Properties

Label 8027.2.a.c.1.2
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $1$
Dimension $143$
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] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, 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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(1\)
Dimension: \(143\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.73897 q^{2} -2.10858 q^{3} +5.50198 q^{4} -1.32967 q^{5} +5.77534 q^{6} +4.16128 q^{7} -9.59184 q^{8} +1.44610 q^{9} +O(q^{10})\) \(q-2.73897 q^{2} -2.10858 q^{3} +5.50198 q^{4} -1.32967 q^{5} +5.77534 q^{6} +4.16128 q^{7} -9.59184 q^{8} +1.44610 q^{9} +3.64193 q^{10} +5.31866 q^{11} -11.6014 q^{12} -6.77846 q^{13} -11.3976 q^{14} +2.80371 q^{15} +15.2679 q^{16} -6.76063 q^{17} -3.96083 q^{18} -3.24262 q^{19} -7.31581 q^{20} -8.77438 q^{21} -14.5677 q^{22} +1.00000 q^{23} +20.2251 q^{24} -3.23198 q^{25} +18.5660 q^{26} +3.27652 q^{27} +22.8953 q^{28} +8.05321 q^{29} -7.67929 q^{30} -5.40902 q^{31} -22.6346 q^{32} -11.2148 q^{33} +18.5172 q^{34} -5.53312 q^{35} +7.95641 q^{36} -8.96409 q^{37} +8.88147 q^{38} +14.2929 q^{39} +12.7540 q^{40} +8.93996 q^{41} +24.0328 q^{42} +1.20205 q^{43} +29.2632 q^{44} -1.92283 q^{45} -2.73897 q^{46} +7.04061 q^{47} -32.1935 q^{48} +10.3162 q^{49} +8.85232 q^{50} +14.2553 q^{51} -37.2950 q^{52} -3.57904 q^{53} -8.97431 q^{54} -7.07205 q^{55} -39.9144 q^{56} +6.83733 q^{57} -22.0575 q^{58} +9.09310 q^{59} +15.4260 q^{60} +5.56372 q^{61} +14.8152 q^{62} +6.01762 q^{63} +31.4598 q^{64} +9.01310 q^{65} +30.7171 q^{66} -12.4016 q^{67} -37.1969 q^{68} -2.10858 q^{69} +15.1551 q^{70} +2.85671 q^{71} -13.8708 q^{72} +12.9418 q^{73} +24.5524 q^{74} +6.81488 q^{75} -17.8409 q^{76} +22.1324 q^{77} -39.1479 q^{78} +4.33291 q^{79} -20.3012 q^{80} -11.2471 q^{81} -24.4863 q^{82} +6.21728 q^{83} -48.2765 q^{84} +8.98940 q^{85} -3.29238 q^{86} -16.9808 q^{87} -51.0157 q^{88} -1.41376 q^{89} +5.26659 q^{90} -28.2071 q^{91} +5.50198 q^{92} +11.4053 q^{93} -19.2841 q^{94} +4.31162 q^{95} +47.7268 q^{96} -0.694735 q^{97} -28.2559 q^{98} +7.69131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73897 −1.93675 −0.968374 0.249504i \(-0.919733\pi\)
−0.968374 + 0.249504i \(0.919733\pi\)
\(3\) −2.10858 −1.21739 −0.608694 0.793405i \(-0.708306\pi\)
−0.608694 + 0.793405i \(0.708306\pi\)
\(4\) 5.50198 2.75099
\(5\) −1.32967 −0.594646 −0.297323 0.954777i \(-0.596094\pi\)
−0.297323 + 0.954777i \(0.596094\pi\)
\(6\) 5.77534 2.35777
\(7\) 4.16128 1.57282 0.786408 0.617707i \(-0.211938\pi\)
0.786408 + 0.617707i \(0.211938\pi\)
\(8\) −9.59184 −3.39123
\(9\) 1.44610 0.482033
\(10\) 3.64193 1.15168
\(11\) 5.31866 1.60364 0.801818 0.597569i \(-0.203866\pi\)
0.801818 + 0.597569i \(0.203866\pi\)
\(12\) −11.6014 −3.34902
\(13\) −6.77846 −1.88001 −0.940003 0.341166i \(-0.889178\pi\)
−0.940003 + 0.341166i \(0.889178\pi\)
\(14\) −11.3976 −3.04615
\(15\) 2.80371 0.723914
\(16\) 15.2679 3.81696
\(17\) −6.76063 −1.63969 −0.819847 0.572582i \(-0.805942\pi\)
−0.819847 + 0.572582i \(0.805942\pi\)
\(18\) −3.96083 −0.933576
\(19\) −3.24262 −0.743909 −0.371955 0.928251i \(-0.621312\pi\)
−0.371955 + 0.928251i \(0.621312\pi\)
\(20\) −7.31581 −1.63587
\(21\) −8.77438 −1.91473
\(22\) −14.5677 −3.10584
\(23\) 1.00000 0.208514
\(24\) 20.2251 4.12844
\(25\) −3.23198 −0.646396
\(26\) 18.5660 3.64110
\(27\) 3.27652 0.630567
\(28\) 22.8953 4.32680
\(29\) 8.05321 1.49544 0.747722 0.664012i \(-0.231148\pi\)
0.747722 + 0.664012i \(0.231148\pi\)
\(30\) −7.67929 −1.40204
\(31\) −5.40902 −0.971488 −0.485744 0.874101i \(-0.661451\pi\)
−0.485744 + 0.874101i \(0.661451\pi\)
\(32\) −22.6346 −4.00127
\(33\) −11.2148 −1.95225
\(34\) 18.5172 3.17567
\(35\) −5.53312 −0.935268
\(36\) 7.95641 1.32607
\(37\) −8.96409 −1.47369 −0.736843 0.676063i \(-0.763685\pi\)
−0.736843 + 0.676063i \(0.763685\pi\)
\(38\) 8.88147 1.44076
\(39\) 14.2929 2.28870
\(40\) 12.7540 2.01658
\(41\) 8.93996 1.39619 0.698093 0.716007i \(-0.254032\pi\)
0.698093 + 0.716007i \(0.254032\pi\)
\(42\) 24.0328 3.70834
\(43\) 1.20205 0.183311 0.0916553 0.995791i \(-0.470784\pi\)
0.0916553 + 0.995791i \(0.470784\pi\)
\(44\) 29.2632 4.41159
\(45\) −1.92283 −0.286639
\(46\) −2.73897 −0.403840
\(47\) 7.04061 1.02698 0.513490 0.858096i \(-0.328353\pi\)
0.513490 + 0.858096i \(0.328353\pi\)
\(48\) −32.1935 −4.64673
\(49\) 10.3162 1.47375
\(50\) 8.85232 1.25191
\(51\) 14.2553 1.99614
\(52\) −37.2950 −5.17188
\(53\) −3.57904 −0.491619 −0.245810 0.969318i \(-0.579054\pi\)
−0.245810 + 0.969318i \(0.579054\pi\)
\(54\) −8.97431 −1.22125
\(55\) −7.07205 −0.953595
\(56\) −39.9144 −5.33378
\(57\) 6.83733 0.905626
\(58\) −22.0575 −2.89630
\(59\) 9.09310 1.18382 0.591911 0.806004i \(-0.298374\pi\)
0.591911 + 0.806004i \(0.298374\pi\)
\(60\) 15.4260 1.99148
\(61\) 5.56372 0.712361 0.356181 0.934417i \(-0.384079\pi\)
0.356181 + 0.934417i \(0.384079\pi\)
\(62\) 14.8152 1.88153
\(63\) 6.01762 0.758149
\(64\) 31.4598 3.93248
\(65\) 9.01310 1.11794
\(66\) 30.7171 3.78101
\(67\) −12.4016 −1.51509 −0.757547 0.652780i \(-0.773603\pi\)
−0.757547 + 0.652780i \(0.773603\pi\)
\(68\) −37.1969 −4.51079
\(69\) −2.10858 −0.253843
\(70\) 15.1551 1.81138
\(71\) 2.85671 0.339029 0.169515 0.985528i \(-0.445780\pi\)
0.169515 + 0.985528i \(0.445780\pi\)
\(72\) −13.8708 −1.63468
\(73\) 12.9418 1.51472 0.757361 0.652997i \(-0.226489\pi\)
0.757361 + 0.652997i \(0.226489\pi\)
\(74\) 24.5524 2.85416
\(75\) 6.81488 0.786915
\(76\) −17.8409 −2.04649
\(77\) 22.1324 2.52222
\(78\) −39.1479 −4.43263
\(79\) 4.33291 0.487490 0.243745 0.969839i \(-0.421624\pi\)
0.243745 + 0.969839i \(0.421624\pi\)
\(80\) −20.3012 −2.26974
\(81\) −11.2471 −1.24968
\(82\) −24.4863 −2.70406
\(83\) 6.21728 0.682435 0.341218 0.939984i \(-0.389161\pi\)
0.341218 + 0.939984i \(0.389161\pi\)
\(84\) −48.2765 −5.26740
\(85\) 8.98940 0.975037
\(86\) −3.29238 −0.355026
\(87\) −16.9808 −1.82053
\(88\) −51.0157 −5.43830
\(89\) −1.41376 −0.149858 −0.0749291 0.997189i \(-0.523873\pi\)
−0.0749291 + 0.997189i \(0.523873\pi\)
\(90\) 5.26659 0.555147
\(91\) −28.2071 −2.95690
\(92\) 5.50198 0.573621
\(93\) 11.4053 1.18268
\(94\) −19.2841 −1.98900
\(95\) 4.31162 0.442362
\(96\) 47.7268 4.87109
\(97\) −0.694735 −0.0705396 −0.0352698 0.999378i \(-0.511229\pi\)
−0.0352698 + 0.999378i \(0.511229\pi\)
\(98\) −28.2559 −2.85428
\(99\) 7.69131 0.773005
\(100\) −17.7823 −1.77823
\(101\) 3.51938 0.350192 0.175096 0.984551i \(-0.443976\pi\)
0.175096 + 0.984551i \(0.443976\pi\)
\(102\) −39.0450 −3.86603
\(103\) 2.21443 0.218194 0.109097 0.994031i \(-0.465204\pi\)
0.109097 + 0.994031i \(0.465204\pi\)
\(104\) 65.0179 6.37553
\(105\) 11.6670 1.13858
\(106\) 9.80290 0.952142
\(107\) −3.65970 −0.353796 −0.176898 0.984229i \(-0.556606\pi\)
−0.176898 + 0.984229i \(0.556606\pi\)
\(108\) 18.0274 1.73468
\(109\) −13.6009 −1.30273 −0.651364 0.758766i \(-0.725803\pi\)
−0.651364 + 0.758766i \(0.725803\pi\)
\(110\) 19.3702 1.84687
\(111\) 18.9015 1.79405
\(112\) 63.5338 6.00338
\(113\) −13.6744 −1.28638 −0.643190 0.765707i \(-0.722389\pi\)
−0.643190 + 0.765707i \(0.722389\pi\)
\(114\) −18.7273 −1.75397
\(115\) −1.32967 −0.123992
\(116\) 44.3086 4.11395
\(117\) −9.80232 −0.906225
\(118\) −24.9058 −2.29276
\(119\) −28.1329 −2.57894
\(120\) −26.8927 −2.45496
\(121\) 17.2881 1.57165
\(122\) −15.2389 −1.37966
\(123\) −18.8506 −1.69970
\(124\) −29.7603 −2.67256
\(125\) 10.9458 0.979023
\(126\) −16.4821 −1.46834
\(127\) 3.87782 0.344100 0.172050 0.985088i \(-0.444961\pi\)
0.172050 + 0.985088i \(0.444961\pi\)
\(128\) −40.8986 −3.61496
\(129\) −2.53461 −0.223160
\(130\) −24.6867 −2.16516
\(131\) −4.93426 −0.431108 −0.215554 0.976492i \(-0.569156\pi\)
−0.215554 + 0.976492i \(0.569156\pi\)
\(132\) −61.7037 −5.37061
\(133\) −13.4935 −1.17003
\(134\) 33.9676 2.93436
\(135\) −4.35669 −0.374964
\(136\) 64.8470 5.56058
\(137\) 5.35120 0.457184 0.228592 0.973522i \(-0.426588\pi\)
0.228592 + 0.973522i \(0.426588\pi\)
\(138\) 5.77534 0.491630
\(139\) −22.3263 −1.89370 −0.946848 0.321681i \(-0.895752\pi\)
−0.946848 + 0.321681i \(0.895752\pi\)
\(140\) −30.4431 −2.57292
\(141\) −14.8457 −1.25023
\(142\) −7.82446 −0.656614
\(143\) −36.0523 −3.01484
\(144\) 22.0788 1.83990
\(145\) −10.7081 −0.889259
\(146\) −35.4472 −2.93363
\(147\) −21.7526 −1.79413
\(148\) −49.3203 −4.05410
\(149\) −6.32361 −0.518050 −0.259025 0.965871i \(-0.583401\pi\)
−0.259025 + 0.965871i \(0.583401\pi\)
\(150\) −18.6658 −1.52406
\(151\) −2.96436 −0.241236 −0.120618 0.992699i \(-0.538488\pi\)
−0.120618 + 0.992699i \(0.538488\pi\)
\(152\) 31.1028 2.52277
\(153\) −9.77655 −0.790387
\(154\) −60.6202 −4.88491
\(155\) 7.19220 0.577691
\(156\) 78.6393 6.29618
\(157\) 18.6522 1.48861 0.744303 0.667842i \(-0.232782\pi\)
0.744303 + 0.667842i \(0.232782\pi\)
\(158\) −11.8677 −0.944145
\(159\) 7.54669 0.598491
\(160\) 30.0965 2.37934
\(161\) 4.16128 0.327955
\(162\) 30.8055 2.42031
\(163\) −2.00945 −0.157392 −0.0786962 0.996899i \(-0.525076\pi\)
−0.0786962 + 0.996899i \(0.525076\pi\)
\(164\) 49.1875 3.84090
\(165\) 14.9120 1.16090
\(166\) −17.0290 −1.32170
\(167\) 21.4783 1.66204 0.831019 0.556244i \(-0.187758\pi\)
0.831019 + 0.556244i \(0.187758\pi\)
\(168\) 84.1625 6.49328
\(169\) 32.9475 2.53442
\(170\) −24.6217 −1.88840
\(171\) −4.68916 −0.358589
\(172\) 6.61365 0.504286
\(173\) 24.2584 1.84433 0.922164 0.386799i \(-0.126419\pi\)
0.922164 + 0.386799i \(0.126419\pi\)
\(174\) 46.5100 3.52592
\(175\) −13.4492 −1.01666
\(176\) 81.2045 6.12102
\(177\) −19.1735 −1.44117
\(178\) 3.87225 0.290238
\(179\) −15.2970 −1.14335 −0.571676 0.820479i \(-0.693707\pi\)
−0.571676 + 0.820479i \(0.693707\pi\)
\(180\) −10.5794 −0.788541
\(181\) 14.5150 1.07889 0.539444 0.842021i \(-0.318634\pi\)
0.539444 + 0.842021i \(0.318634\pi\)
\(182\) 77.2584 5.72678
\(183\) −11.7315 −0.867220
\(184\) −9.59184 −0.707120
\(185\) 11.9193 0.876322
\(186\) −31.2389 −2.29055
\(187\) −35.9575 −2.62947
\(188\) 38.7373 2.82521
\(189\) 13.6345 0.991765
\(190\) −11.8094 −0.856744
\(191\) −12.8433 −0.929306 −0.464653 0.885493i \(-0.653821\pi\)
−0.464653 + 0.885493i \(0.653821\pi\)
\(192\) −66.3355 −4.78735
\(193\) −10.9023 −0.784768 −0.392384 0.919802i \(-0.628349\pi\)
−0.392384 + 0.919802i \(0.628349\pi\)
\(194\) 1.90286 0.136617
\(195\) −19.0048 −1.36096
\(196\) 56.7598 4.05427
\(197\) −3.56179 −0.253767 −0.126883 0.991918i \(-0.540497\pi\)
−0.126883 + 0.991918i \(0.540497\pi\)
\(198\) −21.0663 −1.49712
\(199\) 12.6910 0.899638 0.449819 0.893120i \(-0.351488\pi\)
0.449819 + 0.893120i \(0.351488\pi\)
\(200\) 31.0007 2.19208
\(201\) 26.1497 1.84446
\(202\) −9.63950 −0.678233
\(203\) 33.5117 2.35206
\(204\) 78.4325 5.49138
\(205\) −11.8872 −0.830237
\(206\) −6.06526 −0.422586
\(207\) 1.44610 0.100511
\(208\) −103.493 −7.17591
\(209\) −17.2464 −1.19296
\(210\) −31.9557 −2.20515
\(211\) −19.6175 −1.35052 −0.675261 0.737578i \(-0.735969\pi\)
−0.675261 + 0.737578i \(0.735969\pi\)
\(212\) −19.6918 −1.35244
\(213\) −6.02359 −0.412730
\(214\) 10.0238 0.685214
\(215\) −1.59833 −0.109005
\(216\) −31.4279 −2.13840
\(217\) −22.5084 −1.52797
\(218\) 37.2524 2.52305
\(219\) −27.2888 −1.84400
\(220\) −38.9103 −2.62333
\(221\) 45.8267 3.08264
\(222\) −51.7707 −3.47462
\(223\) 16.5103 1.10561 0.552806 0.833310i \(-0.313557\pi\)
0.552806 + 0.833310i \(0.313557\pi\)
\(224\) −94.1888 −6.29326
\(225\) −4.67377 −0.311584
\(226\) 37.4538 2.49139
\(227\) 2.31861 0.153892 0.0769459 0.997035i \(-0.475483\pi\)
0.0769459 + 0.997035i \(0.475483\pi\)
\(228\) 37.6189 2.49137
\(229\) 11.5411 0.762659 0.381330 0.924439i \(-0.375466\pi\)
0.381330 + 0.924439i \(0.375466\pi\)
\(230\) 3.64193 0.240142
\(231\) −46.6679 −3.07052
\(232\) −77.2451 −5.07139
\(233\) 1.30812 0.0856976 0.0428488 0.999082i \(-0.486357\pi\)
0.0428488 + 0.999082i \(0.486357\pi\)
\(234\) 26.8483 1.75513
\(235\) −9.36168 −0.610689
\(236\) 50.0301 3.25668
\(237\) −9.13627 −0.593465
\(238\) 77.0553 4.99475
\(239\) −19.7265 −1.27600 −0.638001 0.770035i \(-0.720239\pi\)
−0.638001 + 0.770035i \(0.720239\pi\)
\(240\) 42.8066 2.76316
\(241\) −4.22094 −0.271894 −0.135947 0.990716i \(-0.543408\pi\)
−0.135947 + 0.990716i \(0.543408\pi\)
\(242\) −47.3517 −3.04388
\(243\) 13.8858 0.890775
\(244\) 30.6115 1.95970
\(245\) −13.7172 −0.876359
\(246\) 51.6313 3.29189
\(247\) 21.9800 1.39855
\(248\) 51.8825 3.29454
\(249\) −13.1096 −0.830788
\(250\) −29.9803 −1.89612
\(251\) −3.76355 −0.237553 −0.118777 0.992921i \(-0.537897\pi\)
−0.118777 + 0.992921i \(0.537897\pi\)
\(252\) 33.1089 2.08566
\(253\) 5.31866 0.334381
\(254\) −10.6212 −0.666436
\(255\) −18.9548 −1.18700
\(256\) 49.1004 3.06878
\(257\) 6.89460 0.430074 0.215037 0.976606i \(-0.431013\pi\)
0.215037 + 0.976606i \(0.431013\pi\)
\(258\) 6.94224 0.432205
\(259\) −37.3021 −2.31784
\(260\) 49.5899 3.07544
\(261\) 11.6457 0.720853
\(262\) 13.5148 0.834948
\(263\) −21.0001 −1.29492 −0.647460 0.762100i \(-0.724169\pi\)
−0.647460 + 0.762100i \(0.724169\pi\)
\(264\) 107.571 6.62052
\(265\) 4.75894 0.292339
\(266\) 36.9583 2.26606
\(267\) 2.98102 0.182436
\(268\) −68.2333 −4.16801
\(269\) −13.9626 −0.851314 −0.425657 0.904885i \(-0.639957\pi\)
−0.425657 + 0.904885i \(0.639957\pi\)
\(270\) 11.9329 0.726210
\(271\) 3.96012 0.240560 0.120280 0.992740i \(-0.461621\pi\)
0.120280 + 0.992740i \(0.461621\pi\)
\(272\) −103.220 −6.25866
\(273\) 59.4768 3.59970
\(274\) −14.6568 −0.885450
\(275\) −17.1898 −1.03658
\(276\) −11.6014 −0.698320
\(277\) −15.1716 −0.911575 −0.455788 0.890089i \(-0.650642\pi\)
−0.455788 + 0.890089i \(0.650642\pi\)
\(278\) 61.1513 3.66761
\(279\) −7.82197 −0.468289
\(280\) 53.0728 3.17171
\(281\) −26.7344 −1.59484 −0.797421 0.603424i \(-0.793803\pi\)
−0.797421 + 0.603424i \(0.793803\pi\)
\(282\) 40.6619 2.42138
\(283\) 21.8984 1.30172 0.650861 0.759197i \(-0.274408\pi\)
0.650861 + 0.759197i \(0.274408\pi\)
\(284\) 15.7176 0.932666
\(285\) −9.09138 −0.538527
\(286\) 98.7463 5.83899
\(287\) 37.2017 2.19594
\(288\) −32.7318 −1.92874
\(289\) 28.7062 1.68860
\(290\) 29.3292 1.72227
\(291\) 1.46490 0.0858741
\(292\) 71.2055 4.16699
\(293\) −14.0001 −0.817893 −0.408946 0.912558i \(-0.634104\pi\)
−0.408946 + 0.912558i \(0.634104\pi\)
\(294\) 59.5799 3.47477
\(295\) −12.0908 −0.703954
\(296\) 85.9821 4.99761
\(297\) 17.4267 1.01120
\(298\) 17.3202 1.00333
\(299\) −6.77846 −0.392008
\(300\) 37.4954 2.16480
\(301\) 5.00206 0.288314
\(302\) 8.11930 0.467213
\(303\) −7.42089 −0.426319
\(304\) −49.5079 −2.83947
\(305\) −7.39790 −0.423602
\(306\) 26.7777 1.53078
\(307\) −21.6851 −1.23763 −0.618816 0.785536i \(-0.712387\pi\)
−0.618816 + 0.785536i \(0.712387\pi\)
\(308\) 121.772 6.93862
\(309\) −4.66929 −0.265627
\(310\) −19.6993 −1.11884
\(311\) −12.8149 −0.726666 −0.363333 0.931659i \(-0.618361\pi\)
−0.363333 + 0.931659i \(0.618361\pi\)
\(312\) −137.095 −7.76149
\(313\) −21.7396 −1.22880 −0.614399 0.788996i \(-0.710601\pi\)
−0.614399 + 0.788996i \(0.710601\pi\)
\(314\) −51.0878 −2.88305
\(315\) −8.00144 −0.450830
\(316\) 23.8396 1.34108
\(317\) 21.8760 1.22868 0.614338 0.789043i \(-0.289423\pi\)
0.614338 + 0.789043i \(0.289423\pi\)
\(318\) −20.6702 −1.15913
\(319\) 42.8323 2.39815
\(320\) −41.8312 −2.33843
\(321\) 7.71675 0.430707
\(322\) −11.3976 −0.635166
\(323\) 21.9222 1.21978
\(324\) −61.8813 −3.43785
\(325\) 21.9079 1.21523
\(326\) 5.50384 0.304829
\(327\) 28.6785 1.58592
\(328\) −85.7507 −4.73479
\(329\) 29.2980 1.61525
\(330\) −40.8435 −2.24836
\(331\) −1.84728 −0.101536 −0.0507678 0.998710i \(-0.516167\pi\)
−0.0507678 + 0.998710i \(0.516167\pi\)
\(332\) 34.2074 1.87737
\(333\) −12.9630 −0.710366
\(334\) −58.8284 −3.21895
\(335\) 16.4900 0.900945
\(336\) −133.966 −7.30844
\(337\) 8.69672 0.473741 0.236870 0.971541i \(-0.423878\pi\)
0.236870 + 0.971541i \(0.423878\pi\)
\(338\) −90.2423 −4.90854
\(339\) 28.8335 1.56602
\(340\) 49.4595 2.68232
\(341\) −28.7687 −1.55791
\(342\) 12.8435 0.694496
\(343\) 13.7998 0.745121
\(344\) −11.5299 −0.621648
\(345\) 2.80371 0.150947
\(346\) −66.4430 −3.57200
\(347\) 22.5800 1.21216 0.606080 0.795404i \(-0.292741\pi\)
0.606080 + 0.795404i \(0.292741\pi\)
\(348\) −93.4282 −5.00828
\(349\) 1.00000 0.0535288
\(350\) 36.8370 1.96902
\(351\) −22.2098 −1.18547
\(352\) −120.386 −6.41657
\(353\) 26.5455 1.41287 0.706436 0.707777i \(-0.250302\pi\)
0.706436 + 0.707777i \(0.250302\pi\)
\(354\) 52.5158 2.79118
\(355\) −3.79848 −0.201602
\(356\) −7.77848 −0.412259
\(357\) 59.3204 3.13957
\(358\) 41.8981 2.21438
\(359\) 0.894687 0.0472198 0.0236099 0.999721i \(-0.492484\pi\)
0.0236099 + 0.999721i \(0.492484\pi\)
\(360\) 18.4435 0.972058
\(361\) −8.48539 −0.446599
\(362\) −39.7561 −2.08954
\(363\) −36.4533 −1.91330
\(364\) −155.195 −8.13442
\(365\) −17.2083 −0.900723
\(366\) 32.1324 1.67959
\(367\) 9.08076 0.474012 0.237006 0.971508i \(-0.423834\pi\)
0.237006 + 0.971508i \(0.423834\pi\)
\(368\) 15.2679 0.795892
\(369\) 12.9281 0.673008
\(370\) −32.6466 −1.69721
\(371\) −14.8934 −0.773226
\(372\) 62.7519 3.25354
\(373\) 3.66764 0.189903 0.0949516 0.995482i \(-0.469730\pi\)
0.0949516 + 0.995482i \(0.469730\pi\)
\(374\) 98.4867 5.09263
\(375\) −23.0801 −1.19185
\(376\) −67.5325 −3.48272
\(377\) −54.5883 −2.81144
\(378\) −37.3446 −1.92080
\(379\) −12.5678 −0.645564 −0.322782 0.946473i \(-0.604618\pi\)
−0.322782 + 0.946473i \(0.604618\pi\)
\(380\) 23.7224 1.21694
\(381\) −8.17667 −0.418904
\(382\) 35.1774 1.79983
\(383\) 11.0688 0.565589 0.282795 0.959180i \(-0.408738\pi\)
0.282795 + 0.959180i \(0.408738\pi\)
\(384\) 86.2378 4.40080
\(385\) −29.4288 −1.49983
\(386\) 29.8612 1.51990
\(387\) 1.73828 0.0883618
\(388\) −3.82242 −0.194054
\(389\) 0.149388 0.00757425 0.00378713 0.999993i \(-0.498795\pi\)
0.00378713 + 0.999993i \(0.498795\pi\)
\(390\) 52.0537 2.63584
\(391\) −6.76063 −0.341900
\(392\) −98.9519 −4.99782
\(393\) 10.4043 0.524826
\(394\) 9.75564 0.491482
\(395\) −5.76133 −0.289884
\(396\) 42.3174 2.12653
\(397\) −17.5305 −0.879829 −0.439915 0.898040i \(-0.644991\pi\)
−0.439915 + 0.898040i \(0.644991\pi\)
\(398\) −34.7602 −1.74237
\(399\) 28.4520 1.42438
\(400\) −49.3454 −2.46727
\(401\) 30.8471 1.54043 0.770215 0.637784i \(-0.220149\pi\)
0.770215 + 0.637784i \(0.220149\pi\)
\(402\) −71.6234 −3.57225
\(403\) 36.6648 1.82640
\(404\) 19.3636 0.963374
\(405\) 14.9549 0.743115
\(406\) −91.7876 −4.55534
\(407\) −47.6769 −2.36326
\(408\) −136.735 −6.76938
\(409\) −0.689464 −0.0340918 −0.0170459 0.999855i \(-0.505426\pi\)
−0.0170459 + 0.999855i \(0.505426\pi\)
\(410\) 32.5587 1.60796
\(411\) −11.2834 −0.556570
\(412\) 12.1837 0.600249
\(413\) 37.8389 1.86193
\(414\) −3.96083 −0.194664
\(415\) −8.26692 −0.405807
\(416\) 153.428 7.52241
\(417\) 47.0768 2.30536
\(418\) 47.2375 2.31046
\(419\) −11.2200 −0.548131 −0.274065 0.961711i \(-0.588369\pi\)
−0.274065 + 0.961711i \(0.588369\pi\)
\(420\) 64.1917 3.13224
\(421\) −28.8657 −1.40683 −0.703413 0.710781i \(-0.748341\pi\)
−0.703413 + 0.710781i \(0.748341\pi\)
\(422\) 53.7318 2.61562
\(423\) 10.1814 0.495038
\(424\) 34.3296 1.66719
\(425\) 21.8502 1.05989
\(426\) 16.4985 0.799353
\(427\) 23.1522 1.12041
\(428\) −20.1356 −0.973290
\(429\) 76.0191 3.67023
\(430\) 4.37777 0.211115
\(431\) −14.2631 −0.687031 −0.343516 0.939147i \(-0.611618\pi\)
−0.343516 + 0.939147i \(0.611618\pi\)
\(432\) 50.0254 2.40685
\(433\) −4.43156 −0.212967 −0.106484 0.994314i \(-0.533959\pi\)
−0.106484 + 0.994314i \(0.533959\pi\)
\(434\) 61.6500 2.95930
\(435\) 22.5789 1.08257
\(436\) −74.8318 −3.58379
\(437\) −3.24262 −0.155116
\(438\) 74.7432 3.57137
\(439\) 38.7800 1.85087 0.925435 0.378906i \(-0.123700\pi\)
0.925435 + 0.378906i \(0.123700\pi\)
\(440\) 67.8340 3.23386
\(441\) 14.9183 0.710396
\(442\) −125.518 −5.97029
\(443\) 9.21341 0.437742 0.218871 0.975754i \(-0.429763\pi\)
0.218871 + 0.975754i \(0.429763\pi\)
\(444\) 103.996 4.93541
\(445\) 1.87983 0.0891126
\(446\) −45.2213 −2.14129
\(447\) 13.3338 0.630668
\(448\) 130.913 6.18507
\(449\) 18.2640 0.861933 0.430966 0.902368i \(-0.358173\pi\)
0.430966 + 0.902368i \(0.358173\pi\)
\(450\) 12.8013 0.603460
\(451\) 47.5486 2.23898
\(452\) −75.2363 −3.53882
\(453\) 6.25058 0.293678
\(454\) −6.35062 −0.298049
\(455\) 37.5060 1.75831
\(456\) −65.5826 −3.07118
\(457\) −7.84046 −0.366761 −0.183381 0.983042i \(-0.558704\pi\)
−0.183381 + 0.983042i \(0.558704\pi\)
\(458\) −31.6109 −1.47708
\(459\) −22.1514 −1.03394
\(460\) −7.31581 −0.341102
\(461\) 21.0761 0.981610 0.490805 0.871269i \(-0.336703\pi\)
0.490805 + 0.871269i \(0.336703\pi\)
\(462\) 127.822 5.94683
\(463\) 24.0777 1.11899 0.559493 0.828835i \(-0.310996\pi\)
0.559493 + 0.828835i \(0.310996\pi\)
\(464\) 122.955 5.70805
\(465\) −15.1653 −0.703274
\(466\) −3.58290 −0.165975
\(467\) 25.5881 1.18408 0.592039 0.805909i \(-0.298323\pi\)
0.592039 + 0.805909i \(0.298323\pi\)
\(468\) −53.9322 −2.49302
\(469\) −51.6065 −2.38297
\(470\) 25.6414 1.18275
\(471\) −39.3296 −1.81221
\(472\) −87.2196 −4.01461
\(473\) 6.39328 0.293963
\(474\) 25.0240 1.14939
\(475\) 10.4801 0.480860
\(476\) −154.787 −7.09464
\(477\) −5.17565 −0.236977
\(478\) 54.0304 2.47129
\(479\) −21.7024 −0.991609 −0.495804 0.868434i \(-0.665127\pi\)
−0.495804 + 0.868434i \(0.665127\pi\)
\(480\) −63.4608 −2.89657
\(481\) 60.7627 2.77054
\(482\) 11.5610 0.526591
\(483\) −8.77438 −0.399248
\(484\) 95.1190 4.32359
\(485\) 0.923767 0.0419461
\(486\) −38.0329 −1.72521
\(487\) −37.8849 −1.71673 −0.858364 0.513040i \(-0.828519\pi\)
−0.858364 + 0.513040i \(0.828519\pi\)
\(488\) −53.3663 −2.41578
\(489\) 4.23709 0.191608
\(490\) 37.5710 1.69729
\(491\) −12.6115 −0.569150 −0.284575 0.958654i \(-0.591852\pi\)
−0.284575 + 0.958654i \(0.591852\pi\)
\(492\) −103.716 −4.67586
\(493\) −54.4448 −2.45207
\(494\) −60.2027 −2.70865
\(495\) −10.2269 −0.459664
\(496\) −82.5841 −3.70814
\(497\) 11.8876 0.533230
\(498\) 35.9069 1.60903
\(499\) 21.5669 0.965467 0.482733 0.875767i \(-0.339644\pi\)
0.482733 + 0.875767i \(0.339644\pi\)
\(500\) 60.2236 2.69328
\(501\) −45.2886 −2.02335
\(502\) 10.3083 0.460081
\(503\) −21.3957 −0.953988 −0.476994 0.878907i \(-0.658274\pi\)
−0.476994 + 0.878907i \(0.658274\pi\)
\(504\) −57.7201 −2.57106
\(505\) −4.67961 −0.208240
\(506\) −14.5677 −0.647612
\(507\) −69.4723 −3.08537
\(508\) 21.3357 0.946617
\(509\) −19.5809 −0.867909 −0.433954 0.900935i \(-0.642882\pi\)
−0.433954 + 0.900935i \(0.642882\pi\)
\(510\) 51.9169 2.29892
\(511\) 53.8544 2.38238
\(512\) −52.6877 −2.32849
\(513\) −10.6245 −0.469084
\(514\) −18.8841 −0.832944
\(515\) −2.94445 −0.129748
\(516\) −13.9454 −0.613912
\(517\) 37.4466 1.64690
\(518\) 102.169 4.48907
\(519\) −51.1506 −2.24526
\(520\) −86.4523 −3.79118
\(521\) −28.8902 −1.26570 −0.632851 0.774274i \(-0.718115\pi\)
−0.632851 + 0.774274i \(0.718115\pi\)
\(522\) −31.8974 −1.39611
\(523\) 27.2307 1.19072 0.595358 0.803461i \(-0.297010\pi\)
0.595358 + 0.803461i \(0.297010\pi\)
\(524\) −27.1482 −1.18598
\(525\) 28.3586 1.23767
\(526\) 57.5186 2.50793
\(527\) 36.5684 1.59294
\(528\) −171.226 −7.45165
\(529\) 1.00000 0.0434783
\(530\) −13.0346 −0.566187
\(531\) 13.1495 0.570641
\(532\) −74.2408 −3.21875
\(533\) −60.5991 −2.62484
\(534\) −8.16495 −0.353332
\(535\) 4.86618 0.210383
\(536\) 118.954 5.13803
\(537\) 32.2549 1.39190
\(538\) 38.2432 1.64878
\(539\) 54.8686 2.36336
\(540\) −23.9704 −1.03152
\(541\) −1.61460 −0.0694169 −0.0347084 0.999397i \(-0.511050\pi\)
−0.0347084 + 0.999397i \(0.511050\pi\)
\(542\) −10.8467 −0.465905
\(543\) −30.6059 −1.31343
\(544\) 153.024 6.56086
\(545\) 18.0846 0.774661
\(546\) −162.905 −6.97171
\(547\) −7.37294 −0.315244 −0.157622 0.987500i \(-0.550383\pi\)
−0.157622 + 0.987500i \(0.550383\pi\)
\(548\) 29.4422 1.25771
\(549\) 8.04569 0.343382
\(550\) 47.0824 2.00760
\(551\) −26.1135 −1.11247
\(552\) 20.2251 0.860839
\(553\) 18.0304 0.766732
\(554\) 41.5547 1.76549
\(555\) −25.1327 −1.06682
\(556\) −122.839 −5.20954
\(557\) −10.6786 −0.452465 −0.226232 0.974073i \(-0.572641\pi\)
−0.226232 + 0.974073i \(0.572641\pi\)
\(558\) 21.4242 0.906958
\(559\) −8.14803 −0.344625
\(560\) −84.4789 −3.56989
\(561\) 75.8192 3.20109
\(562\) 73.2249 3.08881
\(563\) −15.4854 −0.652631 −0.326316 0.945261i \(-0.605807\pi\)
−0.326316 + 0.945261i \(0.605807\pi\)
\(564\) −81.6807 −3.43938
\(565\) 18.1824 0.764940
\(566\) −59.9791 −2.52111
\(567\) −46.8023 −1.96551
\(568\) −27.4011 −1.14973
\(569\) 25.9639 1.08846 0.544232 0.838935i \(-0.316821\pi\)
0.544232 + 0.838935i \(0.316821\pi\)
\(570\) 24.9010 1.04299
\(571\) 15.3556 0.642610 0.321305 0.946976i \(-0.395879\pi\)
0.321305 + 0.946976i \(0.395879\pi\)
\(572\) −198.359 −8.29381
\(573\) 27.0810 1.13133
\(574\) −101.894 −4.25299
\(575\) −3.23198 −0.134783
\(576\) 45.4940 1.89559
\(577\) 1.00501 0.0418391 0.0209195 0.999781i \(-0.493341\pi\)
0.0209195 + 0.999781i \(0.493341\pi\)
\(578\) −78.6255 −3.27039
\(579\) 22.9884 0.955366
\(580\) −58.9158 −2.44634
\(581\) 25.8718 1.07334
\(582\) −4.01233 −0.166316
\(583\) −19.0357 −0.788378
\(584\) −124.136 −5.13677
\(585\) 13.0338 0.538883
\(586\) 38.3458 1.58405
\(587\) −26.0914 −1.07691 −0.538454 0.842655i \(-0.680991\pi\)
−0.538454 + 0.842655i \(0.680991\pi\)
\(588\) −119.683 −4.93562
\(589\) 17.5394 0.722699
\(590\) 33.1164 1.36338
\(591\) 7.51030 0.308932
\(592\) −136.862 −5.62501
\(593\) −39.0576 −1.60390 −0.801952 0.597389i \(-0.796205\pi\)
−0.801952 + 0.597389i \(0.796205\pi\)
\(594\) −47.7313 −1.95844
\(595\) 37.4074 1.53355
\(596\) −34.7924 −1.42515
\(597\) −26.7599 −1.09521
\(598\) 18.5660 0.759221
\(599\) −5.70685 −0.233175 −0.116588 0.993180i \(-0.537196\pi\)
−0.116588 + 0.993180i \(0.537196\pi\)
\(600\) −65.3673 −2.66861
\(601\) −47.1945 −1.92510 −0.962551 0.271099i \(-0.912613\pi\)
−0.962551 + 0.271099i \(0.912613\pi\)
\(602\) −13.7005 −0.558391
\(603\) −17.9339 −0.730326
\(604\) −16.3099 −0.663638
\(605\) −22.9875 −0.934573
\(606\) 20.3256 0.825673
\(607\) 40.7500 1.65399 0.826996 0.562207i \(-0.190048\pi\)
0.826996 + 0.562207i \(0.190048\pi\)
\(608\) 73.3955 2.97658
\(609\) −70.6619 −2.86337
\(610\) 20.2627 0.820411
\(611\) −47.7245 −1.93073
\(612\) −53.7904 −2.17435
\(613\) −4.86042 −0.196311 −0.0981554 0.995171i \(-0.531294\pi\)
−0.0981554 + 0.995171i \(0.531294\pi\)
\(614\) 59.3949 2.39698
\(615\) 25.0650 1.01072
\(616\) −212.291 −8.55344
\(617\) 15.6782 0.631182 0.315591 0.948895i \(-0.397797\pi\)
0.315591 + 0.948895i \(0.397797\pi\)
\(618\) 12.7891 0.514452
\(619\) −1.78900 −0.0719058 −0.0359529 0.999353i \(-0.511447\pi\)
−0.0359529 + 0.999353i \(0.511447\pi\)
\(620\) 39.5714 1.58922
\(621\) 3.27652 0.131482
\(622\) 35.0997 1.40737
\(623\) −5.88305 −0.235699
\(624\) 218.222 8.73587
\(625\) 1.60562 0.0642247
\(626\) 59.5444 2.37987
\(627\) 36.3654 1.45229
\(628\) 102.624 4.09514
\(629\) 60.6029 2.41640
\(630\) 21.9157 0.873144
\(631\) 49.6501 1.97654 0.988270 0.152717i \(-0.0488024\pi\)
0.988270 + 0.152717i \(0.0488024\pi\)
\(632\) −41.5606 −1.65319
\(633\) 41.3650 1.64411
\(634\) −59.9177 −2.37964
\(635\) −5.15621 −0.204618
\(636\) 41.5217 1.64644
\(637\) −69.9283 −2.77066
\(638\) −117.317 −4.64460
\(639\) 4.13108 0.163423
\(640\) 54.3815 2.14962
\(641\) −7.47091 −0.295083 −0.147542 0.989056i \(-0.547136\pi\)
−0.147542 + 0.989056i \(0.547136\pi\)
\(642\) −21.1360 −0.834171
\(643\) −19.2332 −0.758482 −0.379241 0.925298i \(-0.623815\pi\)
−0.379241 + 0.925298i \(0.623815\pi\)
\(644\) 22.8953 0.902201
\(645\) 3.37019 0.132701
\(646\) −60.0444 −2.36241
\(647\) −36.0011 −1.41535 −0.707674 0.706539i \(-0.750256\pi\)
−0.707674 + 0.706539i \(0.750256\pi\)
\(648\) 107.880 4.23794
\(649\) 48.3631 1.89842
\(650\) −60.0051 −2.35359
\(651\) 47.4608 1.86013
\(652\) −11.0560 −0.432985
\(653\) −19.2876 −0.754780 −0.377390 0.926054i \(-0.623178\pi\)
−0.377390 + 0.926054i \(0.623178\pi\)
\(654\) −78.5497 −3.07153
\(655\) 6.56093 0.256357
\(656\) 136.494 5.32919
\(657\) 18.7151 0.730146
\(658\) −80.2464 −3.12833
\(659\) 18.4018 0.716831 0.358415 0.933562i \(-0.383317\pi\)
0.358415 + 0.933562i \(0.383317\pi\)
\(660\) 82.0454 3.19361
\(661\) 9.08232 0.353261 0.176631 0.984277i \(-0.443480\pi\)
0.176631 + 0.984277i \(0.443480\pi\)
\(662\) 5.05964 0.196649
\(663\) −96.6291 −3.75276
\(664\) −59.6352 −2.31429
\(665\) 17.9418 0.695755
\(666\) 35.5052 1.37580
\(667\) 8.05321 0.311822
\(668\) 118.173 4.57225
\(669\) −34.8133 −1.34596
\(670\) −45.1657 −1.74490
\(671\) 29.5915 1.14237
\(672\) 198.604 7.66133
\(673\) −47.0265 −1.81274 −0.906369 0.422488i \(-0.861157\pi\)
−0.906369 + 0.422488i \(0.861157\pi\)
\(674\) −23.8201 −0.917516
\(675\) −10.5897 −0.407596
\(676\) 181.277 6.97217
\(677\) 7.50622 0.288488 0.144244 0.989542i \(-0.453925\pi\)
0.144244 + 0.989542i \(0.453925\pi\)
\(678\) −78.9743 −3.03299
\(679\) −2.89099 −0.110946
\(680\) −86.2249 −3.30658
\(681\) −4.88897 −0.187346
\(682\) 78.7968 3.01728
\(683\) 4.92760 0.188549 0.0942747 0.995546i \(-0.469947\pi\)
0.0942747 + 0.995546i \(0.469947\pi\)
\(684\) −25.7997 −0.986475
\(685\) −7.11532 −0.271863
\(686\) −37.7974 −1.44311
\(687\) −24.3354 −0.928452
\(688\) 18.3527 0.699690
\(689\) 24.2604 0.924247
\(690\) −7.67929 −0.292345
\(691\) −49.7673 −1.89324 −0.946619 0.322356i \(-0.895525\pi\)
−0.946619 + 0.322356i \(0.895525\pi\)
\(692\) 133.469 5.07373
\(693\) 32.0057 1.21580
\(694\) −61.8461 −2.34765
\(695\) 29.6866 1.12608
\(696\) 162.877 6.17385
\(697\) −60.4398 −2.28932
\(698\) −2.73897 −0.103672
\(699\) −2.75826 −0.104327
\(700\) −73.9972 −2.79683
\(701\) −4.97531 −0.187915 −0.0939575 0.995576i \(-0.529952\pi\)
−0.0939575 + 0.995576i \(0.529952\pi\)
\(702\) 60.8320 2.29595
\(703\) 29.0672 1.09629
\(704\) 167.324 6.30627
\(705\) 19.7398 0.743445
\(706\) −72.7074 −2.73638
\(707\) 14.6451 0.550787
\(708\) −105.492 −3.96464
\(709\) 31.3419 1.17707 0.588535 0.808471i \(-0.299705\pi\)
0.588535 + 0.808471i \(0.299705\pi\)
\(710\) 10.4039 0.390453
\(711\) 6.26581 0.234986
\(712\) 13.5606 0.508204
\(713\) −5.40902 −0.202569
\(714\) −162.477 −6.08055
\(715\) 47.9376 1.79276
\(716\) −84.1639 −3.14535
\(717\) 41.5949 1.55339
\(718\) −2.45053 −0.0914528
\(719\) 4.53010 0.168944 0.0844721 0.996426i \(-0.473080\pi\)
0.0844721 + 0.996426i \(0.473080\pi\)
\(720\) −29.3575 −1.09409
\(721\) 9.21484 0.343179
\(722\) 23.2413 0.864950
\(723\) 8.90017 0.331001
\(724\) 79.8611 2.96801
\(725\) −26.0278 −0.966649
\(726\) 99.8448 3.70559
\(727\) −41.6785 −1.54577 −0.772884 0.634547i \(-0.781187\pi\)
−0.772884 + 0.634547i \(0.781187\pi\)
\(728\) 270.558 10.0275
\(729\) 4.46198 0.165259
\(730\) 47.1331 1.74447
\(731\) −8.12661 −0.300573
\(732\) −64.5467 −2.38571
\(733\) −7.26634 −0.268389 −0.134194 0.990955i \(-0.542845\pi\)
−0.134194 + 0.990955i \(0.542845\pi\)
\(734\) −24.8720 −0.918041
\(735\) 28.9238 1.06687
\(736\) −22.6346 −0.834322
\(737\) −65.9598 −2.42966
\(738\) −35.4096 −1.30345
\(739\) −5.10410 −0.187757 −0.0938787 0.995584i \(-0.529927\pi\)
−0.0938787 + 0.995584i \(0.529927\pi\)
\(740\) 65.5796 2.41075
\(741\) −46.3465 −1.70258
\(742\) 40.7926 1.49754
\(743\) 6.62458 0.243032 0.121516 0.992589i \(-0.461224\pi\)
0.121516 + 0.992589i \(0.461224\pi\)
\(744\) −109.398 −4.01073
\(745\) 8.40830 0.308056
\(746\) −10.0456 −0.367794
\(747\) 8.99080 0.328956
\(748\) −197.838 −7.23366
\(749\) −15.2290 −0.556456
\(750\) 63.2158 2.30831
\(751\) 23.5344 0.858782 0.429391 0.903119i \(-0.358728\pi\)
0.429391 + 0.903119i \(0.358728\pi\)
\(752\) 107.495 3.91994
\(753\) 7.93574 0.289194
\(754\) 149.516 5.44506
\(755\) 3.94161 0.143450
\(756\) 75.0169 2.72834
\(757\) 9.64829 0.350673 0.175337 0.984509i \(-0.443899\pi\)
0.175337 + 0.984509i \(0.443899\pi\)
\(758\) 34.4229 1.25029
\(759\) −11.2148 −0.407072
\(760\) −41.3563 −1.50015
\(761\) −36.5688 −1.32562 −0.662808 0.748789i \(-0.730636\pi\)
−0.662808 + 0.748789i \(0.730636\pi\)
\(762\) 22.3957 0.811311
\(763\) −56.5970 −2.04895
\(764\) −70.6635 −2.55651
\(765\) 12.9996 0.470000
\(766\) −30.3172 −1.09540
\(767\) −61.6372 −2.22559
\(768\) −103.532 −3.73589
\(769\) 17.1423 0.618168 0.309084 0.951035i \(-0.399978\pi\)
0.309084 + 0.951035i \(0.399978\pi\)
\(770\) 80.6047 2.90479
\(771\) −14.5378 −0.523566
\(772\) −59.9845 −2.15889
\(773\) −22.7223 −0.817264 −0.408632 0.912699i \(-0.633994\pi\)
−0.408632 + 0.912699i \(0.633994\pi\)
\(774\) −4.76111 −0.171134
\(775\) 17.4818 0.627966
\(776\) 6.66379 0.239216
\(777\) 78.6543 2.82171
\(778\) −0.409169 −0.0146694
\(779\) −28.9889 −1.03864
\(780\) −104.564 −3.74400
\(781\) 15.1939 0.543679
\(782\) 18.5172 0.662174
\(783\) 26.3865 0.942977
\(784\) 157.507 5.62525
\(785\) −24.8012 −0.885193
\(786\) −28.4970 −1.01646
\(787\) 3.00105 0.106976 0.0534879 0.998568i \(-0.482966\pi\)
0.0534879 + 0.998568i \(0.482966\pi\)
\(788\) −19.5969 −0.698110
\(789\) 44.2802 1.57642
\(790\) 15.7801 0.561432
\(791\) −56.9030 −2.02324
\(792\) −73.7738 −2.62144
\(793\) −37.7134 −1.33924
\(794\) 48.0155 1.70401
\(795\) −10.0346 −0.355890
\(796\) 69.8255 2.47490
\(797\) −15.2158 −0.538971 −0.269486 0.963004i \(-0.586854\pi\)
−0.269486 + 0.963004i \(0.586854\pi\)
\(798\) −77.9294 −2.75867
\(799\) −47.5990 −1.68393
\(800\) 73.1546 2.58640
\(801\) −2.04444 −0.0722366
\(802\) −84.4894 −2.98343
\(803\) 68.8329 2.42906
\(804\) 143.875 5.07409
\(805\) −5.53312 −0.195017
\(806\) −100.424 −3.53728
\(807\) 29.4412 1.03638
\(808\) −33.7574 −1.18758
\(809\) 11.7741 0.413954 0.206977 0.978346i \(-0.433637\pi\)
0.206977 + 0.978346i \(0.433637\pi\)
\(810\) −40.9611 −1.43923
\(811\) −36.0314 −1.26523 −0.632617 0.774465i \(-0.718019\pi\)
−0.632617 + 0.774465i \(0.718019\pi\)
\(812\) 184.381 6.47049
\(813\) −8.35022 −0.292855
\(814\) 130.586 4.57703
\(815\) 2.67190 0.0935927
\(816\) 217.648 7.61921
\(817\) −3.89779 −0.136366
\(818\) 1.88842 0.0660272
\(819\) −40.7902 −1.42532
\(820\) −65.4031 −2.28397
\(821\) −50.7652 −1.77172 −0.885859 0.463954i \(-0.846430\pi\)
−0.885859 + 0.463954i \(0.846430\pi\)
\(822\) 30.9050 1.07794
\(823\) −38.5229 −1.34282 −0.671412 0.741084i \(-0.734312\pi\)
−0.671412 + 0.741084i \(0.734312\pi\)
\(824\) −21.2404 −0.739945
\(825\) 36.2460 1.26193
\(826\) −103.640 −3.60609
\(827\) −0.353748 −0.0123010 −0.00615050 0.999981i \(-0.501958\pi\)
−0.00615050 + 0.999981i \(0.501958\pi\)
\(828\) 7.95641 0.276504
\(829\) 7.99949 0.277834 0.138917 0.990304i \(-0.455638\pi\)
0.138917 + 0.990304i \(0.455638\pi\)
\(830\) 22.6429 0.785946
\(831\) 31.9906 1.10974
\(832\) −213.249 −7.39309
\(833\) −69.7444 −2.41650
\(834\) −128.942 −4.46491
\(835\) −28.5590 −0.988324
\(836\) −94.8895 −3.28182
\(837\) −17.7228 −0.612588
\(838\) 30.7312 1.06159
\(839\) 22.1087 0.763277 0.381639 0.924312i \(-0.375360\pi\)
0.381639 + 0.924312i \(0.375360\pi\)
\(840\) −111.908 −3.86120
\(841\) 35.8542 1.23635
\(842\) 79.0623 2.72467
\(843\) 56.3716 1.94154
\(844\) −107.935 −3.71528
\(845\) −43.8092 −1.50708
\(846\) −27.8867 −0.958763
\(847\) 71.9407 2.47191
\(848\) −54.6443 −1.87649
\(849\) −46.1744 −1.58470
\(850\) −59.8473 −2.05274
\(851\) −8.96409 −0.307285
\(852\) −33.1417 −1.13542
\(853\) −40.9231 −1.40118 −0.700591 0.713563i \(-0.747080\pi\)
−0.700591 + 0.713563i \(0.747080\pi\)
\(854\) −63.4133 −2.16996
\(855\) 6.23502 0.213233
\(856\) 35.1032 1.19980
\(857\) 41.2493 1.40905 0.704525 0.709680i \(-0.251160\pi\)
0.704525 + 0.709680i \(0.251160\pi\)
\(858\) −208.214 −7.10832
\(859\) 3.53732 0.120692 0.0603459 0.998178i \(-0.480780\pi\)
0.0603459 + 0.998178i \(0.480780\pi\)
\(860\) −8.79396 −0.299872
\(861\) −78.4426 −2.67332
\(862\) 39.0664 1.33061
\(863\) 4.80452 0.163548 0.0817740 0.996651i \(-0.473941\pi\)
0.0817740 + 0.996651i \(0.473941\pi\)
\(864\) −74.1627 −2.52307
\(865\) −32.2556 −1.09672
\(866\) 12.1379 0.412464
\(867\) −60.5292 −2.05568
\(868\) −123.841 −4.20344
\(869\) 23.0453 0.781757
\(870\) −61.8429 −2.09667
\(871\) 84.0636 2.84839
\(872\) 130.457 4.41785
\(873\) −1.00466 −0.0340024
\(874\) 8.88147 0.300420
\(875\) 45.5486 1.53982
\(876\) −150.142 −5.07284
\(877\) −14.8789 −0.502426 −0.251213 0.967932i \(-0.580829\pi\)
−0.251213 + 0.967932i \(0.580829\pi\)
\(878\) −106.218 −3.58467
\(879\) 29.5202 0.995693
\(880\) −107.975 −3.63984
\(881\) −31.6261 −1.06551 −0.532755 0.846269i \(-0.678843\pi\)
−0.532755 + 0.846269i \(0.678843\pi\)
\(882\) −40.8609 −1.37586
\(883\) −41.4051 −1.39339 −0.696696 0.717367i \(-0.745347\pi\)
−0.696696 + 0.717367i \(0.745347\pi\)
\(884\) 252.138 8.48031
\(885\) 25.4944 0.856985
\(886\) −25.2353 −0.847796
\(887\) 13.8230 0.464130 0.232065 0.972700i \(-0.425452\pi\)
0.232065 + 0.972700i \(0.425452\pi\)
\(888\) −181.300 −6.08403
\(889\) 16.1367 0.541207
\(890\) −5.14881 −0.172589
\(891\) −59.8194 −2.00403
\(892\) 90.8395 3.04153
\(893\) −22.8301 −0.763979
\(894\) −36.5210 −1.22145
\(895\) 20.3400 0.679890
\(896\) −170.190 −5.68566
\(897\) 14.2929 0.477226
\(898\) −50.0247 −1.66935
\(899\) −43.5599 −1.45281
\(900\) −25.7150 −0.857166
\(901\) 24.1966 0.806105
\(902\) −130.234 −4.33633
\(903\) −10.5472 −0.350990
\(904\) 131.163 4.36241
\(905\) −19.3001 −0.641557
\(906\) −17.1202 −0.568780
\(907\) 11.7196 0.389144 0.194572 0.980888i \(-0.437668\pi\)
0.194572 + 0.980888i \(0.437668\pi\)
\(908\) 12.7570 0.423355
\(909\) 5.08938 0.168804
\(910\) −102.728 −3.40540
\(911\) −55.0134 −1.82267 −0.911337 0.411660i \(-0.864949\pi\)
−0.911337 + 0.411660i \(0.864949\pi\)
\(912\) 104.391 3.45674
\(913\) 33.0676 1.09438
\(914\) 21.4748 0.710324
\(915\) 15.5990 0.515688
\(916\) 63.4991 2.09807
\(917\) −20.5328 −0.678054
\(918\) 60.6720 2.00247
\(919\) −8.95673 −0.295455 −0.147728 0.989028i \(-0.547196\pi\)
−0.147728 + 0.989028i \(0.547196\pi\)
\(920\) 12.7540 0.420486
\(921\) 45.7246 1.50668
\(922\) −57.7268 −1.90113
\(923\) −19.3641 −0.637377
\(924\) −256.766 −8.44699
\(925\) 28.9718 0.952586
\(926\) −65.9482 −2.16719
\(927\) 3.20228 0.105177
\(928\) −182.281 −5.98367
\(929\) 41.2488 1.35333 0.676665 0.736291i \(-0.263425\pi\)
0.676665 + 0.736291i \(0.263425\pi\)
\(930\) 41.5374 1.36206
\(931\) −33.4517 −1.09634
\(932\) 7.19724 0.235753
\(933\) 27.0212 0.884634
\(934\) −70.0853 −2.29326
\(935\) 47.8115 1.56360
\(936\) 94.0223 3.07322
\(937\) −42.7270 −1.39583 −0.697915 0.716180i \(-0.745889\pi\)
−0.697915 + 0.716180i \(0.745889\pi\)
\(938\) 141.349 4.61520
\(939\) 45.8397 1.49592
\(940\) −51.5078 −1.68000
\(941\) −28.3798 −0.925154 −0.462577 0.886579i \(-0.653075\pi\)
−0.462577 + 0.886579i \(0.653075\pi\)
\(942\) 107.723 3.50979
\(943\) 8.93996 0.291125
\(944\) 138.832 4.51860
\(945\) −18.1294 −0.589749
\(946\) −17.5110 −0.569333
\(947\) −31.7402 −1.03142 −0.515709 0.856764i \(-0.672472\pi\)
−0.515709 + 0.856764i \(0.672472\pi\)
\(948\) −50.2676 −1.63262
\(949\) −87.7253 −2.84769
\(950\) −28.7047 −0.931305
\(951\) −46.1271 −1.49578
\(952\) 269.846 8.74577
\(953\) −18.4466 −0.597544 −0.298772 0.954325i \(-0.596577\pi\)
−0.298772 + 0.954325i \(0.596577\pi\)
\(954\) 14.1760 0.458964
\(955\) 17.0773 0.552608
\(956\) −108.535 −3.51027
\(957\) −90.3152 −2.91947
\(958\) 59.4424 1.92050
\(959\) 22.2678 0.719066
\(960\) 88.2042 2.84678
\(961\) −1.74253 −0.0562108
\(962\) −166.427 −5.36584
\(963\) −5.29228 −0.170541
\(964\) −23.2235 −0.747979
\(965\) 14.4965 0.466659
\(966\) 24.0328 0.773243
\(967\) 2.21622 0.0712689 0.0356344 0.999365i \(-0.488655\pi\)
0.0356344 + 0.999365i \(0.488655\pi\)
\(968\) −165.825 −5.32982
\(969\) −46.2247 −1.48495
\(970\) −2.53017 −0.0812390
\(971\) −36.3417 −1.16626 −0.583130 0.812379i \(-0.698172\pi\)
−0.583130 + 0.812379i \(0.698172\pi\)
\(972\) 76.3995 2.45051
\(973\) −92.9062 −2.97844
\(974\) 103.766 3.32487
\(975\) −46.1944 −1.47941
\(976\) 84.9460 2.71906
\(977\) 44.5489 1.42524 0.712622 0.701548i \(-0.247507\pi\)
0.712622 + 0.701548i \(0.247507\pi\)
\(978\) −11.6053 −0.371096
\(979\) −7.51931 −0.240318
\(980\) −75.4718 −2.41086
\(981\) −19.6682 −0.627957
\(982\) 34.5426 1.10230
\(983\) −5.99390 −0.191176 −0.0955878 0.995421i \(-0.530473\pi\)
−0.0955878 + 0.995421i \(0.530473\pi\)
\(984\) 180.812 5.76408
\(985\) 4.73599 0.150901
\(986\) 149.123 4.74904
\(987\) −61.7770 −1.96638
\(988\) 120.934 3.84741
\(989\) 1.20205 0.0382229
\(990\) 28.0112 0.890254
\(991\) 28.2751 0.898187 0.449094 0.893485i \(-0.351747\pi\)
0.449094 + 0.893485i \(0.351747\pi\)
\(992\) 122.431 3.88718
\(993\) 3.89513 0.123608
\(994\) −32.5597 −1.03273
\(995\) −16.8748 −0.534966
\(996\) −72.1289 −2.28549
\(997\) −45.7222 −1.44804 −0.724018 0.689782i \(-0.757707\pi\)
−0.724018 + 0.689782i \(0.757707\pi\)
\(998\) −59.0712 −1.86987
\(999\) −29.3710 −0.929258
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 8027.2.a.c.1.2 143
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.c.1.2 143 1.1 even 1 trivial