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lfunc_lfunctions • Show schema
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{'Lhash': '1127202779363276537322729563751', 'a10': [-632.6418269723767, 365.2559291031184], 'a2': [2.8284271247461903, -4.898979485566356], 'a3': [0, 0], 'a4': [-16.0, -27.712812921102035], 'a5': [-111.83633147860353, -64.56873608435197], 'a6': [0, 0], 'a7': [298.742895211047, 168.52798747069102], 'a8': [-181.01933598375618, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.986814536101228, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.8284271247461903, 4.898979485566356]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-298.742895211047, -168.52798747069102]]]], 'bad_primes': [2, 3, 7], 'central_character': '126.19', 'coefficient_field': 'CDF', 'conductor': 126, 'conductor_radical': 42, 'conjugate': '1277821327723177528672627846703', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.8284271247461903, 4.898979485566356]], [[1.0, 0], [0, 0]], [[1.0, 0], [111.83633147860353, 64.56873608435197], 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['0.889206204896154774329870802088726', '3.27480214183260080501061626120547', '4.21177584064830967784401313026314', '5.70019770618330198411903536875795', '6.90951229549827929870433315629806', '7.979076366795739041542347789028100', '8.694008440378868089751086221598375', '10.52466265760648675004449539377702', '11.38085017497097305565802769736940', '12.23443620634502081773857055141948'], 'prelabel': '2-126-7.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.383940428357397, 'root_angle': 0.10191845553325436, 'root_number': '0.801873221643530766224862532714819943163426269577909730 + 0.597494214541885737525795472897805282867284050190156778*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10191845553325436', 'prec': 64}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.889206204896154774329870802089', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.27480214183260080501061626121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21177584064830967784401313026', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.986814536101228, 'bad_primes': [2, 3, 7], 'central_character': '7.5', 'conductor': 126, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/126/7/n/c/19/3'], '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': '2-126-7.5-c6-0-6', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-126-7.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.383940428357397, 'root_angle': 0.10191845553325436, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.889206204896154774329870802089', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1127202779363276537322729563751', 'Lhash_array': ['1127202779363276537322729563751'], 'factors': ['2-126-7.5-c6-0-6'], 'label': '2-126-7.5-c6-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/126/7/n/c/19/3'}