Properties

Label 8002.2.a.e.1.77
Level $8002$
Weight $2$
Character 8002.1
Self dual yes
Analytic conductor $63.896$
Analytic rank $0$
Dimension $77$
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] = [8002,2,Mod(1,8002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8002, 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("8002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8002.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: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.77
Character \(\chi\) \(=\) 8002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.43355 q^{3} +1.00000 q^{4} +2.08896 q^{5} -3.43355 q^{6} +2.40538 q^{7} -1.00000 q^{8} +8.78926 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.43355 q^{3} +1.00000 q^{4} +2.08896 q^{5} -3.43355 q^{6} +2.40538 q^{7} -1.00000 q^{8} +8.78926 q^{9} -2.08896 q^{10} +4.45759 q^{11} +3.43355 q^{12} -0.0803882 q^{13} -2.40538 q^{14} +7.17254 q^{15} +1.00000 q^{16} +3.60116 q^{17} -8.78926 q^{18} -3.47507 q^{19} +2.08896 q^{20} +8.25898 q^{21} -4.45759 q^{22} -6.45531 q^{23} -3.43355 q^{24} -0.636259 q^{25} +0.0803882 q^{26} +19.8777 q^{27} +2.40538 q^{28} -0.536723 q^{29} -7.17254 q^{30} -5.71930 q^{31} -1.00000 q^{32} +15.3054 q^{33} -3.60116 q^{34} +5.02473 q^{35} +8.78926 q^{36} +10.2724 q^{37} +3.47507 q^{38} -0.276017 q^{39} -2.08896 q^{40} +7.44082 q^{41} -8.25898 q^{42} -12.7213 q^{43} +4.45759 q^{44} +18.3604 q^{45} +6.45531 q^{46} -7.24592 q^{47} +3.43355 q^{48} -1.21416 q^{49} +0.636259 q^{50} +12.3648 q^{51} -0.0803882 q^{52} -4.43522 q^{53} -19.8777 q^{54} +9.31171 q^{55} -2.40538 q^{56} -11.9318 q^{57} +0.536723 q^{58} -11.4846 q^{59} +7.17254 q^{60} -5.67707 q^{61} +5.71930 q^{62} +21.1415 q^{63} +1.00000 q^{64} -0.167927 q^{65} -15.3054 q^{66} +12.8745 q^{67} +3.60116 q^{68} -22.1646 q^{69} -5.02473 q^{70} +3.84772 q^{71} -8.78926 q^{72} +4.11923 q^{73} -10.2724 q^{74} -2.18463 q^{75} -3.47507 q^{76} +10.7222 q^{77} +0.276017 q^{78} +14.8916 q^{79} +2.08896 q^{80} +41.8833 q^{81} -7.44082 q^{82} -7.72704 q^{83} +8.25898 q^{84} +7.52268 q^{85} +12.7213 q^{86} -1.84286 q^{87} -4.45759 q^{88} -14.9446 q^{89} -18.3604 q^{90} -0.193364 q^{91} -6.45531 q^{92} -19.6375 q^{93} +7.24592 q^{94} -7.25928 q^{95} -3.43355 q^{96} -11.6638 q^{97} +1.21416 q^{98} +39.1789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 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
\(3\) 3.43355 1.98236 0.991180 0.132521i \(-0.0423074\pi\)
0.991180 + 0.132521i \(0.0423074\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.08896 0.934210 0.467105 0.884202i \(-0.345297\pi\)
0.467105 + 0.884202i \(0.345297\pi\)
\(6\) −3.43355 −1.40174
\(7\) 2.40538 0.909147 0.454574 0.890709i \(-0.349792\pi\)
0.454574 + 0.890709i \(0.349792\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.78926 2.92975
\(10\) −2.08896 −0.660586
\(11\) 4.45759 1.34401 0.672007 0.740545i \(-0.265433\pi\)
0.672007 + 0.740545i \(0.265433\pi\)
\(12\) 3.43355 0.991180
\(13\) −0.0803882 −0.0222957 −0.0111478 0.999938i \(-0.503549\pi\)
−0.0111478 + 0.999938i \(0.503549\pi\)
\(14\) −2.40538 −0.642864
\(15\) 7.17254 1.85194
\(16\) 1.00000 0.250000
\(17\) 3.60116 0.873410 0.436705 0.899605i \(-0.356145\pi\)
0.436705 + 0.899605i \(0.356145\pi\)
\(18\) −8.78926 −2.07165
\(19\) −3.47507 −0.797237 −0.398618 0.917117i \(-0.630510\pi\)
−0.398618 + 0.917117i \(0.630510\pi\)
\(20\) 2.08896 0.467105
\(21\) 8.25898 1.80226
\(22\) −4.45759 −0.950361
\(23\) −6.45531 −1.34603 −0.673013 0.739631i \(-0.735000\pi\)
−0.673013 + 0.739631i \(0.735000\pi\)
\(24\) −3.43355 −0.700870
\(25\) −0.636259 −0.127252
\(26\) 0.0803882 0.0157654
\(27\) 19.8777 3.82546
\(28\) 2.40538 0.454574
\(29\) −0.536723 −0.0996669 −0.0498334 0.998758i \(-0.515869\pi\)
−0.0498334 + 0.998758i \(0.515869\pi\)
\(30\) −7.17254 −1.30952
\(31\) −5.71930 −1.02722 −0.513608 0.858025i \(-0.671691\pi\)
−0.513608 + 0.858025i \(0.671691\pi\)
\(32\) −1.00000 −0.176777
\(33\) 15.3054 2.66432
\(34\) −3.60116 −0.617594
\(35\) 5.02473 0.849334
\(36\) 8.78926 1.46488
\(37\) 10.2724 1.68877 0.844383 0.535741i \(-0.179968\pi\)
0.844383 + 0.535741i \(0.179968\pi\)
\(38\) 3.47507 0.563732
\(39\) −0.276017 −0.0441980
\(40\) −2.08896 −0.330293
\(41\) 7.44082 1.16206 0.581031 0.813882i \(-0.302650\pi\)
0.581031 + 0.813882i \(0.302650\pi\)
\(42\) −8.25898 −1.27439
\(43\) −12.7213 −1.93998 −0.969988 0.243151i \(-0.921819\pi\)
−0.969988 + 0.243151i \(0.921819\pi\)
\(44\) 4.45759 0.672007
\(45\) 18.3604 2.73700
\(46\) 6.45531 0.951784
\(47\) −7.24592 −1.05693 −0.528463 0.848956i \(-0.677232\pi\)
−0.528463 + 0.848956i \(0.677232\pi\)
\(48\) 3.43355 0.495590
\(49\) −1.21416 −0.173452
\(50\) 0.636259 0.0899806
\(51\) 12.3648 1.73141
\(52\) −0.0803882 −0.0111478
\(53\) −4.43522 −0.609225 −0.304612 0.952476i \(-0.598527\pi\)
−0.304612 + 0.952476i \(0.598527\pi\)
\(54\) −19.8777 −2.70501
\(55\) 9.31171 1.25559
\(56\) −2.40538 −0.321432
\(57\) −11.9318 −1.58041
\(58\) 0.536723 0.0704751
\(59\) −11.4846 −1.49516 −0.747581 0.664170i \(-0.768785\pi\)
−0.747581 + 0.664170i \(0.768785\pi\)
\(60\) 7.17254 0.925970
\(61\) −5.67707 −0.726875 −0.363437 0.931619i \(-0.618397\pi\)
−0.363437 + 0.931619i \(0.618397\pi\)
\(62\) 5.71930 0.726351
\(63\) 21.1415 2.66358
\(64\) 1.00000 0.125000
\(65\) −0.167927 −0.0208288
\(66\) −15.3054 −1.88396
\(67\) 12.8745 1.57287 0.786437 0.617671i \(-0.211924\pi\)
0.786437 + 0.617671i \(0.211924\pi\)
\(68\) 3.60116 0.436705
\(69\) −22.1646 −2.66831
\(70\) −5.02473 −0.600570
\(71\) 3.84772 0.456641 0.228320 0.973586i \(-0.426677\pi\)
0.228320 + 0.973586i \(0.426677\pi\)
\(72\) −8.78926 −1.03582
\(73\) 4.11923 0.482119 0.241060 0.970510i \(-0.422505\pi\)
0.241060 + 0.970510i \(0.422505\pi\)
\(74\) −10.2724 −1.19414
\(75\) −2.18463 −0.252259
\(76\) −3.47507 −0.398618
\(77\) 10.7222 1.22191
\(78\) 0.276017 0.0312527
\(79\) 14.8916 1.67544 0.837720 0.546100i \(-0.183888\pi\)
0.837720 + 0.546100i \(0.183888\pi\)
\(80\) 2.08896 0.233552
\(81\) 41.8833 4.65370
\(82\) −7.44082 −0.821701
\(83\) −7.72704 −0.848152 −0.424076 0.905627i \(-0.639401\pi\)
−0.424076 + 0.905627i \(0.639401\pi\)
\(84\) 8.25898 0.901128
\(85\) 7.52268 0.815949
\(86\) 12.7213 1.37177
\(87\) −1.84286 −0.197576
\(88\) −4.45759 −0.475181
\(89\) −14.9446 −1.58413 −0.792064 0.610438i \(-0.790994\pi\)
−0.792064 + 0.610438i \(0.790994\pi\)
\(90\) −18.3604 −1.93535
\(91\) −0.193364 −0.0202700
\(92\) −6.45531 −0.673013
\(93\) −19.6375 −2.03631
\(94\) 7.24592 0.747360
\(95\) −7.25928 −0.744787
\(96\) −3.43355 −0.350435
\(97\) −11.6638 −1.18427 −0.592137 0.805837i \(-0.701716\pi\)
−0.592137 + 0.805837i \(0.701716\pi\)
\(98\) 1.21416 0.122649
\(99\) 39.1789 3.93763
\(100\) −0.636259 −0.0636259
\(101\) 7.02329 0.698844 0.349422 0.936966i \(-0.386378\pi\)
0.349422 + 0.936966i \(0.386378\pi\)
\(102\) −12.3648 −1.22429
\(103\) 15.1392 1.49171 0.745856 0.666107i \(-0.232040\pi\)
0.745856 + 0.666107i \(0.232040\pi\)
\(104\) 0.0803882 0.00788271
\(105\) 17.2527 1.68369
\(106\) 4.43522 0.430787
\(107\) 12.3144 1.19047 0.595237 0.803550i \(-0.297058\pi\)
0.595237 + 0.803550i \(0.297058\pi\)
\(108\) 19.8777 1.91273
\(109\) −0.398614 −0.0381803 −0.0190901 0.999818i \(-0.506077\pi\)
−0.0190901 + 0.999818i \(0.506077\pi\)
\(110\) −9.31171 −0.887837
\(111\) 35.2706 3.34774
\(112\) 2.40538 0.227287
\(113\) −4.90227 −0.461167 −0.230584 0.973053i \(-0.574064\pi\)
−0.230584 + 0.973053i \(0.574064\pi\)
\(114\) 11.9318 1.11752
\(115\) −13.4849 −1.25747
\(116\) −0.536723 −0.0498334
\(117\) −0.706552 −0.0653208
\(118\) 11.4846 1.05724
\(119\) 8.66216 0.794058
\(120\) −7.17254 −0.654760
\(121\) 8.87010 0.806373
\(122\) 5.67707 0.513978
\(123\) 25.5484 2.30362
\(124\) −5.71930 −0.513608
\(125\) −11.7739 −1.05309
\(126\) −21.1415 −1.88343
\(127\) 3.29909 0.292747 0.146373 0.989229i \(-0.453240\pi\)
0.146373 + 0.989229i \(0.453240\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −43.6791 −3.84573
\(130\) 0.167927 0.0147282
\(131\) −11.5779 −1.01157 −0.505784 0.862660i \(-0.668797\pi\)
−0.505784 + 0.862660i \(0.668797\pi\)
\(132\) 15.3054 1.33216
\(133\) −8.35886 −0.724805
\(134\) −12.8745 −1.11219
\(135\) 41.5236 3.57379
\(136\) −3.60116 −0.308797
\(137\) 6.14494 0.524997 0.262499 0.964932i \(-0.415453\pi\)
0.262499 + 0.964932i \(0.415453\pi\)
\(138\) 22.1646 1.88678
\(139\) −10.3964 −0.881815 −0.440907 0.897553i \(-0.645343\pi\)
−0.440907 + 0.897553i \(0.645343\pi\)
\(140\) 5.02473 0.424667
\(141\) −24.8792 −2.09521
\(142\) −3.84772 −0.322894
\(143\) −0.358337 −0.0299657
\(144\) 8.78926 0.732438
\(145\) −1.12119 −0.0931098
\(146\) −4.11923 −0.340910
\(147\) −4.16888 −0.343844
\(148\) 10.2724 0.844383
\(149\) −13.7946 −1.13010 −0.565049 0.825058i \(-0.691143\pi\)
−0.565049 + 0.825058i \(0.691143\pi\)
\(150\) 2.18463 0.178374
\(151\) 18.2701 1.48680 0.743399 0.668848i \(-0.233212\pi\)
0.743399 + 0.668848i \(0.233212\pi\)
\(152\) 3.47507 0.281866
\(153\) 31.6515 2.55888
\(154\) −10.7222 −0.864018
\(155\) −11.9474 −0.959636
\(156\) −0.276017 −0.0220990
\(157\) −3.86962 −0.308830 −0.154415 0.988006i \(-0.549349\pi\)
−0.154415 + 0.988006i \(0.549349\pi\)
\(158\) −14.8916 −1.18472
\(159\) −15.2286 −1.20770
\(160\) −2.08896 −0.165147
\(161\) −15.5275 −1.22374
\(162\) −41.8833 −3.29066
\(163\) −10.8307 −0.848328 −0.424164 0.905585i \(-0.639432\pi\)
−0.424164 + 0.905585i \(0.639432\pi\)
\(164\) 7.44082 0.581031
\(165\) 31.9722 2.48903
\(166\) 7.72704 0.599734
\(167\) 12.7546 0.986980 0.493490 0.869751i \(-0.335721\pi\)
0.493490 + 0.869751i \(0.335721\pi\)
\(168\) −8.25898 −0.637194
\(169\) −12.9935 −0.999503
\(170\) −7.52268 −0.576963
\(171\) −30.5433 −2.33571
\(172\) −12.7213 −0.969988
\(173\) −21.7963 −1.65714 −0.828570 0.559886i \(-0.810845\pi\)
−0.828570 + 0.559886i \(0.810845\pi\)
\(174\) 1.84286 0.139707
\(175\) −1.53044 −0.115691
\(176\) 4.45759 0.336003
\(177\) −39.4328 −2.96395
\(178\) 14.9446 1.12015
\(179\) −9.63144 −0.719887 −0.359944 0.932974i \(-0.617204\pi\)
−0.359944 + 0.932974i \(0.617204\pi\)
\(180\) 18.3604 1.36850
\(181\) 15.6087 1.16018 0.580092 0.814551i \(-0.303016\pi\)
0.580092 + 0.814551i \(0.303016\pi\)
\(182\) 0.193364 0.0143331
\(183\) −19.4925 −1.44093
\(184\) 6.45531 0.475892
\(185\) 21.4585 1.57766
\(186\) 19.6375 1.43989
\(187\) 16.0525 1.17388
\(188\) −7.24592 −0.528463
\(189\) 47.8133 3.47791
\(190\) 7.25928 0.526644
\(191\) 11.6148 0.840419 0.420210 0.907427i \(-0.361957\pi\)
0.420210 + 0.907427i \(0.361957\pi\)
\(192\) 3.43355 0.247795
\(193\) −25.3588 −1.82537 −0.912683 0.408669i \(-0.865993\pi\)
−0.912683 + 0.408669i \(0.865993\pi\)
\(194\) 11.6638 0.837409
\(195\) −0.576587 −0.0412903
\(196\) −1.21416 −0.0867258
\(197\) −8.48353 −0.604427 −0.302213 0.953240i \(-0.597725\pi\)
−0.302213 + 0.953240i \(0.597725\pi\)
\(198\) −39.1789 −2.78432
\(199\) 11.5177 0.816465 0.408232 0.912878i \(-0.366145\pi\)
0.408232 + 0.912878i \(0.366145\pi\)
\(200\) 0.636259 0.0449903
\(201\) 44.2053 3.11800
\(202\) −7.02329 −0.494157
\(203\) −1.29102 −0.0906118
\(204\) 12.3648 0.865707
\(205\) 15.5436 1.08561
\(206\) −15.1392 −1.05480
\(207\) −56.7374 −3.94352
\(208\) −0.0803882 −0.00557392
\(209\) −15.4905 −1.07150
\(210\) −17.2527 −1.19055
\(211\) −13.1396 −0.904565 −0.452283 0.891875i \(-0.649390\pi\)
−0.452283 + 0.891875i \(0.649390\pi\)
\(212\) −4.43522 −0.304612
\(213\) 13.2113 0.905226
\(214\) −12.3144 −0.841792
\(215\) −26.5742 −1.81235
\(216\) −19.8777 −1.35251
\(217\) −13.7571 −0.933890
\(218\) 0.398614 0.0269975
\(219\) 14.1436 0.955734
\(220\) 9.31171 0.627796
\(221\) −0.289491 −0.0194733
\(222\) −35.2706 −2.36721
\(223\) −11.4947 −0.769739 −0.384870 0.922971i \(-0.625754\pi\)
−0.384870 + 0.922971i \(0.625754\pi\)
\(224\) −2.40538 −0.160716
\(225\) −5.59224 −0.372816
\(226\) 4.90227 0.326094
\(227\) −6.20823 −0.412055 −0.206027 0.978546i \(-0.566054\pi\)
−0.206027 + 0.978546i \(0.566054\pi\)
\(228\) −11.9318 −0.790205
\(229\) −17.0912 −1.12942 −0.564708 0.825291i \(-0.691011\pi\)
−0.564708 + 0.825291i \(0.691011\pi\)
\(230\) 13.4849 0.889166
\(231\) 36.8151 2.42226
\(232\) 0.536723 0.0352376
\(233\) 6.33038 0.414717 0.207358 0.978265i \(-0.433513\pi\)
0.207358 + 0.978265i \(0.433513\pi\)
\(234\) 0.706552 0.0461888
\(235\) −15.1364 −0.987391
\(236\) −11.4846 −0.747581
\(237\) 51.1312 3.32133
\(238\) −8.66216 −0.561484
\(239\) 22.2594 1.43984 0.719920 0.694057i \(-0.244178\pi\)
0.719920 + 0.694057i \(0.244178\pi\)
\(240\) 7.17254 0.462985
\(241\) 23.3716 1.50550 0.752748 0.658309i \(-0.228728\pi\)
0.752748 + 0.658309i \(0.228728\pi\)
\(242\) −8.87010 −0.570192
\(243\) 84.1751 5.39984
\(244\) −5.67707 −0.363437
\(245\) −2.53633 −0.162040
\(246\) −25.5484 −1.62891
\(247\) 0.279355 0.0177749
\(248\) 5.71930 0.363176
\(249\) −26.5312 −1.68134
\(250\) 11.7739 0.744647
\(251\) 13.5974 0.858262 0.429131 0.903242i \(-0.358820\pi\)
0.429131 + 0.903242i \(0.358820\pi\)
\(252\) 21.1415 1.33179
\(253\) −28.7751 −1.80908
\(254\) −3.29909 −0.207003
\(255\) 25.8295 1.61750
\(256\) 1.00000 0.0625000
\(257\) −27.5031 −1.71560 −0.857799 0.513985i \(-0.828169\pi\)
−0.857799 + 0.513985i \(0.828169\pi\)
\(258\) 43.6791 2.71934
\(259\) 24.7089 1.53534
\(260\) −0.167927 −0.0104144
\(261\) −4.71739 −0.291999
\(262\) 11.5779 0.715286
\(263\) 23.7210 1.46270 0.731350 0.682002i \(-0.238891\pi\)
0.731350 + 0.682002i \(0.238891\pi\)
\(264\) −15.3054 −0.941979
\(265\) −9.26499 −0.569144
\(266\) 8.35886 0.512515
\(267\) −51.3132 −3.14031
\(268\) 12.8745 0.786437
\(269\) −5.48744 −0.334575 −0.167288 0.985908i \(-0.553501\pi\)
−0.167288 + 0.985908i \(0.553501\pi\)
\(270\) −41.5236 −2.52705
\(271\) −24.2332 −1.47206 −0.736031 0.676948i \(-0.763302\pi\)
−0.736031 + 0.676948i \(0.763302\pi\)
\(272\) 3.60116 0.218353
\(273\) −0.663924 −0.0401825
\(274\) −6.14494 −0.371229
\(275\) −2.83618 −0.171028
\(276\) −22.1646 −1.33415
\(277\) −9.51697 −0.571819 −0.285910 0.958257i \(-0.592296\pi\)
−0.285910 + 0.958257i \(0.592296\pi\)
\(278\) 10.3964 0.623537
\(279\) −50.2684 −3.00949
\(280\) −5.02473 −0.300285
\(281\) 29.8158 1.77866 0.889332 0.457262i \(-0.151170\pi\)
0.889332 + 0.457262i \(0.151170\pi\)
\(282\) 24.8792 1.48154
\(283\) −11.8968 −0.707193 −0.353596 0.935398i \(-0.615041\pi\)
−0.353596 + 0.935398i \(0.615041\pi\)
\(284\) 3.84772 0.228320
\(285\) −24.9251 −1.47644
\(286\) 0.358337 0.0211889
\(287\) 17.8980 1.05648
\(288\) −8.78926 −0.517912
\(289\) −4.03162 −0.237154
\(290\) 1.12119 0.0658386
\(291\) −40.0481 −2.34766
\(292\) 4.11923 0.241060
\(293\) 22.3570 1.30611 0.653055 0.757311i \(-0.273487\pi\)
0.653055 + 0.757311i \(0.273487\pi\)
\(294\) 4.16888 0.243134
\(295\) −23.9908 −1.39680
\(296\) −10.2724 −0.597069
\(297\) 88.6066 5.14148
\(298\) 13.7946 0.799099
\(299\) 0.518931 0.0300105
\(300\) −2.18463 −0.126129
\(301\) −30.5995 −1.76372
\(302\) −18.2701 −1.05133
\(303\) 24.1148 1.38536
\(304\) −3.47507 −0.199309
\(305\) −11.8592 −0.679053
\(306\) −31.6515 −1.80940
\(307\) −12.4569 −0.710952 −0.355476 0.934685i \(-0.615681\pi\)
−0.355476 + 0.934685i \(0.615681\pi\)
\(308\) 10.7222 0.610953
\(309\) 51.9813 2.95711
\(310\) 11.9474 0.678565
\(311\) −9.15293 −0.519015 −0.259508 0.965741i \(-0.583560\pi\)
−0.259508 + 0.965741i \(0.583560\pi\)
\(312\) 0.276017 0.0156264
\(313\) 13.0712 0.738829 0.369414 0.929265i \(-0.379558\pi\)
0.369414 + 0.929265i \(0.379558\pi\)
\(314\) 3.86962 0.218376
\(315\) 44.1636 2.48834
\(316\) 14.8916 0.837720
\(317\) −0.588556 −0.0330566 −0.0165283 0.999863i \(-0.505261\pi\)
−0.0165283 + 0.999863i \(0.505261\pi\)
\(318\) 15.2286 0.853975
\(319\) −2.39249 −0.133954
\(320\) 2.08896 0.116776
\(321\) 42.2819 2.35995
\(322\) 15.5275 0.865312
\(323\) −12.5143 −0.696315
\(324\) 41.8833 2.32685
\(325\) 0.0511477 0.00283716
\(326\) 10.8307 0.599858
\(327\) −1.36866 −0.0756871
\(328\) −7.44082 −0.410851
\(329\) −17.4292 −0.960902
\(330\) −31.9722 −1.76001
\(331\) 9.55008 0.524920 0.262460 0.964943i \(-0.415466\pi\)
0.262460 + 0.964943i \(0.415466\pi\)
\(332\) −7.72704 −0.424076
\(333\) 90.2864 4.94766
\(334\) −12.7546 −0.697900
\(335\) 26.8943 1.46939
\(336\) 8.25898 0.450564
\(337\) 22.0093 1.19893 0.599463 0.800403i \(-0.295381\pi\)
0.599463 + 0.800403i \(0.295381\pi\)
\(338\) 12.9935 0.706755
\(339\) −16.8322 −0.914200
\(340\) 7.52268 0.407974
\(341\) −25.4943 −1.38059
\(342\) 30.5433 1.65159
\(343\) −19.7582 −1.06684
\(344\) 12.7213 0.685885
\(345\) −46.3010 −2.49276
\(346\) 21.7963 1.17177
\(347\) −14.4373 −0.775035 −0.387518 0.921862i \(-0.626667\pi\)
−0.387518 + 0.921862i \(0.626667\pi\)
\(348\) −1.84286 −0.0987878
\(349\) 14.2407 0.762285 0.381143 0.924516i \(-0.375531\pi\)
0.381143 + 0.924516i \(0.375531\pi\)
\(350\) 1.53044 0.0818056
\(351\) −1.59793 −0.0852913
\(352\) −4.45759 −0.237590
\(353\) −0.617420 −0.0328620 −0.0164310 0.999865i \(-0.505230\pi\)
−0.0164310 + 0.999865i \(0.505230\pi\)
\(354\) 39.4328 2.09583
\(355\) 8.03773 0.426598
\(356\) −14.9446 −0.792064
\(357\) 29.7419 1.57411
\(358\) 9.63144 0.509037
\(359\) 0.756867 0.0399459 0.0199729 0.999801i \(-0.493642\pi\)
0.0199729 + 0.999801i \(0.493642\pi\)
\(360\) −18.3604 −0.967677
\(361\) −6.92386 −0.364414
\(362\) −15.6087 −0.820375
\(363\) 30.4559 1.59852
\(364\) −0.193364 −0.0101350
\(365\) 8.60489 0.450401
\(366\) 19.4925 1.01889
\(367\) 23.5275 1.22813 0.614063 0.789257i \(-0.289534\pi\)
0.614063 + 0.789257i \(0.289534\pi\)
\(368\) −6.45531 −0.336506
\(369\) 65.3993 3.40455
\(370\) −21.4585 −1.11558
\(371\) −10.6684 −0.553875
\(372\) −19.6375 −1.01816
\(373\) −9.93608 −0.514471 −0.257235 0.966349i \(-0.582812\pi\)
−0.257235 + 0.966349i \(0.582812\pi\)
\(374\) −16.0525 −0.830055
\(375\) −40.4263 −2.08760
\(376\) 7.24592 0.373680
\(377\) 0.0431461 0.00222214
\(378\) −47.8133 −2.45925
\(379\) −24.2797 −1.24716 −0.623581 0.781758i \(-0.714323\pi\)
−0.623581 + 0.781758i \(0.714323\pi\)
\(380\) −7.25928 −0.372393
\(381\) 11.3276 0.580330
\(382\) −11.6148 −0.594266
\(383\) 26.3998 1.34897 0.674483 0.738290i \(-0.264367\pi\)
0.674483 + 0.738290i \(0.264367\pi\)
\(384\) −3.43355 −0.175218
\(385\) 22.3982 1.14152
\(386\) 25.3588 1.29073
\(387\) −111.811 −5.68365
\(388\) −11.6638 −0.592137
\(389\) −20.8011 −1.05466 −0.527328 0.849661i \(-0.676806\pi\)
−0.527328 + 0.849661i \(0.676806\pi\)
\(390\) 0.576587 0.0291966
\(391\) −23.2466 −1.17563
\(392\) 1.21416 0.0613244
\(393\) −39.7534 −2.00529
\(394\) 8.48353 0.427394
\(395\) 31.1080 1.56521
\(396\) 39.1789 1.96881
\(397\) 17.9867 0.902729 0.451364 0.892340i \(-0.350937\pi\)
0.451364 + 0.892340i \(0.350937\pi\)
\(398\) −11.5177 −0.577328
\(399\) −28.7006 −1.43683
\(400\) −0.636259 −0.0318129
\(401\) −26.1569 −1.30622 −0.653108 0.757265i \(-0.726535\pi\)
−0.653108 + 0.757265i \(0.726535\pi\)
\(402\) −44.2053 −2.20476
\(403\) 0.459764 0.0229025
\(404\) 7.02329 0.349422
\(405\) 87.4923 4.34753
\(406\) 1.29102 0.0640723
\(407\) 45.7900 2.26972
\(408\) −12.3648 −0.612147
\(409\) −28.2204 −1.39541 −0.697704 0.716386i \(-0.745795\pi\)
−0.697704 + 0.716386i \(0.745795\pi\)
\(410\) −15.5436 −0.767642
\(411\) 21.0989 1.04073
\(412\) 15.1392 0.745856
\(413\) −27.6247 −1.35932
\(414\) 56.7374 2.78849
\(415\) −16.1414 −0.792352
\(416\) 0.0803882 0.00394135
\(417\) −35.6967 −1.74807
\(418\) 15.4905 0.757663
\(419\) −0.106804 −0.00521771 −0.00260885 0.999997i \(-0.500830\pi\)
−0.00260885 + 0.999997i \(0.500830\pi\)
\(420\) 17.2527 0.841843
\(421\) 14.1587 0.690053 0.345026 0.938593i \(-0.387870\pi\)
0.345026 + 0.938593i \(0.387870\pi\)
\(422\) 13.1396 0.639624
\(423\) −63.6863 −3.09653
\(424\) 4.43522 0.215393
\(425\) −2.29127 −0.111143
\(426\) −13.2113 −0.640092
\(427\) −13.6555 −0.660836
\(428\) 12.3144 0.595237
\(429\) −1.23037 −0.0594028
\(430\) 26.5742 1.28152
\(431\) 3.51166 0.169151 0.0845755 0.996417i \(-0.473047\pi\)
0.0845755 + 0.996417i \(0.473047\pi\)
\(432\) 19.8777 0.956366
\(433\) −24.8991 −1.19657 −0.598286 0.801282i \(-0.704151\pi\)
−0.598286 + 0.801282i \(0.704151\pi\)
\(434\) 13.7571 0.660360
\(435\) −3.84966 −0.184577
\(436\) −0.398614 −0.0190901
\(437\) 22.4327 1.07310
\(438\) −14.1436 −0.675806
\(439\) 36.4703 1.74063 0.870316 0.492494i \(-0.163915\pi\)
0.870316 + 0.492494i \(0.163915\pi\)
\(440\) −9.31171 −0.443918
\(441\) −10.6716 −0.508170
\(442\) 0.289491 0.0137697
\(443\) −3.54480 −0.168419 −0.0842094 0.996448i \(-0.526836\pi\)
−0.0842094 + 0.996448i \(0.526836\pi\)
\(444\) 35.2706 1.67387
\(445\) −31.2187 −1.47991
\(446\) 11.4947 0.544288
\(447\) −47.3644 −2.24026
\(448\) 2.40538 0.113643
\(449\) −14.2267 −0.671401 −0.335701 0.941969i \(-0.608973\pi\)
−0.335701 + 0.941969i \(0.608973\pi\)
\(450\) 5.59224 0.263621
\(451\) 33.1681 1.56183
\(452\) −4.90227 −0.230584
\(453\) 62.7312 2.94737
\(454\) 6.20823 0.291367
\(455\) −0.403929 −0.0189365
\(456\) 11.9318 0.558759
\(457\) 5.83438 0.272921 0.136460 0.990646i \(-0.456427\pi\)
0.136460 + 0.990646i \(0.456427\pi\)
\(458\) 17.0912 0.798618
\(459\) 71.5828 3.34120
\(460\) −13.4849 −0.628735
\(461\) 16.8067 0.782767 0.391384 0.920228i \(-0.371997\pi\)
0.391384 + 0.920228i \(0.371997\pi\)
\(462\) −36.8151 −1.71280
\(463\) −12.2503 −0.569318 −0.284659 0.958629i \(-0.591880\pi\)
−0.284659 + 0.958629i \(0.591880\pi\)
\(464\) −0.536723 −0.0249167
\(465\) −41.0219 −1.90234
\(466\) −6.33038 −0.293249
\(467\) 34.7821 1.60953 0.804763 0.593597i \(-0.202293\pi\)
0.804763 + 0.593597i \(0.202293\pi\)
\(468\) −0.706552 −0.0326604
\(469\) 30.9681 1.42997
\(470\) 15.1364 0.698191
\(471\) −13.2865 −0.612212
\(472\) 11.4846 0.528620
\(473\) −56.7062 −2.60736
\(474\) −51.1312 −2.34853
\(475\) 2.21105 0.101450
\(476\) 8.66216 0.397029
\(477\) −38.9823 −1.78488
\(478\) −22.2594 −1.01812
\(479\) 13.3228 0.608736 0.304368 0.952555i \(-0.401555\pi\)
0.304368 + 0.952555i \(0.401555\pi\)
\(480\) −7.17254 −0.327380
\(481\) −0.825776 −0.0376521
\(482\) −23.3716 −1.06455
\(483\) −53.3143 −2.42588
\(484\) 8.87010 0.403187
\(485\) −24.3651 −1.10636
\(486\) −84.1751 −3.81826
\(487\) −4.86783 −0.220583 −0.110291 0.993899i \(-0.535178\pi\)
−0.110291 + 0.993899i \(0.535178\pi\)
\(488\) 5.67707 0.256989
\(489\) −37.1878 −1.68169
\(490\) 2.53633 0.114580
\(491\) 34.9278 1.57627 0.788135 0.615503i \(-0.211047\pi\)
0.788135 + 0.615503i \(0.211047\pi\)
\(492\) 25.5484 1.15181
\(493\) −1.93283 −0.0870501
\(494\) −0.279355 −0.0125688
\(495\) 81.8430 3.67857
\(496\) −5.71930 −0.256804
\(497\) 9.25522 0.415154
\(498\) 26.5312 1.18889
\(499\) 10.7868 0.482881 0.241441 0.970416i \(-0.422380\pi\)
0.241441 + 0.970416i \(0.422380\pi\)
\(500\) −11.7739 −0.526545
\(501\) 43.7935 1.95655
\(502\) −13.5974 −0.606883
\(503\) 20.8016 0.927496 0.463748 0.885967i \(-0.346504\pi\)
0.463748 + 0.885967i \(0.346504\pi\)
\(504\) −21.1415 −0.941716
\(505\) 14.6714 0.652867
\(506\) 28.7751 1.27921
\(507\) −44.6139 −1.98137
\(508\) 3.29909 0.146373
\(509\) 29.1530 1.29218 0.646092 0.763259i \(-0.276402\pi\)
0.646092 + 0.763259i \(0.276402\pi\)
\(510\) −25.8295 −1.14375
\(511\) 9.90830 0.438317
\(512\) −1.00000 −0.0441942
\(513\) −69.0765 −3.04980
\(514\) 27.5031 1.21311
\(515\) 31.6252 1.39357
\(516\) −43.6791 −1.92287
\(517\) −32.2994 −1.42052
\(518\) −24.7089 −1.08565
\(519\) −74.8386 −3.28505
\(520\) 0.167927 0.00736410
\(521\) 22.3117 0.977492 0.488746 0.872426i \(-0.337454\pi\)
0.488746 + 0.872426i \(0.337454\pi\)
\(522\) 4.71739 0.206475
\(523\) −30.9247 −1.35224 −0.676122 0.736790i \(-0.736341\pi\)
−0.676122 + 0.736790i \(0.736341\pi\)
\(524\) −11.5779 −0.505784
\(525\) −5.25485 −0.229340
\(526\) −23.7210 −1.03429
\(527\) −20.5961 −0.897181
\(528\) 15.3054 0.666080
\(529\) 18.6711 0.811786
\(530\) 9.26499 0.402445
\(531\) −100.941 −4.38046
\(532\) −8.35886 −0.362403
\(533\) −0.598154 −0.0259089
\(534\) 51.3132 2.22054
\(535\) 25.7242 1.11215
\(536\) −12.8745 −0.556095
\(537\) −33.0700 −1.42708
\(538\) 5.48744 0.236580
\(539\) −5.41223 −0.233121
\(540\) 41.5236 1.78689
\(541\) −21.8348 −0.938752 −0.469376 0.882998i \(-0.655521\pi\)
−0.469376 + 0.882998i \(0.655521\pi\)
\(542\) 24.2332 1.04090
\(543\) 53.5932 2.29990
\(544\) −3.60116 −0.154399
\(545\) −0.832687 −0.0356684
\(546\) 0.663924 0.0284133
\(547\) −10.0395 −0.429259 −0.214630 0.976696i \(-0.568854\pi\)
−0.214630 + 0.976696i \(0.568854\pi\)
\(548\) 6.14494 0.262499
\(549\) −49.8972 −2.12956
\(550\) 2.83618 0.120935
\(551\) 1.86515 0.0794581
\(552\) 22.1646 0.943389
\(553\) 35.8200 1.52322
\(554\) 9.51697 0.404337
\(555\) 73.6789 3.12749
\(556\) −10.3964 −0.440907
\(557\) 33.3109 1.41143 0.705714 0.708497i \(-0.250626\pi\)
0.705714 + 0.708497i \(0.250626\pi\)
\(558\) 50.2684 2.12803
\(559\) 1.02264 0.0432531
\(560\) 5.02473 0.212334
\(561\) 55.1171 2.32704
\(562\) −29.8158 −1.25771
\(563\) 23.4519 0.988380 0.494190 0.869354i \(-0.335465\pi\)
0.494190 + 0.869354i \(0.335465\pi\)
\(564\) −24.8792 −1.04760
\(565\) −10.2406 −0.430827
\(566\) 11.8968 0.500061
\(567\) 100.745 4.23089
\(568\) −3.84772 −0.161447
\(569\) −18.7244 −0.784968 −0.392484 0.919759i \(-0.628384\pi\)
−0.392484 + 0.919759i \(0.628384\pi\)
\(570\) 24.9251 1.04400
\(571\) −39.5840 −1.65654 −0.828269 0.560330i \(-0.810674\pi\)
−0.828269 + 0.560330i \(0.810674\pi\)
\(572\) −0.358337 −0.0149828
\(573\) 39.8801 1.66601
\(574\) −17.8980 −0.747047
\(575\) 4.10725 0.171284
\(576\) 8.78926 0.366219
\(577\) −44.0722 −1.83475 −0.917375 0.398024i \(-0.869696\pi\)
−0.917375 + 0.398024i \(0.869696\pi\)
\(578\) 4.03162 0.167693
\(579\) −87.0706 −3.61853
\(580\) −1.12119 −0.0465549
\(581\) −18.5864 −0.771095
\(582\) 40.0481 1.66005
\(583\) −19.7704 −0.818807
\(584\) −4.11923 −0.170455
\(585\) −1.47596 −0.0610233
\(586\) −22.3570 −0.923559
\(587\) −25.3849 −1.04775 −0.523873 0.851797i \(-0.675513\pi\)
−0.523873 + 0.851797i \(0.675513\pi\)
\(588\) −4.16888 −0.171922
\(589\) 19.8750 0.818934
\(590\) 23.9908 0.987684
\(591\) −29.1286 −1.19819
\(592\) 10.2724 0.422191
\(593\) 37.5655 1.54263 0.771315 0.636454i \(-0.219599\pi\)
0.771315 + 0.636454i \(0.219599\pi\)
\(594\) −88.6066 −3.63557
\(595\) 18.0949 0.741817
\(596\) −13.7946 −0.565049
\(597\) 39.5464 1.61853
\(598\) −0.518931 −0.0212207
\(599\) −1.42028 −0.0580310 −0.0290155 0.999579i \(-0.509237\pi\)
−0.0290155 + 0.999579i \(0.509237\pi\)
\(600\) 2.18463 0.0891870
\(601\) −9.00275 −0.367230 −0.183615 0.982998i \(-0.558780\pi\)
−0.183615 + 0.982998i \(0.558780\pi\)
\(602\) 30.5995 1.24714
\(603\) 113.158 4.60813
\(604\) 18.2701 0.743399
\(605\) 18.5293 0.753322
\(606\) −24.1148 −0.979597
\(607\) 35.0380 1.42215 0.711074 0.703118i \(-0.248209\pi\)
0.711074 + 0.703118i \(0.248209\pi\)
\(608\) 3.47507 0.140933
\(609\) −4.43278 −0.179625
\(610\) 11.8592 0.480163
\(611\) 0.582487 0.0235649
\(612\) 31.6515 1.27944
\(613\) −19.0816 −0.770700 −0.385350 0.922770i \(-0.625919\pi\)
−0.385350 + 0.922770i \(0.625919\pi\)
\(614\) 12.4569 0.502719
\(615\) 53.3696 2.15207
\(616\) −10.7222 −0.432009
\(617\) −19.1883 −0.772491 −0.386246 0.922396i \(-0.626228\pi\)
−0.386246 + 0.922396i \(0.626228\pi\)
\(618\) −51.9813 −2.09099
\(619\) 8.15411 0.327741 0.163871 0.986482i \(-0.447602\pi\)
0.163871 + 0.986482i \(0.447602\pi\)
\(620\) −11.9474 −0.479818
\(621\) −128.317 −5.14917
\(622\) 9.15293 0.366999
\(623\) −35.9475 −1.44021
\(624\) −0.276017 −0.0110495
\(625\) −21.4139 −0.856555
\(626\) −13.0712 −0.522431
\(627\) −53.1872 −2.12409
\(628\) −3.86962 −0.154415
\(629\) 36.9924 1.47499
\(630\) −44.1636 −1.75952
\(631\) −26.7250 −1.06391 −0.531954 0.846774i \(-0.678542\pi\)
−0.531954 + 0.846774i \(0.678542\pi\)
\(632\) −14.8916 −0.592358
\(633\) −45.1153 −1.79317
\(634\) 0.588556 0.0233745
\(635\) 6.89166 0.273487
\(636\) −15.2286 −0.603852
\(637\) 0.0976042 0.00386722
\(638\) 2.39249 0.0947195
\(639\) 33.8186 1.33784
\(640\) −2.08896 −0.0825733
\(641\) 31.7244 1.25304 0.626519 0.779406i \(-0.284479\pi\)
0.626519 + 0.779406i \(0.284479\pi\)
\(642\) −42.2819 −1.66873
\(643\) 16.0940 0.634684 0.317342 0.948311i \(-0.397210\pi\)
0.317342 + 0.948311i \(0.397210\pi\)
\(644\) −15.5275 −0.611868
\(645\) −91.2438 −3.59272
\(646\) 12.5143 0.492369
\(647\) −48.3086 −1.89921 −0.949603 0.313455i \(-0.898513\pi\)
−0.949603 + 0.313455i \(0.898513\pi\)
\(648\) −41.8833 −1.64533
\(649\) −51.1935 −2.00952
\(650\) −0.0511477 −0.00200618
\(651\) −47.2356 −1.85131
\(652\) −10.8307 −0.424164
\(653\) 27.3298 1.06950 0.534749 0.845011i \(-0.320406\pi\)
0.534749 + 0.845011i \(0.320406\pi\)
\(654\) 1.36866 0.0535189
\(655\) −24.1858 −0.945017
\(656\) 7.44082 0.290515
\(657\) 36.2050 1.41249
\(658\) 17.4292 0.679460
\(659\) 15.3807 0.599148 0.299574 0.954073i \(-0.403155\pi\)
0.299574 + 0.954073i \(0.403155\pi\)
\(660\) 31.9722 1.24452
\(661\) 0.864894 0.0336405 0.0168202 0.999859i \(-0.494646\pi\)
0.0168202 + 0.999859i \(0.494646\pi\)
\(662\) −9.55008 −0.371175
\(663\) −0.993981 −0.0386030
\(664\) 7.72704 0.299867
\(665\) −17.4613 −0.677120
\(666\) −90.2864 −3.49853
\(667\) 3.46471 0.134154
\(668\) 12.7546 0.493490
\(669\) −39.4675 −1.52590
\(670\) −26.8943 −1.03902
\(671\) −25.3061 −0.976929
\(672\) −8.25898 −0.318597
\(673\) −13.3815 −0.515818 −0.257909 0.966169i \(-0.583034\pi\)
−0.257909 + 0.966169i \(0.583034\pi\)
\(674\) −22.0093 −0.847768
\(675\) −12.6474 −0.486797
\(676\) −12.9935 −0.499751
\(677\) −8.27187 −0.317914 −0.158957 0.987286i \(-0.550813\pi\)
−0.158957 + 0.987286i \(0.550813\pi\)
\(678\) 16.8322 0.646437
\(679\) −28.0557 −1.07668
\(680\) −7.52268 −0.288481
\(681\) −21.3163 −0.816840
\(682\) 25.4943 0.976226
\(683\) −7.26621 −0.278034 −0.139017 0.990290i \(-0.544394\pi\)
−0.139017 + 0.990290i \(0.544394\pi\)
\(684\) −30.5433 −1.16785
\(685\) 12.8365 0.490458
\(686\) 19.7582 0.754370
\(687\) −58.6834 −2.23891
\(688\) −12.7213 −0.484994
\(689\) 0.356539 0.0135831
\(690\) 46.3010 1.76265
\(691\) −12.0324 −0.457733 −0.228866 0.973458i \(-0.573502\pi\)
−0.228866 + 0.973458i \(0.573502\pi\)
\(692\) −21.7963 −0.828570
\(693\) 94.2400 3.57988
\(694\) 14.4373 0.548033
\(695\) −21.7177 −0.823800
\(696\) 1.84286 0.0698535
\(697\) 26.7956 1.01496
\(698\) −14.2407 −0.539017
\(699\) 21.7357 0.822118
\(700\) −1.53044 −0.0578453
\(701\) 0.556650 0.0210244 0.0105122 0.999945i \(-0.496654\pi\)
0.0105122 + 0.999945i \(0.496654\pi\)
\(702\) 1.59793 0.0603100
\(703\) −35.6972 −1.34635
\(704\) 4.45759 0.168002
\(705\) −51.9717 −1.95737
\(706\) 0.617420 0.0232369
\(707\) 16.8937 0.635352
\(708\) −39.4328 −1.48198
\(709\) −13.4741 −0.506030 −0.253015 0.967462i \(-0.581422\pi\)
−0.253015 + 0.967462i \(0.581422\pi\)
\(710\) −8.03773 −0.301651
\(711\) 130.886 4.90862
\(712\) 14.9446 0.560074
\(713\) 36.9199 1.38266
\(714\) −29.7419 −1.11306
\(715\) −0.748552 −0.0279942
\(716\) −9.63144 −0.359944
\(717\) 76.4287 2.85428
\(718\) −0.756867 −0.0282460
\(719\) 11.9621 0.446110 0.223055 0.974806i \(-0.428397\pi\)
0.223055 + 0.974806i \(0.428397\pi\)
\(720\) 18.3604 0.684251
\(721\) 36.4156 1.35619
\(722\) 6.92386 0.257679
\(723\) 80.2475 2.98444
\(724\) 15.6087 0.580092
\(725\) 0.341495 0.0126828
\(726\) −30.4559 −1.13033
\(727\) −20.3032 −0.753003 −0.376501 0.926416i \(-0.622873\pi\)
−0.376501 + 0.926416i \(0.622873\pi\)
\(728\) 0.193364 0.00716654
\(729\) 163.370 6.05073
\(730\) −8.60489 −0.318481
\(731\) −45.8114 −1.69440
\(732\) −19.4925 −0.720464
\(733\) −5.44730 −0.201201 −0.100600 0.994927i \(-0.532076\pi\)
−0.100600 + 0.994927i \(0.532076\pi\)
\(734\) −23.5275 −0.868417
\(735\) −8.70862 −0.321222
\(736\) 6.45531 0.237946
\(737\) 57.3893 2.11396
\(738\) −65.3993 −2.40738
\(739\) 43.5350 1.60146 0.800730 0.599025i \(-0.204445\pi\)
0.800730 + 0.599025i \(0.204445\pi\)
\(740\) 21.4585 0.788831
\(741\) 0.959179 0.0352363
\(742\) 10.6684 0.391649
\(743\) 22.6640 0.831461 0.415730 0.909488i \(-0.363526\pi\)
0.415730 + 0.909488i \(0.363526\pi\)
\(744\) 19.6375 0.719945
\(745\) −28.8163 −1.05575
\(746\) 9.93608 0.363786
\(747\) −67.9149 −2.48488
\(748\) 16.0525 0.586938
\(749\) 29.6207 1.08232
\(750\) 40.4263 1.47616
\(751\) 11.7707 0.429519 0.214760 0.976667i \(-0.431103\pi\)
0.214760 + 0.976667i \(0.431103\pi\)
\(752\) −7.24592 −0.264232
\(753\) 46.6874 1.70138
\(754\) −0.0431461 −0.00157129
\(755\) 38.1654 1.38898
\(756\) 47.8133 1.73895
\(757\) 26.0857 0.948102 0.474051 0.880497i \(-0.342791\pi\)
0.474051 + 0.880497i \(0.342791\pi\)
\(758\) 24.2797 0.881877
\(759\) −98.8008 −3.58624
\(760\) 7.25928 0.263322
\(761\) 17.2991 0.627090 0.313545 0.949573i \(-0.398483\pi\)
0.313545 + 0.949573i \(0.398483\pi\)
\(762\) −11.3276 −0.410355
\(763\) −0.958817 −0.0347115
\(764\) 11.6148 0.420210
\(765\) 66.1187 2.39053
\(766\) −26.3998 −0.953863
\(767\) 0.923223 0.0333356
\(768\) 3.43355 0.123898
\(769\) −18.7925 −0.677676 −0.338838 0.940845i \(-0.610034\pi\)
−0.338838 + 0.940845i \(0.610034\pi\)
\(770\) −22.3982 −0.807174
\(771\) −94.4333 −3.40093
\(772\) −25.3588 −0.912683
\(773\) 23.2957 0.837886 0.418943 0.908012i \(-0.362401\pi\)
0.418943 + 0.908012i \(0.362401\pi\)
\(774\) 111.811 4.01895
\(775\) 3.63895 0.130715
\(776\) 11.6638 0.418704
\(777\) 84.8392 3.04359
\(778\) 20.8011 0.745755
\(779\) −25.8574 −0.926438
\(780\) −0.576587 −0.0206451
\(781\) 17.1516 0.613731
\(782\) 23.2466 0.831298
\(783\) −10.6688 −0.381272
\(784\) −1.21416 −0.0433629
\(785\) −8.08348 −0.288512
\(786\) 39.7534 1.41796
\(787\) 41.8803 1.49287 0.746436 0.665457i \(-0.231763\pi\)
0.746436 + 0.665457i \(0.231763\pi\)
\(788\) −8.48353 −0.302213
\(789\) 81.4472 2.89960
\(790\) −31.1080 −1.10677
\(791\) −11.7918 −0.419269
\(792\) −39.1789 −1.39216
\(793\) 0.456369 0.0162062
\(794\) −17.9867 −0.638326
\(795\) −31.8118 −1.12825
\(796\) 11.5177 0.408232
\(797\) −0.265984 −0.00942165 −0.00471083 0.999989i \(-0.501500\pi\)
−0.00471083 + 0.999989i \(0.501500\pi\)
\(798\) 28.7006 1.01599
\(799\) −26.0938 −0.923131
\(800\) 0.636259 0.0224951
\(801\) −131.352 −4.64110
\(802\) 26.1569 0.923634
\(803\) 18.3618 0.647975
\(804\) 44.2053 1.55900
\(805\) −32.4362 −1.14323
\(806\) −0.459764 −0.0161945
\(807\) −18.8414 −0.663248
\(808\) −7.02329 −0.247079
\(809\) −32.6344 −1.14736 −0.573682 0.819078i \(-0.694485\pi\)
−0.573682 + 0.819078i \(0.694485\pi\)
\(810\) −87.4923 −3.07417
\(811\) 7.64978 0.268620 0.134310 0.990939i \(-0.457118\pi\)
0.134310 + 0.990939i \(0.457118\pi\)
\(812\) −1.29102 −0.0453059
\(813\) −83.2058 −2.91816
\(814\) −45.7900 −1.60494
\(815\) −22.6249 −0.792516
\(816\) 12.3648 0.432854
\(817\) 44.2074 1.54662
\(818\) 28.2204 0.986702
\(819\) −1.69952 −0.0593862
\(820\) 15.5436 0.542805
\(821\) −39.1225 −1.36538 −0.682692 0.730706i \(-0.739191\pi\)
−0.682692 + 0.730706i \(0.739191\pi\)
\(822\) −21.0989 −0.735910
\(823\) 21.9452 0.764963 0.382481 0.923963i \(-0.375070\pi\)
0.382481 + 0.923963i \(0.375070\pi\)
\(824\) −15.1392 −0.527400
\(825\) −9.73817 −0.339039
\(826\) 27.6247 0.961186
\(827\) 42.5631 1.48007 0.740033 0.672571i \(-0.234810\pi\)
0.740033 + 0.672571i \(0.234810\pi\)
\(828\) −56.7374 −1.97176
\(829\) −22.3044 −0.774663 −0.387331 0.921941i \(-0.626603\pi\)
−0.387331 + 0.921941i \(0.626603\pi\)
\(830\) 16.1414 0.560278
\(831\) −32.6770 −1.13355
\(832\) −0.0803882 −0.00278696
\(833\) −4.37239 −0.151494
\(834\) 35.6967 1.23608
\(835\) 26.6438 0.922047
\(836\) −15.4905 −0.535749
\(837\) −113.686 −3.92958
\(838\) 0.106804 0.00368947
\(839\) 26.4596 0.913486 0.456743 0.889599i \(-0.349016\pi\)
0.456743 + 0.889599i \(0.349016\pi\)
\(840\) −17.2527 −0.595273
\(841\) −28.7119 −0.990067
\(842\) −14.1587 −0.487941
\(843\) 102.374 3.52595
\(844\) −13.1396 −0.452283
\(845\) −27.1429 −0.933746
\(846\) 63.6863 2.18958
\(847\) 21.3359 0.733112
\(848\) −4.43522 −0.152306
\(849\) −40.8483 −1.40191
\(850\) 2.29127 0.0785900
\(851\) −66.3113 −2.27312
\(852\) 13.2113 0.452613
\(853\) 41.5777 1.42359 0.711796 0.702386i \(-0.247882\pi\)
0.711796 + 0.702386i \(0.247882\pi\)
\(854\) 13.6555 0.467282
\(855\) −63.8037 −2.18204
\(856\) −12.3144 −0.420896
\(857\) 12.6766 0.433025 0.216513 0.976280i \(-0.430532\pi\)
0.216513 + 0.976280i \(0.430532\pi\)
\(858\) 1.23037 0.0420041
\(859\) −16.3223 −0.556909 −0.278454 0.960449i \(-0.589822\pi\)
−0.278454 + 0.960449i \(0.589822\pi\)
\(860\) −26.5742 −0.906173
\(861\) 61.4536 2.09433
\(862\) −3.51166 −0.119608
\(863\) −50.4171 −1.71622 −0.858109 0.513468i \(-0.828361\pi\)
−0.858109 + 0.513468i \(0.828361\pi\)
\(864\) −19.8777 −0.676253
\(865\) −45.5315 −1.54812
\(866\) 24.8991 0.846105
\(867\) −13.8428 −0.470125
\(868\) −13.7571 −0.466945
\(869\) 66.3808 2.25181
\(870\) 3.84966 0.130516
\(871\) −1.03496 −0.0350683
\(872\) 0.398614 0.0134988
\(873\) −102.516 −3.46963
\(874\) −22.4327 −0.758797
\(875\) −28.3207 −0.957413
\(876\) 14.1436 0.477867
\(877\) −21.3978 −0.722554 −0.361277 0.932459i \(-0.617659\pi\)
−0.361277 + 0.932459i \(0.617659\pi\)
\(878\) −36.4703 −1.23081
\(879\) 76.7638 2.58918
\(880\) 9.31171 0.313898
\(881\) 12.7457 0.429412 0.214706 0.976679i \(-0.431121\pi\)
0.214706 + 0.976679i \(0.431121\pi\)
\(882\) 10.6716 0.359331
\(883\) 56.5758 1.90393 0.951964 0.306211i \(-0.0990614\pi\)
0.951964 + 0.306211i \(0.0990614\pi\)
\(884\) −0.289491 −0.00973663
\(885\) −82.3734 −2.76895
\(886\) 3.54480 0.119090
\(887\) 18.1010 0.607771 0.303886 0.952708i \(-0.401716\pi\)
0.303886 + 0.952708i \(0.401716\pi\)
\(888\) −35.2706 −1.18361
\(889\) 7.93555 0.266150
\(890\) 31.2187 1.04645
\(891\) 186.698 6.25463
\(892\) −11.4947 −0.384870
\(893\) 25.1801 0.842621
\(894\) 47.3644 1.58410
\(895\) −20.1197 −0.672526
\(896\) −2.40538 −0.0803580
\(897\) 1.78177 0.0594917
\(898\) 14.2267 0.474752
\(899\) 3.06968 0.102379
\(900\) −5.59224 −0.186408
\(901\) −15.9720 −0.532103
\(902\) −33.1681 −1.10438
\(903\) −105.065 −3.49634
\(904\) 4.90227 0.163047
\(905\) 32.6059 1.08386
\(906\) −62.7312 −2.08411
\(907\) −11.8053 −0.391988 −0.195994 0.980605i \(-0.562793\pi\)
−0.195994 + 0.980605i \(0.562793\pi\)
\(908\) −6.20823 −0.206027
\(909\) 61.7295 2.04744
\(910\) 0.403929 0.0133901
\(911\) −0.323842 −0.0107294 −0.00536468 0.999986i \(-0.501708\pi\)
−0.00536468 + 0.999986i \(0.501708\pi\)
\(912\) −11.9318 −0.395103
\(913\) −34.4440 −1.13993
\(914\) −5.83438 −0.192984
\(915\) −40.7190 −1.34613
\(916\) −17.0912 −0.564708
\(917\) −27.8493 −0.919664
\(918\) −71.5828 −2.36259
\(919\) 1.21792 0.0401754 0.0200877 0.999798i \(-0.493605\pi\)
0.0200877 + 0.999798i \(0.493605\pi\)
\(920\) 13.4849 0.444583
\(921\) −42.7713 −1.40936
\(922\) −16.8067 −0.553500
\(923\) −0.309311 −0.0101811
\(924\) 36.8151 1.21113
\(925\) −6.53588 −0.214898
\(926\) 12.2503 0.402568
\(927\) 133.063 4.37035
\(928\) 0.536723 0.0176188
\(929\) −19.7982 −0.649556 −0.324778 0.945790i \(-0.605290\pi\)
−0.324778 + 0.945790i \(0.605290\pi\)
\(930\) 41.0219 1.34516
\(931\) 4.21930 0.138282
\(932\) 6.33038 0.207358
\(933\) −31.4270 −1.02887
\(934\) −34.7821 −1.13811
\(935\) 33.5330 1.09665
\(936\) 0.706552 0.0230944
\(937\) 50.9316 1.66386 0.831932 0.554878i \(-0.187235\pi\)
0.831932 + 0.554878i \(0.187235\pi\)
\(938\) −30.9681 −1.01114
\(939\) 44.8806 1.46462
\(940\) −15.1364 −0.493696
\(941\) −4.03548 −0.131553 −0.0657764 0.997834i \(-0.520952\pi\)
−0.0657764 + 0.997834i \(0.520952\pi\)
\(942\) 13.2865 0.432899
\(943\) −48.0328 −1.56416
\(944\) −11.4846 −0.373791
\(945\) 99.8800 3.24910
\(946\) 56.7062 1.84368
\(947\) −27.2389 −0.885146 −0.442573 0.896732i \(-0.645934\pi\)
−0.442573 + 0.896732i \(0.645934\pi\)
\(948\) 51.1312 1.66066
\(949\) −0.331137 −0.0107492
\(950\) −2.21105 −0.0717358
\(951\) −2.02083 −0.0655301
\(952\) −8.66216 −0.280742
\(953\) −41.4605 −1.34304 −0.671519 0.740987i \(-0.734358\pi\)
−0.671519 + 0.740987i \(0.734358\pi\)
\(954\) 38.9823 1.26210
\(955\) 24.2629 0.785128
\(956\) 22.2594 0.719920
\(957\) −8.21473 −0.265544
\(958\) −13.3228 −0.430441
\(959\) 14.7809 0.477300
\(960\) 7.17254 0.231493
\(961\) 1.71036 0.0551729
\(962\) 0.825776 0.0266241
\(963\) 108.234 3.48779
\(964\) 23.3716 0.752748
\(965\) −52.9734 −1.70527
\(966\) 53.3143 1.71536
\(967\) 35.7484 1.14959 0.574795 0.818298i \(-0.305082\pi\)
0.574795 + 0.818298i \(0.305082\pi\)
\(968\) −8.87010 −0.285096
\(969\) −42.9685 −1.38035
\(970\) 24.3651 0.782316
\(971\) −7.78210 −0.249739 −0.124870 0.992173i \(-0.539851\pi\)
−0.124870 + 0.992173i \(0.539851\pi\)
\(972\) 84.1751 2.69992
\(973\) −25.0074 −0.801699
\(974\) 4.86783 0.155975
\(975\) 0.175618 0.00562428
\(976\) −5.67707 −0.181719
\(977\) −25.5927 −0.818784 −0.409392 0.912359i \(-0.634259\pi\)
−0.409392 + 0.912359i \(0.634259\pi\)
\(978\) 37.1878 1.18914
\(979\) −66.6171 −2.12909
\(980\) −2.53633 −0.0810201
\(981\) −3.50352 −0.111859
\(982\) −34.9278 −1.11459
\(983\) 25.8265 0.823738 0.411869 0.911243i \(-0.364876\pi\)
0.411869 + 0.911243i \(0.364876\pi\)
\(984\) −25.5484 −0.814454
\(985\) −17.7217 −0.564661
\(986\) 1.93283 0.0615537
\(987\) −59.8439 −1.90485
\(988\) 0.279355 0.00888746
\(989\) 82.1198 2.61126
\(990\) −81.8430 −2.60114
\(991\) 46.1516 1.46605 0.733027 0.680200i \(-0.238107\pi\)
0.733027 + 0.680200i \(0.238107\pi\)
\(992\) 5.71930 0.181588
\(993\) 32.7907 1.04058
\(994\) −9.25522 −0.293558
\(995\) 24.0599 0.762750
\(996\) −26.5312 −0.840672
\(997\) −13.3430 −0.422578 −0.211289 0.977424i \(-0.567766\pi\)
−0.211289 + 0.977424i \(0.567766\pi\)
\(998\) −10.7868 −0.341449
\(999\) 204.191 6.46031
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 8002.2.a.e.1.77 77
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8002.2.a.e.1.77 77 1.1 even 1 trivial