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lfunc_lfunctions • Show schema
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{'Lhash': '312741958973006387234595792704,1445233685856883390048724675626', 'a10': -10, 'a2': -2, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 22, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2284.031974655972, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 4]], [3, [1]], [5, [1, -5, 25]]], 'bad_primes': [2, 3, 5], 'central_character': '810.1', 'coefficient_field': '1.1.1.1', 'conductor': 656100, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 2, 4], [1], [1, -5, 25], [1, -22, 141, -7546, 117649], [1, -12, -1187, -15972, 1771561], [1, 38, -753, 83486, 4826809], [1, 210, 20851, 1031730, 24137569], [1, 314, 38367, 2153726, 47045881], [1, -117, 1522, -1423539, 148035889], [1, 66, -20033, 1609674, 594823321], [1, -25, -29166, -744775, 887503681], [1, -628, 199902, -31810084, 2565726409], [1, -504, 185095, -34736184, 4750104241], [1, 380, 64893, 30212660, 6321363049], [1, -252, -40319, 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{'algebraic': True, 'analytic_conductor': 2284.031974655972, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 656100, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 0, 5, 0, 22, 8, 0, -10, 12, 0, -38, -44, 0, -16, -210, 0, -314, 0, 0, -24, 117, 0, 0, 76, 0, 0, -66, 0, 25, 0, 0, 420, 110, 0, 628, 628, 0, 40, 504, 0, -380, 0, 0, -234, 252, 0, 343, 0, 0, 0, 6, 0, 60, 176, 0, 132, 318, 0, -293, -50, 0, 64, -190, 0, 322, 0, 0, -220, -240, 0, 88, -1256, 0, 0, 264, 0, -917, -80, 0, -1008, -309, 0, -1050, 760, 0, 96, 2544, 0, -836, 0, 0, -504, -1570, 0, -1328, -686, 0, 0], 'euler11': [1, -12, -1187, -15972, 1771561], 'euler13': [1, 38, -753, 83486, 4826809], 'euler17': [1, 210, 20851, 1031730, 24137569], 'euler19': [1, 314, 38367, 2153726, 47045881], 'euler2': [1, 2, 4, 0, 0], 'euler23': [1, -117, 1522, -1423539, 148035889], 'euler29': [1, 66, -20033, 1609674, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -25, -29166, -744775, 887503681], 'euler37': [1, -628, 199902, -31810084, 2565726409], 'euler41': [1, -504, 185095, -34736184, 4750104241], 'euler43': [1, 380, 64893, 30212660, 6321363049], 'euler47': [1, -252, -40319, -26163396, 10779215329], 'euler5': [1, -5, 25, 0, 0], 'euler53': [1, -6, 297763, -893262, 22164361129], 'euler59': [1, -318, -104255, -65310522, 42180533641], 'euler61': [1, 293, -141132, 66505433, 51520374361], 'euler67': [1, -322, -197079, -96845686, 90458382169], 'euler7': [1, -22, 141, -7546, 117649], 'euler71': [1, 240, 730222, 85898640, 128100283921], 'euler73': [1, -88, 779970, -34233496, 151334226289], 'euler79': [1, 917, 347850, 452116763, 243087455521], 'euler83': [1, 309, -476306, 176682183, 326940373369], 'euler89': [1, -2544, 3027922, -1793441136, 496981290961], 'euler97': [1, 1328, 850911, 1212029744, 832972004929], 'euler_factors': [[1, 2, 4, 0, 0], [1, 0, 0, 0, 0], [1, -5, 25, 0, 0], [1, -22, 141, -7546, 117649], [1, -12, -1187, -15972, 1771561], [1, 38, -753, 83486, 4826809], [1, 210, 20851, 1031730, 24137569], [1, 314, 38367, 2153726, 47045881], [1, -117, 1522, -1423539, 148035889], [1, 66, -20033, 1609674, 594823321], [1, -25, -29166, -744775, 887503681], [1, -628, 199902, -31810084, 2565726409], [1, -504, 185095, -34736184, 4750104241], [1, 380, 64893, 30212660, 6321363049], [1, -252, -40319, -26163396, 10779215329], [1, -6, 297763, -893262, 22164361129], [1, -318, -104255, -65310522, 42180533641], [1, 293, -141132, 66505433, 51520374361], [1, -322, -197079, -96845686, 90458382169], [1, 240, 730222, 85898640, 128100283921], [1, -88, 779970, -34233496, 151334226289], [1, 917, 347850, 452116763, 243087455521], [1, 309, -476306, 176682183, 326940373369], [1, -2544, 3027922, -1793441136, 496981290961], [1, 1328, 850911, 1212029744, 832972004929]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/4/e/k'], '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': '4-810e2-1.1-c3e2-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-810e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.91314306988145, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 403448015121681905, 'z1': {'__RealLiteral__': 0, 'data': '0.24670990485603835418528857033', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '312741958973006387234595792704,1445233685856883390048724675626', 'Lhash_array': ['312741958973006387234595792704', '1445233685856883390048724675626'], 'label': '4-810e2-1.1-c3e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/4/e/k'}