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lfunc_lfunctions • Show schema
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{'Lhash': '1414131693113531196643460325440', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.0, 1.7320508075688772], 'a6': [0, 0], 'a7': [-3.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-4.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.577', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '285259178618432483485040986596', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-2.5, 4.330127018922194]], [[1.0, 0], [3.0, 0], [7.0, 0]], [[1.0, 0], [6.0, 0], [11.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-6.5, -11.258330249197702]], [[1.0, 0], [-1.0, -1.7320508075688772], [-8.5, 14.722431864335457]], [[1.0, 0], 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-0.24653541046198418, -0.1769400612277239], 'positive_zeros': ['1.11555320753126228611485908747873', '2.57123971152385969107819401120799', '3.17115571301512295286710814125262', '4.40122110255866120191808017014619', '5.44856397886939491188175788189674', '5.57715049177454703771850884134353', '6.88728570346914776697974970290102', '7.39233269309537169760840267157308', '8.443830514801603050453646626055756', '8.981083274198676911421856097436782'], 'prelabel': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.5311600905421131, 'root_number': '-0.0977360376476314152095947049873239194781033185438401855 + 0.9952123727852969044708116330465434276936656868442795109*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.26558004527105655', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11555320753126228611485908748', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57123971152385969107819401121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17115571301512295286710814125', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/n/577/1'], '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': '2-2736-19.7-c1-0-30', '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': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.26558004527105655, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11555320753126228611485908748', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1414131693113531196643460325440', 'Lhash_array': ['1414131693113531196643460325440'], 'label': '2-2736-19.7-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/n/577/1'}