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lfunc_lfunctions • Show schema
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{'Lhash': '1402163511908421436918728637272', 'a10': [0, -1.7903496262234153], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [1.7903496262234153, 0], 'a6': [0, 0], 'a7': [2.280515753818087, 1.3413604648220114], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.0550355892132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.280515753818087, -1.3413604648220114]]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.1133', 'coefficient_field': 'CDF', 'conductor': 1134, 'conductor_radical': 42, 'conjugate': '1630261076092244678166555806772', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.7903496262234153, 0], [5.0, 0]], [[1.0, 0], [-2.280515753818087, -1.3413604648220114]], [[1.0, 0], [0, -2.401504206824955], [-11.0, 0]], [[1.0, 0], [0, 4.89132614215432], [-13.0, 0]], [[1.0, 0], 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'4.04131041960535421513561566185459', '4.76282771800891582947759938808471', '5.82452671615489855782323529015326', '6.42453936957718447046618170757676', '7.44766737309465782842521769960996', '8.129938399710131029676376671348554', '9.083084625027708500773637051409985', '9.648576849316772603455503509385656'], 'prelabel': '2-1134-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.16924064665005464, 'root_number': '0.86195393508109381254736825351415705283378155130275601330 + 0.5069866012018636310015242276828951798517582476175745395*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08462032332502732', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10611197727195030109843867177', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47618831989350056195962651717', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04131041960535421513561566185', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.0550355892132, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 1134, 'conductor_radical': 42, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/d/a/1133/6'], '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': '2-1134-21.20-c1-0-16', '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': '2-1134-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.08462032332502732, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10611197727195030109843867177', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1402163511908421436918728637272', 'Lhash_array': ['1402163511908421436918728637272'], 'label': '2-1134-21.20-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/d/a/1133/6'}