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  • lfunc_lfunctions • Show schema
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'9.197597557678837991624515590878075', '9.294931415928254051018939433606924', '9.364767229277637071762747060947133', '9.649115803841184355867982660467754', '9.669675818211528110365241235619829', '9.884992226634945096710460414891504', '10.06498246314466627123080379136720', '10.06881685517783487892769755011018', '10.08239747850736511663948037411773', '10.62004828524880075782870915194489'], 'prelabel': '12-912e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6985841962667707, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 371013968186713143, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43176456009906107629938940263', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.945202638916765697906142328138', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.10194035797027313256346712363', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 149152.88977532112, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 575398903529078784, 'conductor_radical': 114, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 0, 9, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 18, 0, 0, 0, 21, 0, 45, 0, -1, 0, -3, 0, -9, 0, 0, 0, -27, 0, -18, 0, 0, 0, -15, 0, -3, 0, 0, 0, 9, 0, 21, 0, 0, 0, 12, 0, 0, 0, 0, 0, -27, 0, 3, 0, 0, 0, -27, 0, -21, 0, 0, 0, -39, 0, 36, 0, 0, 0, 0, 0, 45, 0, 0, 0, 27, 0, -27, 0, 0, 0, -30, 0, 9, 0, 0, 0, 162, 0, -6, 0, 0, 0], 'euler11': [1, 0, -30, 2, 570, -30, -7237, -330, 68970, 2662, -439230, 0, 1771561], 'euler13': [1, 3, 18, 102, 477, 1533, 6821, 19929, 80613, 224094, 514098, 1113879, 4826809], 'euler17': [1, 3, 48, 142, 1407, 3825, 27149, 65025, 406623, 697646, 4009008, 4259571, 24137569], 'euler19': [1, -18, 162, -883, 3078, -6498, 6859, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -21, 210, -1258, 4431, -6129, 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22164361129], 'euler59': [1, 27, 324, 1940, -1485, -146097, -1529227, -8619723, -5169285, 398435260, 3926024964, 19302956073, 42180533641], 'euler61': [1, -3, -60, 806, -720, -27153, 261519, -1656333, -2679120, 182946686, -830750460, -2533788903, 51520374361], 'euler67': [1, 21, 126, -780, -13725, -32307, 306467, -2164569, -61611525, -234595140, 2539041246, 28352627247, 90458382169], 'euler7': [1, 3, -12, -19, 171, 126, -1161, 882, 8379, -6517, -28812, 50421, 117649], 'euler71': [1, 39, 561, 2527, -21102, -349974, -2934895, -24848154, -106375182, 904441097, 14255953041, 70364944689, 128100283921], 'euler73': [1, -36, 558, -4367, 1161, 426735, -5460783, 31151655, 6186969, -1698837239, 15846218478, -74630577348, 151334226289], 'euler79': [1, -45, 1125, -20185, 284850, -3300750, 32006361, -260759250, 1777748850, -9951992215, 43818841125, -138467537955, 243087455521], 'euler83': [1, -27, 258, -2747, 48153, -422916, 2558915, -35102028, 331726017, -1570698889, 12244246818, -106354097361, 326940373369], 'euler89': [1, 30, 246, -1397, -27591, 122913, 4060949, 10939257, -218548311, -984841693, 15434591286, 167521783470, 496981290961], 'euler97': [1, 6, 3, -1129, -4671, -9261, 257046, -898317, -43949439, -1030407817, 265587843, 51524041542, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, -9, 36, -90, 207, -567, 1441, -2835, 5175, -11250, 22500, -28125, 15625], [1, 3, -12, -19, 171, 126, -1161, 882, 8379, -6517, -28812, 50421, 117649], [1, 0, -30, 2, 570, -30, -7237, -330, 68970, 2662, -439230, 0, 1771561], [1, 3, 18, 102, 477, 1533, 6821, 19929, 80613, 224094, 514098, 1113879, 4826809], [1, 3, 48, 142, 1407, 3825, 27149, 65025, 406623, 697646, 4009008, 4259571, 24137569], [1, -18, 162, -883, 3078, -6498, 6859, 0, 0, 0, 0, 0, 0], [1, -21, 210, -1258, 4431, -6129, -7357, -140967, 2343999, -15306086, 58766610, -135163203, 148035889], [1, 3, 18, 90, 81, 4413, 19153, 127977, 68121, 2195010, 12731058, 61533447, 594823321], [1, 9, -12, -225, 987, 6138, -4417, 190278, 948507, -6702975, -11082252, 257662359, 887503681], [1, 18, 189, 1582, 12402, 93546, 631893, 3461202, 16978338, 80133046, 354216429, 1248191226, 2565726409], [1, 15, 177, 1657, 15216, 110376, 759557, 4525416, 25578096, 114202097, 500159697, 1737843015, 4750104241], [1, 3, 99, 561, 8010, 34446, 422585, 1481178, 14810490, 44603427, 338461299, 441025329, 6321363049], [1, -9, 63, -211, 684, 19926, -157555, 936522, 1510956, -21906653, 307419903, -2064105063, 10779215329], [1, -12, 174, -1510, 13782, -123426, 886811, -6541578, 38713638, -224804270, 1372943694, -5018345916, 22164361129], [1, 27, 324, 1940, -1485, -146097, -1529227, -8619723, -5169285, 398435260, 3926024964, 19302956073, 42180533641], [1, -3, -60, 806, -720, -27153, 261519, -1656333, -2679120, 182946686, -830750460, -2533788903, 51520374361], [1, 21, 126, -780, -13725, -32307, 306467, -2164569, -61611525, -234595140, 2539041246, 28352627247, 90458382169], [1, 39, 561, 2527, -21102, -349974, -2934895, -24848154, -106375182, 904441097, 14255953041, 70364944689, 128100283921], [1, -36, 558, -4367, 1161, 426735, -5460783, 31151655, 6186969, -1698837239, 15846218478, -74630577348, 151334226289], [1, -45, 1125, -20185, 284850, -3300750, 32006361, -260759250, 1777748850, -9951992215, 43818841125, -138467537955, 243087455521], [1, -27, 258, -2747, 48153, -422916, 2558915, -35102028, 331726017, -1570698889, 12244246818, -106354097361, 326940373369], [1, 30, 246, -1397, -27591, 122913, 4060949, 10939257, -218548311, -984841693, 15434591286, 167521783470, 496981290961], [1, 6, 3, -1129, -4671, -9261, 257046, -898317, -43949439, -1030407817, 265587843, 51524041542, 832972004929]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bo/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-912e6-1.1-c1e6-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-912e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6985841962667707, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 371013968186713143, 'z1': {'__RealLiteral__': 0, 'data': '0.43176456009906107629938940263', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '547326603766852199946462806958,1198186692560144419583217970520,1396875356196726707042576958133,1806123049590126776126804844689,2102746595367608488138168371540,2127280738516425561106370667912', 'Lhash_array': ['547326603766852199946462806958', '1198186692560144419583217970520', '1396875356196726707042576958133', '1806123049590126776126804844689', '2102746595367608488138168371540', '2127280738516425561106370667912'], 'factors': ['2-912-19.6-c1-0-2', '2-912-19.4-c1-0-11', '2-912-19.9-c1-0-9', '2-912-19.5-c1-0-10', '2-912-19.17-c1-0-16', '2-912-19.16-c1-0-14'], 'label': '12-912e6-1.1-c1e6-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bo/f'}