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lfunc_lfunctions • Show schema
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{'Lhash': '4137733555020847123350930702221', 'a10': [437.60159350683483, -757.9481934269409], 'a2': [7.427505277147094, -4.2882721711682406], 'a3': [6.708419246589311, -26.153338433400624], 'a4': [4.778556428031953, -8.276702520186193], 'a5': [88.37454377580416, -51.0230666384709], 'a6': [-62.32581403173944, -223.02158679677538], 'a7': [-127.73234619609617, -318.3291499929603], 'a8': [0.0, 466.93183571478863], 'a9': [-638.9942224239802, -350.89511781837734], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.831135756016872, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-6.708419246589311, 26.153338433400624]]], [7, [[1.0, 0], [127.73234619609617, 318.3291499929603]]]], 'bad_primes': [3, 7], 'central_character': '21.11', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '2097636950186075741583229683011', 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.427505277147094, 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[603538.6710288841, 1045359.6425546256], [-597026148264.5, 1034079622241.2635]], [[1.0, 0], [1054215.674100405, -608651.7032257916], [750365175924.5, -1299670608931.593]], [[1.0, 0], [-530057.6877185919, 918086.8460710789], [-838550055420.5, -1452411300678.004]], [[1.0, 0], [0, 1933731.050171073], [-2081951752609.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-21-21.11-c6-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/21/7/h/a/11/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [2.5882879992985948, 2.7783554541361895, 2.940100419181301, 3.070625667472587, 3.1669015361676345, 3.22580193664173, 3.244204406025079, 3.21915429239358, 3.148088978570061, 3.0291133987406105, 2.861313036795305, 2.6450852610950117, 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-1.1623837490929827, -1.4416658374923585], 'positive_zeros': ['3.26409623777710071890110916183837', '5.18331983146442969073001702603281', '6.36356604414373061927019237142596', '9.042136188396329614741866537660392', '10.12239357111828637303970513415196', '12.02872626536440272050423759544039', '13.87226720600809752684106853690985', '14.44945307654020475428483058707312', '15.63541972137429925308247003093005', '16.60039651201553933894693838993135'], 'prelabel': '2-21-21.11-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979844758361855, 'root_angle': 0.47863320748400373, 'root_number': '0.06707535979331004 + 0.9977479121043541*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.239316603742', 'prec': 47}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.26409623777710071890110916184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.18331983146442969073001702603', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.36356604414373061927019237143', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.831135756016872, 'bad_primes': [3, 7], 'central_character': '21.11', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/7/h/a/11/11'], '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': '2-21-21.11-c6-0-12', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-21-21.11-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979844758361855, 'root_angle': 0.23931660374200187, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '3.26409623777710071890110916184', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4137733555020847123350930702221', 'Lhash_array': ['4137733555020847123350930702221'], 'label': '2-21-21.11-c6-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/7/h/a/11/11'}