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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '882031016625898391', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '235200.1', 'coefficient_field': '1.1.1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1], [1, -1, 11], [1, -7, 13], [1, -4, 17], [1, 1, 19], [1, 1, 23], [1, -8, 29], [1, -6, 31], [1, 3, 37], [1, -9, 41], [1, 4, 43], [1, -3, 47], [1, 1, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, 14, 71], [1, -14, 73], [1, -4, 79], [1, -12, 83], [1, 2, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 415, 'label': '2-235200-1.1-c1-0-415', 'leading_term': '5.58561054344', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/235200/xs', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.58561054344137, 4.543971204175367, 2.051013288098673, -0.1865704271604163, -0.5352358579217954, 0.746346999952127, 1.393977595626017, -0.1789839945604382, -2.44861254337665, -2.448586578217072, 0.00922274983211324, 1.699490467115629, 0.5916916659654108, -1.062425796956823, -0.4721968369023001, 0.8918786064448311, -0.08668387971272991, -2.09151793110398, -1.028102641992705, 2.26725401073742, 2.173820575426279, -2.246714591543815, -4.745978922550905, -2.031505116817674, 0.8291086276710598, -0.2273144351577474, -1.212777298831963, 1.39495196527471, 3.054596470948423, -0.2792938627866802, -3.839117415442041, -2.572903016789436, 0.01145415328678779, -0.2657480998379359, -0.4094638984021817, 1.82948433020345, 2.317328996949487, -0.03422389178338059, 0.2181845510398696, 3.420628975847397, 3.09651732810716, -0.5432548431473443, -0.7229093868453516, 1.33084791240153, -0.8734163221010202, -4.036640812209504, -1.174045292234561, 3.053989720309146, 1.580007914333924, -0.4384857223331162, 2.57005404097457, 4.313357798957487, 0.7228763918651503, -1.296303869823502, 0.8165270255051194, 1.078789130931177, -0.4045258494179956, 0.7994046811885589, 1.115990724096736, -2.512697933254207, -3.471969849401394, 0.3345986007567761, 1.433835078395612, -0.453430977800298, 0.6986724928999541, 1.427406406166454, -2.307937009075153, -2.680757025515271, 2.8111564412938, 3.564106153002858, -1.353348881997554, -1.320757532680596, 2.150337772012969, 0.6000185579412032, -1.58553075819219, 0.7403716665494126, 1.377402363762139, -0.5967136178883283, 1.186821112576173, 3.155731273059081, 0.05224386660393363, -1.591574208897349, 0.9220025402398868, 0.7460434754995486, -0.9377874154204051, 0.5054173744958814, 0.06533050575966386, -2.091178423774586, 2.540722077280056, 8.494526461342435, 4.916397440282707, -0.5743685518546002, 0.4887220884562467, 0.7157922203298416, -1.174001618125332, 1.91181679132913, 3.939054934346018, -1.075072011512809, -3.190766089810455, 0.654463577232482, 1.148020038416418, -0.446874724303616, 1.065544578894485, 0.6966681801932331, -1.346756116664085, 0.347018807334764, 0.4570457434319224, -2.880809942991163, -0.66417193179285, 3.976026151750736, 1.864012510287865, -0.4535544025268702, 1.201611640062788, -0.7146332746121506, -2.143957122613146, 3.010349113715326, 3.467482765944519, -3.302588046560727, -3.463319842037761, 1.173550829478951, 0.4066440077047913], 'positive_zeros': ['0.7204723680344991', '1.121911713012287', '1.731329851011893', '2.499149051461589', '3.072060825278363', '3.570661177364130', '3.989952696211689', '4.577866189593333', '5.135381661813841', '5.890605342731188', '6.223048371781062', '6.644726580125326', '7.235335516656623', '7.997712620151231', '8.186959587185884', '8.560804723825618', '9.245725005681507', '9.477368097595938', '10.20646906206595', '10.57402897951070', '10.94510800925008', '11.55468803846567', '12.12830310341047', '12.32193281527134', '13.04528895417317', '13.41596106054689', '13.90175794183965', '14.14514208334869', '14.59413054005418', '15.22802746637410', '15.67192433670117', '15.92199541703206', '16.36432030063968', '16.87919717042144', '17.42666455874140', '17.83345520837627', '18.29212288198266', '18.68800827127022', '19.15251746780113', '19.40413853888808'], 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 882031016625898391, 'z1': {'__RealLiteral__': 0, 'data': '0.7204723680344991', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.121911713012287', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.731329851011893', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 7, 0, 0, 0, 4, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 8, 0, 6, 0, 1, 0, 0, 0, -3, 0, 7, 0, 9, 0, -4, 0, 0, 0, 3, 0, 0, 0, 4, 0, -1, 0, 0, 0, -1, 0, -12, 0, 4, 0, 0, 0, 0, 0, 12, 0, -1, 0, -14, 0, 14, 0, 0, 0, 0, 0, 4, 0, 1, 0, 12, 0, 0, 0, 8, 0, -2, 0, 0, 0, 6, 0, 0, 0, 16, 0, 1, 0], 'euler11': [1, -1, 11], 'euler13': [1, -7, 13], 'euler17': [1, -4, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, -8, 29], 'euler3': [1, -1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 3, 37], 'euler41': [1, -9, 41], 'euler43': [1, 4, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, 12, 59], 'euler61': [1, -4, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 14, 71], 'euler73': [1, -14, 73], 'euler79': [1, -4, 79], 'euler83': [1, -12, 83], 'euler89': [1, 2, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, -1, 11], [1, -7, 13], [1, -4, 17], [1, 1, 19], [1, 1, 23], [1, -8, 29], [1, -6, 31], [1, 3, 37], [1, -9, 41], [1, 4, 43], [1, -3, 47], [1, 1, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, 14, 71], [1, -14, 73], [1, -4, 79], [1, -12, 83], [1, 2, 89], [1, -16, 97]], 'index': 415, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/235200/xs'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-235200-1.1-c1-0-415', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 882031016625898391, 'z1': {'__RealLiteral__': 0, 'data': '0.7204723680344991', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '882031016625898391', 'Lhash_array': ['882031016625898391'], 'label': '2-235200-1.1-c1-0-415', 'type': 'ECQ', 'url': 'EllipticCurve/Q/235200/xs'}