Properties

Label 8005.2.a.e.1.15
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 1.15
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)
 
\(f(q)\) \(=\) \(q-2.36778 q^{2} +2.79221 q^{3} +3.60639 q^{4} +1.00000 q^{5} -6.61135 q^{6} -4.83880 q^{7} -3.80359 q^{8} +4.79644 q^{9} +O(q^{10})\) \(q-2.36778 q^{2} +2.79221 q^{3} +3.60639 q^{4} +1.00000 q^{5} -6.61135 q^{6} -4.83880 q^{7} -3.80359 q^{8} +4.79644 q^{9} -2.36778 q^{10} +2.26162 q^{11} +10.0698 q^{12} +3.53108 q^{13} +11.4572 q^{14} +2.79221 q^{15} +1.79329 q^{16} -4.02121 q^{17} -11.3569 q^{18} -2.95196 q^{19} +3.60639 q^{20} -13.5109 q^{21} -5.35503 q^{22} -7.54734 q^{23} -10.6204 q^{24} +1.00000 q^{25} -8.36084 q^{26} +5.01604 q^{27} -17.4506 q^{28} +8.91566 q^{29} -6.61135 q^{30} -8.58965 q^{31} +3.36106 q^{32} +6.31493 q^{33} +9.52136 q^{34} -4.83880 q^{35} +17.2979 q^{36} -0.979194 q^{37} +6.98959 q^{38} +9.85953 q^{39} -3.80359 q^{40} +5.91401 q^{41} +31.9910 q^{42} +2.18281 q^{43} +8.15631 q^{44} +4.79644 q^{45} +17.8705 q^{46} -1.98949 q^{47} +5.00725 q^{48} +16.4140 q^{49} -2.36778 q^{50} -11.2281 q^{51} +12.7345 q^{52} +2.46344 q^{53} -11.8769 q^{54} +2.26162 q^{55} +18.4048 q^{56} -8.24249 q^{57} -21.1103 q^{58} -4.16140 q^{59} +10.0698 q^{60} -4.48728 q^{61} +20.3384 q^{62} -23.2090 q^{63} -11.5448 q^{64} +3.53108 q^{65} -14.9524 q^{66} +4.14563 q^{67} -14.5021 q^{68} -21.0738 q^{69} +11.4572 q^{70} +8.70692 q^{71} -18.2437 q^{72} -9.88283 q^{73} +2.31852 q^{74} +2.79221 q^{75} -10.6459 q^{76} -10.9435 q^{77} -23.3452 q^{78} +13.3332 q^{79} +1.79329 q^{80} -0.383485 q^{81} -14.0031 q^{82} +12.2918 q^{83} -48.7258 q^{84} -4.02121 q^{85} -5.16842 q^{86} +24.8944 q^{87} -8.60230 q^{88} -11.6996 q^{89} -11.3569 q^{90} -17.0862 q^{91} -27.2187 q^{92} -23.9841 q^{93} +4.71068 q^{94} -2.95196 q^{95} +9.38479 q^{96} -2.59114 q^{97} -38.8647 q^{98} +10.8477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36778 −1.67428 −0.837138 0.546992i \(-0.815773\pi\)
−0.837138 + 0.546992i \(0.815773\pi\)
\(3\) 2.79221 1.61208 0.806042 0.591859i \(-0.201606\pi\)
0.806042 + 0.591859i \(0.201606\pi\)
\(4\) 3.60639 1.80320
\(5\) 1.00000 0.447214
\(6\) −6.61135 −2.69907
\(7\) −4.83880 −1.82889 −0.914447 0.404707i \(-0.867374\pi\)
−0.914447 + 0.404707i \(0.867374\pi\)
\(8\) −3.80359 −1.34477
\(9\) 4.79644 1.59881
\(10\) −2.36778 −0.748759
\(11\) 2.26162 0.681905 0.340953 0.940080i \(-0.389250\pi\)
0.340953 + 0.940080i \(0.389250\pi\)
\(12\) 10.0698 2.90690
\(13\) 3.53108 0.979347 0.489673 0.871906i \(-0.337116\pi\)
0.489673 + 0.871906i \(0.337116\pi\)
\(14\) 11.4572 3.06207
\(15\) 2.79221 0.720946
\(16\) 1.79329 0.448323
\(17\) −4.02121 −0.975287 −0.487644 0.873043i \(-0.662143\pi\)
−0.487644 + 0.873043i \(0.662143\pi\)
\(18\) −11.3569 −2.67685
\(19\) −2.95196 −0.677225 −0.338613 0.940926i \(-0.609958\pi\)
−0.338613 + 0.940926i \(0.609958\pi\)
\(20\) 3.60639 0.806414
\(21\) −13.5109 −2.94833
\(22\) −5.35503 −1.14170
\(23\) −7.54734 −1.57373 −0.786865 0.617125i \(-0.788297\pi\)
−0.786865 + 0.617125i \(0.788297\pi\)
\(24\) −10.6204 −2.16789
\(25\) 1.00000 0.200000
\(26\) −8.36084 −1.63970
\(27\) 5.01604 0.965337
\(28\) −17.4506 −3.29786
\(29\) 8.91566 1.65560 0.827798 0.561026i \(-0.189593\pi\)
0.827798 + 0.561026i \(0.189593\pi\)
\(30\) −6.61135 −1.20706
\(31\) −8.58965 −1.54275 −0.771374 0.636383i \(-0.780430\pi\)
−0.771374 + 0.636383i \(0.780430\pi\)
\(32\) 3.36106 0.594157
\(33\) 6.31493 1.09929
\(34\) 9.52136 1.63290
\(35\) −4.83880 −0.817906
\(36\) 17.2979 2.88298
\(37\) −0.979194 −0.160979 −0.0804893 0.996755i \(-0.525648\pi\)
−0.0804893 + 0.996755i \(0.525648\pi\)
\(38\) 6.98959 1.13386
\(39\) 9.85953 1.57879
\(40\) −3.80359 −0.601401
\(41\) 5.91401 0.923614 0.461807 0.886981i \(-0.347201\pi\)
0.461807 + 0.886981i \(0.347201\pi\)
\(42\) 31.9910 4.93631
\(43\) 2.18281 0.332875 0.166438 0.986052i \(-0.446774\pi\)
0.166438 + 0.986052i \(0.446774\pi\)
\(44\) 8.15631 1.22961
\(45\) 4.79644 0.715011
\(46\) 17.8705 2.63486
\(47\) −1.98949 −0.290197 −0.145099 0.989417i \(-0.546350\pi\)
−0.145099 + 0.989417i \(0.546350\pi\)
\(48\) 5.00725 0.722734
\(49\) 16.4140 2.34485
\(50\) −2.36778 −0.334855
\(51\) −11.2281 −1.57224
\(52\) 12.7345 1.76596
\(53\) 2.46344 0.338379 0.169190 0.985584i \(-0.445885\pi\)
0.169190 + 0.985584i \(0.445885\pi\)
\(54\) −11.8769 −1.61624
\(55\) 2.26162 0.304957
\(56\) 18.4048 2.45945
\(57\) −8.24249 −1.09174
\(58\) −21.1103 −2.77192
\(59\) −4.16140 −0.541769 −0.270884 0.962612i \(-0.587316\pi\)
−0.270884 + 0.962612i \(0.587316\pi\)
\(60\) 10.0698 1.30001
\(61\) −4.48728 −0.574537 −0.287269 0.957850i \(-0.592747\pi\)
−0.287269 + 0.957850i \(0.592747\pi\)
\(62\) 20.3384 2.58298
\(63\) −23.2090 −2.92406
\(64\) −11.5448 −1.44311
\(65\) 3.53108 0.437977
\(66\) −14.9524 −1.84051
\(67\) 4.14563 0.506470 0.253235 0.967405i \(-0.418505\pi\)
0.253235 + 0.967405i \(0.418505\pi\)
\(68\) −14.5021 −1.75863
\(69\) −21.0738 −2.53698
\(70\) 11.4572 1.36940
\(71\) 8.70692 1.03332 0.516661 0.856190i \(-0.327175\pi\)
0.516661 + 0.856190i \(0.327175\pi\)
\(72\) −18.2437 −2.15004
\(73\) −9.88283 −1.15670 −0.578349 0.815790i \(-0.696303\pi\)
−0.578349 + 0.815790i \(0.696303\pi\)
\(74\) 2.31852 0.269522
\(75\) 2.79221 0.322417
\(76\) −10.6459 −1.22117
\(77\) −10.9435 −1.24713
\(78\) −23.3452 −2.64333
\(79\) 13.3332 1.50010 0.750052 0.661379i \(-0.230029\pi\)
0.750052 + 0.661379i \(0.230029\pi\)
\(80\) 1.79329 0.200496
\(81\) −0.383485 −0.0426095
\(82\) −14.0031 −1.54638
\(83\) 12.2918 1.34920 0.674598 0.738185i \(-0.264317\pi\)
0.674598 + 0.738185i \(0.264317\pi\)
\(84\) −48.7258 −5.31642
\(85\) −4.02121 −0.436162
\(86\) −5.16842 −0.557325
\(87\) 24.8944 2.66896
\(88\) −8.60230 −0.917008
\(89\) −11.6996 −1.24016 −0.620078 0.784540i \(-0.712899\pi\)
−0.620078 + 0.784540i \(0.712899\pi\)
\(90\) −11.3569 −1.19713
\(91\) −17.0862 −1.79112
\(92\) −27.2187 −2.83774
\(93\) −23.9841 −2.48704
\(94\) 4.71068 0.485870
\(95\) −2.95196 −0.302864
\(96\) 9.38479 0.957831
\(97\) −2.59114 −0.263091 −0.131545 0.991310i \(-0.541994\pi\)
−0.131545 + 0.991310i \(0.541994\pi\)
\(98\) −38.8647 −3.92592
\(99\) 10.8477 1.09024
\(100\) 3.60639 0.360639
\(101\) −6.37806 −0.634641 −0.317320 0.948318i \(-0.602783\pi\)
−0.317320 + 0.948318i \(0.602783\pi\)
\(102\) 26.5856 2.63237
\(103\) −17.1180 −1.68669 −0.843343 0.537376i \(-0.819416\pi\)
−0.843343 + 0.537376i \(0.819416\pi\)
\(104\) −13.4308 −1.31700
\(105\) −13.5109 −1.31853
\(106\) −5.83288 −0.566540
\(107\) −14.3219 −1.38455 −0.692276 0.721633i \(-0.743392\pi\)
−0.692276 + 0.721633i \(0.743392\pi\)
\(108\) 18.0898 1.74069
\(109\) 0.953522 0.0913309 0.0456654 0.998957i \(-0.485459\pi\)
0.0456654 + 0.998957i \(0.485459\pi\)
\(110\) −5.35503 −0.510582
\(111\) −2.73412 −0.259511
\(112\) −8.67737 −0.819935
\(113\) −9.38097 −0.882487 −0.441244 0.897387i \(-0.645463\pi\)
−0.441244 + 0.897387i \(0.645463\pi\)
\(114\) 19.5164 1.82788
\(115\) −7.54734 −0.703793
\(116\) 32.1534 2.98537
\(117\) 16.9366 1.56579
\(118\) 9.85330 0.907070
\(119\) 19.4578 1.78370
\(120\) −10.6204 −0.969508
\(121\) −5.88506 −0.535005
\(122\) 10.6249 0.961934
\(123\) 16.5132 1.48894
\(124\) −30.9777 −2.78188
\(125\) 1.00000 0.0894427
\(126\) 54.9539 4.89568
\(127\) −18.4810 −1.63992 −0.819961 0.572419i \(-0.806005\pi\)
−0.819961 + 0.572419i \(0.806005\pi\)
\(128\) 20.6136 1.82200
\(129\) 6.09487 0.536623
\(130\) −8.36084 −0.733294
\(131\) −15.9517 −1.39370 −0.696851 0.717215i \(-0.745416\pi\)
−0.696851 + 0.717215i \(0.745416\pi\)
\(132\) 22.7741 1.98223
\(133\) 14.2839 1.23857
\(134\) −9.81596 −0.847970
\(135\) 5.01604 0.431712
\(136\) 15.2951 1.31154
\(137\) −1.38198 −0.118070 −0.0590352 0.998256i \(-0.518802\pi\)
−0.0590352 + 0.998256i \(0.518802\pi\)
\(138\) 49.8981 4.24761
\(139\) 3.28084 0.278277 0.139138 0.990273i \(-0.455567\pi\)
0.139138 + 0.990273i \(0.455567\pi\)
\(140\) −17.4506 −1.47485
\(141\) −5.55508 −0.467822
\(142\) −20.6161 −1.73006
\(143\) 7.98599 0.667822
\(144\) 8.60141 0.716784
\(145\) 8.91566 0.740405
\(146\) 23.4004 1.93663
\(147\) 45.8312 3.78009
\(148\) −3.53136 −0.290276
\(149\) 12.6329 1.03493 0.517464 0.855705i \(-0.326876\pi\)
0.517464 + 0.855705i \(0.326876\pi\)
\(150\) −6.61135 −0.539814
\(151\) 15.9896 1.30121 0.650607 0.759415i \(-0.274515\pi\)
0.650607 + 0.759415i \(0.274515\pi\)
\(152\) 11.2280 0.910714
\(153\) −19.2875 −1.55930
\(154\) 25.9119 2.08804
\(155\) −8.58965 −0.689938
\(156\) 35.5574 2.84687
\(157\) 2.87493 0.229444 0.114722 0.993398i \(-0.463402\pi\)
0.114722 + 0.993398i \(0.463402\pi\)
\(158\) −31.5701 −2.51159
\(159\) 6.87844 0.545496
\(160\) 3.36106 0.265715
\(161\) 36.5201 2.87818
\(162\) 0.908009 0.0713399
\(163\) 1.25288 0.0981328 0.0490664 0.998796i \(-0.484375\pi\)
0.0490664 + 0.998796i \(0.484375\pi\)
\(164\) 21.3283 1.66546
\(165\) 6.31493 0.491617
\(166\) −29.1042 −2.25893
\(167\) 8.65766 0.669950 0.334975 0.942227i \(-0.391272\pi\)
0.334975 + 0.942227i \(0.391272\pi\)
\(168\) 51.3901 3.96483
\(169\) −0.531441 −0.0408801
\(170\) 9.52136 0.730255
\(171\) −14.1589 −1.08276
\(172\) 7.87207 0.600240
\(173\) −21.1658 −1.60921 −0.804604 0.593812i \(-0.797622\pi\)
−0.804604 + 0.593812i \(0.797622\pi\)
\(174\) −58.9445 −4.46857
\(175\) −4.83880 −0.365779
\(176\) 4.05575 0.305714
\(177\) −11.6195 −0.873376
\(178\) 27.7021 2.07636
\(179\) −26.1898 −1.95752 −0.978760 0.205010i \(-0.934277\pi\)
−0.978760 + 0.205010i \(0.934277\pi\)
\(180\) 17.2979 1.28931
\(181\) −10.2734 −0.763616 −0.381808 0.924242i \(-0.624698\pi\)
−0.381808 + 0.924242i \(0.624698\pi\)
\(182\) 40.4564 2.99883
\(183\) −12.5294 −0.926202
\(184\) 28.7070 2.11631
\(185\) −0.979194 −0.0719918
\(186\) 56.7892 4.16398
\(187\) −9.09447 −0.665053
\(188\) −7.17489 −0.523283
\(189\) −24.2716 −1.76550
\(190\) 6.98959 0.507078
\(191\) 5.52518 0.399788 0.199894 0.979818i \(-0.435940\pi\)
0.199894 + 0.979818i \(0.435940\pi\)
\(192\) −32.2356 −2.32641
\(193\) 3.63674 0.261779 0.130889 0.991397i \(-0.458217\pi\)
0.130889 + 0.991397i \(0.458217\pi\)
\(194\) 6.13526 0.440486
\(195\) 9.85953 0.706056
\(196\) 59.1952 4.22823
\(197\) 13.0962 0.933064 0.466532 0.884504i \(-0.345503\pi\)
0.466532 + 0.884504i \(0.345503\pi\)
\(198\) −25.6851 −1.82536
\(199\) −4.53308 −0.321342 −0.160671 0.987008i \(-0.551366\pi\)
−0.160671 + 0.987008i \(0.551366\pi\)
\(200\) −3.80359 −0.268955
\(201\) 11.5755 0.816472
\(202\) 15.1019 1.06256
\(203\) −43.1411 −3.02791
\(204\) −40.4928 −2.83507
\(205\) 5.91401 0.413053
\(206\) 40.5317 2.82398
\(207\) −36.2004 −2.51610
\(208\) 6.33226 0.439063
\(209\) −6.67622 −0.461804
\(210\) 31.9910 2.20759
\(211\) −20.4709 −1.40927 −0.704636 0.709569i \(-0.748890\pi\)
−0.704636 + 0.709569i \(0.748890\pi\)
\(212\) 8.88413 0.610164
\(213\) 24.3115 1.66580
\(214\) 33.9112 2.31812
\(215\) 2.18281 0.148866
\(216\) −19.0790 −1.29816
\(217\) 41.5636 2.82152
\(218\) −2.25773 −0.152913
\(219\) −27.5949 −1.86469
\(220\) 8.15631 0.549898
\(221\) −14.1992 −0.955144
\(222\) 6.47379 0.434493
\(223\) −10.0042 −0.669932 −0.334966 0.942230i \(-0.608725\pi\)
−0.334966 + 0.942230i \(0.608725\pi\)
\(224\) −16.2635 −1.08665
\(225\) 4.79644 0.319763
\(226\) 22.2121 1.47753
\(227\) −22.2921 −1.47958 −0.739789 0.672839i \(-0.765075\pi\)
−0.739789 + 0.672839i \(0.765075\pi\)
\(228\) −29.7257 −1.96863
\(229\) −6.42255 −0.424414 −0.212207 0.977225i \(-0.568065\pi\)
−0.212207 + 0.977225i \(0.568065\pi\)
\(230\) 17.8705 1.17834
\(231\) −30.5567 −2.01048
\(232\) −33.9115 −2.22640
\(233\) −3.10920 −0.203690 −0.101845 0.994800i \(-0.532475\pi\)
−0.101845 + 0.994800i \(0.532475\pi\)
\(234\) −40.1023 −2.62157
\(235\) −1.98949 −0.129780
\(236\) −15.0077 −0.976916
\(237\) 37.2291 2.41829
\(238\) −46.0719 −2.98640
\(239\) 16.8554 1.09029 0.545143 0.838343i \(-0.316475\pi\)
0.545143 + 0.838343i \(0.316475\pi\)
\(240\) 5.00725 0.323216
\(241\) −16.1099 −1.03773 −0.518865 0.854856i \(-0.673645\pi\)
−0.518865 + 0.854856i \(0.673645\pi\)
\(242\) 13.9345 0.895746
\(243\) −16.1189 −1.03403
\(244\) −16.1829 −1.03600
\(245\) 16.4140 1.04865
\(246\) −39.0996 −2.49290
\(247\) −10.4236 −0.663238
\(248\) 32.6715 2.07464
\(249\) 34.3212 2.17502
\(250\) −2.36778 −0.149752
\(251\) 2.31475 0.146106 0.0730530 0.997328i \(-0.476726\pi\)
0.0730530 + 0.997328i \(0.476726\pi\)
\(252\) −83.7008 −5.27265
\(253\) −17.0693 −1.07313
\(254\) 43.7590 2.74568
\(255\) −11.2281 −0.703129
\(256\) −25.7187 −1.60742
\(257\) −23.4867 −1.46506 −0.732529 0.680736i \(-0.761660\pi\)
−0.732529 + 0.680736i \(0.761660\pi\)
\(258\) −14.4313 −0.898454
\(259\) 4.73812 0.294413
\(260\) 12.7345 0.789759
\(261\) 42.7634 2.64699
\(262\) 37.7701 2.33344
\(263\) −7.22512 −0.445520 −0.222760 0.974873i \(-0.571507\pi\)
−0.222760 + 0.974873i \(0.571507\pi\)
\(264\) −24.0194 −1.47829
\(265\) 2.46344 0.151328
\(266\) −33.8212 −2.07371
\(267\) −32.6678 −1.99923
\(268\) 14.9508 0.913265
\(269\) 27.7863 1.69416 0.847080 0.531465i \(-0.178358\pi\)
0.847080 + 0.531465i \(0.178358\pi\)
\(270\) −11.8769 −0.722804
\(271\) 19.2702 1.17058 0.585290 0.810824i \(-0.300981\pi\)
0.585290 + 0.810824i \(0.300981\pi\)
\(272\) −7.21120 −0.437243
\(273\) −47.7083 −2.88744
\(274\) 3.27223 0.197682
\(275\) 2.26162 0.136381
\(276\) −76.0003 −4.57468
\(277\) −6.33992 −0.380929 −0.190465 0.981694i \(-0.560999\pi\)
−0.190465 + 0.981694i \(0.560999\pi\)
\(278\) −7.76831 −0.465912
\(279\) −41.1998 −2.46656
\(280\) 18.4048 1.09990
\(281\) −4.22013 −0.251752 −0.125876 0.992046i \(-0.540174\pi\)
−0.125876 + 0.992046i \(0.540174\pi\)
\(282\) 13.1532 0.783263
\(283\) 15.4029 0.915605 0.457802 0.889054i \(-0.348637\pi\)
0.457802 + 0.889054i \(0.348637\pi\)
\(284\) 31.4006 1.86328
\(285\) −8.24249 −0.488243
\(286\) −18.9091 −1.11812
\(287\) −28.6167 −1.68919
\(288\) 16.1211 0.949947
\(289\) −0.829856 −0.0488150
\(290\) −21.1103 −1.23964
\(291\) −7.23501 −0.424124
\(292\) −35.6414 −2.08575
\(293\) −12.9770 −0.758124 −0.379062 0.925371i \(-0.623753\pi\)
−0.379062 + 0.925371i \(0.623753\pi\)
\(294\) −108.518 −6.32892
\(295\) −4.16140 −0.242286
\(296\) 3.72446 0.216480
\(297\) 11.3444 0.658268
\(298\) −29.9120 −1.73276
\(299\) −26.6503 −1.54123
\(300\) 10.0698 0.581381
\(301\) −10.5622 −0.608794
\(302\) −37.8599 −2.17859
\(303\) −17.8089 −1.02309
\(304\) −5.29372 −0.303616
\(305\) −4.48728 −0.256941
\(306\) 45.6686 2.61070
\(307\) 6.91601 0.394717 0.197359 0.980331i \(-0.436764\pi\)
0.197359 + 0.980331i \(0.436764\pi\)
\(308\) −39.4667 −2.24882
\(309\) −47.7970 −2.71908
\(310\) 20.3384 1.15515
\(311\) −2.39808 −0.135983 −0.0679914 0.997686i \(-0.521659\pi\)
−0.0679914 + 0.997686i \(0.521659\pi\)
\(312\) −37.5016 −2.12311
\(313\) 18.8629 1.06619 0.533097 0.846054i \(-0.321028\pi\)
0.533097 + 0.846054i \(0.321028\pi\)
\(314\) −6.80721 −0.384153
\(315\) −23.2090 −1.30768
\(316\) 48.0848 2.70498
\(317\) −1.85221 −0.104030 −0.0520152 0.998646i \(-0.516564\pi\)
−0.0520152 + 0.998646i \(0.516564\pi\)
\(318\) −16.2866 −0.913310
\(319\) 20.1639 1.12896
\(320\) −11.5448 −0.645376
\(321\) −39.9898 −2.23201
\(322\) −86.4716 −4.81887
\(323\) 11.8704 0.660489
\(324\) −1.38300 −0.0768332
\(325\) 3.53108 0.195869
\(326\) −2.96654 −0.164301
\(327\) 2.66243 0.147233
\(328\) −22.4945 −1.24205
\(329\) 9.62674 0.530740
\(330\) −14.9524 −0.823102
\(331\) −11.9931 −0.659200 −0.329600 0.944121i \(-0.606914\pi\)
−0.329600 + 0.944121i \(0.606914\pi\)
\(332\) 44.3290 2.43287
\(333\) −4.69665 −0.257375
\(334\) −20.4995 −1.12168
\(335\) 4.14563 0.226500
\(336\) −24.2290 −1.32180
\(337\) −11.9385 −0.650333 −0.325166 0.945657i \(-0.605420\pi\)
−0.325166 + 0.945657i \(0.605420\pi\)
\(338\) 1.25834 0.0684445
\(339\) −26.1936 −1.42264
\(340\) −14.5021 −0.786485
\(341\) −19.4266 −1.05201
\(342\) 33.5252 1.81283
\(343\) −45.5522 −2.45959
\(344\) −8.30252 −0.447642
\(345\) −21.0738 −1.13457
\(346\) 50.1161 2.69426
\(347\) −33.9129 −1.82054 −0.910269 0.414017i \(-0.864125\pi\)
−0.910269 + 0.414017i \(0.864125\pi\)
\(348\) 89.7790 4.81266
\(349\) −2.94951 −0.157884 −0.0789419 0.996879i \(-0.525154\pi\)
−0.0789419 + 0.996879i \(0.525154\pi\)
\(350\) 11.4572 0.612414
\(351\) 17.7121 0.945400
\(352\) 7.60146 0.405159
\(353\) 0.634803 0.0337872 0.0168936 0.999857i \(-0.494622\pi\)
0.0168936 + 0.999857i \(0.494622\pi\)
\(354\) 27.5125 1.46227
\(355\) 8.70692 0.462115
\(356\) −42.1934 −2.23624
\(357\) 54.3303 2.87547
\(358\) 62.0118 3.27743
\(359\) 8.63389 0.455679 0.227840 0.973699i \(-0.426834\pi\)
0.227840 + 0.973699i \(0.426834\pi\)
\(360\) −18.2437 −0.961528
\(361\) −10.2860 −0.541366
\(362\) 24.3252 1.27850
\(363\) −16.4323 −0.862473
\(364\) −61.6196 −3.22974
\(365\) −9.88283 −0.517291
\(366\) 29.6670 1.55072
\(367\) −6.41382 −0.334799 −0.167399 0.985889i \(-0.553537\pi\)
−0.167399 + 0.985889i \(0.553537\pi\)
\(368\) −13.5346 −0.705539
\(369\) 28.3662 1.47669
\(370\) 2.31852 0.120534
\(371\) −11.9201 −0.618859
\(372\) −86.4962 −4.48462
\(373\) 0.950354 0.0492075 0.0246037 0.999697i \(-0.492168\pi\)
0.0246037 + 0.999697i \(0.492168\pi\)
\(374\) 21.5337 1.11348
\(375\) 2.79221 0.144189
\(376\) 7.56721 0.390249
\(377\) 31.4820 1.62140
\(378\) 57.4698 2.95593
\(379\) −18.4614 −0.948301 −0.474150 0.880444i \(-0.657245\pi\)
−0.474150 + 0.880444i \(0.657245\pi\)
\(380\) −10.6459 −0.546124
\(381\) −51.6028 −2.64369
\(382\) −13.0824 −0.669355
\(383\) 6.69875 0.342290 0.171145 0.985246i \(-0.445253\pi\)
0.171145 + 0.985246i \(0.445253\pi\)
\(384\) 57.5574 2.93721
\(385\) −10.9435 −0.557734
\(386\) −8.61102 −0.438289
\(387\) 10.4697 0.532206
\(388\) −9.34468 −0.474404
\(389\) 35.9446 1.82246 0.911232 0.411894i \(-0.135133\pi\)
0.911232 + 0.411894i \(0.135133\pi\)
\(390\) −23.3452 −1.18213
\(391\) 30.3495 1.53484
\(392\) −62.4320 −3.15329
\(393\) −44.5404 −2.24677
\(394\) −31.0089 −1.56221
\(395\) 13.3332 0.670867
\(396\) 39.1212 1.96592
\(397\) 25.8728 1.29852 0.649259 0.760567i \(-0.275079\pi\)
0.649259 + 0.760567i \(0.275079\pi\)
\(398\) 10.7333 0.538014
\(399\) 39.8837 1.99668
\(400\) 1.79329 0.0896646
\(401\) 24.4433 1.22064 0.610321 0.792154i \(-0.291041\pi\)
0.610321 + 0.792154i \(0.291041\pi\)
\(402\) −27.4082 −1.36700
\(403\) −30.3308 −1.51088
\(404\) −23.0018 −1.14438
\(405\) −0.383485 −0.0190555
\(406\) 102.149 5.06955
\(407\) −2.21457 −0.109772
\(408\) 42.7070 2.11431
\(409\) 15.2936 0.756219 0.378110 0.925761i \(-0.376574\pi\)
0.378110 + 0.925761i \(0.376574\pi\)
\(410\) −14.0031 −0.691564
\(411\) −3.85878 −0.190339
\(412\) −61.7342 −3.04143
\(413\) 20.1362 0.990837
\(414\) 85.7146 4.21264
\(415\) 12.2918 0.603379
\(416\) 11.8682 0.581886
\(417\) 9.16078 0.448606
\(418\) 15.8078 0.773186
\(419\) −20.6955 −1.01104 −0.505522 0.862814i \(-0.668700\pi\)
−0.505522 + 0.862814i \(0.668700\pi\)
\(420\) −48.7258 −2.37757
\(421\) 4.28882 0.209024 0.104512 0.994524i \(-0.466672\pi\)
0.104512 + 0.994524i \(0.466672\pi\)
\(422\) 48.4705 2.35951
\(423\) −9.54247 −0.463971
\(424\) −9.36991 −0.455043
\(425\) −4.02121 −0.195057
\(426\) −57.5645 −2.78901
\(427\) 21.7130 1.05077
\(428\) −51.6505 −2.49662
\(429\) 22.2986 1.07658
\(430\) −5.16842 −0.249243
\(431\) 10.5839 0.509811 0.254905 0.966966i \(-0.417956\pi\)
0.254905 + 0.966966i \(0.417956\pi\)
\(432\) 8.99522 0.432783
\(433\) 3.88275 0.186593 0.0932966 0.995638i \(-0.470260\pi\)
0.0932966 + 0.995638i \(0.470260\pi\)
\(434\) −98.4135 −4.72400
\(435\) 24.8944 1.19360
\(436\) 3.43878 0.164688
\(437\) 22.2794 1.06577
\(438\) 65.3388 3.12201
\(439\) −26.1598 −1.24854 −0.624269 0.781210i \(-0.714603\pi\)
−0.624269 + 0.781210i \(0.714603\pi\)
\(440\) −8.60230 −0.410098
\(441\) 78.7285 3.74898
\(442\) 33.6207 1.59917
\(443\) −17.2850 −0.821236 −0.410618 0.911808i \(-0.634687\pi\)
−0.410618 + 0.911808i \(0.634687\pi\)
\(444\) −9.86030 −0.467949
\(445\) −11.6996 −0.554614
\(446\) 23.6878 1.12165
\(447\) 35.2738 1.66839
\(448\) 55.8632 2.63929
\(449\) −28.8368 −1.36089 −0.680447 0.732797i \(-0.738214\pi\)
−0.680447 + 0.732797i \(0.738214\pi\)
\(450\) −11.3569 −0.535371
\(451\) 13.3753 0.629817
\(452\) −33.8315 −1.59130
\(453\) 44.6463 2.09767
\(454\) 52.7828 2.47722
\(455\) −17.0862 −0.801013
\(456\) 31.3511 1.46815
\(457\) 38.2656 1.78999 0.894994 0.446078i \(-0.147179\pi\)
0.894994 + 0.446078i \(0.147179\pi\)
\(458\) 15.2072 0.710586
\(459\) −20.1706 −0.941481
\(460\) −27.2187 −1.26908
\(461\) −20.8037 −0.968927 −0.484463 0.874812i \(-0.660985\pi\)
−0.484463 + 0.874812i \(0.660985\pi\)
\(462\) 72.3515 3.36610
\(463\) 42.4374 1.97223 0.986116 0.166059i \(-0.0531042\pi\)
0.986116 + 0.166059i \(0.0531042\pi\)
\(464\) 15.9884 0.742242
\(465\) −23.9841 −1.11224
\(466\) 7.36191 0.341034
\(467\) −24.1492 −1.11749 −0.558745 0.829340i \(-0.688717\pi\)
−0.558745 + 0.829340i \(0.688717\pi\)
\(468\) 61.0802 2.82343
\(469\) −20.0599 −0.926279
\(470\) 4.71068 0.217288
\(471\) 8.02741 0.369884
\(472\) 15.8283 0.728556
\(473\) 4.93670 0.226990
\(474\) −88.1505 −4.04889
\(475\) −2.95196 −0.135445
\(476\) 70.1726 3.21636
\(477\) 11.8157 0.541005
\(478\) −39.9099 −1.82544
\(479\) −18.1033 −0.827161 −0.413581 0.910467i \(-0.635722\pi\)
−0.413581 + 0.910467i \(0.635722\pi\)
\(480\) 9.38479 0.428355
\(481\) −3.45762 −0.157654
\(482\) 38.1447 1.73745
\(483\) 101.972 4.63987
\(484\) −21.2238 −0.964720
\(485\) −2.59114 −0.117658
\(486\) 38.1660 1.73125
\(487\) −6.15594 −0.278952 −0.139476 0.990225i \(-0.544542\pi\)
−0.139476 + 0.990225i \(0.544542\pi\)
\(488\) 17.0678 0.772622
\(489\) 3.49829 0.158198
\(490\) −38.8647 −1.75573
\(491\) 29.8563 1.34740 0.673699 0.739006i \(-0.264705\pi\)
0.673699 + 0.739006i \(0.264705\pi\)
\(492\) 59.5530 2.68486
\(493\) −35.8518 −1.61468
\(494\) 24.6808 1.11044
\(495\) 10.8477 0.487570
\(496\) −15.4037 −0.691649
\(497\) −42.1310 −1.88983
\(498\) −81.2651 −3.64158
\(499\) −13.6988 −0.613244 −0.306622 0.951831i \(-0.599199\pi\)
−0.306622 + 0.951831i \(0.599199\pi\)
\(500\) 3.60639 0.161283
\(501\) 24.1740 1.08001
\(502\) −5.48084 −0.244622
\(503\) 6.47760 0.288822 0.144411 0.989518i \(-0.453871\pi\)
0.144411 + 0.989518i \(0.453871\pi\)
\(504\) 88.2776 3.93220
\(505\) −6.37806 −0.283820
\(506\) 40.4163 1.79672
\(507\) −1.48389 −0.0659021
\(508\) −66.6497 −2.95710
\(509\) 4.86666 0.215711 0.107855 0.994167i \(-0.465602\pi\)
0.107855 + 0.994167i \(0.465602\pi\)
\(510\) 26.5856 1.17723
\(511\) 47.8210 2.11548
\(512\) 19.6693 0.869267
\(513\) −14.8071 −0.653751
\(514\) 55.6113 2.45291
\(515\) −17.1180 −0.754309
\(516\) 21.9805 0.967637
\(517\) −4.49948 −0.197887
\(518\) −11.2188 −0.492928
\(519\) −59.0994 −2.59418
\(520\) −13.4308 −0.588980
\(521\) 23.8258 1.04383 0.521914 0.852998i \(-0.325218\pi\)
0.521914 + 0.852998i \(0.325218\pi\)
\(522\) −101.255 −4.43179
\(523\) 32.2397 1.40974 0.704872 0.709334i \(-0.251004\pi\)
0.704872 + 0.709334i \(0.251004\pi\)
\(524\) −57.5280 −2.51312
\(525\) −13.5109 −0.589666
\(526\) 17.1075 0.745923
\(527\) 34.5408 1.50462
\(528\) 11.3245 0.492836
\(529\) 33.9624 1.47663
\(530\) −5.83288 −0.253364
\(531\) −19.9599 −0.866187
\(532\) 51.5134 2.23339
\(533\) 20.8829 0.904538
\(534\) 77.3501 3.34727
\(535\) −14.3219 −0.619190
\(536\) −15.7683 −0.681087
\(537\) −73.1275 −3.15569
\(538\) −65.7919 −2.83649
\(539\) 37.1222 1.59897
\(540\) 18.0898 0.778462
\(541\) 26.0818 1.12135 0.560673 0.828037i \(-0.310542\pi\)
0.560673 + 0.828037i \(0.310542\pi\)
\(542\) −45.6276 −1.95987
\(543\) −28.6855 −1.23101
\(544\) −13.5155 −0.579474
\(545\) 0.953522 0.0408444
\(546\) 112.963 4.83436
\(547\) 44.1205 1.88646 0.943228 0.332147i \(-0.107773\pi\)
0.943228 + 0.332147i \(0.107773\pi\)
\(548\) −4.98396 −0.212904
\(549\) −21.5230 −0.918578
\(550\) −5.35503 −0.228339
\(551\) −26.3186 −1.12121
\(552\) 80.1560 3.41167
\(553\) −64.5167 −2.74353
\(554\) 15.0116 0.637780
\(555\) −2.73412 −0.116057
\(556\) 11.8320 0.501788
\(557\) −21.3819 −0.905982 −0.452991 0.891515i \(-0.649643\pi\)
−0.452991 + 0.891515i \(0.649643\pi\)
\(558\) 97.5521 4.12971
\(559\) 7.70769 0.326000
\(560\) −8.67737 −0.366686
\(561\) −25.3937 −1.07212
\(562\) 9.99235 0.421502
\(563\) −39.9369 −1.68314 −0.841570 0.540148i \(-0.818368\pi\)
−0.841570 + 0.540148i \(0.818368\pi\)
\(564\) −20.0338 −0.843575
\(565\) −9.38097 −0.394660
\(566\) −36.4706 −1.53297
\(567\) 1.85561 0.0779281
\(568\) −33.1176 −1.38958
\(569\) −43.5671 −1.82643 −0.913214 0.407480i \(-0.866408\pi\)
−0.913214 + 0.407480i \(0.866408\pi\)
\(570\) 19.5164 0.817453
\(571\) −14.8029 −0.619481 −0.309740 0.950821i \(-0.600242\pi\)
−0.309740 + 0.950821i \(0.600242\pi\)
\(572\) 28.8006 1.20421
\(573\) 15.4275 0.644491
\(574\) 67.7581 2.82817
\(575\) −7.54734 −0.314746
\(576\) −55.3742 −2.30726
\(577\) 30.9771 1.28959 0.644796 0.764355i \(-0.276942\pi\)
0.644796 + 0.764355i \(0.276942\pi\)
\(578\) 1.96492 0.0817298
\(579\) 10.1546 0.422009
\(580\) 32.1534 1.33510
\(581\) −59.4774 −2.46754
\(582\) 17.1309 0.710100
\(583\) 5.57137 0.230743
\(584\) 37.5902 1.55550
\(585\) 16.9366 0.700244
\(586\) 30.7267 1.26931
\(587\) −26.5565 −1.09610 −0.548051 0.836445i \(-0.684630\pi\)
−0.548051 + 0.836445i \(0.684630\pi\)
\(588\) 165.285 6.81626
\(589\) 25.3563 1.04479
\(590\) 9.85330 0.405654
\(591\) 36.5673 1.50418
\(592\) −1.75598 −0.0721704
\(593\) 7.24201 0.297394 0.148697 0.988883i \(-0.452492\pi\)
0.148697 + 0.988883i \(0.452492\pi\)
\(594\) −26.8611 −1.10212
\(595\) 19.4578 0.797693
\(596\) 45.5593 1.86618
\(597\) −12.6573 −0.518029
\(598\) 63.1021 2.58044
\(599\) −17.4361 −0.712418 −0.356209 0.934406i \(-0.615931\pi\)
−0.356209 + 0.934406i \(0.615931\pi\)
\(600\) −10.6204 −0.433577
\(601\) 4.09401 0.166998 0.0834991 0.996508i \(-0.473390\pi\)
0.0834991 + 0.996508i \(0.473390\pi\)
\(602\) 25.0089 1.01929
\(603\) 19.8843 0.809751
\(604\) 57.6647 2.34635
\(605\) −5.88506 −0.239262
\(606\) 42.1676 1.71294
\(607\) 23.3676 0.948460 0.474230 0.880401i \(-0.342727\pi\)
0.474230 + 0.880401i \(0.342727\pi\)
\(608\) −9.92171 −0.402378
\(609\) −120.459 −4.88124
\(610\) 10.6249 0.430190
\(611\) −7.02506 −0.284204
\(612\) −69.5583 −2.81173
\(613\) 29.4024 1.18755 0.593775 0.804631i \(-0.297637\pi\)
0.593775 + 0.804631i \(0.297637\pi\)
\(614\) −16.3756 −0.660866
\(615\) 16.5132 0.665875
\(616\) 41.6248 1.67711
\(617\) −32.7587 −1.31881 −0.659407 0.751786i \(-0.729193\pi\)
−0.659407 + 0.751786i \(0.729193\pi\)
\(618\) 113.173 4.55249
\(619\) −19.6423 −0.789491 −0.394746 0.918790i \(-0.629167\pi\)
−0.394746 + 0.918790i \(0.629167\pi\)
\(620\) −30.9777 −1.24409
\(621\) −37.8578 −1.51918
\(622\) 5.67814 0.227673
\(623\) 56.6120 2.26811
\(624\) 17.6810 0.707807
\(625\) 1.00000 0.0400000
\(626\) −44.6633 −1.78510
\(627\) −18.6414 −0.744466
\(628\) 10.3681 0.413734
\(629\) 3.93755 0.157000
\(630\) 54.9539 2.18941
\(631\) −25.0025 −0.995332 −0.497666 0.867369i \(-0.665810\pi\)
−0.497666 + 0.867369i \(0.665810\pi\)
\(632\) −50.7141 −2.01730
\(633\) −57.1589 −2.27186
\(634\) 4.38562 0.174175
\(635\) −18.4810 −0.733396
\(636\) 24.8064 0.983636
\(637\) 57.9591 2.29642
\(638\) −47.7437 −1.89019
\(639\) 41.7622 1.65209
\(640\) 20.6136 0.814822
\(641\) −21.4298 −0.846428 −0.423214 0.906030i \(-0.639098\pi\)
−0.423214 + 0.906030i \(0.639098\pi\)
\(642\) 94.6871 3.73700
\(643\) −31.2499 −1.23238 −0.616188 0.787599i \(-0.711324\pi\)
−0.616188 + 0.787599i \(0.711324\pi\)
\(644\) 131.706 5.18993
\(645\) 6.09487 0.239985
\(646\) −28.1066 −1.10584
\(647\) −40.4840 −1.59159 −0.795795 0.605567i \(-0.792947\pi\)
−0.795795 + 0.605567i \(0.792947\pi\)
\(648\) 1.45862 0.0573000
\(649\) −9.41153 −0.369435
\(650\) −8.36084 −0.327939
\(651\) 116.054 4.54853
\(652\) 4.51837 0.176953
\(653\) 6.54743 0.256221 0.128110 0.991760i \(-0.459109\pi\)
0.128110 + 0.991760i \(0.459109\pi\)
\(654\) −6.30407 −0.246508
\(655\) −15.9517 −0.623283
\(656\) 10.6055 0.414077
\(657\) −47.4024 −1.84934
\(658\) −22.7940 −0.888604
\(659\) 34.2884 1.33569 0.667844 0.744301i \(-0.267217\pi\)
0.667844 + 0.744301i \(0.267217\pi\)
\(660\) 22.7741 0.886482
\(661\) −6.84087 −0.266079 −0.133039 0.991111i \(-0.542474\pi\)
−0.133039 + 0.991111i \(0.542474\pi\)
\(662\) 28.3970 1.10368
\(663\) −39.6473 −1.53977
\(664\) −46.7529 −1.81436
\(665\) 14.2839 0.553907
\(666\) 11.1206 0.430916
\(667\) −67.2896 −2.60546
\(668\) 31.2229 1.20805
\(669\) −27.9339 −1.07999
\(670\) −9.81596 −0.379224
\(671\) −10.1485 −0.391780
\(672\) −45.4111 −1.75177
\(673\) 48.1673 1.85671 0.928356 0.371693i \(-0.121223\pi\)
0.928356 + 0.371693i \(0.121223\pi\)
\(674\) 28.2678 1.08884
\(675\) 5.01604 0.193067
\(676\) −1.91658 −0.0737148
\(677\) −9.32497 −0.358388 −0.179194 0.983814i \(-0.557349\pi\)
−0.179194 + 0.983814i \(0.557349\pi\)
\(678\) 62.0208 2.38190
\(679\) 12.5380 0.481165
\(680\) 15.2951 0.586538
\(681\) −62.2442 −2.38520
\(682\) 45.9979 1.76135
\(683\) −25.8000 −0.987210 −0.493605 0.869686i \(-0.664321\pi\)
−0.493605 + 0.869686i \(0.664321\pi\)
\(684\) −51.0625 −1.95242
\(685\) −1.38198 −0.0528027
\(686\) 107.858 4.11803
\(687\) −17.9331 −0.684191
\(688\) 3.91441 0.149236
\(689\) 8.69861 0.331391
\(690\) 49.8981 1.89959
\(691\) 31.4749 1.19736 0.598680 0.800988i \(-0.295692\pi\)
0.598680 + 0.800988i \(0.295692\pi\)
\(692\) −76.3323 −2.90172
\(693\) −52.4900 −1.99393
\(694\) 80.2983 3.04808
\(695\) 3.28084 0.124449
\(696\) −94.6882 −3.58915
\(697\) −23.7815 −0.900789
\(698\) 6.98381 0.264341
\(699\) −8.68154 −0.328366
\(700\) −17.4506 −0.659571
\(701\) 21.9338 0.828426 0.414213 0.910180i \(-0.364057\pi\)
0.414213 + 0.910180i \(0.364057\pi\)
\(702\) −41.9383 −1.58286
\(703\) 2.89054 0.109019
\(704\) −26.1101 −0.984061
\(705\) −5.55508 −0.209216
\(706\) −1.50308 −0.0565690
\(707\) 30.8621 1.16069
\(708\) −41.9046 −1.57487
\(709\) −36.1334 −1.35702 −0.678508 0.734593i \(-0.737373\pi\)
−0.678508 + 0.734593i \(0.737373\pi\)
\(710\) −20.6161 −0.773708
\(711\) 63.9519 2.39839
\(712\) 44.5005 1.66773
\(713\) 64.8291 2.42787
\(714\) −128.642 −4.81432
\(715\) 7.98599 0.298659
\(716\) −94.4509 −3.52979
\(717\) 47.0638 1.75763
\(718\) −20.4432 −0.762933
\(719\) −29.0564 −1.08362 −0.541811 0.840500i \(-0.682261\pi\)
−0.541811 + 0.840500i \(0.682261\pi\)
\(720\) 8.60141 0.320556
\(721\) 82.8305 3.08477
\(722\) 24.3549 0.906395
\(723\) −44.9822 −1.67291
\(724\) −37.0499 −1.37695
\(725\) 8.91566 0.331119
\(726\) 38.9082 1.44402
\(727\) −10.4347 −0.387001 −0.193501 0.981100i \(-0.561984\pi\)
−0.193501 + 0.981100i \(0.561984\pi\)
\(728\) 64.9889 2.40865
\(729\) −43.8569 −1.62433
\(730\) 23.4004 0.866087
\(731\) −8.77754 −0.324649
\(732\) −45.1861 −1.67013
\(733\) −43.2357 −1.59695 −0.798474 0.602030i \(-0.794359\pi\)
−0.798474 + 0.602030i \(0.794359\pi\)
\(734\) 15.1865 0.560545
\(735\) 45.8312 1.69051
\(736\) −25.3671 −0.935043
\(737\) 9.37586 0.345364
\(738\) −67.1650 −2.47238
\(739\) −26.9322 −0.990718 −0.495359 0.868688i \(-0.664963\pi\)
−0.495359 + 0.868688i \(0.664963\pi\)
\(740\) −3.53136 −0.129815
\(741\) −29.1049 −1.06920
\(742\) 28.2241 1.03614
\(743\) −33.5079 −1.22929 −0.614643 0.788806i \(-0.710700\pi\)
−0.614643 + 0.788806i \(0.710700\pi\)
\(744\) 91.2258 3.34450
\(745\) 12.6329 0.462834
\(746\) −2.25023 −0.0823868
\(747\) 58.9567 2.15711
\(748\) −32.7982 −1.19922
\(749\) 69.3008 2.53220
\(750\) −6.61135 −0.241412
\(751\) 28.0379 1.02312 0.511559 0.859248i \(-0.329068\pi\)
0.511559 + 0.859248i \(0.329068\pi\)
\(752\) −3.56774 −0.130102
\(753\) 6.46328 0.235535
\(754\) −74.5424 −2.71468
\(755\) 15.9896 0.581921
\(756\) −87.5329 −3.18354
\(757\) −31.7709 −1.15473 −0.577366 0.816485i \(-0.695920\pi\)
−0.577366 + 0.816485i \(0.695920\pi\)
\(758\) 43.7127 1.58772
\(759\) −47.6609 −1.72998
\(760\) 11.2280 0.407284
\(761\) 2.57964 0.0935118 0.0467559 0.998906i \(-0.485112\pi\)
0.0467559 + 0.998906i \(0.485112\pi\)
\(762\) 122.184 4.42627
\(763\) −4.61390 −0.167034
\(764\) 19.9260 0.720896
\(765\) −19.2875 −0.697341
\(766\) −15.8612 −0.573088
\(767\) −14.6943 −0.530579
\(768\) −71.8121 −2.59130
\(769\) −6.93037 −0.249916 −0.124958 0.992162i \(-0.539880\pi\)
−0.124958 + 0.992162i \(0.539880\pi\)
\(770\) 25.9119 0.933801
\(771\) −65.5797 −2.36179
\(772\) 13.1155 0.472038
\(773\) 0.936234 0.0336740 0.0168370 0.999858i \(-0.494640\pi\)
0.0168370 + 0.999858i \(0.494640\pi\)
\(774\) −24.7900 −0.891059
\(775\) −8.58965 −0.308549
\(776\) 9.85565 0.353797
\(777\) 13.2298 0.474618
\(778\) −85.1090 −3.05131
\(779\) −17.4579 −0.625495
\(780\) 35.5574 1.27316
\(781\) 19.6918 0.704627
\(782\) −71.8609 −2.56974
\(783\) 44.7213 1.59821
\(784\) 29.4350 1.05125
\(785\) 2.87493 0.102611
\(786\) 105.462 3.76170
\(787\) −8.72173 −0.310896 −0.155448 0.987844i \(-0.549682\pi\)
−0.155448 + 0.987844i \(0.549682\pi\)
\(788\) 47.2300 1.68250
\(789\) −20.1740 −0.718215
\(790\) −31.5701 −1.12322
\(791\) 45.3926 1.61397
\(792\) −41.2604 −1.46612
\(793\) −15.8450 −0.562671
\(794\) −61.2611 −2.17408
\(795\) 6.87844 0.243953
\(796\) −16.3481 −0.579442
\(797\) 2.10910 0.0747083 0.0373541 0.999302i \(-0.488107\pi\)
0.0373541 + 0.999302i \(0.488107\pi\)
\(798\) −94.4360 −3.34300
\(799\) 8.00017 0.283025
\(800\) 3.36106 0.118831
\(801\) −56.1164 −1.98278
\(802\) −57.8765 −2.04369
\(803\) −22.3512 −0.788758
\(804\) 41.7457 1.47226
\(805\) 36.5201 1.28716
\(806\) 71.8167 2.52964
\(807\) 77.5852 2.73113
\(808\) 24.2595 0.853448
\(809\) 10.3546 0.364049 0.182024 0.983294i \(-0.441735\pi\)
0.182024 + 0.983294i \(0.441735\pi\)
\(810\) 0.908009 0.0319042
\(811\) 27.6983 0.972619 0.486310 0.873787i \(-0.338343\pi\)
0.486310 + 0.873787i \(0.338343\pi\)
\(812\) −155.584 −5.45992
\(813\) 53.8064 1.88707
\(814\) 5.24362 0.183789
\(815\) 1.25288 0.0438863
\(816\) −20.1352 −0.704873
\(817\) −6.44356 −0.225432
\(818\) −36.2119 −1.26612
\(819\) −81.9529 −2.86367
\(820\) 21.3283 0.744815
\(821\) −14.6702 −0.511995 −0.255997 0.966677i \(-0.582404\pi\)
−0.255997 + 0.966677i \(0.582404\pi\)
\(822\) 9.13674 0.318680
\(823\) 53.3549 1.85984 0.929918 0.367767i \(-0.119877\pi\)
0.929918 + 0.367767i \(0.119877\pi\)
\(824\) 65.1099 2.26821
\(825\) 6.31493 0.219858
\(826\) −47.6781 −1.65893
\(827\) 3.87862 0.134873 0.0674363 0.997724i \(-0.478518\pi\)
0.0674363 + 0.997724i \(0.478518\pi\)
\(828\) −130.553 −4.53702
\(829\) 32.4421 1.12676 0.563381 0.826197i \(-0.309500\pi\)
0.563381 + 0.826197i \(0.309500\pi\)
\(830\) −29.1042 −1.01022
\(831\) −17.7024 −0.614089
\(832\) −40.7658 −1.41330
\(833\) −66.0040 −2.28690
\(834\) −21.6907 −0.751089
\(835\) 8.65766 0.299611
\(836\) −24.0771 −0.832723
\(837\) −43.0860 −1.48927
\(838\) 49.0026 1.69277
\(839\) −4.25650 −0.146951 −0.0734753 0.997297i \(-0.523409\pi\)
−0.0734753 + 0.997297i \(0.523409\pi\)
\(840\) 51.3901 1.77313
\(841\) 50.4890 1.74100
\(842\) −10.1550 −0.349964
\(843\) −11.7835 −0.405845
\(844\) −73.8260 −2.54120
\(845\) −0.531441 −0.0182821
\(846\) 22.5945 0.776815
\(847\) 28.4766 0.978467
\(848\) 4.41766 0.151703
\(849\) 43.0080 1.47603
\(850\) 9.52136 0.326580
\(851\) 7.39032 0.253337
\(852\) 87.6770 3.00377
\(853\) −18.1012 −0.619774 −0.309887 0.950773i \(-0.600291\pi\)
−0.309887 + 0.950773i \(0.600291\pi\)
\(854\) −51.4118 −1.75927
\(855\) −14.1589 −0.484224
\(856\) 54.4747 1.86191
\(857\) 19.8436 0.677844 0.338922 0.940815i \(-0.389938\pi\)
0.338922 + 0.940815i \(0.389938\pi\)
\(858\) −52.7981 −1.80250
\(859\) −4.33114 −0.147777 −0.0738883 0.997267i \(-0.523541\pi\)
−0.0738883 + 0.997267i \(0.523541\pi\)
\(860\) 7.87207 0.268435
\(861\) −79.9039 −2.72312
\(862\) −25.0605 −0.853564
\(863\) −24.3887 −0.830200 −0.415100 0.909776i \(-0.636253\pi\)
−0.415100 + 0.909776i \(0.636253\pi\)
\(864\) 16.8592 0.573562
\(865\) −21.1658 −0.719659
\(866\) −9.19351 −0.312408
\(867\) −2.31713 −0.0786939
\(868\) 149.895 5.08776
\(869\) 30.1547 1.02293
\(870\) −58.9445 −1.99841
\(871\) 14.6386 0.496009
\(872\) −3.62681 −0.122819
\(873\) −12.4283 −0.420633
\(874\) −52.7528 −1.78439
\(875\) −4.83880 −0.163581
\(876\) −99.5182 −3.36241
\(877\) 11.0874 0.374396 0.187198 0.982322i \(-0.440059\pi\)
0.187198 + 0.982322i \(0.440059\pi\)
\(878\) 61.9406 2.09040
\(879\) −36.2345 −1.22216
\(880\) 4.05575 0.136719
\(881\) 49.9000 1.68117 0.840586 0.541678i \(-0.182211\pi\)
0.840586 + 0.541678i \(0.182211\pi\)
\(882\) −186.412 −6.27682
\(883\) −10.1601 −0.341914 −0.170957 0.985279i \(-0.554686\pi\)
−0.170957 + 0.985279i \(0.554686\pi\)
\(884\) −51.2081 −1.72231
\(885\) −11.6195 −0.390586
\(886\) 40.9272 1.37497
\(887\) 16.0136 0.537684 0.268842 0.963184i \(-0.413359\pi\)
0.268842 + 0.963184i \(0.413359\pi\)
\(888\) 10.3995 0.348983
\(889\) 89.4257 2.99924
\(890\) 27.7021 0.928577
\(891\) −0.867299 −0.0290556
\(892\) −36.0792 −1.20802
\(893\) 5.87289 0.196529
\(894\) −83.5206 −2.79335
\(895\) −26.1898 −0.875429
\(896\) −99.7448 −3.33224
\(897\) −74.4133 −2.48459
\(898\) 68.2793 2.27851
\(899\) −76.5824 −2.55417
\(900\) 17.2979 0.576595
\(901\) −9.90600 −0.330017
\(902\) −31.6697 −1.05449
\(903\) −29.4918 −0.981426
\(904\) 35.6814 1.18674
\(905\) −10.2734 −0.341499
\(906\) −105.713 −3.51207
\(907\) 35.9530 1.19380 0.596901 0.802315i \(-0.296399\pi\)
0.596901 + 0.802315i \(0.296399\pi\)
\(908\) −80.3940 −2.66797
\(909\) −30.5920 −1.01467
\(910\) 40.4564 1.34112
\(911\) 24.0272 0.796055 0.398028 0.917373i \(-0.369695\pi\)
0.398028 + 0.917373i \(0.369695\pi\)
\(912\) −14.7812 −0.489454
\(913\) 27.7994 0.920024
\(914\) −90.6046 −2.99693
\(915\) −12.5294 −0.414210
\(916\) −23.1622 −0.765302
\(917\) 77.1868 2.54893
\(918\) 47.7595 1.57630
\(919\) 25.1177 0.828557 0.414279 0.910150i \(-0.364034\pi\)
0.414279 + 0.910150i \(0.364034\pi\)
\(920\) 28.7070 0.946442
\(921\) 19.3110 0.636317
\(922\) 49.2587 1.62225
\(923\) 30.7449 1.01198
\(924\) −110.199 −3.62529
\(925\) −0.979194 −0.0321957
\(926\) −100.482 −3.30206
\(927\) −82.1054 −2.69670
\(928\) 29.9661 0.983685
\(929\) 35.5277 1.16563 0.582813 0.812606i \(-0.301952\pi\)
0.582813 + 0.812606i \(0.301952\pi\)
\(930\) 56.7892 1.86219
\(931\) −48.4533 −1.58799
\(932\) −11.2130 −0.367294
\(933\) −6.69595 −0.219216
\(934\) 57.1800 1.87099
\(935\) −9.09447 −0.297421
\(936\) −64.4201 −2.10564
\(937\) −24.5818 −0.803052 −0.401526 0.915848i \(-0.631520\pi\)
−0.401526 + 0.915848i \(0.631520\pi\)
\(938\) 47.4974 1.55085
\(939\) 52.6692 1.71880
\(940\) −7.17489 −0.234019
\(941\) −0.231228 −0.00753783 −0.00376891 0.999993i \(-0.501200\pi\)
−0.00376891 + 0.999993i \(0.501200\pi\)
\(942\) −19.0072 −0.619287
\(943\) −44.6351 −1.45352
\(944\) −7.46261 −0.242887
\(945\) −24.2716 −0.789555
\(946\) −11.6890 −0.380043
\(947\) −28.9559 −0.940940 −0.470470 0.882416i \(-0.655916\pi\)
−0.470470 + 0.882416i \(0.655916\pi\)
\(948\) 134.263 4.36066
\(949\) −34.8971 −1.13281
\(950\) 6.98959 0.226772
\(951\) −5.17175 −0.167706
\(952\) −74.0096 −2.39867
\(953\) −0.843160 −0.0273126 −0.0136563 0.999907i \(-0.504347\pi\)
−0.0136563 + 0.999907i \(0.504347\pi\)
\(954\) −27.9771 −0.905791
\(955\) 5.52518 0.178791
\(956\) 60.7872 1.96600
\(957\) 56.3018 1.81998
\(958\) 42.8647 1.38490
\(959\) 6.68711 0.215938
\(960\) −32.2356 −1.04040
\(961\) 42.7821 1.38007
\(962\) 8.18689 0.263956
\(963\) −68.6942 −2.21364
\(964\) −58.0987 −1.87123
\(965\) 3.63674 0.117071
\(966\) −241.447 −7.76842
\(967\) 53.0160 1.70488 0.852440 0.522824i \(-0.175122\pi\)
0.852440 + 0.522824i \(0.175122\pi\)
\(968\) 22.3844 0.719460
\(969\) 33.1448 1.06476
\(970\) 6.13526 0.196991
\(971\) −27.6344 −0.886832 −0.443416 0.896316i \(-0.646233\pi\)
−0.443416 + 0.896316i \(0.646233\pi\)
\(972\) −58.1311 −1.86455
\(973\) −15.8753 −0.508939
\(974\) 14.5759 0.467042
\(975\) 9.85953 0.315758
\(976\) −8.04700 −0.257578
\(977\) −28.7830 −0.920851 −0.460425 0.887698i \(-0.652303\pi\)
−0.460425 + 0.887698i \(0.652303\pi\)
\(978\) −8.28320 −0.264868
\(979\) −26.4601 −0.845668
\(980\) 59.1952 1.89092
\(981\) 4.57351 0.146021
\(982\) −70.6933 −2.25591
\(983\) 12.0374 0.383934 0.191967 0.981401i \(-0.438513\pi\)
0.191967 + 0.981401i \(0.438513\pi\)
\(984\) −62.8094 −2.00229
\(985\) 13.0962 0.417279
\(986\) 84.8892 2.70342
\(987\) 26.8799 0.855596
\(988\) −37.5916 −1.19595
\(989\) −16.4744 −0.523856
\(990\) −25.6851 −0.816326
\(991\) −51.7046 −1.64245 −0.821226 0.570603i \(-0.806710\pi\)
−0.821226 + 0.570603i \(0.806710\pi\)
\(992\) −28.8703 −0.916634
\(993\) −33.4872 −1.06268
\(994\) 99.7571 3.16410
\(995\) −4.53308 −0.143708
\(996\) 123.776 3.92199
\(997\) −39.3223 −1.24535 −0.622675 0.782481i \(-0.713954\pi\)
−0.622675 + 0.782481i \(0.713954\pi\)
\(998\) 32.4358 1.02674
\(999\) −4.91168 −0.155399
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.1.15 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8005.2.a.e.1.15 126 1.1 even 1 trivial