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lfunc_lfunctions • Show schema
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{'Lhash': '757967632772780351117856035301', 'a10': [0.9047214656001432, -2.305192699403702], 'a2': [-0.7330518718298263, -0.6801727377709194], 'a3': [-2.8157767036225967, -0.42441005056050235], 'a4': [0.07473009358642425, 0.9972037971811801], 'a5': [0.9047214656001432, 2.305192699403702], 'a6': [1.7754382372181314, 2.226329131441324], 'a7': [-1.3083502362655628, 2.299612936836077], 'a8': [0.6234898018587335, -0.7818314824680298], 'a9': [4.881756136288547, 1.5058223430703894], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7825339398085481, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7330518718298263, 0.6801727377709194]]], [7, [[1.0, 0], [1.3083502362655628, -2.299612936836077]]]], 'bad_primes': [2, 7], 'central_character': '98.9', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'conjugate': '3094509942519846583720002072580', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-1.8020109290385085, -7.8951257373440855], [-74.78041603590079, 36.01235034675732]], [[1.0, 0], [4.696837198188354, 1.448782404803456], [73.53525091412354, 50.13548516766236]], [[1.0, 0], [-12.306524715286146, 0], [97.0, 0]], [[1.0, 0], [-0.6007703232953565, -0.09055155650552824], [96.51285338440022, 29.770272615501327]], [[1.0, 0], [0.31096390762042747, 0.7923231147711847], [-75.50434279847211, 70.0577919904047]], [[1.0, 0], [-2.7621892124105965, -0.8520225336364547], [88.40754885181146, 60.27524621280756]], [[1.0, 0], [7.661601926694295, -2.3632912097281977], [90.06002640044345, -61.4018863289348]], [[1.0, 0], [-3.308822159380546, -14.496897088608906], [-101.80948207297337, 49.028862520284065]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-98-49.9-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 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'0.10469458241296876 - 0.994504421515246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.233306748785', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59793103291736296211181593991', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.60318569468059179528868758002', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.59838297478103755122325483771', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7825339398085481, 'bad_primes': [2, 7], 'central_character': '49.9', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/2/g/b/9/1'], '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': '2-98-49.9-c1-0-0', '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': '2-98-49.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8846094843537164, 'root_angle': -0.23330674878507146, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59793103291736296211181593991', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '757967632772780351117856035301', 'Lhash_array': ['757967632772780351117856035301'], 'label': '2-98-49.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/2/g/b/9/1'}