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lfunc_lfunctions • Show schema
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{'Lhash': '1605305889965222508384828266643', 'a10': [-4.362369917606078, -1.746429468765533], 'a2': [-1.8034419003973936, 0.17220782173107085], 'a3': [0.690079011482112, 0.7237340381050702], 'a4': [1.2588897597181885, -0.24263111385113553], 'a5': [2.3054228072984078, 1.1885280629817954], 'a6': [-1.3691500661063607, -1.1863752856728222], 'a7': [2.6381070359856933, 0.20097578630964516], 'a8': [1.2479700575334831, -0.3664370712856484], 'a9': [-0.0475819158237423, 0.998867339183008], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.690079011482112, -0.7237340381050702]]], [7, [[1.0, 0], [-2.6381070359856933, -0.20097578630964516]]], [23, [[1.0, 0], [-3.9608404417690113, -2.704023482673008]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.178', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '1937088986809325192010136798980', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8034419003973936, -0.17220782173107085], [1.9638573945254134, -0.37850248872082043]], [[1.0, 0], [-0.690079011482112, -0.7237340381050702]], [[1.0, 0], [-2.3054228072984078, -1.1885280629817954], [2.900284547855991, 4.072879760251679]], [[1.0, 0], [-2.6381070359856933, -0.20097578630964516]], [[1.0, 0], [0.33623163892325486, -3.5211770277219587], [-10.801215669889773, -2.081763687964512]], [[1.0, 0], [-3.6755716337445588, 0.5284674189561096], [12.473408656988466, -3.662523238938586]], [[1.0, 0], [1.7823701013157174, 5.149820202234956], [-13.362902610627387, 10.50870276575029]], [[1.0, 0], [-2.687971583803553, 7.766383847600823], [-14.935008800112962, -11.7450207381915]], [[1.0, 0], [-3.9608404417690113, -2.704023482673008]], [[1.0, 0], [5.104918799361237, -5.891390351788375], [-4.127130309925269, -28.70482181454705]], [[1.0, 0], [6.359141619094222, 1.542711064303999], [27.553898908302628, 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[0.23330516510728702, 0.2966716510477333], [-18.62495590524475, 76.7731138975598]], [[1.0, 0], [11.793296519076481, 7.579091464985568], [34.479446079156574, 75.49945561442503]], [[1.0, 0], [3.9288025687215034, 16.19474476202889], [-79.10635493028819, 40.78216043373953]], [[1.0, 0], [-4.666305521162914, 2.9988524659965368], [40.295256261182985, -88.23430354938829]], [[1.0, 0], [6.825811108097616, 13.240226374999859], [-58.585747866691015, 82.2721711570839]], [[1.0, 0], [7.220061515850555, -10.139157703480585], [-33.68800022169443, -97.33508432761086]], [[1.0, 0], [-2.4281720323829754, 2.546593536348815], [-5.091264993140426, -106.87880529258186]], [[1.0, 0], [9.64876277782859, -3.339469265825261], [85.67978732696383, -67.37932949804596]], [[1.0, 0], [-8.807512615654455, -4.022256238161907], [73.99926293581721, 85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-483-161.17-c1-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 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'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.3060917553447641, 'root_number': '0.5721957441283143 - 0.82011708334935*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.153045877672', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26636305751458739947012121941', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91840538952144126629054140110', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85420110403822294134062860069', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.17', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/178/8'], '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': '2-483-161.17-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': '2-483-161.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.15304587767238206, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26636305751458739947012121941', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1605305889965222508384828266643', 'Lhash_array': ['1605305889965222508384828266643'], 'label': '2-483-161.17-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/178/8'}