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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1911087461051491772378906245441', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792515, 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], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 3]]], 'bad_primes': [2, 3], 'central_character': '36864.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -2, 3], [1, 0, 2, 0, 25], [1, 0, 2, 0, 49], [1, -4, 10, -44, 121], [1, -4, 14, -52, 169], [1, 0, 14, 0, 289], [1, 0, -14, 0, 361], [1, 8, 62, 184, 529], [1, 0, -14, 0, 841], [1, 0, -30, 0, 961], [1, -4, 62, -148, 1369], [1, 0, 30, 0, 1681], [1, 0, 66, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -30, 0, 2809], [1, 4, 58, 236, 3481], [1, -20, 206, -1220, 3721], [1, 0, -94, 0, 4489], [1, 8, 94, 568, 5041], [1, -4, 86, -292, 5329], [1, 0, -94, 0, 6241], [1, 20, 250, 1660, 6889], [1, 0, -82, 0, 7921], [1, 4, 198, 388, 9409], [1, 0, -126, 0, 10201], [1, 0, 130, 0, 10609], [1, 4, 154, 428, 11449], [1, 12, 238, 1308, 11881], [1, 0, 94, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 7, 'label': '4-192e2-1.1-c1e2-0-7', 'leading_term': '1.96481161987', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.2.12.1/256.1/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.060546875', 'prec': 37}, 'plot_values': [1.9648116198733334, 1.9676465240763352, 1.9759663734661195, 1.9892186050005436, 2.0064892467889495, 2.0265140916336266, 2.0476957331390637, 2.068127731542535, 2.0856273609953333, 2.097778446357819, 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-3.035711502747541, -2.3295957411551873, -1.4145251734384623, -0.4274914591951958], 'positive_zeros': ['1.50758218448160494122558467671350', '2.39828951388922368151652610486915', '3.34650501351684819915646708152934', '3.94357278164872657753927112928749', '4.29545114391794679641863097735327', '5.51068329881977020855931527273532', '6.01787329173103130344580621765721', '6.56751042591285918771393023230572', '7.22622360838775834162972537899652', '7.912976180298523208679694953656963', '8.348781260172839309711754415931569', '8.688757670023775560985236864470214', '9.248505727642093065314855285982442', '9.822353057501042439003867593911166', '10.03045773630582112349040341123890'], 'prelabel': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1290401098810232135, 'z1': {'__RealLiteral__': 0, 'data': '1.50758218448160494122558467671350', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.39828951388922368151652610486915', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.34650501351684819915646708152934', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -2, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 20, 0, 0, 0, 0, 0, 0, 0, -16, 0, -8, 0, 4, 0, -4, 0, 0, 0, 0, 0, -11, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0], 'euler11': [1, -4, 10, -44, 121], 'euler13': [1, -4, 14, -52, 169], 'euler17': [1, 0, 14, 0, 289], 'euler19': [1, 0, -14, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 0, -14, 0, 841], 'euler3': [1, -2, 3, 0, 0], 'euler31': [1, 0, -30, 0, 961], 'euler37': [1, -4, 62, -148, 1369], 'euler41': [1, 0, 30, 0, 1681], 'euler43': [1, 0, 66, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, -30, 0, 2809], 'euler59': [1, 4, 58, 236, 3481], 'euler61': [1, -20, 206, -1220, 3721], 'euler67': [1, 0, -94, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 8, 94, 568, 5041], 'euler73': [1, -4, 86, -292, 5329], 'euler79': [1, 0, -94, 0, 6241], 'euler83': [1, 20, 250, 1660, 6889], 'euler89': [1, 0, -82, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 3, 0, 0], [1, 0, 2, 0, 25], [1, 0, 2, 0, 49], [1, -4, 10, -44, 121], [1, -4, 14, -52, 169], [1, 0, 14, 0, 289], [1, 0, -14, 0, 361], [1, 8, 62, 184, 529], [1, 0, -14, 0, 841], [1, 0, -30, 0, 961], [1, -4, 62, -148, 1369], [1, 0, 30, 0, 1681], [1, 0, 66, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -30, 0, 2809], [1, 4, 58, 236, 3481], [1, -20, 206, -1220, 3721], [1, 0, -94, 0, 4489], [1, 8, 94, 568, 5041], [1, -4, 86, -292, 5329], [1, 0, -94, 0, 6241], [1, 20, 250, 1660, 6889], [1, 0, -82, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 7, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/256.1/a', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-a', 'EllipticCurve/2.2.12.1/256.1/d', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-192e2-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1290401098810232135, 'z1': {'__RealLiteral__': 0, 'data': '1.50758218448160494122558467671350', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9575546
{'Lhash': '1911087461051491772378906245441', 'Lhash_array': ['1911087461051491772378906245441'], 'label': '4-192e2-1.1-c1e2-0-7', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-d'}
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id: 9575543
{'Lhash': '1911087461051491772378906245441', 'Lhash_array': ['1911087461051491772378906245441'], 'label': '4-192e2-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/256.1/d'}
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id: 9575433
{'Lhash': '1911087461051491772378906245441', 'Lhash_array': ['1911087461051491772378906245441'], 'label': '4-192e2-1.1-c1e2-0-7', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-a'}
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id: 9575431
{'Lhash': '1911087461051491772378906245441', 'Lhash_array': ['1911087461051491772378906245441'], 'label': '4-192e2-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/256.1/a'}