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lfunc_lfunctions • Show schema
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{'Lhash': '1465784478477871402245971817507', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.4648935594050156, 1.7908499979142523], 'a4': [0.0, 0.0], 'a5': [0.5506061293460608, 1.6945914197561593], 'a6': [0.0, 0.0], 'a7': [0.2856289960119397, 0.2075216128341478], 'a8': [0.0, 0.0], 'a9': [1.941505561042008, -5.975339702553192], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.729518915659945, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11], 'central_character': '968.9', 'coefficient_field': 'CDF', 'conductor': 968, 'conductor_radical': 22, 'conjugate': '744623436876326684411465416079', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.4648935594050156, -1.7908499979142523], [0.9270509831248422, -2.853169548885461]], [[1.0, 0], [-0.5506061293460608, -1.6945914197561593], [-4.045084971874737, 2.9389262614623655]], [[1.0, 0], [-0.2856289960119397, 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[-3.7009615369048054, 2.6889059510734232], [33.06481839811937, -101.76304724358143]], [[1.0, 0], [-20.659239941903643, 0], [109.0, 0]], [[1.0, 0], [7.123506260120273, -5.175530246489797], [34.91892036436906, -107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-968-11.9-c1-0-13', '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/968/2/i/t/9/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8832182858170319, 0.9430849973724186, 0.9681690326710111, 0.9571587553694474, 0.906785198976138, 0.8137138571846134, 0.676655395898192, 0.49833900185954966, 0.28709080509687207, 0.057822631979542426, -0.16773524744973706, -0.36169884221984405, -0.4916854338701231, -0.5234665654507634, -0.42450659024285453, -0.16813101788231138, 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'1.93022351177459967814413950345687', '4.05016070354977941547841500529100', '4.96120802478850888578047319823424', '5.91890437587490165666538944035466', '6.39233459214346242393676821899296', '7.35734468242280426309386159918227', '8.207423467258822352735577117968538', '9.166561763788102882464552356124875', '10.19670250919378741249032341873142'], 'prelabel': '2-968-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7802012365402518, 'root_angle': 0.015134948408686913, 'root_number': '0.9988698142765218 + 0.04752992875217496*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00756747420434', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15630007055096233078225971207', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93022351177459967814413950346', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05016070354977941547841500529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.729518915659945, 'bad_primes': [2, 11], 'central_character': '11.9', 'conductor': 968, 'conductor_radical': 22, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/968/2/i/t/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': '2-968-11.9-c1-0-13', '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': '2-968-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7802012365402518, 'root_angle': 0.0075674742043434565, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15630007055096233078225971207', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1465784478477871402245971817507', 'Lhash_array': ['1465784478477871402245971817507'], 'label': '2-968-11.9-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/968/2/i/t/9/1'}