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lfunc_lfunctions • Show schema
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{'Lhash': '1033684519898713670254310011303,2879538507171592694822705214559,2963500081956805938013855203807', 'a10': -9, 'a2': 3, 'a3': 3, 'a4': 3, 'a5': -3, 'a6': 9, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.952614603177704, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '361.1', 'coefficient_field': '1.1.1.1', 'conductor': 47045881, 'conductor_radical': 19, 'degree': 6, 'euler_factors': [[1, -3, 6, -9, 12, -12, 8], [1, -3, 9, -17, 27, -27, 27], [1, 3, 15, 27, 75, 75, 125], [1, 0, 18, 1, 126, 0, 343], [1, 0, 24, -9, 264, 0, 1331], [1, 0, 18, -37, 234, 0, 2197], [1, -6, 60, -207, 1020, -1734, 4913], [1], [1, 6, 69, 252, 1587, 3174, 12167], [1, -15, 159, -981, 4611, -12615, 24389], [1, -9, 99, -505, 3069, -8649, 29791], [1, 0, 90, 17, 3330, 0, 50653], [1, -12, 132, -873, 5412, -20172, 68921], [1, 0, 72, 163, 3096, 0, 79507], [1, 6, 132, 567, 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1]], [[[1, -15, 159, -981, 4611, -12615, 24389], 1]], [[[1, -9, 99, -505, 3069, -8649, 29791], 1]], [[[1, 0, 90, 17, 3330, 0, 50653], 1]], [[[1, -12, 132, -873, 5412, -20172, 68921], 1]], [[[1, 0, 72, 163, 3096, 0, 79507], 1]], [[[1, 6, 132, 567, 6204, 13254, 103823], 1]], [[[1, -6, 150, -585, 7950, -16854, 148877], 1]], [[[1, -21, 312, -2745, 18408, -73101, 205379], 1]], [[[1, -9, 162, -917, 9882, -33489, 226981], 1]], [[[1, 18, 225, 1988, 15075, 80802, 300763], 1]], [[[1, -30, 501, -5148, 35571, -151230, 357911], 1]], [[[1, 0, 171, 64, 12483, 0, 389017], 1]], [[[1, -9, 135, -613, 10665, -56169, 493039], 1]], [[[1, 0, 60, 459, 4980, 0, 571787], 1]], [[[1, -15, 321, -2727, 28569, -118815, 704969], 1]], [[[1, 15, 330, 2783, 32010, 141135, 912673], 1]], [[[1, 15, 339, 2871, 34239, 153015, 1030301], 1]], [[[1, -18, 378, -3709, 38934, -190962, 1092727], 1]], [[[1, 0, 240, 243, 25680, 0, 1225043], 1]], [[[1, 15, 366, 3143, 39894, 178215, 1295029], 1]], [[[1, -9, 195, -2205, 22035, -114921, 1442897], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '6-19e6-1.1-c1e3-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/361/2/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0416666666667', 'prec': 50}, 'plot_values': [5.850860565446554, 5.8403857428590396, 5.824271638193001, 5.796763146511484, 5.752518589420464, 5.688829213104237, 5.603576117968992, 5.494093893686755, 5.35567261197944, 5.182971366561847, 4.970519990172527, 4.712769777074792, 4.404313822961014, 4.04000635383477, 3.6149946854164208, 3.125011964299455, 2.566699492128835, 1.9380779409249396, 1.2385152892949876, 0.46900985567343184, -0.3671922814572128, -1.264888937192641, 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'6.61698226712208514730901470996344', '6.75343168049276423687964865028672', '7.63959083352209911361478424563246', '7.925179242709707989742441980581965', '7.960314767871374497266413243405233', '8.165051593230146577947045230875224', '8.532441758409032066690774716174609', '8.688751395806160089651522372027918', '9.373739471293226371191488784257023', '9.621167918096850934933523719003793', '9.826649694326291032326070763207614', '10.13895912933182563538853339236021', '10.58945491713326664315872157282288', '11.02488772387858565329719848488991', '11.35389859402814717517034514077711', '11.81328802381635186866174799426798', '11.82847035227092728952560802421508'], 'prelabel': '6-19e6-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6978219909543588, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 910441908611221198, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.815433306080246256221657145441', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.27155535338614360775181545455', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.33778935727498860662206296797', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.952614603177704, 'bad_primes': [19], 'central_character': '1.1', 'conductor': 47045881, 'conductor_radical': 19, 'degree': 6, 'dirichlet_coefficients': [1, 3, 3, 3, -3, 9, 0, 0, 0, -9, 0, 9, 0, 0, -9, -3, 6, 0, 0, -9, 0, 0, -6, 0, -6, 0, -10, 0, 15, -27, 9, -6, 0, 18, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -18, -6, -9, -18, -18, 18, 0, 6, -30, 0, 0, 0, 45, 21, -27, 9, 27, 0, -8, 0, 0, -18, 18, -18, 0, 30, 0, 0, 0, -18, 0, 0, 0, 9, 9, -6, 36, 0, 0, -18, 0, 45, 0, 15, 0, 0, -18, 27, -18, 0, -18, -15, -54, 0, -18], 'euler11': [1, 0, 24, -9, 264, 0, 1331], 'euler13': [1, 0, 18, -37, 234, 0, 2197], 'euler17': [1, -6, 60, -207, 1020, -1734, 4913], 'euler19': [1, 0, 0, 0, 0, 0, 0], 'euler2': [1, -3, 6, -9, 12, -12, 8], 'euler23': [1, 6, 69, 252, 1587, 3174, 12167], 'euler29': [1, -15, 159, -981, 4611, -12615, 24389], 'euler3': [1, -3, 9, -17, 27, -27, 27], 'euler31': [1, -9, 99, -505, 3069, -8649, 29791], 'euler37': [1, 0, 90, 17, 3330, 0, 50653], 'euler41': [1, -12, 132, -873, 5412, -20172, 68921], 'euler43': [1, 0, 72, 163, 3096, 0, 79507], 'euler47': [1, 6, 132, 567, 6204, 13254, 103823], 'euler5': [1, 3, 15, 27, 75, 75, 125], 'euler53': [1, -6, 150, -585, 7950, -16854, 148877], 'euler59': [1, -21, 312, -2745, 18408, -73101, 205379], 'euler61': [1, -9, 162, -917, 9882, -33489, 226981], 'euler67': [1, 18, 225, 1988, 15075, 80802, 300763], 'euler7': [1, 0, 18, 1, 126, 0, 343], 'euler71': [1, -30, 501, -5148, 35571, -151230, 357911], 'euler73': [1, 0, 171, 64, 12483, 0, 389017], 'euler79': [1, -9, 135, -613, 10665, -56169, 493039], 'euler83': [1, 0, 60, 459, 4980, 0, 571787], 'euler89': [1, -15, 321, -2727, 28569, -118815, 704969], 'euler97': [1, 15, 330, 2783, 32010, 141135, 912673], 'euler_factors': [[1, -3, 6, -9, 12, -12, 8], [1, -3, 9, -17, 27, -27, 27], [1, 3, 15, 27, 75, 75, 125], [1, 0, 18, 1, 126, 0, 343], [1, 0, 24, -9, 264, 0, 1331], [1, 0, 18, -37, 234, 0, 2197], [1, -6, 60, -207, 1020, -1734, 4913], [1, 0, 0, 0, 0, 0, 0], [1, 6, 69, 252, 1587, 3174, 12167], [1, -15, 159, -981, 4611, -12615, 24389], [1, -9, 99, -505, 3069, -8649, 29791], [1, 0, 90, 17, 3330, 0, 50653], [1, -12, 132, -873, 5412, -20172, 68921], [1, 0, 72, 163, 3096, 0, 79507], [1, 6, 132, 567, 6204, 13254, 103823], [1, -6, 150, -585, 7950, -16854, 148877], [1, -21, 312, -2745, 18408, -73101, 205379], [1, -9, 162, -917, 9882, -33489, 226981], [1, 18, 225, 1988, 15075, 80802, 300763], [1, -30, 501, -5148, 35571, -151230, 357911], [1, 0, 171, 64, 12483, 0, 389017], [1, -9, 135, -613, 10665, -56169, 493039], [1, 0, 60, 459, 4980, 0, 571787], [1, -15, 321, -2727, 28569, -118815, 704969], [1, 15, 330, 2783, 32010, 141135, 912673]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/361/2/a/h'], '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': '6-19e6-1.1-c1e3-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-19e6-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6978219909543588, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 910441908611221198, 'z1': {'__RealLiteral__': 0, 'data': '0.815433306080246256221657145441', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1033684519898713670254310011303,2879538507171592694822705214559,2963500081956805938013855203807', 'Lhash_array': ['1033684519898713670254310011303', '2879538507171592694822705214559', '2963500081956805938013855203807'], 'label': '6-19e6-1.1-c1e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/361/2/a/h'}