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lfunc_lfunctions • Show schema
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{'Lhash': '1968423848801101490004204953220', 'a10': [0, 0], 'a2': [1.224744871391589, -0.7071067811865476], 'a3': [-0.8660254037844386, 1.5], 'a4': [1.0, -1.7320508075688772], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [-4.0103705131194305, 5.73732763118006], 'a8': [0, -2.8284271247461903], 'a9': [-1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.224744871391589, 0.7071067811865476]]], [3, [[1.0, 0], [0.8660254037844386, -1.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [4.0103705131194305, -5.73732763118006]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.199', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '263642693486164250456277616060', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.224744871391589, 0.7071067811865476]], [[1.0, 0], [0.8660254037844386, -1.5]], 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[0]], 'group': 'GL2', 'index': 37, 'label': '2-1050-35.24-c2-0-37', 'leading_term': '0.847673879353904077021144936204961001119438441175437293', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/q/e/199/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.847673879353904, 1.0716930261415354, 1.2863511180864202, 1.4901009934019016, 1.6813674993126617, 1.8585377538494332, 2.019958352602066, 2.1639403332081106, 2.288772352200477, 2.3927421608370985, 2.4741661057046866, 2.5314260397933146, 2.563012720041905, 2.5675744940672245, 2.54396984501999, 2.491322170469992, 2.4090750192266728, 2.2970458993206457, 2.155476701787143, 1.985078759958552, 1.7870705849947661, 1.5632063881675198, 1.3157936218895327, 1.0476979471964916, 0.7623342670421372, 0.46364275271230976, 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'7.898046668892301615734027196461427', '9.427375219238000070668794417298835', '9.938815351015208219201263362402834'], 'prelabel': '2-1050-35.24-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.8014232912305301, 'root_number': '-0.8116371218442962338225356832995580178848172030558225086 + 0.5841619488158288364238471463964233662460007824456832689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.40071164561526507', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55281261922386499504060042663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80969624989166754143400913513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20885484036990919607931185487', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.24', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/q/e/199/15'], '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': '2-1050-35.24-c2-0-37', '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': '2-1050-35.24-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.40071164561526507, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55281261922386499504060042663', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1968423848801101490004204953220', 'Lhash_array': ['1968423848801101490004204953220'], 'label': '2-1050-35.24-c2-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/q/e/199/15'}