Properties

Label 197.14.a.a.1.10
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 1.10
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)
 
\(f(q)\) \(=\) \(q-156.182 q^{2} +145.398 q^{3} +16200.7 q^{4} -42219.2 q^{5} -22708.4 q^{6} +140720. q^{7} -1.25081e6 q^{8} -1.57318e6 q^{9} +O(q^{10})\) \(q-156.182 q^{2} +145.398 q^{3} +16200.7 q^{4} -42219.2 q^{5} -22708.4 q^{6} +140720. q^{7} -1.25081e6 q^{8} -1.57318e6 q^{9} +6.59387e6 q^{10} +1.01012e7 q^{11} +2.35555e6 q^{12} +2.70916e7 q^{13} -2.19779e7 q^{14} -6.13857e6 q^{15} +6.26381e7 q^{16} -7.94734e7 q^{17} +2.45702e8 q^{18} -3.02415e8 q^{19} -6.83982e8 q^{20} +2.04604e7 q^{21} -1.57763e9 q^{22} +1.22651e9 q^{23} -1.81865e8 q^{24} +5.61759e8 q^{25} -4.23121e9 q^{26} -4.60548e8 q^{27} +2.27977e9 q^{28} -2.20816e9 q^{29} +9.58733e8 q^{30} -6.83081e8 q^{31} +4.63754e8 q^{32} +1.46869e9 q^{33} +1.24123e10 q^{34} -5.94110e9 q^{35} -2.54867e10 q^{36} +2.15026e10 q^{37} +4.72317e10 q^{38} +3.93906e9 q^{39} +5.28084e10 q^{40} -2.01349e10 q^{41} -3.19554e9 q^{42} -7.18113e10 q^{43} +1.63647e11 q^{44} +6.64185e10 q^{45} -1.91558e11 q^{46} +1.65782e10 q^{47} +9.10743e9 q^{48} -7.70868e10 q^{49} -8.77365e10 q^{50} -1.15552e10 q^{51} +4.38904e11 q^{52} +2.28728e11 q^{53} +7.19291e10 q^{54} -4.26466e11 q^{55} -1.76015e11 q^{56} -4.39705e10 q^{57} +3.44874e11 q^{58} -5.15415e11 q^{59} -9.94493e10 q^{60} +1.40601e11 q^{61} +1.06685e11 q^{62} -2.21379e11 q^{63} -5.85561e11 q^{64} -1.14379e12 q^{65} -2.29383e11 q^{66} +2.53048e11 q^{67} -1.28753e12 q^{68} +1.78331e11 q^{69} +9.27892e11 q^{70} -1.59034e12 q^{71} +1.96776e12 q^{72} +1.28348e12 q^{73} -3.35832e12 q^{74} +8.16784e10 q^{75} -4.89934e12 q^{76} +1.42145e12 q^{77} -6.15208e11 q^{78} -2.01437e12 q^{79} -2.64453e12 q^{80} +2.44120e12 q^{81} +3.14469e12 q^{82} +1.86340e12 q^{83} +3.31473e11 q^{84} +3.35530e12 q^{85} +1.12156e13 q^{86} -3.21061e11 q^{87} -1.26348e13 q^{88} +4.05006e12 q^{89} -1.03734e13 q^{90} +3.81234e12 q^{91} +1.98703e13 q^{92} -9.93184e10 q^{93} -2.58921e12 q^{94} +1.27677e13 q^{95} +6.74287e10 q^{96} +4.35140e12 q^{97} +1.20395e13 q^{98} -1.58911e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −156.182 −1.72558 −0.862790 0.505562i \(-0.831285\pi\)
−0.862790 + 0.505562i \(0.831285\pi\)
\(3\) 145.398 0.115151 0.0575757 0.998341i \(-0.481663\pi\)
0.0575757 + 0.998341i \(0.481663\pi\)
\(4\) 16200.7 1.97763
\(5\) −42219.2 −1.20838 −0.604192 0.796839i \(-0.706504\pi\)
−0.604192 + 0.796839i \(0.706504\pi\)
\(6\) −22708.4 −0.198703
\(7\) 140720. 0.452085 0.226042 0.974117i \(-0.427421\pi\)
0.226042 + 0.974117i \(0.427421\pi\)
\(8\) −1.25081e6 −1.68697
\(9\) −1.57318e6 −0.986740
\(10\) 6.59387e6 2.08516
\(11\) 1.01012e7 1.71918 0.859590 0.510984i \(-0.170719\pi\)
0.859590 + 0.510984i \(0.170719\pi\)
\(12\) 2.35555e6 0.227726
\(13\) 2.70916e7 1.55669 0.778347 0.627835i \(-0.216059\pi\)
0.778347 + 0.627835i \(0.216059\pi\)
\(14\) −2.19779e7 −0.780108
\(15\) −6.13857e6 −0.139147
\(16\) 6.26381e7 0.933380
\(17\) −7.94734e7 −0.798553 −0.399276 0.916831i \(-0.630739\pi\)
−0.399276 + 0.916831i \(0.630739\pi\)
\(18\) 2.45702e8 1.70270
\(19\) −3.02415e8 −1.47471 −0.737353 0.675508i \(-0.763924\pi\)
−0.737353 + 0.675508i \(0.763924\pi\)
\(20\) −6.83982e8 −2.38973
\(21\) 2.04604e7 0.0520582
\(22\) −1.57763e9 −2.96658
\(23\) 1.22651e9 1.72758 0.863791 0.503850i \(-0.168084\pi\)
0.863791 + 0.503850i \(0.168084\pi\)
\(24\) −1.81865e8 −0.194257
\(25\) 5.61759e8 0.460193
\(26\) −4.23121e9 −2.68620
\(27\) −4.60548e8 −0.228776
\(28\) 2.27977e9 0.894055
\(29\) −2.20816e9 −0.689357 −0.344678 0.938721i \(-0.612012\pi\)
−0.344678 + 0.938721i \(0.612012\pi\)
\(30\) 9.58733e8 0.240110
\(31\) −6.83081e8 −0.138236 −0.0691181 0.997608i \(-0.522019\pi\)
−0.0691181 + 0.997608i \(0.522019\pi\)
\(32\) 4.63754e8 0.0763507
\(33\) 1.46869e9 0.197966
\(34\) 1.24123e10 1.37797
\(35\) −5.94110e9 −0.546292
\(36\) −2.54867e10 −1.95140
\(37\) 2.15026e10 1.37778 0.688890 0.724865i \(-0.258098\pi\)
0.688890 + 0.724865i \(0.258098\pi\)
\(38\) 4.72317e10 2.54472
\(39\) 3.93906e9 0.179255
\(40\) 5.28084e10 2.03851
\(41\) −2.01349e10 −0.661993 −0.330996 0.943632i \(-0.607385\pi\)
−0.330996 + 0.943632i \(0.607385\pi\)
\(42\) −3.19554e9 −0.0898305
\(43\) −7.18113e10 −1.73240 −0.866199 0.499700i \(-0.833444\pi\)
−0.866199 + 0.499700i \(0.833444\pi\)
\(44\) 1.63647e11 3.39990
\(45\) 6.64185e10 1.19236
\(46\) −1.91558e11 −2.98108
\(47\) 1.65782e10 0.224337 0.112168 0.993689i \(-0.464220\pi\)
0.112168 + 0.993689i \(0.464220\pi\)
\(48\) 9.10743e9 0.107480
\(49\) −7.70868e10 −0.795619
\(50\) −8.77365e10 −0.794100
\(51\) −1.15552e10 −0.0919545
\(52\) 4.38904e11 3.07856
\(53\) 2.28728e11 1.41751 0.708754 0.705455i \(-0.249257\pi\)
0.708754 + 0.705455i \(0.249257\pi\)
\(54\) 7.19291e10 0.394771
\(55\) −4.26466e11 −2.07743
\(56\) −1.76015e11 −0.762655
\(57\) −4.39705e10 −0.169814
\(58\) 3.44874e11 1.18954
\(59\) −5.15415e11 −1.59081 −0.795407 0.606076i \(-0.792743\pi\)
−0.795407 + 0.606076i \(0.792743\pi\)
\(60\) −9.94493e10 −0.275181
\(61\) 1.40601e11 0.349418 0.174709 0.984620i \(-0.444102\pi\)
0.174709 + 0.984620i \(0.444102\pi\)
\(62\) 1.06685e11 0.238537
\(63\) −2.21379e11 −0.446090
\(64\) −5.85561e11 −1.06513
\(65\) −1.14379e12 −1.88108
\(66\) −2.29383e11 −0.341606
\(67\) 2.53048e11 0.341757 0.170878 0.985292i \(-0.445339\pi\)
0.170878 + 0.985292i \(0.445339\pi\)
\(68\) −1.28753e12 −1.57924
\(69\) 1.78331e11 0.198933
\(70\) 9.27892e11 0.942671
\(71\) −1.59034e12 −1.47337 −0.736685 0.676236i \(-0.763610\pi\)
−0.736685 + 0.676236i \(0.763610\pi\)
\(72\) 1.96776e12 1.66460
\(73\) 1.28348e12 0.992634 0.496317 0.868141i \(-0.334685\pi\)
0.496317 + 0.868141i \(0.334685\pi\)
\(74\) −3.35832e12 −2.37747
\(75\) 8.16784e10 0.0529919
\(76\) −4.89934e12 −2.91642
\(77\) 1.42145e12 0.777215
\(78\) −6.15208e11 −0.309320
\(79\) −2.01437e12 −0.932315 −0.466157 0.884702i \(-0.654362\pi\)
−0.466157 + 0.884702i \(0.654362\pi\)
\(80\) −2.64453e12 −1.12788
\(81\) 2.44120e12 0.960396
\(82\) 3.14469e12 1.14232
\(83\) 1.86340e12 0.625602 0.312801 0.949819i \(-0.398733\pi\)
0.312801 + 0.949819i \(0.398733\pi\)
\(84\) 3.31473e11 0.102952
\(85\) 3.35530e12 0.964959
\(86\) 1.12156e13 2.98939
\(87\) −3.21061e11 −0.0793804
\(88\) −1.26348e13 −2.90021
\(89\) 4.05006e12 0.863826 0.431913 0.901915i \(-0.357839\pi\)
0.431913 + 0.901915i \(0.357839\pi\)
\(90\) −1.03734e13 −2.05752
\(91\) 3.81234e12 0.703757
\(92\) 1.98703e13 3.41651
\(93\) −9.93184e10 −0.0159181
\(94\) −2.58921e12 −0.387111
\(95\) 1.27677e13 1.78201
\(96\) 6.74287e10 0.00879188
\(97\) 4.35140e12 0.530411 0.265206 0.964192i \(-0.414560\pi\)
0.265206 + 0.964192i \(0.414560\pi\)
\(98\) 1.20395e13 1.37291
\(99\) −1.58911e13 −1.69638
\(100\) 9.10090e12 0.910090
\(101\) −1.38940e13 −1.30238 −0.651192 0.758913i \(-0.725731\pi\)
−0.651192 + 0.758913i \(0.725731\pi\)
\(102\) 1.80472e12 0.158675
\(103\) −2.39762e13 −1.97851 −0.989255 0.146203i \(-0.953295\pi\)
−0.989255 + 0.146203i \(0.953295\pi\)
\(104\) −3.38866e13 −2.62610
\(105\) −8.63822e11 −0.0629063
\(106\) −3.57231e13 −2.44602
\(107\) 3.47469e12 0.223832 0.111916 0.993718i \(-0.464301\pi\)
0.111916 + 0.993718i \(0.464301\pi\)
\(108\) −7.46120e12 −0.452433
\(109\) 1.17165e12 0.0669154 0.0334577 0.999440i \(-0.489348\pi\)
0.0334577 + 0.999440i \(0.489348\pi\)
\(110\) 6.66061e13 3.58477
\(111\) 3.12643e12 0.158653
\(112\) 8.81446e12 0.421967
\(113\) 2.58831e13 1.16952 0.584758 0.811208i \(-0.301190\pi\)
0.584758 + 0.811208i \(0.301190\pi\)
\(114\) 6.86738e12 0.293028
\(115\) −5.17821e13 −2.08758
\(116\) −3.57738e13 −1.36329
\(117\) −4.26201e13 −1.53605
\(118\) 8.04984e13 2.74508
\(119\) −1.11835e13 −0.361014
\(120\) 7.67822e12 0.234737
\(121\) 6.75120e13 1.95558
\(122\) −2.19593e13 −0.602949
\(123\) −2.92756e12 −0.0762294
\(124\) −1.10664e13 −0.273379
\(125\) 2.78201e13 0.652294
\(126\) 3.45753e13 0.769764
\(127\) 8.07463e13 1.70765 0.853825 0.520561i \(-0.174277\pi\)
0.853825 + 0.520561i \(0.174277\pi\)
\(128\) 8.76548e13 1.76162
\(129\) −1.04412e13 −0.199488
\(130\) 1.78639e14 3.24596
\(131\) 8.22895e13 1.42259 0.711297 0.702892i \(-0.248108\pi\)
0.711297 + 0.702892i \(0.248108\pi\)
\(132\) 2.37939e13 0.391503
\(133\) −4.25560e13 −0.666692
\(134\) −3.95215e13 −0.589728
\(135\) 1.94440e13 0.276449
\(136\) 9.94065e13 1.34714
\(137\) −4.05438e13 −0.523890 −0.261945 0.965083i \(-0.584364\pi\)
−0.261945 + 0.965083i \(0.584364\pi\)
\(138\) −2.78520e13 −0.343276
\(139\) −1.58298e14 −1.86157 −0.930783 0.365572i \(-0.880873\pi\)
−0.930783 + 0.365572i \(0.880873\pi\)
\(140\) −9.62501e13 −1.08036
\(141\) 2.41043e12 0.0258327
\(142\) 2.48383e14 2.54242
\(143\) 2.73658e14 2.67624
\(144\) −9.85411e13 −0.921004
\(145\) 9.32269e13 0.833008
\(146\) −2.00455e14 −1.71287
\(147\) −1.12082e13 −0.0916167
\(148\) 3.48358e14 2.72474
\(149\) 1.91701e14 1.43520 0.717602 0.696454i \(-0.245240\pi\)
0.717602 + 0.696454i \(0.245240\pi\)
\(150\) −1.27567e13 −0.0914417
\(151\) 1.41076e14 0.968511 0.484255 0.874927i \(-0.339091\pi\)
0.484255 + 0.874927i \(0.339091\pi\)
\(152\) 3.78265e14 2.48779
\(153\) 1.25026e14 0.787964
\(154\) −2.22004e14 −1.34115
\(155\) 2.88392e13 0.167042
\(156\) 6.38155e13 0.354500
\(157\) 4.64114e13 0.247330 0.123665 0.992324i \(-0.460535\pi\)
0.123665 + 0.992324i \(0.460535\pi\)
\(158\) 3.14607e14 1.60878
\(159\) 3.32565e13 0.163228
\(160\) −1.95793e13 −0.0922610
\(161\) 1.72594e14 0.781013
\(162\) −3.81270e14 −1.65724
\(163\) 2.55936e14 1.06884 0.534418 0.845220i \(-0.320531\pi\)
0.534418 + 0.845220i \(0.320531\pi\)
\(164\) −3.26199e14 −1.30917
\(165\) −6.20071e13 −0.239219
\(166\) −2.91028e14 −1.07953
\(167\) −9.12125e13 −0.325385 −0.162692 0.986677i \(-0.552018\pi\)
−0.162692 + 0.986677i \(0.552018\pi\)
\(168\) −2.55922e13 −0.0878207
\(169\) 4.31081e14 1.42330
\(170\) −5.24037e14 −1.66511
\(171\) 4.75754e14 1.45515
\(172\) −1.16339e15 −3.42604
\(173\) 2.19464e13 0.0622392 0.0311196 0.999516i \(-0.490093\pi\)
0.0311196 + 0.999516i \(0.490093\pi\)
\(174\) 5.01439e13 0.136977
\(175\) 7.90510e13 0.208046
\(176\) 6.32721e14 1.60465
\(177\) −7.49402e13 −0.183184
\(178\) −6.32545e14 −1.49060
\(179\) −1.18994e14 −0.270384 −0.135192 0.990819i \(-0.543165\pi\)
−0.135192 + 0.990819i \(0.543165\pi\)
\(180\) 1.07603e15 2.35805
\(181\) −2.24422e14 −0.474412 −0.237206 0.971459i \(-0.576232\pi\)
−0.237206 + 0.971459i \(0.576232\pi\)
\(182\) −5.95418e14 −1.21439
\(183\) 2.04431e13 0.0402360
\(184\) −1.53413e15 −2.91438
\(185\) −9.07824e14 −1.66489
\(186\) 1.55117e13 0.0274679
\(187\) −8.02778e14 −1.37286
\(188\) 2.68578e14 0.443655
\(189\) −6.48085e13 −0.103426
\(190\) −1.99409e15 −3.07500
\(191\) 1.02189e15 1.52295 0.761474 0.648195i \(-0.224476\pi\)
0.761474 + 0.648195i \(0.224476\pi\)
\(192\) −8.51392e13 −0.122651
\(193\) −1.32634e14 −0.184728 −0.0923640 0.995725i \(-0.529442\pi\)
−0.0923640 + 0.995725i \(0.529442\pi\)
\(194\) −6.79609e14 −0.915267
\(195\) −1.66304e14 −0.216609
\(196\) −1.24886e15 −1.57344
\(197\) −5.84517e13 −0.0712470
\(198\) 2.48189e15 2.92725
\(199\) −1.18083e15 −1.34785 −0.673925 0.738800i \(-0.735393\pi\)
−0.673925 + 0.738800i \(0.735393\pi\)
\(200\) −7.02657e14 −0.776333
\(201\) 3.67926e13 0.0393537
\(202\) 2.16999e15 2.24737
\(203\) −3.10733e14 −0.311648
\(204\) −1.87203e14 −0.181852
\(205\) 8.50078e14 0.799942
\(206\) 3.74464e15 3.41408
\(207\) −1.92952e15 −1.70467
\(208\) 1.69697e15 1.45299
\(209\) −3.05476e15 −2.53529
\(210\) 1.34913e14 0.108550
\(211\) −2.59301e14 −0.202287 −0.101143 0.994872i \(-0.532250\pi\)
−0.101143 + 0.994872i \(0.532250\pi\)
\(212\) 3.70555e15 2.80330
\(213\) −2.31232e14 −0.169661
\(214\) −5.42683e14 −0.386240
\(215\) 3.03181e15 2.09340
\(216\) 5.76060e14 0.385939
\(217\) −9.61235e13 −0.0624944
\(218\) −1.82990e14 −0.115468
\(219\) 1.86614e14 0.114303
\(220\) −6.90905e15 −4.10838
\(221\) −2.15306e15 −1.24310
\(222\) −4.88291e14 −0.273769
\(223\) −2.70804e15 −1.47460 −0.737299 0.675567i \(-0.763899\pi\)
−0.737299 + 0.675567i \(0.763899\pi\)
\(224\) 6.52596e13 0.0345170
\(225\) −8.83750e14 −0.454091
\(226\) −4.04246e15 −2.01809
\(227\) 6.30594e14 0.305902 0.152951 0.988234i \(-0.451122\pi\)
0.152951 + 0.988234i \(0.451122\pi\)
\(228\) −7.12353e14 −0.335829
\(229\) −1.68684e15 −0.772937 −0.386468 0.922303i \(-0.626305\pi\)
−0.386468 + 0.922303i \(0.626305\pi\)
\(230\) 8.08742e15 3.60229
\(231\) 2.06675e14 0.0894974
\(232\) 2.76200e15 1.16293
\(233\) 1.12024e15 0.458667 0.229334 0.973348i \(-0.426345\pi\)
0.229334 + 0.973348i \(0.426345\pi\)
\(234\) 6.65647e15 2.65058
\(235\) −6.99918e14 −0.271085
\(236\) −8.35010e15 −3.14603
\(237\) −2.92884e14 −0.107357
\(238\) 1.74666e15 0.622958
\(239\) 5.25075e15 1.82236 0.911181 0.412006i \(-0.135172\pi\)
0.911181 + 0.412006i \(0.135172\pi\)
\(240\) −3.84508e14 −0.129877
\(241\) 2.28199e15 0.750246 0.375123 0.926975i \(-0.377600\pi\)
0.375123 + 0.926975i \(0.377600\pi\)
\(242\) −1.05441e16 −3.37451
\(243\) 1.08921e15 0.339367
\(244\) 2.27784e15 0.691018
\(245\) 3.25454e15 0.961414
\(246\) 4.57231e14 0.131540
\(247\) −8.19292e15 −2.29566
\(248\) 8.54408e14 0.233201
\(249\) 2.70934e14 0.0720389
\(250\) −4.34499e15 −1.12559
\(251\) 2.18163e15 0.550683 0.275342 0.961346i \(-0.411209\pi\)
0.275342 + 0.961346i \(0.411209\pi\)
\(252\) −3.58650e15 −0.882200
\(253\) 1.23892e16 2.97003
\(254\) −1.26111e16 −2.94669
\(255\) 4.87853e14 0.111116
\(256\) −8.89316e15 −1.97468
\(257\) −5.82816e14 −0.126173 −0.0630864 0.998008i \(-0.520094\pi\)
−0.0630864 + 0.998008i \(0.520094\pi\)
\(258\) 1.63072e15 0.344232
\(259\) 3.02586e15 0.622874
\(260\) −1.85302e16 −3.72008
\(261\) 3.47384e15 0.680216
\(262\) −1.28521e16 −2.45480
\(263\) −8.54114e15 −1.59149 −0.795744 0.605633i \(-0.792920\pi\)
−0.795744 + 0.605633i \(0.792920\pi\)
\(264\) −1.83706e15 −0.333963
\(265\) −9.65671e15 −1.71290
\(266\) 6.64647e15 1.15043
\(267\) 5.88869e14 0.0994707
\(268\) 4.09956e15 0.675867
\(269\) −2.03560e15 −0.327569 −0.163784 0.986496i \(-0.552370\pi\)
−0.163784 + 0.986496i \(0.552370\pi\)
\(270\) −3.03679e15 −0.477035
\(271\) −9.13857e15 −1.40145 −0.700726 0.713431i \(-0.747140\pi\)
−0.700726 + 0.713431i \(0.747140\pi\)
\(272\) −4.97806e15 −0.745353
\(273\) 5.54306e14 0.0810386
\(274\) 6.33219e15 0.904015
\(275\) 5.67445e15 0.791155
\(276\) 2.88909e15 0.393416
\(277\) −1.68445e15 −0.224048 −0.112024 0.993706i \(-0.535733\pi\)
−0.112024 + 0.993706i \(0.535733\pi\)
\(278\) 2.47232e16 3.21228
\(279\) 1.07461e15 0.136403
\(280\) 7.43122e15 0.921580
\(281\) 4.98535e15 0.604094 0.302047 0.953293i \(-0.402330\pi\)
0.302047 + 0.953293i \(0.402330\pi\)
\(282\) −3.76465e14 −0.0445764
\(283\) 4.42735e15 0.512309 0.256154 0.966636i \(-0.417544\pi\)
0.256154 + 0.966636i \(0.417544\pi\)
\(284\) −2.57647e16 −2.91378
\(285\) 1.85640e15 0.205201
\(286\) −4.27404e16 −4.61806
\(287\) −2.83338e15 −0.299277
\(288\) −7.29570e14 −0.0753383
\(289\) −3.58856e15 −0.362313
\(290\) −1.45603e16 −1.43742
\(291\) 6.32683e14 0.0610776
\(292\) 2.07932e16 1.96306
\(293\) 1.20468e16 1.11233 0.556165 0.831072i \(-0.312272\pi\)
0.556165 + 0.831072i \(0.312272\pi\)
\(294\) 1.75052e15 0.158092
\(295\) 2.17604e16 1.92231
\(296\) −2.68958e16 −2.32428
\(297\) −4.65210e15 −0.393307
\(298\) −2.99402e16 −2.47656
\(299\) 3.32280e16 2.68932
\(300\) 1.32325e15 0.104798
\(301\) −1.01053e16 −0.783190
\(302\) −2.20336e16 −1.67124
\(303\) −2.02016e15 −0.149971
\(304\) −1.89427e16 −1.37646
\(305\) −5.93608e15 −0.422231
\(306\) −1.95268e16 −1.35970
\(307\) −9.26126e14 −0.0631351 −0.0315675 0.999502i \(-0.510050\pi\)
−0.0315675 + 0.999502i \(0.510050\pi\)
\(308\) 2.30285e16 1.53704
\(309\) −3.48608e15 −0.227828
\(310\) −4.50415e15 −0.288245
\(311\) −2.90105e16 −1.81808 −0.909038 0.416712i \(-0.863182\pi\)
−0.909038 + 0.416712i \(0.863182\pi\)
\(312\) −4.92703e15 −0.302399
\(313\) −5.07394e15 −0.305005 −0.152503 0.988303i \(-0.548733\pi\)
−0.152503 + 0.988303i \(0.548733\pi\)
\(314\) −7.24860e15 −0.426788
\(315\) 9.34644e15 0.539048
\(316\) −3.26342e16 −1.84377
\(317\) 9.04960e15 0.500892 0.250446 0.968131i \(-0.419423\pi\)
0.250446 + 0.968131i \(0.419423\pi\)
\(318\) −5.19405e15 −0.281663
\(319\) −2.23051e16 −1.18513
\(320\) 2.47219e16 1.28709
\(321\) 5.05212e14 0.0257745
\(322\) −2.69561e16 −1.34770
\(323\) 2.40340e16 1.17763
\(324\) 3.95492e16 1.89931
\(325\) 1.52190e16 0.716380
\(326\) −3.99724e16 −1.84436
\(327\) 1.70355e14 0.00770540
\(328\) 2.51850e16 1.11676
\(329\) 2.33289e15 0.101419
\(330\) 9.68437e15 0.412792
\(331\) −3.09772e16 −1.29467 −0.647337 0.762204i \(-0.724117\pi\)
−0.647337 + 0.762204i \(0.724117\pi\)
\(332\) 3.01884e16 1.23721
\(333\) −3.38275e16 −1.35951
\(334\) 1.42457e16 0.561478
\(335\) −1.06835e16 −0.412973
\(336\) 1.28160e15 0.0485901
\(337\) 2.94553e16 1.09539 0.547696 0.836678i \(-0.315505\pi\)
0.547696 + 0.836678i \(0.315505\pi\)
\(338\) −6.73269e16 −2.45601
\(339\) 3.76334e15 0.134671
\(340\) 5.43583e16 1.90833
\(341\) −6.89996e15 −0.237653
\(342\) −7.43041e16 −2.51098
\(343\) −2.44819e16 −0.811772
\(344\) 8.98226e16 2.92251
\(345\) −7.52900e15 −0.240388
\(346\) −3.42763e15 −0.107399
\(347\) −5.52018e16 −1.69751 −0.848753 0.528790i \(-0.822646\pi\)
−0.848753 + 0.528790i \(0.822646\pi\)
\(348\) −5.20143e15 −0.156985
\(349\) 1.30873e16 0.387689 0.193845 0.981032i \(-0.437904\pi\)
0.193845 + 0.981032i \(0.437904\pi\)
\(350\) −1.23463e16 −0.359000
\(351\) −1.24770e16 −0.356134
\(352\) 4.68448e15 0.131261
\(353\) 6.32311e16 1.73938 0.869692 0.493595i \(-0.164318\pi\)
0.869692 + 0.493595i \(0.164318\pi\)
\(354\) 1.17043e16 0.316099
\(355\) 6.71431e16 1.78040
\(356\) 6.56138e16 1.70832
\(357\) −1.62606e15 −0.0415712
\(358\) 1.85847e16 0.466569
\(359\) −3.74200e14 −0.00922550 −0.00461275 0.999989i \(-0.501468\pi\)
−0.00461275 + 0.999989i \(0.501468\pi\)
\(360\) −8.30773e16 −2.01148
\(361\) 4.94020e16 1.17476
\(362\) 3.50507e16 0.818635
\(363\) 9.81608e15 0.225188
\(364\) 6.17627e16 1.39177
\(365\) −5.41873e16 −1.19948
\(366\) −3.19284e15 −0.0694304
\(367\) −3.98708e16 −0.851775 −0.425888 0.904776i \(-0.640038\pi\)
−0.425888 + 0.904776i \(0.640038\pi\)
\(368\) 7.68260e16 1.61249
\(369\) 3.16758e16 0.653215
\(370\) 1.41785e17 2.87290
\(371\) 3.21867e16 0.640834
\(372\) −1.60903e15 −0.0314800
\(373\) −5.55924e16 −1.06883 −0.534414 0.845223i \(-0.679468\pi\)
−0.534414 + 0.845223i \(0.679468\pi\)
\(374\) 1.25379e17 2.36897
\(375\) 4.04498e15 0.0751126
\(376\) −2.07362e16 −0.378450
\(377\) −5.98227e16 −1.07312
\(378\) 1.01219e16 0.178470
\(379\) −4.87769e16 −0.845394 −0.422697 0.906271i \(-0.638917\pi\)
−0.422697 + 0.906271i \(0.638917\pi\)
\(380\) 2.06846e17 3.52415
\(381\) 1.17403e16 0.196638
\(382\) −1.59600e17 −2.62797
\(383\) −3.53081e16 −0.571587 −0.285793 0.958291i \(-0.592257\pi\)
−0.285793 + 0.958291i \(0.592257\pi\)
\(384\) 1.27448e16 0.202852
\(385\) −6.00124e16 −0.939175
\(386\) 2.07150e16 0.318763
\(387\) 1.12972e17 1.70943
\(388\) 7.04958e16 1.04896
\(389\) 4.31504e16 0.631411 0.315706 0.948857i \(-0.397759\pi\)
0.315706 + 0.948857i \(0.397759\pi\)
\(390\) 2.59736e16 0.373777
\(391\) −9.74746e16 −1.37957
\(392\) 9.64213e16 1.34219
\(393\) 1.19647e16 0.163814
\(394\) 9.12909e15 0.122942
\(395\) 8.50450e16 1.12659
\(396\) −2.57447e17 −3.35481
\(397\) 8.33842e15 0.106892 0.0534460 0.998571i \(-0.482979\pi\)
0.0534460 + 0.998571i \(0.482979\pi\)
\(398\) 1.84424e17 2.32582
\(399\) −6.18754e15 −0.0767705
\(400\) 3.51875e16 0.429535
\(401\) 6.03120e16 0.724378 0.362189 0.932105i \(-0.382030\pi\)
0.362189 + 0.932105i \(0.382030\pi\)
\(402\) −5.74633e15 −0.0679080
\(403\) −1.85058e16 −0.215191
\(404\) −2.25093e17 −2.57563
\(405\) −1.03065e17 −1.16053
\(406\) 4.85309e16 0.537773
\(407\) 2.17203e17 2.36865
\(408\) 1.44535e16 0.155125
\(409\) −4.61200e16 −0.487178 −0.243589 0.969879i \(-0.578325\pi\)
−0.243589 + 0.969879i \(0.578325\pi\)
\(410\) −1.32767e17 −1.38036
\(411\) −5.89497e15 −0.0603267
\(412\) −3.88431e17 −3.91275
\(413\) −7.25294e16 −0.719182
\(414\) 3.01355e17 2.94155
\(415\) −7.86712e16 −0.755967
\(416\) 1.25638e16 0.118855
\(417\) −2.30161e16 −0.214362
\(418\) 4.77098e17 4.37484
\(419\) −1.76604e16 −0.159445 −0.0797223 0.996817i \(-0.525403\pi\)
−0.0797223 + 0.996817i \(0.525403\pi\)
\(420\) −1.39945e16 −0.124405
\(421\) −1.78240e17 −1.56016 −0.780082 0.625677i \(-0.784823\pi\)
−0.780082 + 0.625677i \(0.784823\pi\)
\(422\) 4.04980e16 0.349062
\(423\) −2.60805e16 −0.221362
\(424\) −2.86096e17 −2.39130
\(425\) −4.46449e16 −0.367489
\(426\) 3.61142e16 0.292763
\(427\) 1.97855e16 0.157967
\(428\) 5.62925e16 0.442656
\(429\) 3.97893e16 0.308172
\(430\) −4.73514e17 −3.61233
\(431\) −1.68744e17 −1.26802 −0.634010 0.773325i \(-0.718592\pi\)
−0.634010 + 0.773325i \(0.718592\pi\)
\(432\) −2.88478e16 −0.213535
\(433\) −1.12283e17 −0.818737 −0.409368 0.912369i \(-0.634251\pi\)
−0.409368 + 0.912369i \(0.634251\pi\)
\(434\) 1.50127e16 0.107839
\(435\) 1.35550e16 0.0959220
\(436\) 1.89816e16 0.132334
\(437\) −3.70914e17 −2.54767
\(438\) −2.91457e16 −0.197239
\(439\) 1.39313e17 0.928907 0.464453 0.885598i \(-0.346251\pi\)
0.464453 + 0.885598i \(0.346251\pi\)
\(440\) 5.33430e17 3.50457
\(441\) 1.21272e17 0.785070
\(442\) 3.36269e17 2.14507
\(443\) 2.87843e17 1.80939 0.904694 0.426061i \(-0.140099\pi\)
0.904694 + 0.426061i \(0.140099\pi\)
\(444\) 5.06504e16 0.313757
\(445\) −1.70990e17 −1.04383
\(446\) 4.22946e17 2.54454
\(447\) 2.78728e16 0.165266
\(448\) −8.24004e16 −0.481529
\(449\) −1.92688e17 −1.10982 −0.554911 0.831910i \(-0.687248\pi\)
−0.554911 + 0.831910i \(0.687248\pi\)
\(450\) 1.38025e17 0.783570
\(451\) −2.03387e17 −1.13809
\(452\) 4.19324e17 2.31286
\(453\) 2.05122e16 0.111525
\(454\) −9.84873e16 −0.527858
\(455\) −1.60954e17 −0.850409
\(456\) 5.49989e16 0.286472
\(457\) −1.94202e17 −0.997237 −0.498618 0.866822i \(-0.666159\pi\)
−0.498618 + 0.866822i \(0.666159\pi\)
\(458\) 2.63454e17 1.33376
\(459\) 3.66013e16 0.182690
\(460\) −8.38907e17 −4.12846
\(461\) −1.54263e17 −0.748524 −0.374262 0.927323i \(-0.622104\pi\)
−0.374262 + 0.927323i \(0.622104\pi\)
\(462\) −3.22789e16 −0.154435
\(463\) −5.96965e16 −0.281626 −0.140813 0.990036i \(-0.544972\pi\)
−0.140813 + 0.990036i \(0.544972\pi\)
\(464\) −1.38315e17 −0.643432
\(465\) 4.19315e15 0.0192352
\(466\) −1.74961e17 −0.791467
\(467\) −2.22537e16 −0.0992754 −0.0496377 0.998767i \(-0.515807\pi\)
−0.0496377 + 0.998767i \(0.515807\pi\)
\(468\) −6.90476e17 −3.03774
\(469\) 3.56090e16 0.154503
\(470\) 1.09314e17 0.467779
\(471\) 6.74810e15 0.0284804
\(472\) 6.44689e17 2.68366
\(473\) −7.25381e17 −2.97830
\(474\) 4.57431e16 0.185254
\(475\) −1.69885e17 −0.678649
\(476\) −1.81181e17 −0.713950
\(477\) −3.59831e17 −1.39871
\(478\) −8.20071e17 −3.14463
\(479\) −7.45601e16 −0.282050 −0.141025 0.990006i \(-0.545040\pi\)
−0.141025 + 0.990006i \(0.545040\pi\)
\(480\) −2.84679e15 −0.0106240
\(481\) 5.82541e17 2.14478
\(482\) −3.56406e17 −1.29461
\(483\) 2.50948e16 0.0899348
\(484\) 1.09374e18 3.86741
\(485\) −1.83713e17 −0.640941
\(486\) −1.70114e17 −0.585605
\(487\) 4.65421e16 0.158091 0.0790456 0.996871i \(-0.474813\pi\)
0.0790456 + 0.996871i \(0.474813\pi\)
\(488\) −1.75866e17 −0.589459
\(489\) 3.72124e16 0.123078
\(490\) −5.08300e17 −1.65900
\(491\) −5.75242e17 −1.85277 −0.926383 0.376583i \(-0.877099\pi\)
−0.926383 + 0.376583i \(0.877099\pi\)
\(492\) −4.74286e16 −0.150753
\(493\) 1.75490e17 0.550488
\(494\) 1.27958e18 3.96135
\(495\) 6.70908e17 2.04988
\(496\) −4.27869e16 −0.129027
\(497\) −2.23794e17 −0.666088
\(498\) −4.23148e16 −0.124309
\(499\) −2.60876e16 −0.0756450 −0.0378225 0.999284i \(-0.512042\pi\)
−0.0378225 + 0.999284i \(0.512042\pi\)
\(500\) 4.50706e17 1.28999
\(501\) −1.32621e16 −0.0374685
\(502\) −3.40731e17 −0.950248
\(503\) −2.00565e17 −0.552159 −0.276080 0.961135i \(-0.589035\pi\)
−0.276080 + 0.961135i \(0.589035\pi\)
\(504\) 2.76904e17 0.752542
\(505\) 5.86594e17 1.57378
\(506\) −1.93497e18 −5.12502
\(507\) 6.26781e16 0.163894
\(508\) 1.30815e18 3.37709
\(509\) −2.45371e17 −0.625399 −0.312700 0.949852i \(-0.601233\pi\)
−0.312700 + 0.949852i \(0.601233\pi\)
\(510\) −7.61937e16 −0.191740
\(511\) 1.80611e17 0.448755
\(512\) 6.70881e17 1.64585
\(513\) 1.39277e17 0.337377
\(514\) 9.10251e16 0.217721
\(515\) 1.01226e18 2.39080
\(516\) −1.69155e17 −0.394513
\(517\) 1.67460e17 0.385676
\(518\) −4.72583e17 −1.07482
\(519\) 3.19096e15 0.00716693
\(520\) 1.43067e18 3.17334
\(521\) −1.71991e17 −0.376755 −0.188378 0.982097i \(-0.560323\pi\)
−0.188378 + 0.982097i \(0.560323\pi\)
\(522\) −5.42550e17 −1.17377
\(523\) −1.09598e17 −0.234176 −0.117088 0.993122i \(-0.537356\pi\)
−0.117088 + 0.993122i \(0.537356\pi\)
\(524\) 1.33315e18 2.81336
\(525\) 1.14938e16 0.0239568
\(526\) 1.33397e18 2.74624
\(527\) 5.42868e16 0.110389
\(528\) 9.19962e16 0.184778
\(529\) 1.00028e18 1.98454
\(530\) 1.50820e18 2.95574
\(531\) 8.10842e17 1.56972
\(532\) −6.89438e17 −1.31847
\(533\) −5.45486e17 −1.03052
\(534\) −9.19705e16 −0.171645
\(535\) −1.46699e17 −0.270475
\(536\) −3.16516e17 −0.576534
\(537\) −1.73014e16 −0.0311351
\(538\) 3.17923e17 0.565246
\(539\) −7.78671e17 −1.36781
\(540\) 3.15006e17 0.546713
\(541\) −1.00640e18 −1.72579 −0.862896 0.505381i \(-0.831352\pi\)
−0.862896 + 0.505381i \(0.831352\pi\)
\(542\) 1.42728e18 2.41832
\(543\) −3.26305e16 −0.0546292
\(544\) −3.68561e16 −0.0609701
\(545\) −4.94662e16 −0.0808595
\(546\) −8.65724e16 −0.139839
\(547\) 1.56743e17 0.250190 0.125095 0.992145i \(-0.460076\pi\)
0.125095 + 0.992145i \(0.460076\pi\)
\(548\) −6.56838e17 −1.03606
\(549\) −2.21191e17 −0.344785
\(550\) −8.86246e17 −1.36520
\(551\) 6.67782e17 1.01660
\(552\) −2.23059e17 −0.335595
\(553\) −2.83463e17 −0.421485
\(554\) 2.63081e17 0.386612
\(555\) −1.31995e17 −0.191714
\(556\) −2.56454e18 −3.68148
\(557\) 7.98265e17 1.13263 0.566316 0.824188i \(-0.308368\pi\)
0.566316 + 0.824188i \(0.308368\pi\)
\(558\) −1.67835e17 −0.235375
\(559\) −1.94548e18 −2.69681
\(560\) −3.72139e17 −0.509898
\(561\) −1.16722e17 −0.158086
\(562\) −7.78621e17 −1.04241
\(563\) 6.49635e17 0.859735 0.429867 0.902892i \(-0.358560\pi\)
0.429867 + 0.902892i \(0.358560\pi\)
\(564\) 3.90507e16 0.0510874
\(565\) −1.09276e18 −1.41322
\(566\) −6.91470e17 −0.884029
\(567\) 3.43526e17 0.434180
\(568\) 1.98923e18 2.48554
\(569\) 5.45655e17 0.674045 0.337022 0.941497i \(-0.390580\pi\)
0.337022 + 0.941497i \(0.390580\pi\)
\(570\) −2.89935e17 −0.354091
\(571\) 5.26721e17 0.635983 0.317992 0.948094i \(-0.396992\pi\)
0.317992 + 0.948094i \(0.396992\pi\)
\(572\) 4.43346e18 5.29260
\(573\) 1.48580e17 0.175370
\(574\) 4.42523e17 0.516426
\(575\) 6.89001e17 0.795021
\(576\) 9.21194e17 1.05101
\(577\) −1.14653e18 −1.29343 −0.646717 0.762730i \(-0.723858\pi\)
−0.646717 + 0.762730i \(0.723858\pi\)
\(578\) 5.60467e17 0.625200
\(579\) −1.92847e16 −0.0212717
\(580\) 1.51034e18 1.64738
\(581\) 2.62218e17 0.282825
\(582\) −9.88135e16 −0.105394
\(583\) 2.31043e18 2.43695
\(584\) −1.60539e18 −1.67455
\(585\) 1.79939e18 1.85614
\(586\) −1.88150e18 −1.91942
\(587\) −2.89181e17 −0.291758 −0.145879 0.989302i \(-0.546601\pi\)
−0.145879 + 0.989302i \(0.546601\pi\)
\(588\) −1.81581e17 −0.181184
\(589\) 2.06574e17 0.203858
\(590\) −3.39858e18 −3.31711
\(591\) −8.49874e15 −0.00820420
\(592\) 1.34688e18 1.28599
\(593\) −7.69437e17 −0.726637 −0.363319 0.931665i \(-0.618356\pi\)
−0.363319 + 0.931665i \(0.618356\pi\)
\(594\) 7.26572e17 0.678683
\(595\) 4.72160e17 0.436243
\(596\) 3.10569e18 2.83830
\(597\) −1.71689e17 −0.155207
\(598\) −5.18961e18 −4.64063
\(599\) −1.27078e18 −1.12407 −0.562037 0.827112i \(-0.689982\pi\)
−0.562037 + 0.827112i \(0.689982\pi\)
\(600\) −1.02165e17 −0.0893958
\(601\) −1.71100e18 −1.48104 −0.740519 0.672035i \(-0.765420\pi\)
−0.740519 + 0.672035i \(0.765420\pi\)
\(602\) 1.57826e18 1.35146
\(603\) −3.98091e17 −0.337225
\(604\) 2.28554e18 1.91535
\(605\) −2.85030e18 −2.36309
\(606\) 3.15511e17 0.258787
\(607\) −1.97449e18 −1.60225 −0.801123 0.598500i \(-0.795764\pi\)
−0.801123 + 0.598500i \(0.795764\pi\)
\(608\) −1.40246e17 −0.112595
\(609\) −4.51799e16 −0.0358866
\(610\) 9.27106e17 0.728594
\(611\) 4.49130e17 0.349224
\(612\) 2.02551e18 1.55830
\(613\) −1.66843e18 −1.27003 −0.635016 0.772499i \(-0.719007\pi\)
−0.635016 + 0.772499i \(0.719007\pi\)
\(614\) 1.44644e17 0.108945
\(615\) 1.23599e17 0.0921144
\(616\) −1.77797e18 −1.31114
\(617\) 7.95080e17 0.580173 0.290086 0.957000i \(-0.406316\pi\)
0.290086 + 0.957000i \(0.406316\pi\)
\(618\) 5.44462e17 0.393136
\(619\) 1.95212e18 1.39482 0.697409 0.716673i \(-0.254336\pi\)
0.697409 + 0.716673i \(0.254336\pi\)
\(620\) 4.67215e17 0.330347
\(621\) −5.64864e17 −0.395229
\(622\) 4.53090e18 3.13724
\(623\) 5.69926e17 0.390522
\(624\) 2.46735e17 0.167313
\(625\) −1.86028e18 −1.24842
\(626\) 7.92457e17 0.526311
\(627\) −4.44155e17 −0.291942
\(628\) 7.51897e17 0.489126
\(629\) −1.70889e18 −1.10023
\(630\) −1.45974e18 −0.930171
\(631\) 2.25291e18 1.42087 0.710434 0.703764i \(-0.248499\pi\)
0.710434 + 0.703764i \(0.248499\pi\)
\(632\) 2.51960e18 1.57279
\(633\) −3.77017e16 −0.0232936
\(634\) −1.41338e18 −0.864330
\(635\) −3.40905e18 −2.06350
\(636\) 5.38779e17 0.322804
\(637\) −2.08841e18 −1.23854
\(638\) 3.48365e18 2.04503
\(639\) 2.50190e18 1.45383
\(640\) −3.70072e18 −2.12871
\(641\) 7.02648e17 0.400093 0.200046 0.979786i \(-0.435891\pi\)
0.200046 + 0.979786i \(0.435891\pi\)
\(642\) −7.89049e16 −0.0444760
\(643\) 3.25156e17 0.181435 0.0907174 0.995877i \(-0.471084\pi\)
0.0907174 + 0.995877i \(0.471084\pi\)
\(644\) 2.79615e18 1.54455
\(645\) 4.40819e17 0.241058
\(646\) −3.75367e18 −2.03210
\(647\) 7.77446e16 0.0416670 0.0208335 0.999783i \(-0.493368\pi\)
0.0208335 + 0.999783i \(0.493368\pi\)
\(648\) −3.05349e18 −1.62016
\(649\) −5.20632e18 −2.73490
\(650\) −2.37692e18 −1.23617
\(651\) −1.39761e16 −0.00719632
\(652\) 4.14634e18 2.11376
\(653\) 3.53906e18 1.78629 0.893145 0.449769i \(-0.148494\pi\)
0.893145 + 0.449769i \(0.148494\pi\)
\(654\) −2.66064e16 −0.0132963
\(655\) −3.47420e18 −1.71904
\(656\) −1.26121e18 −0.617891
\(657\) −2.01914e18 −0.979472
\(658\) −3.64354e17 −0.175007
\(659\) −2.41172e18 −1.14702 −0.573512 0.819197i \(-0.694419\pi\)
−0.573512 + 0.819197i \(0.694419\pi\)
\(660\) −1.00456e18 −0.473086
\(661\) 3.41467e18 1.59235 0.796175 0.605066i \(-0.206853\pi\)
0.796175 + 0.605066i \(0.206853\pi\)
\(662\) 4.83807e18 2.23406
\(663\) −3.13050e17 −0.143145
\(664\) −2.33076e18 −1.05537
\(665\) 1.79668e18 0.805620
\(666\) 5.28324e18 2.34595
\(667\) −2.70832e18 −1.19092
\(668\) −1.47771e18 −0.643490
\(669\) −3.93743e17 −0.169802
\(670\) 1.66857e18 0.712619
\(671\) 1.42024e18 0.600713
\(672\) 9.48860e15 0.00397468
\(673\) 5.31727e17 0.220592 0.110296 0.993899i \(-0.464820\pi\)
0.110296 + 0.993899i \(0.464820\pi\)
\(674\) −4.60038e18 −1.89018
\(675\) −2.58717e17 −0.105281
\(676\) 6.98382e18 2.81475
\(677\) −3.10744e18 −1.24044 −0.620221 0.784427i \(-0.712957\pi\)
−0.620221 + 0.784427i \(0.712957\pi\)
\(678\) −5.87764e17 −0.232386
\(679\) 6.12331e17 0.239791
\(680\) −4.19686e18 −1.62786
\(681\) 9.16869e16 0.0352250
\(682\) 1.07765e18 0.410089
\(683\) 2.49420e18 0.940151 0.470075 0.882626i \(-0.344227\pi\)
0.470075 + 0.882626i \(0.344227\pi\)
\(684\) 7.70756e18 2.87775
\(685\) 1.71173e18 0.633061
\(686\) 3.82363e18 1.40078
\(687\) −2.45263e17 −0.0890047
\(688\) −4.49812e18 −1.61699
\(689\) 6.19661e18 2.20663
\(690\) 1.17589e18 0.414809
\(691\) 6.96468e17 0.243385 0.121693 0.992568i \(-0.461168\pi\)
0.121693 + 0.992568i \(0.461168\pi\)
\(692\) 3.55548e17 0.123086
\(693\) −2.23620e18 −0.766909
\(694\) 8.62150e18 2.92918
\(695\) 6.68321e18 2.24949
\(696\) 4.01588e17 0.133913
\(697\) 1.60018e18 0.528636
\(698\) −2.04399e18 −0.668989
\(699\) 1.62880e17 0.0528162
\(700\) 1.28068e18 0.411438
\(701\) 1.48603e18 0.473000 0.236500 0.971632i \(-0.424000\pi\)
0.236500 + 0.971632i \(0.424000\pi\)
\(702\) 1.94868e18 0.614538
\(703\) −6.50272e18 −2.03182
\(704\) −5.91488e18 −1.83115
\(705\) −1.01766e17 −0.0312158
\(706\) −9.87554e18 −3.00145
\(707\) −1.95517e18 −0.588787
\(708\) −1.21408e18 −0.362270
\(709\) −1.31649e18 −0.389240 −0.194620 0.980879i \(-0.562347\pi\)
−0.194620 + 0.980879i \(0.562347\pi\)
\(710\) −1.04865e19 −3.07222
\(711\) 3.16897e18 0.919952
\(712\) −5.06587e18 −1.45725
\(713\) −8.37803e17 −0.238814
\(714\) 2.53960e17 0.0717344
\(715\) −1.15536e19 −3.23392
\(716\) −1.92779e18 −0.534718
\(717\) 7.63446e17 0.209848
\(718\) 5.84432e16 0.0159193
\(719\) −4.49679e18 −1.21385 −0.606925 0.794759i \(-0.707597\pi\)
−0.606925 + 0.794759i \(0.707597\pi\)
\(720\) 4.16033e18 1.11293
\(721\) −3.37394e18 −0.894454
\(722\) −7.71569e18 −2.02714
\(723\) 3.31796e17 0.0863919
\(724\) −3.63580e18 −0.938209
\(725\) −1.24046e18 −0.317237
\(726\) −1.53309e18 −0.388580
\(727\) 1.98219e18 0.497934 0.248967 0.968512i \(-0.419909\pi\)
0.248967 + 0.968512i \(0.419909\pi\)
\(728\) −4.76854e18 −1.18722
\(729\) −3.73369e18 −0.921318
\(730\) 8.46307e18 2.06980
\(731\) 5.70708e18 1.38341
\(732\) 3.31193e17 0.0795717
\(733\) 4.46397e18 1.06303 0.531515 0.847049i \(-0.321623\pi\)
0.531515 + 0.847049i \(0.321623\pi\)
\(734\) 6.22708e18 1.46981
\(735\) 4.73203e17 0.110708
\(736\) 5.68797e17 0.131902
\(737\) 2.55610e18 0.587541
\(738\) −4.94718e18 −1.12717
\(739\) 7.78019e17 0.175712 0.0878560 0.996133i \(-0.471998\pi\)
0.0878560 + 0.996133i \(0.471998\pi\)
\(740\) −1.47074e19 −3.29253
\(741\) −1.19123e18 −0.264349
\(742\) −5.02697e18 −1.10581
\(743\) 4.44055e18 0.968299 0.484150 0.874985i \(-0.339129\pi\)
0.484150 + 0.874985i \(0.339129\pi\)
\(744\) 1.24229e17 0.0268534
\(745\) −8.09346e18 −1.73428
\(746\) 8.68251e18 1.84435
\(747\) −2.93146e18 −0.617306
\(748\) −1.30056e19 −2.71500
\(749\) 4.88960e17 0.101191
\(750\) −6.31751e17 −0.129613
\(751\) 6.91924e18 1.40734 0.703670 0.710527i \(-0.251543\pi\)
0.703670 + 0.710527i \(0.251543\pi\)
\(752\) 1.03843e18 0.209392
\(753\) 3.17204e17 0.0634120
\(754\) 9.34321e18 1.85175
\(755\) −5.95614e18 −1.17033
\(756\) −1.04994e18 −0.204538
\(757\) 7.26685e17 0.140353 0.0701767 0.997535i \(-0.477644\pi\)
0.0701767 + 0.997535i \(0.477644\pi\)
\(758\) 7.61806e18 1.45880
\(759\) 1.80136e18 0.342002
\(760\) −1.59701e19 −3.00620
\(761\) 3.74540e17 0.0699033 0.0349517 0.999389i \(-0.488872\pi\)
0.0349517 + 0.999389i \(0.488872\pi\)
\(762\) −1.83362e18 −0.339315
\(763\) 1.64875e17 0.0302514
\(764\) 1.65553e19 3.01182
\(765\) −5.27851e18 −0.952164
\(766\) 5.51448e18 0.986319
\(767\) −1.39634e19 −2.47641
\(768\) −1.29304e18 −0.227387
\(769\) 6.50731e18 1.13470 0.567349 0.823478i \(-0.307969\pi\)
0.567349 + 0.823478i \(0.307969\pi\)
\(770\) 9.37284e18 1.62062
\(771\) −8.47400e16 −0.0145290
\(772\) −2.14877e18 −0.365323
\(773\) −3.07419e18 −0.518279 −0.259140 0.965840i \(-0.583439\pi\)
−0.259140 + 0.965840i \(0.583439\pi\)
\(774\) −1.76442e19 −2.94975
\(775\) −3.83727e17 −0.0636153
\(776\) −5.44280e18 −0.894789
\(777\) 4.39952e17 0.0717248
\(778\) −6.73930e18 −1.08955
\(779\) 6.08909e18 0.976245
\(780\) −2.69424e18 −0.428373
\(781\) −1.60644e19 −2.53299
\(782\) 1.52237e19 2.38055
\(783\) 1.01696e18 0.157708
\(784\) −4.82857e18 −0.742615
\(785\) −1.95945e18 −0.298870
\(786\) −1.86867e18 −0.282674
\(787\) −6.74413e18 −1.01179 −0.505895 0.862595i \(-0.668838\pi\)
−0.505895 + 0.862595i \(0.668838\pi\)
\(788\) −9.46960e17 −0.140900
\(789\) −1.24186e18 −0.183262
\(790\) −1.32825e19 −1.94403
\(791\) 3.64228e18 0.528720
\(792\) 1.98768e19 2.86175
\(793\) 3.80912e18 0.543937
\(794\) −1.30231e18 −0.184451
\(795\) −1.40406e18 −0.197242
\(796\) −1.91302e19 −2.66554
\(797\) −9.65539e18 −1.33442 −0.667208 0.744872i \(-0.732511\pi\)
−0.667208 + 0.744872i \(0.732511\pi\)
\(798\) 9.66380e17 0.132474
\(799\) −1.31752e18 −0.179145
\(800\) 2.60518e17 0.0351360
\(801\) −6.37148e18 −0.852372
\(802\) −9.41962e18 −1.24997
\(803\) 1.29647e19 1.70652
\(804\) 5.96066e17 0.0778270
\(805\) −7.28680e18 −0.943764
\(806\) 2.89026e18 0.371330
\(807\) −2.95971e17 −0.0377200
\(808\) 1.73788e19 2.19709
\(809\) −6.40206e18 −0.802886 −0.401443 0.915884i \(-0.631491\pi\)
−0.401443 + 0.915884i \(0.631491\pi\)
\(810\) 1.60969e19 2.00258
\(811\) 4.02888e18 0.497220 0.248610 0.968604i \(-0.420026\pi\)
0.248610 + 0.968604i \(0.420026\pi\)
\(812\) −5.03410e18 −0.616322
\(813\) −1.32873e18 −0.161379
\(814\) −3.39231e19 −4.08730
\(815\) −1.08054e19 −1.29156
\(816\) −7.23798e17 −0.0858285
\(817\) 2.17168e19 2.55478
\(818\) 7.20310e18 0.840665
\(819\) −5.99751e18 −0.694426
\(820\) 1.37719e19 1.58199
\(821\) 3.37777e18 0.384946 0.192473 0.981302i \(-0.438349\pi\)
0.192473 + 0.981302i \(0.438349\pi\)
\(822\) 9.20686e17 0.104099
\(823\) −8.89092e17 −0.0997351 −0.0498675 0.998756i \(-0.515880\pi\)
−0.0498675 + 0.998756i \(0.515880\pi\)
\(824\) 2.99898e19 3.33769
\(825\) 8.25052e17 0.0911026
\(826\) 1.13278e19 1.24101
\(827\) 4.34146e18 0.471900 0.235950 0.971765i \(-0.424180\pi\)
0.235950 + 0.971765i \(0.424180\pi\)
\(828\) −3.12596e19 −3.37121
\(829\) 1.34365e19 1.43774 0.718870 0.695144i \(-0.244659\pi\)
0.718870 + 0.695144i \(0.244659\pi\)
\(830\) 1.22870e19 1.30448
\(831\) −2.44916e17 −0.0257994
\(832\) −1.58638e19 −1.65808
\(833\) 6.12635e18 0.635344
\(834\) 3.59470e18 0.369899
\(835\) 3.85092e18 0.393190
\(836\) −4.94894e19 −5.01385
\(837\) 3.14592e17 0.0316251
\(838\) 2.75823e18 0.275135
\(839\) −1.72037e19 −1.70282 −0.851412 0.524497i \(-0.824253\pi\)
−0.851412 + 0.524497i \(0.824253\pi\)
\(840\) 1.08048e18 0.106121
\(841\) −5.38465e18 −0.524788
\(842\) 2.78377e19 2.69219
\(843\) 7.24858e17 0.0695623
\(844\) −4.20086e18 −0.400048
\(845\) −1.81999e19 −1.71989
\(846\) 4.07330e18 0.381978
\(847\) 9.50031e18 0.884088
\(848\) 1.43271e19 1.32307
\(849\) 6.43726e17 0.0589930
\(850\) 6.97271e18 0.634131
\(851\) 2.63731e19 2.38023
\(852\) −3.74613e18 −0.335525
\(853\) 8.79218e18 0.781498 0.390749 0.920497i \(-0.372216\pi\)
0.390749 + 0.920497i \(0.372216\pi\)
\(854\) −3.09013e18 −0.272584
\(855\) −2.00860e19 −1.75838
\(856\) −4.34620e18 −0.377598
\(857\) 7.90188e18 0.681326 0.340663 0.940185i \(-0.389348\pi\)
0.340663 + 0.940185i \(0.389348\pi\)
\(858\) −6.21436e18 −0.531776
\(859\) −1.16614e19 −0.990368 −0.495184 0.868788i \(-0.664899\pi\)
−0.495184 + 0.868788i \(0.664899\pi\)
\(860\) 4.91176e19 4.13997
\(861\) −4.11967e17 −0.0344621
\(862\) 2.63547e19 2.18807
\(863\) 3.51764e18 0.289855 0.144928 0.989442i \(-0.453705\pi\)
0.144928 + 0.989442i \(0.453705\pi\)
\(864\) −2.13581e17 −0.0174672
\(865\) −9.26561e17 −0.0752089
\(866\) 1.75366e19 1.41280
\(867\) −5.21768e17 −0.0417209
\(868\) −1.55727e18 −0.123591
\(869\) −2.03476e19 −1.60282
\(870\) −2.11704e18 −0.165521
\(871\) 6.85548e18 0.532010
\(872\) −1.46552e18 −0.112884
\(873\) −6.84555e18 −0.523378
\(874\) 5.79300e19 4.39622
\(875\) 3.91486e18 0.294892
\(876\) 3.02329e18 0.226049
\(877\) −3.25045e18 −0.241238 −0.120619 0.992699i \(-0.538488\pi\)
−0.120619 + 0.992699i \(0.538488\pi\)
\(878\) −2.17581e19 −1.60290
\(879\) 1.75158e18 0.128086
\(880\) −2.67130e19 −1.93903
\(881\) −1.04161e19 −0.750522 −0.375261 0.926919i \(-0.622447\pi\)
−0.375261 + 0.926919i \(0.622447\pi\)
\(882\) −1.89404e19 −1.35470
\(883\) −5.27239e18 −0.374337 −0.187169 0.982328i \(-0.559931\pi\)
−0.187169 + 0.982328i \(0.559931\pi\)
\(884\) −3.48812e19 −2.45839
\(885\) 3.16391e18 0.221357
\(886\) −4.49558e19 −3.12225
\(887\) −1.33763e19 −0.922214 −0.461107 0.887344i \(-0.652548\pi\)
−0.461107 + 0.887344i \(0.652548\pi\)
\(888\) −3.91058e18 −0.267644
\(889\) 1.13627e19 0.772002
\(890\) 2.67055e19 1.80122
\(891\) 2.46591e19 1.65109
\(892\) −4.38722e19 −2.91620
\(893\) −5.01349e18 −0.330831
\(894\) −4.35323e18 −0.285179
\(895\) 5.02383e18 0.326727
\(896\) 1.23348e19 0.796399
\(897\) 4.83128e18 0.309678
\(898\) 3.00943e19 1.91509
\(899\) 1.50835e18 0.0952940
\(900\) −1.43174e19 −0.898022
\(901\) −1.81778e19 −1.13196
\(902\) 3.17653e19 1.96386
\(903\) −1.46929e18 −0.0901854
\(904\) −3.23749e19 −1.97294
\(905\) 9.47494e18 0.573272
\(906\) −3.20363e18 −0.192446
\(907\) −1.98060e19 −1.18127 −0.590634 0.806939i \(-0.701122\pi\)
−0.590634 + 0.806939i \(0.701122\pi\)
\(908\) 1.02161e19 0.604959
\(909\) 2.18578e19 1.28511
\(910\) 2.51381e19 1.46745
\(911\) 9.01891e18 0.522739 0.261369 0.965239i \(-0.415826\pi\)
0.261369 + 0.965239i \(0.415826\pi\)
\(912\) −2.75423e18 −0.158501
\(913\) 1.88226e19 1.07552
\(914\) 3.03308e19 1.72081
\(915\) −8.63091e17 −0.0486205
\(916\) −2.73281e19 −1.52858
\(917\) 1.15798e19 0.643133
\(918\) −5.71645e18 −0.315246
\(919\) 3.82062e18 0.209210 0.104605 0.994514i \(-0.466642\pi\)
0.104605 + 0.994514i \(0.466642\pi\)
\(920\) 6.47698e19 3.52170
\(921\) −1.34657e17 −0.00727009
\(922\) 2.40931e19 1.29164
\(923\) −4.30850e19 −2.29359
\(924\) 3.34829e18 0.176992
\(925\) 1.20793e19 0.634045
\(926\) 9.32350e18 0.485968
\(927\) 3.77189e19 1.95227
\(928\) −1.02404e18 −0.0526328
\(929\) 1.13165e19 0.577578 0.288789 0.957393i \(-0.406747\pi\)
0.288789 + 0.957393i \(0.406747\pi\)
\(930\) −6.54893e17 −0.0331918
\(931\) 2.33122e19 1.17330
\(932\) 1.81487e19 0.907073
\(933\) −4.21805e18 −0.209354
\(934\) 3.47561e18 0.171308
\(935\) 3.38927e19 1.65894
\(936\) 5.33098e19 2.59128
\(937\) 2.91885e19 1.40898 0.704489 0.709714i \(-0.251176\pi\)
0.704489 + 0.709714i \(0.251176\pi\)
\(938\) −5.56148e18 −0.266607
\(939\) −7.37739e17 −0.0351218
\(940\) −1.13392e19 −0.536105
\(941\) 2.04885e19 0.962005 0.481003 0.876719i \(-0.340273\pi\)
0.481003 + 0.876719i \(0.340273\pi\)
\(942\) −1.05393e18 −0.0491452
\(943\) −2.46955e19 −1.14365
\(944\) −3.22846e19 −1.48483
\(945\) 2.73616e18 0.124978
\(946\) 1.13291e20 5.13930
\(947\) −3.42151e19 −1.54150 −0.770749 0.637139i \(-0.780118\pi\)
−0.770749 + 0.637139i \(0.780118\pi\)
\(948\) −4.74493e18 −0.212313
\(949\) 3.47714e19 1.54523
\(950\) 2.65329e19 1.17106
\(951\) 1.31579e18 0.0576784
\(952\) 1.39885e19 0.609020
\(953\) −2.46294e19 −1.06500 −0.532500 0.846430i \(-0.678747\pi\)
−0.532500 + 0.846430i \(0.678747\pi\)
\(954\) 5.61989e19 2.41359
\(955\) −4.31432e19 −1.84031
\(956\) 8.50659e19 3.60395
\(957\) −3.24311e18 −0.136469
\(958\) 1.16449e19 0.486699
\(959\) −5.70533e18 −0.236843
\(960\) 3.59451e18 0.148210
\(961\) −2.39509e19 −0.980891
\(962\) −9.09822e19 −3.70099
\(963\) −5.46633e18 −0.220864
\(964\) 3.69699e19 1.48371
\(965\) 5.59971e18 0.223222
\(966\) −3.91935e18 −0.155190
\(967\) 2.16923e19 0.853166 0.426583 0.904449i \(-0.359717\pi\)
0.426583 + 0.904449i \(0.359717\pi\)
\(968\) −8.44450e19 −3.29901
\(969\) 3.49448e18 0.135606
\(970\) 2.86926e19 1.10599
\(971\) 2.58227e19 0.988729 0.494365 0.869255i \(-0.335401\pi\)
0.494365 + 0.869255i \(0.335401\pi\)
\(972\) 1.76459e19 0.671141
\(973\) −2.22757e19 −0.841585
\(974\) −7.26903e18 −0.272799
\(975\) 2.21280e18 0.0824921
\(976\) 8.80699e18 0.326140
\(977\) −4.80925e18 −0.176914 −0.0884571 0.996080i \(-0.528194\pi\)
−0.0884571 + 0.996080i \(0.528194\pi\)
\(978\) −5.81190e18 −0.212381
\(979\) 4.09105e19 1.48507
\(980\) 5.27259e19 1.90132
\(981\) −1.84322e18 −0.0660281
\(982\) 8.98422e19 3.19710
\(983\) 2.45382e18 0.0867451 0.0433725 0.999059i \(-0.486190\pi\)
0.0433725 + 0.999059i \(0.486190\pi\)
\(984\) 3.66183e18 0.128597
\(985\) 2.46779e18 0.0860938
\(986\) −2.74083e19 −0.949911
\(987\) 3.39196e17 0.0116786
\(988\) −1.32731e20 −4.53997
\(989\) −8.80769e19 −2.99286
\(990\) −1.04784e20 −3.53724
\(991\) −5.42214e19 −1.81841 −0.909205 0.416348i \(-0.863310\pi\)
−0.909205 + 0.416348i \(0.863310\pi\)
\(992\) −3.16782e17 −0.0105544
\(993\) −4.50401e18 −0.149083
\(994\) 3.49525e19 1.14939
\(995\) 4.98536e19 1.62872
\(996\) 4.38932e18 0.142466
\(997\) −5.05255e18 −0.162927 −0.0814633 0.996676i \(-0.525959\pi\)
−0.0814633 + 0.996676i \(0.525959\pi\)
\(998\) 4.07440e18 0.130532
\(999\) −9.90298e18 −0.315203
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.1.10 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.a.1.10 104 1.1 even 1 trivial