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lfunc_lfunctions • Show schema
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{'Lhash': '1598833842378200470942396962749', 'a10': [0.0, 0.0], 'a2': [0.0, -1.8019377358048383], 'a3': [0.0, 0.4450418679126288], 'a4': [-2.246979603717467, 0.0], 'a5': [0.0, 0.0], 'a6': [0.8019377358048383, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 2.246979603717467], 'a9': [0.8019377358048383, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8858403974235793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [71, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 71], 'central_character': '1775.1774', 'coefficient_field': 'CDF', 'conductor': 1775, 'conductor_radical': 355, 'conjugate': '1365340971574364134536523530329', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.8019377358048383], [-1.0, 0]], [[1.0, 0], [0, -0.4450418679126288], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], 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'1.07980861316353492578570915767', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1775/1/c/a/1774/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.079808613163535, 1.1198313784264529, 1.1699318355749733, 1.2295036486364992, 1.2969223901725933, 1.3697220094652531, 1.4448007757353902, 1.5186066508127214, 1.587281401171345, 1.6467651140184028, 1.6928731270833028, 1.7213589131634222, 1.7279738567375809, 1.708531254650242, 1.6589786653497793, 1.5754802824539755, 1.4545092459814672, 1.2929485470720727, 1.0881982667462637, 0.838286203696581, 0.5419784237462224, 0.19888587124083493, -0.1904370914749989, -0.6244065052653716, -1.1003393130435923, -1.6144047445995433, -2.161600540726375, -2.7357575612140566, -3.3295757555119923, -3.93469375385148, -4.54179346806792, 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'9.703821838208654933130308519391784'], 'prelabel': '2-1775-355.354-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9411909463140725, 'root_angle': 0.6475836176504333, 'root_number': '-0.44721359549995793928183473374601 + 0.89442719099991587856366946749279*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26125751219645572983642261369', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15519378475634476919851249189', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39267957355157035999478368087', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8858403974235793, 'bad_primes': [5, 71], 'central_character': '355.354', 'conductor': 1775, 'conductor_radical': 355, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1775/1/c/a/1774/1'], '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': '2-1775-355.354-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1775-355.354-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9411909463140725, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26125751219645572983642261369', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1598833842378200470942396962749', 'Lhash_array': ['1598833842378200470942396962749'], 'label': '2-1775-355.354-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1775/1/c/a/1774/1'}