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lfunc_lfunctions • Show schema
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{'Lhash': '824017027638932342642791027876,1487618145301975064296925291260', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 167.334019432485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 2, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1', 'coefficient_field': '1.1.1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, 5], [1, 0, -10, 0, 49], [1, -2, 23, -22, 121], [1, 0, -26, 0, 169], [1, 0, -30, 0, 289], [1, -6, 47, -114, 361], [1, 0, -30, 0, 529], [1, -6, 67, -174, 841], [1, -2, 63, -62, 961], [1, 0, 26, 0, 1369], [1, -2, 83, -82, 1681], [1, 0, 14, 0, 1849], [1, 0, 6, 0, 2209], [1, 0, -70, 0, 2809], [1, -26, 287, -1534, 3481], [1, 20, 222, 1220, 3721], [1, 0, -70, 0, 4489], [1, -18, 223, -1278, 5041], [1, 0, 50, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -66, 0, 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3.7753020591534607], 'positive_zeros': ['0.65003481834077567201944889585487', '1.17352379672611871956514233765983', '2.06085513851116566833499558607872', '2.68154440202702238267960927532598', '3.25145784805764919485272193723211', '3.61855226745933147483145720660814', '4.31476067243051768989509818280510', '4.32295660090599444010286213009929', '5.10965468354132988261159119785664', '5.51059894091704824499375695885040', '5.86716026524831793682116781716208', '6.49583072588978968921695620220483', '6.89022073050100050132739702632597', '7.14745750364661776362062473861558', '7.80141195827052797798254659886934', '7.80934416010358008910074318894671', '8.545600757907975704833084053318735', '8.638053333556294759308635496698615', '9.156776869237081681227048108457177', '9.752663051235749526247372434374780'], 'prelabel': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 373170168199359213, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65003481834077567201944889585', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17352379672611871956514233766', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.06085513851116566833499558608', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 167.334019432485, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -1, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -4, 0, 0, 0, 26, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0], 'euler11': [1, -2, 23, -22, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, -6, 47, -114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, -6, 67, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -2, 63, -62, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, -2, 83, -82, 1681], 'euler43': [1, 0, 14, 0, 1849], 'euler47': [1, 0, 6, 0, 2209], 'euler5': [1, 2, 5, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, -26, 287, -1534, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 0, -70, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, -18, 223, -1278, 5041], 'euler73': [1, 0, 50, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, -66, 0, 6889], 'euler89': [1, 26, 347, 2314, 7921], 'euler97': [1, 0, -94, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, 5, 0, 0], [1, 0, -10, 0, 49], [1, -2, 23, -22, 121], [1, 0, -26, 0, 169], [1, 0, -30, 0, 289], [1, -6, 47, -114, 361], [1, 0, -30, 0, 529], [1, -6, 67, -174, 841], [1, -2, 63, -62, 961], [1, 0, 26, 0, 1369], [1, -2, 83, -82, 1681], [1, 0, 14, 0, 1849], [1, 0, 6, 0, 2209], [1, 0, -70, 0, 2809], [1, -26, 287, -1534, 3481], [1, 20, 222, 1220, 3721], [1, 0, -70, 0, 4489], [1, -18, 223, -1278, 5041], [1, 0, 50, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -66, 0, 6889], [1, 26, 347, 2314, 7921], [1, 0, -94, 0, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/d/a'], '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': '4-1620e2-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 373170168199359213, 'z1': {'__RealLiteral__': 0, 'data': '0.65003481834077567201944889585', 'prec': 103}}
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{'Lhash': '824017027638932342642791027876,1487618145301975064296925291260', 'Lhash_array': ['824017027638932342642791027876', '1487618145301975064296925291260'], 'label': '4-1620e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/d/a'}