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lfunc_lfunctions • Show schema
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{'Lhash': '1710299194769846077295242613151', 'a10': [1179.6152422706632, 0], 'a2': [4.898979485566356, 2.8284271247461903], 'a3': [0, 0], 'a4': [16.0, 27.712812921102035], 'a5': [180.59096477329268, -104.26424212507476], 'a6': [0, 0], 'a7': [-2.098076211353316, 3.633974596215561], 'a8': [0, 181.01933598375618], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.26876154641587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, -2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.107', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1485955214955549842445631904554', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, -2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [-180.59096477329268, 104.26424212507476], [7812.5, -13531.646934131853]], [[1.0, 0], [2.098076211353316, -3.633974596215561], 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[1677100110841.0, 0]], [[1.0, 0], [-1073286.5759829495, 619662.2935613677], [1040975876304.5, -1803023107212.929]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-162-9.2-c6-0-19', 'leading_term': '4.144397785909750612197394070843071586637391810122869283', '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/162/7/d/f/107/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [4.14439778590975, 4.148948950112651, 4.115768347423184, 4.045559127280915, 3.939513147222487, 3.799296210467043, 3.627028248334231, 3.4252584239785064, 3.1969351369695773, 2.945370924678354, 2.674202288076067, 2.387344517662595, 2.088941660388099, 1.783311850486908, 1.4748883252249751, 1.1681565590323224, 0.8675880739547382, 0.5775716176908466, 0.3023425388773029, 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'5.29689202147995012176860862777821', '6.34405381032652807383559859410456', '7.03752381753836561064390220696104', '9.211880593775507871573084031520062', '9.607669993870301013455313324452501', '10.99600792435384224087438318703931', '11.54710672264120084873501247525136'], 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.027777777777777783, 'root_number': '0.99619469809174553229501040247388804618356267264585097453 - 0.0871557427476581735580642708374735513777011561497026727*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.013888888888888888', 'prec': 70}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34918817098490835607613431479', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47406291476136074134517621688', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74168090690689966546753062254', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.26876154641587, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/7/d/f/107/4'], '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': '2-162-9.2-c6-0-19', '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': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.013888888888888892, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34918817098490835607613431479', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1710299194769846077295242613151', 'Lhash_array': ['1710299194769846077295242613151'], 'label': '2-162-9.2-c6-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/7/d/f/107/4'}