Properties

Label 619.2.a.b.1.27
Level $619$
Weight $2$
Character 619.1
Self dual yes
Analytic conductor $4.943$
Analytic rank $0$
Dimension $30$
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: \(0\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.27
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)
 
\(f(q)\) \(=\) \(q+2.46595 q^{2} -0.157868 q^{3} +4.08090 q^{4} +2.37765 q^{5} -0.389293 q^{6} +4.70879 q^{7} +5.13138 q^{8} -2.97508 q^{9} +O(q^{10})\) \(q+2.46595 q^{2} -0.157868 q^{3} +4.08090 q^{4} +2.37765 q^{5} -0.389293 q^{6} +4.70879 q^{7} +5.13138 q^{8} -2.97508 q^{9} +5.86316 q^{10} -3.89648 q^{11} -0.644241 q^{12} -6.62279 q^{13} +11.6116 q^{14} -0.375354 q^{15} +4.49192 q^{16} -5.95137 q^{17} -7.33638 q^{18} -0.395246 q^{19} +9.70294 q^{20} -0.743365 q^{21} -9.60851 q^{22} -1.84938 q^{23} -0.810079 q^{24} +0.653219 q^{25} -16.3315 q^{26} +0.943271 q^{27} +19.2161 q^{28} +10.6320 q^{29} -0.925603 q^{30} +7.56721 q^{31} +0.814076 q^{32} +0.615128 q^{33} -14.6758 q^{34} +11.1958 q^{35} -12.1410 q^{36} -5.85939 q^{37} -0.974656 q^{38} +1.04552 q^{39} +12.2006 q^{40} +1.13182 q^{41} -1.83310 q^{42} +3.18315 q^{43} -15.9011 q^{44} -7.07369 q^{45} -4.56048 q^{46} +0.625030 q^{47} -0.709129 q^{48} +15.1727 q^{49} +1.61080 q^{50} +0.939529 q^{51} -27.0269 q^{52} +12.8766 q^{53} +2.32606 q^{54} -9.26447 q^{55} +24.1626 q^{56} +0.0623966 q^{57} +26.2180 q^{58} -0.141655 q^{59} -1.53178 q^{60} -3.91754 q^{61} +18.6603 q^{62} -14.0090 q^{63} -6.97637 q^{64} -15.7467 q^{65} +1.51687 q^{66} +0.202947 q^{67} -24.2869 q^{68} +0.291958 q^{69} +27.6084 q^{70} +6.99318 q^{71} -15.2663 q^{72} +0.952512 q^{73} -14.4490 q^{74} -0.103122 q^{75} -1.61296 q^{76} -18.3477 q^{77} +2.57821 q^{78} -8.10807 q^{79} +10.6802 q^{80} +8.77632 q^{81} +2.79100 q^{82} +9.46455 q^{83} -3.03360 q^{84} -14.1503 q^{85} +7.84947 q^{86} -1.67845 q^{87} -19.9943 q^{88} +10.3042 q^{89} -17.4434 q^{90} -31.1853 q^{91} -7.54714 q^{92} -1.19462 q^{93} +1.54129 q^{94} -0.939757 q^{95} -0.128516 q^{96} -12.2470 q^{97} +37.4150 q^{98} +11.5923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.46595 1.74369 0.871844 0.489784i \(-0.162924\pi\)
0.871844 + 0.489784i \(0.162924\pi\)
\(3\) −0.157868 −0.0911449 −0.0455725 0.998961i \(-0.514511\pi\)
−0.0455725 + 0.998961i \(0.514511\pi\)
\(4\) 4.08090 2.04045
\(5\) 2.37765 1.06332 0.531659 0.846959i \(-0.321569\pi\)
0.531659 + 0.846959i \(0.321569\pi\)
\(6\) −0.389293 −0.158928
\(7\) 4.70879 1.77975 0.889877 0.456200i \(-0.150790\pi\)
0.889877 + 0.456200i \(0.150790\pi\)
\(8\) 5.13138 1.81422
\(9\) −2.97508 −0.991693
\(10\) 5.86316 1.85409
\(11\) −3.89648 −1.17483 −0.587416 0.809285i \(-0.699855\pi\)
−0.587416 + 0.809285i \(0.699855\pi\)
\(12\) −0.644241 −0.185976
\(13\) −6.62279 −1.83683 −0.918416 0.395617i \(-0.870531\pi\)
−0.918416 + 0.395617i \(0.870531\pi\)
\(14\) 11.6116 3.10334
\(15\) −0.375354 −0.0969160
\(16\) 4.49192 1.12298
\(17\) −5.95137 −1.44342 −0.721710 0.692195i \(-0.756644\pi\)
−0.721710 + 0.692195i \(0.756644\pi\)
\(18\) −7.33638 −1.72920
\(19\) −0.395246 −0.0906757 −0.0453378 0.998972i \(-0.514436\pi\)
−0.0453378 + 0.998972i \(0.514436\pi\)
\(20\) 9.70294 2.16964
\(21\) −0.743365 −0.162216
\(22\) −9.60851 −2.04854
\(23\) −1.84938 −0.385623 −0.192812 0.981236i \(-0.561761\pi\)
−0.192812 + 0.981236i \(0.561761\pi\)
\(24\) −0.810079 −0.165357
\(25\) 0.653219 0.130644
\(26\) −16.3315 −3.20286
\(27\) 0.943271 0.181533
\(28\) 19.2161 3.63150
\(29\) 10.6320 1.97432 0.987159 0.159743i \(-0.0510667\pi\)
0.987159 + 0.159743i \(0.0510667\pi\)
\(30\) −0.925603 −0.168991
\(31\) 7.56721 1.35911 0.679556 0.733624i \(-0.262173\pi\)
0.679556 + 0.733624i \(0.262173\pi\)
\(32\) 0.814076 0.143910
\(33\) 0.615128 0.107080
\(34\) −14.6758 −2.51687
\(35\) 11.1958 1.89244
\(36\) −12.1410 −2.02350
\(37\) −5.85939 −0.963278 −0.481639 0.876370i \(-0.659958\pi\)
−0.481639 + 0.876370i \(0.659958\pi\)
\(38\) −0.974656 −0.158110
\(39\) 1.04552 0.167418
\(40\) 12.2006 1.92909
\(41\) 1.13182 0.176760 0.0883801 0.996087i \(-0.471831\pi\)
0.0883801 + 0.996087i \(0.471831\pi\)
\(42\) −1.83310 −0.282853
\(43\) 3.18315 0.485425 0.242713 0.970098i \(-0.421963\pi\)
0.242713 + 0.970098i \(0.421963\pi\)
\(44\) −15.9011 −2.39719
\(45\) −7.07369 −1.05448
\(46\) −4.56048 −0.672406
\(47\) 0.625030 0.0911700 0.0455850 0.998960i \(-0.485485\pi\)
0.0455850 + 0.998960i \(0.485485\pi\)
\(48\) −0.709129 −0.102354
\(49\) 15.1727 2.16753
\(50\) 1.61080 0.227802
\(51\) 0.939529 0.131560
\(52\) −27.0269 −3.74796
\(53\) 12.8766 1.76874 0.884368 0.466790i \(-0.154589\pi\)
0.884368 + 0.466790i \(0.154589\pi\)
\(54\) 2.32606 0.316536
\(55\) −9.26447 −1.24922
\(56\) 24.1626 3.22886
\(57\) 0.0623966 0.00826463
\(58\) 26.2180 3.44259
\(59\) −0.141655 −0.0184419 −0.00922096 0.999957i \(-0.502935\pi\)
−0.00922096 + 0.999957i \(0.502935\pi\)
\(60\) −1.53178 −0.197752
\(61\) −3.91754 −0.501589 −0.250795 0.968040i \(-0.580692\pi\)
−0.250795 + 0.968040i \(0.580692\pi\)
\(62\) 18.6603 2.36987
\(63\) −14.0090 −1.76497
\(64\) −6.97637 −0.872046
\(65\) −15.7467 −1.95313
\(66\) 1.51687 0.186714
\(67\) 0.202947 0.0247939 0.0123970 0.999923i \(-0.496054\pi\)
0.0123970 + 0.999923i \(0.496054\pi\)
\(68\) −24.2869 −2.94522
\(69\) 0.291958 0.0351476
\(70\) 27.6084 3.29983
\(71\) 6.99318 0.829938 0.414969 0.909836i \(-0.363792\pi\)
0.414969 + 0.909836i \(0.363792\pi\)
\(72\) −15.2663 −1.79915
\(73\) 0.952512 0.111483 0.0557415 0.998445i \(-0.482248\pi\)
0.0557415 + 0.998445i \(0.482248\pi\)
\(74\) −14.4490 −1.67966
\(75\) −0.103122 −0.0119075
\(76\) −1.61296 −0.185019
\(77\) −18.3477 −2.09091
\(78\) 2.57821 0.291924
\(79\) −8.10807 −0.912229 −0.456114 0.889921i \(-0.650759\pi\)
−0.456114 + 0.889921i \(0.650759\pi\)
\(80\) 10.6802 1.19408
\(81\) 8.77632 0.975147
\(82\) 2.79100 0.308215
\(83\) 9.46455 1.03887 0.519435 0.854510i \(-0.326142\pi\)
0.519435 + 0.854510i \(0.326142\pi\)
\(84\) −3.03360 −0.330992
\(85\) −14.1503 −1.53481
\(86\) 7.84947 0.846430
\(87\) −1.67845 −0.179949
\(88\) −19.9943 −2.13140
\(89\) 10.3042 1.09224 0.546121 0.837706i \(-0.316104\pi\)
0.546121 + 0.837706i \(0.316104\pi\)
\(90\) −17.4434 −1.83869
\(91\) −31.1853 −3.26911
\(92\) −7.54714 −0.786844
\(93\) −1.19462 −0.123876
\(94\) 1.54129 0.158972
\(95\) −0.939757 −0.0964170
\(96\) −0.128516 −0.0131166
\(97\) −12.2470 −1.24350 −0.621749 0.783216i \(-0.713578\pi\)
−0.621749 + 0.783216i \(0.713578\pi\)
\(98\) 37.4150 3.77949
\(99\) 11.5923 1.16507
\(100\) 2.66572 0.266572
\(101\) 14.8308 1.47572 0.737858 0.674956i \(-0.235838\pi\)
0.737858 + 0.674956i \(0.235838\pi\)
\(102\) 2.31683 0.229400
\(103\) −3.30296 −0.325451 −0.162725 0.986671i \(-0.552028\pi\)
−0.162725 + 0.986671i \(0.552028\pi\)
\(104\) −33.9840 −3.33241
\(105\) −1.76746 −0.172487
\(106\) 31.7530 3.08413
\(107\) −2.29757 −0.222115 −0.111057 0.993814i \(-0.535424\pi\)
−0.111057 + 0.993814i \(0.535424\pi\)
\(108\) 3.84939 0.370408
\(109\) 9.44203 0.904383 0.452191 0.891921i \(-0.350642\pi\)
0.452191 + 0.891921i \(0.350642\pi\)
\(110\) −22.8457 −2.17825
\(111\) 0.925009 0.0877979
\(112\) 21.1515 1.99863
\(113\) −10.3934 −0.977725 −0.488862 0.872361i \(-0.662588\pi\)
−0.488862 + 0.872361i \(0.662588\pi\)
\(114\) 0.153867 0.0144109
\(115\) −4.39719 −0.410040
\(116\) 43.3882 4.02849
\(117\) 19.7033 1.82157
\(118\) −0.349314 −0.0321570
\(119\) −28.0238 −2.56893
\(120\) −1.92608 −0.175827
\(121\) 4.18256 0.380232
\(122\) −9.66044 −0.874615
\(123\) −0.178677 −0.0161108
\(124\) 30.8810 2.77320
\(125\) −10.3351 −0.924402
\(126\) −34.5455 −3.07756
\(127\) −3.47652 −0.308491 −0.154246 0.988033i \(-0.549295\pi\)
−0.154246 + 0.988033i \(0.549295\pi\)
\(128\) −18.8315 −1.66449
\(129\) −0.502516 −0.0442440
\(130\) −38.8305 −3.40566
\(131\) −0.615745 −0.0537979 −0.0268989 0.999638i \(-0.508563\pi\)
−0.0268989 + 0.999638i \(0.508563\pi\)
\(132\) 2.51027 0.218491
\(133\) −1.86113 −0.161380
\(134\) 0.500457 0.0432329
\(135\) 2.24277 0.193027
\(136\) −30.5388 −2.61868
\(137\) 3.33652 0.285058 0.142529 0.989791i \(-0.454477\pi\)
0.142529 + 0.989791i \(0.454477\pi\)
\(138\) 0.719952 0.0612864
\(139\) −2.51131 −0.213007 −0.106503 0.994312i \(-0.533965\pi\)
−0.106503 + 0.994312i \(0.533965\pi\)
\(140\) 45.6891 3.86143
\(141\) −0.0986720 −0.00830968
\(142\) 17.2448 1.44715
\(143\) 25.8056 2.15797
\(144\) −13.3638 −1.11365
\(145\) 25.2792 2.09933
\(146\) 2.34884 0.194392
\(147\) −2.39528 −0.197559
\(148\) −23.9116 −1.96552
\(149\) 2.65229 0.217284 0.108642 0.994081i \(-0.465350\pi\)
0.108642 + 0.994081i \(0.465350\pi\)
\(150\) −0.254294 −0.0207630
\(151\) −7.64268 −0.621953 −0.310976 0.950418i \(-0.600656\pi\)
−0.310976 + 0.950418i \(0.600656\pi\)
\(152\) −2.02816 −0.164505
\(153\) 17.7058 1.43143
\(154\) −45.2445 −3.64590
\(155\) 17.9922 1.44517
\(156\) 4.26667 0.341607
\(157\) −4.49351 −0.358621 −0.179311 0.983793i \(-0.557387\pi\)
−0.179311 + 0.983793i \(0.557387\pi\)
\(158\) −19.9941 −1.59064
\(159\) −2.03280 −0.161211
\(160\) 1.93559 0.153022
\(161\) −8.70835 −0.686314
\(162\) 21.6419 1.70035
\(163\) 16.3285 1.27894 0.639472 0.768815i \(-0.279153\pi\)
0.639472 + 0.768815i \(0.279153\pi\)
\(164\) 4.61883 0.360670
\(165\) 1.46256 0.113860
\(166\) 23.3391 1.81146
\(167\) −21.8457 −1.69047 −0.845234 0.534396i \(-0.820539\pi\)
−0.845234 + 0.534396i \(0.820539\pi\)
\(168\) −3.81449 −0.294294
\(169\) 30.8613 2.37395
\(170\) −34.8939 −2.67624
\(171\) 1.17589 0.0899224
\(172\) 12.9901 0.990485
\(173\) −2.93795 −0.223368 −0.111684 0.993744i \(-0.535625\pi\)
−0.111684 + 0.993744i \(0.535625\pi\)
\(174\) −4.13897 −0.313775
\(175\) 3.07587 0.232514
\(176\) −17.5027 −1.31931
\(177\) 0.0223628 0.00168089
\(178\) 25.4096 1.90453
\(179\) 1.37373 0.102677 0.0513387 0.998681i \(-0.483651\pi\)
0.0513387 + 0.998681i \(0.483651\pi\)
\(180\) −28.8670 −2.15162
\(181\) −12.3352 −0.916865 −0.458433 0.888729i \(-0.651589\pi\)
−0.458433 + 0.888729i \(0.651589\pi\)
\(182\) −76.9013 −5.70031
\(183\) 0.618452 0.0457173
\(184\) −9.48989 −0.699604
\(185\) −13.9316 −1.02427
\(186\) −2.94587 −0.216001
\(187\) 23.1894 1.69578
\(188\) 2.55068 0.186028
\(189\) 4.44166 0.323084
\(190\) −2.31739 −0.168121
\(191\) −13.4793 −0.975329 −0.487665 0.873031i \(-0.662151\pi\)
−0.487665 + 0.873031i \(0.662151\pi\)
\(192\) 1.10134 0.0794826
\(193\) 12.6210 0.908483 0.454241 0.890879i \(-0.349910\pi\)
0.454241 + 0.890879i \(0.349910\pi\)
\(194\) −30.2006 −2.16827
\(195\) 2.48589 0.178018
\(196\) 61.9181 4.42272
\(197\) 5.34673 0.380938 0.190469 0.981693i \(-0.438999\pi\)
0.190469 + 0.981693i \(0.438999\pi\)
\(198\) 28.5861 2.03152
\(199\) −27.4088 −1.94296 −0.971478 0.237129i \(-0.923794\pi\)
−0.971478 + 0.237129i \(0.923794\pi\)
\(200\) 3.35191 0.237016
\(201\) −0.0320388 −0.00225984
\(202\) 36.5719 2.57319
\(203\) 50.0639 3.51380
\(204\) 3.83412 0.268442
\(205\) 2.69107 0.187952
\(206\) −8.14493 −0.567484
\(207\) 5.50206 0.382420
\(208\) −29.7490 −2.06272
\(209\) 1.54007 0.106529
\(210\) −4.35847 −0.300763
\(211\) −0.948427 −0.0652924 −0.0326462 0.999467i \(-0.510393\pi\)
−0.0326462 + 0.999467i \(0.510393\pi\)
\(212\) 52.5481 3.60902
\(213\) −1.10400 −0.0756446
\(214\) −5.66569 −0.387299
\(215\) 7.56841 0.516161
\(216\) 4.84028 0.329340
\(217\) 35.6324 2.41888
\(218\) 23.2836 1.57696
\(219\) −0.150371 −0.0101611
\(220\) −37.8073 −2.54897
\(221\) 39.4147 2.65132
\(222\) 2.28102 0.153092
\(223\) −23.6431 −1.58326 −0.791631 0.611000i \(-0.790768\pi\)
−0.791631 + 0.611000i \(0.790768\pi\)
\(224\) 3.83331 0.256124
\(225\) −1.94338 −0.129558
\(226\) −25.6295 −1.70485
\(227\) 0.104193 0.00691552 0.00345776 0.999994i \(-0.498899\pi\)
0.00345776 + 0.999994i \(0.498899\pi\)
\(228\) 0.254634 0.0168635
\(229\) 15.8886 1.04995 0.524973 0.851119i \(-0.324076\pi\)
0.524973 + 0.851119i \(0.324076\pi\)
\(230\) −10.8432 −0.714981
\(231\) 2.89651 0.190576
\(232\) 54.5569 3.58184
\(233\) 27.7194 1.81596 0.907978 0.419018i \(-0.137626\pi\)
0.907978 + 0.419018i \(0.137626\pi\)
\(234\) 48.5873 3.17625
\(235\) 1.48610 0.0969426
\(236\) −0.578080 −0.0376298
\(237\) 1.28000 0.0831450
\(238\) −69.1051 −4.47942
\(239\) 2.94936 0.190778 0.0953892 0.995440i \(-0.469590\pi\)
0.0953892 + 0.995440i \(0.469590\pi\)
\(240\) −1.68606 −0.108835
\(241\) −11.3904 −0.733722 −0.366861 0.930276i \(-0.619568\pi\)
−0.366861 + 0.930276i \(0.619568\pi\)
\(242\) 10.3140 0.663007
\(243\) −4.21531 −0.270412
\(244\) −15.9871 −1.02347
\(245\) 36.0753 2.30477
\(246\) −0.440609 −0.0280922
\(247\) 2.61763 0.166556
\(248\) 38.8302 2.46572
\(249\) −1.49415 −0.0946877
\(250\) −25.4859 −1.61187
\(251\) −16.0716 −1.01443 −0.507214 0.861820i \(-0.669325\pi\)
−0.507214 + 0.861820i \(0.669325\pi\)
\(252\) −57.1693 −3.60133
\(253\) 7.20608 0.453043
\(254\) −8.57292 −0.537913
\(255\) 2.23387 0.139890
\(256\) −32.4848 −2.03030
\(257\) −18.2023 −1.13543 −0.567714 0.823226i \(-0.692172\pi\)
−0.567714 + 0.823226i \(0.692172\pi\)
\(258\) −1.23918 −0.0771478
\(259\) −27.5906 −1.71440
\(260\) −64.2605 −3.98527
\(261\) −31.6311 −1.95792
\(262\) −1.51839 −0.0938067
\(263\) 9.11949 0.562332 0.281166 0.959659i \(-0.409279\pi\)
0.281166 + 0.959659i \(0.409279\pi\)
\(264\) 3.15646 0.194266
\(265\) 30.6160 1.88073
\(266\) −4.58945 −0.281397
\(267\) −1.62670 −0.0995524
\(268\) 0.828206 0.0505907
\(269\) −14.0578 −0.857119 −0.428559 0.903514i \(-0.640979\pi\)
−0.428559 + 0.903514i \(0.640979\pi\)
\(270\) 5.53055 0.336579
\(271\) −7.13801 −0.433603 −0.216801 0.976216i \(-0.569562\pi\)
−0.216801 + 0.976216i \(0.569562\pi\)
\(272\) −26.7331 −1.62093
\(273\) 4.92315 0.297963
\(274\) 8.22767 0.497052
\(275\) −2.54525 −0.153485
\(276\) 1.19145 0.0717168
\(277\) −4.64697 −0.279210 −0.139605 0.990207i \(-0.544583\pi\)
−0.139605 + 0.990207i \(0.544583\pi\)
\(278\) −6.19276 −0.371417
\(279\) −22.5130 −1.34782
\(280\) 57.4501 3.43330
\(281\) −24.4344 −1.45763 −0.728817 0.684708i \(-0.759930\pi\)
−0.728817 + 0.684708i \(0.759930\pi\)
\(282\) −0.243320 −0.0144895
\(283\) −5.51364 −0.327752 −0.163876 0.986481i \(-0.552400\pi\)
−0.163876 + 0.986481i \(0.552400\pi\)
\(284\) 28.5384 1.69344
\(285\) 0.148357 0.00878792
\(286\) 63.6352 3.76283
\(287\) 5.32949 0.314590
\(288\) −2.42194 −0.142714
\(289\) 18.4189 1.08346
\(290\) 62.3372 3.66057
\(291\) 1.93341 0.113339
\(292\) 3.88710 0.227475
\(293\) −0.925316 −0.0540576 −0.0270288 0.999635i \(-0.508605\pi\)
−0.0270288 + 0.999635i \(0.508605\pi\)
\(294\) −5.90662 −0.344481
\(295\) −0.336806 −0.0196096
\(296\) −30.0668 −1.74760
\(297\) −3.67544 −0.213271
\(298\) 6.54041 0.378876
\(299\) 12.2481 0.708324
\(300\) −0.420831 −0.0242967
\(301\) 14.9888 0.863938
\(302\) −18.8465 −1.08449
\(303\) −2.34130 −0.134504
\(304\) −1.77541 −0.101827
\(305\) −9.31453 −0.533349
\(306\) 43.6616 2.49597
\(307\) −27.4310 −1.56557 −0.782785 0.622292i \(-0.786202\pi\)
−0.782785 + 0.622292i \(0.786202\pi\)
\(308\) −74.8750 −4.26640
\(309\) 0.521431 0.0296632
\(310\) 44.3678 2.51992
\(311\) −22.0958 −1.25294 −0.626468 0.779447i \(-0.715500\pi\)
−0.626468 + 0.779447i \(0.715500\pi\)
\(312\) 5.36498 0.303732
\(313\) −12.0460 −0.680881 −0.340440 0.940266i \(-0.610576\pi\)
−0.340440 + 0.940266i \(0.610576\pi\)
\(314\) −11.0808 −0.625323
\(315\) −33.3085 −1.87672
\(316\) −33.0882 −1.86136
\(317\) 7.65816 0.430125 0.215063 0.976600i \(-0.431004\pi\)
0.215063 + 0.976600i \(0.431004\pi\)
\(318\) −5.01277 −0.281102
\(319\) −41.4275 −2.31949
\(320\) −16.5874 −0.927262
\(321\) 0.362712 0.0202446
\(322\) −21.4743 −1.19672
\(323\) 2.35226 0.130883
\(324\) 35.8153 1.98974
\(325\) −4.32613 −0.239971
\(326\) 40.2651 2.23008
\(327\) −1.49059 −0.0824299
\(328\) 5.80779 0.320681
\(329\) 2.94313 0.162260
\(330\) 3.60659 0.198536
\(331\) 16.9303 0.930575 0.465287 0.885160i \(-0.345951\pi\)
0.465287 + 0.885160i \(0.345951\pi\)
\(332\) 38.6239 2.11976
\(333\) 17.4322 0.955276
\(334\) −53.8703 −2.94765
\(335\) 0.482537 0.0263638
\(336\) −3.33914 −0.182165
\(337\) 9.35829 0.509779 0.254889 0.966970i \(-0.417961\pi\)
0.254889 + 0.966970i \(0.417961\pi\)
\(338\) 76.1024 4.13943
\(339\) 1.64077 0.0891147
\(340\) −57.7458 −3.13171
\(341\) −29.4855 −1.59673
\(342\) 2.89968 0.156797
\(343\) 38.4834 2.07791
\(344\) 16.3339 0.880666
\(345\) 0.694173 0.0373730
\(346\) −7.24484 −0.389485
\(347\) −35.5930 −1.91073 −0.955367 0.295421i \(-0.904540\pi\)
−0.955367 + 0.295421i \(0.904540\pi\)
\(348\) −6.84959 −0.367176
\(349\) −11.8428 −0.633930 −0.316965 0.948437i \(-0.602664\pi\)
−0.316965 + 0.948437i \(0.602664\pi\)
\(350\) 7.58493 0.405432
\(351\) −6.24709 −0.333445
\(352\) −3.17203 −0.169070
\(353\) −3.61444 −0.192377 −0.0961886 0.995363i \(-0.530665\pi\)
−0.0961886 + 0.995363i \(0.530665\pi\)
\(354\) 0.0551454 0.00293094
\(355\) 16.6273 0.882487
\(356\) 42.0504 2.22866
\(357\) 4.42404 0.234145
\(358\) 3.38755 0.179037
\(359\) 19.2576 1.01638 0.508188 0.861246i \(-0.330316\pi\)
0.508188 + 0.861246i \(0.330316\pi\)
\(360\) −36.2978 −1.91306
\(361\) −18.8438 −0.991778
\(362\) −30.4179 −1.59873
\(363\) −0.660290 −0.0346562
\(364\) −127.264 −6.67045
\(365\) 2.26474 0.118542
\(366\) 1.52507 0.0797167
\(367\) 29.0707 1.51748 0.758740 0.651393i \(-0.225815\pi\)
0.758740 + 0.651393i \(0.225815\pi\)
\(368\) −8.30728 −0.433047
\(369\) −3.36725 −0.175292
\(370\) −34.3546 −1.78601
\(371\) 60.6332 3.14792
\(372\) −4.87511 −0.252763
\(373\) 11.0922 0.574334 0.287167 0.957881i \(-0.407287\pi\)
0.287167 + 0.957881i \(0.407287\pi\)
\(374\) 57.1839 2.95691
\(375\) 1.63158 0.0842545
\(376\) 3.20727 0.165402
\(377\) −70.4137 −3.62649
\(378\) 10.9529 0.563357
\(379\) 28.5334 1.46566 0.732830 0.680412i \(-0.238199\pi\)
0.732830 + 0.680412i \(0.238199\pi\)
\(380\) −3.83505 −0.196734
\(381\) 0.548830 0.0281174
\(382\) −33.2393 −1.70067
\(383\) −22.5616 −1.15284 −0.576422 0.817152i \(-0.695552\pi\)
−0.576422 + 0.817152i \(0.695552\pi\)
\(384\) 2.97289 0.151709
\(385\) −43.6244 −2.22331
\(386\) 31.1228 1.58411
\(387\) −9.47011 −0.481393
\(388\) −49.9789 −2.53729
\(389\) −7.21475 −0.365802 −0.182901 0.983131i \(-0.558549\pi\)
−0.182901 + 0.983131i \(0.558549\pi\)
\(390\) 6.13007 0.310408
\(391\) 11.0064 0.556616
\(392\) 77.8568 3.93236
\(393\) 0.0972061 0.00490340
\(394\) 13.1847 0.664238
\(395\) −19.2781 −0.969989
\(396\) 47.3071 2.37727
\(397\) 27.6931 1.38988 0.694939 0.719069i \(-0.255431\pi\)
0.694939 + 0.719069i \(0.255431\pi\)
\(398\) −67.5886 −3.38791
\(399\) 0.293812 0.0147090
\(400\) 2.93421 0.146710
\(401\) 19.7647 0.987002 0.493501 0.869745i \(-0.335717\pi\)
0.493501 + 0.869745i \(0.335717\pi\)
\(402\) −0.0790059 −0.00394046
\(403\) −50.1161 −2.49646
\(404\) 60.5228 3.01112
\(405\) 20.8670 1.03689
\(406\) 123.455 6.12697
\(407\) 22.8310 1.13169
\(408\) 4.82108 0.238679
\(409\) −3.39180 −0.167714 −0.0838569 0.996478i \(-0.526724\pi\)
−0.0838569 + 0.996478i \(0.526724\pi\)
\(410\) 6.63603 0.327730
\(411\) −0.526728 −0.0259816
\(412\) −13.4790 −0.664065
\(413\) −0.667024 −0.0328221
\(414\) 13.5678 0.666820
\(415\) 22.5034 1.10465
\(416\) −5.39146 −0.264338
\(417\) 0.396455 0.0194145
\(418\) 3.79773 0.185753
\(419\) 34.8756 1.70379 0.851893 0.523716i \(-0.175455\pi\)
0.851893 + 0.523716i \(0.175455\pi\)
\(420\) −7.21283 −0.351950
\(421\) −19.5846 −0.954494 −0.477247 0.878769i \(-0.658365\pi\)
−0.477247 + 0.878769i \(0.658365\pi\)
\(422\) −2.33877 −0.113850
\(423\) −1.85951 −0.0904126
\(424\) 66.0747 3.20887
\(425\) −3.88755 −0.188574
\(426\) −2.72240 −0.131901
\(427\) −18.4469 −0.892706
\(428\) −9.37615 −0.453214
\(429\) −4.07386 −0.196688
\(430\) 18.6633 0.900024
\(431\) 38.4490 1.85202 0.926012 0.377493i \(-0.123214\pi\)
0.926012 + 0.377493i \(0.123214\pi\)
\(432\) 4.23710 0.203857
\(433\) 12.4697 0.599253 0.299627 0.954057i \(-0.403138\pi\)
0.299627 + 0.954057i \(0.403138\pi\)
\(434\) 87.8676 4.21778
\(435\) −3.99077 −0.191343
\(436\) 38.5319 1.84535
\(437\) 0.730962 0.0349666
\(438\) −0.370806 −0.0177178
\(439\) −20.4231 −0.974741 −0.487371 0.873195i \(-0.662044\pi\)
−0.487371 + 0.873195i \(0.662044\pi\)
\(440\) −47.5395 −2.26636
\(441\) −45.1399 −2.14952
\(442\) 97.1946 4.62307
\(443\) 32.8537 1.56093 0.780463 0.625202i \(-0.214984\pi\)
0.780463 + 0.625202i \(0.214984\pi\)
\(444\) 3.77486 0.179147
\(445\) 24.4998 1.16140
\(446\) −58.3027 −2.76071
\(447\) −0.418711 −0.0198043
\(448\) −32.8502 −1.55203
\(449\) 17.9950 0.849238 0.424619 0.905372i \(-0.360408\pi\)
0.424619 + 0.905372i \(0.360408\pi\)
\(450\) −4.79227 −0.225910
\(451\) −4.41011 −0.207664
\(452\) −42.4142 −1.99500
\(453\) 1.20653 0.0566878
\(454\) 0.256934 0.0120585
\(455\) −74.1477 −3.47610
\(456\) 0.320180 0.0149938
\(457\) 37.3590 1.74758 0.873791 0.486302i \(-0.161655\pi\)
0.873791 + 0.486302i \(0.161655\pi\)
\(458\) 39.1803 1.83078
\(459\) −5.61376 −0.262028
\(460\) −17.9445 −0.836665
\(461\) 9.41308 0.438411 0.219205 0.975679i \(-0.429654\pi\)
0.219205 + 0.975679i \(0.429654\pi\)
\(462\) 7.14263 0.332305
\(463\) −29.5125 −1.37156 −0.685781 0.727808i \(-0.740539\pi\)
−0.685781 + 0.727808i \(0.740539\pi\)
\(464\) 47.7582 2.21712
\(465\) −2.84038 −0.131720
\(466\) 68.3545 3.16646
\(467\) 15.7255 0.727690 0.363845 0.931460i \(-0.381464\pi\)
0.363845 + 0.931460i \(0.381464\pi\)
\(468\) 80.4072 3.71682
\(469\) 0.955634 0.0441271
\(470\) 3.66465 0.169038
\(471\) 0.709380 0.0326865
\(472\) −0.726886 −0.0334576
\(473\) −12.4031 −0.570294
\(474\) 3.15642 0.144979
\(475\) −0.258182 −0.0118462
\(476\) −114.362 −5.24178
\(477\) −38.3089 −1.75404
\(478\) 7.27297 0.332658
\(479\) −19.5493 −0.893232 −0.446616 0.894726i \(-0.647371\pi\)
−0.446616 + 0.894726i \(0.647371\pi\)
\(480\) −0.305567 −0.0139472
\(481\) 38.8055 1.76938
\(482\) −28.0882 −1.27938
\(483\) 1.37477 0.0625541
\(484\) 17.0686 0.775844
\(485\) −29.1192 −1.32223
\(486\) −10.3947 −0.471515
\(487\) −16.1545 −0.732030 −0.366015 0.930609i \(-0.619278\pi\)
−0.366015 + 0.930609i \(0.619278\pi\)
\(488\) −20.1024 −0.909992
\(489\) −2.57773 −0.116569
\(490\) 88.9598 4.01880
\(491\) 28.8831 1.30348 0.651738 0.758444i \(-0.274040\pi\)
0.651738 + 0.758444i \(0.274040\pi\)
\(492\) −0.729164 −0.0328733
\(493\) −63.2752 −2.84977
\(494\) 6.45494 0.290422
\(495\) 27.5625 1.23884
\(496\) 33.9913 1.52625
\(497\) 32.9294 1.47709
\(498\) −3.68449 −0.165106
\(499\) −1.88279 −0.0842854 −0.0421427 0.999112i \(-0.513418\pi\)
−0.0421427 + 0.999112i \(0.513418\pi\)
\(500\) −42.1766 −1.88619
\(501\) 3.44872 0.154078
\(502\) −39.6316 −1.76884
\(503\) 19.1927 0.855760 0.427880 0.903836i \(-0.359261\pi\)
0.427880 + 0.903836i \(0.359261\pi\)
\(504\) −71.8855 −3.20204
\(505\) 35.2623 1.56915
\(506\) 17.7698 0.789965
\(507\) −4.87201 −0.216373
\(508\) −14.1873 −0.629461
\(509\) 25.9305 1.14935 0.574674 0.818383i \(-0.305129\pi\)
0.574674 + 0.818383i \(0.305129\pi\)
\(510\) 5.50861 0.243925
\(511\) 4.48517 0.198412
\(512\) −42.4427 −1.87572
\(513\) −0.372824 −0.0164606
\(514\) −44.8859 −1.97983
\(515\) −7.85329 −0.346057
\(516\) −2.05071 −0.0902777
\(517\) −2.43542 −0.107110
\(518\) −68.0371 −2.98938
\(519\) 0.463808 0.0203589
\(520\) −80.8022 −3.54341
\(521\) 21.8092 0.955478 0.477739 0.878502i \(-0.341456\pi\)
0.477739 + 0.878502i \(0.341456\pi\)
\(522\) −78.0006 −3.41399
\(523\) 27.0965 1.18485 0.592423 0.805627i \(-0.298172\pi\)
0.592423 + 0.805627i \(0.298172\pi\)
\(524\) −2.51279 −0.109772
\(525\) −0.485580 −0.0211925
\(526\) 22.4882 0.980531
\(527\) −45.0353 −1.96177
\(528\) 2.76311 0.120249
\(529\) −19.5798 −0.851295
\(530\) 75.4975 3.27940
\(531\) 0.421435 0.0182887
\(532\) −7.59508 −0.329288
\(533\) −7.49579 −0.324679
\(534\) −4.01135 −0.173588
\(535\) −5.46282 −0.236178
\(536\) 1.04140 0.0449816
\(537\) −0.216868 −0.00935852
\(538\) −34.6658 −1.49455
\(539\) −59.1200 −2.54648
\(540\) 9.15251 0.393861
\(541\) 17.7634 0.763707 0.381854 0.924223i \(-0.375286\pi\)
0.381854 + 0.924223i \(0.375286\pi\)
\(542\) −17.6019 −0.756068
\(543\) 1.94732 0.0835676
\(544\) −4.84487 −0.207722
\(545\) 22.4498 0.961646
\(546\) 12.1402 0.519554
\(547\) −30.2921 −1.29520 −0.647599 0.761982i \(-0.724227\pi\)
−0.647599 + 0.761982i \(0.724227\pi\)
\(548\) 13.6160 0.581646
\(549\) 11.6550 0.497422
\(550\) −6.27646 −0.267629
\(551\) −4.20227 −0.179023
\(552\) 1.49815 0.0637653
\(553\) −38.1792 −1.62354
\(554\) −11.4592 −0.486854
\(555\) 2.19935 0.0933571
\(556\) −10.2484 −0.434629
\(557\) 5.30744 0.224883 0.112442 0.993658i \(-0.464133\pi\)
0.112442 + 0.993658i \(0.464133\pi\)
\(558\) −55.5160 −2.35018
\(559\) −21.0813 −0.891644
\(560\) 50.2908 2.12518
\(561\) −3.66086 −0.154562
\(562\) −60.2540 −2.54166
\(563\) 0.877218 0.0369703 0.0184852 0.999829i \(-0.494116\pi\)
0.0184852 + 0.999829i \(0.494116\pi\)
\(564\) −0.402670 −0.0169555
\(565\) −24.7118 −1.03963
\(566\) −13.5964 −0.571498
\(567\) 41.3258 1.73552
\(568\) 35.8847 1.50569
\(569\) 5.25733 0.220399 0.110199 0.993910i \(-0.464851\pi\)
0.110199 + 0.993910i \(0.464851\pi\)
\(570\) 0.365841 0.0153234
\(571\) −35.4142 −1.48204 −0.741018 0.671485i \(-0.765657\pi\)
−0.741018 + 0.671485i \(0.765657\pi\)
\(572\) 105.310 4.40323
\(573\) 2.12795 0.0888963
\(574\) 13.1422 0.548547
\(575\) −1.20805 −0.0503793
\(576\) 20.7552 0.864802
\(577\) −7.68971 −0.320127 −0.160063 0.987107i \(-0.551170\pi\)
−0.160063 + 0.987107i \(0.551170\pi\)
\(578\) 45.4199 1.88922
\(579\) −1.99245 −0.0828036
\(580\) 103.162 4.28356
\(581\) 44.5666 1.84893
\(582\) 4.76769 0.197627
\(583\) −50.1734 −2.07797
\(584\) 4.88770 0.202254
\(585\) 46.8476 1.93691
\(586\) −2.28178 −0.0942595
\(587\) −15.4388 −0.637226 −0.318613 0.947885i \(-0.603217\pi\)
−0.318613 + 0.947885i \(0.603217\pi\)
\(588\) −9.77487 −0.403109
\(589\) −2.99091 −0.123238
\(590\) −0.830546 −0.0341930
\(591\) −0.844075 −0.0347206
\(592\) −26.3199 −1.08174
\(593\) −23.4716 −0.963865 −0.481932 0.876208i \(-0.660065\pi\)
−0.481932 + 0.876208i \(0.660065\pi\)
\(594\) −9.06344 −0.371877
\(595\) −66.6307 −2.73159
\(596\) 10.8237 0.443357
\(597\) 4.32696 0.177091
\(598\) 30.2031 1.23510
\(599\) −4.63449 −0.189360 −0.0946801 0.995508i \(-0.530183\pi\)
−0.0946801 + 0.995508i \(0.530183\pi\)
\(600\) −0.529159 −0.0216028
\(601\) 17.8220 0.726973 0.363486 0.931600i \(-0.381586\pi\)
0.363486 + 0.931600i \(0.381586\pi\)
\(602\) 36.9615 1.50644
\(603\) −0.603783 −0.0245880
\(604\) −31.1890 −1.26906
\(605\) 9.94465 0.404308
\(606\) −5.77351 −0.234533
\(607\) 46.4186 1.88407 0.942036 0.335511i \(-0.108909\pi\)
0.942036 + 0.335511i \(0.108909\pi\)
\(608\) −0.321761 −0.0130491
\(609\) −7.90348 −0.320265
\(610\) −22.9691 −0.929993
\(611\) −4.13944 −0.167464
\(612\) 72.2555 2.92076
\(613\) 7.84940 0.317034 0.158517 0.987356i \(-0.449329\pi\)
0.158517 + 0.987356i \(0.449329\pi\)
\(614\) −67.6434 −2.72987
\(615\) −0.424832 −0.0171309
\(616\) −94.1490 −3.79337
\(617\) −26.4714 −1.06570 −0.532849 0.846211i \(-0.678879\pi\)
−0.532849 + 0.846211i \(0.678879\pi\)
\(618\) 1.28582 0.0517233
\(619\) 1.00000 0.0401934
\(620\) 73.4242 2.94879
\(621\) −1.74447 −0.0700032
\(622\) −54.4870 −2.18473
\(623\) 48.5203 1.94392
\(624\) 4.69641 0.188007
\(625\) −27.8394 −1.11358
\(626\) −29.7048 −1.18724
\(627\) −0.243127 −0.00970956
\(628\) −18.3375 −0.731748
\(629\) 34.8714 1.39042
\(630\) −82.1371 −3.27242
\(631\) −25.2324 −1.00448 −0.502242 0.864727i \(-0.667491\pi\)
−0.502242 + 0.864727i \(0.667491\pi\)
\(632\) −41.6056 −1.65498
\(633\) 0.149726 0.00595107
\(634\) 18.8846 0.750004
\(635\) −8.26595 −0.328024
\(636\) −8.29564 −0.328943
\(637\) −100.485 −3.98138
\(638\) −102.158 −4.04447
\(639\) −20.8053 −0.823043
\(640\) −44.7747 −1.76988
\(641\) 24.4105 0.964159 0.482079 0.876128i \(-0.339882\pi\)
0.482079 + 0.876128i \(0.339882\pi\)
\(642\) 0.894430 0.0353003
\(643\) −5.52050 −0.217707 −0.108854 0.994058i \(-0.534718\pi\)
−0.108854 + 0.994058i \(0.534718\pi\)
\(644\) −35.5379 −1.40039
\(645\) −1.19481 −0.0470455
\(646\) 5.80054 0.228219
\(647\) 39.5404 1.55449 0.777247 0.629195i \(-0.216615\pi\)
0.777247 + 0.629195i \(0.216615\pi\)
\(648\) 45.0346 1.76913
\(649\) 0.551956 0.0216662
\(650\) −10.6680 −0.418434
\(651\) −5.62520 −0.220469
\(652\) 66.6347 2.60962
\(653\) 26.1438 1.02308 0.511542 0.859258i \(-0.329074\pi\)
0.511542 + 0.859258i \(0.329074\pi\)
\(654\) −3.67572 −0.143732
\(655\) −1.46402 −0.0572042
\(656\) 5.08403 0.198498
\(657\) −2.83380 −0.110557
\(658\) 7.25761 0.282931
\(659\) 9.69906 0.377822 0.188911 0.981994i \(-0.439504\pi\)
0.188911 + 0.981994i \(0.439504\pi\)
\(660\) 5.96855 0.232326
\(661\) −3.26550 −0.127013 −0.0635067 0.997981i \(-0.520228\pi\)
−0.0635067 + 0.997981i \(0.520228\pi\)
\(662\) 41.7493 1.62263
\(663\) −6.22231 −0.241654
\(664\) 48.5662 1.88473
\(665\) −4.42512 −0.171599
\(666\) 42.9868 1.66570
\(667\) −19.6627 −0.761342
\(668\) −89.1499 −3.44931
\(669\) 3.73249 0.144306
\(670\) 1.18991 0.0459703
\(671\) 15.2646 0.589284
\(672\) −0.605156 −0.0233444
\(673\) −22.2964 −0.859462 −0.429731 0.902957i \(-0.641392\pi\)
−0.429731 + 0.902957i \(0.641392\pi\)
\(674\) 23.0771 0.888895
\(675\) 0.616163 0.0237161
\(676\) 125.942 4.84392
\(677\) 5.74561 0.220822 0.110411 0.993886i \(-0.464783\pi\)
0.110411 + 0.993886i \(0.464783\pi\)
\(678\) 4.04606 0.155388
\(679\) −57.6687 −2.21312
\(680\) −72.6105 −2.78448
\(681\) −0.0164487 −0.000630315 0
\(682\) −72.7097 −2.78420
\(683\) 3.03267 0.116042 0.0580210 0.998315i \(-0.481521\pi\)
0.0580210 + 0.998315i \(0.481521\pi\)
\(684\) 4.79868 0.183482
\(685\) 7.93307 0.303107
\(686\) 94.8981 3.62323
\(687\) −2.50829 −0.0956972
\(688\) 14.2984 0.545123
\(689\) −85.2790 −3.24887
\(690\) 1.71179 0.0651669
\(691\) −12.7010 −0.483168 −0.241584 0.970380i \(-0.577667\pi\)
−0.241584 + 0.970380i \(0.577667\pi\)
\(692\) −11.9895 −0.455772
\(693\) 54.5858 2.07354
\(694\) −87.7705 −3.33172
\(695\) −5.97102 −0.226494
\(696\) −8.61277 −0.326466
\(697\) −6.73587 −0.255139
\(698\) −29.2037 −1.10538
\(699\) −4.37599 −0.165515
\(700\) 12.5523 0.474432
\(701\) 9.73745 0.367778 0.183889 0.982947i \(-0.441131\pi\)
0.183889 + 0.982947i \(0.441131\pi\)
\(702\) −15.4050 −0.581424
\(703\) 2.31590 0.0873459
\(704\) 27.1833 1.02451
\(705\) −0.234608 −0.00883583
\(706\) −8.91302 −0.335446
\(707\) 69.8349 2.62641
\(708\) 0.0912601 0.00342976
\(709\) −36.5973 −1.37444 −0.687220 0.726449i \(-0.741169\pi\)
−0.687220 + 0.726449i \(0.741169\pi\)
\(710\) 41.0021 1.53878
\(711\) 24.1221 0.904650
\(712\) 52.8747 1.98156
\(713\) −13.9947 −0.524105
\(714\) 10.9095 0.408276
\(715\) 61.3566 2.29461
\(716\) 5.60605 0.209508
\(717\) −0.465609 −0.0173885
\(718\) 47.4881 1.77224
\(719\) 8.17131 0.304739 0.152369 0.988324i \(-0.451310\pi\)
0.152369 + 0.988324i \(0.451310\pi\)
\(720\) −31.7745 −1.18416
\(721\) −15.5530 −0.579222
\(722\) −46.4678 −1.72935
\(723\) 1.79818 0.0668750
\(724\) −50.3385 −1.87082
\(725\) 6.94504 0.257932
\(726\) −1.62824 −0.0604297
\(727\) 1.52574 0.0565864 0.0282932 0.999600i \(-0.490993\pi\)
0.0282932 + 0.999600i \(0.490993\pi\)
\(728\) −160.024 −5.93087
\(729\) −25.6635 −0.950500
\(730\) 5.58473 0.206700
\(731\) −18.9441 −0.700673
\(732\) 2.52384 0.0932838
\(733\) −38.8518 −1.43503 −0.717513 0.696545i \(-0.754719\pi\)
−0.717513 + 0.696545i \(0.754719\pi\)
\(734\) 71.6869 2.64601
\(735\) −5.69513 −0.210068
\(736\) −1.50554 −0.0554949
\(737\) −0.790779 −0.0291287
\(738\) −8.30345 −0.305654
\(739\) 44.8177 1.64865 0.824323 0.566120i \(-0.191556\pi\)
0.824323 + 0.566120i \(0.191556\pi\)
\(740\) −56.8534 −2.08997
\(741\) −0.413239 −0.0151807
\(742\) 149.518 5.48899
\(743\) −0.348330 −0.0127790 −0.00638950 0.999980i \(-0.502034\pi\)
−0.00638950 + 0.999980i \(0.502034\pi\)
\(744\) −6.13004 −0.224738
\(745\) 6.30622 0.231042
\(746\) 27.3528 1.00146
\(747\) −28.1578 −1.03024
\(748\) 94.6336 3.46015
\(749\) −10.8188 −0.395310
\(750\) 4.02339 0.146914
\(751\) 6.42985 0.234628 0.117314 0.993095i \(-0.462572\pi\)
0.117314 + 0.993095i \(0.462572\pi\)
\(752\) 2.80758 0.102382
\(753\) 2.53718 0.0924599
\(754\) −173.636 −6.32346
\(755\) −18.1716 −0.661333
\(756\) 18.1260 0.659235
\(757\) −33.2343 −1.20792 −0.603960 0.797014i \(-0.706411\pi\)
−0.603960 + 0.797014i \(0.706411\pi\)
\(758\) 70.3617 2.55565
\(759\) −1.13761 −0.0412925
\(760\) −4.82225 −0.174921
\(761\) −1.37647 −0.0498969 −0.0249484 0.999689i \(-0.507942\pi\)
−0.0249484 + 0.999689i \(0.507942\pi\)
\(762\) 1.35339 0.0490280
\(763\) 44.4605 1.60958
\(764\) −55.0077 −1.99011
\(765\) 42.0982 1.52206
\(766\) −55.6357 −2.01020
\(767\) 0.938152 0.0338747
\(768\) 5.12829 0.185051
\(769\) −4.55292 −0.164183 −0.0820913 0.996625i \(-0.526160\pi\)
−0.0820913 + 0.996625i \(0.526160\pi\)
\(770\) −107.575 −3.87675
\(771\) 2.87355 0.103488
\(772\) 51.5052 1.85371
\(773\) −24.0249 −0.864116 −0.432058 0.901846i \(-0.642212\pi\)
−0.432058 + 0.901846i \(0.642212\pi\)
\(774\) −23.3528 −0.839399
\(775\) 4.94305 0.177559
\(776\) −62.8442 −2.25598
\(777\) 4.35567 0.156259
\(778\) −17.7912 −0.637845
\(779\) −0.447347 −0.0160279
\(780\) 10.1447 0.363237
\(781\) −27.2488 −0.975038
\(782\) 27.1411 0.970565
\(783\) 10.0289 0.358403
\(784\) 68.1544 2.43409
\(785\) −10.6840 −0.381328
\(786\) 0.239705 0.00855000
\(787\) −8.01053 −0.285545 −0.142772 0.989756i \(-0.545602\pi\)
−0.142772 + 0.989756i \(0.545602\pi\)
\(788\) 21.8194 0.777285
\(789\) −1.43967 −0.0512537
\(790\) −47.5389 −1.69136
\(791\) −48.9401 −1.74011
\(792\) 59.4846 2.11369
\(793\) 25.9450 0.921335
\(794\) 68.2898 2.42351
\(795\) −4.83328 −0.171419
\(796\) −111.852 −3.96450
\(797\) 17.7909 0.630185 0.315093 0.949061i \(-0.397964\pi\)
0.315093 + 0.949061i \(0.397964\pi\)
\(798\) 0.724525 0.0256479
\(799\) −3.71979 −0.131597
\(800\) 0.531770 0.0188009
\(801\) −30.6558 −1.08317
\(802\) 48.7387 1.72102
\(803\) −3.71144 −0.130974
\(804\) −0.130747 −0.00461109
\(805\) −20.7054 −0.729770
\(806\) −123.584 −4.35305
\(807\) 2.21927 0.0781220
\(808\) 76.1022 2.67727
\(809\) 16.4208 0.577325 0.288663 0.957431i \(-0.406789\pi\)
0.288663 + 0.957431i \(0.406789\pi\)
\(810\) 51.4570 1.80801
\(811\) −41.4014 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(812\) 204.306 7.16972
\(813\) 1.12686 0.0395207
\(814\) 56.3001 1.97332
\(815\) 38.8234 1.35992
\(816\) 4.22029 0.147740
\(817\) −1.25813 −0.0440163
\(818\) −8.36401 −0.292441
\(819\) 92.7787 3.24195
\(820\) 10.9820 0.383507
\(821\) 3.47859 0.121404 0.0607018 0.998156i \(-0.480666\pi\)
0.0607018 + 0.998156i \(0.480666\pi\)
\(822\) −1.29888 −0.0453038
\(823\) −32.2803 −1.12522 −0.562610 0.826723i \(-0.690203\pi\)
−0.562610 + 0.826723i \(0.690203\pi\)
\(824\) −16.9488 −0.590438
\(825\) 0.401813 0.0139893
\(826\) −1.64485 −0.0572315
\(827\) −32.1878 −1.11928 −0.559641 0.828735i \(-0.689061\pi\)
−0.559641 + 0.828735i \(0.689061\pi\)
\(828\) 22.4533 0.780307
\(829\) 25.5266 0.886576 0.443288 0.896379i \(-0.353812\pi\)
0.443288 + 0.896379i \(0.353812\pi\)
\(830\) 55.4922 1.92616
\(831\) 0.733607 0.0254485
\(832\) 46.2030 1.60180
\(833\) −90.2983 −3.12865
\(834\) 0.977637 0.0338528
\(835\) −51.9413 −1.79750
\(836\) 6.28486 0.217366
\(837\) 7.13794 0.246723
\(838\) 86.0014 2.97087
\(839\) 22.3785 0.772592 0.386296 0.922375i \(-0.373754\pi\)
0.386296 + 0.922375i \(0.373754\pi\)
\(840\) −9.06952 −0.312928
\(841\) 84.0399 2.89793
\(842\) −48.2945 −1.66434
\(843\) 3.85740 0.132856
\(844\) −3.87043 −0.133226
\(845\) 73.3775 2.52426
\(846\) −4.58546 −0.157651
\(847\) 19.6948 0.676720
\(848\) 57.8406 1.98626
\(849\) 0.870426 0.0298729
\(850\) −9.58649 −0.328814
\(851\) 10.8363 0.371462
\(852\) −4.50529 −0.154349
\(853\) 1.03212 0.0353391 0.0176696 0.999844i \(-0.494375\pi\)
0.0176696 + 0.999844i \(0.494375\pi\)
\(854\) −45.4890 −1.55660
\(855\) 2.79585 0.0956161
\(856\) −11.7897 −0.402964
\(857\) 10.9674 0.374639 0.187320 0.982299i \(-0.440020\pi\)
0.187320 + 0.982299i \(0.440020\pi\)
\(858\) −10.0459 −0.342963
\(859\) 2.06472 0.0704474 0.0352237 0.999379i \(-0.488786\pi\)
0.0352237 + 0.999379i \(0.488786\pi\)
\(860\) 30.8859 1.05320
\(861\) −0.841354 −0.0286733
\(862\) 94.8133 3.22935
\(863\) 33.9733 1.15647 0.578233 0.815872i \(-0.303742\pi\)
0.578233 + 0.815872i \(0.303742\pi\)
\(864\) 0.767895 0.0261243
\(865\) −6.98542 −0.237512
\(866\) 30.7495 1.04491
\(867\) −2.90774 −0.0987521
\(868\) 145.412 4.93561
\(869\) 31.5929 1.07172
\(870\) −9.84103 −0.333642
\(871\) −1.34408 −0.0455423
\(872\) 48.4506 1.64075
\(873\) 36.4359 1.23317
\(874\) 1.80251 0.0609709
\(875\) −48.6659 −1.64521
\(876\) −0.613647 −0.0207332
\(877\) 13.8165 0.466549 0.233274 0.972411i \(-0.425056\pi\)
0.233274 + 0.972411i \(0.425056\pi\)
\(878\) −50.3623 −1.69964
\(879\) 0.146077 0.00492707
\(880\) −41.6152 −1.40285
\(881\) −28.9080 −0.973937 −0.486968 0.873420i \(-0.661897\pi\)
−0.486968 + 0.873420i \(0.661897\pi\)
\(882\) −111.313 −3.74809
\(883\) −27.2983 −0.918662 −0.459331 0.888265i \(-0.651911\pi\)
−0.459331 + 0.888265i \(0.651911\pi\)
\(884\) 160.847 5.40988
\(885\) 0.0531708 0.00178732
\(886\) 81.0154 2.72177
\(887\) 7.67238 0.257613 0.128807 0.991670i \(-0.458885\pi\)
0.128807 + 0.991670i \(0.458885\pi\)
\(888\) 4.74657 0.159284
\(889\) −16.3702 −0.549039
\(890\) 60.4152 2.02512
\(891\) −34.1968 −1.14563
\(892\) −96.4852 −3.23056
\(893\) −0.247041 −0.00826690
\(894\) −1.03252 −0.0345326
\(895\) 3.26625 0.109179
\(896\) −88.6736 −2.96238
\(897\) −1.93357 −0.0645602
\(898\) 44.3748 1.48081
\(899\) 80.4548 2.68332
\(900\) −7.93072 −0.264357
\(901\) −76.6335 −2.55303
\(902\) −10.8751 −0.362101
\(903\) −2.36624 −0.0787435
\(904\) −53.3323 −1.77380
\(905\) −29.3287 −0.974919
\(906\) 2.97525 0.0988459
\(907\) 12.5770 0.417612 0.208806 0.977957i \(-0.433042\pi\)
0.208806 + 0.977957i \(0.433042\pi\)
\(908\) 0.425200 0.0141108
\(909\) −44.1227 −1.46346
\(910\) −182.844 −6.06123
\(911\) −45.3692 −1.50315 −0.751574 0.659649i \(-0.770705\pi\)
−0.751574 + 0.659649i \(0.770705\pi\)
\(912\) 0.280280 0.00928101
\(913\) −36.8784 −1.22050
\(914\) 92.1254 3.04724
\(915\) 1.47046 0.0486120
\(916\) 64.8395 2.14236
\(917\) −2.89941 −0.0957470
\(918\) −13.8432 −0.456895
\(919\) −7.95324 −0.262353 −0.131177 0.991359i \(-0.541875\pi\)
−0.131177 + 0.991359i \(0.541875\pi\)
\(920\) −22.5636 −0.743901
\(921\) 4.33047 0.142694
\(922\) 23.2121 0.764451
\(923\) −46.3144 −1.52446
\(924\) 11.8203 0.388861
\(925\) −3.82747 −0.125846
\(926\) −72.7762 −2.39157
\(927\) 9.82657 0.322747
\(928\) 8.65528 0.284123
\(929\) 45.9188 1.50655 0.753273 0.657708i \(-0.228474\pi\)
0.753273 + 0.657708i \(0.228474\pi\)
\(930\) −7.00424 −0.229678
\(931\) −5.99694 −0.196542
\(932\) 113.120 3.70536
\(933\) 3.48821 0.114199
\(934\) 38.7783 1.26886
\(935\) 55.1363 1.80315
\(936\) 101.105 3.30473
\(937\) −22.0280 −0.719623 −0.359812 0.933025i \(-0.617159\pi\)
−0.359812 + 0.933025i \(0.617159\pi\)
\(938\) 2.35654 0.0769439
\(939\) 1.90167 0.0620588
\(940\) 6.06463 0.197806
\(941\) 25.0867 0.817804 0.408902 0.912578i \(-0.365912\pi\)
0.408902 + 0.912578i \(0.365912\pi\)
\(942\) 1.74929 0.0569950
\(943\) −2.09317 −0.0681628
\(944\) −0.636303 −0.0207099
\(945\) 10.5607 0.343540
\(946\) −30.5853 −0.994414
\(947\) −44.2883 −1.43918 −0.719588 0.694401i \(-0.755669\pi\)
−0.719588 + 0.694401i \(0.755669\pi\)
\(948\) 5.22355 0.169653
\(949\) −6.30828 −0.204776
\(950\) −0.636664 −0.0206561
\(951\) −1.20898 −0.0392037
\(952\) −143.801 −4.66060
\(953\) 5.30431 0.171824 0.0859118 0.996303i \(-0.472620\pi\)
0.0859118 + 0.996303i \(0.472620\pi\)
\(954\) −94.4677 −3.05850
\(955\) −32.0491 −1.03708
\(956\) 12.0360 0.389273
\(957\) 6.54006 0.211410
\(958\) −48.2076 −1.55752
\(959\) 15.7109 0.507333
\(960\) 2.61861 0.0845152
\(961\) 26.2627 0.847184
\(962\) 95.6924 3.08525
\(963\) 6.83546 0.220270
\(964\) −46.4832 −1.49712
\(965\) 30.0084 0.966006
\(966\) 3.39010 0.109075
\(967\) −4.04692 −0.130140 −0.0650701 0.997881i \(-0.520727\pi\)
−0.0650701 + 0.997881i \(0.520727\pi\)
\(968\) 21.4623 0.689824
\(969\) −0.371345 −0.0119293
\(970\) −71.8064 −2.30556
\(971\) 38.9428 1.24973 0.624867 0.780732i \(-0.285153\pi\)
0.624867 + 0.780732i \(0.285153\pi\)
\(972\) −17.2022 −0.551762
\(973\) −11.8252 −0.379100
\(974\) −39.8361 −1.27643
\(975\) 0.682956 0.0218721
\(976\) −17.5973 −0.563275
\(977\) 46.3245 1.48205 0.741026 0.671476i \(-0.234339\pi\)
0.741026 + 0.671476i \(0.234339\pi\)
\(978\) −6.35656 −0.203260
\(979\) −40.1501 −1.28320
\(980\) 147.220 4.70276
\(981\) −28.0908 −0.896870
\(982\) 71.2242 2.27285
\(983\) 1.07524 0.0342949 0.0171475 0.999853i \(-0.494542\pi\)
0.0171475 + 0.999853i \(0.494542\pi\)
\(984\) −0.916862 −0.0292285
\(985\) 12.7126 0.405058
\(986\) −156.033 −4.96911
\(987\) −0.464626 −0.0147892
\(988\) 10.6823 0.339849
\(989\) −5.88686 −0.187191
\(990\) 67.9677 2.16015
\(991\) 30.8827 0.981020 0.490510 0.871436i \(-0.336811\pi\)
0.490510 + 0.871436i \(0.336811\pi\)
\(992\) 6.16029 0.195589
\(993\) −2.67275 −0.0848171
\(994\) 81.2021 2.57558
\(995\) −65.1685 −2.06598
\(996\) −6.09746 −0.193205
\(997\) 40.1301 1.27093 0.635466 0.772129i \(-0.280808\pi\)
0.635466 + 0.772129i \(0.280808\pi\)
\(998\) −4.64287 −0.146967
\(999\) −5.52700 −0.174867
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.b.1.27 30
3.2 odd 2 5571.2.a.g.1.4 30
4.3 odd 2 9904.2.a.n.1.16 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
619.2.a.b.1.27 30 1.1 even 1 trivial
5571.2.a.g.1.4 30 3.2 odd 2
9904.2.a.n.1.16 30 4.3 odd 2