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lfunc_lfunctions • Show schema
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{'Lhash': '968507506023151016319659716827', 'a10': [1.2280336376379648, 0], 'a2': [0, -0.3563939586926006], 'a3': [0, 0], 'a4': [3.872983346207417, 0], 'a5': [0, 3.445719568712378], 'a6': [0, 0], 'a7': [3.968118785068667, 0], 'a8': [0, -2.805883701475779], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.485', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '1808408491839581903606583869579', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.3563939586926006], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.445719568712378], [-25.0, 0]], [[1.0, 0], [-3.968118785068667, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.7561538271543515, 0], [169.0, 0]], [[1.0, 0], [0, -29.128018890835587], [-289.0, 0]], [[1.0, 0], 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-1.5708250630859735], 'positive_zeros': ['0.76401770791476745414658371733310', '2.09201628835237726104402598479618', '3.01124383649700552699108117390892', '4.60717939824864066822573971646779', '5.09990130852736522225462523450452', '6.32809750336805255085471587609719', '6.97146993645658815692035097986146', '7.976410793738103177510937030234547', '8.499331705634766999045484248163199', '9.594956438456352994449364324305062'], 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.3040867239846964, 'root_number': '0.57735026918962576450914878050195745564760175127012687602 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1520433619923482', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76401770791476745414658371733', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09201628835237726104402598480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01124383649700552699108117391', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/h/485/4'], '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': '2-33e2-3.2-c2-0-29', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.1520433619923482, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76401770791476745414658371733', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '968507506023151016319659716827', 'Lhash_array': ['968507506023151016319659716827'], 'label': '2-33e2-3.2-c2-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/h/485/4'}