Properties

Label 8005.2.a.e.1.12
Level $8005$
Weight $2$
Character 8005.1
Self dual yes
Analytic conductor $63.920$
Analytic rank $1$
Dimension $126$
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] = [8005,2,Mod(1,8005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8005, 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("8005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8005 = 5 \cdot 1601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8005.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: \(63.9202468180\)
Analytic rank: \(1\)
Dimension: \(126\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 8005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.44890 q^{2} +0.480075 q^{3} +3.99711 q^{4} +1.00000 q^{5} -1.17566 q^{6} -2.53410 q^{7} -4.89071 q^{8} -2.76953 q^{9} +O(q^{10})\) \(q-2.44890 q^{2} +0.480075 q^{3} +3.99711 q^{4} +1.00000 q^{5} -1.17566 q^{6} -2.53410 q^{7} -4.89071 q^{8} -2.76953 q^{9} -2.44890 q^{10} +3.07951 q^{11} +1.91891 q^{12} -3.14784 q^{13} +6.20576 q^{14} +0.480075 q^{15} +3.98264 q^{16} -6.24864 q^{17} +6.78229 q^{18} +5.29043 q^{19} +3.99711 q^{20} -1.21656 q^{21} -7.54140 q^{22} -1.94717 q^{23} -2.34791 q^{24} +1.00000 q^{25} +7.70874 q^{26} -2.76981 q^{27} -10.1291 q^{28} +3.47422 q^{29} -1.17566 q^{30} -3.41518 q^{31} +0.0283274 q^{32} +1.47840 q^{33} +15.3023 q^{34} -2.53410 q^{35} -11.0701 q^{36} +8.02159 q^{37} -12.9557 q^{38} -1.51120 q^{39} -4.89071 q^{40} +7.31748 q^{41} +2.97923 q^{42} -5.82547 q^{43} +12.3091 q^{44} -2.76953 q^{45} +4.76842 q^{46} +5.99700 q^{47} +1.91197 q^{48} -0.578326 q^{49} -2.44890 q^{50} -2.99982 q^{51} -12.5822 q^{52} -1.80401 q^{53} +6.78298 q^{54} +3.07951 q^{55} +12.3936 q^{56} +2.53980 q^{57} -8.50803 q^{58} +9.00745 q^{59} +1.91891 q^{60} +15.1378 q^{61} +8.36343 q^{62} +7.01827 q^{63} -8.03466 q^{64} -3.14784 q^{65} -3.62044 q^{66} -5.98455 q^{67} -24.9765 q^{68} -0.934786 q^{69} +6.20576 q^{70} -14.8288 q^{71} +13.5450 q^{72} -3.35326 q^{73} -19.6441 q^{74} +0.480075 q^{75} +21.1464 q^{76} -7.80379 q^{77} +3.70077 q^{78} +14.7884 q^{79} +3.98264 q^{80} +6.97887 q^{81} -17.9198 q^{82} -4.72106 q^{83} -4.86272 q^{84} -6.24864 q^{85} +14.2660 q^{86} +1.66789 q^{87} -15.0610 q^{88} -0.813636 q^{89} +6.78229 q^{90} +7.97694 q^{91} -7.78303 q^{92} -1.63954 q^{93} -14.6861 q^{94} +5.29043 q^{95} +0.0135993 q^{96} +4.19973 q^{97} +1.41626 q^{98} -8.52878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44890 −1.73163 −0.865817 0.500362i \(-0.833200\pi\)
−0.865817 + 0.500362i \(0.833200\pi\)
\(3\) 0.480075 0.277171 0.138586 0.990350i \(-0.455744\pi\)
0.138586 + 0.990350i \(0.455744\pi\)
\(4\) 3.99711 1.99855
\(5\) 1.00000 0.447214
\(6\) −1.17566 −0.479959
\(7\) −2.53410 −0.957801 −0.478900 0.877869i \(-0.658964\pi\)
−0.478900 + 0.877869i \(0.658964\pi\)
\(8\) −4.89071 −1.72913
\(9\) −2.76953 −0.923176
\(10\) −2.44890 −0.774410
\(11\) 3.07951 0.928507 0.464253 0.885702i \(-0.346323\pi\)
0.464253 + 0.885702i \(0.346323\pi\)
\(12\) 1.91891 0.553942
\(13\) −3.14784 −0.873053 −0.436527 0.899691i \(-0.643792\pi\)
−0.436527 + 0.899691i \(0.643792\pi\)
\(14\) 6.20576 1.65856
\(15\) 0.480075 0.123955
\(16\) 3.98264 0.995661
\(17\) −6.24864 −1.51552 −0.757759 0.652535i \(-0.773706\pi\)
−0.757759 + 0.652535i \(0.773706\pi\)
\(18\) 6.78229 1.59860
\(19\) 5.29043 1.21371 0.606854 0.794813i \(-0.292431\pi\)
0.606854 + 0.794813i \(0.292431\pi\)
\(20\) 3.99711 0.893780
\(21\) −1.21656 −0.265475
\(22\) −7.54140 −1.60783
\(23\) −1.94717 −0.406012 −0.203006 0.979177i \(-0.565071\pi\)
−0.203006 + 0.979177i \(0.565071\pi\)
\(24\) −2.34791 −0.479265
\(25\) 1.00000 0.200000
\(26\) 7.70874 1.51181
\(27\) −2.76981 −0.533050
\(28\) −10.1291 −1.91422
\(29\) 3.47422 0.645147 0.322574 0.946544i \(-0.395452\pi\)
0.322574 + 0.946544i \(0.395452\pi\)
\(30\) −1.17566 −0.214644
\(31\) −3.41518 −0.613385 −0.306692 0.951809i \(-0.599222\pi\)
−0.306692 + 0.951809i \(0.599222\pi\)
\(32\) 0.0283274 0.00500763
\(33\) 1.47840 0.257356
\(34\) 15.3023 2.62432
\(35\) −2.53410 −0.428341
\(36\) −11.0701 −1.84502
\(37\) 8.02159 1.31874 0.659371 0.751818i \(-0.270823\pi\)
0.659371 + 0.751818i \(0.270823\pi\)
\(38\) −12.9557 −2.10170
\(39\) −1.51120 −0.241985
\(40\) −4.89071 −0.773289
\(41\) 7.31748 1.14280 0.571399 0.820672i \(-0.306401\pi\)
0.571399 + 0.820672i \(0.306401\pi\)
\(42\) 2.97923 0.459705
\(43\) −5.82547 −0.888376 −0.444188 0.895934i \(-0.646508\pi\)
−0.444188 + 0.895934i \(0.646508\pi\)
\(44\) 12.3091 1.85567
\(45\) −2.76953 −0.412857
\(46\) 4.76842 0.703065
\(47\) 5.99700 0.874753 0.437376 0.899279i \(-0.355908\pi\)
0.437376 + 0.899279i \(0.355908\pi\)
\(48\) 1.91197 0.275969
\(49\) −0.578326 −0.0826181
\(50\) −2.44890 −0.346327
\(51\) −2.99982 −0.420058
\(52\) −12.5822 −1.74484
\(53\) −1.80401 −0.247800 −0.123900 0.992295i \(-0.539540\pi\)
−0.123900 + 0.992295i \(0.539540\pi\)
\(54\) 6.78298 0.923046
\(55\) 3.07951 0.415241
\(56\) 12.3936 1.65616
\(57\) 2.53980 0.336405
\(58\) −8.50803 −1.11716
\(59\) 9.00745 1.17267 0.586335 0.810069i \(-0.300570\pi\)
0.586335 + 0.810069i \(0.300570\pi\)
\(60\) 1.91891 0.247730
\(61\) 15.1378 1.93819 0.969096 0.246684i \(-0.0793411\pi\)
0.969096 + 0.246684i \(0.0793411\pi\)
\(62\) 8.36343 1.06216
\(63\) 7.01827 0.884218
\(64\) −8.03466 −1.00433
\(65\) −3.14784 −0.390441
\(66\) −3.62044 −0.445645
\(67\) −5.98455 −0.731129 −0.365564 0.930786i \(-0.619124\pi\)
−0.365564 + 0.930786i \(0.619124\pi\)
\(68\) −24.9765 −3.02884
\(69\) −0.934786 −0.112535
\(70\) 6.20576 0.741730
\(71\) −14.8288 −1.75985 −0.879927 0.475109i \(-0.842409\pi\)
−0.879927 + 0.475109i \(0.842409\pi\)
\(72\) 13.5450 1.59629
\(73\) −3.35326 −0.392469 −0.196235 0.980557i \(-0.562871\pi\)
−0.196235 + 0.980557i \(0.562871\pi\)
\(74\) −19.6441 −2.28358
\(75\) 0.480075 0.0554343
\(76\) 21.1464 2.42566
\(77\) −7.80379 −0.889324
\(78\) 3.70077 0.419030
\(79\) 14.7884 1.66382 0.831912 0.554908i \(-0.187247\pi\)
0.831912 + 0.554908i \(0.187247\pi\)
\(80\) 3.98264 0.445273
\(81\) 6.97887 0.775430
\(82\) −17.9198 −1.97891
\(83\) −4.72106 −0.518204 −0.259102 0.965850i \(-0.583427\pi\)
−0.259102 + 0.965850i \(0.583427\pi\)
\(84\) −4.86272 −0.530566
\(85\) −6.24864 −0.677760
\(86\) 14.2660 1.53834
\(87\) 1.66789 0.178816
\(88\) −15.0610 −1.60551
\(89\) −0.813636 −0.0862452 −0.0431226 0.999070i \(-0.513731\pi\)
−0.0431226 + 0.999070i \(0.513731\pi\)
\(90\) 6.78229 0.714917
\(91\) 7.97694 0.836211
\(92\) −7.78303 −0.811437
\(93\) −1.63954 −0.170013
\(94\) −14.6861 −1.51475
\(95\) 5.29043 0.542787
\(96\) 0.0135993 0.00138797
\(97\) 4.19973 0.426418 0.213209 0.977007i \(-0.431608\pi\)
0.213209 + 0.977007i \(0.431608\pi\)
\(98\) 1.41626 0.143064
\(99\) −8.52878 −0.857175
\(100\) 3.99711 0.399711
\(101\) −12.4301 −1.23684 −0.618419 0.785848i \(-0.712227\pi\)
−0.618419 + 0.785848i \(0.712227\pi\)
\(102\) 7.34625 0.727387
\(103\) 11.4006 1.12333 0.561665 0.827365i \(-0.310161\pi\)
0.561665 + 0.827365i \(0.310161\pi\)
\(104\) 15.3952 1.50962
\(105\) −1.21656 −0.118724
\(106\) 4.41785 0.429099
\(107\) 16.7562 1.61988 0.809939 0.586514i \(-0.199500\pi\)
0.809939 + 0.586514i \(0.199500\pi\)
\(108\) −11.0712 −1.06533
\(109\) −5.12379 −0.490770 −0.245385 0.969426i \(-0.578914\pi\)
−0.245385 + 0.969426i \(0.578914\pi\)
\(110\) −7.54140 −0.719045
\(111\) 3.85097 0.365517
\(112\) −10.0924 −0.953645
\(113\) 16.7026 1.57125 0.785623 0.618705i \(-0.212342\pi\)
0.785623 + 0.618705i \(0.212342\pi\)
\(114\) −6.21973 −0.582531
\(115\) −1.94717 −0.181574
\(116\) 13.8868 1.28936
\(117\) 8.71803 0.805982
\(118\) −22.0583 −2.03063
\(119\) 15.8347 1.45156
\(120\) −2.34791 −0.214334
\(121\) −1.51663 −0.137875
\(122\) −37.0708 −3.35624
\(123\) 3.51294 0.316751
\(124\) −13.6508 −1.22588
\(125\) 1.00000 0.0894427
\(126\) −17.1870 −1.53114
\(127\) 7.12946 0.632637 0.316318 0.948653i \(-0.397553\pi\)
0.316318 + 0.948653i \(0.397553\pi\)
\(128\) 19.6194 1.73413
\(129\) −2.79666 −0.246232
\(130\) 7.70874 0.676101
\(131\) 9.41479 0.822574 0.411287 0.911506i \(-0.365079\pi\)
0.411287 + 0.911506i \(0.365079\pi\)
\(132\) 5.90930 0.514339
\(133\) −13.4065 −1.16249
\(134\) 14.6555 1.26605
\(135\) −2.76981 −0.238387
\(136\) 30.5603 2.62052
\(137\) 5.93827 0.507340 0.253670 0.967291i \(-0.418362\pi\)
0.253670 + 0.967291i \(0.418362\pi\)
\(138\) 2.28920 0.194869
\(139\) −18.9302 −1.60564 −0.802821 0.596220i \(-0.796669\pi\)
−0.802821 + 0.596220i \(0.796669\pi\)
\(140\) −10.1291 −0.856063
\(141\) 2.87901 0.242457
\(142\) 36.3142 3.04742
\(143\) −9.69379 −0.810636
\(144\) −11.0300 −0.919170
\(145\) 3.47422 0.288519
\(146\) 8.21179 0.679612
\(147\) −0.277640 −0.0228994
\(148\) 32.0631 2.63557
\(149\) −16.7069 −1.36868 −0.684341 0.729162i \(-0.739910\pi\)
−0.684341 + 0.729162i \(0.739910\pi\)
\(150\) −1.17566 −0.0959919
\(151\) 10.4096 0.847121 0.423560 0.905868i \(-0.360780\pi\)
0.423560 + 0.905868i \(0.360780\pi\)
\(152\) −25.8740 −2.09866
\(153\) 17.3058 1.39909
\(154\) 19.1107 1.53998
\(155\) −3.41518 −0.274314
\(156\) −6.04042 −0.483621
\(157\) −20.5357 −1.63893 −0.819465 0.573130i \(-0.805729\pi\)
−0.819465 + 0.573130i \(0.805729\pi\)
\(158\) −36.2153 −2.88113
\(159\) −0.866062 −0.0686832
\(160\) 0.0283274 0.00223948
\(161\) 4.93432 0.388879
\(162\) −17.0905 −1.34276
\(163\) −20.8535 −1.63337 −0.816687 0.577081i \(-0.804192\pi\)
−0.816687 + 0.577081i \(0.804192\pi\)
\(164\) 29.2487 2.28394
\(165\) 1.47840 0.115093
\(166\) 11.5614 0.897338
\(167\) −2.78002 −0.215124 −0.107562 0.994198i \(-0.534304\pi\)
−0.107562 + 0.994198i \(0.534304\pi\)
\(168\) 5.94984 0.459040
\(169\) −3.09112 −0.237778
\(170\) 15.3023 1.17363
\(171\) −14.6520 −1.12047
\(172\) −23.2850 −1.77547
\(173\) −6.18322 −0.470102 −0.235051 0.971983i \(-0.575526\pi\)
−0.235051 + 0.971983i \(0.575526\pi\)
\(174\) −4.08449 −0.309644
\(175\) −2.53410 −0.191560
\(176\) 12.2646 0.924478
\(177\) 4.32425 0.325031
\(178\) 1.99251 0.149345
\(179\) −1.39814 −0.104502 −0.0522511 0.998634i \(-0.516640\pi\)
−0.0522511 + 0.998634i \(0.516640\pi\)
\(180\) −11.0701 −0.825116
\(181\) 3.58045 0.266133 0.133066 0.991107i \(-0.457518\pi\)
0.133066 + 0.991107i \(0.457518\pi\)
\(182\) −19.5347 −1.44801
\(183\) 7.26726 0.537211
\(184\) 9.52303 0.702047
\(185\) 8.02159 0.589759
\(186\) 4.01508 0.294400
\(187\) −19.2427 −1.40717
\(188\) 23.9707 1.74824
\(189\) 7.01897 0.510555
\(190\) −12.9557 −0.939908
\(191\) −18.3633 −1.32872 −0.664360 0.747413i \(-0.731296\pi\)
−0.664360 + 0.747413i \(0.731296\pi\)
\(192\) −3.85724 −0.278372
\(193\) −19.5531 −1.40747 −0.703733 0.710465i \(-0.748485\pi\)
−0.703733 + 0.710465i \(0.748485\pi\)
\(194\) −10.2847 −0.738400
\(195\) −1.51120 −0.108219
\(196\) −2.31163 −0.165117
\(197\) −19.2963 −1.37481 −0.687403 0.726276i \(-0.741249\pi\)
−0.687403 + 0.726276i \(0.741249\pi\)
\(198\) 20.8861 1.48431
\(199\) −2.35278 −0.166784 −0.0833922 0.996517i \(-0.526575\pi\)
−0.0833922 + 0.996517i \(0.526575\pi\)
\(200\) −4.89071 −0.345825
\(201\) −2.87303 −0.202648
\(202\) 30.4400 2.14175
\(203\) −8.80404 −0.617922
\(204\) −11.9906 −0.839509
\(205\) 7.31748 0.511075
\(206\) −27.9188 −1.94520
\(207\) 5.39273 0.374821
\(208\) −12.5367 −0.869265
\(209\) 16.2919 1.12694
\(210\) 2.97923 0.205586
\(211\) 6.12434 0.421617 0.210809 0.977527i \(-0.432390\pi\)
0.210809 + 0.977527i \(0.432390\pi\)
\(212\) −7.21084 −0.495242
\(213\) −7.11893 −0.487781
\(214\) −41.0341 −2.80504
\(215\) −5.82547 −0.397294
\(216\) 13.5463 0.921711
\(217\) 8.65442 0.587500
\(218\) 12.5476 0.849834
\(219\) −1.60982 −0.108781
\(220\) 12.3091 0.829881
\(221\) 19.6697 1.32313
\(222\) −9.43062 −0.632942
\(223\) −0.391247 −0.0261998 −0.0130999 0.999914i \(-0.504170\pi\)
−0.0130999 + 0.999914i \(0.504170\pi\)
\(224\) −0.0717845 −0.00479631
\(225\) −2.76953 −0.184635
\(226\) −40.9029 −2.72082
\(227\) −7.94013 −0.527005 −0.263503 0.964659i \(-0.584878\pi\)
−0.263503 + 0.964659i \(0.584878\pi\)
\(228\) 10.1519 0.672324
\(229\) −5.83068 −0.385302 −0.192651 0.981267i \(-0.561709\pi\)
−0.192651 + 0.981267i \(0.561709\pi\)
\(230\) 4.76842 0.314420
\(231\) −3.74640 −0.246495
\(232\) −16.9914 −1.11554
\(233\) −14.4254 −0.945040 −0.472520 0.881320i \(-0.656656\pi\)
−0.472520 + 0.881320i \(0.656656\pi\)
\(234\) −21.3496 −1.39566
\(235\) 5.99700 0.391201
\(236\) 36.0037 2.34364
\(237\) 7.09953 0.461164
\(238\) −38.7776 −2.51358
\(239\) −4.48985 −0.290424 −0.145212 0.989401i \(-0.546386\pi\)
−0.145212 + 0.989401i \(0.546386\pi\)
\(240\) 1.91197 0.123417
\(241\) −28.7805 −1.85391 −0.926957 0.375169i \(-0.877585\pi\)
−0.926957 + 0.375169i \(0.877585\pi\)
\(242\) 3.71407 0.238750
\(243\) 11.6598 0.747977
\(244\) 60.5072 3.87358
\(245\) −0.578326 −0.0369479
\(246\) −8.60284 −0.548497
\(247\) −16.6534 −1.05963
\(248\) 16.7027 1.06062
\(249\) −2.26646 −0.143631
\(250\) −2.44890 −0.154882
\(251\) −10.1473 −0.640490 −0.320245 0.947335i \(-0.603765\pi\)
−0.320245 + 0.947335i \(0.603765\pi\)
\(252\) 28.0528 1.76716
\(253\) −5.99632 −0.376985
\(254\) −17.4593 −1.09549
\(255\) −2.99982 −0.187856
\(256\) −31.9766 −1.99854
\(257\) −10.2348 −0.638428 −0.319214 0.947683i \(-0.603419\pi\)
−0.319214 + 0.947683i \(0.603419\pi\)
\(258\) 6.84875 0.426384
\(259\) −20.3275 −1.26309
\(260\) −12.5822 −0.780318
\(261\) −9.62196 −0.595585
\(262\) −23.0559 −1.42440
\(263\) 4.78085 0.294800 0.147400 0.989077i \(-0.452910\pi\)
0.147400 + 0.989077i \(0.452910\pi\)
\(264\) −7.23040 −0.445001
\(265\) −1.80401 −0.110820
\(266\) 32.8312 2.01301
\(267\) −0.390606 −0.0239047
\(268\) −23.9209 −1.46120
\(269\) −14.7226 −0.897652 −0.448826 0.893619i \(-0.648158\pi\)
−0.448826 + 0.893619i \(0.648158\pi\)
\(270\) 6.78298 0.412799
\(271\) 6.47774 0.393495 0.196747 0.980454i \(-0.436962\pi\)
0.196747 + 0.980454i \(0.436962\pi\)
\(272\) −24.8861 −1.50894
\(273\) 3.82953 0.231774
\(274\) −14.5422 −0.878528
\(275\) 3.07951 0.185701
\(276\) −3.73644 −0.224907
\(277\) 31.3309 1.88249 0.941246 0.337722i \(-0.109656\pi\)
0.941246 + 0.337722i \(0.109656\pi\)
\(278\) 46.3582 2.78038
\(279\) 9.45844 0.566262
\(280\) 12.3936 0.740657
\(281\) −14.1883 −0.846401 −0.423201 0.906036i \(-0.639093\pi\)
−0.423201 + 0.906036i \(0.639093\pi\)
\(282\) −7.05041 −0.419846
\(283\) 22.4388 1.33385 0.666925 0.745124i \(-0.267610\pi\)
0.666925 + 0.745124i \(0.267610\pi\)
\(284\) −59.2723 −3.51716
\(285\) 2.53980 0.150445
\(286\) 23.7391 1.40372
\(287\) −18.5432 −1.09457
\(288\) −0.0784535 −0.00462292
\(289\) 22.0455 1.29679
\(290\) −8.50803 −0.499608
\(291\) 2.01619 0.118191
\(292\) −13.4033 −0.784370
\(293\) −28.4697 −1.66322 −0.831610 0.555360i \(-0.812580\pi\)
−0.831610 + 0.555360i \(0.812580\pi\)
\(294\) 0.679913 0.0396533
\(295\) 9.00745 0.524434
\(296\) −39.2313 −2.28027
\(297\) −8.52964 −0.494940
\(298\) 40.9135 2.37005
\(299\) 6.12937 0.354470
\(300\) 1.91891 0.110788
\(301\) 14.7623 0.850887
\(302\) −25.4920 −1.46690
\(303\) −5.96737 −0.342816
\(304\) 21.0699 1.20844
\(305\) 15.1378 0.866786
\(306\) −42.3801 −2.42271
\(307\) −14.3822 −0.820838 −0.410419 0.911897i \(-0.634618\pi\)
−0.410419 + 0.911897i \(0.634618\pi\)
\(308\) −31.1926 −1.77736
\(309\) 5.47312 0.311355
\(310\) 8.36343 0.475011
\(311\) −2.07599 −0.117719 −0.0588593 0.998266i \(-0.518746\pi\)
−0.0588593 + 0.998266i \(0.518746\pi\)
\(312\) 7.39084 0.418424
\(313\) −15.8042 −0.893308 −0.446654 0.894707i \(-0.647384\pi\)
−0.446654 + 0.894707i \(0.647384\pi\)
\(314\) 50.2899 2.83802
\(315\) 7.01827 0.395435
\(316\) 59.1107 3.32524
\(317\) 30.4849 1.71220 0.856102 0.516807i \(-0.172879\pi\)
0.856102 + 0.516807i \(0.172879\pi\)
\(318\) 2.12090 0.118934
\(319\) 10.6989 0.599024
\(320\) −8.03466 −0.449151
\(321\) 8.04421 0.448984
\(322\) −12.0837 −0.673396
\(323\) −33.0580 −1.83940
\(324\) 27.8953 1.54974
\(325\) −3.14784 −0.174611
\(326\) 51.0681 2.82840
\(327\) −2.45980 −0.136027
\(328\) −35.7877 −1.97604
\(329\) −15.1970 −0.837839
\(330\) −3.62044 −0.199299
\(331\) 27.0037 1.48426 0.742129 0.670257i \(-0.233816\pi\)
0.742129 + 0.670257i \(0.233816\pi\)
\(332\) −18.8706 −1.03566
\(333\) −22.2160 −1.21743
\(334\) 6.80798 0.372516
\(335\) −5.98455 −0.326971
\(336\) −4.84512 −0.264323
\(337\) 13.0842 0.712740 0.356370 0.934345i \(-0.384014\pi\)
0.356370 + 0.934345i \(0.384014\pi\)
\(338\) 7.56983 0.411745
\(339\) 8.01849 0.435505
\(340\) −24.9765 −1.35454
\(341\) −10.5171 −0.569532
\(342\) 35.8813 1.94024
\(343\) 19.2043 1.03693
\(344\) 28.4907 1.53612
\(345\) −0.934786 −0.0503272
\(346\) 15.1421 0.814044
\(347\) −12.4848 −0.670218 −0.335109 0.942179i \(-0.608773\pi\)
−0.335109 + 0.942179i \(0.608773\pi\)
\(348\) 6.66673 0.357374
\(349\) 11.1143 0.594936 0.297468 0.954732i \(-0.403858\pi\)
0.297468 + 0.954732i \(0.403858\pi\)
\(350\) 6.20576 0.331712
\(351\) 8.71890 0.465381
\(352\) 0.0872345 0.00464961
\(353\) 0.464677 0.0247323 0.0123661 0.999924i \(-0.496064\pi\)
0.0123661 + 0.999924i \(0.496064\pi\)
\(354\) −10.5897 −0.562834
\(355\) −14.8288 −0.787031
\(356\) −3.25219 −0.172366
\(357\) 7.60184 0.402332
\(358\) 3.42391 0.180960
\(359\) −29.0602 −1.53374 −0.766869 0.641804i \(-0.778186\pi\)
−0.766869 + 0.641804i \(0.778186\pi\)
\(360\) 13.5450 0.713882
\(361\) 8.98868 0.473088
\(362\) −8.76817 −0.460845
\(363\) −0.728096 −0.0382151
\(364\) 31.8847 1.67121
\(365\) −3.35326 −0.175518
\(366\) −17.7968 −0.930253
\(367\) −18.5068 −0.966048 −0.483024 0.875607i \(-0.660462\pi\)
−0.483024 + 0.875607i \(0.660462\pi\)
\(368\) −7.75487 −0.404251
\(369\) −20.2660 −1.05500
\(370\) −19.6441 −1.02125
\(371\) 4.57156 0.237343
\(372\) −6.55343 −0.339779
\(373\) 1.30486 0.0675633 0.0337816 0.999429i \(-0.489245\pi\)
0.0337816 + 0.999429i \(0.489245\pi\)
\(374\) 47.1235 2.43670
\(375\) 0.480075 0.0247910
\(376\) −29.3296 −1.51256
\(377\) −10.9363 −0.563248
\(378\) −17.1888 −0.884094
\(379\) −20.4798 −1.05198 −0.525989 0.850491i \(-0.676305\pi\)
−0.525989 + 0.850491i \(0.676305\pi\)
\(380\) 21.1464 1.08479
\(381\) 3.42267 0.175349
\(382\) 44.9698 2.30085
\(383\) −13.4409 −0.686799 −0.343400 0.939189i \(-0.611579\pi\)
−0.343400 + 0.939189i \(0.611579\pi\)
\(384\) 9.41879 0.480651
\(385\) −7.80379 −0.397718
\(386\) 47.8837 2.43721
\(387\) 16.1338 0.820127
\(388\) 16.7868 0.852220
\(389\) −29.7978 −1.51081 −0.755405 0.655258i \(-0.772560\pi\)
−0.755405 + 0.655258i \(0.772560\pi\)
\(390\) 3.70077 0.187396
\(391\) 12.1671 0.615319
\(392\) 2.82843 0.142857
\(393\) 4.51980 0.227994
\(394\) 47.2547 2.38066
\(395\) 14.7884 0.744084
\(396\) −34.0905 −1.71311
\(397\) −8.76087 −0.439695 −0.219848 0.975534i \(-0.570556\pi\)
−0.219848 + 0.975534i \(0.570556\pi\)
\(398\) 5.76173 0.288809
\(399\) −6.43613 −0.322209
\(400\) 3.98264 0.199132
\(401\) 19.3033 0.963961 0.481980 0.876182i \(-0.339918\pi\)
0.481980 + 0.876182i \(0.339918\pi\)
\(402\) 7.03576 0.350912
\(403\) 10.7504 0.535517
\(404\) −49.6843 −2.47189
\(405\) 6.97887 0.346783
\(406\) 21.5602 1.07001
\(407\) 24.7025 1.22446
\(408\) 14.6712 0.726334
\(409\) 32.6824 1.61604 0.808020 0.589155i \(-0.200539\pi\)
0.808020 + 0.589155i \(0.200539\pi\)
\(410\) −17.9198 −0.884995
\(411\) 2.85081 0.140620
\(412\) 45.5692 2.24503
\(413\) −22.8258 −1.12318
\(414\) −13.2063 −0.649052
\(415\) −4.72106 −0.231748
\(416\) −0.0891701 −0.00437192
\(417\) −9.08794 −0.445038
\(418\) −39.8973 −1.95144
\(419\) −4.29147 −0.209652 −0.104826 0.994491i \(-0.533429\pi\)
−0.104826 + 0.994491i \(0.533429\pi\)
\(420\) −4.86272 −0.237276
\(421\) −20.2011 −0.984542 −0.492271 0.870442i \(-0.663833\pi\)
−0.492271 + 0.870442i \(0.663833\pi\)
\(422\) −14.9979 −0.730086
\(423\) −16.6089 −0.807551
\(424\) 8.82291 0.428479
\(425\) −6.24864 −0.303104
\(426\) 17.4335 0.844658
\(427\) −38.3606 −1.85640
\(428\) 66.9761 3.23741
\(429\) −4.65375 −0.224685
\(430\) 14.2660 0.687967
\(431\) −7.86199 −0.378699 −0.189349 0.981910i \(-0.560638\pi\)
−0.189349 + 0.981910i \(0.560638\pi\)
\(432\) −11.0312 −0.530737
\(433\) 10.3456 0.497177 0.248588 0.968609i \(-0.420033\pi\)
0.248588 + 0.968609i \(0.420033\pi\)
\(434\) −21.1938 −1.01733
\(435\) 1.66789 0.0799691
\(436\) −20.4803 −0.980830
\(437\) −10.3014 −0.492781
\(438\) 3.94228 0.188369
\(439\) 27.2229 1.29928 0.649638 0.760244i \(-0.274920\pi\)
0.649638 + 0.760244i \(0.274920\pi\)
\(440\) −15.0610 −0.718004
\(441\) 1.60169 0.0762710
\(442\) −48.1691 −2.29117
\(443\) −15.9815 −0.759306 −0.379653 0.925129i \(-0.623957\pi\)
−0.379653 + 0.925129i \(0.623957\pi\)
\(444\) 15.3927 0.730506
\(445\) −0.813636 −0.0385700
\(446\) 0.958124 0.0453685
\(447\) −8.02056 −0.379359
\(448\) 20.3606 0.961950
\(449\) −25.0695 −1.18310 −0.591551 0.806267i \(-0.701484\pi\)
−0.591551 + 0.806267i \(0.701484\pi\)
\(450\) 6.78229 0.319720
\(451\) 22.5342 1.06110
\(452\) 66.7620 3.14022
\(453\) 4.99739 0.234798
\(454\) 19.4446 0.912579
\(455\) 7.97694 0.373965
\(456\) −12.4215 −0.581688
\(457\) 0.0485111 0.00226925 0.00113463 0.999999i \(-0.499639\pi\)
0.00113463 + 0.999999i \(0.499639\pi\)
\(458\) 14.2788 0.667202
\(459\) 17.3075 0.807846
\(460\) −7.78303 −0.362886
\(461\) 25.8435 1.20365 0.601825 0.798628i \(-0.294441\pi\)
0.601825 + 0.798628i \(0.294441\pi\)
\(462\) 9.17457 0.426839
\(463\) −11.1217 −0.516871 −0.258436 0.966029i \(-0.583207\pi\)
−0.258436 + 0.966029i \(0.583207\pi\)
\(464\) 13.8366 0.642348
\(465\) −1.63954 −0.0760320
\(466\) 35.3264 1.63646
\(467\) 8.33562 0.385726 0.192863 0.981226i \(-0.438223\pi\)
0.192863 + 0.981226i \(0.438223\pi\)
\(468\) 34.8469 1.61080
\(469\) 15.1654 0.700275
\(470\) −14.6861 −0.677417
\(471\) −9.85869 −0.454265
\(472\) −44.0528 −2.02770
\(473\) −17.9396 −0.824863
\(474\) −17.3860 −0.798567
\(475\) 5.29043 0.242742
\(476\) 63.2929 2.90103
\(477\) 4.99627 0.228763
\(478\) 10.9952 0.502908
\(479\) −32.4588 −1.48308 −0.741541 0.670907i \(-0.765905\pi\)
−0.741541 + 0.670907i \(0.765905\pi\)
\(480\) 0.0135993 0.000620720 0
\(481\) −25.2507 −1.15133
\(482\) 70.4805 3.21030
\(483\) 2.36884 0.107786
\(484\) −6.06213 −0.275551
\(485\) 4.19973 0.190700
\(486\) −28.5537 −1.29522
\(487\) 7.85528 0.355957 0.177978 0.984034i \(-0.443044\pi\)
0.177978 + 0.984034i \(0.443044\pi\)
\(488\) −74.0344 −3.35138
\(489\) −10.0113 −0.452724
\(490\) 1.41626 0.0639802
\(491\) 18.0957 0.816649 0.408325 0.912837i \(-0.366113\pi\)
0.408325 + 0.912837i \(0.366113\pi\)
\(492\) 14.0416 0.633044
\(493\) −21.7092 −0.977732
\(494\) 40.7826 1.83489
\(495\) −8.52878 −0.383340
\(496\) −13.6015 −0.610723
\(497\) 37.5777 1.68559
\(498\) 5.55034 0.248717
\(499\) 23.0160 1.03034 0.515168 0.857089i \(-0.327729\pi\)
0.515168 + 0.857089i \(0.327729\pi\)
\(500\) 3.99711 0.178756
\(501\) −1.33462 −0.0596263
\(502\) 24.8496 1.10909
\(503\) −11.3548 −0.506285 −0.253143 0.967429i \(-0.581464\pi\)
−0.253143 + 0.967429i \(0.581464\pi\)
\(504\) −34.3243 −1.52893
\(505\) −12.4301 −0.553131
\(506\) 14.6844 0.652800
\(507\) −1.48397 −0.0659053
\(508\) 28.4972 1.26436
\(509\) 18.3028 0.811256 0.405628 0.914038i \(-0.367053\pi\)
0.405628 + 0.914038i \(0.367053\pi\)
\(510\) 7.34625 0.325297
\(511\) 8.49750 0.375907
\(512\) 39.0687 1.72661
\(513\) −14.6535 −0.646967
\(514\) 25.0639 1.10552
\(515\) 11.4006 0.502369
\(516\) −11.1786 −0.492109
\(517\) 18.4678 0.812214
\(518\) 49.7801 2.18721
\(519\) −2.96841 −0.130299
\(520\) 15.3952 0.675123
\(521\) −7.18084 −0.314598 −0.157299 0.987551i \(-0.550279\pi\)
−0.157299 + 0.987551i \(0.550279\pi\)
\(522\) 23.5632 1.03133
\(523\) 11.9804 0.523867 0.261934 0.965086i \(-0.415640\pi\)
0.261934 + 0.965086i \(0.415640\pi\)
\(524\) 37.6319 1.64396
\(525\) −1.21656 −0.0530950
\(526\) −11.7078 −0.510485
\(527\) 21.3402 0.929595
\(528\) 5.88792 0.256239
\(529\) −19.2085 −0.835154
\(530\) 4.41785 0.191899
\(531\) −24.9464 −1.08258
\(532\) −53.5872 −2.32330
\(533\) −23.0342 −0.997724
\(534\) 0.956555 0.0413942
\(535\) 16.7562 0.724432
\(536\) 29.2687 1.26421
\(537\) −0.671214 −0.0289650
\(538\) 36.0541 1.55440
\(539\) −1.78096 −0.0767114
\(540\) −11.0712 −0.476429
\(541\) 33.4557 1.43837 0.719186 0.694817i \(-0.244515\pi\)
0.719186 + 0.694817i \(0.244515\pi\)
\(542\) −15.8633 −0.681388
\(543\) 1.71889 0.0737645
\(544\) −0.177008 −0.00758915
\(545\) −5.12379 −0.219479
\(546\) −9.37814 −0.401347
\(547\) 44.9808 1.92324 0.961620 0.274384i \(-0.0884739\pi\)
0.961620 + 0.274384i \(0.0884739\pi\)
\(548\) 23.7359 1.01395
\(549\) −41.9245 −1.78929
\(550\) −7.54140 −0.321567
\(551\) 18.3802 0.783021
\(552\) 4.57177 0.194587
\(553\) −37.4753 −1.59361
\(554\) −76.7262 −3.25978
\(555\) 3.85097 0.163464
\(556\) −75.6662 −3.20896
\(557\) 22.3691 0.947810 0.473905 0.880576i \(-0.342844\pi\)
0.473905 + 0.880576i \(0.342844\pi\)
\(558\) −23.1628 −0.980558
\(559\) 18.3376 0.775599
\(560\) −10.0924 −0.426483
\(561\) −9.23796 −0.390027
\(562\) 34.7456 1.46566
\(563\) −11.8754 −0.500487 −0.250243 0.968183i \(-0.580511\pi\)
−0.250243 + 0.968183i \(0.580511\pi\)
\(564\) 11.5077 0.484562
\(565\) 16.7026 0.702683
\(566\) −54.9505 −2.30974
\(567\) −17.6852 −0.742707
\(568\) 72.5233 3.04301
\(569\) −20.5794 −0.862734 −0.431367 0.902177i \(-0.641969\pi\)
−0.431367 + 0.902177i \(0.641969\pi\)
\(570\) −6.21973 −0.260516
\(571\) 30.1821 1.26308 0.631540 0.775343i \(-0.282423\pi\)
0.631540 + 0.775343i \(0.282423\pi\)
\(572\) −38.7471 −1.62010
\(573\) −8.81575 −0.368283
\(574\) 45.4105 1.89540
\(575\) −1.94717 −0.0812025
\(576\) 22.2522 0.927176
\(577\) 35.0830 1.46052 0.730262 0.683168i \(-0.239398\pi\)
0.730262 + 0.683168i \(0.239398\pi\)
\(578\) −53.9872 −2.24557
\(579\) −9.38698 −0.390109
\(580\) 13.8868 0.576620
\(581\) 11.9636 0.496336
\(582\) −4.93744 −0.204663
\(583\) −5.55548 −0.230084
\(584\) 16.3998 0.678629
\(585\) 8.71803 0.360446
\(586\) 69.7195 2.88009
\(587\) −27.9304 −1.15281 −0.576406 0.817164i \(-0.695545\pi\)
−0.576406 + 0.817164i \(0.695545\pi\)
\(588\) −1.10976 −0.0457656
\(589\) −18.0678 −0.744470
\(590\) −22.0583 −0.908128
\(591\) −9.26368 −0.381057
\(592\) 31.9471 1.31302
\(593\) −25.5426 −1.04891 −0.524454 0.851439i \(-0.675730\pi\)
−0.524454 + 0.851439i \(0.675730\pi\)
\(594\) 20.8882 0.857055
\(595\) 15.8347 0.649159
\(596\) −66.7792 −2.73538
\(597\) −1.12951 −0.0462279
\(598\) −15.0102 −0.613813
\(599\) 20.5384 0.839175 0.419588 0.907715i \(-0.362175\pi\)
0.419588 + 0.907715i \(0.362175\pi\)
\(600\) −2.34791 −0.0958530
\(601\) 23.9576 0.977251 0.488626 0.872494i \(-0.337498\pi\)
0.488626 + 0.872494i \(0.337498\pi\)
\(602\) −36.1515 −1.47342
\(603\) 16.5744 0.674960
\(604\) 41.6083 1.69302
\(605\) −1.51663 −0.0616598
\(606\) 14.6135 0.593632
\(607\) 15.7703 0.640096 0.320048 0.947401i \(-0.396301\pi\)
0.320048 + 0.947401i \(0.396301\pi\)
\(608\) 0.149864 0.00607780
\(609\) −4.22660 −0.171270
\(610\) −37.0708 −1.50095
\(611\) −18.8776 −0.763706
\(612\) 69.1730 2.79615
\(613\) −15.9706 −0.645048 −0.322524 0.946561i \(-0.604531\pi\)
−0.322524 + 0.946561i \(0.604531\pi\)
\(614\) 35.2207 1.42139
\(615\) 3.51294 0.141655
\(616\) 38.1661 1.53775
\(617\) −36.1786 −1.45649 −0.728247 0.685315i \(-0.759665\pi\)
−0.728247 + 0.685315i \(0.759665\pi\)
\(618\) −13.4031 −0.539153
\(619\) −12.4216 −0.499268 −0.249634 0.968340i \(-0.580310\pi\)
−0.249634 + 0.968340i \(0.580310\pi\)
\(620\) −13.6508 −0.548231
\(621\) 5.39328 0.216425
\(622\) 5.08389 0.203845
\(623\) 2.06184 0.0826057
\(624\) −6.01857 −0.240936
\(625\) 1.00000 0.0400000
\(626\) 38.7029 1.54688
\(627\) 7.82135 0.312355
\(628\) −82.0835 −3.27549
\(629\) −50.1240 −1.99858
\(630\) −17.1870 −0.684747
\(631\) −35.9860 −1.43258 −0.716290 0.697803i \(-0.754161\pi\)
−0.716290 + 0.697803i \(0.754161\pi\)
\(632\) −72.3257 −2.87696
\(633\) 2.94014 0.116860
\(634\) −74.6545 −2.96491
\(635\) 7.12946 0.282924
\(636\) −3.46174 −0.137267
\(637\) 1.82048 0.0721300
\(638\) −26.2005 −1.03729
\(639\) 41.0688 1.62465
\(640\) 19.6194 0.775526
\(641\) −7.05860 −0.278798 −0.139399 0.990236i \(-0.544517\pi\)
−0.139399 + 0.990236i \(0.544517\pi\)
\(642\) −19.6995 −0.777476
\(643\) 41.2621 1.62722 0.813610 0.581411i \(-0.197499\pi\)
0.813610 + 0.581411i \(0.197499\pi\)
\(644\) 19.7230 0.777195
\(645\) −2.79666 −0.110119
\(646\) 80.9557 3.18516
\(647\) 19.5248 0.767601 0.383800 0.923416i \(-0.374615\pi\)
0.383800 + 0.923416i \(0.374615\pi\)
\(648\) −34.1316 −1.34082
\(649\) 27.7385 1.08883
\(650\) 7.70874 0.302362
\(651\) 4.15477 0.162838
\(652\) −83.3537 −3.26438
\(653\) −28.2209 −1.10437 −0.552185 0.833721i \(-0.686206\pi\)
−0.552185 + 0.833721i \(0.686206\pi\)
\(654\) 6.02381 0.235550
\(655\) 9.41479 0.367866
\(656\) 29.1429 1.13784
\(657\) 9.28694 0.362318
\(658\) 37.2160 1.45083
\(659\) −34.3936 −1.33978 −0.669891 0.742459i \(-0.733659\pi\)
−0.669891 + 0.742459i \(0.733659\pi\)
\(660\) 5.90930 0.230019
\(661\) 30.1511 1.17274 0.586370 0.810043i \(-0.300556\pi\)
0.586370 + 0.810043i \(0.300556\pi\)
\(662\) −66.1294 −2.57019
\(663\) 9.44294 0.366733
\(664\) 23.0893 0.896040
\(665\) −13.4065 −0.519882
\(666\) 54.4048 2.10814
\(667\) −6.76490 −0.261938
\(668\) −11.1120 −0.429937
\(669\) −0.187828 −0.00726184
\(670\) 14.6555 0.566193
\(671\) 46.6169 1.79962
\(672\) −0.0344620 −0.00132940
\(673\) −13.4327 −0.517791 −0.258896 0.965905i \(-0.583359\pi\)
−0.258896 + 0.965905i \(0.583359\pi\)
\(674\) −32.0418 −1.23420
\(675\) −2.76981 −0.106610
\(676\) −12.3555 −0.475212
\(677\) 16.8522 0.647682 0.323841 0.946112i \(-0.395026\pi\)
0.323841 + 0.946112i \(0.395026\pi\)
\(678\) −19.6365 −0.754134
\(679\) −10.6426 −0.408424
\(680\) 30.5603 1.17193
\(681\) −3.81186 −0.146071
\(682\) 25.7553 0.986220
\(683\) −19.5865 −0.749457 −0.374729 0.927135i \(-0.622264\pi\)
−0.374729 + 0.927135i \(0.622264\pi\)
\(684\) −58.5656 −2.23931
\(685\) 5.93827 0.226890
\(686\) −47.0293 −1.79559
\(687\) −2.79917 −0.106795
\(688\) −23.2008 −0.884521
\(689\) 5.67875 0.216343
\(690\) 2.28920 0.0871483
\(691\) 14.1480 0.538216 0.269108 0.963110i \(-0.413271\pi\)
0.269108 + 0.963110i \(0.413271\pi\)
\(692\) −24.7150 −0.939523
\(693\) 21.6128 0.821003
\(694\) 30.5739 1.16057
\(695\) −18.9302 −0.718065
\(696\) −8.15716 −0.309196
\(697\) −45.7243 −1.73193
\(698\) −27.2178 −1.03021
\(699\) −6.92528 −0.261938
\(700\) −10.1291 −0.382843
\(701\) −2.25243 −0.0850731 −0.0425366 0.999095i \(-0.513544\pi\)
−0.0425366 + 0.999095i \(0.513544\pi\)
\(702\) −21.3517 −0.805868
\(703\) 42.4377 1.60057
\(704\) −24.7428 −0.932529
\(705\) 2.87901 0.108430
\(706\) −1.13795 −0.0428272
\(707\) 31.4991 1.18464
\(708\) 17.2845 0.649591
\(709\) −35.7603 −1.34301 −0.671503 0.741002i \(-0.734351\pi\)
−0.671503 + 0.741002i \(0.734351\pi\)
\(710\) 36.3142 1.36285
\(711\) −40.9568 −1.53600
\(712\) 3.97926 0.149129
\(713\) 6.64993 0.249042
\(714\) −18.6161 −0.696692
\(715\) −9.69379 −0.362527
\(716\) −5.58853 −0.208853
\(717\) −2.15547 −0.0804973
\(718\) 71.1654 2.65587
\(719\) −36.9321 −1.37733 −0.688667 0.725078i \(-0.741804\pi\)
−0.688667 + 0.725078i \(0.741804\pi\)
\(720\) −11.0300 −0.411066
\(721\) −28.8902 −1.07593
\(722\) −22.0124 −0.819215
\(723\) −13.8168 −0.513852
\(724\) 14.3114 0.531881
\(725\) 3.47422 0.129029
\(726\) 1.78303 0.0661746
\(727\) −42.9674 −1.59357 −0.796787 0.604261i \(-0.793469\pi\)
−0.796787 + 0.604261i \(0.793469\pi\)
\(728\) −39.0129 −1.44592
\(729\) −15.3390 −0.568112
\(730\) 8.21179 0.303932
\(731\) 36.4013 1.34635
\(732\) 29.0480 1.07365
\(733\) −47.0090 −1.73632 −0.868158 0.496289i \(-0.834696\pi\)
−0.868158 + 0.496289i \(0.834696\pi\)
\(734\) 45.3213 1.67284
\(735\) −0.277640 −0.0102409
\(736\) −0.0551582 −0.00203316
\(737\) −18.4295 −0.678858
\(738\) 49.6293 1.82688
\(739\) −6.73634 −0.247800 −0.123900 0.992295i \(-0.539540\pi\)
−0.123900 + 0.992295i \(0.539540\pi\)
\(740\) 32.0631 1.17866
\(741\) −7.99489 −0.293700
\(742\) −11.1953 −0.410992
\(743\) 20.2609 0.743300 0.371650 0.928373i \(-0.378792\pi\)
0.371650 + 0.928373i \(0.378792\pi\)
\(744\) 8.01853 0.293974
\(745\) −16.7069 −0.612093
\(746\) −3.19548 −0.116995
\(747\) 13.0751 0.478393
\(748\) −76.9153 −2.81230
\(749\) −42.4618 −1.55152
\(750\) −1.17566 −0.0429289
\(751\) −22.6504 −0.826526 −0.413263 0.910612i \(-0.635611\pi\)
−0.413263 + 0.910612i \(0.635611\pi\)
\(752\) 23.8839 0.870958
\(753\) −4.87145 −0.177525
\(754\) 26.7819 0.975339
\(755\) 10.4096 0.378844
\(756\) 28.0556 1.02037
\(757\) 6.34454 0.230596 0.115298 0.993331i \(-0.463218\pi\)
0.115298 + 0.993331i \(0.463218\pi\)
\(758\) 50.1530 1.82164
\(759\) −2.87868 −0.104490
\(760\) −25.8740 −0.938548
\(761\) 1.28478 0.0465734 0.0232867 0.999729i \(-0.492587\pi\)
0.0232867 + 0.999729i \(0.492587\pi\)
\(762\) −8.38178 −0.303640
\(763\) 12.9842 0.470060
\(764\) −73.3999 −2.65552
\(765\) 17.3058 0.625692
\(766\) 32.9155 1.18928
\(767\) −28.3540 −1.02380
\(768\) −15.3512 −0.553938
\(769\) −21.2973 −0.767999 −0.383999 0.923333i \(-0.625454\pi\)
−0.383999 + 0.923333i \(0.625454\pi\)
\(770\) 19.1107 0.688701
\(771\) −4.91346 −0.176954
\(772\) −78.1560 −2.81290
\(773\) 11.7775 0.423605 0.211803 0.977312i \(-0.432067\pi\)
0.211803 + 0.977312i \(0.432067\pi\)
\(774\) −39.5101 −1.42016
\(775\) −3.41518 −0.122677
\(776\) −20.5397 −0.737332
\(777\) −9.75874 −0.350093
\(778\) 72.9719 2.61617
\(779\) 38.7126 1.38702
\(780\) −6.04042 −0.216282
\(781\) −45.6654 −1.63404
\(782\) −29.7961 −1.06551
\(783\) −9.62293 −0.343895
\(784\) −2.30327 −0.0822596
\(785\) −20.5357 −0.732952
\(786\) −11.0685 −0.394802
\(787\) −21.7232 −0.774350 −0.387175 0.922006i \(-0.626549\pi\)
−0.387175 + 0.922006i \(0.626549\pi\)
\(788\) −77.1294 −2.74762
\(789\) 2.29517 0.0817101
\(790\) −36.2153 −1.28848
\(791\) −42.3260 −1.50494
\(792\) 41.7118 1.48216
\(793\) −47.6512 −1.69214
\(794\) 21.4545 0.761391
\(795\) −0.866062 −0.0307161
\(796\) −9.40432 −0.333327
\(797\) −24.0857 −0.853160 −0.426580 0.904450i \(-0.640282\pi\)
−0.426580 + 0.904450i \(0.640282\pi\)
\(798\) 15.7614 0.557948
\(799\) −37.4731 −1.32570
\(800\) 0.0283274 0.00100153
\(801\) 2.25339 0.0796195
\(802\) −47.2718 −1.66923
\(803\) −10.3264 −0.364410
\(804\) −11.4838 −0.405003
\(805\) 4.93432 0.173912
\(806\) −26.3267 −0.927320
\(807\) −7.06795 −0.248804
\(808\) 60.7919 2.13865
\(809\) −50.5780 −1.77823 −0.889114 0.457685i \(-0.848679\pi\)
−0.889114 + 0.457685i \(0.848679\pi\)
\(810\) −17.0905 −0.600501
\(811\) 13.7040 0.481213 0.240606 0.970623i \(-0.422654\pi\)
0.240606 + 0.970623i \(0.422654\pi\)
\(812\) −35.1907 −1.23495
\(813\) 3.10980 0.109065
\(814\) −60.4940 −2.12032
\(815\) −20.8535 −0.730467
\(816\) −11.9472 −0.418236
\(817\) −30.8193 −1.07823
\(818\) −80.0359 −2.79839
\(819\) −22.0924 −0.771970
\(820\) 29.2487 1.02141
\(821\) 13.6115 0.475044 0.237522 0.971382i \(-0.423665\pi\)
0.237522 + 0.971382i \(0.423665\pi\)
\(822\) −6.98136 −0.243503
\(823\) −20.8170 −0.725634 −0.362817 0.931860i \(-0.618185\pi\)
−0.362817 + 0.931860i \(0.618185\pi\)
\(824\) −55.7568 −1.94238
\(825\) 1.47840 0.0514711
\(826\) 55.8981 1.94494
\(827\) 0.749750 0.0260714 0.0130357 0.999915i \(-0.495850\pi\)
0.0130357 + 0.999915i \(0.495850\pi\)
\(828\) 21.5553 0.749099
\(829\) 26.0817 0.905856 0.452928 0.891547i \(-0.350379\pi\)
0.452928 + 0.891547i \(0.350379\pi\)
\(830\) 11.5614 0.401302
\(831\) 15.0412 0.521773
\(832\) 25.2918 0.876836
\(833\) 3.61375 0.125209
\(834\) 22.2554 0.770643
\(835\) −2.78002 −0.0962065
\(836\) 65.1206 2.25224
\(837\) 9.45939 0.326964
\(838\) 10.5094 0.363040
\(839\) 2.31302 0.0798541 0.0399271 0.999203i \(-0.487287\pi\)
0.0399271 + 0.999203i \(0.487287\pi\)
\(840\) 5.94984 0.205289
\(841\) −16.9298 −0.583785
\(842\) 49.4705 1.70487
\(843\) −6.81144 −0.234598
\(844\) 24.4796 0.842624
\(845\) −3.09112 −0.106338
\(846\) 40.6734 1.39838
\(847\) 3.84330 0.132057
\(848\) −7.18475 −0.246725
\(849\) 10.7723 0.369705
\(850\) 15.3023 0.524864
\(851\) −15.6194 −0.535425
\(852\) −28.4551 −0.974857
\(853\) −6.18254 −0.211686 −0.105843 0.994383i \(-0.533754\pi\)
−0.105843 + 0.994383i \(0.533754\pi\)
\(854\) 93.9413 3.21461
\(855\) −14.6520 −0.501088
\(856\) −81.9495 −2.80098
\(857\) −26.5409 −0.906621 −0.453310 0.891353i \(-0.649757\pi\)
−0.453310 + 0.891353i \(0.649757\pi\)
\(858\) 11.3966 0.389072
\(859\) 35.6768 1.21728 0.608639 0.793447i \(-0.291716\pi\)
0.608639 + 0.793447i \(0.291716\pi\)
\(860\) −23.2850 −0.794013
\(861\) −8.90215 −0.303384
\(862\) 19.2532 0.655767
\(863\) −23.1008 −0.786361 −0.393180 0.919461i \(-0.628625\pi\)
−0.393180 + 0.919461i \(0.628625\pi\)
\(864\) −0.0784614 −0.00266931
\(865\) −6.18322 −0.210236
\(866\) −25.3353 −0.860927
\(867\) 10.5835 0.359434
\(868\) 34.5926 1.17415
\(869\) 45.5409 1.54487
\(870\) −4.08449 −0.138477
\(871\) 18.8384 0.638314
\(872\) 25.0590 0.848604
\(873\) −11.6313 −0.393659
\(874\) 25.2270 0.853315
\(875\) −2.53410 −0.0856683
\(876\) −6.43460 −0.217405
\(877\) −30.7259 −1.03754 −0.518771 0.854913i \(-0.673610\pi\)
−0.518771 + 0.854913i \(0.673610\pi\)
\(878\) −66.6660 −2.24987
\(879\) −13.6676 −0.460997
\(880\) 12.2646 0.413439
\(881\) 13.9479 0.469915 0.234958 0.972006i \(-0.424505\pi\)
0.234958 + 0.972006i \(0.424505\pi\)
\(882\) −3.92238 −0.132073
\(883\) 36.2623 1.22032 0.610161 0.792277i \(-0.291105\pi\)
0.610161 + 0.792277i \(0.291105\pi\)
\(884\) 78.6219 2.64434
\(885\) 4.32425 0.145358
\(886\) 39.1372 1.31484
\(887\) −54.9928 −1.84648 −0.923239 0.384225i \(-0.874469\pi\)
−0.923239 + 0.384225i \(0.874469\pi\)
\(888\) −18.8340 −0.632026
\(889\) −18.0668 −0.605940
\(890\) 1.99251 0.0667891
\(891\) 21.4915 0.719992
\(892\) −1.56385 −0.0523617
\(893\) 31.7267 1.06170
\(894\) 19.6415 0.656911
\(895\) −1.39814 −0.0467348
\(896\) −49.7176 −1.66095
\(897\) 2.94256 0.0982491
\(898\) 61.3927 2.04870
\(899\) −11.8651 −0.395723
\(900\) −11.0701 −0.369003
\(901\) 11.2726 0.375546
\(902\) −55.1841 −1.83743
\(903\) 7.08703 0.235842
\(904\) −81.6875 −2.71689
\(905\) 3.58045 0.119018
\(906\) −12.2381 −0.406584
\(907\) −25.7799 −0.856009 −0.428004 0.903777i \(-0.640783\pi\)
−0.428004 + 0.903777i \(0.640783\pi\)
\(908\) −31.7376 −1.05325
\(909\) 34.4254 1.14182
\(910\) −19.5347 −0.647570
\(911\) −2.23560 −0.0740687 −0.0370344 0.999314i \(-0.511791\pi\)
−0.0370344 + 0.999314i \(0.511791\pi\)
\(912\) 10.1151 0.334946
\(913\) −14.5385 −0.481155
\(914\) −0.118799 −0.00392952
\(915\) 7.26726 0.240248
\(916\) −23.3059 −0.770047
\(917\) −23.8580 −0.787862
\(918\) −42.3844 −1.39889
\(919\) 17.7434 0.585300 0.292650 0.956220i \(-0.405463\pi\)
0.292650 + 0.956220i \(0.405463\pi\)
\(920\) 9.52303 0.313965
\(921\) −6.90456 −0.227513
\(922\) −63.2880 −2.08428
\(923\) 46.6786 1.53645
\(924\) −14.9748 −0.492634
\(925\) 8.02159 0.263748
\(926\) 27.2360 0.895031
\(927\) −31.5742 −1.03703
\(928\) 0.0984158 0.00323066
\(929\) −23.8895 −0.783788 −0.391894 0.920010i \(-0.628180\pi\)
−0.391894 + 0.920010i \(0.628180\pi\)
\(930\) 4.01508 0.131660
\(931\) −3.05960 −0.100274
\(932\) −57.6599 −1.88871
\(933\) −0.996632 −0.0326283
\(934\) −20.4131 −0.667937
\(935\) −19.2427 −0.629305
\(936\) −42.6373 −1.39365
\(937\) −19.1165 −0.624509 −0.312255 0.949998i \(-0.601084\pi\)
−0.312255 + 0.949998i \(0.601084\pi\)
\(938\) −37.1387 −1.21262
\(939\) −7.58721 −0.247599
\(940\) 23.9707 0.781837
\(941\) 25.1192 0.818861 0.409431 0.912341i \(-0.365727\pi\)
0.409431 + 0.912341i \(0.365727\pi\)
\(942\) 24.1429 0.786620
\(943\) −14.2484 −0.463990
\(944\) 35.8735 1.16758
\(945\) 7.01897 0.228327
\(946\) 43.9322 1.42836
\(947\) 22.7177 0.738227 0.369114 0.929384i \(-0.379661\pi\)
0.369114 + 0.929384i \(0.379661\pi\)
\(948\) 28.3776 0.921661
\(949\) 10.5555 0.342646
\(950\) −12.9557 −0.420340
\(951\) 14.6351 0.474574
\(952\) −77.4429 −2.50994
\(953\) 45.5869 1.47670 0.738352 0.674416i \(-0.235605\pi\)
0.738352 + 0.674416i \(0.235605\pi\)
\(954\) −12.2354 −0.396134
\(955\) −18.3633 −0.594221
\(956\) −17.9464 −0.580428
\(957\) 5.13628 0.166032
\(958\) 79.4884 2.56815
\(959\) −15.0482 −0.485931
\(960\) −3.85724 −0.124492
\(961\) −19.3365 −0.623759
\(962\) 61.8363 1.99368
\(963\) −46.4066 −1.49543
\(964\) −115.039 −3.70514
\(965\) −19.5531 −0.629438
\(966\) −5.80106 −0.186646
\(967\) 32.6088 1.04863 0.524314 0.851525i \(-0.324322\pi\)
0.524314 + 0.851525i \(0.324322\pi\)
\(968\) 7.41740 0.238404
\(969\) −15.8703 −0.509828
\(970\) −10.2847 −0.330223
\(971\) 15.7664 0.505969 0.252984 0.967470i \(-0.418588\pi\)
0.252984 + 0.967470i \(0.418588\pi\)
\(972\) 46.6055 1.49487
\(973\) 47.9712 1.53788
\(974\) −19.2368 −0.616386
\(975\) −1.51120 −0.0483971
\(976\) 60.2883 1.92978
\(977\) 22.8696 0.731663 0.365831 0.930681i \(-0.380785\pi\)
0.365831 + 0.930681i \(0.380785\pi\)
\(978\) 24.5165 0.783953
\(979\) −2.50560 −0.0800793
\(980\) −2.31163 −0.0738424
\(981\) 14.1905 0.453067
\(982\) −44.3146 −1.41414
\(983\) 24.5627 0.783430 0.391715 0.920087i \(-0.371882\pi\)
0.391715 + 0.920087i \(0.371882\pi\)
\(984\) −17.1808 −0.547703
\(985\) −19.2963 −0.614832
\(986\) 53.1636 1.69307
\(987\) −7.29571 −0.232225
\(988\) −66.5655 −2.11773
\(989\) 11.3432 0.360692
\(990\) 20.8861 0.663805
\(991\) 12.0385 0.382414 0.191207 0.981550i \(-0.438760\pi\)
0.191207 + 0.981550i \(0.438760\pi\)
\(992\) −0.0967432 −0.00307160
\(993\) 12.9638 0.411394
\(994\) −92.0239 −2.91882
\(995\) −2.35278 −0.0745882
\(996\) −9.05929 −0.287055
\(997\) 37.3739 1.18364 0.591822 0.806069i \(-0.298409\pi\)
0.591822 + 0.806069i \(0.298409\pi\)
\(998\) −56.3638 −1.78417
\(999\) −22.2183 −0.702954
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 8005.2.a.e.1.12 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8005.2.a.e.1.12 126 1.1 even 1 trivial