) −13.5742 −0.763606
\(317\) 32.5314 1.82714 0.913572 0.406678i \(-0.133313\pi\)
0.913572 + 0.406678i \(0.133313\pi\)
\(318\) −23.9549 −1.34332
\(319\) 11.9949 0.671586
\(320\) −11.4951 −0.642598
\(321\) −13.2098 −0.737298
\(322\) 4.19073 0.233540
\(323\) 41.1946 2.29213
\(324\) −24.5645 −1.36469
\(325\) −13.8436 −0.767905
\(326\) −2.18825 −0.121196
\(327\) 22.6533 1.25273
\(328\) −11.8472 −0.654153
\(329\) −9.16041 −0.505030
\(330\) −8.00373 −0.440591
\(331\) 7.71502 0.424056 0.212028 0.977264i \(-0.431993\pi\)
0.212028 + 0.977264i \(0.431993\pi\)
\(332\) 13.1802 0.723359
\(333\) −0.0622604 −0.00341185
\(334\) 45.6261 2.49655
\(335\) 3.99919 0.218499
\(336\) −2.57820 −0.140653
\(337\) 17.0021 0.926161 0.463080 0.886316i \(-0.346744\pi\)
0.463080 + 0.886316i \(0.346744\pi\)
\(338\) 4.26377 0.231918
\(339\) −1.08060 −0.0586901
\(340\) −20.0096 −1.08517
\(341\) 9.22235 0.499418
\(342\) −0.715007 −0.0386631
\(343\) −11.1081 −0.599778
\(344\) −6.45332 −0.347940
\(345\) −3.59366 −0.193476
\(346\) −1.40184 −0.0753633
\(347\) 15.0066 0.805596 0.402798 0.915289i \(-0.368038\pi\)
0.402798 + 0.915289i \(0.368038\pi\)
\(348\) 24.5592 1.31651
\(349\) 12.4938 0.668778 0.334389 0.942435i \(-0.391470\pi\)
0.334389 + 0.942435i \(0.391470\pi\)
\(350\) 7.60909 0.406723
\(351\) −17.4486 −0.931336
\(352\) 17.2565 0.919776
\(353\) −8.10322 −0.431291 −0.215645 0.976472i \(-0.569186\pi\)
−0.215645 + 0.976472i \(0.569186\pi\)
\(354\) 30.8142 1.63776
\(355\) −5.85654 −0.310833
\(356\) −37.8128 −2.00407
\(357\) −11.2342 −0.594578
\(358\) 43.4251 2.29509
\(359\) −37.5566 −1.98216 −0.991080 0.133268i \(-0.957453\pi\)
−0.991080 + 0.133268i \(0.957453\pi\)
\(360\) 0.0982027 0.00517574
\(361\) 8.54232 0.449596
\(362\) 21.8157 1.14661
\(363\) −9.51455 −0.499384
\(364\) 7.74055 0.405715
\(365\) −4.57001 −0.239205
\(366\) 16.7630 0.876217
\(367\) 31.3048 1.63410 0.817050 0.576567i \(-0.195608\pi\)
0.817050 + 0.576567i \(0.195608\pi\)
\(368\) 4.13152 0.215370
\(369\) −0.427515 −0.0222555
\(370\) −2.00047 −0.104000
\(371\) 5.33318 0.276885
\(372\) 18.8825 0.979011
\(373\) −16.2770 −0.842794 −0.421397 0.906876i \(-0.638460\pi\)
−0.421397 + 0.906876i \(0.638460\pi\)
\(374\) 40.0951 2.07327
\(375\) −14.3595 −0.741521
\(376\) 18.9276 0.976115
\(377\) 17.0826 0.879801
\(378\) 9.59055 0.493284
\(379\) −37.8965 −1.94661 −0.973306 0.229511i \(-0.926287\pi\)
−0.973306 + 0.229511i \(0.926287\pi\)
\(380\) −13.3782 −0.686290
\(381\) −6.49631 −0.332816
\(382\) 26.6017 1.36106
\(383\) −5.49565 −0.280815 −0.140407 0.990094i \(-0.544841\pi\)
−0.140407 + 0.990094i \(0.544841\pi\)
\(384\) 21.8193 1.11346
\(385\) 1.78191 0.0908143
\(386\) −11.3589 −0.578152
\(387\) −0.232873 −0.0118376
\(388\) −10.0379 −0.509595
\(389\) 16.7181 0.847642 0.423821 0.905746i \(-0.360689\pi\)
0.423821 + 0.905746i \(0.360689\pi\)
\(390\) −11.3986 −0.577189
\(391\) 18.0026 0.910430
\(392\) 10.8744 0.549241
\(393\) 24.4838 1.23504
\(394\) 49.9244 2.51516
\(395\) −4.45024 −0.223916
\(396\) −0.405256 −0.0203649
\(397\) −15.4876 −0.777301 −0.388651 0.921385i \(-0.627059\pi\)
−0.388651 + 0.921385i \(0.627059\pi\)
\(398\) −31.0464 −1.55622
\(399\) −7.51110 −0.376025
\(400\) 7.50157 0.375079
\(401\) 7.31460 0.365274 0.182637 0.983180i \(-0.441537\pi\)
0.182637 + 0.983180i \(0.441537\pi\)
\(402\) −16.4075 −0.818330
\(403\) 13.1341 0.654255
\(404\) −18.5590 −0.923347
\(405\) −8.05338 −0.400176
\(406\) −9.38941 −0.465989
\(407\) 2.33428 0.115706
\(408\) 23.2126 1.14919
\(409\) 8.50298 0.420445 0.210223 0.977654i \(-0.432581\pi\)
0.210223 + 0.977654i \(0.432581\pi\)
\(410\) −13.7364 −0.678391
\(411\) −11.8024 −0.582169
\(412\) 3.14785 0.155084
\(413\) −6.86029 −0.337573
\(414\) −0.312468 −0.0153569
\(415\) 4.32109 0.212114
\(416\) 24.5760 1.20494
\(417\) 33.3063 1.63102
\(418\) 26.8072 1.31118
\(419\) −13.8256 −0.675426 −0.337713 0.941249i \(-0.609653\pi\)
−0.337713 + 0.941249i \(0.609653\pi\)
\(420\) 3.64840 0.178024
\(421\) 39.1308 1.90712 0.953559 0.301207i \(-0.0973894\pi\)
0.953559 + 0.301207i \(0.0973894\pi\)
\(422\) −1.21382 −0.0590880
\(423\) 0.683015 0.0332093
\(424\) −11.0196 −0.535159
\(425\) 32.6872 1.58556
\(426\) 24.0276 1.16414
\(427\) −3.73202 −0.180605
\(428\) −21.4908 −1.03880
\(429\) 13.3006 0.642158
\(430\) −7.48237 −0.360832
\(431\) −29.1228 −1.40279 −0.701397 0.712771i \(-0.747440\pi\)
−0.701397 + 0.712771i \(0.747440\pi\)
\(432\) 9.45503 0.454905
\(433\) −20.0747 −0.964730 −0.482365 0.875970i \(-0.660222\pi\)
−0.482365 + 0.875970i \(0.660222\pi\)
\(434\) −7.21910 −0.346528
\(435\) 8.05166 0.386047
\(436\) 36.8544 1.76500
\(437\) 12.0364 0.575778
\(438\) 18.7494 0.895880
\(439\) −13.1680 −0.628474 −0.314237 0.949345i \(-0.601749\pi\)
−0.314237 + 0.949345i \(0.601749\pi\)
\(440\) −3.68184 −0.175525
\(441\) 0.392411 0.0186862
\(442\) 57.1017 2.71605
\(443\) −12.9488 −0.615216 −0.307608 0.951513i \(-0.599529\pi\)
−0.307608 + 0.951513i \(0.599529\pi\)
\(444\) 4.77937 0.226819
\(445\) −12.3968 −0.587665
\(446\) −14.7865 −0.700159
\(447\) −31.3987 −1.48511
\(448\) −10.4997 −0.496063
\(449\) −10.9711 −0.517757 −0.258879 0.965910i \(-0.583353\pi\)
−0.258879 + 0.965910i \(0.583353\pi\)
\(450\) −0.567346 −0.0267449
\(451\) 16.0285 0.754752
\(452\) −1.75801 −0.0826900
\(453\) 5.12341 0.240719
\(454\) −25.1126 −1.17860
\(455\) 2.53771 0.118970
\(456\) 15.5197 0.726777
\(457\) −6.38113 −0.298497 −0.149248 0.988800i \(-0.547685\pi\)
−0.149248 + 0.988800i \(0.547685\pi\)
\(458\) −16.9759 −0.793231
\(459\) 41.1992 1.92301
\(460\) −5.84648 −0.272593
\(461\) −0.467707 −0.0217833 −0.0108917 0.999941i \(-0.503467\pi\)
−0.0108917 + 0.999941i \(0.503467\pi\)
\(462\) −7.31062 −0.340121
\(463\) 9.90941 0.460529 0.230265 0.973128i \(-0.426041\pi\)
0.230265 + 0.973128i \(0.426041\pi\)
\(464\) −9.25674 −0.429733
\(465\) 6.19056 0.287080
\(466\) −66.3325 −3.07280
\(467\) 0.794519 0.0367660 0.0183830 0.999831i \(-0.494148\pi\)
0.0183830 + 0.999831i \(0.494148\pi\)
\(468\) −0.577148 −0.0266787
\(469\) 3.65287 0.168674
\(470\) 21.9458 1.01228
\(471\) −4.67547 −0.215434
\(472\) 14.1750 0.652457
\(473\) 8.73092 0.401448
\(474\) 18.2580 0.838618
\(475\) 21.8544 1.00275
\(476\) −18.2768 −0.837717
\(477\) −0.397650 −0.0182072
\(478\) 39.7608 1.81861
\(479\) −8.51874 −0.389231 −0.194616 0.980880i \(-0.562346\pi\)
−0.194616 + 0.980880i \(0.562346\pi\)
\(480\) 11.5836 0.528714
\(481\) 3.32438 0.151579
\(482\) −38.1856 −1.73930
\(483\) −3.28245 −0.149357
\(484\) −15.4791 −0.703595
\(485\) −3.29088 −0.149431
\(486\) −1.41563 −0.0642145
\(487\) 9.02113 0.408786 0.204393 0.978889i \(-0.434478\pi\)
0.204393 + 0.978889i \(0.434478\pi\)
\(488\) 7.71124 0.349072
\(489\) 1.71398 0.0775090
\(490\) 12.6085 0.569592
\(491\) −35.6555 −1.60911 −0.804556 0.593877i \(-0.797596\pi\)
−0.804556 + 0.593877i \(0.797596\pi\)
\(492\) 32.8179 1.47954
\(493\) −40.3352 −1.81660
\(494\) 38.1776 1.71769
\(495\) −0.132862 −0.00597169
\(496\) −7.11709 −0.319567
\(497\) −5.34938 −0.239952
\(498\) −17.7281 −0.794417
\(499\) 28.8981 1.29365 0.646827 0.762636i \(-0.276095\pi\)
0.646827 + 0.762636i \(0.276095\pi\)
\(500\) −23.3613 −1.04475
\(501\) −35.7373 −1.59663
\(502\) −64.0545 −2.85889
\(503\) −41.8313 −1.86516 −0.932582 0.360958i \(-0.882450\pi\)
−0.932582 + 0.360958i \(0.882450\pi\)
\(504\) 0.0896985 0.00399549
\(505\) −6.08452 −0.270758
\(506\) 11.7151 0.520800
\(507\) −3.33966 −0.148320
\(508\) −10.5688 −0.468913
\(509\) −19.2245 −0.852109 −0.426055 0.904697i \(-0.640097\pi\)
−0.426055 + 0.904697i \(0.640097\pi\)
\(510\) 26.9141 1.19177
\(511\) −4.17425 −0.184658
\(512\) −19.5334 −0.863262
\(513\) 27.5454 1.21616
\(514\) −24.5158 −1.08135
\(515\) 1.03201 0.0454759
\(516\) 17.8763 0.786960
\(517\) −25.6078 −1.12623
\(518\) −1.82724 −0.0802841
\(519\) 1.09801 0.0481973
\(520\) −5.24351 −0.229943
\(521\) 6.54734 0.286844 0.143422 0.989662i \(-0.454189\pi\)
0.143422 + 0.989662i \(0.454189\pi\)
\(522\) 0.700090 0.0306421
\(523\) −45.0246 −1.96879 −0.984395 0.175972i \(-0.943693\pi\)
−0.984395 + 0.175972i \(0.943693\pi\)
\(524\) 39.8323 1.74008
\(525\) −5.95993 −0.260113
\(526\) −18.5545 −0.809013
\(527\) −31.0119 −1.35090
\(528\) −7.20732 −0.313658
\(529\) −17.7399 −0.771302
\(530\) −12.7768 −0.554989
\(531\) 0.511515 0.0221978
\(532\) −12.2197 −0.529792
\(533\) 22.8271 0.988751
\(534\) 50.8603 2.20094
\(535\) −7.04569 −0.304612
\(536\) −7.54769 −0.326010
\(537\) −34.0133 −1.46778
\(538\) 37.8598 1.63225
\(539\) −14.7124 −0.633707
\(540\) −13.3797 −0.575772
\(541\) −0.681663 −0.0293070 −0.0146535 0.999893i \(-0.504665\pi\)
−0.0146535 + 0.999893i \(0.504665\pi\)
\(542\) 67.7135 2.90854
\(543\) −17.0875 −0.733293
\(544\) −58.0283 −2.48794
\(545\) 12.0826 0.517561
\(546\) −10.4115 −0.445570
\(547\) −20.8613 −0.891963 −0.445981 0.895042i \(-0.647145\pi\)
−0.445981 + 0.895042i \(0.647145\pi\)
\(548\) −19.2012 −0.820233
\(549\) 0.278266 0.0118761
\(550\) 21.2711 0.907001
\(551\) −26.9677 −1.14886
\(552\) 6.78233 0.288675
\(553\) −4.06486 −0.172855
\(554\) 67.7214 2.87721
\(555\) 1.56690 0.0665112
\(556\) 54.1857 2.29798
\(557\) 16.9391 0.717731 0.358866 0.933389i \(-0.383164\pi\)
0.358866 + 0.933389i \(0.383164\pi\)
\(558\) 0.538267 0.0227867
\(559\) 12.4342 0.525910
\(560\) −1.37514 −0.0581101
\(561\) −31.4051 −1.32592
\(562\) −8.52893 −0.359771
\(563\) −4.76445 −0.200797 −0.100399 0.994947i \(-0.532012\pi\)
−0.100399 + 0.994947i \(0.532012\pi\)
\(564\) −52.4311 −2.20775
\(565\) −0.576359 −0.0242476
\(566\) 21.0699 0.885635
\(567\) −7.35597 −0.308922
\(568\) 11.0531 0.463777
\(569\) −18.6340 −0.781176 −0.390588 0.920566i \(-0.627728\pi\)
−0.390588 + 0.920566i \(0.627728\pi\)
\(570\) 17.9945 0.753706
\(571\) −1.46100 −0.0611410 −0.0305705 0.999533i \(-0.509732\pi\)
−0.0305705 + 0.999533i \(0.509732\pi\)
\(572\) 21.6386 0.904754
\(573\) −20.8362 −0.870445
\(574\) −12.5468 −0.523695
\(575\) 9.55066 0.398290
\(576\) 0.782873 0.0326197
\(577\) −13.0993 −0.545330 −0.272665 0.962109i \(-0.587905\pi\)
−0.272665 + 0.962109i \(0.587905\pi\)
\(578\) −97.6268 −4.06074
\(579\) 8.89702 0.369748
\(580\) 13.0991 0.543912
\(581\) 3.94689 0.163745
\(582\) 13.5015 0.559655
\(583\) 14.9088 0.617459
\(584\) 8.62500 0.356905
\(585\) −0.189216 −0.00782312
\(586\) 55.4458 2.29044
\(587\) 27.2257 1.12372 0.561862 0.827231i \(-0.310085\pi\)
0.561862 + 0.827231i \(0.310085\pi\)
\(588\) −30.1231 −1.24226
\(589\) −20.7343 −0.854341
\(590\) 16.4353 0.676632
\(591\) −39.1041 −1.60853
\(592\) −1.80142 −0.0740378
\(593\) 21.8241 0.896210 0.448105 0.893981i \(-0.352099\pi\)
0.448105 + 0.893981i \(0.352099\pi\)
\(594\) 26.8102 1.10004
\(595\) −5.99199 −0.245648
\(596\) −51.0822 −2.09241
\(597\) 24.3176 0.995252
\(598\) 16.6842 0.682266
\(599\) 3.63381 0.148473 0.0742367 0.997241i \(-0.476348\pi\)
0.0742367 + 0.997241i \(0.476348\pi\)
\(600\) 12.3146 0.502743
\(601\) 44.5867 1.81873 0.909365 0.415999i \(-0.136568\pi\)
0.909365 + 0.415999i \(0.136568\pi\)
\(602\) −6.83441 −0.278550
\(603\) −0.272364 −0.0110915
\(604\) 8.33522 0.339155
\(605\) −5.07477 −0.206319
\(606\) 24.9630 1.01405
\(607\) 42.8481 1.73915 0.869575 0.493801i \(-0.164393\pi\)
0.869575 + 0.493801i \(0.164393\pi\)
\(608\) −38.7972 −1.57344
\(609\) 7.35440 0.298015
\(610\) 8.94088 0.362006
\(611\) −36.4695 −1.47540
\(612\) 1.36275 0.0550859
\(613\) 22.1752 0.895647 0.447824 0.894122i \(-0.352199\pi\)
0.447824 + 0.894122i \(0.352199\pi\)
\(614\) 17.6223 0.711176
\(615\) 10.7592 0.433854
\(616\) −3.36300 −0.135499
\(617\) −37.0742 −1.49255 −0.746275 0.665638i \(-0.768160\pi\)
−0.746275 + 0.665638i \(0.768160\pi\)
\(618\) −4.23404 −0.170318
\(619\) 22.9627 0.922947 0.461474 0.887154i \(-0.347321\pi\)
0.461474 + 0.887154i \(0.347321\pi\)
\(620\) 10.0713 0.404475
\(621\) 12.0377 0.483057
\(622\) −68.6906 −2.75424
\(623\) −11.3233 −0.453657
\(624\) −10.2644 −0.410903
\(625\) 13.1624 0.526496
\(626\) −28.3708 −1.13393
\(627\) −20.9971 −0.838545
\(628\) −7.60646 −0.303531
\(629\) −7.84946 −0.312978
\(630\) 0.104002 0.00414353
\(631\) 44.4583 1.76986 0.884928 0.465727i \(-0.154207\pi\)
0.884928 + 0.465727i \(0.154207\pi\)
\(632\) 8.39896 0.334093
\(633\) 0.950746 0.0377888
\(634\) −71.1869 −2.82719
\(635\) −3.46493 −0.137502
\(636\) 30.5253 1.21041
\(637\) −20.9527 −0.830177
\(638\) −26.2479 −1.03917
\(639\) 0.398858 0.0157786
\(640\) 11.6378 0.460023
\(641\) 6.44954 0.254741 0.127371 0.991855i \(-0.459346\pi\)
0.127371 + 0.991855i \(0.459346\pi\)
\(642\) 28.9064 1.14084
\(643\) 22.6561 0.893468 0.446734 0.894667i \(-0.352587\pi\)
0.446734 + 0.894667i \(0.352587\pi\)
\(644\) −5.34018 −0.210433
\(645\) 5.86068 0.230764
\(646\) −90.1442 −3.54668
\(647\) −18.2558 −0.717709 −0.358855 0.933393i \(-0.616833\pi\)
−0.358855 + 0.933393i \(0.616833\pi\)
\(648\) 15.1992 0.597080
\(649\) −19.1778 −0.752795
\(650\) 30.2933 1.18820
\(651\) 5.65447 0.221616
\(652\) 2.78846 0.109204
\(653\) −4.17584 −0.163413 −0.0817067 0.996656i \(-0.526037\pi\)
−0.0817067 + 0.996656i \(0.526037\pi\)
\(654\) −49.5712 −1.93839
\(655\) 13.0589 0.510253
\(656\) −12.3695 −0.482949
\(657\) 0.311239 0.0121426
\(658\) 20.0453 0.781448
\(659\) −5.16924 −0.201365 −0.100683 0.994919i \(-0.532103\pi\)
−0.100683 + 0.994919i \(0.532103\pi\)
\(660\) 10.1990 0.396997
\(661\) −13.8351 −0.538123 −0.269061 0.963123i \(-0.586713\pi\)
−0.269061 + 0.963123i \(0.586713\pi\)
\(662\) −16.8824 −0.656155
\(663\) −44.7257 −1.73700
\(664\) −8.15521 −0.316484
\(665\) −4.00619 −0.155353
\(666\) 0.136242 0.00527925
\(667\) −11.7853 −0.456327
\(668\) −58.1406 −2.24953
\(669\) 11.5817 0.447775
\(670\) −8.75124 −0.338090
\(671\) −10.4328 −0.402754
\(672\) 10.5804 0.408149
\(673\) 16.8321 0.648829 0.324414 0.945915i \(-0.394833\pi\)
0.324414 + 0.945915i \(0.394833\pi\)
\(674\) −37.2048 −1.43308
\(675\) 21.8568 0.841269
\(676\) −5.43325 −0.208971
\(677\) −20.0077 −0.768957 −0.384478 0.923134i \(-0.625619\pi\)
−0.384478 + 0.923134i \(0.625619\pi\)
\(678\) 2.36463 0.0908130
\(679\) −3.00589 −0.115356
\(680\) 12.3809 0.474785
\(681\) 19.6699 0.753751
\(682\) −20.1808 −0.772765
\(683\) 5.50311 0.210571 0.105285 0.994442i \(-0.466424\pi\)
0.105285 + 0.994442i \(0.466424\pi\)
\(684\) 0.911122 0.0348376
\(685\) −6.29503 −0.240521
\(686\) 24.3072 0.928055
\(687\) 13.2966 0.507298
\(688\) −6.73784 −0.256878
\(689\) 21.2325 0.808893
\(690\) 7.86384 0.299371
\(691\) 21.2934 0.810040 0.405020 0.914308i \(-0.367265\pi\)
0.405020 + 0.914308i \(0.367265\pi\)
\(692\) 1.78634 0.0679065
\(693\) −0.121356 −0.00460994
\(694\) −32.8382 −1.24652
\(695\) 17.7646 0.673849
\(696\) −15.1959 −0.576000
\(697\) −53.8988 −2.04156
\(698\) −27.3396 −1.03482
\(699\) 51.9560 1.96515
\(700\) −9.69614 −0.366480
\(701\) 23.2634 0.878648 0.439324 0.898329i \(-0.355218\pi\)
0.439324 + 0.898329i \(0.355218\pi\)
\(702\) 38.1819 1.44108
\(703\) −5.24808 −0.197935
\(704\) −29.3517 −1.10623
\(705\) −17.1894 −0.647389
\(706\) 17.7319 0.667349
\(707\) −5.55761 −0.209015
\(708\) −39.2660 −1.47571
\(709\) 46.7812 1.75690 0.878452 0.477831i \(-0.158577\pi\)
0.878452 + 0.477831i \(0.158577\pi\)
\(710\) 12.8156 0.480961
\(711\) 0.303082 0.0113665
\(712\) 23.3965 0.876822
\(713\) −9.06116 −0.339343
\(714\) 24.5833 0.920009
\(715\) 7.09413 0.265305
\(716\) −55.3359 −2.06800
\(717\) −31.1432 −1.16306
\(718\) 82.1833 3.06706
\(719\) 25.0578 0.934498 0.467249 0.884126i \(-0.345245\pi\)
0.467249 + 0.884126i \(0.345245\pi\)
\(720\) 0.102532 0.00382115
\(721\) 0.942642 0.0351058
\(722\) −18.6928 −0.695673
\(723\) 29.9094 1.11234
\(724\) −27.7994 −1.03316
\(725\) −21.3984 −0.794718
\(726\) 20.8203 0.772712
\(727\) 9.48198 0.351667 0.175833 0.984420i \(-0.443738\pi\)
0.175833 + 0.984420i \(0.443738\pi\)
\(728\) −4.78944 −0.177508
\(729\) 27.5368 1.01988
\(730\) 10.0003 0.370129
\(731\) −29.3593 −1.08589
\(732\) −21.3608 −0.789520
\(733\) 25.3630 0.936803 0.468401 0.883516i \(-0.344830\pi\)
0.468401 + 0.883516i \(0.344830\pi\)
\(734\) −68.5030 −2.52849
\(735\) −9.87577 −0.364273
\(736\) −16.9549 −0.624967
\(737\) 10.2115 0.376146
\(738\) 0.935512 0.0344367
\(739\) −29.0231 −1.06763 −0.533816 0.845600i \(-0.679243\pi\)
−0.533816 + 0.845600i \(0.679243\pi\)
\(740\) 2.54917 0.0937094
\(741\) −29.9032 −1.09852
\(742\) −11.6704 −0.428432
\(743\) −13.1053 −0.480787 −0.240393 0.970676i \(-0.577276\pi\)
−0.240393 + 0.970676i \(0.577276\pi\)
\(744\) −11.6835 −0.428337
\(745\) −16.7471 −0.613567
\(746\) 35.6183 1.30408
\(747\) −0.294287 −0.0107674
\(748\) −51.0925 −1.86813
\(749\) −6.43555 −0.235150
\(750\) 31.4222 1.14738
\(751\) 5.05435 0.184436 0.0922180 0.995739i \(-0.470604\pi\)
0.0922180 + 0.995739i \(0.470604\pi\)
\(752\) 19.7621 0.720648
\(753\) 50.1716 1.82836
\(754\) −37.3812 −1.36134
\(755\) 2.73267 0.0994521
\(756\) −12.2211 −0.444476
\(757\) 3.41290 0.124044 0.0620219 0.998075i \(-0.480245\pi\)
0.0620219 + 0.998075i \(0.480245\pi\)
\(758\) 82.9272 3.01205
\(759\) −9.17604 −0.333069
\(760\) 8.27774 0.300265
\(761\) −6.65851 −0.241371 −0.120685 0.992691i \(-0.538509\pi\)
−0.120685 + 0.992691i \(0.538509\pi\)
\(762\) 14.2156 0.514976
\(763\) 11.0362 0.399539
\(764\) −33.8982 −1.22639
\(765\) 0.446772 0.0161531
\(766\) 12.0259 0.434513
\(767\) −27.3122 −0.986187
\(768\) −4.64241 −0.167519
\(769\) −16.0066 −0.577212 −0.288606 0.957448i \(-0.593192\pi\)
−0.288606 + 0.957448i \(0.593192\pi\)
\(770\) −3.89926 −0.140520
\(771\) 19.2024 0.691556
\(772\) 14.4745 0.520947
\(773\) 16.2364 0.583982 0.291991 0.956421i \(-0.405682\pi\)
0.291991 + 0.956421i \(0.405682\pi\)
\(774\) 0.509585 0.0183166
\(775\) −16.4523 −0.590984
\(776\) 6.21089 0.222958
\(777\) 1.43121 0.0513444
\(778\) −36.5835 −1.31158
\(779\) −36.0363 −1.29113
\(780\) 14.5250 0.520079
\(781\) −14.9541 −0.535099
\(782\) −39.3943 −1.40874
\(783\) −26.9707 −0.963855
\(784\) 11.3539 0.405495
\(785\) −2.49375 −0.0890058
\(786\) −53.5767 −1.91102
\(787\) −40.8762 −1.45708 −0.728539 0.685005i \(-0.759800\pi\)
−0.728539 + 0.685005i \(0.759800\pi\)
\(788\) −63.6179 −2.26629
\(789\) 14.5331 0.517391
\(790\) 9.73826 0.346472
\(791\) −0.526447 −0.0187183
\(792\) 0.250750 0.00891003
\(793\) −14.8579 −0.527621
\(794\) 33.8908 1.20274
\(795\) 10.0076 0.354934
\(796\) 39.5619 1.40224
\(797\) 43.0186 1.52380 0.761898 0.647697i \(-0.224268\pi\)
0.761898 + 0.647697i \(0.224268\pi\)
\(798\) 16.4362 0.581835
\(799\) 86.1109 3.04638
\(800\) −30.7850 −1.08841
\(801\) 0.844280 0.0298312
\(802\) −16.0062 −0.565199
\(803\) −11.6690 −0.411792
\(804\) 20.9078 0.737361
\(805\) −1.75076 −0.0617062
\(806\) −28.7407 −1.01235
\(807\) −29.6542 −1.04388
\(808\) 11.4833 0.403982
\(809\) −12.2106 −0.429303 −0.214652 0.976691i \(-0.568862\pi\)
−0.214652 + 0.976691i \(0.568862\pi\)
\(810\) 17.6228 0.619204
\(811\) −27.6071 −0.969417 −0.484708 0.874676i \(-0.661074\pi\)
−0.484708 + 0.874676i \(0.661074\pi\)
\(812\) 11.9648 0.419882
\(813\) −53.0376 −1.86011
\(814\) −5.10800 −0.179035
\(815\) 0.914186 0.0320226
\(816\) 24.2360 0.848429
\(817\) −19.6294 −0.686746
\(818\) −18.6067 −0.650567
\(819\) −0.172830 −0.00603918
\(820\) 17.5040 0.611268
\(821\) −20.4762 −0.714624 −0.357312 0.933985i \(-0.616307\pi\)
−0.357312 + 0.933985i \(0.616307\pi\)
\(822\) 25.8266 0.900807
\(823\) −0.0564176 −0.00196660 −0.000983298 1.00000i \(-0.500313\pi\)
−0.000983298 1.00000i \(0.500313\pi\)
\(824\) −1.94772 −0.0678521
\(825\) −16.6609 −0.580057
\(826\) 15.0121 0.522337
\(827\) −33.2434 −1.15599 −0.577993 0.816042i \(-0.696164\pi\)
−0.577993 + 0.816042i \(0.696164\pi\)
\(828\) 0.398173 0.0138375
\(829\) −8.71472 −0.302675 −0.151337 0.988482i \(-0.548358\pi\)
−0.151337 + 0.988482i \(0.548358\pi\)
\(830\) −9.45565 −0.328210
\(831\) −53.0438 −1.84007
\(832\) −41.8014 −1.44920
\(833\) 49.4731 1.71414
\(834\) −72.8828 −2.52372
\(835\) −19.0612 −0.659640
\(836\) −34.1600 −1.18145
\(837\) −20.7366 −0.716761
\(838\) 30.2540 1.04511
\(839\) 34.8972 1.20479 0.602393 0.798199i \(-0.294214\pi\)
0.602393 + 0.798199i \(0.294214\pi\)
\(840\) −2.25743 −0.0778888
\(841\) −2.59490 −0.0894793
\(842\) −85.6281 −2.95094
\(843\) 6.68041 0.230086
\(844\) 1.54676 0.0532416
\(845\) −1.78127 −0.0612776
\(846\) −1.49461 −0.0513858
\(847\) −4.63530 −0.159271
\(848\) −11.5054 −0.395099
\(849\) −16.5033 −0.566393
\(850\) −71.5280 −2.45339
\(851\) −2.29348 −0.0786196
\(852\) −30.6180 −1.04896
\(853\) −0.236114 −0.00808440 −0.00404220 0.999992i \(-0.501287\pi\)
−0.00404220 + 0.999992i \(0.501287\pi\)
\(854\) 8.16662 0.279456
\(855\) 0.298708 0.0102156
\(856\) 13.2974 0.454495
\(857\) −50.1929 −1.71456 −0.857278 0.514854i \(-0.827846\pi\)
−0.857278 + 0.514854i \(0.827846\pi\)
\(858\) −29.1051 −0.993631
\(859\) 10.9770 0.374529 0.187264 0.982310i \(-0.440038\pi\)
0.187264 + 0.982310i \(0.440038\pi\)
\(860\) 9.53467 0.325129
\(861\) 9.82749 0.334920
\(862\) 63.7280 2.17059
\(863\) −24.4521 −0.832361 −0.416180 0.909282i \(-0.636632\pi\)
−0.416180 + 0.909282i \(0.636632\pi\)
\(864\) −38.8016 −1.32006
\(865\) 0.585645 0.0199125
\(866\) 43.9286 1.49275
\(867\) 76.4677 2.59698
\(868\) 9.19918 0.312241
\(869\) −11.3632 −0.385471
\(870\) −17.6191 −0.597343
\(871\) 14.5428 0.492764
\(872\) −22.8035 −0.772224
\(873\) 0.224124 0.00758546
\(874\) −26.3386 −0.890918
\(875\) −6.99566 −0.236497
\(876\) −23.8920 −0.807237
\(877\) 13.8825 0.468779 0.234390 0.972143i \(-0.424691\pi\)
0.234390 + 0.972143i \(0.424691\pi\)
\(878\) 28.8149 0.972456
\(879\) −43.4287 −1.46481
\(880\) −3.84416 −0.129587
\(881\) −14.4570 −0.487069 −0.243535 0.969892i \(-0.578307\pi\)
−0.243535 + 0.969892i \(0.578307\pi\)
\(882\) −0.858696 −0.0289138
\(883\) −16.1102 −0.542150 −0.271075 0.962558i \(-0.587379\pi\)
−0.271075 + 0.962558i \(0.587379\pi\)
\(884\) −72.7637 −2.44731
\(885\) −12.8732 −0.432729
\(886\) 28.3353 0.951942
\(887\) −55.6919 −1.86995 −0.934976 0.354711i \(-0.884579\pi\)
−0.934976 + 0.354711i \(0.884579\pi\)
\(888\) −2.95722 −0.0992377
\(889\) −3.16488 −0.106147
\(890\) 27.1274 0.909311
\(891\) −20.5635 −0.688903
\(892\) 18.8421 0.630882
\(893\) 57.5730 1.92661
\(894\) 68.7084 2.29795
\(895\) −18.1417 −0.606409
\(896\) 10.6300 0.355122
\(897\) −13.0681 −0.436332
\(898\) 24.0075 0.801141
\(899\) 20.3017 0.677099
\(900\) 0.722960 0.0240987
\(901\) −50.1336 −1.67019
\(902\) −35.0744 −1.16785
\(903\) 5.35316 0.178142
\(904\) 1.08776 0.0361785
\(905\) −9.11393 −0.302957
\(906\) −11.2113 −0.372472
\(907\) 30.2278 1.00370 0.501849 0.864955i \(-0.332653\pi\)
0.501849 + 0.864955i \(0.332653\pi\)
\(908\) 32.0007 1.06198
\(909\) 0.414384 0.0137443
\(910\) −5.55316 −0.184086
\(911\) −9.80346 −0.324803 −0.162401 0.986725i \(-0.551924\pi\)
−0.162401 + 0.986725i \(0.551924\pi\)
\(912\) 16.2040 0.536567
\(913\) 11.0335 0.365154
\(914\) 13.9635 0.461873
\(915\) −7.00308 −0.231515
\(916\) 21.6321 0.714745
\(917\) 11.9280 0.393898
\(918\) −90.1543 −2.97554
\(919\) −37.6404 −1.24164 −0.620821 0.783953i \(-0.713200\pi\)
−0.620821 + 0.783953i \(0.713200\pi\)
\(920\) 3.61749 0.119265
\(921\) −13.8029 −0.454821
\(922\) 1.02346 0.0337060
\(923\) −21.2970 −0.700998
\(924\) 9.31581 0.306468
\(925\) −4.16426 −0.136920
\(926\) −21.6843 −0.712591
\(927\) −0.0702849 −0.00230846
\(928\) 37.9878 1.24701
\(929\) −21.5188 −0.706010 −0.353005 0.935621i \(-0.614840\pi\)
−0.353005 + 0.935621i \(0.614840\pi\)
\(930\) −13.5465 −0.444208
\(931\) 33.0773 1.08406
\(932\) 84.5265 2.76876
\(933\) 53.8029 1.76143
\(934\) −1.73861 −0.0568891
\(935\) −16.7505 −0.547800
\(936\) 0.357108 0.0116724
\(937\) −45.8465 −1.49774 −0.748870 0.662717i \(-0.769403\pi\)
−0.748870 + 0.662717i \(0.769403\pi\)
\(938\) −7.99340 −0.260994
\(939\) 22.2219 0.725183
\(940\) −27.9652 −0.912123
\(941\) −3.70795 −0.120876 −0.0604378 0.998172i \(-0.519250\pi\)
−0.0604378 + 0.998172i \(0.519250\pi\)
\(942\) 10.2311 0.333348
\(943\) −15.7483 −0.512837
\(944\) 14.7999 0.481697
\(945\) −4.00664 −0.130336
\(946\) −19.1055 −0.621172
\(947\) −37.7647 −1.22719 −0.613594 0.789622i \(-0.710277\pi\)
−0.613594 + 0.789622i \(0.710277\pi\)
\(948\) −23.2659 −0.755641
\(949\) −16.6186 −0.539461
\(950\) −47.8229 −1.55158
\(951\) 55.7582 1.80808
\(952\) 11.3087 0.366517
\(953\) 28.4079 0.920221 0.460110 0.887862i \(-0.347810\pi\)
0.460110 + 0.887862i \(0.347810\pi\)
\(954\) 0.870160 0.0281725
\(955\) −11.1134 −0.359621
\(956\) −50.6665 −1.63867
\(957\) 20.5591 0.664581
\(958\) 18.6412 0.602269
\(959\) −5.74990 −0.185674
\(960\) −19.7025 −0.635895
\(961\) −15.3909 −0.496482
\(962\) −7.27460 −0.234542
\(963\) 0.479845 0.0154628
\(964\) 48.6593 1.56721
\(965\) 4.74540 0.152760
\(966\) 7.18285 0.231104
\(967\) 39.5934 1.27324 0.636619 0.771178i \(-0.280332\pi\)
0.636619 + 0.771178i \(0.280332\pi\)
\(968\) 9.57763 0.307837
\(969\) 70.6068 2.26822
\(970\) 7.20128 0.231219
\(971\) −16.2409 −0.521197 −0.260598 0.965447i \(-0.583920\pi\)
−0.260598 + 0.965447i \(0.583920\pi\)
\(972\) 1.80392 0.0578608
\(973\) 16.2262 0.520188
\(974\) −19.7405 −0.632527
\(975\) −23.7277 −0.759895
\(976\) 8.05122 0.257713
\(977\) −36.7740 −1.17651 −0.588253 0.808677i \(-0.700184\pi\)
−0.588253 + 0.808677i \(0.700184\pi\)
\(978\) −3.75063 −0.119932
\(979\) −31.6540 −1.01166
\(980\) −16.0668 −0.513234
\(981\) −0.822880 −0.0262725
\(982\) 78.0234 2.48983
\(983\) 11.9710 0.381816 0.190908 0.981608i \(-0.438857\pi\)
0.190908 + 0.981608i \(0.438857\pi\)
\(984\) −20.3059 −0.647329
\(985\) −20.8569 −0.664557
\(986\) 88.2636 2.81089
\(987\) −15.7008 −0.499762
\(988\) −48.6492 −1.54774
\(989\) −8.57832 −0.272775
\(990\) 0.290735 0.00924017
\(991\) −39.6244 −1.25871 −0.629354 0.777118i \(-0.716681\pi\)
−0.629354 + 0.777118i \(0.716681\pi\)
\(992\) 29.2071 0.927327
\(993\) 13.2234 0.419633
\(994\) 11.7058 0.371286
\(995\) 12.9702 0.411184
\(996\) 22.5907 0.715813
\(997\) 34.2298 1.08407 0.542034 0.840356i \(-0.317654\pi\)
0.542034 + 0.840356i \(0.317654\pi\)
\(998\) −63.2363 −2.00171
\(999\) −5.24866 −0.166060
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 6031.2.a.b.1.16 109
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6031.2.a.b.1.16 109 1.1 even 1 trivial