Properties

Label 6019.2.a.d.1.5
Level $6019$
Weight $2$
Character 6019.1
Self dual yes
Analytic conductor $48.062$
Analytic rank $0$
Dimension $123$
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] = [6019,2,Mod(1,6019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6019, 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("6019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6019 = 13 \cdot 463 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6019.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: \(48.0619569766\)
Analytic rank: \(0\)
Dimension: \(123\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.68053 q^{2} +2.57455 q^{3} +5.18522 q^{4} +0.534092 q^{5} -6.90114 q^{6} -0.399106 q^{7} -8.53805 q^{8} +3.62830 q^{9} +O(q^{10})\) \(q-2.68053 q^{2} +2.57455 q^{3} +5.18522 q^{4} +0.534092 q^{5} -6.90114 q^{6} -0.399106 q^{7} -8.53805 q^{8} +3.62830 q^{9} -1.43165 q^{10} +4.50922 q^{11} +13.3496 q^{12} -1.00000 q^{13} +1.06981 q^{14} +1.37505 q^{15} +12.5160 q^{16} +1.29289 q^{17} -9.72575 q^{18} +7.30769 q^{19} +2.76938 q^{20} -1.02752 q^{21} -12.0871 q^{22} -7.37895 q^{23} -21.9816 q^{24} -4.71475 q^{25} +2.68053 q^{26} +1.61759 q^{27} -2.06945 q^{28} +6.66639 q^{29} -3.68584 q^{30} -2.72165 q^{31} -16.4735 q^{32} +11.6092 q^{33} -3.46563 q^{34} -0.213159 q^{35} +18.8135 q^{36} +3.40931 q^{37} -19.5885 q^{38} -2.57455 q^{39} -4.56010 q^{40} -4.05490 q^{41} +2.75429 q^{42} -4.22886 q^{43} +23.3813 q^{44} +1.93785 q^{45} +19.7795 q^{46} +9.87568 q^{47} +32.2232 q^{48} -6.84071 q^{49} +12.6380 q^{50} +3.32861 q^{51} -5.18522 q^{52} +9.58305 q^{53} -4.33600 q^{54} +2.40834 q^{55} +3.40759 q^{56} +18.8140 q^{57} -17.8694 q^{58} +4.38788 q^{59} +7.12991 q^{60} -3.61920 q^{61} +7.29546 q^{62} -1.44808 q^{63} +19.1254 q^{64} -0.534092 q^{65} -31.1188 q^{66} +16.2603 q^{67} +6.70392 q^{68} -18.9975 q^{69} +0.571379 q^{70} +10.5362 q^{71} -30.9786 q^{72} -9.52713 q^{73} -9.13874 q^{74} -12.1383 q^{75} +37.8920 q^{76} -1.79966 q^{77} +6.90114 q^{78} +16.4921 q^{79} +6.68471 q^{80} -6.72033 q^{81} +10.8693 q^{82} +0.686373 q^{83} -5.32791 q^{84} +0.690522 q^{85} +11.3356 q^{86} +17.1630 q^{87} -38.5000 q^{88} +12.1340 q^{89} -5.19445 q^{90} +0.399106 q^{91} -38.2614 q^{92} -7.00702 q^{93} -26.4720 q^{94} +3.90298 q^{95} -42.4117 q^{96} -10.1592 q^{97} +18.3367 q^{98} +16.3608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68053 −1.89542 −0.947709 0.319136i \(-0.896607\pi\)
−0.947709 + 0.319136i \(0.896607\pi\)
\(3\) 2.57455 1.48642 0.743208 0.669060i \(-0.233303\pi\)
0.743208 + 0.669060i \(0.233303\pi\)
\(4\) 5.18522 2.59261
\(5\) 0.534092 0.238853 0.119427 0.992843i \(-0.461894\pi\)
0.119427 + 0.992843i \(0.461894\pi\)
\(6\) −6.90114 −2.81738
\(7\) −0.399106 −0.150848 −0.0754240 0.997152i \(-0.524031\pi\)
−0.0754240 + 0.997152i \(0.524031\pi\)
\(8\) −8.53805 −3.01866
\(9\) 3.62830 1.20943
\(10\) −1.43165 −0.452726
\(11\) 4.50922 1.35958 0.679791 0.733406i \(-0.262071\pi\)
0.679791 + 0.733406i \(0.262071\pi\)
\(12\) 13.3496 3.85370
\(13\) −1.00000 −0.277350
\(14\) 1.06981 0.285920
\(15\) 1.37505 0.355035
\(16\) 12.5160 3.12901
\(17\) 1.29289 0.313572 0.156786 0.987633i \(-0.449887\pi\)
0.156786 + 0.987633i \(0.449887\pi\)
\(18\) −9.72575 −2.29238
\(19\) 7.30769 1.67650 0.838250 0.545287i \(-0.183579\pi\)
0.838250 + 0.545287i \(0.183579\pi\)
\(20\) 2.76938 0.619253
\(21\) −1.02752 −0.224223
\(22\) −12.0871 −2.57698
\(23\) −7.37895 −1.53862 −0.769308 0.638878i \(-0.779399\pi\)
−0.769308 + 0.638878i \(0.779399\pi\)
\(24\) −21.9816 −4.48698
\(25\) −4.71475 −0.942949
\(26\) 2.68053 0.525694
\(27\) 1.61759 0.311306
\(28\) −2.06945 −0.391090
\(29\) 6.66639 1.23792 0.618959 0.785423i \(-0.287555\pi\)
0.618959 + 0.785423i \(0.287555\pi\)
\(30\) −3.68584 −0.672940
\(31\) −2.72165 −0.488823 −0.244412 0.969672i \(-0.578595\pi\)
−0.244412 + 0.969672i \(0.578595\pi\)
\(32\) −16.4735 −2.91212
\(33\) 11.6092 2.02090
\(34\) −3.46563 −0.594350
\(35\) −0.213159 −0.0360305
\(36\) 18.8135 3.13559
\(37\) 3.40931 0.560487 0.280243 0.959929i \(-0.409585\pi\)
0.280243 + 0.959929i \(0.409585\pi\)
\(38\) −19.5885 −3.17767
\(39\) −2.57455 −0.412258
\(40\) −4.56010 −0.721016
\(41\) −4.05490 −0.633269 −0.316635 0.948548i \(-0.602553\pi\)
−0.316635 + 0.948548i \(0.602553\pi\)
\(42\) 2.75429 0.424996
\(43\) −4.22886 −0.644895 −0.322447 0.946587i \(-0.604506\pi\)
−0.322447 + 0.946587i \(0.604506\pi\)
\(44\) 23.3813 3.52486
\(45\) 1.93785 0.288877
\(46\) 19.7795 2.91632
\(47\) 9.87568 1.44052 0.720258 0.693706i \(-0.244023\pi\)
0.720258 + 0.693706i \(0.244023\pi\)
\(48\) 32.2232 4.65101
\(49\) −6.84071 −0.977245
\(50\) 12.6380 1.78728
\(51\) 3.32861 0.466099
\(52\) −5.18522 −0.719060
\(53\) 9.58305 1.31633 0.658167 0.752872i \(-0.271332\pi\)
0.658167 + 0.752872i \(0.271332\pi\)
\(54\) −4.33600 −0.590055
\(55\) 2.40834 0.324740
\(56\) 3.40759 0.455359
\(57\) 18.8140 2.49198
\(58\) −17.8694 −2.34637
\(59\) 4.38788 0.571253 0.285627 0.958341i \(-0.407798\pi\)
0.285627 + 0.958341i \(0.407798\pi\)
\(60\) 7.12991 0.920467
\(61\) −3.61920 −0.463391 −0.231696 0.972788i \(-0.574427\pi\)
−0.231696 + 0.972788i \(0.574427\pi\)
\(62\) 7.29546 0.926524
\(63\) −1.44808 −0.182441
\(64\) 19.1254 2.39068
\(65\) −0.534092 −0.0662459
\(66\) −31.1188 −3.83046
\(67\) 16.2603 1.98651 0.993253 0.115969i \(-0.0369972\pi\)
0.993253 + 0.115969i \(0.0369972\pi\)
\(68\) 6.70392 0.812969
\(69\) −18.9975 −2.28703
\(70\) 0.571379 0.0682929
\(71\) 10.5362 1.25041 0.625207 0.780459i \(-0.285014\pi\)
0.625207 + 0.780459i \(0.285014\pi\)
\(72\) −30.9786 −3.65087
\(73\) −9.52713 −1.11507 −0.557533 0.830155i \(-0.688252\pi\)
−0.557533 + 0.830155i \(0.688252\pi\)
\(74\) −9.13874 −1.06236
\(75\) −12.1383 −1.40162
\(76\) 37.8920 4.34651
\(77\) −1.79966 −0.205090
\(78\) 6.90114 0.781401
\(79\) 16.4921 1.85551 0.927754 0.373192i \(-0.121737\pi\)
0.927754 + 0.373192i \(0.121737\pi\)
\(80\) 6.68471 0.747374
\(81\) −6.72033 −0.746704
\(82\) 10.8693 1.20031
\(83\) 0.686373 0.0753392 0.0376696 0.999290i \(-0.488007\pi\)
0.0376696 + 0.999290i \(0.488007\pi\)
\(84\) −5.32791 −0.581322
\(85\) 0.690522 0.0748976
\(86\) 11.3356 1.22234
\(87\) 17.1630 1.84006
\(88\) −38.5000 −4.10411
\(89\) 12.1340 1.28620 0.643099 0.765783i \(-0.277649\pi\)
0.643099 + 0.765783i \(0.277649\pi\)
\(90\) −5.19445 −0.547543
\(91\) 0.399106 0.0418377
\(92\) −38.2614 −3.98903
\(93\) −7.00702 −0.726595
\(94\) −26.4720 −2.73038
\(95\) 3.90298 0.400437
\(96\) −42.4117 −4.32863
\(97\) −10.1592 −1.03151 −0.515754 0.856737i \(-0.672488\pi\)
−0.515754 + 0.856737i \(0.672488\pi\)
\(98\) 18.3367 1.85229
\(99\) 16.3608 1.64432
\(100\) −24.4470 −2.44470
\(101\) −15.2241 −1.51486 −0.757428 0.652919i \(-0.773544\pi\)
−0.757428 + 0.652919i \(0.773544\pi\)
\(102\) −8.92242 −0.883452
\(103\) 17.5776 1.73198 0.865988 0.500065i \(-0.166691\pi\)
0.865988 + 0.500065i \(0.166691\pi\)
\(104\) 8.53805 0.837225
\(105\) −0.548789 −0.0535564
\(106\) −25.6876 −2.49500
\(107\) −1.70932 −0.165247 −0.0826233 0.996581i \(-0.526330\pi\)
−0.0826233 + 0.996581i \(0.526330\pi\)
\(108\) 8.38757 0.807094
\(109\) 3.14229 0.300977 0.150488 0.988612i \(-0.451915\pi\)
0.150488 + 0.988612i \(0.451915\pi\)
\(110\) −6.45561 −0.615519
\(111\) 8.77743 0.833117
\(112\) −4.99523 −0.472005
\(113\) −12.4763 −1.17367 −0.586837 0.809705i \(-0.699627\pi\)
−0.586837 + 0.809705i \(0.699627\pi\)
\(114\) −50.4314 −4.72334
\(115\) −3.94103 −0.367503
\(116\) 34.5667 3.20944
\(117\) −3.62830 −0.335437
\(118\) −11.7618 −1.08276
\(119\) −0.516001 −0.0473017
\(120\) −11.7402 −1.07173
\(121\) 9.33309 0.848463
\(122\) 9.70136 0.878320
\(123\) −10.4395 −0.941302
\(124\) −14.1124 −1.26733
\(125\) −5.18857 −0.464079
\(126\) 3.88161 0.345801
\(127\) −8.07482 −0.716525 −0.358262 0.933621i \(-0.616631\pi\)
−0.358262 + 0.933621i \(0.616631\pi\)
\(128\) −18.3193 −1.61921
\(129\) −10.8874 −0.958582
\(130\) 1.43165 0.125564
\(131\) 8.27049 0.722596 0.361298 0.932450i \(-0.382334\pi\)
0.361298 + 0.932450i \(0.382334\pi\)
\(132\) 60.1963 5.23941
\(133\) −2.91655 −0.252897
\(134\) −43.5860 −3.76526
\(135\) 0.863943 0.0743564
\(136\) −11.0388 −0.946567
\(137\) 9.89499 0.845386 0.422693 0.906273i \(-0.361085\pi\)
0.422693 + 0.906273i \(0.361085\pi\)
\(138\) 50.9232 4.33487
\(139\) −6.42624 −0.545067 −0.272533 0.962146i \(-0.587862\pi\)
−0.272533 + 0.962146i \(0.587862\pi\)
\(140\) −1.10528 −0.0934130
\(141\) 25.4254 2.14121
\(142\) −28.2425 −2.37006
\(143\) −4.50922 −0.377080
\(144\) 45.4120 3.78433
\(145\) 3.56047 0.295681
\(146\) 25.5377 2.11352
\(147\) −17.6118 −1.45259
\(148\) 17.6780 1.45312
\(149\) 21.2671 1.74227 0.871135 0.491043i \(-0.163384\pi\)
0.871135 + 0.491043i \(0.163384\pi\)
\(150\) 32.5371 2.65665
\(151\) −14.7604 −1.20118 −0.600591 0.799557i \(-0.705068\pi\)
−0.600591 + 0.799557i \(0.705068\pi\)
\(152\) −62.3935 −5.06078
\(153\) 4.69100 0.379245
\(154\) 4.82403 0.388732
\(155\) −1.45361 −0.116757
\(156\) −13.3496 −1.06882
\(157\) 10.7573 0.858526 0.429263 0.903179i \(-0.358773\pi\)
0.429263 + 0.903179i \(0.358773\pi\)
\(158\) −44.2075 −3.51696
\(159\) 24.6720 1.95662
\(160\) −8.79833 −0.695569
\(161\) 2.94498 0.232097
\(162\) 18.0140 1.41532
\(163\) −14.1107 −1.10524 −0.552618 0.833435i \(-0.686371\pi\)
−0.552618 + 0.833435i \(0.686371\pi\)
\(164\) −21.0255 −1.64182
\(165\) 6.20039 0.482699
\(166\) −1.83984 −0.142799
\(167\) −8.49873 −0.657651 −0.328826 0.944391i \(-0.606653\pi\)
−0.328826 + 0.944391i \(0.606653\pi\)
\(168\) 8.77301 0.676853
\(169\) 1.00000 0.0769231
\(170\) −1.85096 −0.141962
\(171\) 26.5145 2.02761
\(172\) −21.9275 −1.67196
\(173\) 1.71633 0.130491 0.0652453 0.997869i \(-0.479217\pi\)
0.0652453 + 0.997869i \(0.479217\pi\)
\(174\) −46.0057 −3.48769
\(175\) 1.88169 0.142242
\(176\) 56.4376 4.25414
\(177\) 11.2968 0.849120
\(178\) −32.5254 −2.43788
\(179\) 20.1867 1.50882 0.754412 0.656402i \(-0.227922\pi\)
0.754412 + 0.656402i \(0.227922\pi\)
\(180\) 10.0482 0.748945
\(181\) 16.6693 1.23902 0.619511 0.784988i \(-0.287331\pi\)
0.619511 + 0.784988i \(0.287331\pi\)
\(182\) −1.06981 −0.0793000
\(183\) −9.31781 −0.688792
\(184\) 63.0018 4.64456
\(185\) 1.82088 0.133874
\(186\) 18.7825 1.37720
\(187\) 5.82993 0.426327
\(188\) 51.2075 3.73469
\(189\) −0.645592 −0.0469599
\(190\) −10.4620 −0.758995
\(191\) −1.23290 −0.0892094 −0.0446047 0.999005i \(-0.514203\pi\)
−0.0446047 + 0.999005i \(0.514203\pi\)
\(192\) 49.2394 3.55354
\(193\) −4.02322 −0.289598 −0.144799 0.989461i \(-0.546254\pi\)
−0.144799 + 0.989461i \(0.546254\pi\)
\(194\) 27.2319 1.95514
\(195\) −1.37505 −0.0984690
\(196\) −35.4706 −2.53361
\(197\) 18.0764 1.28789 0.643945 0.765072i \(-0.277297\pi\)
0.643945 + 0.765072i \(0.277297\pi\)
\(198\) −43.8556 −3.11668
\(199\) −13.0350 −0.924028 −0.462014 0.886873i \(-0.652873\pi\)
−0.462014 + 0.886873i \(0.652873\pi\)
\(200\) 40.2548 2.84644
\(201\) 41.8628 2.95277
\(202\) 40.8086 2.87128
\(203\) −2.66060 −0.186738
\(204\) 17.2596 1.20841
\(205\) −2.16569 −0.151258
\(206\) −47.1173 −3.28282
\(207\) −26.7730 −1.86086
\(208\) −12.5160 −0.867831
\(209\) 32.9520 2.27934
\(210\) 1.47104 0.101512
\(211\) 15.6901 1.08015 0.540074 0.841618i \(-0.318396\pi\)
0.540074 + 0.841618i \(0.318396\pi\)
\(212\) 49.6902 3.41274
\(213\) 27.1259 1.85864
\(214\) 4.58189 0.313211
\(215\) −2.25860 −0.154035
\(216\) −13.8111 −0.939726
\(217\) 1.08623 0.0737380
\(218\) −8.42299 −0.570477
\(219\) −24.5281 −1.65745
\(220\) 12.4878 0.841924
\(221\) −1.29289 −0.0869692
\(222\) −23.5281 −1.57910
\(223\) 21.1053 1.41332 0.706659 0.707555i \(-0.250202\pi\)
0.706659 + 0.707555i \(0.250202\pi\)
\(224\) 6.57466 0.439288
\(225\) −17.1065 −1.14043
\(226\) 33.4431 2.22460
\(227\) 6.40630 0.425201 0.212601 0.977139i \(-0.431807\pi\)
0.212601 + 0.977139i \(0.431807\pi\)
\(228\) 97.5547 6.46072
\(229\) −12.5060 −0.826418 −0.413209 0.910636i \(-0.635592\pi\)
−0.413209 + 0.910636i \(0.635592\pi\)
\(230\) 10.5640 0.696572
\(231\) −4.63331 −0.304850
\(232\) −56.9180 −3.73685
\(233\) −11.9281 −0.781437 −0.390718 0.920510i \(-0.627773\pi\)
−0.390718 + 0.920510i \(0.627773\pi\)
\(234\) 9.72575 0.635792
\(235\) 5.27452 0.344072
\(236\) 22.7521 1.48104
\(237\) 42.4598 2.75806
\(238\) 1.38315 0.0896565
\(239\) 15.9409 1.03113 0.515566 0.856850i \(-0.327582\pi\)
0.515566 + 0.856850i \(0.327582\pi\)
\(240\) 17.2101 1.11091
\(241\) −6.11585 −0.393957 −0.196978 0.980408i \(-0.563113\pi\)
−0.196978 + 0.980408i \(0.563113\pi\)
\(242\) −25.0176 −1.60819
\(243\) −22.1546 −1.42122
\(244\) −18.7663 −1.20139
\(245\) −3.65357 −0.233418
\(246\) 27.9835 1.78416
\(247\) −7.30769 −0.464977
\(248\) 23.2376 1.47559
\(249\) 1.76710 0.111985
\(250\) 13.9081 0.879624
\(251\) 17.9038 1.13007 0.565037 0.825065i \(-0.308862\pi\)
0.565037 + 0.825065i \(0.308862\pi\)
\(252\) −7.50860 −0.472997
\(253\) −33.2733 −2.09188
\(254\) 21.6448 1.35811
\(255\) 1.77778 0.111329
\(256\) 10.8545 0.678405
\(257\) 4.72125 0.294503 0.147252 0.989099i \(-0.452957\pi\)
0.147252 + 0.989099i \(0.452957\pi\)
\(258\) 29.1840 1.81691
\(259\) −1.36068 −0.0845483
\(260\) −2.76938 −0.171750
\(261\) 24.1877 1.49718
\(262\) −22.1693 −1.36962
\(263\) −18.2069 −1.12269 −0.561344 0.827583i \(-0.689715\pi\)
−0.561344 + 0.827583i \(0.689715\pi\)
\(264\) −99.1201 −6.10042
\(265\) 5.11823 0.314410
\(266\) 7.81788 0.479345
\(267\) 31.2395 1.91182
\(268\) 84.3129 5.15023
\(269\) −1.17983 −0.0719357 −0.0359679 0.999353i \(-0.511451\pi\)
−0.0359679 + 0.999353i \(0.511451\pi\)
\(270\) −2.31582 −0.140936
\(271\) −15.5142 −0.942420 −0.471210 0.882021i \(-0.656183\pi\)
−0.471210 + 0.882021i \(0.656183\pi\)
\(272\) 16.1819 0.981170
\(273\) 1.02752 0.0621883
\(274\) −26.5238 −1.60236
\(275\) −21.2598 −1.28202
\(276\) −98.5059 −5.92936
\(277\) −19.9138 −1.19650 −0.598251 0.801309i \(-0.704137\pi\)
−0.598251 + 0.801309i \(0.704137\pi\)
\(278\) 17.2257 1.03313
\(279\) −9.87497 −0.591199
\(280\) 1.81997 0.108764
\(281\) −3.92335 −0.234047 −0.117024 0.993129i \(-0.537335\pi\)
−0.117024 + 0.993129i \(0.537335\pi\)
\(282\) −68.1535 −4.05848
\(283\) −11.8402 −0.703829 −0.351914 0.936032i \(-0.614469\pi\)
−0.351914 + 0.936032i \(0.614469\pi\)
\(284\) 54.6324 3.24183
\(285\) 10.0484 0.595216
\(286\) 12.0871 0.714724
\(287\) 1.61834 0.0955274
\(288\) −59.7706 −3.52202
\(289\) −15.3284 −0.901673
\(290\) −9.54392 −0.560438
\(291\) −26.1553 −1.53325
\(292\) −49.4002 −2.89093
\(293\) −14.3153 −0.836309 −0.418154 0.908376i \(-0.637323\pi\)
−0.418154 + 0.908376i \(0.637323\pi\)
\(294\) 47.2087 2.75327
\(295\) 2.34353 0.136446
\(296\) −29.1089 −1.69192
\(297\) 7.29409 0.423246
\(298\) −57.0071 −3.30233
\(299\) 7.37895 0.426735
\(300\) −62.9399 −3.63384
\(301\) 1.68776 0.0972811
\(302\) 39.5655 2.27674
\(303\) −39.1952 −2.25171
\(304\) 91.4633 5.24578
\(305\) −1.93299 −0.110682
\(306\) −12.5743 −0.718827
\(307\) −27.8312 −1.58841 −0.794206 0.607649i \(-0.792113\pi\)
−0.794206 + 0.607649i \(0.792113\pi\)
\(308\) −9.33163 −0.531719
\(309\) 45.2545 2.57444
\(310\) 3.89644 0.221303
\(311\) 25.4016 1.44039 0.720196 0.693770i \(-0.244052\pi\)
0.720196 + 0.693770i \(0.244052\pi\)
\(312\) 21.9816 1.24447
\(313\) −10.8694 −0.614377 −0.307188 0.951649i \(-0.599388\pi\)
−0.307188 + 0.951649i \(0.599388\pi\)
\(314\) −28.8352 −1.62727
\(315\) −0.773407 −0.0435765
\(316\) 85.5152 4.81061
\(317\) −21.2662 −1.19443 −0.597214 0.802082i \(-0.703726\pi\)
−0.597214 + 0.802082i \(0.703726\pi\)
\(318\) −66.1340 −3.70861
\(319\) 30.0603 1.68305
\(320\) 10.2147 0.571021
\(321\) −4.40074 −0.245625
\(322\) −7.89411 −0.439921
\(323\) 9.44804 0.525703
\(324\) −34.8464 −1.93591
\(325\) 4.71475 0.261527
\(326\) 37.8241 2.09488
\(327\) 8.08998 0.447377
\(328\) 34.6210 1.91162
\(329\) −3.94145 −0.217299
\(330\) −16.6203 −0.914917
\(331\) −10.1876 −0.559962 −0.279981 0.960006i \(-0.590328\pi\)
−0.279981 + 0.960006i \(0.590328\pi\)
\(332\) 3.55899 0.195325
\(333\) 12.3700 0.677872
\(334\) 22.7811 1.24652
\(335\) 8.68447 0.474483
\(336\) −12.8605 −0.701596
\(337\) 8.26483 0.450214 0.225107 0.974334i \(-0.427727\pi\)
0.225107 + 0.974334i \(0.427727\pi\)
\(338\) −2.68053 −0.145801
\(339\) −32.1209 −1.74457
\(340\) 3.58051 0.194180
\(341\) −12.2725 −0.664595
\(342\) −71.0728 −3.84318
\(343\) 5.52392 0.298264
\(344\) 36.1062 1.94672
\(345\) −10.1464 −0.546263
\(346\) −4.60068 −0.247334
\(347\) 32.5233 1.74594 0.872972 0.487771i \(-0.162190\pi\)
0.872972 + 0.487771i \(0.162190\pi\)
\(348\) 88.9936 4.77056
\(349\) 29.9808 1.60484 0.802419 0.596761i \(-0.203546\pi\)
0.802419 + 0.596761i \(0.203546\pi\)
\(350\) −5.04391 −0.269608
\(351\) −1.61759 −0.0863407
\(352\) −74.2825 −3.95927
\(353\) 4.76639 0.253689 0.126845 0.991923i \(-0.459515\pi\)
0.126845 + 0.991923i \(0.459515\pi\)
\(354\) −30.2814 −1.60944
\(355\) 5.62729 0.298665
\(356\) 62.9172 3.33461
\(357\) −1.32847 −0.0703101
\(358\) −54.1109 −2.85985
\(359\) −22.3661 −1.18044 −0.590219 0.807243i \(-0.700959\pi\)
−0.590219 + 0.807243i \(0.700959\pi\)
\(360\) −16.5454 −0.872021
\(361\) 34.4023 1.81065
\(362\) −44.6826 −2.34846
\(363\) 24.0285 1.26117
\(364\) 2.06945 0.108469
\(365\) −5.08836 −0.266337
\(366\) 24.9766 1.30555
\(367\) −15.8433 −0.827015 −0.413508 0.910501i \(-0.635697\pi\)
−0.413508 + 0.910501i \(0.635697\pi\)
\(368\) −92.3552 −4.81435
\(369\) −14.7124 −0.765897
\(370\) −4.88092 −0.253747
\(371\) −3.82466 −0.198566
\(372\) −36.3329 −1.88378
\(373\) 32.5864 1.68726 0.843631 0.536924i \(-0.180414\pi\)
0.843631 + 0.536924i \(0.180414\pi\)
\(374\) −15.6273 −0.808067
\(375\) −13.3582 −0.689815
\(376\) −84.3191 −4.34843
\(377\) −6.66639 −0.343337
\(378\) 1.73052 0.0890086
\(379\) 19.5206 1.00271 0.501354 0.865242i \(-0.332836\pi\)
0.501354 + 0.865242i \(0.332836\pi\)
\(380\) 20.2378 1.03818
\(381\) −20.7890 −1.06505
\(382\) 3.30482 0.169089
\(383\) −20.3850 −1.04163 −0.520813 0.853671i \(-0.674371\pi\)
−0.520813 + 0.853671i \(0.674371\pi\)
\(384\) −47.1639 −2.40682
\(385\) −0.961183 −0.0489864
\(386\) 10.7843 0.548909
\(387\) −15.3436 −0.779958
\(388\) −52.6775 −2.67430
\(389\) −29.4252 −1.49192 −0.745959 0.665991i \(-0.768009\pi\)
−0.745959 + 0.665991i \(0.768009\pi\)
\(390\) 3.68584 0.186640
\(391\) −9.54017 −0.482467
\(392\) 58.4064 2.94997
\(393\) 21.2928 1.07408
\(394\) −48.4543 −2.44109
\(395\) 8.80831 0.443194
\(396\) 84.8344 4.26309
\(397\) 33.3559 1.67408 0.837042 0.547138i \(-0.184283\pi\)
0.837042 + 0.547138i \(0.184283\pi\)
\(398\) 34.9407 1.75142
\(399\) −7.50879 −0.375910
\(400\) −59.0099 −2.95050
\(401\) 32.7964 1.63777 0.818887 0.573954i \(-0.194591\pi\)
0.818887 + 0.573954i \(0.194591\pi\)
\(402\) −112.214 −5.59674
\(403\) 2.72165 0.135575
\(404\) −78.9403 −3.92743
\(405\) −3.58927 −0.178352
\(406\) 7.13181 0.353946
\(407\) 15.3733 0.762027
\(408\) −28.4199 −1.40699
\(409\) −28.8141 −1.42476 −0.712382 0.701791i \(-0.752384\pi\)
−0.712382 + 0.701791i \(0.752384\pi\)
\(410\) 5.80519 0.286698
\(411\) 25.4751 1.25660
\(412\) 91.1438 4.49033
\(413\) −1.75123 −0.0861724
\(414\) 71.7658 3.52710
\(415\) 0.366586 0.0179950
\(416\) 16.4735 0.807677
\(417\) −16.5447 −0.810196
\(418\) −88.3287 −4.32030
\(419\) 17.8069 0.869924 0.434962 0.900449i \(-0.356762\pi\)
0.434962 + 0.900449i \(0.356762\pi\)
\(420\) −2.84559 −0.138851
\(421\) 31.8425 1.55191 0.775955 0.630788i \(-0.217268\pi\)
0.775955 + 0.630788i \(0.217268\pi\)
\(422\) −42.0576 −2.04733
\(423\) 35.8319 1.74221
\(424\) −81.8206 −3.97356
\(425\) −6.09565 −0.295682
\(426\) −72.7117 −3.52289
\(427\) 1.44445 0.0699017
\(428\) −8.86322 −0.428420
\(429\) −11.6092 −0.560498
\(430\) 6.05423 0.291961
\(431\) 24.1099 1.16133 0.580666 0.814142i \(-0.302792\pi\)
0.580666 + 0.814142i \(0.302792\pi\)
\(432\) 20.2459 0.974079
\(433\) −7.24476 −0.348161 −0.174080 0.984731i \(-0.555695\pi\)
−0.174080 + 0.984731i \(0.555695\pi\)
\(434\) −2.91166 −0.139764
\(435\) 9.16659 0.439504
\(436\) 16.2934 0.780315
\(437\) −53.9231 −2.57949
\(438\) 65.7481 3.14157
\(439\) −18.9953 −0.906595 −0.453298 0.891359i \(-0.649753\pi\)
−0.453298 + 0.891359i \(0.649753\pi\)
\(440\) −20.5625 −0.980280
\(441\) −24.8202 −1.18191
\(442\) 3.46563 0.164843
\(443\) 18.7614 0.891381 0.445690 0.895187i \(-0.352958\pi\)
0.445690 + 0.895187i \(0.352958\pi\)
\(444\) 45.5129 2.15995
\(445\) 6.48065 0.307212
\(446\) −56.5734 −2.67883
\(447\) 54.7532 2.58974
\(448\) −7.63308 −0.360629
\(449\) −12.7693 −0.602620 −0.301310 0.953526i \(-0.597424\pi\)
−0.301310 + 0.953526i \(0.597424\pi\)
\(450\) 45.8545 2.16160
\(451\) −18.2845 −0.860981
\(452\) −64.6925 −3.04288
\(453\) −38.0013 −1.78546
\(454\) −17.1723 −0.805934
\(455\) 0.213159 0.00999307
\(456\) −160.635 −7.52242
\(457\) −32.2774 −1.50988 −0.754938 0.655797i \(-0.772333\pi\)
−0.754938 + 0.655797i \(0.772333\pi\)
\(458\) 33.5226 1.56641
\(459\) 2.09137 0.0976168
\(460\) −20.4351 −0.952792
\(461\) −3.07885 −0.143396 −0.0716982 0.997426i \(-0.522842\pi\)
−0.0716982 + 0.997426i \(0.522842\pi\)
\(462\) 12.4197 0.577817
\(463\) 1.00000 0.0464739
\(464\) 83.4368 3.87346
\(465\) −3.74239 −0.173549
\(466\) 31.9736 1.48115
\(467\) 5.37733 0.248833 0.124417 0.992230i \(-0.460294\pi\)
0.124417 + 0.992230i \(0.460294\pi\)
\(468\) −18.8135 −0.869656
\(469\) −6.48957 −0.299661
\(470\) −14.1385 −0.652160
\(471\) 27.6952 1.27613
\(472\) −37.4639 −1.72442
\(473\) −19.0689 −0.876787
\(474\) −113.814 −5.22767
\(475\) −34.4539 −1.58085
\(476\) −2.67558 −0.122635
\(477\) 34.7702 1.59202
\(478\) −42.7300 −1.95443
\(479\) 20.0439 0.915829 0.457914 0.888996i \(-0.348597\pi\)
0.457914 + 0.888996i \(0.348597\pi\)
\(480\) −22.6517 −1.03391
\(481\) −3.40931 −0.155451
\(482\) 16.3937 0.746712
\(483\) 7.58201 0.344993
\(484\) 48.3941 2.19973
\(485\) −5.42593 −0.246379
\(486\) 59.3860 2.69380
\(487\) −5.29203 −0.239805 −0.119902 0.992786i \(-0.538258\pi\)
−0.119902 + 0.992786i \(0.538258\pi\)
\(488\) 30.9009 1.39882
\(489\) −36.3287 −1.64284
\(490\) 9.79348 0.442425
\(491\) −1.37754 −0.0621674 −0.0310837 0.999517i \(-0.509896\pi\)
−0.0310837 + 0.999517i \(0.509896\pi\)
\(492\) −54.1313 −2.44043
\(493\) 8.61892 0.388177
\(494\) 19.5885 0.881326
\(495\) 8.73818 0.392752
\(496\) −34.0643 −1.52953
\(497\) −4.20506 −0.188623
\(498\) −4.73676 −0.212259
\(499\) −14.4239 −0.645702 −0.322851 0.946450i \(-0.604641\pi\)
−0.322851 + 0.946450i \(0.604641\pi\)
\(500\) −26.9038 −1.20318
\(501\) −21.8804 −0.977544
\(502\) −47.9915 −2.14196
\(503\) −20.1771 −0.899653 −0.449827 0.893116i \(-0.648514\pi\)
−0.449827 + 0.893116i \(0.648514\pi\)
\(504\) 12.3638 0.550726
\(505\) −8.13107 −0.361828
\(506\) 89.1900 3.96498
\(507\) 2.57455 0.114340
\(508\) −41.8697 −1.85767
\(509\) −38.9812 −1.72781 −0.863905 0.503654i \(-0.831988\pi\)
−0.863905 + 0.503654i \(0.831988\pi\)
\(510\) −4.76539 −0.211015
\(511\) 3.80234 0.168206
\(512\) 7.54288 0.333351
\(513\) 11.8209 0.521904
\(514\) −12.6554 −0.558207
\(515\) 9.38807 0.413688
\(516\) −56.4535 −2.48523
\(517\) 44.5316 1.95850
\(518\) 3.64733 0.160254
\(519\) 4.41879 0.193963
\(520\) 4.56010 0.199974
\(521\) −26.3797 −1.15571 −0.577857 0.816138i \(-0.696111\pi\)
−0.577857 + 0.816138i \(0.696111\pi\)
\(522\) −64.8357 −2.83778
\(523\) −21.3338 −0.932861 −0.466430 0.884558i \(-0.654460\pi\)
−0.466430 + 0.884558i \(0.654460\pi\)
\(524\) 42.8843 1.87341
\(525\) 4.84449 0.211431
\(526\) 48.8041 2.12796
\(527\) −3.51880 −0.153281
\(528\) 145.301 6.32343
\(529\) 31.4488 1.36734
\(530\) −13.7195 −0.595939
\(531\) 15.9205 0.690893
\(532\) −15.1229 −0.655662
\(533\) 4.05490 0.175637
\(534\) −83.7382 −3.62371
\(535\) −0.912936 −0.0394697
\(536\) −138.831 −5.99658
\(537\) 51.9716 2.24274
\(538\) 3.16257 0.136348
\(539\) −30.8463 −1.32864
\(540\) 4.47973 0.192777
\(541\) 22.1475 0.952194 0.476097 0.879393i \(-0.342051\pi\)
0.476097 + 0.879393i \(0.342051\pi\)
\(542\) 41.5862 1.78628
\(543\) 42.9160 1.84170
\(544\) −21.2984 −0.913160
\(545\) 1.67827 0.0718892
\(546\) −2.75429 −0.117873
\(547\) −32.4608 −1.38792 −0.693962 0.720012i \(-0.744136\pi\)
−0.693962 + 0.720012i \(0.744136\pi\)
\(548\) 51.3077 2.19176
\(549\) −13.1316 −0.560441
\(550\) 56.9875 2.42996
\(551\) 48.7159 2.07537
\(552\) 162.201 6.90375
\(553\) −6.58211 −0.279900
\(554\) 53.3793 2.26787
\(555\) 4.68795 0.198992
\(556\) −33.3215 −1.41314
\(557\) −3.19164 −0.135234 −0.0676171 0.997711i \(-0.521540\pi\)
−0.0676171 + 0.997711i \(0.521540\pi\)
\(558\) 26.4701 1.12057
\(559\) 4.22886 0.178862
\(560\) −2.66791 −0.112740
\(561\) 15.0094 0.633699
\(562\) 10.5166 0.443618
\(563\) 0.748163 0.0315313 0.0157656 0.999876i \(-0.494981\pi\)
0.0157656 + 0.999876i \(0.494981\pi\)
\(564\) 131.836 5.55131
\(565\) −6.66350 −0.280336
\(566\) 31.7380 1.33405
\(567\) 2.68213 0.112639
\(568\) −89.9585 −3.77457
\(569\) −35.8158 −1.50148 −0.750738 0.660600i \(-0.770302\pi\)
−0.750738 + 0.660600i \(0.770302\pi\)
\(570\) −26.9350 −1.12818
\(571\) 7.39058 0.309286 0.154643 0.987970i \(-0.450577\pi\)
0.154643 + 0.987970i \(0.450577\pi\)
\(572\) −23.3813 −0.977621
\(573\) −3.17416 −0.132602
\(574\) −4.33799 −0.181064
\(575\) 34.7899 1.45084
\(576\) 69.3928 2.89137
\(577\) −12.6445 −0.526397 −0.263198 0.964742i \(-0.584777\pi\)
−0.263198 + 0.964742i \(0.584777\pi\)
\(578\) 41.0883 1.70905
\(579\) −10.3580 −0.430463
\(580\) 18.4618 0.766584
\(581\) −0.273936 −0.0113648
\(582\) 70.1100 2.90615
\(583\) 43.2121 1.78966
\(584\) 81.3432 3.36600
\(585\) −1.93785 −0.0801201
\(586\) 38.3725 1.58515
\(587\) −3.36445 −0.138866 −0.0694328 0.997587i \(-0.522119\pi\)
−0.0694328 + 0.997587i \(0.522119\pi\)
\(588\) −91.3208 −3.76600
\(589\) −19.8890 −0.819511
\(590\) −6.28189 −0.258621
\(591\) 46.5386 1.91434
\(592\) 42.6710 1.75377
\(593\) 5.86069 0.240670 0.120335 0.992733i \(-0.461603\pi\)
0.120335 + 0.992733i \(0.461603\pi\)
\(594\) −19.5520 −0.802228
\(595\) −0.275592 −0.0112982
\(596\) 110.275 4.51702
\(597\) −33.5593 −1.37349
\(598\) −19.7795 −0.808842
\(599\) 33.8138 1.38159 0.690797 0.723049i \(-0.257260\pi\)
0.690797 + 0.723049i \(0.257260\pi\)
\(600\) 103.638 4.23100
\(601\) −28.6189 −1.16739 −0.583694 0.811973i \(-0.698393\pi\)
−0.583694 + 0.811973i \(0.698393\pi\)
\(602\) −4.52410 −0.184388
\(603\) 58.9971 2.40255
\(604\) −76.5357 −3.11419
\(605\) 4.98473 0.202658
\(606\) 105.064 4.26792
\(607\) 20.9237 0.849269 0.424634 0.905365i \(-0.360403\pi\)
0.424634 + 0.905365i \(0.360403\pi\)
\(608\) −120.383 −4.88217
\(609\) −6.84985 −0.277570
\(610\) 5.18142 0.209789
\(611\) −9.87568 −0.399527
\(612\) 24.3238 0.983233
\(613\) −14.6232 −0.590626 −0.295313 0.955401i \(-0.595424\pi\)
−0.295313 + 0.955401i \(0.595424\pi\)
\(614\) 74.6023 3.01070
\(615\) −5.57567 −0.224833
\(616\) 15.3656 0.619097
\(617\) 40.9032 1.64670 0.823350 0.567533i \(-0.192102\pi\)
0.823350 + 0.567533i \(0.192102\pi\)
\(618\) −121.306 −4.87963
\(619\) 39.6735 1.59461 0.797306 0.603576i \(-0.206258\pi\)
0.797306 + 0.603576i \(0.206258\pi\)
\(620\) −7.53729 −0.302705
\(621\) −11.9361 −0.478980
\(622\) −68.0896 −2.73015
\(623\) −4.84274 −0.194020
\(624\) −32.2232 −1.28996
\(625\) 20.8026 0.832102
\(626\) 29.1358 1.16450
\(627\) 84.8365 3.38805
\(628\) 55.7790 2.22582
\(629\) 4.40786 0.175753
\(630\) 2.07314 0.0825957
\(631\) 34.0368 1.35498 0.677491 0.735531i \(-0.263067\pi\)
0.677491 + 0.735531i \(0.263067\pi\)
\(632\) −140.811 −5.60115
\(633\) 40.3948 1.60555
\(634\) 57.0046 2.26394
\(635\) −4.31270 −0.171144
\(636\) 127.930 5.07275
\(637\) 6.84071 0.271039
\(638\) −80.5773 −3.19008
\(639\) 38.2284 1.51229
\(640\) −9.78418 −0.386754
\(641\) −38.9063 −1.53671 −0.768353 0.640026i \(-0.778924\pi\)
−0.768353 + 0.640026i \(0.778924\pi\)
\(642\) 11.7963 0.465563
\(643\) −30.6463 −1.20857 −0.604286 0.796767i \(-0.706542\pi\)
−0.604286 + 0.796767i \(0.706542\pi\)
\(644\) 15.2704 0.601737
\(645\) −5.81487 −0.228960
\(646\) −25.3257 −0.996427
\(647\) −6.08696 −0.239303 −0.119652 0.992816i \(-0.538178\pi\)
−0.119652 + 0.992816i \(0.538178\pi\)
\(648\) 57.3786 2.25404
\(649\) 19.7859 0.776665
\(650\) −12.6380 −0.495703
\(651\) 2.79655 0.109605
\(652\) −73.1671 −2.86544
\(653\) 10.2487 0.401063 0.200531 0.979687i \(-0.435733\pi\)
0.200531 + 0.979687i \(0.435733\pi\)
\(654\) −21.6854 −0.847966
\(655\) 4.41720 0.172594
\(656\) −50.7513 −1.98151
\(657\) −34.5673 −1.34860
\(658\) 10.5652 0.411872
\(659\) 24.0251 0.935884 0.467942 0.883759i \(-0.344996\pi\)
0.467942 + 0.883759i \(0.344996\pi\)
\(660\) 32.1503 1.25145
\(661\) −47.0392 −1.82961 −0.914806 0.403893i \(-0.867657\pi\)
−0.914806 + 0.403893i \(0.867657\pi\)
\(662\) 27.3081 1.06136
\(663\) −3.32861 −0.129272
\(664\) −5.86029 −0.227423
\(665\) −1.55770 −0.0604051
\(666\) −33.1581 −1.28485
\(667\) −49.1910 −1.90468
\(668\) −44.0677 −1.70503
\(669\) 54.3367 2.10078
\(670\) −23.2789 −0.899344
\(671\) −16.3198 −0.630018
\(672\) 16.9268 0.652965
\(673\) 29.8624 1.15111 0.575555 0.817763i \(-0.304786\pi\)
0.575555 + 0.817763i \(0.304786\pi\)
\(674\) −22.1541 −0.853344
\(675\) −7.62654 −0.293546
\(676\) 5.18522 0.199431
\(677\) −6.20140 −0.238339 −0.119170 0.992874i \(-0.538023\pi\)
−0.119170 + 0.992874i \(0.538023\pi\)
\(678\) 86.1009 3.30669
\(679\) 4.05459 0.155601
\(680\) −5.89572 −0.226090
\(681\) 16.4933 0.632026
\(682\) 32.8968 1.25969
\(683\) 22.8985 0.876186 0.438093 0.898930i \(-0.355654\pi\)
0.438093 + 0.898930i \(0.355654\pi\)
\(684\) 137.483 5.25681
\(685\) 5.28484 0.201923
\(686\) −14.8070 −0.565334
\(687\) −32.1972 −1.22840
\(688\) −52.9285 −2.01788
\(689\) −9.58305 −0.365085
\(690\) 27.1976 1.03540
\(691\) 39.8928 1.51759 0.758797 0.651328i \(-0.225788\pi\)
0.758797 + 0.651328i \(0.225788\pi\)
\(692\) 8.89957 0.338311
\(693\) −6.52971 −0.248043
\(694\) −87.1796 −3.30929
\(695\) −3.43220 −0.130191
\(696\) −146.538 −5.55452
\(697\) −5.24254 −0.198576
\(698\) −80.3644 −3.04184
\(699\) −30.7095 −1.16154
\(700\) 9.75695 0.368778
\(701\) −33.7442 −1.27450 −0.637250 0.770657i \(-0.719928\pi\)
−0.637250 + 0.770657i \(0.719928\pi\)
\(702\) 4.33600 0.163652
\(703\) 24.9142 0.939655
\(704\) 86.2408 3.25032
\(705\) 13.5795 0.511434
\(706\) −12.7764 −0.480847
\(707\) 6.07604 0.228513
\(708\) 58.5764 2.20144
\(709\) −21.7408 −0.816492 −0.408246 0.912872i \(-0.633860\pi\)
−0.408246 + 0.912872i \(0.633860\pi\)
\(710\) −15.0841 −0.566096
\(711\) 59.8384 2.24411
\(712\) −103.600 −3.88259
\(713\) 20.0829 0.752111
\(714\) 3.56100 0.133267
\(715\) −2.40834 −0.0900668
\(716\) 104.672 3.91179
\(717\) 41.0407 1.53269
\(718\) 59.9529 2.23742
\(719\) 41.5480 1.54948 0.774740 0.632280i \(-0.217881\pi\)
0.774740 + 0.632280i \(0.217881\pi\)
\(720\) 24.2542 0.903899
\(721\) −7.01535 −0.261265
\(722\) −92.2164 −3.43194
\(723\) −15.7456 −0.585584
\(724\) 86.4341 3.21230
\(725\) −31.4304 −1.16729
\(726\) −64.4090 −2.39044
\(727\) 15.7901 0.585621 0.292810 0.956171i \(-0.405410\pi\)
0.292810 + 0.956171i \(0.405410\pi\)
\(728\) −3.40759 −0.126294
\(729\) −36.8771 −1.36582
\(730\) 13.6395 0.504820
\(731\) −5.46745 −0.202221
\(732\) −48.3149 −1.78577
\(733\) 25.5095 0.942213 0.471107 0.882076i \(-0.343855\pi\)
0.471107 + 0.882076i \(0.343855\pi\)
\(734\) 42.4685 1.56754
\(735\) −9.40629 −0.346956
\(736\) 121.557 4.48064
\(737\) 73.3211 2.70082
\(738\) 39.4370 1.45170
\(739\) −41.1172 −1.51252 −0.756260 0.654271i \(-0.772976\pi\)
−0.756260 + 0.654271i \(0.772976\pi\)
\(740\) 9.44167 0.347083
\(741\) −18.8140 −0.691150
\(742\) 10.2521 0.376366
\(743\) 4.09095 0.150082 0.0750412 0.997180i \(-0.476091\pi\)
0.0750412 + 0.997180i \(0.476091\pi\)
\(744\) 59.8264 2.19334
\(745\) 11.3586 0.416147
\(746\) −87.3488 −3.19807
\(747\) 2.49037 0.0911178
\(748\) 30.2295 1.10530
\(749\) 0.682203 0.0249271
\(750\) 35.8070 1.30749
\(751\) 49.9960 1.82438 0.912190 0.409767i \(-0.134390\pi\)
0.912190 + 0.409767i \(0.134390\pi\)
\(752\) 123.604 4.50739
\(753\) 46.0941 1.67976
\(754\) 17.8694 0.650767
\(755\) −7.88339 −0.286906
\(756\) −3.34753 −0.121749
\(757\) 0.816196 0.0296652 0.0148326 0.999890i \(-0.495278\pi\)
0.0148326 + 0.999890i \(0.495278\pi\)
\(758\) −52.3255 −1.90055
\(759\) −85.6638 −3.10940
\(760\) −33.3238 −1.20878
\(761\) −16.9510 −0.614474 −0.307237 0.951633i \(-0.599404\pi\)
−0.307237 + 0.951633i \(0.599404\pi\)
\(762\) 55.7255 2.01872
\(763\) −1.25411 −0.0454017
\(764\) −6.39285 −0.231285
\(765\) 2.50542 0.0905837
\(766\) 54.6426 1.97432
\(767\) −4.38788 −0.158437
\(768\) 27.9454 1.00839
\(769\) −47.5932 −1.71625 −0.858127 0.513438i \(-0.828372\pi\)
−0.858127 + 0.513438i \(0.828372\pi\)
\(770\) 2.57648 0.0928498
\(771\) 12.1551 0.437754
\(772\) −20.8613 −0.750814
\(773\) 23.9051 0.859808 0.429904 0.902875i \(-0.358547\pi\)
0.429904 + 0.902875i \(0.358547\pi\)
\(774\) 41.1288 1.47835
\(775\) 12.8319 0.460935
\(776\) 86.7396 3.11377
\(777\) −3.50313 −0.125674
\(778\) 78.8751 2.82781
\(779\) −29.6320 −1.06168
\(780\) −7.12991 −0.255292
\(781\) 47.5100 1.70004
\(782\) 25.5727 0.914477
\(783\) 10.7835 0.385371
\(784\) −85.6186 −3.05781
\(785\) 5.74539 0.205062
\(786\) −57.0758 −2.03583
\(787\) −13.1609 −0.469134 −0.234567 0.972100i \(-0.575367\pi\)
−0.234567 + 0.972100i \(0.575367\pi\)
\(788\) 93.7301 3.33899
\(789\) −46.8746 −1.66878
\(790\) −23.6109 −0.840038
\(791\) 4.97938 0.177046
\(792\) −139.690 −4.96365
\(793\) 3.61920 0.128522
\(794\) −89.4114 −3.17309
\(795\) 13.1771 0.467345
\(796\) −67.5894 −2.39564
\(797\) 1.17269 0.0415388 0.0207694 0.999784i \(-0.493388\pi\)
0.0207694 + 0.999784i \(0.493388\pi\)
\(798\) 20.1275 0.712506
\(799\) 12.7682 0.451706
\(800\) 77.6681 2.74598
\(801\) 44.0257 1.55557
\(802\) −87.9116 −3.10427
\(803\) −42.9600 −1.51602
\(804\) 217.068 7.65539
\(805\) 1.57289 0.0554372
\(806\) −7.29546 −0.256971
\(807\) −3.03754 −0.106926
\(808\) 129.984 4.57283
\(809\) 28.0039 0.984565 0.492283 0.870435i \(-0.336163\pi\)
0.492283 + 0.870435i \(0.336163\pi\)
\(810\) 9.62114 0.338052
\(811\) −24.9459 −0.875967 −0.437984 0.898983i \(-0.644307\pi\)
−0.437984 + 0.898983i \(0.644307\pi\)
\(812\) −13.7958 −0.484137
\(813\) −39.9421 −1.40083
\(814\) −41.2086 −1.44436
\(815\) −7.53641 −0.263989
\(816\) 41.6610 1.45843
\(817\) −30.9032 −1.08117
\(818\) 77.2369 2.70052
\(819\) 1.44808 0.0506000
\(820\) −11.2296 −0.392154
\(821\) 5.87643 0.205089 0.102544 0.994728i \(-0.467302\pi\)
0.102544 + 0.994728i \(0.467302\pi\)
\(822\) −68.2868 −2.38177
\(823\) 36.0569 1.25687 0.628433 0.777864i \(-0.283697\pi\)
0.628433 + 0.777864i \(0.283697\pi\)
\(824\) −150.079 −5.22824
\(825\) −54.7345 −1.90561
\(826\) 4.69422 0.163333
\(827\) 11.4005 0.396433 0.198216 0.980158i \(-0.436485\pi\)
0.198216 + 0.980158i \(0.436485\pi\)
\(828\) −138.824 −4.82447
\(829\) −1.75217 −0.0608554 −0.0304277 0.999537i \(-0.509687\pi\)
−0.0304277 + 0.999537i \(0.509687\pi\)
\(830\) −0.982643 −0.0341081
\(831\) −51.2689 −1.77850
\(832\) −19.1254 −0.663055
\(833\) −8.84429 −0.306437
\(834\) 44.3484 1.53566
\(835\) −4.53910 −0.157082
\(836\) 170.863 5.90943
\(837\) −4.40252 −0.152173
\(838\) −47.7318 −1.64887
\(839\) −20.9643 −0.723769 −0.361884 0.932223i \(-0.617866\pi\)
−0.361884 + 0.932223i \(0.617866\pi\)
\(840\) 4.68559 0.161668
\(841\) 15.4408 0.532441
\(842\) −85.3547 −2.94152
\(843\) −10.1009 −0.347892
\(844\) 81.3563 2.80040
\(845\) 0.534092 0.0183733
\(846\) −96.0485 −3.30221
\(847\) −3.72490 −0.127989
\(848\) 119.942 4.11882
\(849\) −30.4833 −1.04618
\(850\) 16.3395 0.560442
\(851\) −25.1571 −0.862374
\(852\) 140.654 4.81872
\(853\) −20.0121 −0.685200 −0.342600 0.939481i \(-0.611307\pi\)
−0.342600 + 0.939481i \(0.611307\pi\)
\(854\) −3.87188 −0.132493
\(855\) 14.1612 0.484302
\(856\) 14.5943 0.498823
\(857\) 6.76113 0.230956 0.115478 0.993310i \(-0.463160\pi\)
0.115478 + 0.993310i \(0.463160\pi\)
\(858\) 31.1188 1.06238
\(859\) −7.54434 −0.257409 −0.128705 0.991683i \(-0.541082\pi\)
−0.128705 + 0.991683i \(0.541082\pi\)
\(860\) −11.7113 −0.399353
\(861\) 4.16649 0.141994
\(862\) −64.6271 −2.20121
\(863\) 44.4288 1.51238 0.756188 0.654355i \(-0.227060\pi\)
0.756188 + 0.654355i \(0.227060\pi\)
\(864\) −26.6473 −0.906561
\(865\) 0.916680 0.0311681
\(866\) 19.4198 0.659910
\(867\) −39.4638 −1.34026
\(868\) 5.63233 0.191174
\(869\) 74.3666 2.52272
\(870\) −24.5713 −0.833045
\(871\) −16.2603 −0.550958
\(872\) −26.8290 −0.908546
\(873\) −36.8606 −1.24754
\(874\) 144.542 4.88921
\(875\) 2.07079 0.0700055
\(876\) −127.183 −4.29713
\(877\) 32.6181 1.10143 0.550717 0.834692i \(-0.314354\pi\)
0.550717 + 0.834692i \(0.314354\pi\)
\(878\) 50.9173 1.71838
\(879\) −36.8554 −1.24310
\(880\) 30.1429 1.01612
\(881\) −36.2011 −1.21965 −0.609824 0.792537i \(-0.708760\pi\)
−0.609824 + 0.792537i \(0.708760\pi\)
\(882\) 66.5311 2.24022
\(883\) −36.1826 −1.21764 −0.608821 0.793307i \(-0.708357\pi\)
−0.608821 + 0.793307i \(0.708357\pi\)
\(884\) −6.70392 −0.225477
\(885\) 6.03353 0.202815
\(886\) −50.2904 −1.68954
\(887\) 17.8718 0.600078 0.300039 0.953927i \(-0.403000\pi\)
0.300039 + 0.953927i \(0.403000\pi\)
\(888\) −74.9422 −2.51489
\(889\) 3.22271 0.108086
\(890\) −17.3715 −0.582295
\(891\) −30.3035 −1.01520
\(892\) 109.436 3.66418
\(893\) 72.1684 2.41502
\(894\) −146.767 −4.90864
\(895\) 10.7815 0.360387
\(896\) 7.31135 0.244255
\(897\) 18.9975 0.634307
\(898\) 34.2284 1.14222
\(899\) −18.1436 −0.605123
\(900\) −88.7010 −2.95670
\(901\) 12.3898 0.412765
\(902\) 49.0119 1.63192
\(903\) 4.34523 0.144600
\(904\) 106.524 3.54292
\(905\) 8.90295 0.295944
\(906\) 101.863 3.38419
\(907\) −29.1853 −0.969083 −0.484541 0.874768i \(-0.661013\pi\)
−0.484541 + 0.874768i \(0.661013\pi\)
\(908\) 33.2181 1.10238
\(909\) −55.2377 −1.83212
\(910\) −0.571379 −0.0189410
\(911\) −54.3230 −1.79980 −0.899901 0.436094i \(-0.856361\pi\)
−0.899901 + 0.436094i \(0.856361\pi\)
\(912\) 235.477 7.79742
\(913\) 3.09501 0.102430
\(914\) 86.5205 2.86184
\(915\) −4.97657 −0.164520
\(916\) −64.8462 −2.14258
\(917\) −3.30080 −0.109002
\(918\) −5.60597 −0.185025
\(919\) 46.5673 1.53611 0.768057 0.640381i \(-0.221223\pi\)
0.768057 + 0.640381i \(0.221223\pi\)
\(920\) 33.6488 1.10937
\(921\) −71.6528 −2.36104
\(922\) 8.25293 0.271796
\(923\) −10.5362 −0.346803
\(924\) −24.0247 −0.790355
\(925\) −16.0740 −0.528510
\(926\) −2.68053 −0.0880875
\(927\) 63.7769 2.09471
\(928\) −109.819 −3.60497
\(929\) 14.1758 0.465093 0.232547 0.972585i \(-0.425294\pi\)
0.232547 + 0.972585i \(0.425294\pi\)
\(930\) 10.0316 0.328949
\(931\) −49.9898 −1.63835
\(932\) −61.8498 −2.02596
\(933\) 65.3977 2.14102
\(934\) −14.4141 −0.471643
\(935\) 3.11372 0.101829
\(936\) 30.9786 1.01257
\(937\) −19.9395 −0.651397 −0.325698 0.945474i \(-0.605599\pi\)
−0.325698 + 0.945474i \(0.605599\pi\)
\(938\) 17.3955 0.567982
\(939\) −27.9839 −0.913220
\(940\) 27.3495 0.892043
\(941\) −17.7825 −0.579694 −0.289847 0.957073i \(-0.593604\pi\)
−0.289847 + 0.957073i \(0.593604\pi\)
\(942\) −74.2377 −2.41880
\(943\) 29.9209 0.974359
\(944\) 54.9189 1.78746
\(945\) −0.344805 −0.0112165
\(946\) 51.1146 1.66188
\(947\) −27.3882 −0.889997 −0.444998 0.895531i \(-0.646796\pi\)
−0.444998 + 0.895531i \(0.646796\pi\)
\(948\) 220.163 7.15057
\(949\) 9.52713 0.309264
\(950\) 92.3546 2.99638
\(951\) −54.7509 −1.77542
\(952\) 4.40564 0.142788
\(953\) 47.9609 1.55361 0.776803 0.629743i \(-0.216840\pi\)
0.776803 + 0.629743i \(0.216840\pi\)
\(954\) −93.2024 −3.01754
\(955\) −0.658481 −0.0213079
\(956\) 82.6571 2.67332
\(957\) 77.3916 2.50171
\(958\) −53.7282 −1.73588
\(959\) −3.94916 −0.127525
\(960\) 26.2983 0.848775
\(961\) −23.5926 −0.761052
\(962\) 9.13874 0.294645
\(963\) −6.20195 −0.199855
\(964\) −31.7120 −1.02138
\(965\) −2.14877 −0.0691713
\(966\) −20.3238 −0.653906
\(967\) −48.9064 −1.57273 −0.786363 0.617765i \(-0.788038\pi\)
−0.786363 + 0.617765i \(0.788038\pi\)
\(968\) −79.6864 −2.56122
\(969\) 24.3245 0.781414
\(970\) 14.5444 0.466991
\(971\) −15.2905 −0.490696 −0.245348 0.969435i \(-0.578902\pi\)
−0.245348 + 0.969435i \(0.578902\pi\)
\(972\) −114.876 −3.68466
\(973\) 2.56475 0.0822223
\(974\) 14.1854 0.454530
\(975\) 12.1383 0.388738
\(976\) −45.2981 −1.44996
\(977\) −19.9463 −0.638137 −0.319069 0.947732i \(-0.603370\pi\)
−0.319069 + 0.947732i \(0.603370\pi\)
\(978\) 97.3800 3.11387
\(979\) 54.7147 1.74869
\(980\) −18.9445 −0.605161
\(981\) 11.4012 0.364011
\(982\) 3.69252 0.117833
\(983\) 40.7526 1.29980 0.649902 0.760018i \(-0.274810\pi\)
0.649902 + 0.760018i \(0.274810\pi\)
\(984\) 89.1334 2.84147
\(985\) 9.65446 0.307617
\(986\) −23.1032 −0.735757
\(987\) −10.1474 −0.322997
\(988\) −37.8920 −1.20550
\(989\) 31.2045 0.992246
\(990\) −23.4229 −0.744429
\(991\) −26.2320 −0.833286 −0.416643 0.909070i \(-0.636794\pi\)
−0.416643 + 0.909070i \(0.636794\pi\)
\(992\) 44.8350 1.42351
\(993\) −26.2285 −0.832336
\(994\) 11.2718 0.357519
\(995\) −6.96189 −0.220707
\(996\) 9.16280 0.290334
\(997\) 12.5685 0.398050 0.199025 0.979994i \(-0.436223\pi\)
0.199025 + 0.979994i \(0.436223\pi\)
\(998\) 38.6636 1.22388
\(999\) 5.51487 0.174483
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 6019.2.a.d.1.5 123
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6019.2.a.d.1.5 123 1.1 even 1 trivial