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lfunc_lfunctions • Show schema
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{'Lhash': '2172500598291990102833014128959', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0394321555534851, -1.385489369862301], 'a4': [0.0, 0.0], 'a5': [0.6920940482867404, 1.1987420552486623], 'a6': [0.0, 0.0], 'a7': [-2.088625963907451, -1.6240817660732696], 'a8': [0.0, 0.0], 'a9': [-0.8391615880028713, 2.8802444044248223], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.365947015830044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0394321555534851, 1.385489369862301]]], [7, [[1.0, 0], [2.088625963907451, 1.6240817660732696]]]], 'bad_primes': [2, 3, 7], 'central_character': '672.431', 'coefficient_field': 'CDF', 'conductor': 672, 'conductor_radical': 42, 'conjugate': '597434230988963348238489299242', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0394321555534851, 1.385489369862301]], [[1.0, 0], [-0.6920940482867404, -1.1987420552486623], [-2.5, 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[[1.0, 0], [-2.9932111212320947, 1.7281312465847314], [30.5, -52.827549630850754]], [[1.0, 0], [-3.368055218445851, 5.8336427610457084], [-33.5, -58.023702053557386]], [[1.0, 0], [1.904372365060992, 0], [71.0, 0]], [[1.0, 0], [-3.235153108644473, 5.603449554436623], [-36.5, -63.21985447626402]], [[1.0, 0], [1.6507274801477803, -0.9530479550220335], [39.5, -68.41600689897065]], [[1.0, 0], [0, -7.000636754235003], [-83.0, 0]], [[1.0, 0], [-8.227758600413104, 4.750298642775764], [44.5, -77.07626093681505]], [[1.0, 0], [-1.1921421046853473, 0], [97.0, 0]], [[1.0, 0], [-1.0356604743092386, 1.7938165608944834], [-50.5, -87.4685657822283]], [[1.0, 0], [-4.800428364806, 2.771528608646259], [51.5, -89.20061658979718]], [[1.0, 0], [-5.175223991813245, 2.987916964789987], [53.5, -92.66471820493493]], [[1.0, 0], [-1.4359524847130536, -0.8290475535925935], [54.5, 94.39676901250381]], [[1.0, 0], [0, -16.454509525240997], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-672-168.11-c1-0-20', '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': 'ModularForm/GL2/Q/holomorphic/672/2/bd/a/431/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8315310918972729, 1.0294730322163013, 1.2227968016781114, 1.4095947875019796, 1.5837597210768577, 1.7350203425714767, 1.849624346923632, 1.911507482930008, 1.9038186039181713, 1.8107054452315974, 1.6192677782368563, 1.3215542335180475, 0.9164338474529727, 0.4111319687007215, -0.17780251517198206, -0.8243250291562886, -1.4937023115194994, -2.1444028040014254, -2.731060746748522, -3.208365454126198, -3.5355784070139693, -3.6812416795929046, -3.6275344199598987, -3.3736821902685006, -2.9378458785197017, -2.3570240812832908, -1.6846958393861098, -0.9861965499028069, -0.3321319123241802, 0.20954644004070122, 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'10.89634866941042231619797093009891'], 'prelabel': '2-672-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.36121076579957756, 'root_number': '-0.6432671415145419 + 0.7656418122384059*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3612107658', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71380078856180904625846779373', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57256343303906118053060970656', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24964531797280380953600697767', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.365947015830044, 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'conductor': 672, 'conductor_radical': 42, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/2/bd/a/431/8'], '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': '2-672-168.11-c1-0-20', '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': '2-672-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.36121076579957756, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71380078856180904625846779373', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2172500598291990102833014128959', 'Lhash_array': ['2172500598291990102833014128959'], 'factors': ['2-672-168.11-c1-0-20'], 'label': '2-672-168.11-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/2/bd/a/431/8'}