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lfunc_lfunctions • Show schema
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{'Lhash': '1073554215189463842256072700930', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.6942516769581215, -0.35987672212105215], 'a4': [0, 0], 'a5': [1.7426049511543429, 3.018280312920403], 'a6': [0, 0], 'a7': [-1.349883167691174, 2.338066230723132], 'a8': [0, 0], 'a9': [2.740977489750814, 1.219443479903569], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.6942516769581215, 0.35987672212105215]]]], 'bad_primes': [2, 3], 'central_character': '1152.385', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1518965831283640750041290538936', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.6942516769581215, 0.35987672212105215]], [[1.0, 0], [-1.7426049511543429, -3.018280312920403], [-2.5, 4.330127018922194]], [[1.0, 0], [1.349883167691174, -2.338066230723132], [-3.5, 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2.5293451713657884], [-30.5, -52.827549630850754]], [[1.0, 0], [1.5682870218550966, 2.7163528027039097], [-33.5, 58.023702053557386]], [[1.0, 0], [-8.196471636644853, 0], [71.0, 0]], [[1.0, 0], [-5.217962665636132, 0], [73.0, 0]], [[1.0, 0], [0.7162595493548972, -1.2405979308890698], [-39.5, -68.41600689897065]], [[1.0, 0], [1.7405198410467497, -3.014668796274677], [-41.5, -71.88010851410841]], [[1.0, 0], [12.405846133431721, 0], [89.0, 0]], [[1.0, 0], [3.502650873297709, -6.06676927372713], [-48.5, -84.00446416709055]], [[1.0, 0], [-4.442371286536691, 7.6944127743666675], [-50.5, -87.4685657822283]], [[1.0, 0], [2.650116832308826, 4.590136999552377], [-51.5, 89.20061658979718]], [[1.0, 0], [7.5399255589565515, 0], [107.0, 0]], [[1.0, 0], [-13.883978585420666, 0], [109.0, 0]], [[1.0, 0], [-1.365488529801561, -2.3650955107688327], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1152-9.7-c1-0-15', 'leading_term': '1.384377534194544318632346478720809021504557596225133478', '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/1152/2/i/l/385/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3843775341945443, 1.3323477854532921, 1.2741860294991616, 1.2097697280814699, 1.1388719117316646, 1.0612144379599708, 0.97652623456325, 0.8846031966235465, 0.7853666885151773, 0.6789180812888629, 0.5655873053682082, 0.44597391607630643, 0.3209795930814684, 0.19183130373015997, 0.060094565342366645, -0.07232362807565648, -0.20318255856627865, -0.329926476716095, -0.44971439219971504, -0.5594609830177079, -0.6558884617764809, -0.7355890082454836, -0.7950971047931482, -0.8309708025772694, -0.8398806120416317, -0.8187043640687384, -0.7646260423480898, -0.6752362584544289, -0.5486317446352724, 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'9.387789834838286918609324212609730', '9.778943889629185930155853574105543'], 'prelabel': '2-1152-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.3112001244570185, 'root_number': '0.5589610464968425461116907154121535645798062687794839306 - 0.8291939148951556465524517239691072153813328713313003580*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15560006222850925', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.846884949998193348373297510134', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.80186529329824185921418904981', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89696803061324049781504461681', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/i/l/385/1'], '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': '2-1152-9.7-c1-0-15', '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': '2-1152-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.15560006222850925, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.846884949998193348373297510134', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1073554215189463842256072700930', 'Lhash_array': ['1073554215189463842256072700930'], 'label': '2-1152-9.7-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/i/l/385/1'}