Properties

Label 4011.2.a.m.1.11
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $29$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.630217 q^{2} +1.00000 q^{3} -1.60283 q^{4} -2.79883 q^{5} -0.630217 q^{6} -1.00000 q^{7} +2.27056 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.630217 q^{2} +1.00000 q^{3} -1.60283 q^{4} -2.79883 q^{5} -0.630217 q^{6} -1.00000 q^{7} +2.27056 q^{8} +1.00000 q^{9} +1.76387 q^{10} +1.05357 q^{11} -1.60283 q^{12} -2.76000 q^{13} +0.630217 q^{14} -2.79883 q^{15} +1.77470 q^{16} -0.136595 q^{17} -0.630217 q^{18} -0.161750 q^{19} +4.48604 q^{20} -1.00000 q^{21} -0.663975 q^{22} -0.925481 q^{23} +2.27056 q^{24} +2.83346 q^{25} +1.73940 q^{26} +1.00000 q^{27} +1.60283 q^{28} -0.490039 q^{29} +1.76387 q^{30} +5.37505 q^{31} -5.65958 q^{32} +1.05357 q^{33} +0.0860842 q^{34} +2.79883 q^{35} -1.60283 q^{36} -7.86861 q^{37} +0.101937 q^{38} -2.76000 q^{39} -6.35493 q^{40} -10.3578 q^{41} +0.630217 q^{42} -8.97705 q^{43} -1.68868 q^{44} -2.79883 q^{45} +0.583254 q^{46} +3.64355 q^{47} +1.77470 q^{48} +1.00000 q^{49} -1.78570 q^{50} -0.136595 q^{51} +4.42381 q^{52} -9.32669 q^{53} -0.630217 q^{54} -2.94875 q^{55} -2.27056 q^{56} -0.161750 q^{57} +0.308831 q^{58} -2.93568 q^{59} +4.48604 q^{60} +12.4971 q^{61} -3.38745 q^{62} -1.00000 q^{63} +0.0173536 q^{64} +7.72479 q^{65} -0.663975 q^{66} -11.3408 q^{67} +0.218937 q^{68} -0.925481 q^{69} -1.76387 q^{70} +5.60512 q^{71} +2.27056 q^{72} +11.1905 q^{73} +4.95894 q^{74} +2.83346 q^{75} +0.259257 q^{76} -1.05357 q^{77} +1.73940 q^{78} +10.3167 q^{79} -4.96710 q^{80} +1.00000 q^{81} +6.52765 q^{82} +11.9571 q^{83} +1.60283 q^{84} +0.382305 q^{85} +5.65749 q^{86} -0.490039 q^{87} +2.39219 q^{88} +1.58305 q^{89} +1.76387 q^{90} +2.76000 q^{91} +1.48338 q^{92} +5.37505 q^{93} -2.29623 q^{94} +0.452710 q^{95} -5.65958 q^{96} -12.4149 q^{97} -0.630217 q^{98} +1.05357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.630217 −0.445631 −0.222815 0.974861i \(-0.571525\pi\)
−0.222815 + 0.974861i \(0.571525\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.60283 −0.801413
\(5\) −2.79883 −1.25168 −0.625838 0.779953i \(-0.715243\pi\)
−0.625838 + 0.779953i \(0.715243\pi\)
\(6\) −0.630217 −0.257285
\(7\) −1.00000 −0.377964
\(8\) 2.27056 0.802765
\(9\) 1.00000 0.333333
\(10\) 1.76387 0.557785
\(11\) 1.05357 0.317662 0.158831 0.987306i \(-0.449227\pi\)
0.158831 + 0.987306i \(0.449227\pi\)
\(12\) −1.60283 −0.462696
\(13\) −2.76000 −0.765487 −0.382744 0.923855i \(-0.625021\pi\)
−0.382744 + 0.923855i \(0.625021\pi\)
\(14\) 0.630217 0.168433
\(15\) −2.79883 −0.722655
\(16\) 1.77470 0.443676
\(17\) −0.136595 −0.0331290 −0.0165645 0.999863i \(-0.505273\pi\)
−0.0165645 + 0.999863i \(0.505273\pi\)
\(18\) −0.630217 −0.148544
\(19\) −0.161750 −0.0371079 −0.0185540 0.999828i \(-0.505906\pi\)
−0.0185540 + 0.999828i \(0.505906\pi\)
\(20\) 4.48604 1.00311
\(21\) −1.00000 −0.218218
\(22\) −0.663975 −0.141560
\(23\) −0.925481 −0.192976 −0.0964880 0.995334i \(-0.530761\pi\)
−0.0964880 + 0.995334i \(0.530761\pi\)
\(24\) 2.27056 0.463477
\(25\) 2.83346 0.566693
\(26\) 1.73940 0.341125
\(27\) 1.00000 0.192450
\(28\) 1.60283 0.302906
\(29\) −0.490039 −0.0909980 −0.0454990 0.998964i \(-0.514488\pi\)
−0.0454990 + 0.998964i \(0.514488\pi\)
\(30\) 1.76387 0.322038
\(31\) 5.37505 0.965387 0.482694 0.875789i \(-0.339658\pi\)
0.482694 + 0.875789i \(0.339658\pi\)
\(32\) −5.65958 −1.00048
\(33\) 1.05357 0.183402
\(34\) 0.0860842 0.0147633
\(35\) 2.79883 0.473089
\(36\) −1.60283 −0.267138
\(37\) −7.86861 −1.29359 −0.646796 0.762663i \(-0.723892\pi\)
−0.646796 + 0.762663i \(0.723892\pi\)
\(38\) 0.101937 0.0165364
\(39\) −2.76000 −0.441954
\(40\) −6.35493 −1.00480
\(41\) −10.3578 −1.61761 −0.808807 0.588074i \(-0.799886\pi\)
−0.808807 + 0.588074i \(0.799886\pi\)
\(42\) 0.630217 0.0972446
\(43\) −8.97705 −1.36899 −0.684493 0.729019i \(-0.739977\pi\)
−0.684493 + 0.729019i \(0.739977\pi\)
\(44\) −1.68868 −0.254579
\(45\) −2.79883 −0.417225
\(46\) 0.583254 0.0859961
\(47\) 3.64355 0.531466 0.265733 0.964047i \(-0.414386\pi\)
0.265733 + 0.964047i \(0.414386\pi\)
\(48\) 1.77470 0.256157
\(49\) 1.00000 0.142857
\(50\) −1.78570 −0.252536
\(51\) −0.136595 −0.0191271
\(52\) 4.42381 0.613472
\(53\) −9.32669 −1.28112 −0.640560 0.767908i \(-0.721298\pi\)
−0.640560 + 0.767908i \(0.721298\pi\)
\(54\) −0.630217 −0.0857617
\(55\) −2.94875 −0.397610
\(56\) −2.27056 −0.303417
\(57\) −0.161750 −0.0214243
\(58\) 0.308831 0.0405515
\(59\) −2.93568 −0.382193 −0.191096 0.981571i \(-0.561204\pi\)
−0.191096 + 0.981571i \(0.561204\pi\)
\(60\) 4.48604 0.579146
\(61\) 12.4971 1.60008 0.800042 0.599944i \(-0.204810\pi\)
0.800042 + 0.599944i \(0.204810\pi\)
\(62\) −3.38745 −0.430206
\(63\) −1.00000 −0.125988
\(64\) 0.0173536 0.00216920
\(65\) 7.72479 0.958142
\(66\) −0.663975 −0.0817297
\(67\) −11.3408 −1.38550 −0.692752 0.721176i \(-0.743602\pi\)
−0.692752 + 0.721176i \(0.743602\pi\)
\(68\) 0.218937 0.0265500
\(69\) −0.925481 −0.111415
\(70\) −1.76387 −0.210823
\(71\) 5.60512 0.665205 0.332603 0.943067i \(-0.392073\pi\)
0.332603 + 0.943067i \(0.392073\pi\)
\(72\) 2.27056 0.267588
\(73\) 11.1905 1.30975 0.654873 0.755739i \(-0.272722\pi\)
0.654873 + 0.755739i \(0.272722\pi\)
\(74\) 4.95894 0.576465
\(75\) 2.83346 0.327180
\(76\) 0.259257 0.0297388
\(77\) −1.05357 −0.120065
\(78\) 1.73940 0.196948
\(79\) 10.3167 1.16072 0.580359 0.814361i \(-0.302912\pi\)
0.580359 + 0.814361i \(0.302912\pi\)
\(80\) −4.96710 −0.555339
\(81\) 1.00000 0.111111
\(82\) 6.52765 0.720859
\(83\) 11.9571 1.31247 0.656233 0.754558i \(-0.272149\pi\)
0.656233 + 0.754558i \(0.272149\pi\)
\(84\) 1.60283 0.174883
\(85\) 0.382305 0.0414668
\(86\) 5.65749 0.610063
\(87\) −0.490039 −0.0525377
\(88\) 2.39219 0.255008
\(89\) 1.58305 0.167803 0.0839017 0.996474i \(-0.473262\pi\)
0.0839017 + 0.996474i \(0.473262\pi\)
\(90\) 1.76387 0.185928
\(91\) 2.76000 0.289327
\(92\) 1.48338 0.154654
\(93\) 5.37505 0.557367
\(94\) −2.29623 −0.236838
\(95\) 0.452710 0.0464471
\(96\) −5.65958 −0.577628
\(97\) −12.4149 −1.26055 −0.630273 0.776373i \(-0.717057\pi\)
−0.630273 + 0.776373i \(0.717057\pi\)
\(98\) −0.630217 −0.0636616
\(99\) 1.05357 0.105887
\(100\) −4.54155 −0.454155
\(101\) 4.96651 0.494187 0.247093 0.968992i \(-0.420525\pi\)
0.247093 + 0.968992i \(0.420525\pi\)
\(102\) 0.0860842 0.00852361
\(103\) −6.79070 −0.669107 −0.334554 0.942377i \(-0.608586\pi\)
−0.334554 + 0.942377i \(0.608586\pi\)
\(104\) −6.26676 −0.614507
\(105\) 2.79883 0.273138
\(106\) 5.87784 0.570906
\(107\) 18.7427 1.81192 0.905961 0.423361i \(-0.139150\pi\)
0.905961 + 0.423361i \(0.139150\pi\)
\(108\) −1.60283 −0.154232
\(109\) 2.36857 0.226868 0.113434 0.993546i \(-0.463815\pi\)
0.113434 + 0.993546i \(0.463815\pi\)
\(110\) 1.85836 0.177187
\(111\) −7.86861 −0.746856
\(112\) −1.77470 −0.167694
\(113\) 10.3546 0.974082 0.487041 0.873379i \(-0.338076\pi\)
0.487041 + 0.873379i \(0.338076\pi\)
\(114\) 0.101937 0.00954731
\(115\) 2.59026 0.241543
\(116\) 0.785448 0.0729270
\(117\) −2.76000 −0.255162
\(118\) 1.85012 0.170317
\(119\) 0.136595 0.0125216
\(120\) −6.35493 −0.580123
\(121\) −9.89000 −0.899091
\(122\) −7.87586 −0.713047
\(123\) −10.3578 −0.933930
\(124\) −8.61527 −0.773674
\(125\) 6.06377 0.542360
\(126\) 0.630217 0.0561442
\(127\) 12.9282 1.14720 0.573598 0.819137i \(-0.305547\pi\)
0.573598 + 0.819137i \(0.305547\pi\)
\(128\) 11.3082 0.999514
\(129\) −8.97705 −0.790385
\(130\) −4.86829 −0.426978
\(131\) 15.4387 1.34888 0.674441 0.738329i \(-0.264385\pi\)
0.674441 + 0.738329i \(0.264385\pi\)
\(132\) −1.68868 −0.146981
\(133\) 0.161750 0.0140255
\(134\) 7.14719 0.617424
\(135\) −2.79883 −0.240885
\(136\) −0.310147 −0.0265948
\(137\) −13.0607 −1.11585 −0.557924 0.829892i \(-0.688402\pi\)
−0.557924 + 0.829892i \(0.688402\pi\)
\(138\) 0.583254 0.0496499
\(139\) −11.8431 −1.00452 −0.502261 0.864716i \(-0.667498\pi\)
−0.502261 + 0.864716i \(0.667498\pi\)
\(140\) −4.48604 −0.379140
\(141\) 3.64355 0.306842
\(142\) −3.53244 −0.296436
\(143\) −2.90785 −0.243166
\(144\) 1.77470 0.147892
\(145\) 1.37154 0.113900
\(146\) −7.05243 −0.583663
\(147\) 1.00000 0.0824786
\(148\) 12.6120 1.03670
\(149\) 20.8541 1.70844 0.854218 0.519915i \(-0.174036\pi\)
0.854218 + 0.519915i \(0.174036\pi\)
\(150\) −1.78570 −0.145802
\(151\) 19.0122 1.54719 0.773595 0.633680i \(-0.218456\pi\)
0.773595 + 0.633680i \(0.218456\pi\)
\(152\) −0.367263 −0.0297889
\(153\) −0.136595 −0.0110430
\(154\) 0.663975 0.0535047
\(155\) −15.0439 −1.20835
\(156\) 4.42381 0.354188
\(157\) −15.6456 −1.24865 −0.624326 0.781164i \(-0.714626\pi\)
−0.624326 + 0.781164i \(0.714626\pi\)
\(158\) −6.50176 −0.517252
\(159\) −9.32669 −0.739655
\(160\) 15.8402 1.25228
\(161\) 0.925481 0.0729381
\(162\) −0.630217 −0.0495145
\(163\) 12.5969 0.986669 0.493334 0.869840i \(-0.335778\pi\)
0.493334 + 0.869840i \(0.335778\pi\)
\(164\) 16.6017 1.29638
\(165\) −2.94875 −0.229560
\(166\) −7.53559 −0.584875
\(167\) −0.0346152 −0.00267860 −0.00133930 0.999999i \(-0.500426\pi\)
−0.00133930 + 0.999999i \(0.500426\pi\)
\(168\) −2.27056 −0.175178
\(169\) −5.38238 −0.414029
\(170\) −0.240935 −0.0184789
\(171\) −0.161750 −0.0123693
\(172\) 14.3886 1.09712
\(173\) −19.6553 −1.49436 −0.747181 0.664621i \(-0.768593\pi\)
−0.747181 + 0.664621i \(0.768593\pi\)
\(174\) 0.308831 0.0234124
\(175\) −2.83346 −0.214190
\(176\) 1.86977 0.140939
\(177\) −2.93568 −0.220659
\(178\) −0.997668 −0.0747783
\(179\) 14.4193 1.07775 0.538874 0.842387i \(-0.318850\pi\)
0.538874 + 0.842387i \(0.318850\pi\)
\(180\) 4.48604 0.334370
\(181\) 25.7574 1.91453 0.957266 0.289209i \(-0.0933923\pi\)
0.957266 + 0.289209i \(0.0933923\pi\)
\(182\) −1.73940 −0.128933
\(183\) 12.4971 0.923809
\(184\) −2.10136 −0.154914
\(185\) 22.0229 1.61916
\(186\) −3.38745 −0.248380
\(187\) −0.143911 −0.0105238
\(188\) −5.83997 −0.425924
\(189\) −1.00000 −0.0727393
\(190\) −0.285306 −0.0206983
\(191\) −1.00000 −0.0723575
\(192\) 0.0173536 0.00125239
\(193\) −22.2471 −1.60138 −0.800691 0.599078i \(-0.795534\pi\)
−0.800691 + 0.599078i \(0.795534\pi\)
\(194\) 7.82411 0.561738
\(195\) 7.72479 0.553184
\(196\) −1.60283 −0.114488
\(197\) 14.1243 1.00631 0.503156 0.864195i \(-0.332172\pi\)
0.503156 + 0.864195i \(0.332172\pi\)
\(198\) −0.663975 −0.0471867
\(199\) 2.88412 0.204450 0.102225 0.994761i \(-0.467404\pi\)
0.102225 + 0.994761i \(0.467404\pi\)
\(200\) 6.43356 0.454921
\(201\) −11.3408 −0.799921
\(202\) −3.12998 −0.220225
\(203\) 0.490039 0.0343940
\(204\) 0.218937 0.0153287
\(205\) 28.9897 2.02473
\(206\) 4.27961 0.298175
\(207\) −0.925481 −0.0643253
\(208\) −4.89819 −0.339628
\(209\) −0.170414 −0.0117878
\(210\) −1.76387 −0.121719
\(211\) 3.75758 0.258683 0.129341 0.991600i \(-0.458714\pi\)
0.129341 + 0.991600i \(0.458714\pi\)
\(212\) 14.9491 1.02671
\(213\) 5.60512 0.384056
\(214\) −11.8120 −0.807449
\(215\) 25.1253 1.71353
\(216\) 2.27056 0.154492
\(217\) −5.37505 −0.364882
\(218\) −1.49272 −0.101099
\(219\) 11.1905 0.756182
\(220\) 4.72634 0.318650
\(221\) 0.377001 0.0253599
\(222\) 4.95894 0.332822
\(223\) −14.4001 −0.964303 −0.482152 0.876088i \(-0.660145\pi\)
−0.482152 + 0.876088i \(0.660145\pi\)
\(224\) 5.65958 0.378146
\(225\) 2.83346 0.188898
\(226\) −6.52567 −0.434081
\(227\) 17.6252 1.16982 0.584912 0.811097i \(-0.301129\pi\)
0.584912 + 0.811097i \(0.301129\pi\)
\(228\) 0.259257 0.0171697
\(229\) 24.4011 1.61247 0.806236 0.591594i \(-0.201501\pi\)
0.806236 + 0.591594i \(0.201501\pi\)
\(230\) −1.63243 −0.107639
\(231\) −1.05357 −0.0693195
\(232\) −1.11267 −0.0730501
\(233\) 13.8079 0.904586 0.452293 0.891869i \(-0.350606\pi\)
0.452293 + 0.891869i \(0.350606\pi\)
\(234\) 1.73940 0.113708
\(235\) −10.1977 −0.665223
\(236\) 4.70538 0.306294
\(237\) 10.3167 0.670141
\(238\) −0.0860842 −0.00558001
\(239\) 10.4988 0.679113 0.339557 0.940586i \(-0.389723\pi\)
0.339557 + 0.940586i \(0.389723\pi\)
\(240\) −4.96710 −0.320625
\(241\) 4.39472 0.283089 0.141544 0.989932i \(-0.454793\pi\)
0.141544 + 0.989932i \(0.454793\pi\)
\(242\) 6.23285 0.400663
\(243\) 1.00000 0.0641500
\(244\) −20.0306 −1.28233
\(245\) −2.79883 −0.178811
\(246\) 6.52765 0.416188
\(247\) 0.446429 0.0284056
\(248\) 12.2044 0.774980
\(249\) 11.9571 0.757752
\(250\) −3.82149 −0.241693
\(251\) 9.09002 0.573757 0.286878 0.957967i \(-0.407382\pi\)
0.286878 + 0.957967i \(0.407382\pi\)
\(252\) 1.60283 0.100969
\(253\) −0.975055 −0.0613012
\(254\) −8.14760 −0.511226
\(255\) 0.382305 0.0239409
\(256\) −7.16134 −0.447584
\(257\) −18.7230 −1.16791 −0.583955 0.811786i \(-0.698495\pi\)
−0.583955 + 0.811786i \(0.698495\pi\)
\(258\) 5.65749 0.352220
\(259\) 7.86861 0.488932
\(260\) −12.3815 −0.767868
\(261\) −0.490039 −0.0303327
\(262\) −9.72970 −0.601103
\(263\) 23.3921 1.44242 0.721210 0.692717i \(-0.243586\pi\)
0.721210 + 0.692717i \(0.243586\pi\)
\(264\) 2.39219 0.147229
\(265\) 26.1038 1.60355
\(266\) −0.101937 −0.00625018
\(267\) 1.58305 0.0968813
\(268\) 18.1774 1.11036
\(269\) −21.5915 −1.31646 −0.658228 0.752819i \(-0.728694\pi\)
−0.658228 + 0.752819i \(0.728694\pi\)
\(270\) 1.76387 0.107346
\(271\) −12.2493 −0.744095 −0.372047 0.928214i \(-0.621344\pi\)
−0.372047 + 0.928214i \(0.621344\pi\)
\(272\) −0.242415 −0.0146986
\(273\) 2.76000 0.167043
\(274\) 8.23106 0.497257
\(275\) 2.98524 0.180017
\(276\) 1.48338 0.0892893
\(277\) 4.71527 0.283313 0.141657 0.989916i \(-0.454757\pi\)
0.141657 + 0.989916i \(0.454757\pi\)
\(278\) 7.46374 0.447646
\(279\) 5.37505 0.321796
\(280\) 6.35493 0.379779
\(281\) 17.4265 1.03958 0.519788 0.854295i \(-0.326011\pi\)
0.519788 + 0.854295i \(0.326011\pi\)
\(282\) −2.29623 −0.136738
\(283\) −15.2066 −0.903937 −0.451968 0.892034i \(-0.649278\pi\)
−0.451968 + 0.892034i \(0.649278\pi\)
\(284\) −8.98403 −0.533104
\(285\) 0.452710 0.0268162
\(286\) 1.83257 0.108362
\(287\) 10.3578 0.611400
\(288\) −5.65958 −0.333494
\(289\) −16.9813 −0.998902
\(290\) −0.864367 −0.0507574
\(291\) −12.4149 −0.727777
\(292\) −17.9364 −1.04965
\(293\) −3.78217 −0.220957 −0.110478 0.993879i \(-0.535238\pi\)
−0.110478 + 0.993879i \(0.535238\pi\)
\(294\) −0.630217 −0.0367550
\(295\) 8.21647 0.478381
\(296\) −17.8662 −1.03845
\(297\) 1.05357 0.0611341
\(298\) −13.1426 −0.761332
\(299\) 2.55433 0.147721
\(300\) −4.54155 −0.262207
\(301\) 8.97705 0.517428
\(302\) −11.9818 −0.689476
\(303\) 4.96651 0.285319
\(304\) −0.287058 −0.0164639
\(305\) −34.9772 −2.00279
\(306\) 0.0860842 0.00492111
\(307\) −16.0020 −0.913280 −0.456640 0.889652i \(-0.650947\pi\)
−0.456640 + 0.889652i \(0.650947\pi\)
\(308\) 1.68868 0.0962216
\(309\) −6.79070 −0.386309
\(310\) 9.48090 0.538479
\(311\) −14.9728 −0.849029 −0.424514 0.905421i \(-0.639555\pi\)
−0.424514 + 0.905421i \(0.639555\pi\)
\(312\) −6.26676 −0.354786
\(313\) −16.6362 −0.940335 −0.470168 0.882577i \(-0.655807\pi\)
−0.470168 + 0.882577i \(0.655807\pi\)
\(314\) 9.86011 0.556438
\(315\) 2.79883 0.157696
\(316\) −16.5359 −0.930215
\(317\) 34.7996 1.95454 0.977269 0.212002i \(-0.0679983\pi\)
0.977269 + 0.212002i \(0.0679983\pi\)
\(318\) 5.87784 0.329613
\(319\) −0.516289 −0.0289066
\(320\) −0.0485698 −0.00271514
\(321\) 18.7427 1.04611
\(322\) −0.583254 −0.0325035
\(323\) 0.0220941 0.00122935
\(324\) −1.60283 −0.0890459
\(325\) −7.82037 −0.433796
\(326\) −7.93881 −0.439690
\(327\) 2.36857 0.130982
\(328\) −23.5180 −1.29856
\(329\) −3.64355 −0.200875
\(330\) 1.85836 0.102299
\(331\) 24.8449 1.36560 0.682800 0.730605i \(-0.260762\pi\)
0.682800 + 0.730605i \(0.260762\pi\)
\(332\) −19.1652 −1.05183
\(333\) −7.86861 −0.431197
\(334\) 0.0218151 0.00119367
\(335\) 31.7411 1.73420
\(336\) −1.77470 −0.0968181
\(337\) −19.6563 −1.07074 −0.535372 0.844616i \(-0.679829\pi\)
−0.535372 + 0.844616i \(0.679829\pi\)
\(338\) 3.39207 0.184504
\(339\) 10.3546 0.562387
\(340\) −0.612769 −0.0332321
\(341\) 5.66297 0.306667
\(342\) 0.101937 0.00551214
\(343\) −1.00000 −0.0539949
\(344\) −20.3830 −1.09898
\(345\) 2.59026 0.139455
\(346\) 12.3871 0.665934
\(347\) 19.7723 1.06143 0.530716 0.847549i \(-0.321923\pi\)
0.530716 + 0.847549i \(0.321923\pi\)
\(348\) 0.785448 0.0421044
\(349\) 7.50169 0.401556 0.200778 0.979637i \(-0.435653\pi\)
0.200778 + 0.979637i \(0.435653\pi\)
\(350\) 1.78570 0.0954496
\(351\) −2.76000 −0.147318
\(352\) −5.96274 −0.317815
\(353\) 16.2391 0.864318 0.432159 0.901797i \(-0.357752\pi\)
0.432159 + 0.901797i \(0.357752\pi\)
\(354\) 1.85012 0.0983325
\(355\) −15.6878 −0.832621
\(356\) −2.53736 −0.134480
\(357\) 0.136595 0.00722935
\(358\) −9.08728 −0.480278
\(359\) 3.52732 0.186165 0.0930825 0.995658i \(-0.470328\pi\)
0.0930825 + 0.995658i \(0.470328\pi\)
\(360\) −6.35493 −0.334934
\(361\) −18.9738 −0.998623
\(362\) −16.2328 −0.853175
\(363\) −9.89000 −0.519090
\(364\) −4.42381 −0.231870
\(365\) −31.3203 −1.63938
\(366\) −7.87586 −0.411678
\(367\) −19.8507 −1.03620 −0.518100 0.855320i \(-0.673360\pi\)
−0.518100 + 0.855320i \(0.673360\pi\)
\(368\) −1.64245 −0.0856188
\(369\) −10.3578 −0.539205
\(370\) −13.8792 −0.721547
\(371\) 9.32669 0.484218
\(372\) −8.61527 −0.446681
\(373\) 36.8570 1.90838 0.954192 0.299195i \(-0.0967180\pi\)
0.954192 + 0.299195i \(0.0967180\pi\)
\(374\) 0.0906954 0.00468975
\(375\) 6.06377 0.313132
\(376\) 8.27290 0.426642
\(377\) 1.35251 0.0696578
\(378\) 0.630217 0.0324149
\(379\) 28.5680 1.46744 0.733720 0.679452i \(-0.237782\pi\)
0.733720 + 0.679452i \(0.237782\pi\)
\(380\) −0.725616 −0.0372233
\(381\) 12.9282 0.662334
\(382\) 0.630217 0.0322447
\(383\) 4.46037 0.227914 0.113957 0.993486i \(-0.463647\pi\)
0.113957 + 0.993486i \(0.463647\pi\)
\(384\) 11.3082 0.577070
\(385\) 2.94875 0.150282
\(386\) 14.0205 0.713625
\(387\) −8.97705 −0.456329
\(388\) 19.8990 1.01022
\(389\) 16.3109 0.826995 0.413497 0.910505i \(-0.364307\pi\)
0.413497 + 0.910505i \(0.364307\pi\)
\(390\) −4.86829 −0.246516
\(391\) 0.126416 0.00639311
\(392\) 2.27056 0.114681
\(393\) 15.4387 0.778777
\(394\) −8.90136 −0.448444
\(395\) −28.8747 −1.45284
\(396\) −1.68868 −0.0848595
\(397\) 11.0036 0.552256 0.276128 0.961121i \(-0.410949\pi\)
0.276128 + 0.961121i \(0.410949\pi\)
\(398\) −1.81762 −0.0911090
\(399\) 0.161750 0.00809761
\(400\) 5.02856 0.251428
\(401\) 33.8060 1.68819 0.844096 0.536192i \(-0.180138\pi\)
0.844096 + 0.536192i \(0.180138\pi\)
\(402\) 7.14719 0.356470
\(403\) −14.8352 −0.738992
\(404\) −7.96046 −0.396048
\(405\) −2.79883 −0.139075
\(406\) −0.308831 −0.0153270
\(407\) −8.29010 −0.410925
\(408\) −0.310147 −0.0153545
\(409\) 10.5452 0.521426 0.260713 0.965416i \(-0.416042\pi\)
0.260713 + 0.965416i \(0.416042\pi\)
\(410\) −18.2698 −0.902281
\(411\) −13.0607 −0.644235
\(412\) 10.8843 0.536231
\(413\) 2.93568 0.144455
\(414\) 0.583254 0.0286654
\(415\) −33.4660 −1.64278
\(416\) 15.6204 0.765856
\(417\) −11.8431 −0.579961
\(418\) 0.107398 0.00525300
\(419\) −14.4031 −0.703637 −0.351819 0.936068i \(-0.614437\pi\)
−0.351819 + 0.936068i \(0.614437\pi\)
\(420\) −4.48604 −0.218896
\(421\) 2.81960 0.137419 0.0687095 0.997637i \(-0.478112\pi\)
0.0687095 + 0.997637i \(0.478112\pi\)
\(422\) −2.36809 −0.115277
\(423\) 3.64355 0.177155
\(424\) −21.1768 −1.02844
\(425\) −0.387036 −0.0187740
\(426\) −3.53244 −0.171147
\(427\) −12.4971 −0.604775
\(428\) −30.0412 −1.45210
\(429\) −2.90785 −0.140392
\(430\) −15.8344 −0.763601
\(431\) −18.1076 −0.872211 −0.436105 0.899896i \(-0.643642\pi\)
−0.436105 + 0.899896i \(0.643642\pi\)
\(432\) 1.77470 0.0853855
\(433\) −24.3620 −1.17076 −0.585382 0.810758i \(-0.699055\pi\)
−0.585382 + 0.810758i \(0.699055\pi\)
\(434\) 3.38745 0.162603
\(435\) 1.37154 0.0657602
\(436\) −3.79641 −0.181815
\(437\) 0.149696 0.00716094
\(438\) −7.05243 −0.336978
\(439\) −1.86612 −0.0890648 −0.0445324 0.999008i \(-0.514180\pi\)
−0.0445324 + 0.999008i \(0.514180\pi\)
\(440\) −6.69533 −0.319187
\(441\) 1.00000 0.0476190
\(442\) −0.237593 −0.0113011
\(443\) 27.9040 1.32576 0.662879 0.748727i \(-0.269335\pi\)
0.662879 + 0.748727i \(0.269335\pi\)
\(444\) 12.6120 0.598540
\(445\) −4.43070 −0.210035
\(446\) 9.07520 0.429723
\(447\) 20.8541 0.986366
\(448\) −0.0173536 −0.000819880 0
\(449\) −39.4282 −1.86073 −0.930366 0.366632i \(-0.880511\pi\)
−0.930366 + 0.366632i \(0.880511\pi\)
\(450\) −1.78570 −0.0841786
\(451\) −10.9126 −0.513854
\(452\) −16.5967 −0.780642
\(453\) 19.0122 0.893271
\(454\) −11.1077 −0.521310
\(455\) −7.72479 −0.362144
\(456\) −0.367263 −0.0171987
\(457\) −12.1071 −0.566348 −0.283174 0.959069i \(-0.591387\pi\)
−0.283174 + 0.959069i \(0.591387\pi\)
\(458\) −15.3780 −0.718567
\(459\) −0.136595 −0.00637569
\(460\) −4.15174 −0.193576
\(461\) −13.0305 −0.606893 −0.303446 0.952849i \(-0.598137\pi\)
−0.303446 + 0.952849i \(0.598137\pi\)
\(462\) 0.663975 0.0308909
\(463\) 34.8486 1.61955 0.809777 0.586738i \(-0.199588\pi\)
0.809777 + 0.586738i \(0.199588\pi\)
\(464\) −0.869675 −0.0403736
\(465\) −15.0439 −0.697643
\(466\) −8.70198 −0.403111
\(467\) −4.22272 −0.195404 −0.0977020 0.995216i \(-0.531149\pi\)
−0.0977020 + 0.995216i \(0.531149\pi\)
\(468\) 4.42381 0.204491
\(469\) 11.3408 0.523671
\(470\) 6.42675 0.296444
\(471\) −15.6456 −0.720910
\(472\) −6.66564 −0.306811
\(473\) −9.45791 −0.434875
\(474\) −6.50176 −0.298636
\(475\) −0.458312 −0.0210288
\(476\) −0.218937 −0.0100350
\(477\) −9.32669 −0.427040
\(478\) −6.61655 −0.302634
\(479\) −25.7175 −1.17506 −0.587531 0.809202i \(-0.699900\pi\)
−0.587531 + 0.809202i \(0.699900\pi\)
\(480\) 15.8402 0.723003
\(481\) 21.7174 0.990228
\(482\) −2.76963 −0.126153
\(483\) 0.925481 0.0421108
\(484\) 15.8519 0.720543
\(485\) 34.7473 1.57780
\(486\) −0.630217 −0.0285872
\(487\) −15.3784 −0.696864 −0.348432 0.937334i \(-0.613286\pi\)
−0.348432 + 0.937334i \(0.613286\pi\)
\(488\) 28.3754 1.28449
\(489\) 12.5969 0.569654
\(490\) 1.76387 0.0796836
\(491\) 12.6021 0.568726 0.284363 0.958717i \(-0.408218\pi\)
0.284363 + 0.958717i \(0.408218\pi\)
\(492\) 16.6017 0.748463
\(493\) 0.0669367 0.00301468
\(494\) −0.281348 −0.0126584
\(495\) −2.94875 −0.132537
\(496\) 9.53912 0.428319
\(497\) −5.60512 −0.251424
\(498\) −7.53559 −0.337678
\(499\) −33.3896 −1.49472 −0.747362 0.664417i \(-0.768680\pi\)
−0.747362 + 0.664417i \(0.768680\pi\)
\(500\) −9.71917 −0.434655
\(501\) −0.0346152 −0.00154649
\(502\) −5.72868 −0.255684
\(503\) −10.0887 −0.449835 −0.224917 0.974378i \(-0.572211\pi\)
−0.224917 + 0.974378i \(0.572211\pi\)
\(504\) −2.27056 −0.101139
\(505\) −13.9004 −0.618562
\(506\) 0.614496 0.0273177
\(507\) −5.38238 −0.239040
\(508\) −20.7217 −0.919378
\(509\) −11.3443 −0.502826 −0.251413 0.967880i \(-0.580895\pi\)
−0.251413 + 0.967880i \(0.580895\pi\)
\(510\) −0.240935 −0.0106688
\(511\) −11.1905 −0.495037
\(512\) −18.1032 −0.800057
\(513\) −0.161750 −0.00714142
\(514\) 11.7996 0.520456
\(515\) 19.0060 0.837506
\(516\) 14.3886 0.633425
\(517\) 3.83872 0.168827
\(518\) −4.95894 −0.217883
\(519\) −19.6553 −0.862770
\(520\) 17.5396 0.769163
\(521\) −1.59553 −0.0699014 −0.0349507 0.999389i \(-0.511127\pi\)
−0.0349507 + 0.999389i \(0.511127\pi\)
\(522\) 0.308831 0.0135172
\(523\) 34.3878 1.50367 0.751836 0.659351i \(-0.229169\pi\)
0.751836 + 0.659351i \(0.229169\pi\)
\(524\) −24.7455 −1.08101
\(525\) −2.83346 −0.123662
\(526\) −14.7421 −0.642787
\(527\) −0.734202 −0.0319824
\(528\) 1.86977 0.0813712
\(529\) −22.1435 −0.962760
\(530\) −16.4511 −0.714590
\(531\) −2.93568 −0.127398
\(532\) −0.259257 −0.0112402
\(533\) 28.5875 1.23826
\(534\) −0.997668 −0.0431733
\(535\) −52.4576 −2.26794
\(536\) −25.7501 −1.11223
\(537\) 14.4193 0.622238
\(538\) 13.6073 0.586653
\(539\) 1.05357 0.0453803
\(540\) 4.48604 0.193049
\(541\) 8.66011 0.372327 0.186164 0.982519i \(-0.440395\pi\)
0.186164 + 0.982519i \(0.440395\pi\)
\(542\) 7.71975 0.331592
\(543\) 25.7574 1.10536
\(544\) 0.773067 0.0331450
\(545\) −6.62924 −0.283965
\(546\) −1.73940 −0.0744395
\(547\) 13.8428 0.591876 0.295938 0.955207i \(-0.404368\pi\)
0.295938 + 0.955207i \(0.404368\pi\)
\(548\) 20.9340 0.894256
\(549\) 12.4971 0.533362
\(550\) −1.88135 −0.0802210
\(551\) 0.0792637 0.00337675
\(552\) −2.10136 −0.0894399
\(553\) −10.3167 −0.438710
\(554\) −2.97165 −0.126253
\(555\) 22.0229 0.934822
\(556\) 18.9825 0.805036
\(557\) 22.7232 0.962811 0.481406 0.876498i \(-0.340126\pi\)
0.481406 + 0.876498i \(0.340126\pi\)
\(558\) −3.38745 −0.143402
\(559\) 24.7767 1.04794
\(560\) 4.96710 0.209898
\(561\) −0.143911 −0.00607594
\(562\) −10.9825 −0.463267
\(563\) −20.2508 −0.853471 −0.426736 0.904376i \(-0.640337\pi\)
−0.426736 + 0.904376i \(0.640337\pi\)
\(564\) −5.83997 −0.245907
\(565\) −28.9809 −1.21924
\(566\) 9.58344 0.402822
\(567\) −1.00000 −0.0419961
\(568\) 12.7268 0.534004
\(569\) −32.2811 −1.35329 −0.676647 0.736308i \(-0.736567\pi\)
−0.676647 + 0.736308i \(0.736567\pi\)
\(570\) −0.285306 −0.0119501
\(571\) −7.72882 −0.323441 −0.161721 0.986837i \(-0.551704\pi\)
−0.161721 + 0.986837i \(0.551704\pi\)
\(572\) 4.66077 0.194877
\(573\) −1.00000 −0.0417756
\(574\) −6.52765 −0.272459
\(575\) −2.62232 −0.109358
\(576\) 0.0173536 0.000723067 0
\(577\) −33.8600 −1.40961 −0.704805 0.709401i \(-0.748965\pi\)
−0.704805 + 0.709401i \(0.748965\pi\)
\(578\) 10.7019 0.445142
\(579\) −22.2471 −0.924558
\(580\) −2.19834 −0.0912810
\(581\) −11.9571 −0.496065
\(582\) 7.82411 0.324320
\(583\) −9.82628 −0.406963
\(584\) 25.4087 1.05142
\(585\) 7.72479 0.319381
\(586\) 2.38359 0.0984652
\(587\) 28.5033 1.17646 0.588228 0.808695i \(-0.299826\pi\)
0.588228 + 0.808695i \(0.299826\pi\)
\(588\) −1.60283 −0.0660994
\(589\) −0.869412 −0.0358235
\(590\) −5.17816 −0.213182
\(591\) 14.1243 0.580995
\(592\) −13.9645 −0.573936
\(593\) 11.7239 0.481443 0.240722 0.970594i \(-0.422616\pi\)
0.240722 + 0.970594i \(0.422616\pi\)
\(594\) −0.663975 −0.0272432
\(595\) −0.382305 −0.0156730
\(596\) −33.4255 −1.36916
\(597\) 2.88412 0.118039
\(598\) −1.60978 −0.0658289
\(599\) 44.7437 1.82818 0.914090 0.405512i \(-0.132907\pi\)
0.914090 + 0.405512i \(0.132907\pi\)
\(600\) 6.43356 0.262649
\(601\) 5.87076 0.239473 0.119737 0.992806i \(-0.461795\pi\)
0.119737 + 0.992806i \(0.461795\pi\)
\(602\) −5.65749 −0.230582
\(603\) −11.3408 −0.461835
\(604\) −30.4733 −1.23994
\(605\) 27.6805 1.12537
\(606\) −3.12998 −0.127147
\(607\) 14.3774 0.583559 0.291779 0.956486i \(-0.405753\pi\)
0.291779 + 0.956486i \(0.405753\pi\)
\(608\) 0.915434 0.0371258
\(609\) 0.490039 0.0198574
\(610\) 22.0432 0.892504
\(611\) −10.0562 −0.406830
\(612\) 0.218937 0.00885002
\(613\) −20.6085 −0.832371 −0.416186 0.909280i \(-0.636633\pi\)
−0.416186 + 0.909280i \(0.636633\pi\)
\(614\) 10.0847 0.406986
\(615\) 28.9897 1.16898
\(616\) −2.39219 −0.0963840
\(617\) 20.5442 0.827079 0.413539 0.910486i \(-0.364292\pi\)
0.413539 + 0.910486i \(0.364292\pi\)
\(618\) 4.27961 0.172151
\(619\) 44.6946 1.79643 0.898215 0.439557i \(-0.144865\pi\)
0.898215 + 0.439557i \(0.144865\pi\)
\(620\) 24.1127 0.968389
\(621\) −0.925481 −0.0371383
\(622\) 9.43611 0.378353
\(623\) −1.58305 −0.0634237
\(624\) −4.89819 −0.196085
\(625\) −31.1388 −1.24555
\(626\) 10.4844 0.419043
\(627\) −0.170414 −0.00680567
\(628\) 25.0771 1.00069
\(629\) 1.07481 0.0428555
\(630\) −1.76387 −0.0702744
\(631\) 32.7954 1.30556 0.652782 0.757546i \(-0.273602\pi\)
0.652782 + 0.757546i \(0.273602\pi\)
\(632\) 23.4247 0.931785
\(633\) 3.75758 0.149350
\(634\) −21.9313 −0.871003
\(635\) −36.1840 −1.43592
\(636\) 14.9491 0.592769
\(637\) −2.76000 −0.109355
\(638\) 0.325374 0.0128817
\(639\) 5.60512 0.221735
\(640\) −31.6498 −1.25107
\(641\) 30.6688 1.21134 0.605672 0.795714i \(-0.292904\pi\)
0.605672 + 0.795714i \(0.292904\pi\)
\(642\) −11.8120 −0.466181
\(643\) 40.6256 1.60212 0.801058 0.598587i \(-0.204271\pi\)
0.801058 + 0.598587i \(0.204271\pi\)
\(644\) −1.48338 −0.0584535
\(645\) 25.1253 0.989306
\(646\) −0.0139241 −0.000547836 0
\(647\) −13.2387 −0.520465 −0.260233 0.965546i \(-0.583799\pi\)
−0.260233 + 0.965546i \(0.583799\pi\)
\(648\) 2.27056 0.0891961
\(649\) −3.09293 −0.121408
\(650\) 4.92853 0.193313
\(651\) −5.37505 −0.210665
\(652\) −20.1907 −0.790729
\(653\) 30.4110 1.19008 0.595038 0.803698i \(-0.297137\pi\)
0.595038 + 0.803698i \(0.297137\pi\)
\(654\) −1.49272 −0.0583698
\(655\) −43.2102 −1.68836
\(656\) −18.3820 −0.717696
\(657\) 11.1905 0.436582
\(658\) 2.29623 0.0895162
\(659\) −24.8780 −0.969109 −0.484555 0.874761i \(-0.661018\pi\)
−0.484555 + 0.874761i \(0.661018\pi\)
\(660\) 4.72634 0.183973
\(661\) 26.7177 1.03920 0.519599 0.854410i \(-0.326081\pi\)
0.519599 + 0.854410i \(0.326081\pi\)
\(662\) −15.6577 −0.608554
\(663\) 0.377001 0.0146415
\(664\) 27.1494 1.05360
\(665\) −0.452710 −0.0175553
\(666\) 4.95894 0.192155
\(667\) 0.453522 0.0175604
\(668\) 0.0554821 0.00214667
\(669\) −14.4001 −0.556741
\(670\) −20.0038 −0.772814
\(671\) 13.1665 0.508286
\(672\) 5.65958 0.218323
\(673\) 6.60622 0.254651 0.127325 0.991861i \(-0.459361\pi\)
0.127325 + 0.991861i \(0.459361\pi\)
\(674\) 12.3877 0.477157
\(675\) 2.83346 0.109060
\(676\) 8.62702 0.331808
\(677\) 2.80381 0.107759 0.0538797 0.998547i \(-0.482841\pi\)
0.0538797 + 0.998547i \(0.482841\pi\)
\(678\) −6.52567 −0.250617
\(679\) 12.4149 0.476442
\(680\) 0.868048 0.0332881
\(681\) 17.6252 0.675398
\(682\) −3.56890 −0.136660
\(683\) 1.41732 0.0542322 0.0271161 0.999632i \(-0.491368\pi\)
0.0271161 + 0.999632i \(0.491368\pi\)
\(684\) 0.259257 0.00991292
\(685\) 36.5546 1.39668
\(686\) 0.630217 0.0240618
\(687\) 24.4011 0.930961
\(688\) −15.9316 −0.607387
\(689\) 25.7417 0.980681
\(690\) −1.63243 −0.0621455
\(691\) −15.8855 −0.604314 −0.302157 0.953258i \(-0.597707\pi\)
−0.302157 + 0.953258i \(0.597707\pi\)
\(692\) 31.5040 1.19760
\(693\) −1.05357 −0.0400217
\(694\) −12.4608 −0.473007
\(695\) 33.1469 1.25733
\(696\) −1.11267 −0.0421755
\(697\) 1.41482 0.0535900
\(698\) −4.72769 −0.178946
\(699\) 13.8079 0.522263
\(700\) 4.54155 0.171654
\(701\) −42.2541 −1.59591 −0.797957 0.602714i \(-0.794086\pi\)
−0.797957 + 0.602714i \(0.794086\pi\)
\(702\) 1.73940 0.0656495
\(703\) 1.27275 0.0480025
\(704\) 0.0182832 0.000689072 0
\(705\) −10.1977 −0.384067
\(706\) −10.2341 −0.385167
\(707\) −4.96651 −0.186785
\(708\) 4.70538 0.176839
\(709\) −42.1888 −1.58443 −0.792217 0.610240i \(-0.791073\pi\)
−0.792217 + 0.610240i \(0.791073\pi\)
\(710\) 9.88672 0.371042
\(711\) 10.3167 0.386906
\(712\) 3.59442 0.134707
\(713\) −4.97450 −0.186297
\(714\) −0.0860842 −0.00322162
\(715\) 8.13857 0.304365
\(716\) −23.1116 −0.863721
\(717\) 10.4988 0.392086
\(718\) −2.22298 −0.0829609
\(719\) 33.8749 1.26332 0.631660 0.775245i \(-0.282374\pi\)
0.631660 + 0.775245i \(0.282374\pi\)
\(720\) −4.96710 −0.185113
\(721\) 6.79070 0.252899
\(722\) 11.9576 0.445017
\(723\) 4.39472 0.163441
\(724\) −41.2846 −1.53433
\(725\) −1.38851 −0.0515679
\(726\) 6.23285 0.231323
\(727\) −36.7976 −1.36475 −0.682374 0.731003i \(-0.739052\pi\)
−0.682374 + 0.731003i \(0.739052\pi\)
\(728\) 6.26676 0.232262
\(729\) 1.00000 0.0370370
\(730\) 19.7386 0.730557
\(731\) 1.22622 0.0453532
\(732\) −20.0306 −0.740353
\(733\) 1.68998 0.0624210 0.0312105 0.999513i \(-0.490064\pi\)
0.0312105 + 0.999513i \(0.490064\pi\)
\(734\) 12.5103 0.461762
\(735\) −2.79883 −0.103236
\(736\) 5.23783 0.193069
\(737\) −11.9483 −0.440122
\(738\) 6.52765 0.240286
\(739\) −17.0080 −0.625649 −0.312824 0.949811i \(-0.601275\pi\)
−0.312824 + 0.949811i \(0.601275\pi\)
\(740\) −35.2989 −1.29761
\(741\) 0.446429 0.0164000
\(742\) −5.87784 −0.215782
\(743\) 18.8028 0.689807 0.344904 0.938638i \(-0.387912\pi\)
0.344904 + 0.938638i \(0.387912\pi\)
\(744\) 12.2044 0.447435
\(745\) −58.3672 −2.13841
\(746\) −23.2279 −0.850435
\(747\) 11.9571 0.437489
\(748\) 0.230665 0.00843394
\(749\) −18.7427 −0.684842
\(750\) −3.82149 −0.139541
\(751\) 43.6044 1.59115 0.795574 0.605856i \(-0.207169\pi\)
0.795574 + 0.605856i \(0.207169\pi\)
\(752\) 6.46622 0.235799
\(753\) 9.09002 0.331259
\(754\) −0.852375 −0.0310417
\(755\) −53.2120 −1.93658
\(756\) 1.60283 0.0582942
\(757\) −21.8607 −0.794539 −0.397270 0.917702i \(-0.630042\pi\)
−0.397270 + 0.917702i \(0.630042\pi\)
\(758\) −18.0041 −0.653937
\(759\) −0.975055 −0.0353922
\(760\) 1.02791 0.0372861
\(761\) 45.8129 1.66072 0.830358 0.557231i \(-0.188136\pi\)
0.830358 + 0.557231i \(0.188136\pi\)
\(762\) −8.14760 −0.295156
\(763\) −2.36857 −0.0857481
\(764\) 1.60283 0.0579882
\(765\) 0.382305 0.0138223
\(766\) −2.81100 −0.101566
\(767\) 8.10248 0.292564
\(768\) −7.16134 −0.258413
\(769\) 38.5576 1.39042 0.695211 0.718805i \(-0.255311\pi\)
0.695211 + 0.718805i \(0.255311\pi\)
\(770\) −1.85836 −0.0669705
\(771\) −18.7230 −0.674293
\(772\) 35.6582 1.28337
\(773\) −30.5446 −1.09861 −0.549306 0.835621i \(-0.685108\pi\)
−0.549306 + 0.835621i \(0.685108\pi\)
\(774\) 5.65749 0.203354
\(775\) 15.2300 0.547078
\(776\) −28.1889 −1.01192
\(777\) 7.86861 0.282285
\(778\) −10.2794 −0.368534
\(779\) 1.67537 0.0600263
\(780\) −12.3815 −0.443329
\(781\) 5.90536 0.211310
\(782\) −0.0796693 −0.00284897
\(783\) −0.490039 −0.0175126
\(784\) 1.77470 0.0633823
\(785\) 43.7893 1.56291
\(786\) −9.72970 −0.347047
\(787\) −17.3830 −0.619637 −0.309818 0.950796i \(-0.600268\pi\)
−0.309818 + 0.950796i \(0.600268\pi\)
\(788\) −22.6388 −0.806472
\(789\) 23.3921 0.832781
\(790\) 18.1973 0.647432
\(791\) −10.3546 −0.368169
\(792\) 2.39219 0.0850027
\(793\) −34.4919 −1.22484
\(794\) −6.93467 −0.246102
\(795\) 26.1038 0.925808
\(796\) −4.62274 −0.163849
\(797\) −40.1037 −1.42055 −0.710273 0.703926i \(-0.751428\pi\)
−0.710273 + 0.703926i \(0.751428\pi\)
\(798\) −0.101937 −0.00360854
\(799\) −0.497689 −0.0176070
\(800\) −16.0362 −0.566965
\(801\) 1.58305 0.0559344
\(802\) −21.3051 −0.752310
\(803\) 11.7899 0.416057
\(804\) 18.1774 0.641067
\(805\) −2.59026 −0.0912948
\(806\) 9.34937 0.329318
\(807\) −21.5915 −0.760056
\(808\) 11.2768 0.396716
\(809\) 17.1149 0.601726 0.300863 0.953667i \(-0.402725\pi\)
0.300863 + 0.953667i \(0.402725\pi\)
\(810\) 1.76387 0.0619762
\(811\) −29.9348 −1.05115 −0.525576 0.850746i \(-0.676150\pi\)
−0.525576 + 0.850746i \(0.676150\pi\)
\(812\) −0.785448 −0.0275638
\(813\) −12.2493 −0.429603
\(814\) 5.22457 0.183121
\(815\) −35.2567 −1.23499
\(816\) −0.242415 −0.00848622
\(817\) 1.45203 0.0508002
\(818\) −6.64576 −0.232363
\(819\) 2.76000 0.0964423
\(820\) −46.4654 −1.62264
\(821\) 37.4553 1.30720 0.653599 0.756841i \(-0.273258\pi\)
0.653599 + 0.756841i \(0.273258\pi\)
\(822\) 8.23106 0.287091
\(823\) 39.6390 1.38173 0.690864 0.722985i \(-0.257230\pi\)
0.690864 + 0.722985i \(0.257230\pi\)
\(824\) −15.4187 −0.537136
\(825\) 2.98524 0.103933
\(826\) −1.85012 −0.0643737
\(827\) −17.1286 −0.595619 −0.297809 0.954625i \(-0.596256\pi\)
−0.297809 + 0.954625i \(0.596256\pi\)
\(828\) 1.48338 0.0515512
\(829\) −23.2860 −0.808757 −0.404378 0.914592i \(-0.632512\pi\)
−0.404378 + 0.914592i \(0.632512\pi\)
\(830\) 21.0909 0.732074
\(831\) 4.71527 0.163571
\(832\) −0.0478960 −0.00166049
\(833\) −0.136595 −0.00473272
\(834\) 7.46374 0.258448
\(835\) 0.0968821 0.00335274
\(836\) 0.273144 0.00944688
\(837\) 5.37505 0.185789
\(838\) 9.07708 0.313563
\(839\) 30.4584 1.05154 0.525770 0.850627i \(-0.323777\pi\)
0.525770 + 0.850627i \(0.323777\pi\)
\(840\) 6.35493 0.219266
\(841\) −28.7599 −0.991719
\(842\) −1.77696 −0.0612381
\(843\) 17.4265 0.600199
\(844\) −6.02275 −0.207312
\(845\) 15.0644 0.518230
\(846\) −2.29623 −0.0789459
\(847\) 9.89000 0.339824
\(848\) −16.5521 −0.568402
\(849\) −15.2066 −0.521888
\(850\) 0.243917 0.00836627
\(851\) 7.28225 0.249632
\(852\) −8.98403 −0.307788
\(853\) 10.8946 0.373024 0.186512 0.982453i \(-0.440282\pi\)
0.186512 + 0.982453i \(0.440282\pi\)
\(854\) 7.87586 0.269507
\(855\) 0.452710 0.0154824
\(856\) 42.5564 1.45455
\(857\) 3.14257 0.107348 0.0536741 0.998559i \(-0.482907\pi\)
0.0536741 + 0.998559i \(0.482907\pi\)
\(858\) 1.83257 0.0625631
\(859\) 35.1275 1.19854 0.599268 0.800549i \(-0.295458\pi\)
0.599268 + 0.800549i \(0.295458\pi\)
\(860\) −40.2714 −1.37324
\(861\) 10.3578 0.352992
\(862\) 11.4117 0.388684
\(863\) −27.2388 −0.927220 −0.463610 0.886039i \(-0.653446\pi\)
−0.463610 + 0.886039i \(0.653446\pi\)
\(864\) −5.65958 −0.192543
\(865\) 55.0118 1.87046
\(866\) 15.3534 0.521729
\(867\) −16.9813 −0.576717
\(868\) 8.61527 0.292421
\(869\) 10.8693 0.368716
\(870\) −0.864367 −0.0293048
\(871\) 31.3008 1.06059
\(872\) 5.37799 0.182122
\(873\) −12.4149 −0.420182
\(874\) −0.0943411 −0.00319113
\(875\) −6.06377 −0.204993
\(876\) −17.9364 −0.606014
\(877\) −15.2811 −0.516006 −0.258003 0.966144i \(-0.583064\pi\)
−0.258003 + 0.966144i \(0.583064\pi\)
\(878\) 1.17606 0.0396900
\(879\) −3.78217 −0.127569
\(880\) −5.23317 −0.176410
\(881\) 24.6078 0.829060 0.414530 0.910036i \(-0.363946\pi\)
0.414530 + 0.910036i \(0.363946\pi\)
\(882\) −0.630217 −0.0212205
\(883\) 0.103313 0.00347676 0.00173838 0.999998i \(-0.499447\pi\)
0.00173838 + 0.999998i \(0.499447\pi\)
\(884\) −0.604268 −0.0203237
\(885\) 8.21647 0.276194
\(886\) −17.5856 −0.590798
\(887\) 6.99559 0.234889 0.117444 0.993079i \(-0.462530\pi\)
0.117444 + 0.993079i \(0.462530\pi\)
\(888\) −17.8662 −0.599550
\(889\) −12.9282 −0.433599
\(890\) 2.79230 0.0935983
\(891\) 1.05357 0.0352958
\(892\) 23.0809 0.772805
\(893\) −0.589342 −0.0197216
\(894\) −13.1426 −0.439555
\(895\) −40.3571 −1.34899
\(896\) −11.3082 −0.377781
\(897\) 2.55433 0.0852866
\(898\) 24.8483 0.829200
\(899\) −2.63399 −0.0878484
\(900\) −4.54155 −0.151385
\(901\) 1.27398 0.0424423
\(902\) 6.87731 0.228989
\(903\) 8.97705 0.298737
\(904\) 23.5109 0.781960
\(905\) −72.0906 −2.39637
\(906\) −11.9818 −0.398069
\(907\) 26.6735 0.885679 0.442839 0.896601i \(-0.353971\pi\)
0.442839 + 0.896601i \(0.353971\pi\)
\(908\) −28.2501 −0.937513
\(909\) 4.96651 0.164729
\(910\) 4.86829 0.161382
\(911\) 28.7475 0.952447 0.476223 0.879324i \(-0.342005\pi\)
0.476223 + 0.879324i \(0.342005\pi\)
\(912\) −0.287058 −0.00950543
\(913\) 12.5976 0.416920
\(914\) 7.63013 0.252382
\(915\) −34.9772 −1.15631
\(916\) −39.1108 −1.29226
\(917\) −15.4387 −0.509829
\(918\) 0.0860842 0.00284120
\(919\) −3.57141 −0.117810 −0.0589049 0.998264i \(-0.518761\pi\)
−0.0589049 + 0.998264i \(0.518761\pi\)
\(920\) 5.88136 0.193903
\(921\) −16.0020 −0.527283
\(922\) 8.21207 0.270450
\(923\) −15.4701 −0.509206
\(924\) 1.68868 0.0555536
\(925\) −22.2954 −0.733069
\(926\) −21.9622 −0.721723
\(927\) −6.79070 −0.223036
\(928\) 2.77341 0.0910418
\(929\) −46.0524 −1.51093 −0.755464 0.655190i \(-0.772589\pi\)
−0.755464 + 0.655190i \(0.772589\pi\)
\(930\) 9.48090 0.310891
\(931\) −0.161750 −0.00530113
\(932\) −22.1317 −0.724947
\(933\) −14.9728 −0.490187
\(934\) 2.66123 0.0870781
\(935\) 0.402784 0.0131724
\(936\) −6.26676 −0.204836
\(937\) −36.2809 −1.18525 −0.592623 0.805480i \(-0.701907\pi\)
−0.592623 + 0.805480i \(0.701907\pi\)
\(938\) −7.14719 −0.233364
\(939\) −16.6362 −0.542903
\(940\) 16.3451 0.533118
\(941\) −51.6167 −1.68266 −0.841328 0.540524i \(-0.818226\pi\)
−0.841328 + 0.540524i \(0.818226\pi\)
\(942\) 9.86011 0.321260
\(943\) 9.58592 0.312161
\(944\) −5.20996 −0.169570
\(945\) 2.79883 0.0910460
\(946\) 5.96054 0.193794
\(947\) −5.47498 −0.177913 −0.0889565 0.996036i \(-0.528353\pi\)
−0.0889565 + 0.996036i \(0.528353\pi\)
\(948\) −16.5359 −0.537060
\(949\) −30.8858 −1.00259
\(950\) 0.288836 0.00937107
\(951\) 34.7996 1.12845
\(952\) 0.310147 0.0100519
\(953\) −5.78476 −0.187387 −0.0936934 0.995601i \(-0.529867\pi\)
−0.0936934 + 0.995601i \(0.529867\pi\)
\(954\) 5.87784 0.190302
\(955\) 2.79883 0.0905681
\(956\) −16.8278 −0.544250
\(957\) −0.516289 −0.0166892
\(958\) 16.2076 0.523644
\(959\) 13.0607 0.421751
\(960\) −0.0485698 −0.00156758
\(961\) −2.10884 −0.0680270
\(962\) −13.6867 −0.441276
\(963\) 18.7427 0.603974
\(964\) −7.04397 −0.226871
\(965\) 62.2659 2.00441
\(966\) −0.583254 −0.0187659
\(967\) −7.45410 −0.239708 −0.119854 0.992792i \(-0.538243\pi\)
−0.119854 + 0.992792i \(0.538243\pi\)
\(968\) −22.4559 −0.721759
\(969\) 0.0220941 0.000709765 0
\(970\) −21.8984 −0.703114
\(971\) 4.23396 0.135874 0.0679371 0.997690i \(-0.478358\pi\)
0.0679371 + 0.997690i \(0.478358\pi\)
\(972\) −1.60283 −0.0514107
\(973\) 11.8431 0.379673
\(974\) 9.69176 0.310544
\(975\) −7.82037 −0.250452
\(976\) 22.1786 0.709919
\(977\) −31.4322 −1.00561 −0.502803 0.864401i \(-0.667698\pi\)
−0.502803 + 0.864401i \(0.667698\pi\)
\(978\) −7.93881 −0.253855
\(979\) 1.66785 0.0533047
\(980\) 4.48604 0.143301
\(981\) 2.36857 0.0756227
\(982\) −7.94208 −0.253442
\(983\) 54.4740 1.73745 0.868725 0.495295i \(-0.164940\pi\)
0.868725 + 0.495295i \(0.164940\pi\)
\(984\) −23.5180 −0.749726
\(985\) −39.5315 −1.25958
\(986\) −0.0421847 −0.00134343
\(987\) −3.64355 −0.115975
\(988\) −0.715549 −0.0227646
\(989\) 8.30808 0.264182
\(990\) 1.85836 0.0590624
\(991\) −18.3507 −0.582930 −0.291465 0.956581i \(-0.594143\pi\)
−0.291465 + 0.956581i \(0.594143\pi\)
\(992\) −30.4205 −0.965852
\(993\) 24.8449 0.788430
\(994\) 3.53244 0.112042
\(995\) −8.07216 −0.255905
\(996\) −19.1652 −0.607273
\(997\) 8.20240 0.259773 0.129886 0.991529i \(-0.458539\pi\)
0.129886 + 0.991529i \(0.458539\pi\)
\(998\) 21.0427 0.666095
\(999\) −7.86861 −0.248952
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 4011.2.a.m.1.11 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.m.1.11 29 1.1 even 1 trivial