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lfunc_lfunctions • Show schema
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{'Lhash': '1403377469740045712061739261343,1991707302631006246364655729702', 'a10': 0, 'a2': 2, 'a3': 2, 'a4': 3, 'a5': 0, 'a6': 4, 'a7': 6, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 218.22156740880962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [5, [1]], [37, [1, 2, 1]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': '1.1.1.1', 'conductor': 3422500, 'conductor_radical': 370, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -2, 4, -6, 9], [1], [1, -6, 20, -42, 49], [1, 4, 14, 44, 121], [1, -4, 18, -52, 169], [1, 4, 26, 68, 289], [1, -2, 12, -38, 361], [1, -16, 110, -368, 529], [1, 4, 14, 116, 841], [1, 2, 60, 62, 961], [1, 2, 1], [1, 4, 86, 164, 1681], [1, 0, 38, 0, 1849], [1, -6, 100, -282, 2209], [1, -12, 142, -636, 2809], [1, 10, 116, 590, 3481], [1, -4, 78, -244, 3721], [1, 10, 84, 670, 4489], [1, 8, 110, 568, 5041], [1, 12, 134, 876, 5329], [1, -14, 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'4.09544556474249645892883802568589', '4.70847845368273107965005237560045', '4.95707356291623409317770773447443', '5.08025389328291495328963856726312', '5.73891220942164057182818500067461', '5.99270558720571648066210713443824', '6.75436080125806691900573851387718', '7.23218117195997713434059500337496', '7.47499756616071603867196585267974', '7.72120075724208239820633257685516', '8.357825002388308440132058755782128', '8.598733423047630184155344837902655', '8.963076370905079983796561663383887', '9.004001430377689944915927007537745'], 'prelabel': '4-1850e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 858334122555377129, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10706962114590556341978402535', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.57118002568879529537407800860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.39039497173098737359083859503', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 218.22156740880962, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 3422500, 'conductor_radical': 370, 'degree': 4, 'dirichlet_coefficients': [1, 2, 2, 3, 0, 4, 6, 4, 0, 0, -4, 6, 4, 12, 0, 5, -4, 0, 2, 0, 12, -8, 16, 8, 0, 8, -2, 18, -4, 0, -2, 6, -8, -8, 0, 0, -2, 4, 8, 0, -4, 24, 0, -12, 0, 32, 6, 10, 16, 0, -8, 12, 12, -4, 0, 24, 4, -8, -10, 0, 4, -4, 0, 7, 0, -16, -10, -12, 32, 0, -8, 0, -12, -4, 0, 6, -24, 16, 14, 0, -1, -8, 14, 36, 0, 0, -8, -16, -4, 0, 24, 48, -4, 12, 0, 12, 4, 32, 0, 0], 'euler11': [1, 4, 14, 44, 121], 'euler13': [1, -4, 18, -52, 169], 'euler17': [1, 4, 26, 68, 289], 'euler19': [1, -2, 12, -38, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -16, 110, -368, 529], 'euler29': [1, 4, 14, 116, 841], 'euler3': [1, -2, 4, -6, 9], 'euler31': [1, 2, 60, 62, 961], 'euler37': [1, 2, 1, 0, 0], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, 0, 38, 0, 1849], 'euler47': [1, -6, 100, -282, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 10, 116, 590, 3481], 'euler61': [1, -4, 78, -244, 3721], 'euler67': [1, 10, 84, 670, 4489], 'euler7': [1, -6, 20, -42, 49], 'euler71': [1, 8, 110, 568, 5041], 'euler73': [1, 12, 134, 876, 5329], 'euler79': [1, -14, 204, -1106, 6241], 'euler83': [1, -14, 212, -1162, 6889], 'euler89': [1, 4, 182, 356, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -2, 4, -6, 9], [1, 0, 0, 0, 0], [1, -6, 20, -42, 49], [1, 4, 14, 44, 121], [1, -4, 18, -52, 169], [1, 4, 26, 68, 289], [1, -2, 12, -38, 361], [1, -16, 110, -368, 529], [1, 4, 14, 116, 841], [1, 2, 60, 62, 961], [1, 2, 1, 0, 0], [1, 4, 86, 164, 1681], [1, 0, 38, 0, 1849], [1, -6, 100, -282, 2209], [1, -12, 142, -636, 2809], [1, 10, 116, 590, 3481], [1, -4, 78, -244, 3721], [1, 10, 84, 670, 4489], [1, 8, 110, 568, 5041], [1, 12, 134, 876, 5329], [1, -14, 204, -1106, 6241], [1, -14, 212, -1162, 6889], [1, 4, 182, 356, 7921], [1, -4, 198, -388, 9409]], 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1850/2/a/x'], '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': '4-1850e2-1.1-c1e2-0-20', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1850e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 858334122555377129, 'z1': {'__RealLiteral__': 0, 'data': '1.10706962114590556341978402535', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1403377469740045712061739261343,1991707302631006246364655729702', 'Lhash_array': ['1403377469740045712061739261343', '1991707302631006246364655729702'], 'label': '4-1850e2-1.1-c1e2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/x'}