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lfunc_lfunctions • Show schema
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{'Lhash': '1135837813659815181156576844313,3221819660183817795529496639061', 'a10': 14, 'a2': 2, 'a3': -1, 'a4': 0, 'a5': 7, 'a6': -2, 'a7': 0, 'a8': -8, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.43368859106227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 4]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '98.1', 'coefficient_field': '1.1.1.1', 'conductor': 9604, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1, -2, 4], [1, 1, -26, 27, 729], [1, -7, -76, -875, 15625], [1], [1, 35, -106, 46585, 1771561], [1, 132, 8750, 290004, 4826809], [1, -59, -1432, -289867, 24137569], [1, -137, 11910, -939683, 47045881], [1, -7, -12118, -85169, 148035889], [1, -212, 60014, -5170468, 594823321], [1, -75, -24166, -2234325, 887503681], [1, 11, -50532, 557183, 2565726409], [1, -996, 385846, -68645316, 4750104241], [1, -520, 226614, -41343640, 6321363049], [1, 171, -74582, 17753733, 10779215329], 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['0.896018045867936731791782438672707', '2.54156757359145915234473106195257', '2.89144620221992818889475911496246', '4.51651740539359137357503085798225', '4.62028414642847223046156168396929', '5.57830663988827454210390884203766', '5.81549740700953971713696179582660', '7.16358221752932503464067860583060', '7.33146557393786375184961152935834', '7.80806810345649549707131232111220', '8.958782792089562890978329087003904', '9.701020819243641939159994261176865', '9.825213500095759776591501489114205', '10.32716730388733783864823702040500', '11.04352786611972326818903308024673', '11.92991772655909124463845465724858', '12.23304108328036510648978664058920', '12.83754641785020293197941347850071', '12.85164898889506516891526159190166', '14.08871258689931858751094523210822'], 'prelabel': '4-98e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.4046178866012333, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 2026936979453010465, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.896018045867936731791782438673', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.54156757359145915234473106195', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89144620221992818889475911496', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.43368859106227, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 9604, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 2, -1, 0, 7, -2, 0, -8, 27, 14, -35, 0, -132, 0, -7, -16, 59, 54, 137, 0, 0, -70, 7, 8, 125, -264, -80, 0, 212, -14, 75, 0, 35, 118, 0, 0, -11, 274, 132, -56, 996, 0, 520, 0, 189, 14, -171, 16, 0, 250, -59, 0, 417, -160, -245, 0, -137, 424, -17, 0, 51, 150, 0, 64, -924, 70, -439, 0, -7, 0, -1568, -216, 295, -22, -125, 0, 0, 264, 495, -112, 80, 1992, -1864, 0, 413, 1040, -212, 280, -873, 378, 0, 0, -75, -342, 959, 0, 580, 0, -945, 0], 'euler11': [1, 35, -106, 46585, 1771561], 'euler13': [1, 132, 8750, 290004, 4826809], 'euler17': [1, -59, -1432, -289867, 24137569], 'euler19': [1, -137, 11910, -939683, 47045881], 'euler2': [1, -2, 4, 0, 0], 'euler23': [1, -7, -12118, -85169, 148035889], 'euler29': [1, -212, 60014, -5170468, 594823321], 'euler3': [1, 1, -26, 27, 729], 'euler31': [1, -75, -24166, -2234325, 887503681], 'euler37': [1, 11, -50532, 557183, 2565726409], 'euler41': [1, -996, 385846, -68645316, 4750104241], 'euler43': [1, -520, 226614, -41343640, 6321363049], 'euler47': [1, 171, -74582, 17753733, 10779215329], 'euler5': [1, -7, -76, -875, 15625], 'euler53': [1, -417, 25012, -62081709, 22164361129], 'euler59': [1, 17, -205090, 3491443, 42180533641], 'euler61': [1, -51, -224380, -11576031, 51520374361], 'euler67': [1, 439, -108042, 132034957, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 1568, 1330478, 561204448, 128100283921], 'euler73': [1, -295, -301992, -114760015, 151334226289], 'euler79': [1, -495, -248014, -244054305, 243087455521], 'euler83': [1, 1864, 2012198, 1065810968, 326940373369], 'euler89': [1, 873, 57160, 615437937, 496981290961], 'euler97': [1, -580, 1909446, -529350340, 832972004929], 'euler_factors': [[1, -2, 4, 0, 0], [1, 1, -26, 27, 729], [1, -7, -76, -875, 15625], [1, 0, 0, 0, 0], [1, 35, -106, 46585, 1771561], [1, 132, 8750, 290004, 4826809], [1, -59, -1432, -289867, 24137569], [1, -137, 11910, -939683, 47045881], [1, -7, -12118, -85169, 148035889], [1, -212, 60014, -5170468, 594823321], [1, -75, -24166, -2234325, 887503681], [1, 11, -50532, 557183, 2565726409], [1, -996, 385846, -68645316, 4750104241], [1, -520, 226614, -41343640, 6321363049], [1, 171, -74582, 17753733, 10779215329], [1, -417, 25012, -62081709, 22164361129], [1, 17, -205090, 3491443, 42180533641], [1, -51, -224380, -11576031, 51520374361], [1, 439, -108042, 132034957, 90458382169], [1, 1568, 1330478, 561204448, 128100283921], [1, -295, -301992, -114760015, 151334226289], [1, -495, -248014, -244054305, 243087455521], [1, 1864, 2012198, 1065810968, 326940373369], [1, 873, 57160, 615437937, 496981290961], [1, -580, 1909446, -529350340, 832972004929]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/4/c/e'], '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': '4-98e2-1.1-c3e2-0-4', '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': '4-98e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.4046178866012333, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2026936979453010465, 'z1': {'__RealLiteral__': 0, 'data': '0.896018045867936731791782438673', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1135837813659815181156576844313,3221819660183817795529496639061', 'Lhash_array': ['1135837813659815181156576844313', '3221819660183817795529496639061'], 'label': '4-98e2-1.1-c3e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/4/c/e'}