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lfunc_lfunctions • Show schema
{'Lhash': '527250333230180648855043285509,1062094014314784231741302701394', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 8, 'a6': 0, 'a7': -12, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12199.550537224195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1, -26, 169]]], 'bad_primes': [2, 3, 13], 'central_character': '1872.1', 'coefficient_field': '1.1.1.1', 'conductor': 3504384, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1], [1], [1, -8, 178, -1000, 15625], [1, 12, 634, 4116, 117649], [1, 44, 946, 58564, 1771561], [1, -26, 169], [1, -56, 9202, -275128, 24137569], [1, 60, 3970, 411540, 47045881], [1, 168, 18718, 2044056, 148035889], [1, -216, 47770, -5268024, 594823321], [1, -116, 24138, -3455756, 887503681], [1, 108, 14110, 5470524, 2565726409], [1, -464, 187354, -31979344, 4750104241], [1, -432, 163078, -34347024, 6321363049], [1, 308, 227050, 31977484, 10779215329], [1, -416, 340666, -61932832, 22164361129], [1, 148, 253522, 30396092, 42180533641], [1, 852, 465070, 193387812, 51520374361], [1, -380, 598818, -114289940, 90458382169], [1, -860, 845722, -307803460, 128100283921], [1, 404, 616086, 157162868, 151334226289], [1, -728, 307566, -358932392, 243087455521], [1, -1092, 946690, -624391404, 326940373369], [1, 1792, 2197882, 1263304448, 496981290961], [1, -684, 1434022, -624268332, 832972004929], [1, -352, 738490, -362665952, 1061520150601], [1, -216, 709918, -236029032, 1194052296529], [1, -1656, 2818870, -2028671208, 1500730351849], [1, -1404, 3081454, -1818220716, 1677100110841], [1, 1272, 1893202, 1835364984, 2081951752609]], 'euler_factors_factorization': [[1], [1], [[[1, -8, 178, -1000, 15625], 1]], [[[1, 12, 634, 4116, 117649], 1]], [[[1, 44, 946, 58564, 1771561], 1]], [[[1, -13], 2]], [[[1, -56, 9202, -275128, 24137569], 1]], [[[1, 60, 3970, 411540, 47045881], 1]], [[[1, 168, 18718, 2044056, 148035889], 1]], [[[1, -216, 47770, -5268024, 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1893202, 1835364984, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 3, 'label': '4-1872e2-1.1-c3e2-0-3', 'leading_term': '2.65016491899312699202998932019544616721337555228857202266909440000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1872/4/a/bg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [2.650164918993127, 2.6266563804377014, 2.5774231521073756, 2.4871218691314594, 2.361526712565777, 2.2059715929014083, 2.022180256729427, 1.813344286445966, 1.5838621255061986, 1.338296014476518, 1.081478461150621, 0.8185808399274748, 0.5549686264821809, 0.29607441245607835, 0.04733706771815436, -0.1859262689000419, -0.3985996395126715, -0.5858825068886643, 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'4.62582597919480796252973200878947', '5.00736294209181984914737642351621', '5.74763535301356381520756427142988', '5.78366275052439601870626874148101', '6.32743981278490144138719285302132', '6.43037197773822141927867403422447', '7.10061831436141253845213338291587', '7.68290405311072902474538336398428', '7.934443645068471352531605143013626', '8.164651389729053288420877211120785', '8.644054785491324264791761698843134', '9.145802262897093197403581091645715'], 'prelabel': '4-1872e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 431812900511999955, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41592717515004042802041438895', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.837844445562178959551874520853', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.79743085641532931659034312279', 'prec': 103}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12199.550537224195, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 3504384, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 8, 0, -12, 0, 0, 0, -44, 0, 26, 0, 0, 0, 56, 0, -60, 0, 0, 0, -168, 0, -114, 0, 0, 0, 216, 0, 116, 0, 0, 0, -96, 0, -108, 0, 0, 0, 464, 0, 432, 0, 0, 0, -308, 0, -490, 0, 0, 0, 416, 0, -352, 0, 0, 0, -148, 0, -852, 0, 0, 0, 208, 0, 380, 0, 0, 0, 860, 0, -404, 0, 0, 0, 528, 0, 728, 0, 0, 0, 1092, 0, 448, 0, 0, 0, -1792, 0, -312, 0, 0, 0, -480, 0, 684, 0, 0, 0], 'euler11': [1, 44, 946, 58564, 1771561], 'euler13': [1, -26, 169, 0, 0], 'euler17': [1, -56, 9202, -275128, 24137569], 'euler19': [1, 60, 3970, 411540, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 168, 18718, 2044056, 148035889], 'euler29': [1, -216, 47770, -5268024, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -116, 24138, -3455756, 887503681], 'euler37': [1, 108, 14110, 5470524, 2565726409], 'euler41': [1, -464, 187354, -31979344, 4750104241], 'euler43': [1, -432, 163078, -34347024, 6321363049], 'euler47': [1, 308, 227050, 31977484, 10779215329], 'euler5': [1, -8, 178, -1000, 15625], 'euler53': [1, -416, 340666, -61932832, 22164361129], 'euler59': [1, 148, 253522, 30396092, 42180533641], 'euler61': [1, 852, 465070, 193387812, 51520374361], 'euler67': [1, -380, 598818, -114289940, 90458382169], 'euler7': [1, 12, 634, 4116, 117649], 'euler71': [1, -860, 845722, -307803460, 128100283921], 'euler73': [1, 404, 616086, 157162868, 151334226289], 'euler79': [1, -728, 307566, -358932392, 243087455521], 'euler83': [1, -1092, 946690, -624391404, 326940373369], 'euler89': [1, 1792, 2197882, 1263304448, 496981290961], 'euler97': [1, -684, 1434022, -624268332, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -8, 178, -1000, 15625], [1, 12, 634, 4116, 117649], [1, 44, 946, 58564, 1771561], [1, -26, 169, 0, 0], [1, -56, 9202, -275128, 24137569], [1, 60, 3970, 411540, 47045881], [1, 168, 18718, 2044056, 148035889], [1, -216, 47770, -5268024, 594823321], [1, -116, 24138, -3455756, 887503681], [1, 108, 14110, 5470524, 2565726409], [1, -464, 187354, -31979344, 4750104241], [1, -432, 163078, -34347024, 6321363049], [1, 308, 227050, 31977484, 10779215329], [1, -416, 340666, -61932832, 22164361129], [1, 148, 253522, 30396092, 42180533641], [1, 852, 465070, 193387812, 51520374361], [1, -380, 598818, -114289940, 90458382169], [1, -860, 845722, -307803460, 128100283921], [1, 404, 616086, 157162868, 151334226289], [1, -728, 307566, -358932392, 243087455521], [1, -1092, 946690, -624391404, 326940373369], [1, 1792, 2197882, 1263304448, 496981290961], [1, -684, 1434022, -624268332, 832972004929]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1872/4/a/bg'], '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': '4-1872e2-1.1-c3e2-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-1872e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 431812900511999955, 'z1': {'__RealLiteral__': 0, 'data': '0.41592717515004042802041438895', 'prec': 103}} -
lfunc_instances • Show schema
{'Lhash': '527250333230180648855043285509,1062094014314784231741302701394', 'Lhash_array': ['527250333230180648855043285509', '1062094014314784231741302701394'], 'factors': ['2-1872-1.1-c3-0-8', '2-1872-1.1-c3-0-33'], 'label': '4-1872e2-1.1-c3e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/4/a/bg'}
Lfunction data - 4-1872e2-1.1-c3e2-0-3