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lfunc_lfunctions • Show schema
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{'Lhash': '854230488227215657706624938696,2264415908027723295312251492154', 'a10': 0, 'a2': 0, 'a3': 42, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1035, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1951.0228275672052, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -42, 729]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -42, 729], [1, 0, -2450, 0, 244140625], [1, 4, 235302, 470596, 13841287201], [1, 0, -3541970, 0, 3138428376721], [1, -5900, 18356118, -28478173100, 23298085122481], [1, 0, -28202690, 0, 582622237229761], [1, -10516, 121738326, -494734484596, 2213314919066161], [1, 0, -191004770, 0, 21914624432020321], [1, 0, -1184779442, 0, 353814783205469041], [1, 45796, 2299325766, 40644118575076, 787662783788549761], [1, 68116, 6291400182, 174767020075444, 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{'algebraic': True, 'analytic_conductor': 1951.0228275672052, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 42, 0, 0, 0, -4, 0, 1035, 0, 0, 0, 5900, 0, 0, 0, 0, 0, 10516, 0, -168, 0, 0, 0, 2450, 0, 12852, 0, 0, 0, -45796, 0, 0, 0, 0, 0, -68116, 0, 247800, 0, 0, 0, -12812, 0, 0, 0, 0, 0, -235286, 0, 0, 0, 0, 0, 0, 0, 441672, 0, 0, 0, 125132, 0, -4140, 0, 0, 0, 877396, 0, 0, 0, 0, 0, -1461020, 0, 102900, 0, 0, 0, -681124, 0, -214731, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23600, 0, -1923432, 0, 0, 0, -562172, 0, 0, 0], 'euler11': [1, 0, -3541970, 0, 3138428376721], 'euler13': [1, -5900, 18356118, -28478173100, 23298085122481], 'euler17': [1, 0, -28202690, 0, 582622237229761], 'euler19': [1, -10516, 121738326, -494734484596, 2213314919066161], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -191004770, 0, 21914624432020321], 'euler29': [1, 0, -1184779442, 0, 353814783205469041], 'euler3': [1, -42, 729, 0, 0], 'euler31': [1, 45796, 2299325766, 40644118575076, 787662783788549761], 'euler37': [1, 68116, 6291400182, 174767020075444, 6582952005840035281], 'euler41': [1, 0, -9219079010, 0, 22563490300366186081], 'euler43': [1, 12812, 12683762934, 80989303383788, 39959630797262576401], 'euler47': [1, 0, 10801249342, 0, 116191483108948578241], 'euler5': [1, 0, -2450, 0, 244140625], 'euler53': [1, 0, -7253988050, 0, 491258904256726154641], 'euler59': [1, 0, 22449655150, 0, 1779197418239532716881], 'euler61': [1, -125132, 106955253078, -6446847484540652, 2654348974297586158321], 'euler67': [1, -877396, 373372699542, -79367822681551924, 8182718904632857144561], 'euler7': [1, 4, 235302, 470596, 13841287201], 'euler71': [1, 0, -251546372642, 0, 16409682740640811134241], 'euler73': [1, 1461020, 836313312678, 221102331292754780, 22902048046490258711521], 'euler79': [1, 681124, 602157386886, 165572700054285604, 59091511031674153381441], 'euler83': [1, 0, -407613512306, 0, 106890007738661124410161], 'euler89': [1, 0, -844406214050, 0, 246990403565262140303521], 'euler97': [1, 562172, 1744953349254, 468273537954945788, 693842360995438000295041], 'euler_factors': [[1, 0, 0, 0, 0], [1, -42, 729, 0, 0], [1, 0, -2450, 0, 244140625], [1, 4, 235302, 470596, 13841287201], [1, 0, -3541970, 0, 3138428376721], [1, -5900, 18356118, -28478173100, 23298085122481], [1, 0, -28202690, 0, 582622237229761], [1, -10516, 121738326, -494734484596, 2213314919066161], [1, 0, -191004770, 0, 21914624432020321], [1, 0, -1184779442, 0, 353814783205469041], [1, 45796, 2299325766, 40644118575076, 787662783788549761], [1, 68116, 6291400182, 174767020075444, 6582952005840035281], [1, 0, -9219079010, 0, 22563490300366186081], [1, 12812, 12683762934, 80989303383788, 39959630797262576401], [1, 0, 10801249342, 0, 116191483108948578241], [1, 0, -7253988050, 0, 491258904256726154641], [1, 0, 22449655150, 0, 1779197418239532716881], [1, -125132, 106955253078, -6446847484540652, 2654348974297586158321], [1, -877396, 373372699542, -79367822681551924, 8182718904632857144561], [1, 0, -251546372642, 0, 16409682740640811134241], [1, 1461020, 836313312678, 221102331292754780, 22902048046490258711521], [1, 681124, 602157386886, 165572700054285604, 59091511031674153381441], [1, 0, -407613512306, 0, 106890007738661124410161], [1, 0, -844406214050, 0, 246990403565262140303521], [1, 562172, 1744953349254, 468273537954945788, 693842360995438000295041]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/7/e/f'], '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': '4-192e2-1.1-c6e2-0-6', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6, 6], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.646080352735091, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c6e2-0', 'trace_hash': 2020629220119325546, 'z1': {'__RealLiteral__': 0, 'data': '0.67386903621030821180945764961', 'prec': 103}}
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{'Lhash': '854230488227215657706624938696,2264415908027723295312251492154', 'Lhash_array': ['854230488227215657706624938696', '2264415908027723295312251492154'], 'label': '4-192e2-1.1-c6e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/7/e/f'}