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lfunc_lfunctions • Show schema
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{'Lhash': '1513154584543683289298208793752', 'a10': [98.03199590504823, -169.79639767492768], 'a2': [-2.723110997362451, -4.716566602081325], 'a3': [-4.5, 7.794228634059948], 'a4': [1.1693329920873534, -2.025344153261832], 'a5': [18.0, 31.176914536239792], 'a6': [49.01599795252412, 0], 'a7': [0, 0], 'a8': [-187.01599795252412, 0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [4.5, -7.794228634059948]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.67', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '624250517694990872624087618832', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.723110997362451, 4.716566602081325], [-16.0, 27.712812921102035]], [[1.0, 0], [4.5, -7.794228634059948]], [[1.0, 0], [-18.0, -31.176914536239792], [-1562.5, 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[-7693119774.5, -13324874318.146824]], [[1.0, 0], [26584.467126040614, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-147-7.4-c5-0-16', 'leading_term': '1.074914322364639828852689753354482176878050532005329784', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/147/6/e/m/67/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [1.0749143223646398, 1.1899019681953211, 1.2856417051748037, 1.3601582391902518, 1.411707444337035, 1.4388003007140193, 1.4402268183501596, 1.4150798281555634, 1.3627783984583814, 1.2830905101692256, 1.1761544997905629, 1.0424986623640933, 0.8830583010362982, 0.6991894211266149, 0.4926781990902308, 0.26574531493194814, 0.021044224356326476, -0.23834753242204837, -0.5089448320691798, 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'5.13393218386062056853210059318243', '6.15056555912752834632810224664915', '7.18036492138922651352710120274938', '8.206762316558817103292743599757071', '8.979475802117528928242096572000304', '10.28318524510038007904870296454073', '11.62303347943035976234938067510470', '12.50269142519634616817399501586790'], 'prelabel': '2-147-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.6263207605587745, 'root_number': '-0.3865135727591552881869185769990697126707082293252108640 + 0.922283718859306965671513774586725112483883643078436164*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.31316038027938725', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19366849530245403822619531518', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08689152358515393756691772641', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.13393218386062056853210059318', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/e/m/67/1'], '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': '2-147-7.4-c5-0-16', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-147-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.31316038027938725, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19366849530245403822619531518', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1513154584543683289298208793752', 'Lhash_array': ['1513154584543683289298208793752'], 'label': '2-147-7.4-c5-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/e/m/67/1'}