Properties

Label 8018.2.a.e.1.3
Level $8018$
Weight $2$
Character 8018.1
Self dual yes
Analytic conductor $64.024$
Analytic rank $1$
Dimension $32$
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] = [8018,2,Mod(1,8018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.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: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(32\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 8018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.87951 q^{3} +1.00000 q^{4} -0.727191 q^{5} -2.87951 q^{6} -4.06984 q^{7} +1.00000 q^{8} +5.29156 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.87951 q^{3} +1.00000 q^{4} -0.727191 q^{5} -2.87951 q^{6} -4.06984 q^{7} +1.00000 q^{8} +5.29156 q^{9} -0.727191 q^{10} +3.61815 q^{11} -2.87951 q^{12} +1.25152 q^{13} -4.06984 q^{14} +2.09395 q^{15} +1.00000 q^{16} -2.13118 q^{17} +5.29156 q^{18} -1.00000 q^{19} -0.727191 q^{20} +11.7191 q^{21} +3.61815 q^{22} -5.63090 q^{23} -2.87951 q^{24} -4.47119 q^{25} +1.25152 q^{26} -6.59857 q^{27} -4.06984 q^{28} +0.443419 q^{29} +2.09395 q^{30} +8.17728 q^{31} +1.00000 q^{32} -10.4185 q^{33} -2.13118 q^{34} +2.95955 q^{35} +5.29156 q^{36} +0.0414686 q^{37} -1.00000 q^{38} -3.60376 q^{39} -0.727191 q^{40} -2.66115 q^{41} +11.7191 q^{42} +0.595822 q^{43} +3.61815 q^{44} -3.84798 q^{45} -5.63090 q^{46} +8.94221 q^{47} -2.87951 q^{48} +9.56364 q^{49} -4.47119 q^{50} +6.13674 q^{51} +1.25152 q^{52} -5.80482 q^{53} -6.59857 q^{54} -2.63109 q^{55} -4.06984 q^{56} +2.87951 q^{57} +0.443419 q^{58} +10.8913 q^{59} +2.09395 q^{60} -6.38286 q^{61} +8.17728 q^{62} -21.5358 q^{63} +1.00000 q^{64} -0.910093 q^{65} -10.4185 q^{66} +11.4714 q^{67} -2.13118 q^{68} +16.2142 q^{69} +2.95955 q^{70} -3.38669 q^{71} +5.29156 q^{72} -0.0581009 q^{73} +0.0414686 q^{74} +12.8748 q^{75} -1.00000 q^{76} -14.7253 q^{77} -3.60376 q^{78} -2.17699 q^{79} -0.727191 q^{80} +3.12595 q^{81} -2.66115 q^{82} +3.33356 q^{83} +11.7191 q^{84} +1.54977 q^{85} +0.595822 q^{86} -1.27683 q^{87} +3.61815 q^{88} +13.4876 q^{89} -3.84798 q^{90} -5.09349 q^{91} -5.63090 q^{92} -23.5465 q^{93} +8.94221 q^{94} +0.727191 q^{95} -2.87951 q^{96} -3.24683 q^{97} +9.56364 q^{98} +19.1457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.87951 −1.66248 −0.831242 0.555910i \(-0.812370\pi\)
−0.831242 + 0.555910i \(0.812370\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.727191 −0.325210 −0.162605 0.986691i \(-0.551990\pi\)
−0.162605 + 0.986691i \(0.551990\pi\)
\(6\) −2.87951 −1.17555
\(7\) −4.06984 −1.53826 −0.769128 0.639094i \(-0.779309\pi\)
−0.769128 + 0.639094i \(0.779309\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.29156 1.76385
\(10\) −0.727191 −0.229958
\(11\) 3.61815 1.09091 0.545457 0.838139i \(-0.316356\pi\)
0.545457 + 0.838139i \(0.316356\pi\)
\(12\) −2.87951 −0.831242
\(13\) 1.25152 0.347109 0.173554 0.984824i \(-0.444475\pi\)
0.173554 + 0.984824i \(0.444475\pi\)
\(14\) −4.06984 −1.08771
\(15\) 2.09395 0.540656
\(16\) 1.00000 0.250000
\(17\) −2.13118 −0.516886 −0.258443 0.966026i \(-0.583209\pi\)
−0.258443 + 0.966026i \(0.583209\pi\)
\(18\) 5.29156 1.24723
\(19\) −1.00000 −0.229416
\(20\) −0.727191 −0.162605
\(21\) 11.7191 2.55733
\(22\) 3.61815 0.771392
\(23\) −5.63090 −1.17412 −0.587062 0.809542i \(-0.699716\pi\)
−0.587062 + 0.809542i \(0.699716\pi\)
\(24\) −2.87951 −0.587777
\(25\) −4.47119 −0.894239
\(26\) 1.25152 0.245443
\(27\) −6.59857 −1.26990
\(28\) −4.06984 −0.769128
\(29\) 0.443419 0.0823408 0.0411704 0.999152i \(-0.486891\pi\)
0.0411704 + 0.999152i \(0.486891\pi\)
\(30\) 2.09395 0.382302
\(31\) 8.17728 1.46868 0.734341 0.678780i \(-0.237491\pi\)
0.734341 + 0.678780i \(0.237491\pi\)
\(32\) 1.00000 0.176777
\(33\) −10.4185 −1.81363
\(34\) −2.13118 −0.365494
\(35\) 2.95955 0.500256
\(36\) 5.29156 0.881927
\(37\) 0.0414686 0.00681740 0.00340870 0.999994i \(-0.498915\pi\)
0.00340870 + 0.999994i \(0.498915\pi\)
\(38\) −1.00000 −0.162221
\(39\) −3.60376 −0.577063
\(40\) −0.727191 −0.114979
\(41\) −2.66115 −0.415601 −0.207801 0.978171i \(-0.566631\pi\)
−0.207801 + 0.978171i \(0.566631\pi\)
\(42\) 11.7191 1.80830
\(43\) 0.595822 0.0908620 0.0454310 0.998967i \(-0.485534\pi\)
0.0454310 + 0.998967i \(0.485534\pi\)
\(44\) 3.61815 0.545457
\(45\) −3.84798 −0.573623
\(46\) −5.63090 −0.830231
\(47\) 8.94221 1.30436 0.652178 0.758066i \(-0.273856\pi\)
0.652178 + 0.758066i \(0.273856\pi\)
\(48\) −2.87951 −0.415621
\(49\) 9.56364 1.36623
\(50\) −4.47119 −0.632322
\(51\) 6.13674 0.859315
\(52\) 1.25152 0.173554
\(53\) −5.80482 −0.797353 −0.398677 0.917092i \(-0.630530\pi\)
−0.398677 + 0.917092i \(0.630530\pi\)
\(54\) −6.59857 −0.897952
\(55\) −2.63109 −0.354776
\(56\) −4.06984 −0.543856
\(57\) 2.87951 0.381400
\(58\) 0.443419 0.0582237
\(59\) 10.8913 1.41792 0.708960 0.705249i \(-0.249165\pi\)
0.708960 + 0.705249i \(0.249165\pi\)
\(60\) 2.09395 0.270328
\(61\) −6.38286 −0.817242 −0.408621 0.912704i \(-0.633990\pi\)
−0.408621 + 0.912704i \(0.633990\pi\)
\(62\) 8.17728 1.03852
\(63\) −21.5358 −2.71326
\(64\) 1.00000 0.125000
\(65\) −0.910093 −0.112883
\(66\) −10.4185 −1.28243
\(67\) 11.4714 1.40146 0.700728 0.713428i \(-0.252859\pi\)
0.700728 + 0.713428i \(0.252859\pi\)
\(68\) −2.13118 −0.258443
\(69\) 16.2142 1.95196
\(70\) 2.95955 0.353734
\(71\) −3.38669 −0.401926 −0.200963 0.979599i \(-0.564407\pi\)
−0.200963 + 0.979599i \(0.564407\pi\)
\(72\) 5.29156 0.623617
\(73\) −0.0581009 −0.00680019 −0.00340010 0.999994i \(-0.501082\pi\)
−0.00340010 + 0.999994i \(0.501082\pi\)
\(74\) 0.0414686 0.00482063
\(75\) 12.8748 1.48666
\(76\) −1.00000 −0.114708
\(77\) −14.7253 −1.67810
\(78\) −3.60376 −0.408045
\(79\) −2.17699 −0.244930 −0.122465 0.992473i \(-0.539080\pi\)
−0.122465 + 0.992473i \(0.539080\pi\)
\(80\) −0.727191 −0.0813024
\(81\) 3.12595 0.347328
\(82\) −2.66115 −0.293874
\(83\) 3.33356 0.365905 0.182953 0.983122i \(-0.441434\pi\)
0.182953 + 0.983122i \(0.441434\pi\)
\(84\) 11.7191 1.27866
\(85\) 1.54977 0.168096
\(86\) 0.595822 0.0642491
\(87\) −1.27683 −0.136890
\(88\) 3.61815 0.385696
\(89\) 13.4876 1.42969 0.714844 0.699284i \(-0.246498\pi\)
0.714844 + 0.699284i \(0.246498\pi\)
\(90\) −3.84798 −0.405612
\(91\) −5.09349 −0.533943
\(92\) −5.63090 −0.587062
\(93\) −23.5465 −2.44166
\(94\) 8.94221 0.922319
\(95\) 0.727191 0.0746082
\(96\) −2.87951 −0.293889
\(97\) −3.24683 −0.329666 −0.164833 0.986321i \(-0.552709\pi\)
−0.164833 + 0.986321i \(0.552709\pi\)
\(98\) 9.56364 0.966073
\(99\) 19.1457 1.92421
\(100\) −4.47119 −0.447119
\(101\) 2.82422 0.281021 0.140510 0.990079i \(-0.455126\pi\)
0.140510 + 0.990079i \(0.455126\pi\)
\(102\) 6.13674 0.607628
\(103\) −9.44507 −0.930651 −0.465325 0.885140i \(-0.654063\pi\)
−0.465325 + 0.885140i \(0.654063\pi\)
\(104\) 1.25152 0.122722
\(105\) −8.52206 −0.831668
\(106\) −5.80482 −0.563814
\(107\) 3.86570 0.373712 0.186856 0.982387i \(-0.440170\pi\)
0.186856 + 0.982387i \(0.440170\pi\)
\(108\) −6.59857 −0.634948
\(109\) 9.32825 0.893485 0.446742 0.894663i \(-0.352584\pi\)
0.446742 + 0.894663i \(0.352584\pi\)
\(110\) −2.63109 −0.250864
\(111\) −0.119409 −0.0113338
\(112\) −4.06984 −0.384564
\(113\) −0.836958 −0.0787344 −0.0393672 0.999225i \(-0.512534\pi\)
−0.0393672 + 0.999225i \(0.512534\pi\)
\(114\) 2.87951 0.269691
\(115\) 4.09474 0.381837
\(116\) 0.443419 0.0411704
\(117\) 6.62249 0.612250
\(118\) 10.8913 1.00262
\(119\) 8.67356 0.795104
\(120\) 2.09395 0.191151
\(121\) 2.09101 0.190092
\(122\) −6.38286 −0.577877
\(123\) 7.66279 0.690931
\(124\) 8.17728 0.734341
\(125\) 6.88737 0.616025
\(126\) −21.5358 −1.91857
\(127\) −3.18628 −0.282736 −0.141368 0.989957i \(-0.545150\pi\)
−0.141368 + 0.989957i \(0.545150\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.71567 −0.151057
\(130\) −0.910093 −0.0798205
\(131\) −3.63269 −0.317389 −0.158695 0.987328i \(-0.550729\pi\)
−0.158695 + 0.987328i \(0.550729\pi\)
\(132\) −10.4185 −0.906813
\(133\) 4.06984 0.352900
\(134\) 11.4714 0.990979
\(135\) 4.79842 0.412983
\(136\) −2.13118 −0.182747
\(137\) −17.3661 −1.48368 −0.741841 0.670576i \(-0.766047\pi\)
−0.741841 + 0.670576i \(0.766047\pi\)
\(138\) 16.2142 1.38025
\(139\) 4.12808 0.350139 0.175069 0.984556i \(-0.443985\pi\)
0.175069 + 0.984556i \(0.443985\pi\)
\(140\) 2.95955 0.250128
\(141\) −25.7492 −2.16847
\(142\) −3.38669 −0.284205
\(143\) 4.52818 0.378666
\(144\) 5.29156 0.440964
\(145\) −0.322450 −0.0267780
\(146\) −0.0581009 −0.00480846
\(147\) −27.5386 −2.27134
\(148\) 0.0414686 0.00340870
\(149\) 9.75805 0.799411 0.399705 0.916644i \(-0.369112\pi\)
0.399705 + 0.916644i \(0.369112\pi\)
\(150\) 12.8748 1.05123
\(151\) 5.86077 0.476943 0.238471 0.971150i \(-0.423354\pi\)
0.238471 + 0.971150i \(0.423354\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −11.2773 −0.911712
\(154\) −14.7253 −1.18660
\(155\) −5.94644 −0.477630
\(156\) −3.60376 −0.288532
\(157\) −0.0193246 −0.00154227 −0.000771136 1.00000i \(-0.500245\pi\)
−0.000771136 1.00000i \(0.500245\pi\)
\(158\) −2.17699 −0.173192
\(159\) 16.7150 1.32559
\(160\) −0.727191 −0.0574895
\(161\) 22.9169 1.80610
\(162\) 3.12595 0.245598
\(163\) 8.32582 0.652129 0.326064 0.945348i \(-0.394277\pi\)
0.326064 + 0.945348i \(0.394277\pi\)
\(164\) −2.66115 −0.207801
\(165\) 7.57623 0.589809
\(166\) 3.33356 0.258734
\(167\) −13.2062 −1.02192 −0.510962 0.859603i \(-0.670711\pi\)
−0.510962 + 0.859603i \(0.670711\pi\)
\(168\) 11.7191 0.904152
\(169\) −11.4337 −0.879515
\(170\) 1.54977 0.118862
\(171\) −5.29156 −0.404656
\(172\) 0.595822 0.0454310
\(173\) 11.3203 0.860664 0.430332 0.902671i \(-0.358396\pi\)
0.430332 + 0.902671i \(0.358396\pi\)
\(174\) −1.27683 −0.0967961
\(175\) 18.1971 1.37557
\(176\) 3.61815 0.272728
\(177\) −31.3614 −2.35727
\(178\) 13.4876 1.01094
\(179\) −17.2073 −1.28613 −0.643067 0.765810i \(-0.722338\pi\)
−0.643067 + 0.765810i \(0.722338\pi\)
\(180\) −3.84798 −0.286811
\(181\) −1.10634 −0.0822333 −0.0411167 0.999154i \(-0.513092\pi\)
−0.0411167 + 0.999154i \(0.513092\pi\)
\(182\) −5.09349 −0.377554
\(183\) 18.3795 1.35865
\(184\) −5.63090 −0.415116
\(185\) −0.0301556 −0.00221708
\(186\) −23.5465 −1.72652
\(187\) −7.71092 −0.563878
\(188\) 8.94221 0.652178
\(189\) 26.8552 1.95343
\(190\) 0.727191 0.0527560
\(191\) 17.6307 1.27572 0.637858 0.770154i \(-0.279821\pi\)
0.637858 + 0.770154i \(0.279821\pi\)
\(192\) −2.87951 −0.207811
\(193\) −12.4341 −0.895029 −0.447514 0.894277i \(-0.647691\pi\)
−0.447514 + 0.894277i \(0.647691\pi\)
\(194\) −3.24683 −0.233109
\(195\) 2.62062 0.187667
\(196\) 9.56364 0.683117
\(197\) −9.18547 −0.654438 −0.327219 0.944949i \(-0.606111\pi\)
−0.327219 + 0.944949i \(0.606111\pi\)
\(198\) 19.1457 1.36062
\(199\) −2.41467 −0.171172 −0.0855858 0.996331i \(-0.527276\pi\)
−0.0855858 + 0.996331i \(0.527276\pi\)
\(200\) −4.47119 −0.316161
\(201\) −33.0320 −2.32990
\(202\) 2.82422 0.198712
\(203\) −1.80465 −0.126661
\(204\) 6.13674 0.429658
\(205\) 1.93516 0.135158
\(206\) −9.44507 −0.658070
\(207\) −29.7963 −2.07098
\(208\) 1.25152 0.0867772
\(209\) −3.61815 −0.250273
\(210\) −8.52206 −0.588078
\(211\) 1.00000 0.0688428
\(212\) −5.80482 −0.398677
\(213\) 9.75200 0.668196
\(214\) 3.86570 0.264254
\(215\) −0.433276 −0.0295492
\(216\) −6.59857 −0.448976
\(217\) −33.2803 −2.25921
\(218\) 9.32825 0.631789
\(219\) 0.167302 0.0113052
\(220\) −2.63109 −0.177388
\(221\) −2.66721 −0.179416
\(222\) −0.119409 −0.00801422
\(223\) 5.31025 0.355601 0.177800 0.984067i \(-0.443102\pi\)
0.177800 + 0.984067i \(0.443102\pi\)
\(224\) −4.06984 −0.271928
\(225\) −23.6596 −1.57731
\(226\) −0.836958 −0.0556736
\(227\) 2.23883 0.148596 0.0742982 0.997236i \(-0.476328\pi\)
0.0742982 + 0.997236i \(0.476328\pi\)
\(228\) 2.87951 0.190700
\(229\) −11.3240 −0.748311 −0.374156 0.927366i \(-0.622067\pi\)
−0.374156 + 0.927366i \(0.622067\pi\)
\(230\) 4.09474 0.269999
\(231\) 42.4016 2.78982
\(232\) 0.443419 0.0291119
\(233\) −28.2061 −1.84784 −0.923921 0.382584i \(-0.875034\pi\)
−0.923921 + 0.382584i \(0.875034\pi\)
\(234\) 6.62249 0.432926
\(235\) −6.50270 −0.424189
\(236\) 10.8913 0.708960
\(237\) 6.26866 0.407193
\(238\) 8.67356 0.562223
\(239\) −21.9897 −1.42239 −0.711197 0.702992i \(-0.751847\pi\)
−0.711197 + 0.702992i \(0.751847\pi\)
\(240\) 2.09395 0.135164
\(241\) −9.92311 −0.639203 −0.319602 0.947552i \(-0.603549\pi\)
−0.319602 + 0.947552i \(0.603549\pi\)
\(242\) 2.09101 0.134415
\(243\) 10.7945 0.692468
\(244\) −6.38286 −0.408621
\(245\) −6.95459 −0.444313
\(246\) 7.66279 0.488562
\(247\) −1.25152 −0.0796322
\(248\) 8.17728 0.519258
\(249\) −9.59900 −0.608312
\(250\) 6.88737 0.435595
\(251\) −19.4864 −1.22997 −0.614986 0.788538i \(-0.710838\pi\)
−0.614986 + 0.788538i \(0.710838\pi\)
\(252\) −21.5358 −1.35663
\(253\) −20.3735 −1.28087
\(254\) −3.18628 −0.199925
\(255\) −4.46258 −0.279458
\(256\) 1.00000 0.0625000
\(257\) 0.644104 0.0401781 0.0200890 0.999798i \(-0.493605\pi\)
0.0200890 + 0.999798i \(0.493605\pi\)
\(258\) −1.71567 −0.106813
\(259\) −0.168771 −0.0104869
\(260\) −0.910093 −0.0564416
\(261\) 2.34638 0.145237
\(262\) −3.63269 −0.224428
\(263\) −0.0603677 −0.00372243 −0.00186121 0.999998i \(-0.500592\pi\)
−0.00186121 + 0.999998i \(0.500592\pi\)
\(264\) −10.4185 −0.641214
\(265\) 4.22121 0.259307
\(266\) 4.06984 0.249538
\(267\) −38.8378 −2.37683
\(268\) 11.4714 0.700728
\(269\) −9.66382 −0.589213 −0.294607 0.955619i \(-0.595189\pi\)
−0.294607 + 0.955619i \(0.595189\pi\)
\(270\) 4.79842 0.292023
\(271\) 8.86078 0.538254 0.269127 0.963105i \(-0.413265\pi\)
0.269127 + 0.963105i \(0.413265\pi\)
\(272\) −2.13118 −0.129222
\(273\) 14.6667 0.887671
\(274\) −17.3661 −1.04912
\(275\) −16.1774 −0.975537
\(276\) 16.2142 0.975982
\(277\) −14.2875 −0.858450 −0.429225 0.903198i \(-0.641213\pi\)
−0.429225 + 0.903198i \(0.641213\pi\)
\(278\) 4.12808 0.247586
\(279\) 43.2706 2.59054
\(280\) 2.95955 0.176867
\(281\) −5.91818 −0.353049 −0.176524 0.984296i \(-0.556485\pi\)
−0.176524 + 0.984296i \(0.556485\pi\)
\(282\) −25.7492 −1.53334
\(283\) −13.7719 −0.818652 −0.409326 0.912388i \(-0.634236\pi\)
−0.409326 + 0.912388i \(0.634236\pi\)
\(284\) −3.38669 −0.200963
\(285\) −2.09395 −0.124035
\(286\) 4.52818 0.267757
\(287\) 10.8305 0.639301
\(288\) 5.29156 0.311808
\(289\) −12.4581 −0.732829
\(290\) −0.322450 −0.0189349
\(291\) 9.34929 0.548065
\(292\) −0.0581009 −0.00340010
\(293\) −18.6214 −1.08787 −0.543937 0.839126i \(-0.683067\pi\)
−0.543937 + 0.839126i \(0.683067\pi\)
\(294\) −27.5386 −1.60608
\(295\) −7.92002 −0.461122
\(296\) 0.0414686 0.00241031
\(297\) −23.8746 −1.38535
\(298\) 9.75805 0.565269
\(299\) −7.04718 −0.407549
\(300\) 12.8748 0.743329
\(301\) −2.42490 −0.139769
\(302\) 5.86077 0.337249
\(303\) −8.13237 −0.467192
\(304\) −1.00000 −0.0573539
\(305\) 4.64156 0.265775
\(306\) −11.2773 −0.644678
\(307\) 14.2345 0.812408 0.406204 0.913782i \(-0.366852\pi\)
0.406204 + 0.913782i \(0.366852\pi\)
\(308\) −14.7253 −0.839052
\(309\) 27.1972 1.54719
\(310\) −5.94644 −0.337735
\(311\) 7.14179 0.404974 0.202487 0.979285i \(-0.435098\pi\)
0.202487 + 0.979285i \(0.435098\pi\)
\(312\) −3.60376 −0.204023
\(313\) −28.6539 −1.61961 −0.809806 0.586698i \(-0.800428\pi\)
−0.809806 + 0.586698i \(0.800428\pi\)
\(314\) −0.0193246 −0.00109055
\(315\) 15.6607 0.882379
\(316\) −2.17699 −0.122465
\(317\) −21.7416 −1.22113 −0.610564 0.791967i \(-0.709057\pi\)
−0.610564 + 0.791967i \(0.709057\pi\)
\(318\) 16.7150 0.937332
\(319\) 1.60436 0.0898267
\(320\) −0.727191 −0.0406512
\(321\) −11.1313 −0.621290
\(322\) 22.9169 1.27711
\(323\) 2.13118 0.118582
\(324\) 3.12595 0.173664
\(325\) −5.59578 −0.310398
\(326\) 8.32582 0.461125
\(327\) −26.8608 −1.48540
\(328\) −2.66115 −0.146937
\(329\) −36.3934 −2.00643
\(330\) 7.57623 0.417058
\(331\) −30.5077 −1.67685 −0.838426 0.545015i \(-0.816524\pi\)
−0.838426 + 0.545015i \(0.816524\pi\)
\(332\) 3.33356 0.182953
\(333\) 0.219434 0.0120249
\(334\) −13.2062 −0.722609
\(335\) −8.34191 −0.455767
\(336\) 11.7191 0.639332
\(337\) −1.44029 −0.0784574 −0.0392287 0.999230i \(-0.512490\pi\)
−0.0392287 + 0.999230i \(0.512490\pi\)
\(338\) −11.4337 −0.621911
\(339\) 2.41003 0.130895
\(340\) 1.54977 0.0840482
\(341\) 29.5866 1.60221
\(342\) −5.29156 −0.286135
\(343\) −10.4336 −0.563362
\(344\) 0.595822 0.0321246
\(345\) −11.7908 −0.634798
\(346\) 11.3203 0.608582
\(347\) −18.2248 −0.978360 −0.489180 0.872183i \(-0.662704\pi\)
−0.489180 + 0.872183i \(0.662704\pi\)
\(348\) −1.27683 −0.0684452
\(349\) −7.30817 −0.391197 −0.195599 0.980684i \(-0.562665\pi\)
−0.195599 + 0.980684i \(0.562665\pi\)
\(350\) 18.1971 0.972674
\(351\) −8.25824 −0.440792
\(352\) 3.61815 0.192848
\(353\) −23.4595 −1.24862 −0.624312 0.781175i \(-0.714621\pi\)
−0.624312 + 0.781175i \(0.714621\pi\)
\(354\) −31.3614 −1.66684
\(355\) 2.46277 0.130710
\(356\) 13.4876 0.714844
\(357\) −24.9756 −1.32185
\(358\) −17.2073 −0.909434
\(359\) 30.3218 1.60032 0.800161 0.599785i \(-0.204747\pi\)
0.800161 + 0.599785i \(0.204747\pi\)
\(360\) −3.84798 −0.202806
\(361\) 1.00000 0.0526316
\(362\) −1.10634 −0.0581477
\(363\) −6.02109 −0.316025
\(364\) −5.09349 −0.266971
\(365\) 0.0422504 0.00221149
\(366\) 18.3795 0.960712
\(367\) −12.2097 −0.637339 −0.318670 0.947866i \(-0.603236\pi\)
−0.318670 + 0.947866i \(0.603236\pi\)
\(368\) −5.63090 −0.293531
\(369\) −14.0816 −0.733060
\(370\) −0.0301556 −0.00156772
\(371\) 23.6247 1.22653
\(372\) −23.5465 −1.22083
\(373\) 31.6590 1.63924 0.819621 0.572906i \(-0.194184\pi\)
0.819621 + 0.572906i \(0.194184\pi\)
\(374\) −7.71092 −0.398722
\(375\) −19.8322 −1.02413
\(376\) 8.94221 0.461159
\(377\) 0.554947 0.0285812
\(378\) 26.8552 1.38128
\(379\) −0.430657 −0.0221213 −0.0110607 0.999939i \(-0.503521\pi\)
−0.0110607 + 0.999939i \(0.503521\pi\)
\(380\) 0.727191 0.0373041
\(381\) 9.17491 0.470045
\(382\) 17.6307 0.902067
\(383\) −7.69215 −0.393050 −0.196525 0.980499i \(-0.562966\pi\)
−0.196525 + 0.980499i \(0.562966\pi\)
\(384\) −2.87951 −0.146944
\(385\) 10.7081 0.545736
\(386\) −12.4341 −0.632881
\(387\) 3.15283 0.160267
\(388\) −3.24683 −0.164833
\(389\) −3.32939 −0.168807 −0.0844034 0.996432i \(-0.526898\pi\)
−0.0844034 + 0.996432i \(0.526898\pi\)
\(390\) 2.62062 0.132700
\(391\) 12.0004 0.606889
\(392\) 9.56364 0.483037
\(393\) 10.4604 0.527655
\(394\) −9.18547 −0.462757
\(395\) 1.58309 0.0796538
\(396\) 19.1457 0.962106
\(397\) 31.1952 1.56564 0.782821 0.622247i \(-0.213780\pi\)
0.782821 + 0.622247i \(0.213780\pi\)
\(398\) −2.41467 −0.121037
\(399\) −11.7191 −0.586691
\(400\) −4.47119 −0.223560
\(401\) −22.8724 −1.14219 −0.571097 0.820883i \(-0.693482\pi\)
−0.571097 + 0.820883i \(0.693482\pi\)
\(402\) −33.0320 −1.64749
\(403\) 10.2340 0.509793
\(404\) 2.82422 0.140510
\(405\) −2.27317 −0.112955
\(406\) −1.80465 −0.0895631
\(407\) 0.150040 0.00743719
\(408\) 6.13674 0.303814
\(409\) 15.5779 0.770276 0.385138 0.922859i \(-0.374154\pi\)
0.385138 + 0.922859i \(0.374154\pi\)
\(410\) 1.93516 0.0955708
\(411\) 50.0057 2.46660
\(412\) −9.44507 −0.465325
\(413\) −44.3257 −2.18113
\(414\) −29.7963 −1.46441
\(415\) −2.42413 −0.118996
\(416\) 1.25152 0.0613608
\(417\) −11.8868 −0.582100
\(418\) −3.61815 −0.176970
\(419\) 22.7946 1.11359 0.556795 0.830650i \(-0.312031\pi\)
0.556795 + 0.830650i \(0.312031\pi\)
\(420\) −8.52206 −0.415834
\(421\) −3.48327 −0.169764 −0.0848822 0.996391i \(-0.527051\pi\)
−0.0848822 + 0.996391i \(0.527051\pi\)
\(422\) 1.00000 0.0486792
\(423\) 47.3183 2.30069
\(424\) −5.80482 −0.281907
\(425\) 9.52890 0.462220
\(426\) 9.75200 0.472486
\(427\) 25.9773 1.25713
\(428\) 3.86570 0.186856
\(429\) −13.0389 −0.629526
\(430\) −0.433276 −0.0208944
\(431\) −13.5984 −0.655014 −0.327507 0.944849i \(-0.606208\pi\)
−0.327507 + 0.944849i \(0.606208\pi\)
\(432\) −6.59857 −0.317474
\(433\) 18.4255 0.885474 0.442737 0.896652i \(-0.354008\pi\)
0.442737 + 0.896652i \(0.354008\pi\)
\(434\) −33.2803 −1.59750
\(435\) 0.928498 0.0445181
\(436\) 9.32825 0.446742
\(437\) 5.63090 0.269363
\(438\) 0.167302 0.00799399
\(439\) −6.20274 −0.296041 −0.148020 0.988984i \(-0.547290\pi\)
−0.148020 + 0.988984i \(0.547290\pi\)
\(440\) −2.63109 −0.125432
\(441\) 50.6066 2.40984
\(442\) −2.66721 −0.126866
\(443\) 28.2064 1.34013 0.670064 0.742303i \(-0.266267\pi\)
0.670064 + 0.742303i \(0.266267\pi\)
\(444\) −0.119409 −0.00566691
\(445\) −9.80810 −0.464948
\(446\) 5.31025 0.251448
\(447\) −28.0984 −1.32901
\(448\) −4.06984 −0.192282
\(449\) 5.81064 0.274221 0.137111 0.990556i \(-0.456218\pi\)
0.137111 + 0.990556i \(0.456218\pi\)
\(450\) −23.6596 −1.11532
\(451\) −9.62843 −0.453385
\(452\) −0.836958 −0.0393672
\(453\) −16.8761 −0.792910
\(454\) 2.23883 0.105074
\(455\) 3.70394 0.173643
\(456\) 2.87951 0.134845
\(457\) 10.2851 0.481115 0.240557 0.970635i \(-0.422670\pi\)
0.240557 + 0.970635i \(0.422670\pi\)
\(458\) −11.3240 −0.529136
\(459\) 14.0627 0.656392
\(460\) 4.09474 0.190918
\(461\) −33.1091 −1.54205 −0.771023 0.636808i \(-0.780255\pi\)
−0.771023 + 0.636808i \(0.780255\pi\)
\(462\) 42.4016 1.97270
\(463\) 5.33782 0.248070 0.124035 0.992278i \(-0.460417\pi\)
0.124035 + 0.992278i \(0.460417\pi\)
\(464\) 0.443419 0.0205852
\(465\) 17.1228 0.794052
\(466\) −28.2061 −1.30662
\(467\) −1.53163 −0.0708753 −0.0354377 0.999372i \(-0.511283\pi\)
−0.0354377 + 0.999372i \(0.511283\pi\)
\(468\) 6.62249 0.306125
\(469\) −46.6869 −2.15580
\(470\) −6.50270 −0.299947
\(471\) 0.0556453 0.00256400
\(472\) 10.8913 0.501311
\(473\) 2.15577 0.0991225
\(474\) 6.26866 0.287929
\(475\) 4.47119 0.205152
\(476\) 8.67356 0.397552
\(477\) −30.7166 −1.40641
\(478\) −21.9897 −1.00578
\(479\) 3.56502 0.162890 0.0814449 0.996678i \(-0.474047\pi\)
0.0814449 + 0.996678i \(0.474047\pi\)
\(480\) 2.09395 0.0955754
\(481\) 0.0518988 0.00236638
\(482\) −9.92311 −0.451985
\(483\) −65.9894 −3.00262
\(484\) 2.09101 0.0950461
\(485\) 2.36107 0.107211
\(486\) 10.7945 0.489649
\(487\) −10.4722 −0.474539 −0.237270 0.971444i \(-0.576253\pi\)
−0.237270 + 0.971444i \(0.576253\pi\)
\(488\) −6.38286 −0.288939
\(489\) −23.9743 −1.08415
\(490\) −6.95459 −0.314176
\(491\) −12.1043 −0.546258 −0.273129 0.961977i \(-0.588059\pi\)
−0.273129 + 0.961977i \(0.588059\pi\)
\(492\) 7.66279 0.345465
\(493\) −0.945004 −0.0425608
\(494\) −1.25152 −0.0563085
\(495\) −13.9226 −0.625773
\(496\) 8.17728 0.367171
\(497\) 13.7833 0.618266
\(498\) −9.59900 −0.430142
\(499\) −2.11949 −0.0948813 −0.0474407 0.998874i \(-0.515107\pi\)
−0.0474407 + 0.998874i \(0.515107\pi\)
\(500\) 6.88737 0.308012
\(501\) 38.0273 1.69893
\(502\) −19.4864 −0.869721
\(503\) 9.18172 0.409393 0.204696 0.978826i \(-0.434379\pi\)
0.204696 + 0.978826i \(0.434379\pi\)
\(504\) −21.5358 −0.959283
\(505\) −2.05375 −0.0913906
\(506\) −20.3735 −0.905710
\(507\) 32.9234 1.46218
\(508\) −3.18628 −0.141368
\(509\) −27.0872 −1.20062 −0.600310 0.799768i \(-0.704956\pi\)
−0.600310 + 0.799768i \(0.704956\pi\)
\(510\) −4.46258 −0.197606
\(511\) 0.236462 0.0104604
\(512\) 1.00000 0.0441942
\(513\) 6.59857 0.291334
\(514\) 0.644104 0.0284102
\(515\) 6.86837 0.302657
\(516\) −1.71567 −0.0755283
\(517\) 32.3543 1.42294
\(518\) −0.168771 −0.00741536
\(519\) −32.5968 −1.43084
\(520\) −0.910093 −0.0399102
\(521\) 13.3292 0.583962 0.291981 0.956424i \(-0.405686\pi\)
0.291981 + 0.956424i \(0.405686\pi\)
\(522\) 2.34638 0.102698
\(523\) −13.2761 −0.580524 −0.290262 0.956947i \(-0.593743\pi\)
−0.290262 + 0.956947i \(0.593743\pi\)
\(524\) −3.63269 −0.158695
\(525\) −52.3986 −2.28686
\(526\) −0.0603677 −0.00263216
\(527\) −17.4272 −0.759142
\(528\) −10.4185 −0.453407
\(529\) 8.70707 0.378568
\(530\) 4.22121 0.183358
\(531\) 57.6318 2.50101
\(532\) 4.06984 0.176450
\(533\) −3.33048 −0.144259
\(534\) −38.8378 −1.68068
\(535\) −2.81111 −0.121535
\(536\) 11.4714 0.495490
\(537\) 49.5485 2.13818
\(538\) −9.66382 −0.416637
\(539\) 34.6027 1.49044
\(540\) 4.79842 0.206491
\(541\) −13.0079 −0.559254 −0.279627 0.960109i \(-0.590211\pi\)
−0.279627 + 0.960109i \(0.590211\pi\)
\(542\) 8.86078 0.380603
\(543\) 3.18570 0.136712
\(544\) −2.13118 −0.0913734
\(545\) −6.78342 −0.290570
\(546\) 14.6667 0.627678
\(547\) −41.0881 −1.75680 −0.878401 0.477925i \(-0.841389\pi\)
−0.878401 + 0.477925i \(0.841389\pi\)
\(548\) −17.3661 −0.741841
\(549\) −33.7753 −1.44150
\(550\) −16.1774 −0.689809
\(551\) −0.443419 −0.0188903
\(552\) 16.2142 0.690123
\(553\) 8.86001 0.376766
\(554\) −14.2875 −0.607016
\(555\) 0.0868333 0.00368587
\(556\) 4.12808 0.175069
\(557\) 0.106449 0.00451039 0.00225519 0.999997i \(-0.499282\pi\)
0.00225519 + 0.999997i \(0.499282\pi\)
\(558\) 43.2706 1.83179
\(559\) 0.745682 0.0315390
\(560\) 2.95955 0.125064
\(561\) 22.2036 0.937439
\(562\) −5.91818 −0.249643
\(563\) 1.13878 0.0479937 0.0239969 0.999712i \(-0.492361\pi\)
0.0239969 + 0.999712i \(0.492361\pi\)
\(564\) −25.7492 −1.08424
\(565\) 0.608629 0.0256052
\(566\) −13.7719 −0.578874
\(567\) −12.7222 −0.534280
\(568\) −3.38669 −0.142102
\(569\) −10.9775 −0.460199 −0.230099 0.973167i \(-0.573905\pi\)
−0.230099 + 0.973167i \(0.573905\pi\)
\(570\) −2.09395 −0.0877060
\(571\) −0.745682 −0.0312058 −0.0156029 0.999878i \(-0.504967\pi\)
−0.0156029 + 0.999878i \(0.504967\pi\)
\(572\) 4.52818 0.189333
\(573\) −50.7678 −2.12086
\(574\) 10.8305 0.452054
\(575\) 25.1769 1.04995
\(576\) 5.29156 0.220482
\(577\) −20.6012 −0.857640 −0.428820 0.903390i \(-0.641071\pi\)
−0.428820 + 0.903390i \(0.641071\pi\)
\(578\) −12.4581 −0.518188
\(579\) 35.8042 1.48797
\(580\) −0.322450 −0.0133890
\(581\) −13.5671 −0.562856
\(582\) 9.34929 0.387540
\(583\) −21.0027 −0.869843
\(584\) −0.0581009 −0.00240423
\(585\) −4.81582 −0.199110
\(586\) −18.6214 −0.769243
\(587\) 32.2233 1.33000 0.664999 0.746844i \(-0.268432\pi\)
0.664999 + 0.746844i \(0.268432\pi\)
\(588\) −27.5386 −1.13567
\(589\) −8.17728 −0.336939
\(590\) −7.92002 −0.326062
\(591\) 26.4496 1.08799
\(592\) 0.0414686 0.00170435
\(593\) −10.3355 −0.424430 −0.212215 0.977223i \(-0.568068\pi\)
−0.212215 + 0.977223i \(0.568068\pi\)
\(594\) −23.8746 −0.979588
\(595\) −6.30733 −0.258575
\(596\) 9.75805 0.399705
\(597\) 6.95307 0.284570
\(598\) −7.04718 −0.288181
\(599\) −15.9956 −0.653562 −0.326781 0.945100i \(-0.605964\pi\)
−0.326781 + 0.945100i \(0.605964\pi\)
\(600\) 12.8748 0.525613
\(601\) 39.0766 1.59397 0.796983 0.604002i \(-0.206428\pi\)
0.796983 + 0.604002i \(0.206428\pi\)
\(602\) −2.42490 −0.0988316
\(603\) 60.7017 2.47196
\(604\) 5.86077 0.238471
\(605\) −1.52057 −0.0618198
\(606\) −8.13237 −0.330355
\(607\) −11.8746 −0.481975 −0.240988 0.970528i \(-0.577471\pi\)
−0.240988 + 0.970528i \(0.577471\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 5.19649 0.210572
\(610\) 4.64156 0.187931
\(611\) 11.1913 0.452753
\(612\) −11.2773 −0.455856
\(613\) −43.5432 −1.75869 −0.879346 0.476184i \(-0.842020\pi\)
−0.879346 + 0.476184i \(0.842020\pi\)
\(614\) 14.2345 0.574459
\(615\) −5.57231 −0.224697
\(616\) −14.7253 −0.593300
\(617\) −40.7667 −1.64121 −0.820603 0.571499i \(-0.806362\pi\)
−0.820603 + 0.571499i \(0.806362\pi\)
\(618\) 27.1972 1.09403
\(619\) 18.8604 0.758064 0.379032 0.925384i \(-0.376257\pi\)
0.379032 + 0.925384i \(0.376257\pi\)
\(620\) −5.94644 −0.238815
\(621\) 37.1559 1.49102
\(622\) 7.14179 0.286360
\(623\) −54.8926 −2.19923
\(624\) −3.60376 −0.144266
\(625\) 17.3475 0.693901
\(626\) −28.6539 −1.14524
\(627\) 10.4185 0.416074
\(628\) −0.0193246 −0.000771136 0
\(629\) −0.0883769 −0.00352382
\(630\) 15.6607 0.623936
\(631\) 11.6827 0.465080 0.232540 0.972587i \(-0.425296\pi\)
0.232540 + 0.972587i \(0.425296\pi\)
\(632\) −2.17699 −0.0865960
\(633\) −2.87951 −0.114450
\(634\) −21.7416 −0.863467
\(635\) 2.31703 0.0919486
\(636\) 16.7150 0.662794
\(637\) 11.9691 0.474232
\(638\) 1.60436 0.0635171
\(639\) −17.9209 −0.708939
\(640\) −0.727191 −0.0287448
\(641\) −35.7350 −1.41145 −0.705723 0.708487i \(-0.749378\pi\)
−0.705723 + 0.708487i \(0.749378\pi\)
\(642\) −11.1313 −0.439318
\(643\) −46.6155 −1.83834 −0.919168 0.393867i \(-0.871137\pi\)
−0.919168 + 0.393867i \(0.871137\pi\)
\(644\) 22.9169 0.903052
\(645\) 1.24762 0.0491251
\(646\) 2.13118 0.0838500
\(647\) 16.3173 0.641501 0.320751 0.947164i \(-0.396065\pi\)
0.320751 + 0.947164i \(0.396065\pi\)
\(648\) 3.12595 0.122799
\(649\) 39.4062 1.54683
\(650\) −5.59578 −0.219485
\(651\) 95.8308 3.75590
\(652\) 8.32582 0.326064
\(653\) 27.1392 1.06204 0.531019 0.847360i \(-0.321809\pi\)
0.531019 + 0.847360i \(0.321809\pi\)
\(654\) −26.8608 −1.05034
\(655\) 2.64166 0.103218
\(656\) −2.66115 −0.103900
\(657\) −0.307444 −0.0119945
\(658\) −36.3934 −1.41876
\(659\) −7.66391 −0.298544 −0.149272 0.988796i \(-0.547693\pi\)
−0.149272 + 0.988796i \(0.547693\pi\)
\(660\) 7.57623 0.294905
\(661\) 23.2412 0.903976 0.451988 0.892024i \(-0.350715\pi\)
0.451988 + 0.892024i \(0.350715\pi\)
\(662\) −30.5077 −1.18571
\(663\) 7.68024 0.298276
\(664\) 3.33356 0.129367
\(665\) −2.95955 −0.114767
\(666\) 0.219434 0.00850289
\(667\) −2.49685 −0.0966784
\(668\) −13.2062 −0.510962
\(669\) −15.2909 −0.591181
\(670\) −8.34191 −0.322276
\(671\) −23.0942 −0.891540
\(672\) 11.7191 0.452076
\(673\) 25.5452 0.984696 0.492348 0.870399i \(-0.336139\pi\)
0.492348 + 0.870399i \(0.336139\pi\)
\(674\) −1.44029 −0.0554778
\(675\) 29.5035 1.13559
\(676\) −11.4337 −0.439758
\(677\) 22.6780 0.871585 0.435792 0.900047i \(-0.356468\pi\)
0.435792 + 0.900047i \(0.356468\pi\)
\(678\) 2.41003 0.0925566
\(679\) 13.2141 0.507111
\(680\) 1.54977 0.0594311
\(681\) −6.44673 −0.247039
\(682\) 29.5866 1.13293
\(683\) −13.8440 −0.529726 −0.264863 0.964286i \(-0.585327\pi\)
−0.264863 + 0.964286i \(0.585327\pi\)
\(684\) −5.29156 −0.202328
\(685\) 12.6284 0.482508
\(686\) −10.4336 −0.398357
\(687\) 32.6076 1.24406
\(688\) 0.595822 0.0227155
\(689\) −7.26484 −0.276768
\(690\) −11.7908 −0.448870
\(691\) −23.2928 −0.886100 −0.443050 0.896497i \(-0.646104\pi\)
−0.443050 + 0.896497i \(0.646104\pi\)
\(692\) 11.3203 0.430332
\(693\) −77.9199 −2.95993
\(694\) −18.2248 −0.691805
\(695\) −3.00190 −0.113869
\(696\) −1.27683 −0.0483980
\(697\) 5.67137 0.214819
\(698\) −7.30817 −0.276618
\(699\) 81.2196 3.07201
\(700\) 18.1971 0.687784
\(701\) −10.8702 −0.410563 −0.205281 0.978703i \(-0.565811\pi\)
−0.205281 + 0.978703i \(0.565811\pi\)
\(702\) −8.25824 −0.311687
\(703\) −0.0414686 −0.00156402
\(704\) 3.61815 0.136364
\(705\) 18.7246 0.705208
\(706\) −23.4595 −0.882911
\(707\) −11.4941 −0.432282
\(708\) −31.3614 −1.17864
\(709\) 8.42575 0.316436 0.158218 0.987404i \(-0.449425\pi\)
0.158218 + 0.987404i \(0.449425\pi\)
\(710\) 2.46277 0.0924261
\(711\) −11.5197 −0.432022
\(712\) 13.4876 0.505471
\(713\) −46.0455 −1.72442
\(714\) −24.9756 −0.934687
\(715\) −3.29286 −0.123146
\(716\) −17.2073 −0.643067
\(717\) 63.3195 2.36471
\(718\) 30.3218 1.13160
\(719\) −19.2836 −0.719157 −0.359578 0.933115i \(-0.617079\pi\)
−0.359578 + 0.933115i \(0.617079\pi\)
\(720\) −3.84798 −0.143406
\(721\) 38.4400 1.43158
\(722\) 1.00000 0.0372161
\(723\) 28.5737 1.06267
\(724\) −1.10634 −0.0411167
\(725\) −1.98261 −0.0736323
\(726\) −6.02109 −0.223464
\(727\) 16.1273 0.598128 0.299064 0.954233i \(-0.403326\pi\)
0.299064 + 0.954233i \(0.403326\pi\)
\(728\) −5.09349 −0.188777
\(729\) −40.4607 −1.49855
\(730\) 0.0422504 0.00156376
\(731\) −1.26980 −0.0469653
\(732\) 18.3795 0.679326
\(733\) 15.4925 0.572227 0.286113 0.958196i \(-0.407637\pi\)
0.286113 + 0.958196i \(0.407637\pi\)
\(734\) −12.2097 −0.450667
\(735\) 20.0258 0.738663
\(736\) −5.63090 −0.207558
\(737\) 41.5053 1.52887
\(738\) −14.0816 −0.518352
\(739\) −42.0235 −1.54586 −0.772929 0.634492i \(-0.781209\pi\)
−0.772929 + 0.634492i \(0.781209\pi\)
\(740\) −0.0301556 −0.00110854
\(741\) 3.60376 0.132387
\(742\) 23.6247 0.867290
\(743\) −12.5997 −0.462237 −0.231119 0.972926i \(-0.574239\pi\)
−0.231119 + 0.972926i \(0.574239\pi\)
\(744\) −23.5465 −0.863258
\(745\) −7.09597 −0.259976
\(746\) 31.6590 1.15912
\(747\) 17.6397 0.645404
\(748\) −7.71092 −0.281939
\(749\) −15.7328 −0.574865
\(750\) −19.8322 −0.724171
\(751\) 22.2269 0.811071 0.405536 0.914079i \(-0.367085\pi\)
0.405536 + 0.914079i \(0.367085\pi\)
\(752\) 8.94221 0.326089
\(753\) 56.1113 2.04481
\(754\) 0.554947 0.0202100
\(755\) −4.26190 −0.155106
\(756\) 26.8552 0.976713
\(757\) 16.6377 0.604708 0.302354 0.953196i \(-0.402228\pi\)
0.302354 + 0.953196i \(0.402228\pi\)
\(758\) −0.430657 −0.0156422
\(759\) 58.6655 2.12942
\(760\) 0.727191 0.0263780
\(761\) 2.68070 0.0971751 0.0485876 0.998819i \(-0.484528\pi\)
0.0485876 + 0.998819i \(0.484528\pi\)
\(762\) 9.17491 0.332372
\(763\) −37.9645 −1.37441
\(764\) 17.6307 0.637858
\(765\) 8.20072 0.296498
\(766\) −7.69215 −0.277929
\(767\) 13.6306 0.492173
\(768\) −2.87951 −0.103905
\(769\) 9.33180 0.336513 0.168257 0.985743i \(-0.446186\pi\)
0.168257 + 0.985743i \(0.446186\pi\)
\(770\) 10.7081 0.385894
\(771\) −1.85470 −0.0667955
\(772\) −12.4341 −0.447514
\(773\) 30.6134 1.10109 0.550544 0.834806i \(-0.314420\pi\)
0.550544 + 0.834806i \(0.314420\pi\)
\(774\) 3.15283 0.113326
\(775\) −36.5622 −1.31335
\(776\) −3.24683 −0.116555
\(777\) 0.485977 0.0174343
\(778\) −3.32939 −0.119364
\(779\) 2.66115 0.0953455
\(780\) 2.62062 0.0938333
\(781\) −12.2536 −0.438467
\(782\) 12.0004 0.429135
\(783\) −2.92593 −0.104564
\(784\) 9.56364 0.341558
\(785\) 0.0140527 0.000501562 0
\(786\) 10.4604 0.373108
\(787\) −44.4661 −1.58504 −0.792522 0.609843i \(-0.791232\pi\)
−0.792522 + 0.609843i \(0.791232\pi\)
\(788\) −9.18547 −0.327219
\(789\) 0.173829 0.00618848
\(790\) 1.58309 0.0563237
\(791\) 3.40629 0.121114
\(792\) 19.1457 0.680312
\(793\) −7.98827 −0.283672
\(794\) 31.1952 1.10708
\(795\) −12.1550 −0.431094
\(796\) −2.41467 −0.0855858
\(797\) −26.0737 −0.923579 −0.461789 0.886990i \(-0.652792\pi\)
−0.461789 + 0.886990i \(0.652792\pi\)
\(798\) −11.7191 −0.414853
\(799\) −19.0574 −0.674203
\(800\) −4.47119 −0.158081
\(801\) 71.3708 2.52176
\(802\) −22.8724 −0.807653
\(803\) −0.210218 −0.00741842
\(804\) −33.0320 −1.16495
\(805\) −16.6650 −0.587363
\(806\) 10.2340 0.360478
\(807\) 27.8270 0.979558
\(808\) 2.82422 0.0993558
\(809\) 56.0474 1.97052 0.985260 0.171061i \(-0.0547196\pi\)
0.985260 + 0.171061i \(0.0547196\pi\)
\(810\) −2.27317 −0.0798709
\(811\) 17.3713 0.609990 0.304995 0.952354i \(-0.401345\pi\)
0.304995 + 0.952354i \(0.401345\pi\)
\(812\) −1.80465 −0.0633307
\(813\) −25.5147 −0.894839
\(814\) 0.150040 0.00525889
\(815\) −6.05446 −0.212079
\(816\) 6.13674 0.214829
\(817\) −0.595822 −0.0208452
\(818\) 15.5779 0.544667
\(819\) −26.9525 −0.941797
\(820\) 1.93516 0.0675788
\(821\) 23.8709 0.833100 0.416550 0.909113i \(-0.363239\pi\)
0.416550 + 0.909113i \(0.363239\pi\)
\(822\) 50.0057 1.74415
\(823\) 30.6630 1.06885 0.534423 0.845217i \(-0.320529\pi\)
0.534423 + 0.845217i \(0.320529\pi\)
\(824\) −9.44507 −0.329035
\(825\) 46.5831 1.62181
\(826\) −44.3257 −1.54229
\(827\) −3.72261 −0.129448 −0.0647239 0.997903i \(-0.520617\pi\)
−0.0647239 + 0.997903i \(0.520617\pi\)
\(828\) −29.7963 −1.03549
\(829\) 30.8489 1.07143 0.535714 0.844400i \(-0.320043\pi\)
0.535714 + 0.844400i \(0.320043\pi\)
\(830\) −2.42413 −0.0841429
\(831\) 41.1408 1.42716
\(832\) 1.25152 0.0433886
\(833\) −20.3818 −0.706187
\(834\) −11.8868 −0.411607
\(835\) 9.60341 0.332340
\(836\) −3.61815 −0.125136
\(837\) −53.9584 −1.86507
\(838\) 22.7946 0.787427
\(839\) −1.73237 −0.0598079 −0.0299039 0.999553i \(-0.509520\pi\)
−0.0299039 + 0.999553i \(0.509520\pi\)
\(840\) −8.52206 −0.294039
\(841\) −28.8034 −0.993220
\(842\) −3.48327 −0.120042
\(843\) 17.0414 0.586938
\(844\) 1.00000 0.0344214
\(845\) 8.31449 0.286027
\(846\) 47.3183 1.62684
\(847\) −8.51010 −0.292411
\(848\) −5.80482 −0.199338
\(849\) 39.6562 1.36100
\(850\) 9.52890 0.326839
\(851\) −0.233506 −0.00800447
\(852\) 9.75200 0.334098
\(853\) 17.7543 0.607895 0.303948 0.952689i \(-0.401695\pi\)
0.303948 + 0.952689i \(0.401695\pi\)
\(854\) 25.9773 0.888923
\(855\) 3.84798 0.131598
\(856\) 3.86570 0.132127
\(857\) −30.0164 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(858\) −13.0389 −0.445142
\(859\) 20.4155 0.696568 0.348284 0.937389i \(-0.386765\pi\)
0.348284 + 0.937389i \(0.386765\pi\)
\(860\) −0.433276 −0.0147746
\(861\) −31.1864 −1.06283
\(862\) −13.5984 −0.463165
\(863\) 38.7224 1.31813 0.659063 0.752088i \(-0.270953\pi\)
0.659063 + 0.752088i \(0.270953\pi\)
\(864\) −6.59857 −0.224488
\(865\) −8.23200 −0.279896
\(866\) 18.4255 0.626124
\(867\) 35.8732 1.21832
\(868\) −33.2803 −1.12961
\(869\) −7.87667 −0.267198
\(870\) 0.928498 0.0314790
\(871\) 14.3567 0.486458
\(872\) 9.32825 0.315895
\(873\) −17.1808 −0.581483
\(874\) 5.63090 0.190468
\(875\) −28.0305 −0.947604
\(876\) 0.167302 0.00565261
\(877\) 8.77146 0.296191 0.148096 0.988973i \(-0.452686\pi\)
0.148096 + 0.988973i \(0.452686\pi\)
\(878\) −6.20274 −0.209332
\(879\) 53.6205 1.80857
\(880\) −2.63109 −0.0886939
\(881\) 34.1193 1.14951 0.574754 0.818326i \(-0.305098\pi\)
0.574754 + 0.818326i \(0.305098\pi\)
\(882\) 50.6066 1.70401
\(883\) 9.55329 0.321494 0.160747 0.986996i \(-0.448610\pi\)
0.160747 + 0.986996i \(0.448610\pi\)
\(884\) −2.66721 −0.0897079
\(885\) 22.8058 0.766607
\(886\) 28.2064 0.947614
\(887\) −46.7395 −1.56936 −0.784680 0.619901i \(-0.787173\pi\)
−0.784680 + 0.619901i \(0.787173\pi\)
\(888\) −0.119409 −0.00400711
\(889\) 12.9677 0.434921
\(890\) −9.80810 −0.328768
\(891\) 11.3102 0.378905
\(892\) 5.31025 0.177800
\(893\) −8.94221 −0.299240
\(894\) −28.0984 −0.939750
\(895\) 12.5130 0.418263
\(896\) −4.06984 −0.135964
\(897\) 20.2924 0.677544
\(898\) 5.81064 0.193904
\(899\) 3.62596 0.120933
\(900\) −23.6596 −0.788653
\(901\) 12.3711 0.412141
\(902\) −9.62843 −0.320592
\(903\) 6.98252 0.232364
\(904\) −0.836958 −0.0278368
\(905\) 0.804518 0.0267431
\(906\) −16.8761 −0.560672
\(907\) −12.2840 −0.407885 −0.203942 0.978983i \(-0.565376\pi\)
−0.203942 + 0.978983i \(0.565376\pi\)
\(908\) 2.23883 0.0742982
\(909\) 14.9445 0.495679
\(910\) 3.70394 0.122784
\(911\) −26.7451 −0.886106 −0.443053 0.896495i \(-0.646105\pi\)
−0.443053 + 0.896495i \(0.646105\pi\)
\(912\) 2.87951 0.0953500
\(913\) 12.0613 0.399171
\(914\) 10.2851 0.340199
\(915\) −13.3654 −0.441847
\(916\) −11.3240 −0.374156
\(917\) 14.7845 0.488226
\(918\) 14.0627 0.464139
\(919\) 2.88795 0.0952646 0.0476323 0.998865i \(-0.484832\pi\)
0.0476323 + 0.998865i \(0.484832\pi\)
\(920\) 4.09474 0.135000
\(921\) −40.9885 −1.35062
\(922\) −33.1091 −1.09039
\(923\) −4.23851 −0.139512
\(924\) 42.4016 1.39491
\(925\) −0.185414 −0.00609638
\(926\) 5.33782 0.175412
\(927\) −49.9792 −1.64153
\(928\) 0.443419 0.0145559
\(929\) −11.4850 −0.376810 −0.188405 0.982091i \(-0.560332\pi\)
−0.188405 + 0.982091i \(0.560332\pi\)
\(930\) 17.1228 0.561480
\(931\) −9.56364 −0.313436
\(932\) −28.2061 −0.923921
\(933\) −20.5648 −0.673263
\(934\) −1.53163 −0.0501164
\(935\) 5.60731 0.183379
\(936\) 6.62249 0.216463
\(937\) 30.1168 0.983872 0.491936 0.870631i \(-0.336289\pi\)
0.491936 + 0.870631i \(0.336289\pi\)
\(938\) −46.6869 −1.52438
\(939\) 82.5090 2.69258
\(940\) −6.50270 −0.212095
\(941\) −25.0710 −0.817292 −0.408646 0.912693i \(-0.633999\pi\)
−0.408646 + 0.912693i \(0.633999\pi\)
\(942\) 0.0556453 0.00181302
\(943\) 14.9847 0.487968
\(944\) 10.8913 0.354480
\(945\) −19.5288 −0.635273
\(946\) 2.15577 0.0700902
\(947\) −52.8944 −1.71884 −0.859419 0.511272i \(-0.829174\pi\)
−0.859419 + 0.511272i \(0.829174\pi\)
\(948\) 6.26866 0.203596
\(949\) −0.0727143 −0.00236041
\(950\) 4.47119 0.145065
\(951\) 62.6050 2.03011
\(952\) 8.67356 0.281112
\(953\) −12.0514 −0.390382 −0.195191 0.980765i \(-0.562533\pi\)
−0.195191 + 0.980765i \(0.562533\pi\)
\(954\) −30.7166 −0.994486
\(955\) −12.8209 −0.414875
\(956\) −21.9897 −0.711197
\(957\) −4.61976 −0.149335
\(958\) 3.56502 0.115181
\(959\) 70.6772 2.28228
\(960\) 2.09395 0.0675820
\(961\) 35.8679 1.15703
\(962\) 0.0518988 0.00167328
\(963\) 20.4556 0.659173
\(964\) −9.92311 −0.319602
\(965\) 9.04199 0.291072
\(966\) −65.9894 −2.12317
\(967\) −9.90806 −0.318622 −0.159311 0.987228i \(-0.550927\pi\)
−0.159311 + 0.987228i \(0.550927\pi\)
\(968\) 2.09101 0.0672077
\(969\) −6.13674 −0.197140
\(970\) 2.36107 0.0758094
\(971\) −1.45812 −0.0467932 −0.0233966 0.999726i \(-0.507448\pi\)
−0.0233966 + 0.999726i \(0.507448\pi\)
\(972\) 10.7945 0.346234
\(973\) −16.8006 −0.538604
\(974\) −10.4722 −0.335550
\(975\) 16.1131 0.516032
\(976\) −6.38286 −0.204310
\(977\) 4.69463 0.150195 0.0750973 0.997176i \(-0.476073\pi\)
0.0750973 + 0.997176i \(0.476073\pi\)
\(978\) −23.9743 −0.766612
\(979\) 48.8003 1.55967
\(980\) −6.95459 −0.222156
\(981\) 49.3610 1.57598
\(982\) −12.1043 −0.386263
\(983\) −39.8447 −1.27085 −0.635424 0.772163i \(-0.719175\pi\)
−0.635424 + 0.772163i \(0.719175\pi\)
\(984\) 7.66279 0.244281
\(985\) 6.67959 0.212830
\(986\) −0.945004 −0.0300950
\(987\) 104.795 3.33566
\(988\) −1.25152 −0.0398161
\(989\) −3.35501 −0.106683
\(990\) −13.9226 −0.442488
\(991\) −47.9852 −1.52430 −0.762150 0.647400i \(-0.775856\pi\)
−0.762150 + 0.647400i \(0.775856\pi\)
\(992\) 8.17728 0.259629
\(993\) 87.8471 2.78774
\(994\) 13.7833 0.437180
\(995\) 1.75593 0.0556667
\(996\) −9.59900 −0.304156
\(997\) 7.25910 0.229898 0.114949 0.993371i \(-0.463330\pi\)
0.114949 + 0.993371i \(0.463330\pi\)
\(998\) −2.11949 −0.0670912
\(999\) −0.273634 −0.00865739
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 8018.2.a.e.1.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8018.2.a.e.1.3 32 1.1 even 1 trivial