Properties

Label 8021.2.a.b.1.2
Level $8021$
Weight $2$
Character 8021.1
Self dual yes
Analytic conductor $64.048$
Analytic rank $1$
Dimension $140$
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] = [8021,2,Mod(1,8021)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8021, 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("8021.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8021 = 13 \cdot 617 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8021.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: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(140\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 8021.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.72092 q^{2} +2.93492 q^{3} +5.40338 q^{4} -0.339682 q^{5} -7.98568 q^{6} -0.916249 q^{7} -9.26032 q^{8} +5.61377 q^{9} +O(q^{10})\) \(q-2.72092 q^{2} +2.93492 q^{3} +5.40338 q^{4} -0.339682 q^{5} -7.98568 q^{6} -0.916249 q^{7} -9.26032 q^{8} +5.61377 q^{9} +0.924245 q^{10} -0.141261 q^{11} +15.8585 q^{12} -1.00000 q^{13} +2.49304 q^{14} -0.996939 q^{15} +14.3898 q^{16} -1.87864 q^{17} -15.2746 q^{18} +0.543254 q^{19} -1.83543 q^{20} -2.68912 q^{21} +0.384361 q^{22} +4.12163 q^{23} -27.1783 q^{24} -4.88462 q^{25} +2.72092 q^{26} +7.67121 q^{27} -4.95085 q^{28} +3.91353 q^{29} +2.71259 q^{30} -6.91321 q^{31} -20.6328 q^{32} -0.414592 q^{33} +5.11162 q^{34} +0.311233 q^{35} +30.3334 q^{36} -5.24871 q^{37} -1.47815 q^{38} -2.93492 q^{39} +3.14556 q^{40} +7.80986 q^{41} +7.31687 q^{42} +1.62979 q^{43} -0.763290 q^{44} -1.90689 q^{45} -11.2146 q^{46} +0.413613 q^{47} +42.2329 q^{48} -6.16049 q^{49} +13.2906 q^{50} -5.51367 q^{51} -5.40338 q^{52} -6.17696 q^{53} -20.8727 q^{54} +0.0479839 q^{55} +8.48476 q^{56} +1.59441 q^{57} -10.6484 q^{58} -11.2268 q^{59} -5.38685 q^{60} +4.33420 q^{61} +18.8103 q^{62} -5.14361 q^{63} +27.3605 q^{64} +0.339682 q^{65} +1.12807 q^{66} -4.97675 q^{67} -10.1510 q^{68} +12.0967 q^{69} -0.846839 q^{70} -11.4122 q^{71} -51.9853 q^{72} +2.14580 q^{73} +14.2813 q^{74} -14.3360 q^{75} +2.93541 q^{76} +0.129431 q^{77} +7.98568 q^{78} -8.27677 q^{79} -4.88795 q^{80} +5.67311 q^{81} -21.2500 q^{82} -8.73569 q^{83} -14.5304 q^{84} +0.638140 q^{85} -4.43451 q^{86} +11.4859 q^{87} +1.30813 q^{88} -0.171967 q^{89} +5.18850 q^{90} +0.916249 q^{91} +22.2707 q^{92} -20.2897 q^{93} -1.12541 q^{94} -0.184533 q^{95} -60.5556 q^{96} -0.278775 q^{97} +16.7622 q^{98} -0.793010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72092 −1.92398 −0.961989 0.273088i \(-0.911955\pi\)
−0.961989 + 0.273088i \(0.911955\pi\)
\(3\) 2.93492 1.69448 0.847239 0.531212i \(-0.178263\pi\)
0.847239 + 0.531212i \(0.178263\pi\)
\(4\) 5.40338 2.70169
\(5\) −0.339682 −0.151910 −0.0759551 0.997111i \(-0.524201\pi\)
−0.0759551 + 0.997111i \(0.524201\pi\)
\(6\) −7.98568 −3.26014
\(7\) −0.916249 −0.346310 −0.173155 0.984895i \(-0.555396\pi\)
−0.173155 + 0.984895i \(0.555396\pi\)
\(8\) −9.26032 −3.27402
\(9\) 5.61377 1.87126
\(10\) 0.924245 0.292272
\(11\) −0.141261 −0.0425919 −0.0212960 0.999773i \(-0.506779\pi\)
−0.0212960 + 0.999773i \(0.506779\pi\)
\(12\) 15.8585 4.57796
\(13\) −1.00000 −0.277350
\(14\) 2.49304 0.666292
\(15\) −0.996939 −0.257409
\(16\) 14.3898 3.59745
\(17\) −1.87864 −0.455637 −0.227819 0.973704i \(-0.573159\pi\)
−0.227819 + 0.973704i \(0.573159\pi\)
\(18\) −15.2746 −3.60026
\(19\) 0.543254 0.124631 0.0623155 0.998057i \(-0.480152\pi\)
0.0623155 + 0.998057i \(0.480152\pi\)
\(20\) −1.83543 −0.410415
\(21\) −2.68912 −0.586814
\(22\) 0.384361 0.0819460
\(23\) 4.12163 0.859419 0.429710 0.902967i \(-0.358616\pi\)
0.429710 + 0.902967i \(0.358616\pi\)
\(24\) −27.1783 −5.54775
\(25\) −4.88462 −0.976923
\(26\) 2.72092 0.533616
\(27\) 7.67121 1.47633
\(28\) −4.95085 −0.935622
\(29\) 3.91353 0.726724 0.363362 0.931648i \(-0.381629\pi\)
0.363362 + 0.931648i \(0.381629\pi\)
\(30\) 2.71259 0.495249
\(31\) −6.91321 −1.24165 −0.620824 0.783950i \(-0.713202\pi\)
−0.620824 + 0.783950i \(0.713202\pi\)
\(32\) −20.6328 −3.64739
\(33\) −0.414592 −0.0721711
\(34\) 5.11162 0.876636
\(35\) 0.311233 0.0526080
\(36\) 30.3334 5.05556
\(37\) −5.24871 −0.862882 −0.431441 0.902141i \(-0.641995\pi\)
−0.431441 + 0.902141i \(0.641995\pi\)
\(38\) −1.47815 −0.239787
\(39\) −2.93492 −0.469964
\(40\) 3.14556 0.497357
\(41\) 7.80986 1.21970 0.609848 0.792519i \(-0.291231\pi\)
0.609848 + 0.792519i \(0.291231\pi\)
\(42\) 7.31687 1.12902
\(43\) 1.62979 0.248540 0.124270 0.992248i \(-0.460341\pi\)
0.124270 + 0.992248i \(0.460341\pi\)
\(44\) −0.763290 −0.115070
\(45\) −1.90689 −0.284263
\(46\) −11.2146 −1.65350
\(47\) 0.413613 0.0603316 0.0301658 0.999545i \(-0.490396\pi\)
0.0301658 + 0.999545i \(0.490396\pi\)
\(48\) 42.2329 6.09580
\(49\) −6.16049 −0.880070
\(50\) 13.2906 1.87958
\(51\) −5.51367 −0.772068
\(52\) −5.40338 −0.749315
\(53\) −6.17696 −0.848470 −0.424235 0.905552i \(-0.639457\pi\)
−0.424235 + 0.905552i \(0.639457\pi\)
\(54\) −20.8727 −2.84042
\(55\) 0.0479839 0.00647015
\(56\) 8.48476 1.13382
\(57\) 1.59441 0.211184
\(58\) −10.6484 −1.39820
\(59\) −11.2268 −1.46160 −0.730802 0.682589i \(-0.760854\pi\)
−0.730802 + 0.682589i \(0.760854\pi\)
\(60\) −5.38685 −0.695439
\(61\) 4.33420 0.554937 0.277469 0.960735i \(-0.410505\pi\)
0.277469 + 0.960735i \(0.410505\pi\)
\(62\) 18.8103 2.38890
\(63\) −5.14361 −0.648034
\(64\) 27.3605 3.42006
\(65\) 0.339682 0.0421323
\(66\) 1.12807 0.138856
\(67\) −4.97675 −0.608007 −0.304003 0.952671i \(-0.598323\pi\)
−0.304003 + 0.952671i \(0.598323\pi\)
\(68\) −10.1510 −1.23099
\(69\) 12.0967 1.45627
\(70\) −0.846839 −0.101217
\(71\) −11.4122 −1.35438 −0.677188 0.735810i \(-0.736802\pi\)
−0.677188 + 0.735810i \(0.736802\pi\)
\(72\) −51.9853 −6.12653
\(73\) 2.14580 0.251147 0.125573 0.992084i \(-0.459923\pi\)
0.125573 + 0.992084i \(0.459923\pi\)
\(74\) 14.2813 1.66017
\(75\) −14.3360 −1.65538
\(76\) 2.93541 0.336714
\(77\) 0.129431 0.0147500
\(78\) 7.98568 0.904200
\(79\) −8.27677 −0.931210 −0.465605 0.884993i \(-0.654163\pi\)
−0.465605 + 0.884993i \(0.654163\pi\)
\(80\) −4.88795 −0.546489
\(81\) 5.67311 0.630345
\(82\) −21.2500 −2.34667
\(83\) −8.73569 −0.958867 −0.479433 0.877578i \(-0.659158\pi\)
−0.479433 + 0.877578i \(0.659158\pi\)
\(84\) −14.5304 −1.58539
\(85\) 0.638140 0.0692160
\(86\) −4.43451 −0.478185
\(87\) 11.4859 1.23142
\(88\) 1.30813 0.139447
\(89\) −0.171967 −0.0182285 −0.00911425 0.999958i \(-0.502901\pi\)
−0.00911425 + 0.999958i \(0.502901\pi\)
\(90\) 5.18850 0.546916
\(91\) 0.916249 0.0960490
\(92\) 22.2707 2.32189
\(93\) −20.2897 −2.10395
\(94\) −1.12541 −0.116077
\(95\) −0.184533 −0.0189327
\(96\) −60.5556 −6.18043
\(97\) −0.278775 −0.0283053 −0.0141526 0.999900i \(-0.504505\pi\)
−0.0141526 + 0.999900i \(0.504505\pi\)
\(98\) 16.7622 1.69323
\(99\) −0.793010 −0.0797005
\(100\) −26.3935 −2.63935
\(101\) −4.05663 −0.403649 −0.201825 0.979422i \(-0.564687\pi\)
−0.201825 + 0.979422i \(0.564687\pi\)
\(102\) 15.0022 1.48544
\(103\) −17.3849 −1.71298 −0.856491 0.516162i \(-0.827360\pi\)
−0.856491 + 0.516162i \(0.827360\pi\)
\(104\) 9.26032 0.908049
\(105\) 0.913445 0.0891431
\(106\) 16.8070 1.63244
\(107\) 14.1339 1.36637 0.683187 0.730244i \(-0.260594\pi\)
0.683187 + 0.730244i \(0.260594\pi\)
\(108\) 41.4505 3.98858
\(109\) 4.07202 0.390029 0.195015 0.980800i \(-0.437525\pi\)
0.195015 + 0.980800i \(0.437525\pi\)
\(110\) −0.130560 −0.0124484
\(111\) −15.4046 −1.46214
\(112\) −13.1846 −1.24583
\(113\) 2.37104 0.223049 0.111524 0.993762i \(-0.464427\pi\)
0.111524 + 0.993762i \(0.464427\pi\)
\(114\) −4.33825 −0.406314
\(115\) −1.40004 −0.130555
\(116\) 21.1463 1.96338
\(117\) −5.61377 −0.518993
\(118\) 30.5472 2.81210
\(119\) 1.72130 0.157792
\(120\) 9.23198 0.842761
\(121\) −10.9800 −0.998186
\(122\) −11.7930 −1.06769
\(123\) 22.9213 2.06675
\(124\) −37.3547 −3.35455
\(125\) 3.35762 0.300315
\(126\) 13.9953 1.24680
\(127\) 21.9292 1.94590 0.972949 0.231020i \(-0.0742062\pi\)
0.972949 + 0.231020i \(0.0742062\pi\)
\(128\) −33.1800 −2.93272
\(129\) 4.78329 0.421145
\(130\) −0.924245 −0.0810617
\(131\) −4.03182 −0.352262 −0.176131 0.984367i \(-0.556358\pi\)
−0.176131 + 0.984367i \(0.556358\pi\)
\(132\) −2.24020 −0.194984
\(133\) −0.497756 −0.0431609
\(134\) 13.5413 1.16979
\(135\) −2.60577 −0.224269
\(136\) 17.3968 1.49177
\(137\) 5.94862 0.508225 0.254113 0.967175i \(-0.418217\pi\)
0.254113 + 0.967175i \(0.418217\pi\)
\(138\) −32.9140 −2.80183
\(139\) −20.3388 −1.72512 −0.862558 0.505959i \(-0.831139\pi\)
−0.862558 + 0.505959i \(0.831139\pi\)
\(140\) 1.68171 0.142131
\(141\) 1.21392 0.102231
\(142\) 31.0516 2.60579
\(143\) 0.141261 0.0118129
\(144\) 80.7810 6.73175
\(145\) −1.32935 −0.110397
\(146\) −5.83854 −0.483201
\(147\) −18.0806 −1.49126
\(148\) −28.3608 −2.33124
\(149\) 16.6320 1.36255 0.681273 0.732030i \(-0.261427\pi\)
0.681273 + 0.732030i \(0.261427\pi\)
\(150\) 39.0070 3.18491
\(151\) −10.8420 −0.882311 −0.441156 0.897431i \(-0.645431\pi\)
−0.441156 + 0.897431i \(0.645431\pi\)
\(152\) −5.03070 −0.408044
\(153\) −10.5463 −0.852615
\(154\) −0.352170 −0.0283787
\(155\) 2.34829 0.188619
\(156\) −15.8585 −1.26970
\(157\) 21.9287 1.75010 0.875051 0.484030i \(-0.160827\pi\)
0.875051 + 0.484030i \(0.160827\pi\)
\(158\) 22.5204 1.79163
\(159\) −18.1289 −1.43771
\(160\) 7.00857 0.554076
\(161\) −3.77644 −0.297625
\(162\) −15.4361 −1.21277
\(163\) 0.0564064 0.00441809 0.00220904 0.999998i \(-0.499297\pi\)
0.00220904 + 0.999998i \(0.499297\pi\)
\(164\) 42.1997 3.29524
\(165\) 0.140829 0.0109635
\(166\) 23.7691 1.84484
\(167\) 14.9477 1.15669 0.578344 0.815793i \(-0.303699\pi\)
0.578344 + 0.815793i \(0.303699\pi\)
\(168\) 24.9021 1.92124
\(169\) 1.00000 0.0769231
\(170\) −1.73633 −0.133170
\(171\) 3.04970 0.233216
\(172\) 8.80636 0.671478
\(173\) 9.91576 0.753881 0.376941 0.926237i \(-0.376976\pi\)
0.376941 + 0.926237i \(0.376976\pi\)
\(174\) −31.2522 −2.36922
\(175\) 4.47553 0.338318
\(176\) −2.03272 −0.153222
\(177\) −32.9498 −2.47666
\(178\) 0.467909 0.0350712
\(179\) 6.47838 0.484217 0.242108 0.970249i \(-0.422161\pi\)
0.242108 + 0.970249i \(0.422161\pi\)
\(180\) −10.3037 −0.767991
\(181\) −12.9390 −0.961750 −0.480875 0.876789i \(-0.659681\pi\)
−0.480875 + 0.876789i \(0.659681\pi\)
\(182\) −2.49304 −0.184796
\(183\) 12.7205 0.940329
\(184\) −38.1676 −2.81375
\(185\) 1.78289 0.131081
\(186\) 55.2066 4.04795
\(187\) 0.265380 0.0194065
\(188\) 2.23491 0.162997
\(189\) −7.02874 −0.511266
\(190\) 0.502100 0.0364261
\(191\) −4.96058 −0.358935 −0.179468 0.983764i \(-0.557438\pi\)
−0.179468 + 0.983764i \(0.557438\pi\)
\(192\) 80.3008 5.79521
\(193\) 2.68022 0.192926 0.0964632 0.995337i \(-0.469247\pi\)
0.0964632 + 0.995337i \(0.469247\pi\)
\(194\) 0.758523 0.0544588
\(195\) 0.996939 0.0713923
\(196\) −33.2875 −2.37768
\(197\) −2.25526 −0.160681 −0.0803403 0.996767i \(-0.525601\pi\)
−0.0803403 + 0.996767i \(0.525601\pi\)
\(198\) 2.15771 0.153342
\(199\) −16.7644 −1.18840 −0.594200 0.804317i \(-0.702531\pi\)
−0.594200 + 0.804317i \(0.702531\pi\)
\(200\) 45.2331 3.19846
\(201\) −14.6064 −1.03025
\(202\) 11.0377 0.776613
\(203\) −3.58577 −0.251671
\(204\) −29.7925 −2.08589
\(205\) −2.65287 −0.185284
\(206\) 47.3028 3.29574
\(207\) 23.1379 1.60819
\(208\) −14.3898 −0.997753
\(209\) −0.0767408 −0.00530827
\(210\) −2.48541 −0.171509
\(211\) −12.4928 −0.860040 −0.430020 0.902819i \(-0.641494\pi\)
−0.430020 + 0.902819i \(0.641494\pi\)
\(212\) −33.3765 −2.29231
\(213\) −33.4939 −2.29496
\(214\) −38.4571 −2.62887
\(215\) −0.553608 −0.0377558
\(216\) −71.0379 −4.83352
\(217\) 6.33422 0.429995
\(218\) −11.0796 −0.750407
\(219\) 6.29775 0.425563
\(220\) 0.259276 0.0174804
\(221\) 1.87864 0.126371
\(222\) 41.9145 2.81312
\(223\) 10.3767 0.694875 0.347437 0.937703i \(-0.387052\pi\)
0.347437 + 0.937703i \(0.387052\pi\)
\(224\) 18.9048 1.26313
\(225\) −27.4211 −1.82807
\(226\) −6.45140 −0.429141
\(227\) −16.4239 −1.09010 −0.545048 0.838405i \(-0.683488\pi\)
−0.545048 + 0.838405i \(0.683488\pi\)
\(228\) 8.61519 0.570555
\(229\) 4.78607 0.316273 0.158136 0.987417i \(-0.449451\pi\)
0.158136 + 0.987417i \(0.449451\pi\)
\(230\) 3.80940 0.251184
\(231\) 0.379869 0.0249936
\(232\) −36.2405 −2.37931
\(233\) −4.48572 −0.293870 −0.146935 0.989146i \(-0.546941\pi\)
−0.146935 + 0.989146i \(0.546941\pi\)
\(234\) 15.2746 0.998532
\(235\) −0.140497 −0.00916499
\(236\) −60.6627 −3.94881
\(237\) −24.2917 −1.57791
\(238\) −4.68352 −0.303588
\(239\) −13.3209 −0.861658 −0.430829 0.902434i \(-0.641779\pi\)
−0.430829 + 0.902434i \(0.641779\pi\)
\(240\) −14.3457 −0.926014
\(241\) −6.13820 −0.395396 −0.197698 0.980263i \(-0.563347\pi\)
−0.197698 + 0.980263i \(0.563347\pi\)
\(242\) 29.8758 1.92049
\(243\) −6.36351 −0.408219
\(244\) 23.4193 1.49927
\(245\) 2.09260 0.133692
\(246\) −62.3670 −3.97638
\(247\) −0.543254 −0.0345664
\(248\) 64.0185 4.06518
\(249\) −25.6386 −1.62478
\(250\) −9.13581 −0.577799
\(251\) 5.20804 0.328729 0.164364 0.986400i \(-0.447443\pi\)
0.164364 + 0.986400i \(0.447443\pi\)
\(252\) −27.7929 −1.75079
\(253\) −0.582227 −0.0366043
\(254\) −59.6674 −3.74387
\(255\) 1.87289 0.117285
\(256\) 35.5590 2.22244
\(257\) 19.2781 1.20254 0.601268 0.799047i \(-0.294662\pi\)
0.601268 + 0.799047i \(0.294662\pi\)
\(258\) −13.0149 −0.810275
\(259\) 4.80912 0.298824
\(260\) 1.83543 0.113829
\(261\) 21.9696 1.35989
\(262\) 10.9702 0.677744
\(263\) 13.5061 0.832822 0.416411 0.909176i \(-0.363288\pi\)
0.416411 + 0.909176i \(0.363288\pi\)
\(264\) 3.83925 0.236290
\(265\) 2.09820 0.128891
\(266\) 1.35435 0.0830406
\(267\) −0.504711 −0.0308878
\(268\) −26.8913 −1.64265
\(269\) 18.3837 1.12088 0.560438 0.828197i \(-0.310633\pi\)
0.560438 + 0.828197i \(0.310633\pi\)
\(270\) 7.09008 0.431489
\(271\) −1.88480 −0.114493 −0.0572467 0.998360i \(-0.518232\pi\)
−0.0572467 + 0.998360i \(0.518232\pi\)
\(272\) −27.0333 −1.63913
\(273\) 2.68912 0.162753
\(274\) −16.1857 −0.977814
\(275\) 0.690008 0.0416091
\(276\) 65.3629 3.93439
\(277\) −10.7232 −0.644297 −0.322148 0.946689i \(-0.604405\pi\)
−0.322148 + 0.946689i \(0.604405\pi\)
\(278\) 55.3402 3.31908
\(279\) −38.8091 −2.32344
\(280\) −2.88212 −0.172240
\(281\) −7.76933 −0.463479 −0.231740 0.972778i \(-0.574442\pi\)
−0.231740 + 0.972778i \(0.574442\pi\)
\(282\) −3.30298 −0.196690
\(283\) −16.3991 −0.974823 −0.487411 0.873173i \(-0.662059\pi\)
−0.487411 + 0.873173i \(0.662059\pi\)
\(284\) −61.6644 −3.65911
\(285\) −0.541591 −0.0320811
\(286\) −0.384361 −0.0227277
\(287\) −7.15578 −0.422392
\(288\) −115.828 −6.82521
\(289\) −13.4707 −0.792395
\(290\) 3.61706 0.212401
\(291\) −0.818182 −0.0479627
\(292\) 11.5946 0.678521
\(293\) −21.2182 −1.23958 −0.619792 0.784766i \(-0.712783\pi\)
−0.619792 + 0.784766i \(0.712783\pi\)
\(294\) 49.1957 2.86915
\(295\) 3.81354 0.222033
\(296\) 48.6047 2.82509
\(297\) −1.08365 −0.0628796
\(298\) −45.2542 −2.62151
\(299\) −4.12163 −0.238360
\(300\) −77.4628 −4.47231
\(301\) −1.49329 −0.0860718
\(302\) 29.5002 1.69755
\(303\) −11.9059 −0.683975
\(304\) 7.81731 0.448353
\(305\) −1.47225 −0.0843006
\(306\) 28.6955 1.64041
\(307\) −2.52879 −0.144325 −0.0721627 0.997393i \(-0.522990\pi\)
−0.0721627 + 0.997393i \(0.522990\pi\)
\(308\) 0.699364 0.0398500
\(309\) −51.0232 −2.90261
\(310\) −6.38950 −0.362899
\(311\) 8.00889 0.454143 0.227071 0.973878i \(-0.427085\pi\)
0.227071 + 0.973878i \(0.427085\pi\)
\(312\) 27.1783 1.53867
\(313\) −18.7701 −1.06095 −0.530475 0.847700i \(-0.677987\pi\)
−0.530475 + 0.847700i \(0.677987\pi\)
\(314\) −59.6662 −3.36716
\(315\) 1.74719 0.0984431
\(316\) −44.7226 −2.51584
\(317\) −2.58701 −0.145301 −0.0726505 0.997357i \(-0.523146\pi\)
−0.0726505 + 0.997357i \(0.523146\pi\)
\(318\) 49.3272 2.76613
\(319\) −0.552831 −0.0309526
\(320\) −9.29384 −0.519542
\(321\) 41.4818 2.31529
\(322\) 10.2754 0.572624
\(323\) −1.02058 −0.0567865
\(324\) 30.6540 1.70300
\(325\) 4.88462 0.270950
\(326\) −0.153477 −0.00850031
\(327\) 11.9511 0.660896
\(328\) −72.3218 −3.99330
\(329\) −0.378972 −0.0208934
\(330\) −0.383184 −0.0210936
\(331\) −8.90017 −0.489198 −0.244599 0.969624i \(-0.578656\pi\)
−0.244599 + 0.969624i \(0.578656\pi\)
\(332\) −47.2023 −2.59056
\(333\) −29.4650 −1.61467
\(334\) −40.6714 −2.22544
\(335\) 1.69051 0.0923624
\(336\) −38.6959 −2.11103
\(337\) −30.3247 −1.65189 −0.825945 0.563751i \(-0.809358\pi\)
−0.825945 + 0.563751i \(0.809358\pi\)
\(338\) −2.72092 −0.147998
\(339\) 6.95882 0.377951
\(340\) 3.44811 0.187000
\(341\) 0.976570 0.0528842
\(342\) −8.29798 −0.448703
\(343\) 12.0583 0.651086
\(344\) −15.0923 −0.813724
\(345\) −4.10901 −0.221222
\(346\) −26.9799 −1.45045
\(347\) 23.4907 1.26105 0.630523 0.776171i \(-0.282841\pi\)
0.630523 + 0.776171i \(0.282841\pi\)
\(348\) 62.0627 3.32691
\(349\) 12.5047 0.669363 0.334681 0.942331i \(-0.391371\pi\)
0.334681 + 0.942331i \(0.391371\pi\)
\(350\) −12.1775 −0.650916
\(351\) −7.67121 −0.409459
\(352\) 2.91462 0.155350
\(353\) −29.4684 −1.56845 −0.784223 0.620479i \(-0.786938\pi\)
−0.784223 + 0.620479i \(0.786938\pi\)
\(354\) 89.6536 4.76503
\(355\) 3.87651 0.205744
\(356\) −0.929206 −0.0492478
\(357\) 5.05189 0.267375
\(358\) −17.6271 −0.931623
\(359\) −27.6530 −1.45947 −0.729734 0.683731i \(-0.760356\pi\)
−0.729734 + 0.683731i \(0.760356\pi\)
\(360\) 17.6585 0.930683
\(361\) −18.7049 −0.984467
\(362\) 35.2060 1.85039
\(363\) −32.2256 −1.69140
\(364\) 4.95085 0.259495
\(365\) −0.728889 −0.0381518
\(366\) −34.6115 −1.80917
\(367\) 1.64682 0.0859631 0.0429816 0.999076i \(-0.486314\pi\)
0.0429816 + 0.999076i \(0.486314\pi\)
\(368\) 59.3094 3.09172
\(369\) 43.8428 2.28236
\(370\) −4.85109 −0.252196
\(371\) 5.65963 0.293833
\(372\) −109.633 −5.68421
\(373\) −5.79690 −0.300152 −0.150076 0.988674i \(-0.547952\pi\)
−0.150076 + 0.988674i \(0.547952\pi\)
\(374\) −0.722076 −0.0373376
\(375\) 9.85436 0.508877
\(376\) −3.83019 −0.197527
\(377\) −3.91353 −0.201557
\(378\) 19.1246 0.983664
\(379\) −4.99393 −0.256521 −0.128261 0.991741i \(-0.540939\pi\)
−0.128261 + 0.991741i \(0.540939\pi\)
\(380\) −0.997104 −0.0511504
\(381\) 64.3604 3.29728
\(382\) 13.4973 0.690584
\(383\) 19.7483 1.00909 0.504545 0.863386i \(-0.331660\pi\)
0.504545 + 0.863386i \(0.331660\pi\)
\(384\) −97.3806 −4.96943
\(385\) −0.0439652 −0.00224068
\(386\) −7.29265 −0.371186
\(387\) 9.14924 0.465082
\(388\) −1.50633 −0.0764722
\(389\) −37.7425 −1.91362 −0.956811 0.290709i \(-0.906109\pi\)
−0.956811 + 0.290709i \(0.906109\pi\)
\(390\) −2.71259 −0.137357
\(391\) −7.74306 −0.391583
\(392\) 57.0481 2.88136
\(393\) −11.8331 −0.596900
\(394\) 6.13637 0.309146
\(395\) 2.81147 0.141460
\(396\) −4.28494 −0.215326
\(397\) −12.7327 −0.639034 −0.319517 0.947581i \(-0.603521\pi\)
−0.319517 + 0.947581i \(0.603521\pi\)
\(398\) 45.6146 2.28646
\(399\) −1.46087 −0.0731352
\(400\) −70.2886 −3.51443
\(401\) 26.2938 1.31305 0.656525 0.754304i \(-0.272026\pi\)
0.656525 + 0.754304i \(0.272026\pi\)
\(402\) 39.7427 1.98219
\(403\) 6.91321 0.344371
\(404\) −21.9195 −1.09054
\(405\) −1.92705 −0.0957559
\(406\) 9.75657 0.484210
\(407\) 0.741440 0.0367518
\(408\) 51.0583 2.52776
\(409\) −12.4813 −0.617159 −0.308579 0.951199i \(-0.599854\pi\)
−0.308579 + 0.951199i \(0.599854\pi\)
\(410\) 7.21823 0.356483
\(411\) 17.4587 0.861177
\(412\) −93.9371 −4.62795
\(413\) 10.2865 0.506168
\(414\) −62.9562 −3.09413
\(415\) 2.96735 0.145662
\(416\) 20.6328 1.01160
\(417\) −59.6928 −2.92317
\(418\) 0.208805 0.0102130
\(419\) 8.91406 0.435480 0.217740 0.976007i \(-0.430131\pi\)
0.217740 + 0.976007i \(0.430131\pi\)
\(420\) 4.93569 0.240837
\(421\) 36.5538 1.78152 0.890761 0.454471i \(-0.150172\pi\)
0.890761 + 0.454471i \(0.150172\pi\)
\(422\) 33.9919 1.65470
\(423\) 2.32193 0.112896
\(424\) 57.2006 2.77791
\(425\) 9.17644 0.445123
\(426\) 91.1340 4.41546
\(427\) −3.97121 −0.192180
\(428\) 76.3707 3.69152
\(429\) 0.414592 0.0200167
\(430\) 1.50632 0.0726413
\(431\) −22.3038 −1.07433 −0.537167 0.843476i \(-0.680505\pi\)
−0.537167 + 0.843476i \(0.680505\pi\)
\(432\) 110.387 5.31101
\(433\) −9.22629 −0.443387 −0.221694 0.975116i \(-0.571158\pi\)
−0.221694 + 0.975116i \(0.571158\pi\)
\(434\) −17.2349 −0.827301
\(435\) −3.90155 −0.187065
\(436\) 22.0027 1.05374
\(437\) 2.23909 0.107110
\(438\) −17.1357 −0.818774
\(439\) −22.3566 −1.06702 −0.533510 0.845794i \(-0.679127\pi\)
−0.533510 + 0.845794i \(0.679127\pi\)
\(440\) −0.444347 −0.0211834
\(441\) −34.5836 −1.64684
\(442\) −5.11162 −0.243135
\(443\) −15.7742 −0.749455 −0.374728 0.927135i \(-0.622264\pi\)
−0.374728 + 0.927135i \(0.622264\pi\)
\(444\) −83.2367 −3.95024
\(445\) 0.0584141 0.00276910
\(446\) −28.2341 −1.33692
\(447\) 48.8136 2.30880
\(448\) −25.0690 −1.18440
\(449\) −16.5762 −0.782281 −0.391140 0.920331i \(-0.627919\pi\)
−0.391140 + 0.920331i \(0.627919\pi\)
\(450\) 74.6106 3.51718
\(451\) −1.10323 −0.0519492
\(452\) 12.8116 0.602609
\(453\) −31.8205 −1.49506
\(454\) 44.6882 2.09732
\(455\) −0.311233 −0.0145908
\(456\) −14.7647 −0.691422
\(457\) 0.632841 0.0296031 0.0148015 0.999890i \(-0.495288\pi\)
0.0148015 + 0.999890i \(0.495288\pi\)
\(458\) −13.0225 −0.608502
\(459\) −14.4115 −0.672669
\(460\) −7.56496 −0.352718
\(461\) 12.6252 0.588014 0.294007 0.955803i \(-0.405011\pi\)
0.294007 + 0.955803i \(0.405011\pi\)
\(462\) −1.03359 −0.0480871
\(463\) 12.4025 0.576395 0.288198 0.957571i \(-0.406944\pi\)
0.288198 + 0.957571i \(0.406944\pi\)
\(464\) 56.3148 2.61435
\(465\) 6.89205 0.319611
\(466\) 12.2053 0.565399
\(467\) −14.9898 −0.693646 −0.346823 0.937931i \(-0.612740\pi\)
−0.346823 + 0.937931i \(0.612740\pi\)
\(468\) −30.3334 −1.40216
\(469\) 4.55994 0.210559
\(470\) 0.382280 0.0176332
\(471\) 64.3591 2.96551
\(472\) 103.964 4.78532
\(473\) −0.230226 −0.0105858
\(474\) 66.0956 3.03587
\(475\) −2.65359 −0.121755
\(476\) 9.30086 0.426304
\(477\) −34.6760 −1.58771
\(478\) 36.2451 1.65781
\(479\) 32.8969 1.50310 0.751548 0.659678i \(-0.229307\pi\)
0.751548 + 0.659678i \(0.229307\pi\)
\(480\) 20.5696 0.938870
\(481\) 5.24871 0.239320
\(482\) 16.7015 0.760734
\(483\) −11.0836 −0.504319
\(484\) −59.3294 −2.69679
\(485\) 0.0946947 0.00429986
\(486\) 17.3146 0.785405
\(487\) 16.0678 0.728100 0.364050 0.931379i \(-0.381394\pi\)
0.364050 + 0.931379i \(0.381394\pi\)
\(488\) −40.1361 −1.81687
\(489\) 0.165548 0.00748636
\(490\) −5.69380 −0.257220
\(491\) −4.82964 −0.217959 −0.108979 0.994044i \(-0.534758\pi\)
−0.108979 + 0.994044i \(0.534758\pi\)
\(492\) 123.853 5.58371
\(493\) −7.35211 −0.331123
\(494\) 1.47815 0.0665050
\(495\) 0.269371 0.0121073
\(496\) −99.4796 −4.46677
\(497\) 10.4564 0.469034
\(498\) 69.7604 3.12604
\(499\) 25.2221 1.12910 0.564549 0.825400i \(-0.309050\pi\)
0.564549 + 0.825400i \(0.309050\pi\)
\(500\) 18.1425 0.811358
\(501\) 43.8703 1.95998
\(502\) −14.1706 −0.632467
\(503\) 37.3377 1.66480 0.832402 0.554172i \(-0.186965\pi\)
0.832402 + 0.554172i \(0.186965\pi\)
\(504\) 47.6315 2.12168
\(505\) 1.37796 0.0613185
\(506\) 1.58419 0.0704259
\(507\) 2.93492 0.130344
\(508\) 118.492 5.25722
\(509\) 2.30116 0.101997 0.0509986 0.998699i \(-0.483760\pi\)
0.0509986 + 0.998699i \(0.483760\pi\)
\(510\) −5.09598 −0.225654
\(511\) −1.96609 −0.0869746
\(512\) −30.3931 −1.34320
\(513\) 4.16741 0.183996
\(514\) −52.4542 −2.31365
\(515\) 5.90532 0.260220
\(516\) 25.8460 1.13781
\(517\) −0.0584276 −0.00256964
\(518\) −13.0852 −0.574932
\(519\) 29.1020 1.27744
\(520\) −3.14556 −0.137942
\(521\) 18.4466 0.808162 0.404081 0.914723i \(-0.367591\pi\)
0.404081 + 0.914723i \(0.367591\pi\)
\(522\) −59.7776 −2.61639
\(523\) 14.6846 0.642114 0.321057 0.947060i \(-0.395962\pi\)
0.321057 + 0.947060i \(0.395962\pi\)
\(524\) −21.7855 −0.951703
\(525\) 13.1353 0.573272
\(526\) −36.7490 −1.60233
\(527\) 12.9874 0.565741
\(528\) −5.96589 −0.259632
\(529\) −6.01217 −0.261399
\(530\) −5.70902 −0.247984
\(531\) −63.0247 −2.73504
\(532\) −2.68957 −0.116607
\(533\) −7.80986 −0.338283
\(534\) 1.37328 0.0594275
\(535\) −4.80102 −0.207566
\(536\) 46.0863 1.99063
\(537\) 19.0135 0.820495
\(538\) −50.0206 −2.15654
\(539\) 0.870240 0.0374839
\(540\) −14.0800 −0.605906
\(541\) −31.3502 −1.34785 −0.673925 0.738800i \(-0.735393\pi\)
−0.673925 + 0.738800i \(0.735393\pi\)
\(542\) 5.12838 0.220283
\(543\) −37.9750 −1.62967
\(544\) 38.7616 1.66189
\(545\) −1.38319 −0.0592494
\(546\) −7.31687 −0.313133
\(547\) 9.37126 0.400686 0.200343 0.979726i \(-0.435794\pi\)
0.200343 + 0.979726i \(0.435794\pi\)
\(548\) 32.1427 1.37307
\(549\) 24.3312 1.03843
\(550\) −1.87745 −0.0800549
\(551\) 2.12604 0.0905723
\(552\) −112.019 −4.76785
\(553\) 7.58359 0.322487
\(554\) 29.1770 1.23961
\(555\) 5.23264 0.222113
\(556\) −109.898 −4.66073
\(557\) −10.4499 −0.442774 −0.221387 0.975186i \(-0.571058\pi\)
−0.221387 + 0.975186i \(0.571058\pi\)
\(558\) 105.596 4.47025
\(559\) −1.62979 −0.0689326
\(560\) 4.47858 0.189255
\(561\) 0.778869 0.0328839
\(562\) 21.1397 0.891724
\(563\) −2.82873 −0.119217 −0.0596085 0.998222i \(-0.518985\pi\)
−0.0596085 + 0.998222i \(0.518985\pi\)
\(564\) 6.55928 0.276196
\(565\) −0.805399 −0.0338834
\(566\) 44.6204 1.87554
\(567\) −5.19798 −0.218295
\(568\) 105.680 4.43425
\(569\) −5.71832 −0.239724 −0.119862 0.992791i \(-0.538245\pi\)
−0.119862 + 0.992791i \(0.538245\pi\)
\(570\) 1.47362 0.0617233
\(571\) 3.46274 0.144911 0.0724555 0.997372i \(-0.476916\pi\)
0.0724555 + 0.997372i \(0.476916\pi\)
\(572\) 0.763290 0.0319148
\(573\) −14.5589 −0.608208
\(574\) 19.4703 0.812673
\(575\) −20.1326 −0.839587
\(576\) 153.595 6.39980
\(577\) 25.6526 1.06793 0.533966 0.845506i \(-0.320701\pi\)
0.533966 + 0.845506i \(0.320701\pi\)
\(578\) 36.6527 1.52455
\(579\) 7.86623 0.326909
\(580\) −7.18301 −0.298258
\(581\) 8.00407 0.332065
\(582\) 2.22621 0.0922792
\(583\) 0.872566 0.0361380
\(584\) −19.8708 −0.822259
\(585\) 1.90689 0.0788404
\(586\) 57.7331 2.38493
\(587\) −25.9961 −1.07298 −0.536488 0.843908i \(-0.680249\pi\)
−0.536488 + 0.843908i \(0.680249\pi\)
\(588\) −97.6962 −4.02892
\(589\) −3.75562 −0.154748
\(590\) −10.3763 −0.427186
\(591\) −6.61901 −0.272270
\(592\) −75.5278 −3.10417
\(593\) −15.5139 −0.637078 −0.318539 0.947910i \(-0.603192\pi\)
−0.318539 + 0.947910i \(0.603192\pi\)
\(594\) 2.94851 0.120979
\(595\) −0.584695 −0.0239702
\(596\) 89.8690 3.68118
\(597\) −49.2023 −2.01372
\(598\) 11.2146 0.458599
\(599\) −35.8101 −1.46316 −0.731581 0.681755i \(-0.761217\pi\)
−0.731581 + 0.681755i \(0.761217\pi\)
\(600\) 132.756 5.41973
\(601\) 21.9562 0.895613 0.447807 0.894130i \(-0.352205\pi\)
0.447807 + 0.894130i \(0.352205\pi\)
\(602\) 4.06312 0.165600
\(603\) −27.9383 −1.13774
\(604\) −58.5836 −2.38373
\(605\) 3.72972 0.151635
\(606\) 32.3949 1.31595
\(607\) −23.8046 −0.966199 −0.483100 0.875565i \(-0.660489\pi\)
−0.483100 + 0.875565i \(0.660489\pi\)
\(608\) −11.2088 −0.454578
\(609\) −10.5239 −0.426452
\(610\) 4.00586 0.162193
\(611\) −0.413613 −0.0167330
\(612\) −56.9855 −2.30350
\(613\) 33.7696 1.36394 0.681971 0.731379i \(-0.261123\pi\)
0.681971 + 0.731379i \(0.261123\pi\)
\(614\) 6.88062 0.277679
\(615\) −7.78596 −0.313960
\(616\) −1.19857 −0.0482918
\(617\) −1.00000 −0.0402585
\(618\) 138.830 5.58456
\(619\) 18.0793 0.726668 0.363334 0.931659i \(-0.381638\pi\)
0.363334 + 0.931659i \(0.381638\pi\)
\(620\) 12.6887 0.509591
\(621\) 31.6179 1.26878
\(622\) −21.7915 −0.873760
\(623\) 0.157565 0.00631271
\(624\) −42.2329 −1.69067
\(625\) 23.2826 0.931302
\(626\) 51.0720 2.04125
\(627\) −0.225228 −0.00899475
\(628\) 118.489 4.72824
\(629\) 9.86044 0.393161
\(630\) −4.75396 −0.189402
\(631\) 3.45034 0.137356 0.0686780 0.997639i \(-0.478122\pi\)
0.0686780 + 0.997639i \(0.478122\pi\)
\(632\) 76.6456 3.04880
\(633\) −36.6654 −1.45732
\(634\) 7.03904 0.279556
\(635\) −7.44893 −0.295602
\(636\) −97.9573 −3.88426
\(637\) 6.16049 0.244087
\(638\) 1.50421 0.0595521
\(639\) −64.0654 −2.53439
\(640\) 11.2706 0.445510
\(641\) 10.0031 0.395100 0.197550 0.980293i \(-0.436701\pi\)
0.197550 + 0.980293i \(0.436701\pi\)
\(642\) −112.869 −4.45457
\(643\) −14.6630 −0.578252 −0.289126 0.957291i \(-0.593365\pi\)
−0.289126 + 0.957291i \(0.593365\pi\)
\(644\) −20.4056 −0.804092
\(645\) −1.62480 −0.0639763
\(646\) 2.77691 0.109256
\(647\) −5.28800 −0.207893 −0.103946 0.994583i \(-0.533147\pi\)
−0.103946 + 0.994583i \(0.533147\pi\)
\(648\) −52.5348 −2.06376
\(649\) 1.58591 0.0622526
\(650\) −13.2906 −0.521301
\(651\) 18.5904 0.728617
\(652\) 0.304785 0.0119363
\(653\) 7.61096 0.297840 0.148920 0.988849i \(-0.452420\pi\)
0.148920 + 0.988849i \(0.452420\pi\)
\(654\) −32.5179 −1.27155
\(655\) 1.36954 0.0535122
\(656\) 112.382 4.38779
\(657\) 12.0460 0.469960
\(658\) 1.03115 0.0401985
\(659\) −10.8727 −0.423541 −0.211771 0.977319i \(-0.567923\pi\)
−0.211771 + 0.977319i \(0.567923\pi\)
\(660\) 0.760954 0.0296201
\(661\) −32.9464 −1.28146 −0.640732 0.767764i \(-0.721369\pi\)
−0.640732 + 0.767764i \(0.721369\pi\)
\(662\) 24.2166 0.941206
\(663\) 5.51367 0.214133
\(664\) 80.8953 3.13935
\(665\) 0.169078 0.00655658
\(666\) 80.1719 3.10660
\(667\) 16.1301 0.624560
\(668\) 80.7681 3.12501
\(669\) 30.4548 1.17745
\(670\) −4.59974 −0.177703
\(671\) −0.612255 −0.0236358
\(672\) 55.4840 2.14034
\(673\) 23.1745 0.893312 0.446656 0.894706i \(-0.352615\pi\)
0.446656 + 0.894706i \(0.352615\pi\)
\(674\) 82.5109 3.17820
\(675\) −37.4709 −1.44226
\(676\) 5.40338 0.207822
\(677\) 44.7560 1.72011 0.860057 0.510199i \(-0.170428\pi\)
0.860057 + 0.510199i \(0.170428\pi\)
\(678\) −18.9344 −0.727170
\(679\) 0.255427 0.00980240
\(680\) −5.90938 −0.226614
\(681\) −48.2030 −1.84714
\(682\) −2.65716 −0.101748
\(683\) −20.7697 −0.794729 −0.397364 0.917661i \(-0.630075\pi\)
−0.397364 + 0.917661i \(0.630075\pi\)
\(684\) 16.4787 0.630079
\(685\) −2.02064 −0.0772046
\(686\) −32.8096 −1.25268
\(687\) 14.0468 0.535917
\(688\) 23.4523 0.894109
\(689\) 6.17696 0.235323
\(690\) 11.1803 0.425626
\(691\) −13.7788 −0.524171 −0.262086 0.965045i \(-0.584410\pi\)
−0.262086 + 0.965045i \(0.584410\pi\)
\(692\) 53.5786 2.03675
\(693\) 0.726594 0.0276010
\(694\) −63.9161 −2.42622
\(695\) 6.90872 0.262063
\(696\) −106.363 −4.03168
\(697\) −14.6719 −0.555739
\(698\) −34.0243 −1.28784
\(699\) −13.1653 −0.497956
\(700\) 24.1830 0.914031
\(701\) −7.94853 −0.300212 −0.150106 0.988670i \(-0.547961\pi\)
−0.150106 + 0.988670i \(0.547961\pi\)
\(702\) 20.8727 0.787790
\(703\) −2.85138 −0.107542
\(704\) −3.86498 −0.145667
\(705\) −0.412347 −0.0155299
\(706\) 80.1811 3.01766
\(707\) 3.71688 0.139788
\(708\) −178.040 −6.69116
\(709\) −28.1949 −1.05888 −0.529440 0.848347i \(-0.677598\pi\)
−0.529440 + 0.848347i \(0.677598\pi\)
\(710\) −10.5477 −0.395846
\(711\) −46.4639 −1.74253
\(712\) 1.59247 0.0596805
\(713\) −28.4937 −1.06710
\(714\) −13.7458 −0.514423
\(715\) −0.0479839 −0.00179450
\(716\) 35.0052 1.30820
\(717\) −39.0958 −1.46006
\(718\) 75.2414 2.80798
\(719\) −1.20833 −0.0450633 −0.0225316 0.999746i \(-0.507173\pi\)
−0.0225316 + 0.999746i \(0.507173\pi\)
\(720\) −27.4398 −1.02262
\(721\) 15.9289 0.593222
\(722\) 50.8944 1.89409
\(723\) −18.0151 −0.669990
\(724\) −69.9145 −2.59835
\(725\) −19.1161 −0.709953
\(726\) 87.6831 3.25423
\(727\) −38.9710 −1.44535 −0.722677 0.691186i \(-0.757089\pi\)
−0.722677 + 0.691186i \(0.757089\pi\)
\(728\) −8.48476 −0.314466
\(729\) −35.6957 −1.32206
\(730\) 1.98324 0.0734032
\(731\) −3.06178 −0.113244
\(732\) 68.7339 2.54048
\(733\) 9.17060 0.338724 0.169362 0.985554i \(-0.445829\pi\)
0.169362 + 0.985554i \(0.445829\pi\)
\(734\) −4.48085 −0.165391
\(735\) 6.14163 0.226538
\(736\) −85.0406 −3.13464
\(737\) 0.703023 0.0258962
\(738\) −119.292 −4.39122
\(739\) 9.34542 0.343777 0.171888 0.985116i \(-0.445013\pi\)
0.171888 + 0.985116i \(0.445013\pi\)
\(740\) 9.63364 0.354140
\(741\) −1.59441 −0.0585720
\(742\) −15.3994 −0.565329
\(743\) 30.4263 1.11623 0.558116 0.829763i \(-0.311524\pi\)
0.558116 + 0.829763i \(0.311524\pi\)
\(744\) 187.889 6.88836
\(745\) −5.64958 −0.206985
\(746\) 15.7729 0.577486
\(747\) −49.0402 −1.79429
\(748\) 1.43395 0.0524303
\(749\) −12.9502 −0.473188
\(750\) −26.8129 −0.979068
\(751\) 15.3942 0.561741 0.280870 0.959746i \(-0.409377\pi\)
0.280870 + 0.959746i \(0.409377\pi\)
\(752\) 5.95180 0.217040
\(753\) 15.2852 0.557024
\(754\) 10.6484 0.387791
\(755\) 3.68284 0.134032
\(756\) −37.9790 −1.38128
\(757\) −0.0813838 −0.00295794 −0.00147897 0.999999i \(-0.500471\pi\)
−0.00147897 + 0.999999i \(0.500471\pi\)
\(758\) 13.5881 0.493541
\(759\) −1.70879 −0.0620252
\(760\) 1.70884 0.0619861
\(761\) −23.0825 −0.836739 −0.418369 0.908277i \(-0.637398\pi\)
−0.418369 + 0.908277i \(0.637398\pi\)
\(762\) −175.119 −6.34390
\(763\) −3.73099 −0.135071
\(764\) −26.8039 −0.969733
\(765\) 3.58237 0.129521
\(766\) −53.7334 −1.94147
\(767\) 11.2268 0.405376
\(768\) 104.363 3.76587
\(769\) 22.6610 0.817178 0.408589 0.912718i \(-0.366021\pi\)
0.408589 + 0.912718i \(0.366021\pi\)
\(770\) 0.119626 0.00431101
\(771\) 56.5798 2.03767
\(772\) 14.4822 0.521228
\(773\) 13.6021 0.489235 0.244617 0.969620i \(-0.421338\pi\)
0.244617 + 0.969620i \(0.421338\pi\)
\(774\) −24.8943 −0.894808
\(775\) 33.7684 1.21300
\(776\) 2.58154 0.0926720
\(777\) 14.1144 0.506352
\(778\) 102.694 3.68177
\(779\) 4.24273 0.152012
\(780\) 5.38685 0.192880
\(781\) 1.61210 0.0576855
\(782\) 21.0682 0.753398
\(783\) 30.0215 1.07288
\(784\) −88.6481 −3.16600
\(785\) −7.44878 −0.265859
\(786\) 32.1968 1.14842
\(787\) −43.2051 −1.54010 −0.770048 0.637986i \(-0.779768\pi\)
−0.770048 + 0.637986i \(0.779768\pi\)
\(788\) −12.1860 −0.434109
\(789\) 39.6394 1.41120
\(790\) −7.64977 −0.272167
\(791\) −2.17246 −0.0772439
\(792\) 7.34352 0.260941
\(793\) −4.33420 −0.153912
\(794\) 34.6445 1.22949
\(795\) 6.15805 0.218404
\(796\) −90.5847 −3.21069
\(797\) −12.8182 −0.454045 −0.227023 0.973890i \(-0.572899\pi\)
−0.227023 + 0.973890i \(0.572899\pi\)
\(798\) 3.97492 0.140711
\(799\) −0.777030 −0.0274893
\(800\) 100.783 3.56322
\(801\) −0.965385 −0.0341102
\(802\) −71.5432 −2.52628
\(803\) −0.303119 −0.0106968
\(804\) −78.9238 −2.78343
\(805\) 1.28279 0.0452123
\(806\) −18.8103 −0.662563
\(807\) 53.9548 1.89930
\(808\) 37.5657 1.32156
\(809\) −41.5073 −1.45932 −0.729660 0.683810i \(-0.760322\pi\)
−0.729660 + 0.683810i \(0.760322\pi\)
\(810\) 5.24334 0.184232
\(811\) −24.6821 −0.866705 −0.433352 0.901225i \(-0.642669\pi\)
−0.433352 + 0.901225i \(0.642669\pi\)
\(812\) −19.3753 −0.679939
\(813\) −5.53174 −0.194007
\(814\) −2.01740 −0.0707097
\(815\) −0.0191602 −0.000671153 0
\(816\) −79.3405 −2.77747
\(817\) 0.885387 0.0309758
\(818\) 33.9605 1.18740
\(819\) 5.14361 0.179732
\(820\) −14.3345 −0.500581
\(821\) 39.0831 1.36401 0.682005 0.731348i \(-0.261108\pi\)
0.682005 + 0.731348i \(0.261108\pi\)
\(822\) −47.5038 −1.65688
\(823\) 31.0180 1.08122 0.540609 0.841274i \(-0.318194\pi\)
0.540609 + 0.841274i \(0.318194\pi\)
\(824\) 160.989 5.60833
\(825\) 2.02512 0.0705056
\(826\) −27.9888 −0.973856
\(827\) 24.2810 0.844333 0.422167 0.906518i \(-0.361270\pi\)
0.422167 + 0.906518i \(0.361270\pi\)
\(828\) 125.023 4.34484
\(829\) −17.7059 −0.614951 −0.307475 0.951556i \(-0.599484\pi\)
−0.307475 + 0.951556i \(0.599484\pi\)
\(830\) −8.07392 −0.280250
\(831\) −31.4719 −1.09175
\(832\) −27.3605 −0.948553
\(833\) 11.5733 0.400993
\(834\) 162.419 5.62412
\(835\) −5.07746 −0.175713
\(836\) −0.414660 −0.0143413
\(837\) −53.0327 −1.83308
\(838\) −24.2544 −0.837855
\(839\) −27.7243 −0.957148 −0.478574 0.878047i \(-0.658846\pi\)
−0.478574 + 0.878047i \(0.658846\pi\)
\(840\) −8.45879 −0.291856
\(841\) −13.6843 −0.471873
\(842\) −99.4598 −3.42761
\(843\) −22.8024 −0.785356
\(844\) −67.5034 −2.32356
\(845\) −0.339682 −0.0116854
\(846\) −6.31777 −0.217209
\(847\) 10.0605 0.345681
\(848\) −88.8851 −3.05233
\(849\) −48.1300 −1.65182
\(850\) −24.9683 −0.856407
\(851\) −21.6332 −0.741578
\(852\) −180.980 −6.20028
\(853\) 31.2073 1.06852 0.534259 0.845321i \(-0.320591\pi\)
0.534259 + 0.845321i \(0.320591\pi\)
\(854\) 10.8053 0.369750
\(855\) −1.03593 −0.0354280
\(856\) −130.884 −4.47353
\(857\) −5.53797 −0.189173 −0.0945867 0.995517i \(-0.530153\pi\)
−0.0945867 + 0.995517i \(0.530153\pi\)
\(858\) −1.12807 −0.0385116
\(859\) 22.4391 0.765612 0.382806 0.923829i \(-0.374958\pi\)
0.382806 + 0.923829i \(0.374958\pi\)
\(860\) −2.99136 −0.102004
\(861\) −21.0017 −0.715735
\(862\) 60.6866 2.06699
\(863\) 22.3406 0.760484 0.380242 0.924887i \(-0.375841\pi\)
0.380242 + 0.924887i \(0.375841\pi\)
\(864\) −158.278 −5.38474
\(865\) −3.36820 −0.114522
\(866\) 25.1040 0.853067
\(867\) −39.5355 −1.34270
\(868\) 34.2262 1.16171
\(869\) 1.16919 0.0396620
\(870\) 10.6158 0.359909
\(871\) 4.97675 0.168631
\(872\) −37.7082 −1.27696
\(873\) −1.56498 −0.0529665
\(874\) −6.09238 −0.206078
\(875\) −3.07642 −0.104002
\(876\) 34.0292 1.14974
\(877\) 2.94357 0.0993972 0.0496986 0.998764i \(-0.484174\pi\)
0.0496986 + 0.998764i \(0.484174\pi\)
\(878\) 60.8303 2.05292
\(879\) −62.2739 −2.10045
\(880\) 0.690479 0.0232760
\(881\) −38.8817 −1.30996 −0.654979 0.755647i \(-0.727322\pi\)
−0.654979 + 0.755647i \(0.727322\pi\)
\(882\) 94.0990 3.16848
\(883\) −34.5946 −1.16420 −0.582100 0.813117i \(-0.697769\pi\)
−0.582100 + 0.813117i \(0.697769\pi\)
\(884\) 10.1510 0.341416
\(885\) 11.1924 0.376230
\(886\) 42.9203 1.44194
\(887\) 37.2524 1.25081 0.625406 0.780300i \(-0.284933\pi\)
0.625406 + 0.780300i \(0.284933\pi\)
\(888\) 142.651 4.78706
\(889\) −20.0926 −0.673883
\(890\) −0.158940 −0.00532768
\(891\) −0.801392 −0.0268476
\(892\) 56.0692 1.87734
\(893\) 0.224697 0.00751919
\(894\) −132.818 −4.44209
\(895\) −2.20059 −0.0735575
\(896\) 30.4011 1.01563
\(897\) −12.0967 −0.403896
\(898\) 45.1025 1.50509
\(899\) −27.0550 −0.902335
\(900\) −148.167 −4.93889
\(901\) 11.6043 0.386595
\(902\) 3.00180 0.0999491
\(903\) −4.38269 −0.145847
\(904\) −21.9566 −0.730265
\(905\) 4.39515 0.146100
\(906\) 86.5809 2.87646
\(907\) 36.8032 1.22203 0.611015 0.791619i \(-0.290762\pi\)
0.611015 + 0.791619i \(0.290762\pi\)
\(908\) −88.7449 −2.94510
\(909\) −22.7730 −0.755332
\(910\) 0.846839 0.0280724
\(911\) −44.8063 −1.48450 −0.742250 0.670123i \(-0.766241\pi\)
−0.742250 + 0.670123i \(0.766241\pi\)
\(912\) 22.9432 0.759725
\(913\) 1.23402 0.0408400
\(914\) −1.72191 −0.0569556
\(915\) −4.32093 −0.142846
\(916\) 25.8610 0.854471
\(917\) 3.69415 0.121992
\(918\) 39.2124 1.29420
\(919\) −42.3690 −1.39762 −0.698812 0.715305i \(-0.746288\pi\)
−0.698812 + 0.715305i \(0.746288\pi\)
\(920\) 12.9648 0.427438
\(921\) −7.42179 −0.244556
\(922\) −34.3521 −1.13133
\(923\) 11.4122 0.375637
\(924\) 2.05258 0.0675249
\(925\) 25.6379 0.842970
\(926\) −33.7463 −1.10897
\(927\) −97.5947 −3.20543
\(928\) −80.7469 −2.65065
\(929\) 9.83207 0.322580 0.161290 0.986907i \(-0.448435\pi\)
0.161290 + 0.986907i \(0.448435\pi\)
\(930\) −18.7527 −0.614925
\(931\) −3.34671 −0.109684
\(932\) −24.2381 −0.793945
\(933\) 23.5055 0.769535
\(934\) 40.7860 1.33456
\(935\) −0.0901446 −0.00294804
\(936\) 51.9853 1.69919
\(937\) −5.42285 −0.177157 −0.0885784 0.996069i \(-0.528232\pi\)
−0.0885784 + 0.996069i \(0.528232\pi\)
\(938\) −12.4072 −0.405110
\(939\) −55.0889 −1.79776
\(940\) −0.759157 −0.0247610
\(941\) −49.1300 −1.60159 −0.800796 0.598937i \(-0.795590\pi\)
−0.800796 + 0.598937i \(0.795590\pi\)
\(942\) −175.116 −5.70558
\(943\) 32.1893 1.04823
\(944\) −161.551 −5.25805
\(945\) 2.38754 0.0776665
\(946\) 0.626425 0.0203668
\(947\) −31.3713 −1.01943 −0.509716 0.860343i \(-0.670249\pi\)
−0.509716 + 0.860343i \(0.670249\pi\)
\(948\) −131.257 −4.26304
\(949\) −2.14580 −0.0696556
\(950\) 7.22018 0.234254
\(951\) −7.59268 −0.246209
\(952\) −15.9398 −0.516613
\(953\) 41.1524 1.33306 0.666529 0.745479i \(-0.267779\pi\)
0.666529 + 0.745479i \(0.267779\pi\)
\(954\) 94.3505 3.05471
\(955\) 1.68502 0.0545260
\(956\) −71.9780 −2.32794
\(957\) −1.62252 −0.0524485
\(958\) −89.5096 −2.89193
\(959\) −5.45042 −0.176003
\(960\) −27.2767 −0.880352
\(961\) 16.7924 0.541691
\(962\) −14.2813 −0.460447
\(963\) 79.3443 2.55683
\(964\) −33.1670 −1.06824
\(965\) −0.910421 −0.0293075
\(966\) 30.1574 0.970300
\(967\) −24.3093 −0.781735 −0.390868 0.920447i \(-0.627825\pi\)
−0.390868 + 0.920447i \(0.627825\pi\)
\(968\) 101.679 3.26808
\(969\) −2.99532 −0.0962235
\(970\) −0.257656 −0.00827284
\(971\) 13.8394 0.444127 0.222064 0.975032i \(-0.428721\pi\)
0.222064 + 0.975032i \(0.428721\pi\)
\(972\) −34.3845 −1.10288
\(973\) 18.6354 0.597424
\(974\) −43.7191 −1.40085
\(975\) 14.3360 0.459119
\(976\) 62.3682 1.99636
\(977\) −16.7100 −0.534599 −0.267299 0.963614i \(-0.586131\pi\)
−0.267299 + 0.963614i \(0.586131\pi\)
\(978\) −0.450443 −0.0144036
\(979\) 0.0242924 0.000776387 0
\(980\) 11.3071 0.361194
\(981\) 22.8594 0.729844
\(982\) 13.1411 0.419348
\(983\) −10.9191 −0.348267 −0.174133 0.984722i \(-0.555712\pi\)
−0.174133 + 0.984722i \(0.555712\pi\)
\(984\) −212.259 −6.76657
\(985\) 0.766070 0.0244090
\(986\) 20.0045 0.637073
\(987\) −1.11225 −0.0354035
\(988\) −2.93541 −0.0933878
\(989\) 6.71737 0.213600
\(990\) −0.732935 −0.0232942
\(991\) 25.4467 0.808341 0.404171 0.914684i \(-0.367560\pi\)
0.404171 + 0.914684i \(0.367560\pi\)
\(992\) 142.639 4.52878
\(993\) −26.1213 −0.828935
\(994\) −28.4510 −0.902411
\(995\) 5.69457 0.180530
\(996\) −138.535 −4.38965
\(997\) 24.6748 0.781458 0.390729 0.920506i \(-0.372223\pi\)
0.390729 + 0.920506i \(0.372223\pi\)
\(998\) −68.6273 −2.17236
\(999\) −40.2640 −1.27390
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 8021.2.a.b.1.2 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8021.2.a.b.1.2 140 1.1 even 1 trivial