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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '168641265264732028', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 788.4109293973144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [11, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '98736.1', 'coefficient_field': '1.1.1.1', 'conductor': 98736, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -2, 5], [1, -2, 7], [1], [1, -1, 13], [1, -1], [1, 1, 19], [1, 8, 23], [1, -6, 29], [1, -4, 31], [1, -2, 37], [1, -4, 41], [1, 7, 43], [1, 13, 47], [1, 6, 53], [1, -4, 59], [1, 0, 61], [1, 3, 67], [1, 12, 71], [1, -8, 73], [1, -14, 79], [1, 17, 83], [1, 17, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 79, 'label': '2-98736-1.1-c1-0-79', 'leading_term': '11.1846266113', '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/98736/dj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.595774715349772, 4.034692784081163, 3.570290597902668, 1.584373721702719, -0.3289434860511289, -0.6766683642120819, 0.3127802657686095, 0.8544707157043715, -0.1485561001639051, -1.435936700833236, -0.8906149045814086, 1.291404158231711, 2.270159288126457, 0.3021999348765642, -2.375017859822641, -2.241098828053712, 0.4217432605357835, 1.694859427985283, -0.1149930612669901, -1.679745888450345, 0.2024430564154468, 3.266075134426113, 3.165394826177215, 0.5598271117139219, 0.03236805996010116, 2.143684322940586, 2.138651453165681, -1.829758219932861, -4.87768956765778, 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0.9824734854443725, 4.263498730559187, 3.057243933568593, -0.1848140576205343, -0.208789260805336, -0.04835802817482608, -1.400758022068136, 0.2871055113987172, 2.880295526699555, 0.1499068007341354, -2.410215057355803, 2.519162675766885, 6.712388839988224, 2.087126187417477, -2.540077367865389, -0.2294590273944683, 1.196115769723186, -1.551518652527262, -1.285206579060511, 1.538678350927953, 0.670893600074777, -1.035665944047584, 0.003893291783130671, -0.7333230063196378, -3.001945498482527, -1.083316609594725, 1.524106612488367, -0.1667872136483659, 0.1261898618474814, 4.715295668254547, 4.598778344090305, -0.1241557532136492, -0.371775574816011, 0.6925611450269624, -3.453786509768163, -5.074613684581869, 0.3995359113646968, 2.912129038321338, -0.06235075090064387, -0.04684777103678228, 1.515849171598098], 'positive_zeros': ['1.193668223383443', '1.681420858008620', '2.225420501519881', '2.859593317354498', '3.524986394002590', '4.211822370064992', '4.738513839057850', '5.234402855433498', '6.078352452333169', '6.243659459660279', '6.901112851045684', '7.729705203155392', '8.075829177461254', '8.439588228283798', '9.004586290199142', '9.782097585149815', '9.959516714233188', '10.32258993349651', '11.22179720865699', '11.43418714614970', '12.16729740546286', '12.52464587741537', '13.29150442113234', '13.52609739167494', '14.05831010259366', '14.42823824404419', '14.75386957778623', '15.40178493466451', '16.01293794424973', '16.17771625707779', '16.96068962619831', '17.41459243434402', '17.80543513425266', '18.26927748888956', '18.43207985220320', '19.31025538807831', '19.70843634856296', '19.91268905746133'], 'prelabel': '2-98736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.078656118078626, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 168641265264732028, 'z1': {'__RealLiteral__': 0, 'data': '1.193668223383443', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.681420858008620', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.225420501519881', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 788.4109293973144, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 98736, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, -1, 0, 2, 0, -8, 0, -1, 0, 1, 0, 6, 0, 4, 0, 0, 0, 4, 0, 2, 0, 1, 0, 4, 0, -7, 0, 2, 0, -13, 0, -3, 0, 1, 0, -6, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, 0, 2, 0, -3, 0, -8, 0, -12, 0, 8, 0, -1, 0, 0, 0, 14, 0, 1, 0, -17, 0, 2, 0, 6, 0, -17, 0, 2, 0, 4, 0, -2, 0, 10, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -1, 13], 'euler17': [1, -1, 0], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -4, 41], 'euler43': [1, 7, 43], 'euler47': [1, 13, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 0, 61], 'euler67': [1, 3, 67], 'euler7': [1, -2, 7], 'euler71': [1, 12, 71], 'euler73': [1, -8, 73], 'euler79': [1, -14, 79], 'euler83': [1, 17, 83], 'euler89': [1, 17, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -2, 5], [1, -2, 7], [1, 0, 0], [1, -1, 13], [1, -1, 0], [1, 1, 19], [1, 8, 23], [1, -6, 29], [1, -4, 31], [1, -2, 37], [1, -4, 41], [1, 7, 43], [1, 13, 47], [1, 6, 53], [1, -4, 59], [1, 0, 61], [1, 3, 67], [1, 12, 71], [1, -8, 73], [1, -14, 79], [1, 17, 83], [1, 17, 89], [1, -10, 97]], 'index': 79, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/98736/dj'], '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': '2-98736-1.1-c1-0-79', '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': '2-98736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.078656118078626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 168641265264732028, 'z1': {'__RealLiteral__': 0, 'data': '1.193668223383443', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '168641265264732028', 'Lhash_array': ['168641265264732028'], 'factors': ['2-98736-1.1-c1-0-79'], 'label': '2-98736-1.1-c1-0-79', 'type': 'ECQ', 'url': 'EllipticCurve/Q/98736/dj'}