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lfunc_lfunctions • Show schema
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{'Lhash': '1428433896680708592564453524476,4466908589877813502197252613988', 'a10': 15, 'a2': -3, 'a3': 2, 'a4': 8, 'a5': -5, 'a6': -6, 'a7': -28, 'a8': -45, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.264501095798759, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 5, 25]], [7, [1, 28, 343]]], 'bad_primes': [5, 7], 'central_character': '35.1', 'coefficient_field': '1.1.1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'euler_factors': [[1, 3, 1, 24, 64], [1, -2, -23, -54, 729], [1, 5, 25], [1, 28, 343], [1, -45, 694, -59895, 1771561], [1, -118, 7875, -259246, 4826809], [1, -54, -1997, -265302, 24137569], [1, -121, 7782, -829939, 47045881], [1, 69, -7406, 839523, 148035889], [1, 324, 75022, 7902036, 594823321], [1, -88, -22047, -2621608, 887503681], [1, -259, 16428, -13119127, 2565726409], [1, -390, 175867, -26879190, 4750104241], [1, 572, 240810, 45478004, 6321363049], [1, 45, -101798, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 49518558479408203, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12683565678392103078838503175', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49957138537137634703060155228', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52376955375052533082259834212', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 4.264501095798759, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'dirichlet_coefficients': [1, -3, 2, 8, -5, -6, -28, -45, 27, 15, 45, 16, 118, 84, -10, 135, 54, -81, 121, -40, -56, -135, -69, -90, 0, -354, 154, -224, -324, 30, 88, -360, 90, -162, 140, 216, 259, -363, 236, 225, 390, 168, -572, 360, -135, 207, -45, 270, 441, 0, 108, 944, -597, -462, -225, 1260, 242, 972, 360, -80, -392, -264, -756, 1513, -590, -270, 280, 432, -138, -420, 96, -1215, -668, -777, 0, 968, -1260, -708, -782, -675, 308, -1170, 1536, -448, -270, 1716, -648, -2025, 1194, 405, -3304, -552, 176, 135, -605, -720, 1804, -1323, 1215, 0], 'euler11': [1, -45, 694, -59895, 1771561], 'euler13': [1, -118, 7875, -259246, 4826809], 'euler17': [1, -54, -1997, -265302, 24137569], 'euler19': [1, -121, 7782, -829939, 47045881], 'euler2': [1, 3, 1, 24, 64], 'euler23': [1, 69, -7406, 839523, 148035889], 'euler29': [1, 324, 75022, 7902036, 594823321], 'euler3': [1, -2, -23, -54, 729], 'euler31': [1, -88, -22047, -2621608, 887503681], 'euler37': [1, -259, 16428, -13119127, 2565726409], 'euler41': [1, -390, 175867, -26879190, 4750104241], 'euler43': [1, 572, 240810, 45478004, 6321363049], 'euler47': [1, 45, -101798, 4672035, 10779215329], 'euler5': [1, 5, 25, 0, 0], 'euler53': [1, 597, 207532, 88879569, 22164361129], 'euler59': [1, -360, -75779, -73936440, 42180533641], 'euler61': [1, 392, -73317, 88976552, 51520374361], 'euler67': [1, -280, -222363, -84213640, 90458382169], 'euler7': [1, 28, 343, 0, 0], 'euler71': [1, -96, 718126, -34359456, 128100283921], 'euler73': [1, 668, 57207, 259863356, 151334226289], 'euler79': [1, 782, 118485, 385556498, 243087455521], 'euler83': [1, -1536, 1733398, -878264832, 326940373369], 'euler89': [1, -1194, 720667, -841732986, 496981290961], 'euler97': [1, -1804, 2638950, -1646462092, 832972004929], 'euler_factors': [[1, 3, 1, 24, 64], [1, -2, -23, -54, 729], [1, 5, 25, 0, 0], [1, 28, 343, 0, 0], [1, -45, 694, -59895, 1771561], [1, -118, 7875, -259246, 4826809], [1, -54, -1997, -265302, 24137569], [1, -121, 7782, -829939, 47045881], [1, 69, -7406, 839523, 148035889], [1, 324, 75022, 7902036, 594823321], [1, -88, -22047, -2621608, 887503681], [1, -259, 16428, -13119127, 2565726409], [1, -390, 175867, -26879190, 4750104241], [1, 572, 240810, 45478004, 6321363049], [1, 45, -101798, 4672035, 10779215329], [1, 597, 207532, 88879569, 22164361129], [1, -360, -75779, -73936440, 42180533641], [1, 392, -73317, 88976552, 51520374361], [1, -280, -222363, -84213640, 90458382169], [1, -96, 718126, -34359456, 128100283921], [1, 668, 57207, 259863356, 151334226289], [1, 782, 118485, 385556498, 243087455521], [1, -1536, 1733398, -878264832, 326940373369], [1, -1194, 720667, -841732986, 496981290961], [1, -1804, 2638950, -1646462092, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/4/e/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': '4-35e2-1.1-c3e2-0-0', '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': '4-35e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4370340462915006, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 49518558479408203, 'z1': {'__RealLiteral__': 0, 'data': '1.12683565678392103078838503175', 'prec': 103}}
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{'Lhash': '1428433896680708592564453524476,4466908589877813502197252613988', 'Lhash_array': ['1428433896680708592564453524476', '4466908589877813502197252613988'], 'label': '4-35e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/4/e/a'}