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lfunc_lfunctions • Show schema
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{'Lhash': '936222627137495215910339577881', 'a10': [0, 0], 'a2': [1910.6298725064883, 0], 'a3': [-59049.0, 0], 'a4': [1553354.5097141596, 0], 'a5': [0, 0], 'a6': [-112820783.34163563, 0], 'a7': [148600982.6813378, 0], 'a8': [-1038995729.5341836, 0], 'a9': [3486784401.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 209.6080082152966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [59049.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1910.6298725064883, 0], [2097152.0, 0]], [[1.0, 0], [59049.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-148600982.6813378, 0], [558545864083284030, 0]], [[1.0, 0], [-136386190375.5702, 0], [7400249944258161000000, 0]], [[1.0, 0], [-560883580532.8793, 0], [247064529073450400000000, 0]], [[1.0, 0], [16033168514150.637, 0], 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[0]], 'group': 'GL2', 'index': 23, 'label': '2-75-1.1-c21-0-23', 'leading_term': '4.264619870074533122565083296261285892028456023919592287', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/75/22/a/l/1/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [4.264619870074533, 4.213299605669335, 4.0608943133042965, 3.8120210712584015, 3.4742118755907767, 3.0576745314659246, 2.57496889724347, 2.0406090414239766, 1.4706042827344783, 0.8819540661822282, 0.29211311731483547, -0.28155573606909834, -0.8223233123183983, -1.314612845089101, -1.7444790164050372, -2.1000318425558935, -2.3717918564168188, -2.5529653318545815, -2.6396309690081625, -2.6308324145119943, -2.528574129695581, -2.3377213376196195, -2.065807968782098, -1.7227595784227345, -1.3205410228101808, 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'6.25432169813242528024392965635296', '6.73968824897499610480769981278245', '8.555434625770197511591687451456152', '9.613883481327292047964137937195342', '11.37940693748591910982853255935921'], 'prelabel': '2-75-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.477845427248372, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73854942913207828854717027817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88428314701229523235116282577', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39632857401460406604528075568', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 209.6080082152966, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/22/a/l/1/7'], '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': '2-75-1.1-c21-0-23', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-75-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.477845427248372, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73854942913207828854717027817', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '936222627137495215910339577881', 'Lhash_array': ['936222627137495215910339577881'], 'label': '2-75-1.1-c21-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/22/a/l/1/7'}