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lfunc_lfunctions • Show schema
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{'Lhash': '907807587642212140005100613335,1657111172067346388363082969101', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 38, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1994.1426217828985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '432.1', 'coefficient_field': '1.1.1.1', 'conductor': 186624, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -161, 0, 390625], [1, -38, 5163, -91238, 5764801], [1, 0, -14153, 0, 214358881], [1, -604, 148326, -17250844, 815730721], [1, 0, 4354, 0, 6975757441], [1, -608, 353058, -79235168, 16983563041], [1, 0, -469682, 0, 78310985281], [1, 0, -954878, 0, 500246412961], [1, 478, 1904163, 441443038, 852891037441], [1, -1480, 4295922, -2773758280, 3512479453921], [1, 0, -5599538, 0, 7984925229121], [1, -1964, 7801926, -6714525164, 11688200277601], [1, 0, -5067806, 0, 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'5.01502644700367161956130388075522', '5.61916975788905037051490954414740', '6.19787216911581109782498043429453', '6.24307762093820969345085424807919', '7.10318271440601160754626563772920', '7.77244114411234898435382920482352', '7.938443686123466830008390377041924', '8.509852563490533973890280676430045', '9.087360742199890235217641431340637', '9.102404334340660728381761442421757', '9.899310952965056480293515345853151', '10.42268196153872591871060427051082', '11.01291695289338665195092322068321'], 'prelabel': '4-432e2-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.682501332002917, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c4e2-0', 'trace_hash': 1595610708011457571, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71613391535393847887768168932', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.30723021924889872477913291184', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.58674060797695215265115305654', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1994.1426217828985, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 186624, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 604, 0, 0, 0, 0, 0, 608, 0, 0, 0, 0, 0, 161, 0, 0, 0, 0, 0, -478, 0, 0, 0, 0, 0, 1480, 0, 0, 0, 0, 0, 1964, 0, 0, 0, 0, 0, -3719, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -632, 0, 0, 0, 0, 0, -9244, 0, 0, 0, 0, 0, -6062, 0, 0, 0, 0, 0, 20900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22952, 0, 0, 0, 0, 0, -13034, 0, 0, 0], 'euler11': [1, 0, -14153, 0, 214358881], 'euler13': [1, -604, 148326, -17250844, 815730721], 'euler17': [1, 0, 4354, 0, 6975757441], 'euler19': [1, -608, 353058, -79235168, 16983563041], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -469682, 0, 78310985281], 'euler29': [1, 0, -954878, 0, 500246412961], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 478, 1904163, 441443038, 852891037441], 'euler37': [1, -1480, 4295922, -2773758280, 3512479453921], 'euler41': [1, 0, -5599538, 0, 7984925229121], 'euler43': [1, -1964, 7801926, -6714525164, 11688200277601], 'euler47': [1, 0, -5067806, 0, 23811286661761], 'euler5': [1, 0, -161, 0, 390625], 'euler53': [1, 0, -13243313, 0, 62259690411361], 'euler59': [1, 0, -15696638, 0, 146830437604321], 'euler61': [1, 632, 27791538, 8750571512, 191707312997281], 'euler67': [1, 9244, 61665126, 186276962524, 406067677556641], 'euler7': [1, -38, 5163, -91238, 5764801], 'euler71': [1, 0, -47518238, 0, 645753531245761], 'euler73': [1, 6062, 65983443, 172150136942, 806460091894081], 'euler79': [1, -20900, 187102662, -814056692900, 1517108809906561], 'euler83': [1, 0, 64676047, 0, 2252292232139041], 'euler89': [1, 0, -76456478, 0, 3936588805702081], 'euler97': [1, 13034, 219529851, 1153890648554, 7837433594376961], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -161, 0, 390625], [1, -38, 5163, -91238, 5764801], [1, 0, -14153, 0, 214358881], [1, -604, 148326, -17250844, 815730721], [1, 0, 4354, 0, 6975757441], [1, -608, 353058, -79235168, 16983563041], [1, 0, -469682, 0, 78310985281], [1, 0, -954878, 0, 500246412961], [1, 478, 1904163, 441443038, 852891037441], [1, -1480, 4295922, -2773758280, 3512479453921], [1, 0, -5599538, 0, 7984925229121], [1, -1964, 7801926, -6714525164, 11688200277601], [1, 0, -5067806, 0, 23811286661761], [1, 0, -13243313, 0, 62259690411361], [1, 0, -15696638, 0, 146830437604321], [1, 632, 27791538, 8750571512, 191707312997281], [1, 9244, 61665126, 186276962524, 406067677556641], [1, 0, -47518238, 0, 645753531245761], [1, 6062, 65983443, 172150136942, 806460091894081], [1, -20900, 187102662, -814056692900, 1517108809906561], [1, 0, 64676047, 0, 2252292232139041], [1, 0, -76456478, 0, 3936588805702081], [1, 13034, 219529851, 1153890648554, 7837433594376961]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/5/e/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': '4-432e2-1.1-c4e2-0-5', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4, 4], 'order_of_vanishing': 0, 'prelabel': '4-432e2-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.682501332002917, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4e2-0', 'trace_hash': 1595610708011457571, 'z1': {'__RealLiteral__': 0, 'data': '0.71613391535393847887768168932', 'prec': 103}}
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{'Lhash': '907807587642212140005100613335,1657111172067346388363082969101', 'Lhash_array': ['907807587642212140005100613335', '1657111172067346388363082969101'], 'factors': ['2-432-3.2-c4-0-13', '2-432-3.2-c4-0-25'], 'label': '4-432e2-1.1-c4e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/5/e/e'}