Properties

Label 197.14.a.a.1.1
Level $197$
Weight $14$
Character 197.1
Self dual yes
Analytic conductor $211.245$
Analytic rank $1$
Dimension $104$
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] = [197,14,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.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: \(211.244930035\)
Analytic rank: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-178.085 q^{2} -2212.53 q^{3} +23522.4 q^{4} +69269.3 q^{5} +394020. q^{6} -342836. q^{7} -2.73012e6 q^{8} +3.30098e6 q^{9} +O(q^{10})\) \(q-178.085 q^{2} -2212.53 q^{3} +23522.4 q^{4} +69269.3 q^{5} +394020. q^{6} -342836. q^{7} -2.73012e6 q^{8} +3.30098e6 q^{9} -1.23359e7 q^{10} -2.18757e6 q^{11} -5.20441e7 q^{12} -2.49702e7 q^{13} +6.10541e7 q^{14} -1.53261e8 q^{15} +2.93499e8 q^{16} +8.28915e7 q^{17} -5.87855e8 q^{18} -1.48465e6 q^{19} +1.62938e9 q^{20} +7.58535e8 q^{21} +3.89575e8 q^{22} -7.83219e8 q^{23} +6.04048e9 q^{24} +3.57753e9 q^{25} +4.44683e9 q^{26} -3.77602e9 q^{27} -8.06432e9 q^{28} +7.67316e8 q^{29} +2.72935e10 q^{30} -6.82093e9 q^{31} -2.99028e10 q^{32} +4.84008e9 q^{33} -1.47618e10 q^{34} -2.37480e10 q^{35} +7.76469e10 q^{36} +1.40105e10 q^{37} +2.64395e8 q^{38} +5.52473e10 q^{39} -1.89114e11 q^{40} +4.28687e10 q^{41} -1.35084e11 q^{42} +4.73352e9 q^{43} -5.14570e10 q^{44} +2.28656e11 q^{45} +1.39480e11 q^{46} -1.20240e10 q^{47} -6.49376e11 q^{48} +2.06474e10 q^{49} -6.37107e11 q^{50} -1.83400e11 q^{51} -5.87359e11 q^{52} -3.29928e10 q^{53} +6.72455e11 q^{54} -1.51532e11 q^{55} +9.35984e11 q^{56} +3.28484e9 q^{57} -1.36648e11 q^{58} -4.61096e11 q^{59} -3.60506e12 q^{60} +5.00977e11 q^{61} +1.21471e12 q^{62} -1.13169e12 q^{63} +2.92090e12 q^{64} -1.72967e12 q^{65} -8.61947e11 q^{66} +7.79136e11 q^{67} +1.94981e12 q^{68} +1.73290e12 q^{69} +4.22917e12 q^{70} -9.28434e11 q^{71} -9.01206e12 q^{72} +2.57941e11 q^{73} -2.49507e12 q^{74} -7.91541e12 q^{75} -3.49226e10 q^{76} +7.49979e11 q^{77} -9.83874e12 q^{78} +1.44273e12 q^{79} +2.03305e13 q^{80} +3.09175e12 q^{81} -7.63429e12 q^{82} -8.27855e11 q^{83} +1.78426e13 q^{84} +5.74184e12 q^{85} -8.42970e11 q^{86} -1.69771e12 q^{87} +5.97234e12 q^{88} -1.42047e12 q^{89} -4.07203e13 q^{90} +8.56068e12 q^{91} -1.84232e13 q^{92} +1.50915e13 q^{93} +2.14130e12 q^{94} -1.02841e11 q^{95} +6.61608e13 q^{96} -9.65413e12 q^{97} -3.67700e12 q^{98} -7.22113e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9} - 9626347 q^{10} - 10688800 q^{11} - 68157440 q^{12} - 94762650 q^{13} - 52465903 q^{14} - 186128761 q^{15} + 1543503872 q^{16} - 109572251 q^{17} - 449658263 q^{18} - 1495268031 q^{19} - 1194030741 q^{20} - 832275538 q^{21} - 2695120703 q^{22} - 2632554532 q^{23} - 190649667 q^{24} + 22696779124 q^{25} - 2460454754 q^{26} - 16267542277 q^{27} - 18137835250 q^{28} + 47556769 q^{29} - 9613748117 q^{30} - 24774628288 q^{31} - 29246249180 q^{32} - 42367036666 q^{33} - 39395206606 q^{34} - 26216433864 q^{35} + 190013501626 q^{36} - 82419664050 q^{37} - 34593622142 q^{38} - 39498281801 q^{39} - 150303128514 q^{40} - 25862853768 q^{41} - 138889965149 q^{42} - 258164897781 q^{43} - 197365738094 q^{44} - 240782892021 q^{45} - 218441397971 q^{46} - 208905762731 q^{47} - 664063830814 q^{48} + 1113758315863 q^{49} - 1516068087607 q^{50} - 1019253294393 q^{51} - 1162941441840 q^{52} + 161684855900 q^{53} + 1679137315823 q^{54} - 557952233701 q^{55} + 2842561845328 q^{56} + 801593765429 q^{57} - 7249760433 q^{58} - 775487110641 q^{59} - 57598844627 q^{60} - 36786715662 q^{61} + 681529132643 q^{62} - 4349115033663 q^{63} + 4600420238797 q^{64} - 2531819073161 q^{65} - 3958922748734 q^{66} - 7314072405766 q^{67} - 10297353950393 q^{68} - 2089200206275 q^{69} - 14268943913713 q^{70} - 6055724651085 q^{71} - 26860198563805 q^{72} - 7572811533391 q^{73} - 11175265675817 q^{74} - 24431657592434 q^{75} - 26425925198106 q^{76} - 9735327037686 q^{77} - 35310017230907 q^{78} - 8981210762721 q^{79} - 25913753436330 q^{80} + 15437375349812 q^{81} - 19721330628227 q^{82} - 22209909714532 q^{83} - 18837805278768 q^{84} - 5905005171430 q^{85} - 8913876797772 q^{86} - 7341562344401 q^{87} - 35154329886441 q^{88} - 4646484034146 q^{89} + 9564902968095 q^{90} - 22752431457047 q^{91} - 13601121953458 q^{92} - 9615114240293 q^{93} + 15352521272967 q^{94} + 5258551767043 q^{95} + 87277848810881 q^{96} - 42298840804040 q^{97} + 27000102375354 q^{98} - 8666459567773 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −178.085 −1.96758 −0.983792 0.179313i \(-0.942613\pi\)
−0.983792 + 0.179313i \(0.942613\pi\)
\(3\) −2212.53 −1.75227 −0.876136 0.482064i \(-0.839887\pi\)
−0.876136 + 0.482064i \(0.839887\pi\)
\(4\) 23522.4 2.87139
\(5\) 69269.3 1.98260 0.991302 0.131609i \(-0.0420143\pi\)
0.991302 + 0.131609i \(0.0420143\pi\)
\(6\) 394020. 3.44774
\(7\) −342836. −1.10141 −0.550705 0.834700i \(-0.685641\pi\)
−0.550705 + 0.834700i \(0.685641\pi\)
\(8\) −2.73012e6 −3.68211
\(9\) 3.30098e6 2.07046
\(10\) −1.23359e7 −3.90094
\(11\) −2.18757e6 −0.372315 −0.186157 0.982520i \(-0.559603\pi\)
−0.186157 + 0.982520i \(0.559603\pi\)
\(12\) −5.20441e7 −5.03145
\(13\) −2.49702e7 −1.43480 −0.717398 0.696664i \(-0.754667\pi\)
−0.717398 + 0.696664i \(0.754667\pi\)
\(14\) 6.10541e7 2.16712
\(15\) −1.53261e8 −3.47406
\(16\) 2.93499e8 4.37348
\(17\) 8.28915e7 0.832898 0.416449 0.909159i \(-0.363274\pi\)
0.416449 + 0.909159i \(0.363274\pi\)
\(18\) −5.87855e8 −4.07380
\(19\) −1.48465e6 −0.00723980 −0.00361990 0.999993i \(-0.501152\pi\)
−0.00361990 + 0.999993i \(0.501152\pi\)
\(20\) 1.62938e9 5.69282
\(21\) 7.58535e8 1.92997
\(22\) 3.89575e8 0.732561
\(23\) −7.83219e8 −1.10320 −0.551598 0.834110i \(-0.685982\pi\)
−0.551598 + 0.834110i \(0.685982\pi\)
\(24\) 6.04048e9 6.45206
\(25\) 3.57753e9 2.93072
\(26\) 4.44683e9 2.82308
\(27\) −3.77602e9 −1.87573
\(28\) −8.06432e9 −3.16257
\(29\) 7.67316e8 0.239545 0.119773 0.992801i \(-0.461783\pi\)
0.119773 + 0.992801i \(0.461783\pi\)
\(30\) 2.72935e10 6.83550
\(31\) −6.82093e9 −1.38036 −0.690180 0.723637i \(-0.742469\pi\)
−0.690180 + 0.723637i \(0.742469\pi\)
\(32\) −2.99028e10 −4.92307
\(33\) 4.84008e9 0.652397
\(34\) −1.47618e10 −1.63880
\(35\) −2.37480e10 −2.18366
\(36\) 7.76469e10 5.94508
\(37\) 1.40105e10 0.897724 0.448862 0.893601i \(-0.351829\pi\)
0.448862 + 0.893601i \(0.351829\pi\)
\(38\) 2.64395e8 0.0142449
\(39\) 5.52473e10 2.51415
\(40\) −1.89114e11 −7.30017
\(41\) 4.28687e10 1.40944 0.704718 0.709488i \(-0.251074\pi\)
0.704718 + 0.709488i \(0.251074\pi\)
\(42\) −1.35084e11 −3.79738
\(43\) 4.73352e9 0.114193 0.0570964 0.998369i \(-0.481816\pi\)
0.0570964 + 0.998369i \(0.481816\pi\)
\(44\) −5.14570e10 −1.06906
\(45\) 2.28656e11 4.10489
\(46\) 1.39480e11 2.17063
\(47\) −1.20240e10 −0.162709 −0.0813546 0.996685i \(-0.525925\pi\)
−0.0813546 + 0.996685i \(0.525925\pi\)
\(48\) −6.49376e11 −7.66352
\(49\) 2.06474e10 0.213104
\(50\) −6.37107e11 −5.76643
\(51\) −1.83400e11 −1.45946
\(52\) −5.87359e11 −4.11985
\(53\) −3.29928e10 −0.204469 −0.102234 0.994760i \(-0.532599\pi\)
−0.102234 + 0.994760i \(0.532599\pi\)
\(54\) 6.72455e11 3.69066
\(55\) −1.51532e11 −0.738153
\(56\) 9.35984e11 4.05552
\(57\) 3.28484e9 0.0126861
\(58\) −1.36648e11 −0.471325
\(59\) −4.61096e11 −1.42316 −0.711580 0.702605i \(-0.752020\pi\)
−0.711580 + 0.702605i \(0.752020\pi\)
\(60\) −3.60506e12 −9.97537
\(61\) 5.00977e11 1.24501 0.622506 0.782615i \(-0.286115\pi\)
0.622506 + 0.782615i \(0.286115\pi\)
\(62\) 1.21471e12 2.71598
\(63\) −1.13169e12 −2.28042
\(64\) 2.92090e12 5.31309
\(65\) −1.72967e12 −2.84463
\(66\) −8.61947e11 −1.28365
\(67\) 7.79136e11 1.05227 0.526135 0.850401i \(-0.323641\pi\)
0.526135 + 0.850401i \(0.323641\pi\)
\(68\) 1.94981e12 2.39157
\(69\) 1.73290e12 1.93310
\(70\) 4.22917e12 4.29653
\(71\) −9.28434e11 −0.860145 −0.430073 0.902794i \(-0.641512\pi\)
−0.430073 + 0.902794i \(0.641512\pi\)
\(72\) −9.01206e12 −7.62365
\(73\) 2.57941e11 0.199491 0.0997453 0.995013i \(-0.468197\pi\)
0.0997453 + 0.995013i \(0.468197\pi\)
\(74\) −2.49507e12 −1.76635
\(75\) −7.91541e12 −5.13541
\(76\) −3.49226e10 −0.0207883
\(77\) 7.49979e11 0.410071
\(78\) −9.83874e12 −4.94680
\(79\) 1.44273e12 0.667741 0.333871 0.942619i \(-0.391645\pi\)
0.333871 + 0.942619i \(0.391645\pi\)
\(80\) 2.03305e13 8.67087
\(81\) 3.09175e12 1.21633
\(82\) −7.63429e12 −2.77318
\(83\) −8.27855e11 −0.277937 −0.138969 0.990297i \(-0.544379\pi\)
−0.138969 + 0.990297i \(0.544379\pi\)
\(84\) 1.78426e13 5.54169
\(85\) 5.74184e12 1.65131
\(86\) −8.42970e11 −0.224684
\(87\) −1.69771e12 −0.419748
\(88\) 5.97234e12 1.37091
\(89\) −1.42047e12 −0.302969 −0.151485 0.988460i \(-0.548405\pi\)
−0.151485 + 0.988460i \(0.548405\pi\)
\(90\) −4.07203e13 −8.07672
\(91\) 8.56068e12 1.58030
\(92\) −1.84232e13 −3.16770
\(93\) 1.50915e13 2.41877
\(94\) 2.14130e12 0.320144
\(95\) −1.02841e11 −0.0143537
\(96\) 6.61608e13 8.62656
\(97\) −9.65413e12 −1.17678 −0.588392 0.808576i \(-0.700239\pi\)
−0.588392 + 0.808576i \(0.700239\pi\)
\(98\) −3.67700e12 −0.419300
\(99\) −7.22113e12 −0.770861
\(100\) 8.41522e13 8.41522
\(101\) −3.33558e10 −0.00312667 −0.00156334 0.999999i \(-0.500498\pi\)
−0.00156334 + 0.999999i \(0.500498\pi\)
\(102\) 3.26609e13 2.87162
\(103\) 5.85816e12 0.483414 0.241707 0.970349i \(-0.422293\pi\)
0.241707 + 0.970349i \(0.422293\pi\)
\(104\) 6.81716e13 5.28308
\(105\) 5.25432e13 3.82636
\(106\) 5.87554e12 0.402309
\(107\) 9.37894e12 0.604170 0.302085 0.953281i \(-0.402317\pi\)
0.302085 + 0.953281i \(0.402317\pi\)
\(108\) −8.88211e13 −5.38595
\(109\) 5.90348e12 0.337160 0.168580 0.985688i \(-0.446082\pi\)
0.168580 + 0.985688i \(0.446082\pi\)
\(110\) 2.69856e13 1.45238
\(111\) −3.09987e13 −1.57306
\(112\) −1.00622e14 −4.81699
\(113\) −8.98954e12 −0.406188 −0.203094 0.979159i \(-0.565100\pi\)
−0.203094 + 0.979159i \(0.565100\pi\)
\(114\) −5.84983e11 −0.0249610
\(115\) −5.42530e13 −2.18720
\(116\) 1.80491e13 0.687827
\(117\) −8.24260e13 −2.97068
\(118\) 8.21145e13 2.80019
\(119\) −2.84182e13 −0.917362
\(120\) 4.18420e14 12.7919
\(121\) −2.97372e13 −0.861382
\(122\) −8.92166e13 −2.44967
\(123\) −9.48484e13 −2.46971
\(124\) −1.60445e14 −3.96355
\(125\) 1.63256e14 3.82784
\(126\) 2.01538e14 4.48692
\(127\) −2.88674e13 −0.610497 −0.305249 0.952273i \(-0.598740\pi\)
−0.305249 + 0.952273i \(0.598740\pi\)
\(128\) −2.75206e14 −5.53087
\(129\) −1.04731e13 −0.200097
\(130\) 3.08029e14 5.59705
\(131\) 4.43197e13 0.766185 0.383092 0.923710i \(-0.374859\pi\)
0.383092 + 0.923710i \(0.374859\pi\)
\(132\) 1.13850e14 1.87328
\(133\) 5.08992e11 0.00797399
\(134\) −1.38753e14 −2.07043
\(135\) −2.61563e14 −3.71883
\(136\) −2.26304e14 −3.06682
\(137\) −5.69473e13 −0.735850 −0.367925 0.929855i \(-0.619932\pi\)
−0.367925 + 0.929855i \(0.619932\pi\)
\(138\) −3.08604e14 −3.80353
\(139\) 1.42557e14 1.67645 0.838226 0.545322i \(-0.183593\pi\)
0.838226 + 0.545322i \(0.183593\pi\)
\(140\) −5.58610e14 −6.27013
\(141\) 2.66034e13 0.285111
\(142\) 1.65341e14 1.69241
\(143\) 5.46241e13 0.534196
\(144\) 9.68834e14 9.05509
\(145\) 5.31515e13 0.474923
\(146\) −4.59356e13 −0.392515
\(147\) −4.56831e13 −0.373416
\(148\) 3.29561e14 2.57771
\(149\) −8.06929e13 −0.604122 −0.302061 0.953289i \(-0.597675\pi\)
−0.302061 + 0.953289i \(0.597675\pi\)
\(150\) 1.40962e15 10.1044
\(151\) −1.48573e14 −1.01998 −0.509988 0.860181i \(-0.670350\pi\)
−0.509988 + 0.860181i \(0.670350\pi\)
\(152\) 4.05328e12 0.0266578
\(153\) 2.73623e14 1.72448
\(154\) −1.33560e14 −0.806850
\(155\) −4.72481e14 −2.73671
\(156\) 1.29955e15 7.21910
\(157\) −2.48016e13 −0.132170 −0.0660848 0.997814i \(-0.521051\pi\)
−0.0660848 + 0.997814i \(0.521051\pi\)
\(158\) −2.56929e14 −1.31384
\(159\) 7.29977e13 0.358285
\(160\) −2.07134e15 −9.76050
\(161\) 2.68516e14 1.21507
\(162\) −5.50596e14 −2.39323
\(163\) −2.62399e14 −1.09583 −0.547915 0.836534i \(-0.684578\pi\)
−0.547915 + 0.836534i \(0.684578\pi\)
\(164\) 1.00838e15 4.04704
\(165\) 3.35269e14 1.29344
\(166\) 1.47429e14 0.546865
\(167\) 4.02884e14 1.43722 0.718610 0.695413i \(-0.244779\pi\)
0.718610 + 0.695413i \(0.244779\pi\)
\(168\) −2.07089e15 −7.10636
\(169\) 3.20635e14 1.05864
\(170\) −1.02254e15 −3.24909
\(171\) −4.90080e12 −0.0149897
\(172\) 1.11344e14 0.327892
\(173\) 3.80550e13 0.107923 0.0539613 0.998543i \(-0.482815\pi\)
0.0539613 + 0.998543i \(0.482815\pi\)
\(174\) 3.02338e14 0.825890
\(175\) −1.22651e15 −3.22792
\(176\) −6.42051e14 −1.62831
\(177\) 1.02019e15 2.49376
\(178\) 2.52966e14 0.596117
\(179\) −1.63728e14 −0.372031 −0.186015 0.982547i \(-0.559557\pi\)
−0.186015 + 0.982547i \(0.559557\pi\)
\(180\) 5.37855e15 11.7867
\(181\) 2.83963e14 0.600277 0.300138 0.953896i \(-0.402967\pi\)
0.300138 + 0.953896i \(0.402967\pi\)
\(182\) −1.52453e15 −3.10937
\(183\) −1.10843e15 −2.18160
\(184\) 2.13828e15 4.06209
\(185\) 9.70499e14 1.77983
\(186\) −2.68758e15 −4.75913
\(187\) −1.81331e14 −0.310100
\(188\) −2.82833e14 −0.467201
\(189\) 1.29456e15 2.06595
\(190\) 1.83145e13 0.0282420
\(191\) 8.97492e14 1.33756 0.668781 0.743460i \(-0.266816\pi\)
0.668781 + 0.743460i \(0.266816\pi\)
\(192\) −6.46258e15 −9.30997
\(193\) −9.10942e14 −1.26873 −0.634364 0.773035i \(-0.718738\pi\)
−0.634364 + 0.773035i \(0.718738\pi\)
\(194\) 1.71926e15 2.31542
\(195\) 3.82695e15 4.98457
\(196\) 4.85677e14 0.611904
\(197\) −5.84517e13 −0.0712470
\(198\) 1.28598e15 1.51673
\(199\) 1.57907e15 1.80243 0.901213 0.433376i \(-0.142678\pi\)
0.901213 + 0.433376i \(0.142678\pi\)
\(200\) −9.76710e15 −10.7912
\(201\) −1.72386e15 −1.84386
\(202\) 5.94018e12 0.00615199
\(203\) −2.63064e14 −0.263837
\(204\) −4.31401e15 −4.19069
\(205\) 2.96949e15 2.79435
\(206\) −1.04325e15 −0.951158
\(207\) −2.58539e15 −2.28412
\(208\) −7.32873e15 −6.27505
\(209\) 3.24779e12 0.00269549
\(210\) −9.35718e15 −7.52869
\(211\) 1.03026e15 0.803732 0.401866 0.915698i \(-0.368362\pi\)
0.401866 + 0.915698i \(0.368362\pi\)
\(212\) −7.76071e14 −0.587109
\(213\) 2.05419e15 1.50721
\(214\) −1.67025e15 −1.18875
\(215\) 3.27887e14 0.226399
\(216\) 1.03090e16 6.90665
\(217\) 2.33846e15 1.52034
\(218\) −1.05132e15 −0.663390
\(219\) −5.70704e14 −0.349562
\(220\) −3.56439e15 −2.11952
\(221\) −2.06982e15 −1.19504
\(222\) 5.52042e15 3.09512
\(223\) −2.01761e15 −1.09864 −0.549321 0.835611i \(-0.685114\pi\)
−0.549321 + 0.835611i \(0.685114\pi\)
\(224\) 1.02517e16 5.42232
\(225\) 1.18094e16 6.06792
\(226\) 1.60091e15 0.799210
\(227\) 2.58569e15 1.25432 0.627160 0.778890i \(-0.284217\pi\)
0.627160 + 0.778890i \(0.284217\pi\)
\(228\) 7.72674e13 0.0364267
\(229\) 1.89717e15 0.869314 0.434657 0.900596i \(-0.356870\pi\)
0.434657 + 0.900596i \(0.356870\pi\)
\(230\) 9.66168e15 4.30350
\(231\) −1.65935e15 −0.718556
\(232\) −2.09487e15 −0.882032
\(233\) 3.75124e15 1.53590 0.767948 0.640512i \(-0.221278\pi\)
0.767948 + 0.640512i \(0.221278\pi\)
\(234\) 1.46789e16 5.84506
\(235\) −8.32893e14 −0.322588
\(236\) −1.08461e16 −4.08644
\(237\) −3.19208e15 −1.17006
\(238\) 5.06086e15 1.80499
\(239\) 3.82096e14 0.132613 0.0663065 0.997799i \(-0.478878\pi\)
0.0663065 + 0.997799i \(0.478878\pi\)
\(240\) −4.49819e16 −15.1937
\(241\) 5.91654e14 0.194517 0.0972583 0.995259i \(-0.468993\pi\)
0.0972583 + 0.995259i \(0.468993\pi\)
\(242\) 5.29577e15 1.69484
\(243\) −8.20399e14 −0.255614
\(244\) 1.17842e16 3.57491
\(245\) 1.43023e15 0.422501
\(246\) 1.68911e16 4.85937
\(247\) 3.70721e13 0.0103876
\(248\) 1.86220e16 5.08264
\(249\) 1.83165e15 0.487021
\(250\) −2.90735e16 −7.53161
\(251\) −2.87355e15 −0.725337 −0.362669 0.931918i \(-0.618134\pi\)
−0.362669 + 0.931918i \(0.618134\pi\)
\(252\) −2.66201e16 −6.54797
\(253\) 1.71335e15 0.410736
\(254\) 5.14086e15 1.20120
\(255\) −1.27040e16 −2.89354
\(256\) 2.50822e16 5.56936
\(257\) 6.27074e14 0.135754 0.0678771 0.997694i \(-0.478377\pi\)
0.0678771 + 0.997694i \(0.478377\pi\)
\(258\) 1.86510e15 0.393707
\(259\) −4.80331e15 −0.988762
\(260\) −4.06859e16 −8.16804
\(261\) 2.53289e15 0.495968
\(262\) −7.89269e15 −1.50753
\(263\) −1.88438e14 −0.0351121 −0.0175560 0.999846i \(-0.505589\pi\)
−0.0175560 + 0.999846i \(0.505589\pi\)
\(264\) −1.32140e16 −2.40220
\(265\) −2.28539e15 −0.405380
\(266\) −9.06441e13 −0.0156895
\(267\) 3.14285e15 0.530884
\(268\) 1.83272e16 3.02148
\(269\) −2.98520e15 −0.480379 −0.240190 0.970726i \(-0.577210\pi\)
−0.240190 + 0.970726i \(0.577210\pi\)
\(270\) 4.65805e16 7.31711
\(271\) 3.45220e15 0.529414 0.264707 0.964329i \(-0.414725\pi\)
0.264707 + 0.964329i \(0.414725\pi\)
\(272\) 2.43286e16 3.64266
\(273\) −1.89408e16 −2.76911
\(274\) 1.01415e16 1.44785
\(275\) −7.82612e15 −1.09115
\(276\) 4.07619e16 5.55067
\(277\) −6.24722e15 −0.830937 −0.415469 0.909607i \(-0.636382\pi\)
−0.415469 + 0.909607i \(0.636382\pi\)
\(278\) −2.53873e16 −3.29856
\(279\) −2.25157e16 −2.85798
\(280\) 6.48349e16 8.04048
\(281\) −7.50392e15 −0.909279 −0.454639 0.890676i \(-0.650232\pi\)
−0.454639 + 0.890676i \(0.650232\pi\)
\(282\) −4.73768e15 −0.560979
\(283\) 3.25678e15 0.376857 0.188428 0.982087i \(-0.439661\pi\)
0.188428 + 0.982087i \(0.439661\pi\)
\(284\) −2.18390e16 −2.46981
\(285\) 2.27539e14 0.0251515
\(286\) −9.72776e15 −1.05108
\(287\) −1.46969e16 −1.55237
\(288\) −9.87083e16 −10.1930
\(289\) −3.03358e15 −0.306281
\(290\) −9.46550e15 −0.934451
\(291\) 2.13601e16 2.06205
\(292\) 6.06740e15 0.572815
\(293\) −1.52824e16 −1.41108 −0.705542 0.708668i \(-0.749296\pi\)
−0.705542 + 0.708668i \(0.749296\pi\)
\(294\) 8.13549e15 0.734727
\(295\) −3.19398e16 −2.82156
\(296\) −3.82504e16 −3.30552
\(297\) 8.26033e15 0.698362
\(298\) 1.43702e16 1.18866
\(299\) 1.95571e16 1.58286
\(300\) −1.86189e17 −14.7458
\(301\) −1.62282e15 −0.125773
\(302\) 2.64587e16 2.00689
\(303\) 7.38007e13 0.00547878
\(304\) −4.35745e14 −0.0316631
\(305\) 3.47023e16 2.46836
\(306\) −4.87282e16 −3.39306
\(307\) 2.65054e16 1.80690 0.903451 0.428692i \(-0.141026\pi\)
0.903451 + 0.428692i \(0.141026\pi\)
\(308\) 1.76413e16 1.17747
\(309\) −1.29614e16 −0.847073
\(310\) 8.41420e16 5.38470
\(311\) 5.88672e14 0.0368919 0.0184460 0.999830i \(-0.494128\pi\)
0.0184460 + 0.999830i \(0.494128\pi\)
\(312\) −1.50832e17 −9.25739
\(313\) −1.23821e16 −0.744315 −0.372158 0.928170i \(-0.621382\pi\)
−0.372158 + 0.928170i \(0.621382\pi\)
\(314\) 4.41680e15 0.260055
\(315\) −7.83916e16 −4.52117
\(316\) 3.39364e16 1.91734
\(317\) 6.78117e15 0.375335 0.187668 0.982233i \(-0.439907\pi\)
0.187668 + 0.982233i \(0.439907\pi\)
\(318\) −1.29998e16 −0.704955
\(319\) −1.67856e15 −0.0891862
\(320\) 2.02329e17 10.5337
\(321\) −2.07512e16 −1.05867
\(322\) −4.78187e16 −2.39075
\(323\) −1.23065e14 −0.00603002
\(324\) 7.27254e16 3.49256
\(325\) −8.93317e16 −4.20498
\(326\) 4.67295e16 2.15614
\(327\) −1.30616e16 −0.590795
\(328\) −1.17037e17 −5.18970
\(329\) 4.12225e15 0.179210
\(330\) −5.97065e16 −2.54496
\(331\) 4.20545e16 1.75764 0.878821 0.477151i \(-0.158330\pi\)
0.878821 + 0.477151i \(0.158330\pi\)
\(332\) −1.94731e16 −0.798065
\(333\) 4.62484e16 1.85870
\(334\) −7.17478e16 −2.82785
\(335\) 5.39702e16 2.08623
\(336\) 2.22630e17 8.44068
\(337\) 1.15299e16 0.428779 0.214389 0.976748i \(-0.431224\pi\)
0.214389 + 0.976748i \(0.431224\pi\)
\(338\) −5.71004e16 −2.08296
\(339\) 1.98896e16 0.711752
\(340\) 1.35062e17 4.74154
\(341\) 1.49213e16 0.513929
\(342\) 8.72762e14 0.0294935
\(343\) 2.61384e16 0.866695
\(344\) −1.29231e16 −0.420471
\(345\) 1.20037e17 3.83257
\(346\) −6.77705e15 −0.212347
\(347\) 3.34090e16 1.02736 0.513679 0.857982i \(-0.328282\pi\)
0.513679 + 0.857982i \(0.328282\pi\)
\(348\) −3.99343e16 −1.20526
\(349\) −9.97927e15 −0.295620 −0.147810 0.989016i \(-0.547222\pi\)
−0.147810 + 0.989016i \(0.547222\pi\)
\(350\) 2.18423e17 6.35120
\(351\) 9.42880e16 2.69129
\(352\) 6.54145e16 1.83293
\(353\) −5.09999e16 −1.40292 −0.701461 0.712708i \(-0.747469\pi\)
−0.701461 + 0.712708i \(0.747469\pi\)
\(354\) −1.81681e17 −4.90669
\(355\) −6.43120e16 −1.70533
\(356\) −3.34130e16 −0.869942
\(357\) 6.28761e16 1.60747
\(358\) 2.91576e16 0.732002
\(359\) 2.84374e16 0.701093 0.350547 0.936545i \(-0.385996\pi\)
0.350547 + 0.936545i \(0.385996\pi\)
\(360\) −6.24259e17 −15.1147
\(361\) −4.20508e16 −0.999948
\(362\) −5.05697e16 −1.18109
\(363\) 6.57946e16 1.50937
\(364\) 2.01368e17 4.53765
\(365\) 1.78674e16 0.395511
\(366\) 1.97395e17 4.29248
\(367\) 2.03905e16 0.435612 0.217806 0.975992i \(-0.430110\pi\)
0.217806 + 0.975992i \(0.430110\pi\)
\(368\) −2.29874e17 −4.82480
\(369\) 1.41509e17 2.91817
\(370\) −1.72832e17 −3.50197
\(371\) 1.13111e16 0.225204
\(372\) 3.54989e17 6.94522
\(373\) −6.12728e15 −0.117804 −0.0589020 0.998264i \(-0.518760\pi\)
−0.0589020 + 0.998264i \(0.518760\pi\)
\(374\) 3.22925e16 0.610149
\(375\) −3.61209e17 −6.70742
\(376\) 3.28269e16 0.599114
\(377\) −1.91600e16 −0.343698
\(378\) −2.30542e17 −4.06492
\(379\) −8.67573e16 −1.50367 −0.751833 0.659354i \(-0.770830\pi\)
−0.751833 + 0.659354i \(0.770830\pi\)
\(380\) −2.41907e15 −0.0412149
\(381\) 6.38701e16 1.06976
\(382\) −1.59830e17 −2.63176
\(383\) −1.29511e14 −0.00209660 −0.00104830 0.999999i \(-0.500334\pi\)
−0.00104830 + 0.999999i \(0.500334\pi\)
\(384\) 6.08902e17 9.69158
\(385\) 5.19505e16 0.813009
\(386\) 1.62226e17 2.49633
\(387\) 1.56252e16 0.236431
\(388\) −2.27088e17 −3.37900
\(389\) 6.67342e16 0.976509 0.488255 0.872701i \(-0.337634\pi\)
0.488255 + 0.872701i \(0.337634\pi\)
\(390\) −6.81523e17 −9.80755
\(391\) −6.49222e16 −0.918849
\(392\) −5.63700e16 −0.784672
\(393\) −9.80588e16 −1.34256
\(394\) 1.04094e16 0.140185
\(395\) 9.99367e16 1.32387
\(396\) −1.69858e17 −2.21344
\(397\) −8.21917e16 −1.05363 −0.526817 0.849979i \(-0.676615\pi\)
−0.526817 + 0.849979i \(0.676615\pi\)
\(398\) −2.81210e17 −3.54643
\(399\) −1.12616e15 −0.0139726
\(400\) 1.05000e18 12.8174
\(401\) 1.44947e17 1.74089 0.870445 0.492266i \(-0.163831\pi\)
0.870445 + 0.492266i \(0.163831\pi\)
\(402\) 3.06995e17 3.62796
\(403\) 1.70320e17 1.98054
\(404\) −7.84608e14 −0.00897788
\(405\) 2.14163e17 2.41150
\(406\) 4.68478e16 0.519122
\(407\) −3.06490e16 −0.334236
\(408\) 5.00704e17 5.37391
\(409\) −1.29062e17 −1.36332 −0.681658 0.731671i \(-0.738741\pi\)
−0.681658 + 0.731671i \(0.738741\pi\)
\(410\) −5.28822e17 −5.49812
\(411\) 1.25998e17 1.28941
\(412\) 1.37798e17 1.38807
\(413\) 1.58080e17 1.56748
\(414\) 4.60420e17 4.49419
\(415\) −5.73449e16 −0.551039
\(416\) 7.46678e17 7.06361
\(417\) −3.15411e17 −2.93760
\(418\) −5.78384e14 −0.00530360
\(419\) −1.16966e17 −1.05601 −0.528007 0.849240i \(-0.677061\pi\)
−0.528007 + 0.849240i \(0.677061\pi\)
\(420\) 1.23594e18 10.9870
\(421\) −6.65288e16 −0.582339 −0.291169 0.956671i \(-0.594044\pi\)
−0.291169 + 0.956671i \(0.594044\pi\)
\(422\) −1.83474e17 −1.58141
\(423\) −3.96909e16 −0.336882
\(424\) 9.00745e16 0.752876
\(425\) 2.96547e17 2.44099
\(426\) −3.65821e17 −2.96556
\(427\) −1.71753e17 −1.37127
\(428\) 2.20615e17 1.73481
\(429\) −1.20858e17 −0.936056
\(430\) −5.83920e16 −0.445459
\(431\) −1.36907e16 −0.102878 −0.0514391 0.998676i \(-0.516381\pi\)
−0.0514391 + 0.998676i \(0.516381\pi\)
\(432\) −1.10826e18 −8.20346
\(433\) −1.53714e17 −1.12084 −0.560419 0.828209i \(-0.689360\pi\)
−0.560419 + 0.828209i \(0.689360\pi\)
\(434\) −4.16446e17 −2.99140
\(435\) −1.17599e17 −0.832194
\(436\) 1.38864e17 0.968116
\(437\) 1.16281e15 0.00798691
\(438\) 1.01634e17 0.687792
\(439\) −2.35077e16 −0.156744 −0.0783720 0.996924i \(-0.524972\pi\)
−0.0783720 + 0.996924i \(0.524972\pi\)
\(440\) 4.13700e17 2.71796
\(441\) 6.81566e16 0.441222
\(442\) 3.68604e17 2.35134
\(443\) 1.30104e17 0.817837 0.408918 0.912571i \(-0.365906\pi\)
0.408918 + 0.912571i \(0.365906\pi\)
\(444\) −7.29164e17 −4.51685
\(445\) −9.83953e16 −0.600668
\(446\) 3.59308e17 2.16167
\(447\) 1.78536e17 1.05859
\(448\) −1.00139e18 −5.85189
\(449\) 3.14233e17 1.80988 0.904942 0.425536i \(-0.139914\pi\)
0.904942 + 0.425536i \(0.139914\pi\)
\(450\) −2.10307e18 −11.9391
\(451\) −9.37785e16 −0.524754
\(452\) −2.11456e17 −1.16632
\(453\) 3.28723e17 1.78728
\(454\) −4.60474e17 −2.46798
\(455\) 5.92992e17 3.13310
\(456\) −8.96802e15 −0.0467116
\(457\) 2.87374e17 1.47568 0.737839 0.674977i \(-0.235846\pi\)
0.737839 + 0.674977i \(0.235846\pi\)
\(458\) −3.37859e17 −1.71045
\(459\) −3.13000e17 −1.56229
\(460\) −1.27616e18 −6.28029
\(461\) −2.17081e17 −1.05333 −0.526667 0.850072i \(-0.676558\pi\)
−0.526667 + 0.850072i \(0.676558\pi\)
\(462\) 2.95506e17 1.41382
\(463\) −3.60580e16 −0.170108 −0.0850540 0.996376i \(-0.527106\pi\)
−0.0850540 + 0.996376i \(0.527106\pi\)
\(464\) 2.25207e17 1.04765
\(465\) 1.04538e18 4.79546
\(466\) −6.68042e17 −3.02200
\(467\) 1.64369e17 0.733262 0.366631 0.930366i \(-0.380511\pi\)
0.366631 + 0.930366i \(0.380511\pi\)
\(468\) −1.93886e18 −8.52998
\(469\) −2.67116e17 −1.15898
\(470\) 1.48326e17 0.634719
\(471\) 5.48743e16 0.231597
\(472\) 1.25885e18 5.24023
\(473\) −1.03549e16 −0.0425157
\(474\) 5.68463e17 2.30220
\(475\) −5.31140e15 −0.0212178
\(476\) −6.68464e17 −2.63410
\(477\) −1.08909e17 −0.423343
\(478\) −6.80457e16 −0.260927
\(479\) 2.36207e17 0.893534 0.446767 0.894650i \(-0.352575\pi\)
0.446767 + 0.894650i \(0.352575\pi\)
\(480\) 4.58291e18 17.1031
\(481\) −3.49845e17 −1.28805
\(482\) −1.05365e17 −0.382728
\(483\) −5.94099e17 −2.12913
\(484\) −6.99491e17 −2.47336
\(485\) −6.68735e17 −2.33310
\(486\) 1.46101e17 0.502942
\(487\) 1.77167e16 0.0601791 0.0300895 0.999547i \(-0.490421\pi\)
0.0300895 + 0.999547i \(0.490421\pi\)
\(488\) −1.36773e18 −4.58427
\(489\) 5.80567e17 1.92019
\(490\) −2.54704e17 −0.831305
\(491\) −4.33637e17 −1.39668 −0.698339 0.715767i \(-0.746077\pi\)
−0.698339 + 0.715767i \(0.746077\pi\)
\(492\) −2.23106e18 −7.09151
\(493\) 6.36040e16 0.199517
\(494\) −6.60200e15 −0.0204385
\(495\) −5.00203e17 −1.52831
\(496\) −2.00194e18 −6.03698
\(497\) 3.18300e17 0.947372
\(498\) −3.26191e17 −0.958255
\(499\) 3.40601e17 0.987625 0.493813 0.869568i \(-0.335603\pi\)
0.493813 + 0.869568i \(0.335603\pi\)
\(500\) 3.84018e18 10.9912
\(501\) −8.91394e17 −2.51840
\(502\) 5.11738e17 1.42716
\(503\) 6.25663e17 1.72246 0.861228 0.508218i \(-0.169696\pi\)
0.861228 + 0.508218i \(0.169696\pi\)
\(504\) 3.08966e18 8.39677
\(505\) −2.31053e15 −0.00619895
\(506\) −3.05123e17 −0.808158
\(507\) −7.09416e17 −1.85502
\(508\) −6.79031e17 −1.75297
\(509\) −6.84799e17 −1.74541 −0.872706 0.488247i \(-0.837637\pi\)
−0.872706 + 0.488247i \(0.837637\pi\)
\(510\) 2.26240e18 5.69328
\(511\) −8.84316e16 −0.219721
\(512\) −2.21228e18 −5.42732
\(513\) 5.60609e15 0.0135799
\(514\) −1.11673e17 −0.267108
\(515\) 4.05791e17 0.958419
\(516\) −2.46351e17 −0.574556
\(517\) 2.63034e16 0.0605791
\(518\) 8.55399e17 1.94547
\(519\) −8.41980e16 −0.189110
\(520\) 4.72220e18 10.4742
\(521\) −8.01589e17 −1.75593 −0.877963 0.478728i \(-0.841098\pi\)
−0.877963 + 0.478728i \(0.841098\pi\)
\(522\) −4.51071e17 −0.975858
\(523\) −1.93207e17 −0.412821 −0.206411 0.978465i \(-0.566178\pi\)
−0.206411 + 0.978465i \(0.566178\pi\)
\(524\) 1.04251e18 2.20001
\(525\) 2.71369e18 5.65619
\(526\) 3.35581e16 0.0690859
\(527\) −5.65397e17 −1.14970
\(528\) 1.42056e18 2.85324
\(529\) 1.09396e17 0.217039
\(530\) 4.06995e17 0.797620
\(531\) −1.52207e18 −2.94659
\(532\) 1.19727e16 0.0228964
\(533\) −1.07044e18 −2.02225
\(534\) −5.59695e17 −1.04456
\(535\) 6.49672e17 1.19783
\(536\) −2.12714e18 −3.87458
\(537\) 3.62254e17 0.651899
\(538\) 5.31621e17 0.945187
\(539\) −4.51678e16 −0.0793417
\(540\) −6.15258e18 −10.6782
\(541\) 4.64430e17 0.796412 0.398206 0.917296i \(-0.369633\pi\)
0.398206 + 0.917296i \(0.369633\pi\)
\(542\) −6.14786e17 −1.04167
\(543\) −6.28278e17 −1.05185
\(544\) −2.47868e18 −4.10042
\(545\) 4.08930e17 0.668454
\(546\) 3.37307e18 5.44846
\(547\) 1.15138e18 1.83781 0.918903 0.394483i \(-0.129076\pi\)
0.918903 + 0.394483i \(0.129076\pi\)
\(548\) −1.33954e18 −2.11291
\(549\) 1.65371e18 2.57774
\(550\) 1.39372e18 2.14693
\(551\) −1.13920e15 −0.00173426
\(552\) −4.73102e18 −7.11788
\(553\) −4.94619e17 −0.735457
\(554\) 1.11254e18 1.63494
\(555\) −2.14726e18 −3.11875
\(556\) 3.35328e18 4.81375
\(557\) −6.20451e17 −0.880336 −0.440168 0.897915i \(-0.645081\pi\)
−0.440168 + 0.897915i \(0.645081\pi\)
\(558\) 4.00972e18 5.62331
\(559\) −1.18197e17 −0.163843
\(560\) −6.97002e18 −9.55019
\(561\) 4.01201e17 0.543380
\(562\) 1.33634e18 1.78908
\(563\) 1.00927e17 0.133569 0.0667844 0.997767i \(-0.478726\pi\)
0.0667844 + 0.997767i \(0.478726\pi\)
\(564\) 6.25777e17 0.818663
\(565\) −6.22699e17 −0.805311
\(566\) −5.79985e17 −0.741498
\(567\) −1.05996e18 −1.33968
\(568\) 2.53474e18 3.16715
\(569\) −3.73997e17 −0.461996 −0.230998 0.972954i \(-0.574199\pi\)
−0.230998 + 0.972954i \(0.574199\pi\)
\(570\) −4.05213e16 −0.0494877
\(571\) −9.79136e17 −1.18225 −0.591123 0.806581i \(-0.701315\pi\)
−0.591123 + 0.806581i \(0.701315\pi\)
\(572\) 1.28489e18 1.53388
\(573\) −1.98573e18 −2.34377
\(574\) 2.61731e18 3.05441
\(575\) −2.80199e18 −3.23315
\(576\) 9.64182e18 11.0005
\(577\) 1.45364e17 0.163989 0.0819944 0.996633i \(-0.473871\pi\)
0.0819944 + 0.996633i \(0.473871\pi\)
\(578\) 5.40236e17 0.602633
\(579\) 2.01549e18 2.22316
\(580\) 1.25025e18 1.36369
\(581\) 2.83818e17 0.306123
\(582\) −3.80392e18 −4.05725
\(583\) 7.21743e16 0.0761267
\(584\) −7.04211e17 −0.734547
\(585\) −5.70959e18 −5.88968
\(586\) 2.72158e18 2.77643
\(587\) −4.65718e17 −0.469868 −0.234934 0.972011i \(-0.575487\pi\)
−0.234934 + 0.972011i \(0.575487\pi\)
\(588\) −1.07458e18 −1.07222
\(589\) 1.01267e16 0.00999354
\(590\) 5.68802e18 5.55166
\(591\) 1.29326e17 0.124844
\(592\) 4.11207e18 3.92618
\(593\) 1.31998e18 1.24656 0.623278 0.782000i \(-0.285800\pi\)
0.623278 + 0.782000i \(0.285800\pi\)
\(594\) −1.47104e18 −1.37409
\(595\) −1.96851e18 −1.81877
\(596\) −1.89809e18 −1.73467
\(597\) −3.49375e18 −3.15834
\(598\) −3.48284e18 −3.11441
\(599\) 7.50536e16 0.0663891 0.0331946 0.999449i \(-0.489432\pi\)
0.0331946 + 0.999449i \(0.489432\pi\)
\(600\) 2.16100e19 18.9092
\(601\) −8.02156e17 −0.694344 −0.347172 0.937801i \(-0.612858\pi\)
−0.347172 + 0.937801i \(0.612858\pi\)
\(602\) 2.89000e17 0.247469
\(603\) 2.57191e18 2.17868
\(604\) −3.49480e18 −2.92875
\(605\) −2.05988e18 −1.70778
\(606\) −1.31428e16 −0.0107800
\(607\) −3.24862e17 −0.263617 −0.131808 0.991275i \(-0.542078\pi\)
−0.131808 + 0.991275i \(0.542078\pi\)
\(608\) 4.43952e16 0.0356421
\(609\) 5.82036e17 0.462315
\(610\) −6.17997e18 −4.85671
\(611\) 3.00241e17 0.233454
\(612\) 6.43627e18 4.95165
\(613\) −2.25554e18 −1.71695 −0.858476 0.512854i \(-0.828588\pi\)
−0.858476 + 0.512854i \(0.828588\pi\)
\(614\) −4.72022e18 −3.55523
\(615\) −6.57008e18 −4.89646
\(616\) −2.04753e18 −1.50993
\(617\) 1.09822e18 0.801373 0.400687 0.916215i \(-0.368772\pi\)
0.400687 + 0.916215i \(0.368772\pi\)
\(618\) 2.30823e18 1.66669
\(619\) 1.18029e18 0.843333 0.421666 0.906751i \(-0.361445\pi\)
0.421666 + 0.906751i \(0.361445\pi\)
\(620\) −1.11139e19 −7.85815
\(621\) 2.95745e18 2.06930
\(622\) −1.04834e17 −0.0725879
\(623\) 4.86990e17 0.333693
\(624\) 1.62150e19 10.9956
\(625\) 6.94153e18 4.65838
\(626\) 2.20508e18 1.46450
\(627\) −7.18584e15 −0.00472322
\(628\) −5.83392e17 −0.379510
\(629\) 1.16135e18 0.747713
\(630\) 1.39604e19 8.89578
\(631\) −1.91174e18 −1.20569 −0.602847 0.797857i \(-0.705967\pi\)
−0.602847 + 0.797857i \(0.705967\pi\)
\(632\) −3.93882e18 −2.45870
\(633\) −2.27949e18 −1.40836
\(634\) −1.20763e18 −0.738504
\(635\) −1.99963e18 −1.21037
\(636\) 1.71708e18 1.02877
\(637\) −5.15570e17 −0.305761
\(638\) 2.98927e17 0.175481
\(639\) −3.06474e18 −1.78089
\(640\) −1.90633e19 −10.9655
\(641\) 2.33767e18 1.33109 0.665544 0.746358i \(-0.268200\pi\)
0.665544 + 0.746358i \(0.268200\pi\)
\(642\) 3.69548e18 2.08302
\(643\) −1.43444e18 −0.800405 −0.400202 0.916427i \(-0.631060\pi\)
−0.400202 + 0.916427i \(0.631060\pi\)
\(644\) 6.31613e18 3.48894
\(645\) −7.25461e17 −0.396713
\(646\) 2.19161e16 0.0118646
\(647\) −1.59309e17 −0.0853814 −0.0426907 0.999088i \(-0.513593\pi\)
−0.0426907 + 0.999088i \(0.513593\pi\)
\(648\) −8.44086e18 −4.47867
\(649\) 1.00868e18 0.529863
\(650\) 1.59087e19 8.27365
\(651\) −5.17392e18 −2.66405
\(652\) −6.17226e18 −3.14655
\(653\) 1.39803e18 0.705635 0.352818 0.935692i \(-0.385224\pi\)
0.352818 + 0.935692i \(0.385224\pi\)
\(654\) 2.32609e18 1.16244
\(655\) 3.07000e18 1.51904
\(656\) 1.25819e19 6.16414
\(657\) 8.51458e17 0.413037
\(658\) −7.34113e17 −0.352610
\(659\) 1.98080e17 0.0942074 0.0471037 0.998890i \(-0.485001\pi\)
0.0471037 + 0.998890i \(0.485001\pi\)
\(660\) 7.88633e18 3.71398
\(661\) 4.09992e18 1.91190 0.955951 0.293528i \(-0.0948293\pi\)
0.955951 + 0.293528i \(0.0948293\pi\)
\(662\) −7.48929e18 −3.45831
\(663\) 4.57953e18 2.09403
\(664\) 2.26014e18 1.02340
\(665\) 3.52576e16 0.0158093
\(666\) −8.23616e18 −3.65714
\(667\) −6.00977e17 −0.264265
\(668\) 9.47681e18 4.12682
\(669\) 4.46404e18 1.92512
\(670\) −9.61131e18 −4.10484
\(671\) −1.09592e18 −0.463536
\(672\) −2.26823e19 −9.50138
\(673\) −1.34946e18 −0.559839 −0.279920 0.960023i \(-0.590308\pi\)
−0.279920 + 0.960023i \(0.590308\pi\)
\(674\) −2.05332e18 −0.843658
\(675\) −1.35089e19 −5.49723
\(676\) 7.54211e18 3.03976
\(677\) 1.82857e18 0.729936 0.364968 0.931020i \(-0.381080\pi\)
0.364968 + 0.931020i \(0.381080\pi\)
\(678\) −3.54206e18 −1.40043
\(679\) 3.30978e18 1.29612
\(680\) −1.56759e19 −6.08030
\(681\) −5.72092e18 −2.19791
\(682\) −2.65726e18 −1.01120
\(683\) 1.26830e18 0.478065 0.239032 0.971012i \(-0.423170\pi\)
0.239032 + 0.971012i \(0.423170\pi\)
\(684\) −1.15279e17 −0.0430412
\(685\) −3.94470e18 −1.45890
\(686\) −4.65486e18 −1.70530
\(687\) −4.19756e18 −1.52327
\(688\) 1.38928e18 0.499420
\(689\) 8.23838e17 0.293371
\(690\) −2.13768e19 −7.54090
\(691\) −2.66885e18 −0.932645 −0.466323 0.884615i \(-0.654421\pi\)
−0.466323 + 0.884615i \(0.654421\pi\)
\(692\) 8.95146e17 0.309888
\(693\) 2.47566e18 0.849035
\(694\) −5.94965e18 −2.02141
\(695\) 9.87480e18 3.32374
\(696\) 4.63496e18 1.54556
\(697\) 3.55345e18 1.17392
\(698\) 1.77716e18 0.581657
\(699\) −8.29975e18 −2.69131
\(700\) −2.88504e19 −9.26861
\(701\) −3.51309e18 −1.11821 −0.559104 0.829097i \(-0.688855\pi\)
−0.559104 + 0.829097i \(0.688855\pi\)
\(702\) −1.67913e19 −5.29534
\(703\) −2.08008e16 −0.00649934
\(704\) −6.38969e18 −1.97814
\(705\) 1.84280e18 0.565262
\(706\) 9.08234e18 2.76037
\(707\) 1.14356e16 0.00344375
\(708\) 2.39973e19 7.16056
\(709\) −3.85661e18 −1.14026 −0.570131 0.821554i \(-0.693108\pi\)
−0.570131 + 0.821554i \(0.693108\pi\)
\(710\) 1.14530e19 3.35537
\(711\) 4.76241e18 1.38253
\(712\) 3.87807e18 1.11557
\(713\) 5.34228e18 1.52281
\(714\) −1.11973e19 −3.16283
\(715\) 3.78378e18 1.05910
\(716\) −3.85128e18 −1.06824
\(717\) −8.45400e17 −0.232374
\(718\) −5.06428e18 −1.37946
\(719\) 2.57885e18 0.696127 0.348063 0.937471i \(-0.386839\pi\)
0.348063 + 0.937471i \(0.386839\pi\)
\(720\) 6.71104e19 17.9527
\(721\) −2.00839e18 −0.532437
\(722\) 7.48863e18 1.96748
\(723\) −1.30905e18 −0.340846
\(724\) 6.67950e18 1.72363
\(725\) 2.74510e18 0.702039
\(726\) −1.17171e19 −2.96982
\(727\) −6.19582e18 −1.55641 −0.778206 0.628009i \(-0.783870\pi\)
−0.778206 + 0.628009i \(0.783870\pi\)
\(728\) −2.33717e19 −5.81884
\(729\) −3.11409e18 −0.768427
\(730\) −3.18193e18 −0.778201
\(731\) 3.92368e17 0.0951110
\(732\) −2.60729e19 −6.26422
\(733\) −8.44589e17 −0.201127 −0.100563 0.994931i \(-0.532065\pi\)
−0.100563 + 0.994931i \(0.532065\pi\)
\(734\) −3.63126e18 −0.857102
\(735\) −3.16444e18 −0.740336
\(736\) 2.34204e19 5.43111
\(737\) −1.70442e18 −0.391776
\(738\) −2.52006e19 −5.74175
\(739\) −4.17152e18 −0.942117 −0.471059 0.882102i \(-0.656128\pi\)
−0.471059 + 0.882102i \(0.656128\pi\)
\(740\) 2.28285e19 5.11058
\(741\) −8.20232e16 −0.0182020
\(742\) −2.01435e18 −0.443107
\(743\) 3.56985e18 0.778436 0.389218 0.921146i \(-0.372745\pi\)
0.389218 + 0.921146i \(0.372745\pi\)
\(744\) −4.12017e19 −8.90617
\(745\) −5.58954e18 −1.19773
\(746\) 1.09118e18 0.231789
\(747\) −2.73273e18 −0.575456
\(748\) −4.26535e18 −0.890418
\(749\) −3.21544e18 −0.665439
\(750\) 6.43261e19 13.1974
\(751\) −2.79175e18 −0.567828 −0.283914 0.958850i \(-0.591633\pi\)
−0.283914 + 0.958850i \(0.591633\pi\)
\(752\) −3.52903e18 −0.711605
\(753\) 6.35783e18 1.27099
\(754\) 3.41212e18 0.676255
\(755\) −1.02916e19 −2.02221
\(756\) 3.04511e19 5.93213
\(757\) 6.80907e18 1.31512 0.657559 0.753403i \(-0.271589\pi\)
0.657559 + 0.753403i \(0.271589\pi\)
\(758\) 1.54502e19 2.95859
\(759\) −3.79084e18 −0.719721
\(760\) 2.80768e17 0.0528518
\(761\) −1.38388e18 −0.258284 −0.129142 0.991626i \(-0.541222\pi\)
−0.129142 + 0.991626i \(0.541222\pi\)
\(762\) −1.13743e19 −2.10484
\(763\) −2.02392e18 −0.371351
\(764\) 2.11112e19 3.84066
\(765\) 1.89537e19 3.41896
\(766\) 2.30640e16 0.00412523
\(767\) 1.15137e19 2.04194
\(768\) −5.54951e19 −9.75904
\(769\) −1.00650e19 −1.75506 −0.877532 0.479517i \(-0.840812\pi\)
−0.877532 + 0.479517i \(0.840812\pi\)
\(770\) −9.25163e18 −1.59966
\(771\) −1.38742e18 −0.237878
\(772\) −2.14276e19 −3.64301
\(773\) 1.17031e18 0.197303 0.0986516 0.995122i \(-0.468547\pi\)
0.0986516 + 0.995122i \(0.468547\pi\)
\(774\) −2.78262e18 −0.465198
\(775\) −2.44021e19 −4.04545
\(776\) 2.63569e19 4.33305
\(777\) 1.06275e19 1.73258
\(778\) −1.18844e19 −1.92136
\(779\) −6.36452e16 −0.0102040
\(780\) 9.00190e19 14.3126
\(781\) 2.03102e18 0.320245
\(782\) 1.15617e19 1.80791
\(783\) −2.89740e18 −0.449322
\(784\) 6.06000e18 0.932005
\(785\) −1.71799e18 −0.262040
\(786\) 1.74628e19 2.64161
\(787\) −9.73964e17 −0.146119 −0.0730596 0.997328i \(-0.523276\pi\)
−0.0730596 + 0.997328i \(0.523276\pi\)
\(788\) −1.37493e18 −0.204578
\(789\) 4.16925e17 0.0615259
\(790\) −1.77973e19 −2.60482
\(791\) 3.08194e18 0.447380
\(792\) 1.97146e19 2.83840
\(793\) −1.25095e19 −1.78634
\(794\) 1.46371e19 2.07311
\(795\) 5.05650e18 0.710336
\(796\) 3.71436e19 5.17546
\(797\) 1.30069e18 0.179760 0.0898802 0.995953i \(-0.471352\pi\)
0.0898802 + 0.995953i \(0.471352\pi\)
\(798\) 2.00553e17 0.0274923
\(799\) −9.96686e17 −0.135520
\(800\) −1.06978e20 −14.4281
\(801\) −4.68895e18 −0.627284
\(802\) −2.58130e19 −3.42535
\(803\) −5.64266e17 −0.0742733
\(804\) −4.05494e19 −5.29445
\(805\) 1.85999e19 2.40900
\(806\) −3.03315e19 −3.89687
\(807\) 6.60486e18 0.841755
\(808\) 9.10653e16 0.0115128
\(809\) −7.49277e18 −0.939674 −0.469837 0.882753i \(-0.655687\pi\)
−0.469837 + 0.882753i \(0.655687\pi\)
\(810\) −3.81394e19 −4.74484
\(811\) −1.49228e19 −1.84168 −0.920840 0.389940i \(-0.872496\pi\)
−0.920840 + 0.389940i \(0.872496\pi\)
\(812\) −6.18789e18 −0.757579
\(813\) −7.63810e18 −0.927677
\(814\) 5.45815e18 0.657637
\(815\) −1.81762e19 −2.17260
\(816\) −5.38278e19 −6.38293
\(817\) −7.02763e15 −0.000826734 0
\(818\) 2.29840e19 2.68244
\(819\) 2.82586e19 3.27194
\(820\) 6.98495e19 8.02367
\(821\) 1.17393e18 0.133787 0.0668933 0.997760i \(-0.478691\pi\)
0.0668933 + 0.997760i \(0.478691\pi\)
\(822\) −2.24383e19 −2.53702
\(823\) −2.20418e18 −0.247257 −0.123628 0.992329i \(-0.539453\pi\)
−0.123628 + 0.992329i \(0.539453\pi\)
\(824\) −1.59935e19 −1.77999
\(825\) 1.73155e19 1.91199
\(826\) −2.81518e19 −3.08415
\(827\) −5.49950e18 −0.597774 −0.298887 0.954288i \(-0.596615\pi\)
−0.298887 + 0.954288i \(0.596615\pi\)
\(828\) −6.08145e19 −6.55858
\(829\) −6.12336e18 −0.655217 −0.327608 0.944814i \(-0.606243\pi\)
−0.327608 + 0.944814i \(0.606243\pi\)
\(830\) 1.02123e19 1.08422
\(831\) 1.38222e19 1.45603
\(832\) −7.29354e19 −7.62319
\(833\) 1.71150e18 0.177494
\(834\) 5.61701e19 5.77998
\(835\) 2.79075e19 2.84944
\(836\) 7.63958e16 0.00773978
\(837\) 2.57560e19 2.58918
\(838\) 2.08300e19 2.07780
\(839\) −9.02974e18 −0.893763 −0.446882 0.894593i \(-0.647465\pi\)
−0.446882 + 0.894593i \(0.647465\pi\)
\(840\) −1.43449e20 −14.0891
\(841\) −9.67185e18 −0.942618
\(842\) 1.18478e19 1.14580
\(843\) 1.66027e19 1.59330
\(844\) 2.42342e19 2.30783
\(845\) 2.22102e19 2.09886
\(846\) 7.06836e18 0.662844
\(847\) 1.01950e19 0.948734
\(848\) −9.68337e18 −0.894239
\(849\) −7.20573e18 −0.660356
\(850\) −5.28107e19 −4.80285
\(851\) −1.09733e19 −0.990365
\(852\) 4.83195e19 4.32778
\(853\) −6.55050e18 −0.582245 −0.291122 0.956686i \(-0.594029\pi\)
−0.291122 + 0.956686i \(0.594029\pi\)
\(854\) 3.05867e19 2.69809
\(855\) −3.39475e17 −0.0297186
\(856\) −2.56056e19 −2.22462
\(857\) 6.50889e18 0.561218 0.280609 0.959822i \(-0.409464\pi\)
0.280609 + 0.959822i \(0.409464\pi\)
\(858\) 2.15230e19 1.84177
\(859\) 9.41857e18 0.799888 0.399944 0.916540i \(-0.369030\pi\)
0.399944 + 0.916540i \(0.369030\pi\)
\(860\) 7.71270e18 0.650080
\(861\) 3.25174e19 2.72017
\(862\) 2.43811e18 0.202422
\(863\) −2.27295e19 −1.87292 −0.936462 0.350770i \(-0.885920\pi\)
−0.936462 + 0.350770i \(0.885920\pi\)
\(864\) 1.12914e20 9.23436
\(865\) 2.63605e18 0.213968
\(866\) 2.73743e19 2.20534
\(867\) 6.71189e18 0.536687
\(868\) 5.50062e19 4.36549
\(869\) −3.15607e18 −0.248610
\(870\) 2.09427e19 1.63741
\(871\) −1.94552e19 −1.50979
\(872\) −1.61172e19 −1.24146
\(873\) −3.18680e19 −2.43648
\(874\) −2.07079e17 −0.0157149
\(875\) −5.59700e19 −4.21603
\(876\) −1.34243e19 −1.00373
\(877\) 1.76604e19 1.31070 0.655349 0.755326i \(-0.272521\pi\)
0.655349 + 0.755326i \(0.272521\pi\)
\(878\) 4.18638e18 0.308407
\(879\) 3.38129e19 2.47260
\(880\) −4.44745e19 −3.22830
\(881\) 5.96749e18 0.429980 0.214990 0.976616i \(-0.431028\pi\)
0.214990 + 0.976616i \(0.431028\pi\)
\(882\) −1.21377e19 −0.868142
\(883\) −2.08226e19 −1.47840 −0.739199 0.673487i \(-0.764796\pi\)
−0.739199 + 0.673487i \(0.764796\pi\)
\(884\) −4.86871e19 −3.43142
\(885\) 7.06679e19 4.94414
\(886\) −2.31696e19 −1.60916
\(887\) 2.04703e19 1.41130 0.705652 0.708559i \(-0.250654\pi\)
0.705652 + 0.708559i \(0.250654\pi\)
\(888\) 8.46302e19 5.79217
\(889\) 9.89678e18 0.672408
\(890\) 1.75228e19 1.18186
\(891\) −6.76344e18 −0.452858
\(892\) −4.74591e19 −3.15463
\(893\) 1.78514e16 0.00117798
\(894\) −3.17946e19 −2.08286
\(895\) −1.13413e19 −0.737589
\(896\) 9.43505e19 6.09175
\(897\) −4.32708e19 −2.77360
\(898\) −5.59603e19 −3.56110
\(899\) −5.23381e18 −0.330659
\(900\) 2.77784e20 17.4233
\(901\) −2.73483e18 −0.170302
\(902\) 1.67006e19 1.03250
\(903\) 3.59054e18 0.220389
\(904\) 2.45425e19 1.49563
\(905\) 1.96699e19 1.19011
\(906\) −5.85407e19 −3.51662
\(907\) 4.29432e18 0.256122 0.128061 0.991766i \(-0.459125\pi\)
0.128061 + 0.991766i \(0.459125\pi\)
\(908\) 6.08217e19 3.60164
\(909\) −1.10107e17 −0.00647363
\(910\) −1.05603e20 −6.16465
\(911\) 7.01680e18 0.406696 0.203348 0.979107i \(-0.434818\pi\)
0.203348 + 0.979107i \(0.434818\pi\)
\(912\) 9.64099e17 0.0554824
\(913\) 1.81099e18 0.103480
\(914\) −5.11771e19 −2.90352
\(915\) −7.67800e19 −4.32525
\(916\) 4.46261e19 2.49614
\(917\) −1.51944e19 −0.843884
\(918\) 5.57408e19 3.07394
\(919\) −1.05945e19 −0.580138 −0.290069 0.957006i \(-0.593678\pi\)
−0.290069 + 0.957006i \(0.593678\pi\)
\(920\) 1.48117e20 8.05351
\(921\) −5.86440e19 −3.16618
\(922\) 3.86590e19 2.07252
\(923\) 2.31832e19 1.23413
\(924\) −3.90320e19 −2.06325
\(925\) 5.01231e19 2.63097
\(926\) 6.42140e18 0.334702
\(927\) 1.93376e19 1.00089
\(928\) −2.29449e19 −1.17930
\(929\) 3.37128e19 1.72065 0.860325 0.509745i \(-0.170260\pi\)
0.860325 + 0.509745i \(0.170260\pi\)
\(930\) −1.86167e20 −9.43546
\(931\) −3.06543e16 −0.00154283
\(932\) 8.82383e19 4.41015
\(933\) −1.30246e18 −0.0646446
\(934\) −2.92716e19 −1.44275
\(935\) −1.25607e19 −0.614806
\(936\) 2.25033e20 10.9384
\(937\) −2.27391e19 −1.09765 −0.548827 0.835936i \(-0.684926\pi\)
−0.548827 + 0.835936i \(0.684926\pi\)
\(938\) 4.75694e19 2.28039
\(939\) 2.73958e19 1.30424
\(940\) −1.95916e19 −0.926275
\(941\) −3.61551e19 −1.69761 −0.848803 0.528710i \(-0.822676\pi\)
−0.848803 + 0.528710i \(0.822676\pi\)
\(942\) −9.77230e18 −0.455686
\(943\) −3.35756e19 −1.55488
\(944\) −1.35331e20 −6.22416
\(945\) 8.96730e19 4.09595
\(946\) 1.84406e18 0.0836532
\(947\) −9.62334e18 −0.433562 −0.216781 0.976220i \(-0.569556\pi\)
−0.216781 + 0.976220i \(0.569556\pi\)
\(948\) −7.50854e19 −3.35971
\(949\) −6.44085e18 −0.286228
\(950\) 9.45883e17 0.0417478
\(951\) −1.50036e19 −0.657689
\(952\) 7.75851e19 3.37783
\(953\) 3.47215e18 0.150139 0.0750696 0.997178i \(-0.476082\pi\)
0.0750696 + 0.997178i \(0.476082\pi\)
\(954\) 1.93950e19 0.832963
\(955\) 6.21687e19 2.65185
\(956\) 8.98782e18 0.380783
\(957\) 3.71387e18 0.156278
\(958\) −4.20650e19 −1.75810
\(959\) 1.95236e19 0.810472
\(960\) −4.47659e20 −18.4580
\(961\) 2.21076e19 0.905396
\(962\) 6.23023e19 2.53435
\(963\) 3.09596e19 1.25091
\(964\) 1.39171e19 0.558533
\(965\) −6.31004e19 −2.51538
\(966\) 1.05800e20 4.18925
\(967\) −3.43617e19 −1.35146 −0.675728 0.737151i \(-0.736171\pi\)
−0.675728 + 0.737151i \(0.736171\pi\)
\(968\) 8.11862e19 3.17170
\(969\) 2.72286e17 0.0105662
\(970\) 1.19092e20 4.59056
\(971\) −1.02390e19 −0.392043 −0.196022 0.980600i \(-0.562802\pi\)
−0.196022 + 0.980600i \(0.562802\pi\)
\(972\) −1.92978e19 −0.733966
\(973\) −4.88735e19 −1.84646
\(974\) −3.15509e18 −0.118407
\(975\) 1.97649e20 7.36827
\(976\) 1.47036e20 5.44503
\(977\) −3.73637e19 −1.37447 −0.687234 0.726436i \(-0.741175\pi\)
−0.687234 + 0.726436i \(0.741175\pi\)
\(978\) −1.03390e20 −3.77814
\(979\) 3.10739e18 0.112800
\(980\) 3.36425e19 1.21316
\(981\) 1.94872e19 0.698074
\(982\) 7.72244e19 2.74808
\(983\) −1.02116e19 −0.360990 −0.180495 0.983576i \(-0.557770\pi\)
−0.180495 + 0.983576i \(0.557770\pi\)
\(984\) 2.58948e20 9.09377
\(985\) −4.04891e18 −0.141255
\(986\) −1.13269e19 −0.392566
\(987\) −9.12061e18 −0.314024
\(988\) 8.72024e17 0.0298269
\(989\) −3.70738e18 −0.125977
\(990\) 8.90788e19 3.00708
\(991\) 4.03029e19 1.35163 0.675815 0.737071i \(-0.263792\pi\)
0.675815 + 0.737071i \(0.263792\pi\)
\(992\) 2.03965e20 6.79562
\(993\) −9.30470e19 −3.07987
\(994\) −5.66847e19 −1.86403
\(995\) 1.09381e20 3.57350
\(996\) 4.30849e19 1.39843
\(997\) 1.98736e19 0.640851 0.320426 0.947274i \(-0.396174\pi\)
0.320426 + 0.947274i \(0.396174\pi\)
\(998\) −6.06560e19 −1.94324
\(999\) −5.29040e19 −1.68389
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 197.14.a.a.1.1 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.a.1.1 104 1.1 even 1 trivial