Properties

Label 619.2.a.a.1.11
Level $619$
Weight $2$
Character 619.1
Self dual yes
Analytic conductor $4.943$
Analytic rank $1$
Dimension $21$
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] = [619,2,Mod(1,619)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(619, 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("619.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 619 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 619.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: \(4.94273988512\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 619.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.723996 q^{2} +3.01745 q^{3} -1.47583 q^{4} -2.02994 q^{5} -2.18462 q^{6} -2.86695 q^{7} +2.51649 q^{8} +6.10499 q^{9} +O(q^{10})\) \(q-0.723996 q^{2} +3.01745 q^{3} -1.47583 q^{4} -2.02994 q^{5} -2.18462 q^{6} -2.86695 q^{7} +2.51649 q^{8} +6.10499 q^{9} +1.46966 q^{10} -5.18357 q^{11} -4.45324 q^{12} -4.90825 q^{13} +2.07566 q^{14} -6.12522 q^{15} +1.12974 q^{16} +7.18967 q^{17} -4.41998 q^{18} -2.17482 q^{19} +2.99584 q^{20} -8.65088 q^{21} +3.75288 q^{22} -7.89290 q^{23} +7.59336 q^{24} -0.879360 q^{25} +3.55355 q^{26} +9.36913 q^{27} +4.23113 q^{28} -7.73709 q^{29} +4.43464 q^{30} +4.00031 q^{31} -5.85090 q^{32} -15.6412 q^{33} -5.20529 q^{34} +5.81973 q^{35} -9.00992 q^{36} -9.16541 q^{37} +1.57456 q^{38} -14.8104 q^{39} -5.10831 q^{40} +3.94489 q^{41} +6.26320 q^{42} +7.18177 q^{43} +7.65007 q^{44} -12.3927 q^{45} +5.71442 q^{46} +3.57199 q^{47} +3.40892 q^{48} +1.21942 q^{49} +0.636652 q^{50} +21.6944 q^{51} +7.24375 q^{52} +4.73766 q^{53} -6.78321 q^{54} +10.5223 q^{55} -7.21465 q^{56} -6.56241 q^{57} +5.60162 q^{58} -8.30292 q^{59} +9.03979 q^{60} +1.43844 q^{61} -2.89621 q^{62} -17.5027 q^{63} +1.97655 q^{64} +9.96344 q^{65} +11.3241 q^{66} +10.0813 q^{67} -10.6107 q^{68} -23.8164 q^{69} -4.21346 q^{70} +6.02509 q^{71} +15.3631 q^{72} -2.63460 q^{73} +6.63571 q^{74} -2.65342 q^{75} +3.20967 q^{76} +14.8611 q^{77} +10.7227 q^{78} +14.9656 q^{79} -2.29329 q^{80} +9.95591 q^{81} -2.85608 q^{82} -9.64957 q^{83} +12.7672 q^{84} -14.5946 q^{85} -5.19957 q^{86} -23.3462 q^{87} -13.0444 q^{88} -6.74228 q^{89} +8.97229 q^{90} +14.0717 q^{91} +11.6486 q^{92} +12.0707 q^{93} -2.58610 q^{94} +4.41475 q^{95} -17.6548 q^{96} +2.43425 q^{97} -0.882851 q^{98} -31.6456 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.723996 −0.511942 −0.255971 0.966684i \(-0.582395\pi\)
−0.255971 + 0.966684i \(0.582395\pi\)
\(3\) 3.01745 1.74212 0.871062 0.491173i \(-0.163432\pi\)
0.871062 + 0.491173i \(0.163432\pi\)
\(4\) −1.47583 −0.737915
\(5\) −2.02994 −0.907815 −0.453908 0.891049i \(-0.649970\pi\)
−0.453908 + 0.891049i \(0.649970\pi\)
\(6\) −2.18462 −0.891867
\(7\) −2.86695 −1.08361 −0.541803 0.840505i \(-0.682258\pi\)
−0.541803 + 0.840505i \(0.682258\pi\)
\(8\) 2.51649 0.889712
\(9\) 6.10499 2.03500
\(10\) 1.46966 0.464749
\(11\) −5.18357 −1.56291 −0.781453 0.623964i \(-0.785521\pi\)
−0.781453 + 0.623964i \(0.785521\pi\)
\(12\) −4.45324 −1.28554
\(13\) −4.90825 −1.36130 −0.680652 0.732607i \(-0.738303\pi\)
−0.680652 + 0.732607i \(0.738303\pi\)
\(14\) 2.07566 0.554744
\(15\) −6.12522 −1.58153
\(16\) 1.12974 0.282434
\(17\) 7.18967 1.74375 0.871875 0.489728i \(-0.162904\pi\)
0.871875 + 0.489728i \(0.162904\pi\)
\(18\) −4.41998 −1.04180
\(19\) −2.17482 −0.498938 −0.249469 0.968383i \(-0.580256\pi\)
−0.249469 + 0.968383i \(0.580256\pi\)
\(20\) 2.99584 0.669890
\(21\) −8.65088 −1.88778
\(22\) 3.75288 0.800118
\(23\) −7.89290 −1.64578 −0.822892 0.568198i \(-0.807641\pi\)
−0.822892 + 0.568198i \(0.807641\pi\)
\(24\) 7.59336 1.54999
\(25\) −0.879360 −0.175872
\(26\) 3.55355 0.696909
\(27\) 9.36913 1.80309
\(28\) 4.23113 0.799609
\(29\) −7.73709 −1.43674 −0.718370 0.695661i \(-0.755112\pi\)
−0.718370 + 0.695661i \(0.755112\pi\)
\(30\) 4.43464 0.809650
\(31\) 4.00031 0.718477 0.359238 0.933246i \(-0.383037\pi\)
0.359238 + 0.933246i \(0.383037\pi\)
\(32\) −5.85090 −1.03430
\(33\) −15.6412 −2.72278
\(34\) −5.20529 −0.892700
\(35\) 5.81973 0.983714
\(36\) −9.00992 −1.50165
\(37\) −9.16541 −1.50678 −0.753392 0.657572i \(-0.771584\pi\)
−0.753392 + 0.657572i \(0.771584\pi\)
\(38\) 1.57456 0.255427
\(39\) −14.8104 −2.37156
\(40\) −5.10831 −0.807694
\(41\) 3.94489 0.616088 0.308044 0.951372i \(-0.400326\pi\)
0.308044 + 0.951372i \(0.400326\pi\)
\(42\) 6.26320 0.966432
\(43\) 7.18177 1.09521 0.547605 0.836737i \(-0.315540\pi\)
0.547605 + 0.836737i \(0.315540\pi\)
\(44\) 7.65007 1.15329
\(45\) −12.3927 −1.84740
\(46\) 5.71442 0.842546
\(47\) 3.57199 0.521028 0.260514 0.965470i \(-0.416108\pi\)
0.260514 + 0.965470i \(0.416108\pi\)
\(48\) 3.40892 0.492035
\(49\) 1.21942 0.174202
\(50\) 0.636652 0.0900363
\(51\) 21.6944 3.03783
\(52\) 7.24375 1.00453
\(53\) 4.73766 0.650768 0.325384 0.945582i \(-0.394506\pi\)
0.325384 + 0.945582i \(0.394506\pi\)
\(54\) −6.78321 −0.923078
\(55\) 10.5223 1.41883
\(56\) −7.21465 −0.964098
\(57\) −6.56241 −0.869212
\(58\) 5.60162 0.735528
\(59\) −8.30292 −1.08095 −0.540474 0.841361i \(-0.681755\pi\)
−0.540474 + 0.841361i \(0.681755\pi\)
\(60\) 9.03979 1.16703
\(61\) 1.43844 0.184173 0.0920865 0.995751i \(-0.470646\pi\)
0.0920865 + 0.995751i \(0.470646\pi\)
\(62\) −2.89621 −0.367818
\(63\) −17.5027 −2.20513
\(64\) 1.97655 0.247069
\(65\) 9.96344 1.23581
\(66\) 11.3241 1.39390
\(67\) 10.0813 1.23163 0.615814 0.787891i \(-0.288827\pi\)
0.615814 + 0.787891i \(0.288827\pi\)
\(68\) −10.6107 −1.28674
\(69\) −23.8164 −2.86716
\(70\) −4.21346 −0.503605
\(71\) 6.02509 0.715046 0.357523 0.933904i \(-0.383621\pi\)
0.357523 + 0.933904i \(0.383621\pi\)
\(72\) 15.3631 1.81056
\(73\) −2.63460 −0.308356 −0.154178 0.988043i \(-0.549273\pi\)
−0.154178 + 0.988043i \(0.549273\pi\)
\(74\) 6.63571 0.771386
\(75\) −2.65342 −0.306391
\(76\) 3.20967 0.368174
\(77\) 14.8611 1.69357
\(78\) 10.7227 1.21410
\(79\) 14.9656 1.68376 0.841880 0.539665i \(-0.181449\pi\)
0.841880 + 0.539665i \(0.181449\pi\)
\(80\) −2.29329 −0.256398
\(81\) 9.95591 1.10621
\(82\) −2.85608 −0.315402
\(83\) −9.64957 −1.05918 −0.529589 0.848255i \(-0.677654\pi\)
−0.529589 + 0.848255i \(0.677654\pi\)
\(84\) 12.7672 1.39302
\(85\) −14.5946 −1.58300
\(86\) −5.19957 −0.560684
\(87\) −23.3462 −2.50298
\(88\) −13.0444 −1.39054
\(89\) −6.74228 −0.714680 −0.357340 0.933974i \(-0.616316\pi\)
−0.357340 + 0.933974i \(0.616316\pi\)
\(90\) 8.97229 0.945762
\(91\) 14.0717 1.47512
\(92\) 11.6486 1.21445
\(93\) 12.0707 1.25168
\(94\) −2.58610 −0.266736
\(95\) 4.41475 0.452943
\(96\) −17.6548 −1.80188
\(97\) 2.43425 0.247161 0.123580 0.992335i \(-0.460562\pi\)
0.123580 + 0.992335i \(0.460562\pi\)
\(98\) −0.882851 −0.0891814
\(99\) −31.6456 −3.18051
\(100\) 1.29779 0.129779
\(101\) −5.04301 −0.501798 −0.250899 0.968013i \(-0.580726\pi\)
−0.250899 + 0.968013i \(0.580726\pi\)
\(102\) −15.7067 −1.55519
\(103\) 3.31694 0.326828 0.163414 0.986558i \(-0.447749\pi\)
0.163414 + 0.986558i \(0.447749\pi\)
\(104\) −12.3515 −1.21117
\(105\) 17.5607 1.71375
\(106\) −3.43005 −0.333155
\(107\) −7.73295 −0.747573 −0.373786 0.927515i \(-0.621941\pi\)
−0.373786 + 0.927515i \(0.621941\pi\)
\(108\) −13.8273 −1.33053
\(109\) −4.04022 −0.386983 −0.193491 0.981102i \(-0.561981\pi\)
−0.193491 + 0.981102i \(0.561981\pi\)
\(110\) −7.61812 −0.726359
\(111\) −27.6561 −2.62500
\(112\) −3.23890 −0.306047
\(113\) −12.4332 −1.16961 −0.584807 0.811173i \(-0.698830\pi\)
−0.584807 + 0.811173i \(0.698830\pi\)
\(114\) 4.75115 0.444986
\(115\) 16.0221 1.49407
\(116\) 11.4186 1.06019
\(117\) −29.9648 −2.77025
\(118\) 6.01128 0.553383
\(119\) −20.6124 −1.88954
\(120\) −15.4140 −1.40710
\(121\) 15.8694 1.44268
\(122\) −1.04142 −0.0942859
\(123\) 11.9035 1.07330
\(124\) −5.90378 −0.530175
\(125\) 11.9347 1.06747
\(126\) 12.6719 1.12890
\(127\) 5.40366 0.479498 0.239749 0.970835i \(-0.422935\pi\)
0.239749 + 0.970835i \(0.422935\pi\)
\(128\) 10.2708 0.907817
\(129\) 21.6706 1.90799
\(130\) −7.21349 −0.632665
\(131\) −6.97739 −0.609618 −0.304809 0.952414i \(-0.598593\pi\)
−0.304809 + 0.952414i \(0.598593\pi\)
\(132\) 23.0837 2.00918
\(133\) 6.23511 0.540652
\(134\) −7.29883 −0.630523
\(135\) −19.0187 −1.63687
\(136\) 18.0927 1.55144
\(137\) 10.6937 0.913625 0.456812 0.889563i \(-0.348991\pi\)
0.456812 + 0.889563i \(0.348991\pi\)
\(138\) 17.2430 1.46782
\(139\) −1.23971 −0.105151 −0.0525756 0.998617i \(-0.516743\pi\)
−0.0525756 + 0.998617i \(0.516743\pi\)
\(140\) −8.58893 −0.725897
\(141\) 10.7783 0.907695
\(142\) −4.36214 −0.366062
\(143\) 25.4423 2.12759
\(144\) 6.89702 0.574752
\(145\) 15.7058 1.30429
\(146\) 1.90744 0.157861
\(147\) 3.67952 0.303482
\(148\) 13.5266 1.11188
\(149\) −16.2201 −1.32880 −0.664402 0.747375i \(-0.731314\pi\)
−0.664402 + 0.747375i \(0.731314\pi\)
\(150\) 1.92107 0.156854
\(151\) 2.09958 0.170861 0.0854306 0.996344i \(-0.472773\pi\)
0.0854306 + 0.996344i \(0.472773\pi\)
\(152\) −5.47291 −0.443911
\(153\) 43.8928 3.54852
\(154\) −10.7593 −0.867012
\(155\) −8.12037 −0.652244
\(156\) 21.8576 1.75001
\(157\) −2.50097 −0.199599 −0.0997995 0.995008i \(-0.531820\pi\)
−0.0997995 + 0.995008i \(0.531820\pi\)
\(158\) −10.8350 −0.861988
\(159\) 14.2956 1.13372
\(160\) 11.8769 0.938955
\(161\) 22.6286 1.78338
\(162\) −7.20803 −0.566317
\(163\) 0.785063 0.0614909 0.0307454 0.999527i \(-0.490212\pi\)
0.0307454 + 0.999527i \(0.490212\pi\)
\(164\) −5.82199 −0.454621
\(165\) 31.7506 2.47178
\(166\) 6.98624 0.542238
\(167\) −21.4744 −1.66174 −0.830869 0.556468i \(-0.812156\pi\)
−0.830869 + 0.556468i \(0.812156\pi\)
\(168\) −21.7698 −1.67958
\(169\) 11.0909 0.853149
\(170\) 10.5664 0.810406
\(171\) −13.2773 −1.01534
\(172\) −10.5991 −0.808171
\(173\) −15.8400 −1.20429 −0.602145 0.798387i \(-0.705687\pi\)
−0.602145 + 0.798387i \(0.705687\pi\)
\(174\) 16.9026 1.28138
\(175\) 2.52108 0.190576
\(176\) −5.85607 −0.441418
\(177\) −25.0536 −1.88315
\(178\) 4.88138 0.365875
\(179\) 18.1996 1.36031 0.680153 0.733071i \(-0.261914\pi\)
0.680153 + 0.733071i \(0.261914\pi\)
\(180\) 18.2896 1.36322
\(181\) 11.9843 0.890784 0.445392 0.895336i \(-0.353064\pi\)
0.445392 + 0.895336i \(0.353064\pi\)
\(182\) −10.1879 −0.755175
\(183\) 4.34041 0.320852
\(184\) −19.8624 −1.46427
\(185\) 18.6052 1.36788
\(186\) −8.73915 −0.640785
\(187\) −37.2682 −2.72532
\(188\) −5.27164 −0.384474
\(189\) −26.8609 −1.95384
\(190\) −3.19626 −0.231881
\(191\) 25.2836 1.82946 0.914728 0.404071i \(-0.132405\pi\)
0.914728 + 0.404071i \(0.132405\pi\)
\(192\) 5.96414 0.430425
\(193\) −3.69290 −0.265821 −0.132910 0.991128i \(-0.542432\pi\)
−0.132910 + 0.991128i \(0.542432\pi\)
\(194\) −1.76239 −0.126532
\(195\) 30.0641 2.15294
\(196\) −1.79965 −0.128546
\(197\) 7.91038 0.563592 0.281796 0.959474i \(-0.409070\pi\)
0.281796 + 0.959474i \(0.409070\pi\)
\(198\) 22.9113 1.62824
\(199\) 3.74720 0.265632 0.132816 0.991141i \(-0.457598\pi\)
0.132816 + 0.991141i \(0.457598\pi\)
\(200\) −2.21290 −0.156475
\(201\) 30.4198 2.14565
\(202\) 3.65112 0.256892
\(203\) 22.1819 1.55686
\(204\) −32.0173 −2.24166
\(205\) −8.00787 −0.559294
\(206\) −2.40145 −0.167317
\(207\) −48.1860 −3.34916
\(208\) −5.54503 −0.384478
\(209\) 11.2733 0.779793
\(210\) −12.7139 −0.877342
\(211\) −23.8535 −1.64214 −0.821072 0.570825i \(-0.806623\pi\)
−0.821072 + 0.570825i \(0.806623\pi\)
\(212\) −6.99198 −0.480211
\(213\) 18.1804 1.24570
\(214\) 5.59863 0.382714
\(215\) −14.5785 −0.994247
\(216\) 23.5773 1.60423
\(217\) −11.4687 −0.778546
\(218\) 2.92510 0.198113
\(219\) −7.94976 −0.537195
\(220\) −15.5292 −1.04698
\(221\) −35.2887 −2.37378
\(222\) 20.0229 1.34385
\(223\) −4.04669 −0.270986 −0.135493 0.990778i \(-0.543262\pi\)
−0.135493 + 0.990778i \(0.543262\pi\)
\(224\) 16.7742 1.12078
\(225\) −5.36848 −0.357899
\(226\) 9.00156 0.598775
\(227\) −18.5395 −1.23051 −0.615256 0.788328i \(-0.710947\pi\)
−0.615256 + 0.788328i \(0.710947\pi\)
\(228\) 9.68500 0.641405
\(229\) −8.56190 −0.565786 −0.282893 0.959151i \(-0.591294\pi\)
−0.282893 + 0.959151i \(0.591294\pi\)
\(230\) −11.5999 −0.764876
\(231\) 44.8425 2.95042
\(232\) −19.4703 −1.27829
\(233\) −24.0792 −1.57748 −0.788739 0.614728i \(-0.789266\pi\)
−0.788739 + 0.614728i \(0.789266\pi\)
\(234\) 21.6944 1.41821
\(235\) −7.25090 −0.472997
\(236\) 12.2537 0.797648
\(237\) 45.1579 2.93332
\(238\) 14.9233 0.967335
\(239\) 11.4142 0.738322 0.369161 0.929366i \(-0.379645\pi\)
0.369161 + 0.929366i \(0.379645\pi\)
\(240\) −6.91988 −0.446677
\(241\) 11.1865 0.720588 0.360294 0.932839i \(-0.382676\pi\)
0.360294 + 0.932839i \(0.382676\pi\)
\(242\) −11.4894 −0.738567
\(243\) 1.93402 0.124067
\(244\) −2.12289 −0.135904
\(245\) −2.47533 −0.158143
\(246\) −8.61808 −0.549469
\(247\) 10.6746 0.679207
\(248\) 10.0667 0.639237
\(249\) −29.1171 −1.84522
\(250\) −8.64069 −0.546485
\(251\) −7.05319 −0.445194 −0.222597 0.974911i \(-0.571453\pi\)
−0.222597 + 0.974911i \(0.571453\pi\)
\(252\) 25.8310 1.62720
\(253\) 40.9134 2.57220
\(254\) −3.91223 −0.245475
\(255\) −44.0383 −2.75779
\(256\) −11.3891 −0.711819
\(257\) −4.15606 −0.259248 −0.129624 0.991563i \(-0.541377\pi\)
−0.129624 + 0.991563i \(0.541377\pi\)
\(258\) −15.6894 −0.976781
\(259\) 26.2768 1.63276
\(260\) −14.7043 −0.911925
\(261\) −47.2348 −2.92376
\(262\) 5.05160 0.312089
\(263\) −4.84381 −0.298682 −0.149341 0.988786i \(-0.547715\pi\)
−0.149341 + 0.988786i \(0.547715\pi\)
\(264\) −39.3608 −2.42249
\(265\) −9.61715 −0.590777
\(266\) −4.51419 −0.276783
\(267\) −20.3445 −1.24506
\(268\) −14.8783 −0.908837
\(269\) −21.0700 −1.28466 −0.642329 0.766429i \(-0.722032\pi\)
−0.642329 + 0.766429i \(0.722032\pi\)
\(270\) 13.7695 0.837984
\(271\) 13.2461 0.804644 0.402322 0.915498i \(-0.368203\pi\)
0.402322 + 0.915498i \(0.368203\pi\)
\(272\) 8.12242 0.492494
\(273\) 42.4607 2.56984
\(274\) −7.74220 −0.467723
\(275\) 4.55822 0.274871
\(276\) 35.1490 2.11572
\(277\) 32.4384 1.94903 0.974516 0.224319i \(-0.0720157\pi\)
0.974516 + 0.224319i \(0.0720157\pi\)
\(278\) 0.897548 0.0538313
\(279\) 24.4218 1.46210
\(280\) 14.6453 0.875222
\(281\) −16.6018 −0.990382 −0.495191 0.868784i \(-0.664902\pi\)
−0.495191 + 0.868784i \(0.664902\pi\)
\(282\) −7.80343 −0.464687
\(283\) 10.2724 0.610630 0.305315 0.952251i \(-0.401238\pi\)
0.305315 + 0.952251i \(0.401238\pi\)
\(284\) −8.89201 −0.527643
\(285\) 13.3213 0.789084
\(286\) −18.4201 −1.08920
\(287\) −11.3098 −0.667597
\(288\) −35.7196 −2.10480
\(289\) 34.6913 2.04067
\(290\) −11.3709 −0.667724
\(291\) 7.34522 0.430584
\(292\) 3.88822 0.227541
\(293\) −16.9631 −0.990997 −0.495499 0.868609i \(-0.665015\pi\)
−0.495499 + 0.868609i \(0.665015\pi\)
\(294\) −2.66396 −0.155365
\(295\) 16.8544 0.981301
\(296\) −23.0646 −1.34060
\(297\) −48.5656 −2.81806
\(298\) 11.7433 0.680271
\(299\) 38.7403 2.24041
\(300\) 3.91600 0.226090
\(301\) −20.5898 −1.18678
\(302\) −1.52009 −0.0874711
\(303\) −15.2170 −0.874195
\(304\) −2.45697 −0.140917
\(305\) −2.91993 −0.167195
\(306\) −31.7782 −1.81664
\(307\) −34.1607 −1.94965 −0.974826 0.222967i \(-0.928426\pi\)
−0.974826 + 0.222967i \(0.928426\pi\)
\(308\) −21.9324 −1.24971
\(309\) 10.0087 0.569374
\(310\) 5.87911 0.333911
\(311\) 21.4133 1.21424 0.607120 0.794610i \(-0.292325\pi\)
0.607120 + 0.794610i \(0.292325\pi\)
\(312\) −37.2701 −2.11001
\(313\) −15.9294 −0.900381 −0.450191 0.892932i \(-0.648644\pi\)
−0.450191 + 0.892932i \(0.648644\pi\)
\(314\) 1.81069 0.102183
\(315\) 35.5294 2.00185
\(316\) −22.0867 −1.24247
\(317\) −4.07966 −0.229136 −0.114568 0.993415i \(-0.536548\pi\)
−0.114568 + 0.993415i \(0.536548\pi\)
\(318\) −10.3500 −0.580398
\(319\) 40.1058 2.24549
\(320\) −4.01227 −0.224293
\(321\) −23.3338 −1.30236
\(322\) −16.3830 −0.912988
\(323\) −15.6362 −0.870024
\(324\) −14.6932 −0.816290
\(325\) 4.31612 0.239415
\(326\) −0.568382 −0.0314798
\(327\) −12.1912 −0.674172
\(328\) 9.92726 0.548141
\(329\) −10.2407 −0.564589
\(330\) −22.9873 −1.26541
\(331\) −7.12795 −0.391787 −0.195894 0.980625i \(-0.562761\pi\)
−0.195894 + 0.980625i \(0.562761\pi\)
\(332\) 14.2411 0.781583
\(333\) −55.9547 −3.06630
\(334\) 15.5474 0.850714
\(335\) −20.4644 −1.11809
\(336\) −9.77320 −0.533172
\(337\) −1.19451 −0.0650689 −0.0325345 0.999471i \(-0.510358\pi\)
−0.0325345 + 0.999471i \(0.510358\pi\)
\(338\) −8.02979 −0.436763
\(339\) −37.5164 −2.03761
\(340\) 21.5391 1.16812
\(341\) −20.7359 −1.12291
\(342\) 9.61267 0.519794
\(343\) 16.5727 0.894840
\(344\) 18.0728 0.974421
\(345\) 48.3458 2.60285
\(346\) 11.4681 0.616527
\(347\) −8.45278 −0.453769 −0.226884 0.973922i \(-0.572854\pi\)
−0.226884 + 0.973922i \(0.572854\pi\)
\(348\) 34.4551 1.84699
\(349\) −18.6796 −0.999895 −0.499948 0.866056i \(-0.666647\pi\)
−0.499948 + 0.866056i \(0.666647\pi\)
\(350\) −1.82525 −0.0975638
\(351\) −45.9861 −2.45456
\(352\) 30.3285 1.61652
\(353\) 0.0957780 0.00509775 0.00254887 0.999997i \(-0.499189\pi\)
0.00254887 + 0.999997i \(0.499189\pi\)
\(354\) 18.1387 0.964062
\(355\) −12.2305 −0.649130
\(356\) 9.95045 0.527373
\(357\) −62.1969 −3.29181
\(358\) −13.1765 −0.696398
\(359\) −34.0926 −1.79934 −0.899669 0.436572i \(-0.856192\pi\)
−0.899669 + 0.436572i \(0.856192\pi\)
\(360\) −31.1861 −1.64365
\(361\) −14.2702 −0.751061
\(362\) −8.67656 −0.456030
\(363\) 47.8852 2.51332
\(364\) −20.7675 −1.08851
\(365\) 5.34807 0.279931
\(366\) −3.14244 −0.164258
\(367\) 20.9122 1.09161 0.545804 0.837913i \(-0.316224\pi\)
0.545804 + 0.837913i \(0.316224\pi\)
\(368\) −8.91689 −0.464825
\(369\) 24.0835 1.25374
\(370\) −13.4701 −0.700276
\(371\) −13.5826 −0.705176
\(372\) −17.8143 −0.923630
\(373\) 11.3183 0.586039 0.293020 0.956106i \(-0.405340\pi\)
0.293020 + 0.956106i \(0.405340\pi\)
\(374\) 26.9820 1.39521
\(375\) 36.0124 1.85967
\(376\) 8.98885 0.463565
\(377\) 37.9756 1.95584
\(378\) 19.4471 1.00025
\(379\) 25.6376 1.31691 0.658456 0.752619i \(-0.271210\pi\)
0.658456 + 0.752619i \(0.271210\pi\)
\(380\) −6.51542 −0.334234
\(381\) 16.3053 0.835344
\(382\) −18.3052 −0.936576
\(383\) −4.30051 −0.219746 −0.109873 0.993946i \(-0.535044\pi\)
−0.109873 + 0.993946i \(0.535044\pi\)
\(384\) 30.9915 1.58153
\(385\) −30.1670 −1.53745
\(386\) 2.67364 0.136085
\(387\) 43.8446 2.22875
\(388\) −3.59254 −0.182383
\(389\) −24.8065 −1.25774 −0.628870 0.777510i \(-0.716482\pi\)
−0.628870 + 0.777510i \(0.716482\pi\)
\(390\) −21.7663 −1.10218
\(391\) −56.7473 −2.86984
\(392\) 3.06864 0.154990
\(393\) −21.0539 −1.06203
\(394\) −5.72708 −0.288526
\(395\) −30.3792 −1.52854
\(396\) 46.7036 2.34694
\(397\) −26.1155 −1.31070 −0.655349 0.755326i \(-0.727479\pi\)
−0.655349 + 0.755326i \(0.727479\pi\)
\(398\) −2.71295 −0.135988
\(399\) 18.8141 0.941883
\(400\) −0.993444 −0.0496722
\(401\) −1.61342 −0.0805704 −0.0402852 0.999188i \(-0.512827\pi\)
−0.0402852 + 0.999188i \(0.512827\pi\)
\(402\) −22.0238 −1.09845
\(403\) −19.6345 −0.978065
\(404\) 7.44263 0.370285
\(405\) −20.2099 −1.00424
\(406\) −16.0596 −0.797023
\(407\) 47.5096 2.35496
\(408\) 54.5938 2.70279
\(409\) −19.2122 −0.949981 −0.474990 0.879991i \(-0.657548\pi\)
−0.474990 + 0.879991i \(0.657548\pi\)
\(410\) 5.79767 0.286326
\(411\) 32.2677 1.59165
\(412\) −4.89524 −0.241171
\(413\) 23.8041 1.17132
\(414\) 34.8865 1.71458
\(415\) 19.5880 0.961537
\(416\) 28.7177 1.40800
\(417\) −3.74077 −0.183186
\(418\) −8.16185 −0.399209
\(419\) −23.6883 −1.15725 −0.578625 0.815594i \(-0.696410\pi\)
−0.578625 + 0.815594i \(0.696410\pi\)
\(420\) −25.9167 −1.26460
\(421\) 14.8015 0.721381 0.360690 0.932686i \(-0.382541\pi\)
0.360690 + 0.932686i \(0.382541\pi\)
\(422\) 17.2698 0.840683
\(423\) 21.8069 1.06029
\(424\) 11.9223 0.578996
\(425\) −6.32230 −0.306677
\(426\) −13.1625 −0.637726
\(427\) −4.12393 −0.199571
\(428\) 11.4125 0.551645
\(429\) 76.7708 3.70653
\(430\) 10.5548 0.508997
\(431\) −16.3188 −0.786048 −0.393024 0.919528i \(-0.628571\pi\)
−0.393024 + 0.919528i \(0.628571\pi\)
\(432\) 10.5846 0.509254
\(433\) −0.0993936 −0.00477655 −0.00238828 0.999997i \(-0.500760\pi\)
−0.00238828 + 0.999997i \(0.500760\pi\)
\(434\) 8.30328 0.398570
\(435\) 47.3914 2.27224
\(436\) 5.96268 0.285561
\(437\) 17.1656 0.821144
\(438\) 5.75559 0.275013
\(439\) −22.9969 −1.09758 −0.548791 0.835960i \(-0.684912\pi\)
−0.548791 + 0.835960i \(0.684912\pi\)
\(440\) 26.4793 1.26235
\(441\) 7.44451 0.354501
\(442\) 25.5489 1.21524
\(443\) 10.5680 0.502100 0.251050 0.967974i \(-0.419224\pi\)
0.251050 + 0.967974i \(0.419224\pi\)
\(444\) 40.8157 1.93703
\(445\) 13.6864 0.648797
\(446\) 2.92978 0.138729
\(447\) −48.9434 −2.31494
\(448\) −5.66668 −0.267726
\(449\) −37.6403 −1.77636 −0.888178 0.459500i \(-0.848029\pi\)
−0.888178 + 0.459500i \(0.848029\pi\)
\(450\) 3.88676 0.183223
\(451\) −20.4486 −0.962888
\(452\) 18.3492 0.863076
\(453\) 6.33537 0.297661
\(454\) 13.4225 0.629951
\(455\) −28.5647 −1.33913
\(456\) −16.5142 −0.773348
\(457\) −9.61456 −0.449750 −0.224875 0.974388i \(-0.572197\pi\)
−0.224875 + 0.974388i \(0.572197\pi\)
\(458\) 6.19878 0.289650
\(459\) 67.3610 3.14414
\(460\) −23.6459 −1.10249
\(461\) −2.72760 −0.127037 −0.0635185 0.997981i \(-0.520232\pi\)
−0.0635185 + 0.997981i \(0.520232\pi\)
\(462\) −32.4657 −1.51044
\(463\) −21.3890 −0.994030 −0.497015 0.867742i \(-0.665571\pi\)
−0.497015 + 0.867742i \(0.665571\pi\)
\(464\) −8.74086 −0.405784
\(465\) −24.5028 −1.13629
\(466\) 17.4332 0.807578
\(467\) 29.3105 1.35633 0.678165 0.734910i \(-0.262776\pi\)
0.678165 + 0.734910i \(0.262776\pi\)
\(468\) 44.2230 2.04421
\(469\) −28.9026 −1.33460
\(470\) 5.24962 0.242147
\(471\) −7.54654 −0.347726
\(472\) −20.8942 −0.961733
\(473\) −37.2272 −1.71171
\(474\) −32.6941 −1.50169
\(475\) 1.91245 0.0877492
\(476\) 30.4205 1.39432
\(477\) 28.9234 1.32431
\(478\) −8.26381 −0.377978
\(479\) −16.8279 −0.768885 −0.384442 0.923149i \(-0.625606\pi\)
−0.384442 + 0.923149i \(0.625606\pi\)
\(480\) 35.8381 1.63578
\(481\) 44.9861 2.05119
\(482\) −8.09900 −0.368899
\(483\) 68.2805 3.10687
\(484\) −23.4206 −1.06457
\(485\) −4.94137 −0.224376
\(486\) −1.40022 −0.0635152
\(487\) −9.26965 −0.420048 −0.210024 0.977696i \(-0.567354\pi\)
−0.210024 + 0.977696i \(0.567354\pi\)
\(488\) 3.61981 0.163861
\(489\) 2.36889 0.107125
\(490\) 1.79213 0.0809602
\(491\) 7.02225 0.316910 0.158455 0.987366i \(-0.449349\pi\)
0.158455 + 0.987366i \(0.449349\pi\)
\(492\) −17.5675 −0.792006
\(493\) −55.6271 −2.50532
\(494\) −7.72834 −0.347715
\(495\) 64.2386 2.88731
\(496\) 4.51929 0.202922
\(497\) −17.2736 −0.774829
\(498\) 21.0806 0.944645
\(499\) 0.207296 0.00927984 0.00463992 0.999989i \(-0.498523\pi\)
0.00463992 + 0.999989i \(0.498523\pi\)
\(500\) −17.6136 −0.787705
\(501\) −64.7978 −2.89495
\(502\) 5.10648 0.227913
\(503\) 22.9333 1.02254 0.511272 0.859419i \(-0.329175\pi\)
0.511272 + 0.859419i \(0.329175\pi\)
\(504\) −44.0453 −1.96193
\(505\) 10.2370 0.455540
\(506\) −29.6211 −1.31682
\(507\) 33.4663 1.48629
\(508\) −7.97489 −0.353829
\(509\) 34.6558 1.53609 0.768046 0.640394i \(-0.221229\pi\)
0.768046 + 0.640394i \(0.221229\pi\)
\(510\) 31.8836 1.41183
\(511\) 7.55327 0.334137
\(512\) −12.2959 −0.543407
\(513\) −20.3762 −0.899631
\(514\) 3.00897 0.132720
\(515\) −6.73318 −0.296699
\(516\) −31.9821 −1.40793
\(517\) −18.5156 −0.814317
\(518\) −19.0243 −0.835879
\(519\) −47.7962 −2.09802
\(520\) 25.0729 1.09952
\(521\) 27.2351 1.19319 0.596596 0.802542i \(-0.296520\pi\)
0.596596 + 0.802542i \(0.296520\pi\)
\(522\) 34.1978 1.49680
\(523\) 13.6302 0.596006 0.298003 0.954565i \(-0.403679\pi\)
0.298003 + 0.954565i \(0.403679\pi\)
\(524\) 10.2974 0.449846
\(525\) 7.60723 0.332007
\(526\) 3.50690 0.152908
\(527\) 28.7609 1.25284
\(528\) −17.6704 −0.769004
\(529\) 39.2979 1.70860
\(530\) 6.96277 0.302444
\(531\) −50.6892 −2.19973
\(532\) −9.20196 −0.398956
\(533\) −19.3625 −0.838684
\(534\) 14.7293 0.637399
\(535\) 15.6974 0.678658
\(536\) 25.3695 1.09579
\(537\) 54.9165 2.36982
\(538\) 15.2546 0.657670
\(539\) −6.32093 −0.272262
\(540\) 28.0684 1.20787
\(541\) 25.8331 1.11065 0.555325 0.831634i \(-0.312594\pi\)
0.555325 + 0.831634i \(0.312594\pi\)
\(542\) −9.59013 −0.411931
\(543\) 36.1619 1.55186
\(544\) −42.0660 −1.80356
\(545\) 8.20139 0.351309
\(546\) −30.7414 −1.31561
\(547\) −34.8074 −1.48826 −0.744129 0.668036i \(-0.767135\pi\)
−0.744129 + 0.668036i \(0.767135\pi\)
\(548\) −15.7821 −0.674178
\(549\) 8.78164 0.374791
\(550\) −3.30013 −0.140718
\(551\) 16.8268 0.716845
\(552\) −59.9337 −2.55095
\(553\) −42.9056 −1.82453
\(554\) −23.4852 −0.997792
\(555\) 56.1402 2.38302
\(556\) 1.82961 0.0775926
\(557\) 12.8327 0.543737 0.271869 0.962334i \(-0.412358\pi\)
0.271869 + 0.962334i \(0.412358\pi\)
\(558\) −17.6813 −0.748509
\(559\) −35.2499 −1.49091
\(560\) 6.57476 0.277834
\(561\) −112.455 −4.74784
\(562\) 12.0196 0.507018
\(563\) 6.10554 0.257318 0.128659 0.991689i \(-0.458933\pi\)
0.128659 + 0.991689i \(0.458933\pi\)
\(564\) −15.9069 −0.669802
\(565\) 25.2385 1.06179
\(566\) −7.43716 −0.312607
\(567\) −28.5431 −1.19870
\(568\) 15.1620 0.636185
\(569\) −23.9940 −1.00588 −0.502940 0.864321i \(-0.667748\pi\)
−0.502940 + 0.864321i \(0.667748\pi\)
\(570\) −9.64454 −0.403965
\(571\) 35.8875 1.50184 0.750922 0.660390i \(-0.229609\pi\)
0.750922 + 0.660390i \(0.229609\pi\)
\(572\) −37.5485 −1.56998
\(573\) 76.2919 3.18714
\(574\) 8.18825 0.341771
\(575\) 6.94070 0.289447
\(576\) 12.0668 0.502784
\(577\) 20.8231 0.866876 0.433438 0.901183i \(-0.357300\pi\)
0.433438 + 0.901183i \(0.357300\pi\)
\(578\) −25.1164 −1.04470
\(579\) −11.1431 −0.463093
\(580\) −23.1791 −0.962459
\(581\) 27.6648 1.14773
\(582\) −5.31791 −0.220434
\(583\) −24.5580 −1.01709
\(584\) −6.62993 −0.274349
\(585\) 60.8267 2.51487
\(586\) 12.2812 0.507333
\(587\) −5.35770 −0.221136 −0.110568 0.993869i \(-0.535267\pi\)
−0.110568 + 0.993869i \(0.535267\pi\)
\(588\) −5.43035 −0.223944
\(589\) −8.69995 −0.358475
\(590\) −12.2025 −0.502370
\(591\) 23.8692 0.981846
\(592\) −10.3545 −0.425567
\(593\) 30.9114 1.26938 0.634690 0.772767i \(-0.281128\pi\)
0.634690 + 0.772767i \(0.281128\pi\)
\(594\) 35.1613 1.44268
\(595\) 41.8419 1.71535
\(596\) 23.9381 0.980545
\(597\) 11.3070 0.462763
\(598\) −28.0478 −1.14696
\(599\) 4.77015 0.194903 0.0974515 0.995240i \(-0.468931\pi\)
0.0974515 + 0.995240i \(0.468931\pi\)
\(600\) −6.67730 −0.272599
\(601\) −44.5777 −1.81836 −0.909181 0.416402i \(-0.863291\pi\)
−0.909181 + 0.416402i \(0.863291\pi\)
\(602\) 14.9069 0.607560
\(603\) 61.5463 2.50636
\(604\) −3.09862 −0.126081
\(605\) −32.2139 −1.30968
\(606\) 11.0171 0.447537
\(607\) 8.95911 0.363639 0.181819 0.983332i \(-0.441801\pi\)
0.181819 + 0.983332i \(0.441801\pi\)
\(608\) 12.7246 0.516053
\(609\) 66.9326 2.71225
\(610\) 2.11402 0.0855942
\(611\) −17.5322 −0.709277
\(612\) −64.7784 −2.61851
\(613\) 23.4711 0.947989 0.473995 0.880528i \(-0.342812\pi\)
0.473995 + 0.880528i \(0.342812\pi\)
\(614\) 24.7322 0.998109
\(615\) −24.1633 −0.974360
\(616\) 37.3976 1.50679
\(617\) 25.6789 1.03379 0.516896 0.856048i \(-0.327087\pi\)
0.516896 + 0.856048i \(0.327087\pi\)
\(618\) −7.24625 −0.291487
\(619\) −1.00000 −0.0401934
\(620\) 11.9843 0.481301
\(621\) −73.9496 −2.96750
\(622\) −15.5032 −0.621620
\(623\) 19.3298 0.774431
\(624\) −16.7318 −0.669809
\(625\) −19.8299 −0.793197
\(626\) 11.5328 0.460943
\(627\) 34.0167 1.35850
\(628\) 3.69101 0.147287
\(629\) −65.8962 −2.62745
\(630\) −25.7231 −1.02483
\(631\) −11.0957 −0.441711 −0.220856 0.975306i \(-0.570885\pi\)
−0.220856 + 0.975306i \(0.570885\pi\)
\(632\) 37.6607 1.49806
\(633\) −71.9767 −2.86082
\(634\) 2.95365 0.117305
\(635\) −10.9691 −0.435295
\(636\) −21.0979 −0.836588
\(637\) −5.98520 −0.237142
\(638\) −29.0364 −1.14956
\(639\) 36.7831 1.45512
\(640\) −20.8490 −0.824130
\(641\) −36.8740 −1.45644 −0.728218 0.685345i \(-0.759651\pi\)
−0.728218 + 0.685345i \(0.759651\pi\)
\(642\) 16.8936 0.666736
\(643\) 26.6767 1.05203 0.526013 0.850476i \(-0.323686\pi\)
0.526013 + 0.850476i \(0.323686\pi\)
\(644\) −33.3959 −1.31598
\(645\) −43.9899 −1.73210
\(646\) 11.3206 0.445402
\(647\) 4.92648 0.193680 0.0968399 0.995300i \(-0.469127\pi\)
0.0968399 + 0.995300i \(0.469127\pi\)
\(648\) 25.0539 0.984210
\(649\) 43.0388 1.68942
\(650\) −3.12485 −0.122567
\(651\) −34.6062 −1.35632
\(652\) −1.15862 −0.0453751
\(653\) 30.5281 1.19466 0.597328 0.801997i \(-0.296229\pi\)
0.597328 + 0.801997i \(0.296229\pi\)
\(654\) 8.82634 0.345137
\(655\) 14.1637 0.553420
\(656\) 4.45668 0.174004
\(657\) −16.0842 −0.627504
\(658\) 7.41423 0.289037
\(659\) 5.69587 0.221879 0.110940 0.993827i \(-0.464614\pi\)
0.110940 + 0.993827i \(0.464614\pi\)
\(660\) −46.8584 −1.82396
\(661\) −16.0281 −0.623421 −0.311711 0.950177i \(-0.600902\pi\)
−0.311711 + 0.950177i \(0.600902\pi\)
\(662\) 5.16060 0.200573
\(663\) −106.482 −4.13541
\(664\) −24.2830 −0.942363
\(665\) −12.6569 −0.490812
\(666\) 40.5109 1.56977
\(667\) 61.0680 2.36456
\(668\) 31.6926 1.22622
\(669\) −12.2107 −0.472091
\(670\) 14.8162 0.572398
\(671\) −7.45624 −0.287845
\(672\) 50.6154 1.95253
\(673\) −38.4585 −1.48247 −0.741233 0.671247i \(-0.765759\pi\)
−0.741233 + 0.671247i \(0.765759\pi\)
\(674\) 0.864817 0.0333115
\(675\) −8.23884 −0.317113
\(676\) −16.3683 −0.629552
\(677\) 23.1687 0.890446 0.445223 0.895420i \(-0.353124\pi\)
0.445223 + 0.895420i \(0.353124\pi\)
\(678\) 27.1617 1.04314
\(679\) −6.97888 −0.267825
\(680\) −36.7270 −1.40842
\(681\) −55.9420 −2.14370
\(682\) 15.0127 0.574866
\(683\) 34.7337 1.32905 0.664523 0.747267i \(-0.268635\pi\)
0.664523 + 0.747267i \(0.268635\pi\)
\(684\) 19.5950 0.749232
\(685\) −21.7075 −0.829402
\(686\) −11.9985 −0.458106
\(687\) −25.8351 −0.985670
\(688\) 8.11350 0.309324
\(689\) −23.2536 −0.885893
\(690\) −35.0021 −1.33251
\(691\) 15.8030 0.601173 0.300586 0.953755i \(-0.402818\pi\)
0.300586 + 0.953755i \(0.402818\pi\)
\(692\) 23.3771 0.888664
\(693\) 90.7266 3.44642
\(694\) 6.11977 0.232303
\(695\) 2.51654 0.0954578
\(696\) −58.7505 −2.22693
\(697\) 28.3624 1.07430
\(698\) 13.5239 0.511889
\(699\) −72.6576 −2.74816
\(700\) −3.72069 −0.140629
\(701\) −17.4822 −0.660295 −0.330147 0.943929i \(-0.607098\pi\)
−0.330147 + 0.943929i \(0.607098\pi\)
\(702\) 33.2937 1.25659
\(703\) 19.9331 0.751792
\(704\) −10.2456 −0.386146
\(705\) −21.8792 −0.824019
\(706\) −0.0693428 −0.00260975
\(707\) 14.4581 0.543752
\(708\) 36.9749 1.38960
\(709\) 1.40984 0.0529478 0.0264739 0.999650i \(-0.491572\pi\)
0.0264739 + 0.999650i \(0.491572\pi\)
\(710\) 8.85486 0.332317
\(711\) 91.3647 3.42644
\(712\) −16.9668 −0.635859
\(713\) −31.5740 −1.18246
\(714\) 45.0303 1.68522
\(715\) −51.6462 −1.93146
\(716\) −26.8596 −1.00379
\(717\) 34.4417 1.28625
\(718\) 24.6829 0.921157
\(719\) −13.1497 −0.490402 −0.245201 0.969472i \(-0.578854\pi\)
−0.245201 + 0.969472i \(0.578854\pi\)
\(720\) −14.0005 −0.521768
\(721\) −9.50951 −0.354153
\(722\) 10.3315 0.384500
\(723\) 33.7548 1.25535
\(724\) −17.6868 −0.657323
\(725\) 6.80368 0.252682
\(726\) −34.6687 −1.28667
\(727\) 15.4676 0.573661 0.286831 0.957981i \(-0.407398\pi\)
0.286831 + 0.957981i \(0.407398\pi\)
\(728\) 35.4113 1.31243
\(729\) −24.0319 −0.890071
\(730\) −3.87198 −0.143308
\(731\) 51.6345 1.90977
\(732\) −6.40570 −0.236762
\(733\) −5.10122 −0.188418 −0.0942089 0.995552i \(-0.530032\pi\)
−0.0942089 + 0.995552i \(0.530032\pi\)
\(734\) −15.1403 −0.558840
\(735\) −7.46919 −0.275505
\(736\) 46.1805 1.70224
\(737\) −52.2572 −1.92492
\(738\) −17.4364 −0.641841
\(739\) 16.1116 0.592673 0.296337 0.955084i \(-0.404235\pi\)
0.296337 + 0.955084i \(0.404235\pi\)
\(740\) −27.4581 −1.00938
\(741\) 32.2099 1.18326
\(742\) 9.83378 0.361009
\(743\) 32.9642 1.20934 0.604670 0.796476i \(-0.293305\pi\)
0.604670 + 0.796476i \(0.293305\pi\)
\(744\) 30.3758 1.11363
\(745\) 32.9258 1.20631
\(746\) −8.19440 −0.300018
\(747\) −58.9105 −2.15542
\(748\) 55.0015 2.01105
\(749\) 22.1700 0.810075
\(750\) −26.0728 −0.952045
\(751\) 29.0599 1.06041 0.530205 0.847869i \(-0.322115\pi\)
0.530205 + 0.847869i \(0.322115\pi\)
\(752\) 4.03540 0.147156
\(753\) −21.2826 −0.775582
\(754\) −27.4941 −1.00128
\(755\) −4.26201 −0.155110
\(756\) 39.6421 1.44177
\(757\) −51.6796 −1.87833 −0.939164 0.343468i \(-0.888398\pi\)
−0.939164 + 0.343468i \(0.888398\pi\)
\(758\) −18.5615 −0.674183
\(759\) 123.454 4.48110
\(760\) 11.1096 0.402989
\(761\) 5.32890 0.193173 0.0965863 0.995325i \(-0.469208\pi\)
0.0965863 + 0.995325i \(0.469208\pi\)
\(762\) −11.8049 −0.427648
\(763\) 11.5831 0.419337
\(764\) −37.3143 −1.34998
\(765\) −89.0996 −3.22140
\(766\) 3.11355 0.112497
\(767\) 40.7528 1.47150
\(768\) −34.3660 −1.24008
\(769\) 5.94381 0.214339 0.107170 0.994241i \(-0.465821\pi\)
0.107170 + 0.994241i \(0.465821\pi\)
\(770\) 21.8408 0.787087
\(771\) −12.5407 −0.451642
\(772\) 5.45009 0.196153
\(773\) 21.8886 0.787278 0.393639 0.919265i \(-0.371216\pi\)
0.393639 + 0.919265i \(0.371216\pi\)
\(774\) −31.7433 −1.14099
\(775\) −3.51771 −0.126360
\(776\) 6.12575 0.219902
\(777\) 79.2888 2.84447
\(778\) 17.9598 0.643891
\(779\) −8.57943 −0.307390
\(780\) −44.3696 −1.58869
\(781\) −31.2315 −1.11755
\(782\) 41.0848 1.46919
\(783\) −72.4898 −2.59057
\(784\) 1.37762 0.0492006
\(785\) 5.07681 0.181199
\(786\) 15.2429 0.543698
\(787\) 17.2063 0.613339 0.306670 0.951816i \(-0.400785\pi\)
0.306670 + 0.951816i \(0.400785\pi\)
\(788\) −11.6744 −0.415883
\(789\) −14.6159 −0.520341
\(790\) 21.9944 0.782526
\(791\) 35.6453 1.26740
\(792\) −79.6358 −2.82974
\(793\) −7.06021 −0.250715
\(794\) 18.9075 0.671002
\(795\) −29.0192 −1.02921
\(796\) −5.53022 −0.196014
\(797\) 26.2860 0.931099 0.465549 0.885022i \(-0.345857\pi\)
0.465549 + 0.885022i \(0.345857\pi\)
\(798\) −13.6213 −0.482190
\(799\) 25.6814 0.908542
\(800\) 5.14504 0.181905
\(801\) −41.1615 −1.45437
\(802\) 1.16811 0.0412474
\(803\) 13.6566 0.481932
\(804\) −44.8945 −1.58331
\(805\) −45.9345 −1.61898
\(806\) 14.2153 0.500713
\(807\) −63.5775 −2.23803
\(808\) −12.6907 −0.446456
\(809\) −3.27058 −0.114987 −0.0574937 0.998346i \(-0.518311\pi\)
−0.0574937 + 0.998346i \(0.518311\pi\)
\(810\) 14.6318 0.514111
\(811\) −11.2065 −0.393512 −0.196756 0.980452i \(-0.563041\pi\)
−0.196756 + 0.980452i \(0.563041\pi\)
\(812\) −32.7367 −1.14883
\(813\) 39.9695 1.40179
\(814\) −34.3967 −1.20560
\(815\) −1.59363 −0.0558224
\(816\) 24.5090 0.857986
\(817\) −15.6191 −0.546441
\(818\) 13.9095 0.486335
\(819\) 85.9077 3.00186
\(820\) 11.8183 0.412712
\(821\) −24.6391 −0.859910 −0.429955 0.902850i \(-0.641471\pi\)
−0.429955 + 0.902850i \(0.641471\pi\)
\(822\) −23.3617 −0.814832
\(823\) −9.88862 −0.344696 −0.172348 0.985036i \(-0.555135\pi\)
−0.172348 + 0.985036i \(0.555135\pi\)
\(824\) 8.34703 0.290783
\(825\) 13.7542 0.478860
\(826\) −17.2341 −0.599649
\(827\) 18.9840 0.660140 0.330070 0.943957i \(-0.392928\pi\)
0.330070 + 0.943957i \(0.392928\pi\)
\(828\) 71.1144 2.47140
\(829\) −23.6093 −0.819986 −0.409993 0.912089i \(-0.634469\pi\)
−0.409993 + 0.912089i \(0.634469\pi\)
\(830\) −14.1816 −0.492252
\(831\) 97.8810 3.39545
\(832\) −9.70142 −0.336336
\(833\) 8.76719 0.303765
\(834\) 2.70830 0.0937808
\(835\) 43.5916 1.50855
\(836\) −16.6375 −0.575421
\(837\) 37.4794 1.29548
\(838\) 17.1502 0.592445
\(839\) −48.9383 −1.68954 −0.844768 0.535132i \(-0.820262\pi\)
−0.844768 + 0.535132i \(0.820262\pi\)
\(840\) 44.1913 1.52475
\(841\) 30.8625 1.06422
\(842\) −10.7162 −0.369305
\(843\) −50.0951 −1.72537
\(844\) 35.2037 1.21176
\(845\) −22.5139 −0.774502
\(846\) −15.7881 −0.542807
\(847\) −45.4969 −1.56329
\(848\) 5.35230 0.183799
\(849\) 30.9964 1.06379
\(850\) 4.57732 0.157001
\(851\) 72.3416 2.47984
\(852\) −26.8312 −0.919220
\(853\) 6.33675 0.216966 0.108483 0.994098i \(-0.465401\pi\)
0.108483 + 0.994098i \(0.465401\pi\)
\(854\) 2.98571 0.102169
\(855\) 26.9520 0.921738
\(856\) −19.4599 −0.665125
\(857\) 2.41085 0.0823529 0.0411765 0.999152i \(-0.486889\pi\)
0.0411765 + 0.999152i \(0.486889\pi\)
\(858\) −55.5817 −1.89753
\(859\) 21.5349 0.734760 0.367380 0.930071i \(-0.380255\pi\)
0.367380 + 0.930071i \(0.380255\pi\)
\(860\) 21.5154 0.733670
\(861\) −34.1268 −1.16304
\(862\) 11.8147 0.402411
\(863\) 22.3824 0.761905 0.380953 0.924595i \(-0.375596\pi\)
0.380953 + 0.924595i \(0.375596\pi\)
\(864\) −54.8178 −1.86494
\(865\) 32.1541 1.09327
\(866\) 0.0719606 0.00244532
\(867\) 104.679 3.55509
\(868\) 16.9258 0.574501
\(869\) −77.5752 −2.63156
\(870\) −34.3112 −1.16326
\(871\) −49.4816 −1.67662
\(872\) −10.1672 −0.344303
\(873\) 14.8611 0.502971
\(874\) −12.4278 −0.420378
\(875\) −34.2163 −1.15672
\(876\) 11.7325 0.396404
\(877\) −17.6514 −0.596045 −0.298022 0.954559i \(-0.596327\pi\)
−0.298022 + 0.954559i \(0.596327\pi\)
\(878\) 16.6497 0.561899
\(879\) −51.1854 −1.72644
\(880\) 11.8874 0.400726
\(881\) −43.5861 −1.46845 −0.734227 0.678904i \(-0.762455\pi\)
−0.734227 + 0.678904i \(0.762455\pi\)
\(882\) −5.38980 −0.181484
\(883\) −10.0998 −0.339887 −0.169943 0.985454i \(-0.554358\pi\)
−0.169943 + 0.985454i \(0.554358\pi\)
\(884\) 52.0801 1.75164
\(885\) 50.8573 1.70955
\(886\) −7.65118 −0.257046
\(887\) 15.5185 0.521060 0.260530 0.965466i \(-0.416103\pi\)
0.260530 + 0.965466i \(0.416103\pi\)
\(888\) −69.5963 −2.33550
\(889\) −15.4920 −0.519586
\(890\) −9.90889 −0.332147
\(891\) −51.6072 −1.72891
\(892\) 5.97222 0.199965
\(893\) −7.76843 −0.259961
\(894\) 35.4348 1.18512
\(895\) −36.9441 −1.23491
\(896\) −29.4458 −0.983716
\(897\) 116.897 3.90307
\(898\) 27.2514 0.909392
\(899\) −30.9507 −1.03226
\(900\) 7.92296 0.264099
\(901\) 34.0622 1.13478
\(902\) 14.8047 0.492943
\(903\) −62.1286 −2.06751
\(904\) −31.2879 −1.04062
\(905\) −24.3273 −0.808667
\(906\) −4.58678 −0.152385
\(907\) 2.33484 0.0775271 0.0387636 0.999248i \(-0.487658\pi\)
0.0387636 + 0.999248i \(0.487658\pi\)
\(908\) 27.3612 0.908013
\(909\) −30.7875 −1.02116
\(910\) 20.6807 0.685559
\(911\) −7.30115 −0.241898 −0.120949 0.992659i \(-0.538594\pi\)
−0.120949 + 0.992659i \(0.538594\pi\)
\(912\) −7.41378 −0.245495
\(913\) 50.0192 1.65540
\(914\) 6.96090 0.230246
\(915\) −8.81075 −0.291274
\(916\) 12.6359 0.417502
\(917\) 20.0039 0.660585
\(918\) −48.7690 −1.60962
\(919\) −23.9848 −0.791185 −0.395593 0.918426i \(-0.629461\pi\)
−0.395593 + 0.918426i \(0.629461\pi\)
\(920\) 40.3193 1.32929
\(921\) −103.078 −3.39654
\(922\) 1.97477 0.0650356
\(923\) −29.5726 −0.973396
\(924\) −66.1798 −2.17716
\(925\) 8.05969 0.265001
\(926\) 15.4855 0.508886
\(927\) 20.2499 0.665093
\(928\) 45.2689 1.48602
\(929\) 12.0761 0.396204 0.198102 0.980181i \(-0.436522\pi\)
0.198102 + 0.980181i \(0.436522\pi\)
\(930\) 17.7399 0.581715
\(931\) −2.65201 −0.0869161
\(932\) 35.5368 1.16405
\(933\) 64.6136 2.11536
\(934\) −21.2207 −0.694362
\(935\) 75.6520 2.47409
\(936\) −75.4060 −2.46472
\(937\) 57.3121 1.87230 0.936152 0.351595i \(-0.114360\pi\)
0.936152 + 0.351595i \(0.114360\pi\)
\(938\) 20.9254 0.683238
\(939\) −48.0660 −1.56858
\(940\) 10.7011 0.349031
\(941\) 46.7239 1.52316 0.761578 0.648074i \(-0.224425\pi\)
0.761578 + 0.648074i \(0.224425\pi\)
\(942\) 5.46366 0.178016
\(943\) −31.1366 −1.01395
\(944\) −9.38011 −0.305296
\(945\) 54.5258 1.77373
\(946\) 26.9523 0.876296
\(947\) 45.7966 1.48819 0.744095 0.668074i \(-0.232881\pi\)
0.744095 + 0.668074i \(0.232881\pi\)
\(948\) −66.6454 −2.16454
\(949\) 12.9313 0.419767
\(950\) −1.38460 −0.0449225
\(951\) −12.3101 −0.399184
\(952\) −51.8709 −1.68115
\(953\) 8.74797 0.283375 0.141687 0.989911i \(-0.454747\pi\)
0.141687 + 0.989911i \(0.454747\pi\)
\(954\) −20.9404 −0.677970
\(955\) −51.3241 −1.66081
\(956\) −16.8454 −0.544819
\(957\) 121.017 3.91192
\(958\) 12.1833 0.393625
\(959\) −30.6583 −0.990010
\(960\) −12.1068 −0.390746
\(961\) −14.9975 −0.483792
\(962\) −32.5698 −1.05009
\(963\) −47.2096 −1.52131
\(964\) −16.5094 −0.531732
\(965\) 7.49635 0.241316
\(966\) −49.4348 −1.59054
\(967\) 5.02074 0.161456 0.0807281 0.996736i \(-0.474275\pi\)
0.0807281 + 0.996736i \(0.474275\pi\)
\(968\) 39.9352 1.28357
\(969\) −47.1815 −1.51569
\(970\) 3.57753 0.114868
\(971\) 49.8646 1.60023 0.800115 0.599846i \(-0.204772\pi\)
0.800115 + 0.599846i \(0.204772\pi\)
\(972\) −2.85428 −0.0915510
\(973\) 3.55420 0.113942
\(974\) 6.71118 0.215040
\(975\) 13.0237 0.417091
\(976\) 1.62505 0.0520167
\(977\) 29.5958 0.946854 0.473427 0.880833i \(-0.343017\pi\)
0.473427 + 0.880833i \(0.343017\pi\)
\(978\) −1.71506 −0.0548417
\(979\) 34.9491 1.11698
\(980\) 3.65317 0.116696
\(981\) −24.6655 −0.787509
\(982\) −5.08408 −0.162240
\(983\) −36.7308 −1.17153 −0.585765 0.810481i \(-0.699206\pi\)
−0.585765 + 0.810481i \(0.699206\pi\)
\(984\) 29.9550 0.954930
\(985\) −16.0576 −0.511637
\(986\) 40.2738 1.28258
\(987\) −30.9008 −0.983583
\(988\) −15.7539 −0.501197
\(989\) −56.6850 −1.80248
\(990\) −46.5085 −1.47814
\(991\) 1.77182 0.0562838 0.0281419 0.999604i \(-0.491041\pi\)
0.0281419 + 0.999604i \(0.491041\pi\)
\(992\) −23.4054 −0.743122
\(993\) −21.5082 −0.682542
\(994\) 12.5060 0.396667
\(995\) −7.60657 −0.241144
\(996\) 42.9718 1.36161
\(997\) −11.3713 −0.360134 −0.180067 0.983654i \(-0.557631\pi\)
−0.180067 + 0.983654i \(0.557631\pi\)
\(998\) −0.150081 −0.00475074
\(999\) −85.8719 −2.71687
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 619.2.a.a.1.11 21
3.2 odd 2 5571.2.a.e.1.11 21
4.3 odd 2 9904.2.a.j.1.1 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
619.2.a.a.1.11 21 1.1 even 1 trivial
5571.2.a.e.1.11 21 3.2 odd 2
9904.2.a.j.1.1 21 4.3 odd 2