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lfunc_lfunctions • Show schema
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{'Lhash': '3013900003244382169119021761870', 'a10': [20.233687939614086, -5.987966856197524e-61], 'a2': [2.186140661634507, 3.786506698443208], 'a3': [0.0, 0.0], 'a4': [-5.5584219849035215, 9.627469287760746], 'a5': [2.313859338365493, -4.00772193561674], 'a6': [0.0, 0.0], 'a7': [-6.0584219849035215, -10.493494691545186], 'a8': [-13.627718676730986, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5930515701549974, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '27.10', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '5363968247484700925055012931685', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.186140661634507, -3.786506698443208], [-4.0, 6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.313859338365493, 4.00772193561674], [-62.5, -108.25317547305482]], [[1.0, 0], [6.0584219849035215, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3e3-9.4-c3-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/27/4/c/a/10/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.6280685530676904, 1.5416795127260912, 1.4606411471912841, 1.3820104533087159, 1.3024437108079288, 1.2184187039223286, 1.1264704231025562, 1.0234376440294979, 0.9067199204549742, 0.7745437971642143, 0.6262331215551958, 0.4624719956306351, 0.285541448684802, 0.0995036586974163, -0.08969827193683289, -0.2742602655494155, -0.4446919502758033, -0.5901763471169927, -0.6991349506894746, -0.760003219357539, -0.7622008329815857, -0.6972560293981731, -0.5600156038810763, -0.34984431225174323, -0.07169280135556325, 0.26310428562455507, 0.6364445904191085, 1.023624370527808, 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'13.73552702169019275909827147914755', '14.92787385430361298138781226323156', '16.52028607045628524172164355629746'], 'prelabel': '2-3e3-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2621614675448611, 'root_angle': -0.4623408062168869, 'root_number': '0.11803403814000664 - 0.9930095497226417*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.231170403108', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.37754788480497373514455004333', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.25871935047567256819406160559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.32298392977254693961268418088', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5930515701549974, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/4/c/a/10/2'], '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': '2-3e3-9.4-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-3e3-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2621614675448611, 'root_angle': -0.23117040310844345, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37754788480497373514455004333', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3013900003244382169119021761870', 'Lhash_array': ['3013900003244382169119021761870'], 'label': '2-3e3-9.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/4/c/a/10/2'}