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lfunc_lfunctions • Show schema
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{'Lhash': '1465082654299527465202272847958,2340781288922356043149155385670', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 100, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1442, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.19507854353348, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '32.1', 'coefficient_field': '1.1.1.1', 'conductor': 1024, 'conductor_radical': 2, 'degree': 4, 'euler_factors': [[1], [1, 0, -1442, 0, 531441], [1, -100, 33750, -1562500, 244140625], [1, 0, -201442, 0, 13841287201], [1, 0, 900542, 0, 3138428376721], [1, -4484, 14680182, -21643411556, 23298085122481], [1, -5796, 56673542, -139901349924, 582622237229761], [1, 0, -29257058, 0, 2213314919066161], [1, 0, 49293278, 0, 21914624432020321], [1, 41980, 1630226742, 24970683015580, 353814783205469041], [1, 0, 422727038, 0, 787662783788549761], [1, -804, 5131614422, -2062844032836, 6582952005840035281], [1, -26660, 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'14.62744028540702363745568140669278', '15.54426792500702816774303018505931', '15.58884467137024277747438973153664'], 'prelabel': '4-2e10-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.713250942289569, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c6e2-0', 'trace_hash': 840671464753109386, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15574642889432793977596692190', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84655084650369656166958470320', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62455928271443368042648450628', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 54.19507854353348, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 1024, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 100, 0, 0, 0, 1442, 0, 0, 0, 4484, 0, 0, 0, 5796, 0, 0, 0, 0, 0, 0, 0, -23750, 0, 0, 0, -41980, 0, 0, 0, 0, 0, 0, 0, 804, 0, 0, 0, 26660, 0, 0, 0, 144200, 0, 0, 0, 201442, 0, 0, 0, 343140, 0, 0, 0, 0, 0, 0, 0, -541756, 0, 0, 0, 448400, 0, 0, 0, 0, 0, 0, 0, -1393212, 0, 0, 0, 0, 0, 0, 0, 1547923, 0, 0, 0, 579600, 0, 0, 0, -323196, 0, 0, 0, 0, 0, 0, 0, 1040612, 0, 0, 0], 'euler11': [1, 0, 900542, 0, 3138428376721], 'euler13': [1, -4484, 14680182, -21643411556, 23298085122481], 'euler17': [1, -5796, 56673542, -139901349924, 582622237229761], 'euler19': [1, 0, -29257058, 0, 2213314919066161], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 49293278, 0, 21914624432020321], 'euler29': [1, 41980, 1630226742, 24970683015580, 353814783205469041], 'euler3': [1, 0, -1442, 0, 531441], 'euler31': [1, 0, 422727038, 0, 787662783788549761], 'euler37': [1, -804, 5131614422, -2062844032836, 6582952005840035281], 'euler41': [1, -26660, 9677897382, -126637779065060, 22563490300366186081], 'euler43': [1, 0, -12606965698, 0, 39959630797262576401], 'euler47': [1, 0, -596024002, 0, 116191483108948578241], 'euler5': [1, -100, 33750, -1562500, 244140625], 'euler53': [1, -343140, 73764987158, -7605478877805060, 491258904256726154641], 'euler59': [1, 0, -62659063426, 0, 1779197418239532716881], 'euler61': [1, 541756, 176415639606, 27911471932317916, 2654348974297586158321], 'euler67': [1, 0, 5372154206, 0, 8182718904632857144561], 'euler7': [1, 0, -201442, 0, 13841287201], 'euler71': [1, 0, -254706899938, 0, 16409682740640811134241], 'euler73': [1, 1393212, 787928371814, 210840660076550268, 22902048046490258711521], 'euler79': [1, 0, -37146261826, 0, 59091511031674153381441], 'euler83': [1, 0, -563099056738, 0, 106890007738661124410161], 'euler89': [1, 323196, 1020076495526, 160622365313431356, 246990403565262140303521], 'euler97': [1, -1040612, 1936662343494, -866800663993176548, 693842360995438000295041], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1442, 0, 531441], [1, -100, 33750, -1562500, 244140625], [1, 0, -201442, 0, 13841287201], [1, 0, 900542, 0, 3138428376721], [1, -4484, 14680182, -21643411556, 23298085122481], [1, -5796, 56673542, -139901349924, 582622237229761], [1, 0, -29257058, 0, 2213314919066161], [1, 0, 49293278, 0, 21914624432020321], [1, 41980, 1630226742, 24970683015580, 353814783205469041], [1, 0, 422727038, 0, 787662783788549761], [1, -804, 5131614422, -2062844032836, 6582952005840035281], [1, -26660, 9677897382, -126637779065060, 22563490300366186081], [1, 0, -12606965698, 0, 39959630797262576401], [1, 0, -596024002, 0, 116191483108948578241], [1, -343140, 73764987158, -7605478877805060, 491258904256726154641], [1, 0, -62659063426, 0, 1779197418239532716881], [1, 541756, 176415639606, 27911471932317916, 2654348974297586158321], [1, 0, 5372154206, 0, 8182718904632857144561], [1, 0, -254706899938, 0, 16409682740640811134241], [1, 1393212, 787928371814, 210840660076550268, 22902048046490258711521], [1, 0, -37146261826, 0, 59091511031674153381441], [1, 0, -563099056738, 0, 106890007738661124410161], [1, 323196, 1020076495526, 160622365313431356, 246990403565262140303521], [1, -1040612, 1936662343494, -866800663993176548, 693842360995438000295041]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/32/7/c/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': '4-2e10-1.1-c6e2-0-0', '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': '4-2e10-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.713250942289569, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c6e2-0', 'trace_hash': 840671464753109386, 'z1': {'__RealLiteral__': 0, 'data': '1.15574642889432793977596692190', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1465082654299527465202272847958,2340781288922356043149155385670', 'Lhash_array': ['1465082654299527465202272847958', '2340781288922356043149155385670'], 'label': '4-2e10-1.1-c6e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/7/c/a'}