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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': -1, 'A8': -1, 'A9': 1, 'Lhash': '2125250985339519975', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3026.7294886166346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1]], [7, [1, 1]], [19, [1]]], 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '379050.1', 'coefficient_field': '1.1.1.1', 'conductor': 379050, 'conductor_radical': 3990, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1], [1, 1], [1, 3, 11], [1, 4, 13], [1, -3, 17], [1], [1, -6, 23], [1, 0, 29], [1, -4, 31], [1, -8, 37], [1, 9, 41], [1, -4, 43], [1, 6, 47], [1, 6, 53], [1, -3, 59], [1, 4, 61], [1, -5, 67], [1, 6, 71], [1, 2, 73], [1, 2, 79], [1, 0, 83], [1, 3, 89], [1, 1, 97]], 'gamma_factors': [[], [0]], 'index': 142, 'label': '2-379050-1.1-c1-0-142', 'leading_term': '6.2679997318', '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': 1, 'origin': 'EllipticCurve/Q/379050/cw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.301645501738969, 1.2559944496272, -0.2661787894455878, -1.629479947583376, -0.954136643049787, 1.279932725727668, 2.297380021978937, 0.710234738393991, -1.203438179616197, -0.8108621118753875, 0.6281821780657121, 0.2830254594220703, -0.5360192494584537, 2.029532483526897, 6.528269276810787, 6.389614750472045, 0.6319834514033802, -2.909942314846427, 0.1388379534722289, 3.130695099236676, 0.1716284222411719, -2.990851094895144, 0.5210497863836929, 5.592235252064345, 4.14871090862578, -0.4249257230213824, -0.4405106475386242, 2.16838799745063, 1.608514146515513, -0.2135765543918835, 0.4355931564168154, 0.7818958610329197, -1.137074969889203, -1.391396230024961, 0.6606255678847582, 0.3498978458662716, -1.885699915575201, -1.511273151839941, -0.01368672829041247, -0.4466718352268743, 0.3875072836945927, 3.178770090050114, 2.214530841779174, -1.025001420957058, 1.233704727977854, 5.345568593863587, 2.360967010253652, -2.239734780313062, 0.1103414784085168, 2.602016648081927, -0.7302223898703231, -1.725739576687195, 1.385093628879715, -0.926777479437102, -5.799536253321438, -2.494446298756156, 3.288758014983774, 1.793569250696811, -0.4778652238102151, 1.77887699407947, 1.46817303781954, -1.271975742166301, 0.424308041634019, 1.994932449801517, -1.32221974795513, -2.218661955746109, 0.6729488726118312, 0.07948981903749805, -0.9323442102189676, 2.708260114402092, 3.820109000870831, 0.0964229207486207, -0.2080371709430014, 1.969788525581467, 0.6583711526216063, -0.3461896350469214, 0.7378484083648852, -0.4388418129092928, -0.8126731883669045, 1.892014941475653, 1.205676442064313, -1.405383020916252, 0.1593403920564157, 0.2111221101469004, -2.761041016417942, -0.1576757862274149, 2.535181819127257, -2.3840368779663, -1.84481140239621, 7.197008366914398, 6.041747689734232, -3.028316275840348, -2.220385184547283, 0.9398832299810101, -3.840559413486084, -4.385288874310808, 1.144116360473687, 0.5008586058194145, -2.104808499992955, 0.1023871129401805, 0.3625607016867998, -0.9984781012284902, 0.820716072224405, 0.679233699528481, -1.376560942411401, -0.04455385282825943, 0.5515077283215674, -0.512519556654305, 1.072322128553921, 0.1460132259211818, -3.448335763899669, -0.8611058596221931, 2.289610031922384, -1.186018865794475, -2.184713855928366, 0.4524649434434104, -0.1017491027039453, 1.843888725931658, 5.46203755617003, 1.500409482861028], 'positive_zeros': ['0.7135698168688426', '1.362262434914463', '2.075586453558849', '2.625611722594774', '3.054349362662791', '3.352422059034124', '4.276086342261302', '4.742601369911039', '5.258977534572081', '5.728141438705567', '6.468146546181116', '6.790880949862512', '7.447473639354725', '7.664862156603544', '8.116546892455113', '8.665363143456744', '9.039114417684019', '9.757316387510706', '9.839214985146656', '10.20697145149321', '10.89699632587768', '11.18240011726479', '11.84922134694148', '12.24386482469824', '12.70565822247796', '13.13075930453344', '13.45641996897845', '14.08751385343315', '14.63050024302581', '14.83315231140062', '15.36322770161967', '15.71766574243617', '16.16617310790542', '16.68255711466843', '17.00838646377807', '17.33884920745134', '18.00775831964099', '18.27162813229537', '18.82971488397480', '19.08021419460485', '19.44408918469348', '19.83341610924618'], 'prelabel': '2-379050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.01572037714888, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2125250985339519975, 'z1': {'__RealLiteral__': 0, 'data': '0.7135698168688426', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.362262434914463', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.075586453558849', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3026.7294886166346, 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '1.1', 'conductor': 379050, 'conductor_radical': 3990, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -1, -1, 1, 0, -3, 1, -4, 1, 0, 1, 3, -1, 0, 0, -1, 3, 6, -1, 0, 4, 1, -1, 0, 0, 4, -1, -3, -3, 0, 1, 8, 0, -4, 0, -9, 1, 4, -3, 0, -6, -6, 1, 1, 0, 3, -4, -6, -1, 0, 1, 0, 0, 3, 0, -4, -4, -1, 1, 0, 3, 5, 3, 6, 0, -6, -1, -2, -8, 0, 0, 3, 4, -2, 0, 1, 9, 0, -1, 0, -4, 0, 3, -3, 0, 4, 6, 4, 6, 0, -1, -1, -1, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, 4, 13], 'euler17': [1, -3, 17], 'euler19': [1, 0, 0], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -8, 37], 'euler41': [1, 9, 41], 'euler43': [1, -4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -3, 59], 'euler61': [1, 4, 61], 'euler67': [1, -5, 67], 'euler7': [1, 1, 0], 'euler71': [1, 6, 71], 'euler73': [1, 2, 73], 'euler79': [1, 2, 79], 'euler83': [1, 0, 83], 'euler89': [1, 3, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, 3, 11], [1, 4, 13], [1, -3, 17], [1, 0, 0], [1, -6, 23], [1, 0, 29], [1, -4, 31], [1, -8, 37], [1, 9, 41], [1, -4, 43], [1, 6, 47], [1, 6, 53], [1, -3, 59], [1, 4, 61], [1, -5, 67], [1, 6, 71], [1, 2, 73], [1, 2, 79], [1, 0, 83], [1, 3, 89], [1, 1, 97]], 'index': 142, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/379050/cw'], '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': '2-379050-1.1-c1-0-142', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-379050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.01572037714888, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2125250985339519975, 'z1': {'__RealLiteral__': 0, 'data': '0.7135698168688426', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2125250985339519975', 'Lhash_array': ['2125250985339519975'], 'label': '2-379050-1.1-c1-0-142', 'type': 'ECQ', 'url': 'EllipticCurve/Q/379050/cw'}