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{'Lhash': '1447354340613704658291815486193,1780147602687795901274429021840,2410402753340229037535942269347', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -3, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 223938.60897877818, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -3, 3, -1]], [13, [1]]], 'bad_primes': [3, 5, 13], 'central_character': '7605.1', 'coefficient_field': '1.1.1.1', 'conductor': 439842970125, 'conductor_radical': 195, 'degree': 6, 'euler_factors': [[1, 0, 0, -2, 0, 0, 8], [1], [1, -3, 3, -1], [1, 3, 18, 39, 126, 147, 343], [1, 0, 9, 16, 99, 0, 1331], [1], [1, 0, 9, 98, 153, 0, 4913], [1, 12, 93, 460, 1767, 4332, 6859], [1, 0, 21, -96, 483, 0, 12167], [1, 6, 87, 334, 2523, 5046, 24389], [1, 3, 0, -177, 0, 2883, 29791], [1, 6, 75, 452, 2775, 8214, 50653], [1, 0, 99, 26, 4059, 0, 68921], [1, -9, 144, -763, 6192, -16641, 79507], [1, 12, 135, 922, 6345, 26508, 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'6.34252055364059662500374024089787', '6.47198296561747758070656703589565', '6.72448111164943452419810166337389', '7.04910265352168294128889649272128', '7.26751085836695021815108974995303', '7.58867237689709544653542528707461', '7.70231887915285523439777515848877'], 'prelabel': '6-7605e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.792703685960589, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 22621541632491578, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14176125531208770803233411891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40428884928330874270402697359', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.65912598273195686657349874909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 223938.60897877818, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 439842970125, 'conductor_radical': 195, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 6, 0, 0, 0, -6, 0, -3, 0, 0, 0, -9, 0, -6, 0, 0, 6, 0, 0, 9, 0, 0, 0, -12, 0, -9, 0, 0, 0, 0, 0, 0, -6, 0, 0, -6, 0, -3, 0, 0, -4, 0, 0, -9, 0, 0, 0, -12, 0, -21, 0, 0, 0, 0, 0, -3, 0, 0, 0, -18, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, -36, 0, -15, 0, 0, 0], 'euler11': [1, 0, 9, 16, 99, 0, 1331], 'euler13': [1, 0, 0, 0, 0, 0, 0], 'euler17': [1, 0, 9, 98, 153, 0, 4913], 'euler19': [1, 12, 93, 460, 1767, 4332, 6859], 'euler2': [1, 0, 0, -2, 0, 0, 8], 'euler23': [1, 0, 21, -96, 483, 0, 12167], 'euler29': [1, 6, 87, 334, 2523, 5046, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 3, 0, -177, 0, 2883, 29791], 'euler37': [1, 6, 75, 452, 2775, 8214, 50653], 'euler41': [1, 0, 99, 26, 4059, 0, 68921], 'euler43': [1, -9, 144, -763, 6192, -16641, 79507], 'euler47': [1, 12, 135, 922, 6345, 26508, 103823], 'euler5': [1, -3, 3, -1, 0, 0, 0], 'euler53': [1, 0, 135, -16, 7155, 0, 148877], 'euler59': [1, 6, 165, 694, 9735, 20886, 205379], 'euler61': [1, 3, 162, 299, 9882, 11163, 226981], 'euler67': [1, 9, 120, 855, 8040, 40401, 300763], 'euler7': [1, 3, 18, 39, 126, 147, 343], 'euler71': [1, 12, 165, 1022, 11715, 60492, 357911], 'euler73': [1, 21, 312, 2977, 22776, 111909, 389017], 'euler79': [1, 3, 144, 111, 11376, 18723, 493039], 'euler83': [1, 18, 309, 2820, 25647, 124002, 571787], 'euler89': [1, -30, 555, -6222, 49395, -237630, 704969], 'euler97': [1, 15, 282, 2321, 27354, 141135, 912673], 'euler_factors': [[1, 0, 0, -2, 0, 0, 8], [1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 3, 18, 39, 126, 147, 343], [1, 0, 9, 16, 99, 0, 1331], [1, 0, 0, 0, 0, 0, 0], [1, 0, 9, 98, 153, 0, 4913], [1, 12, 93, 460, 1767, 4332, 6859], [1, 0, 21, -96, 483, 0, 12167], [1, 6, 87, 334, 2523, 5046, 24389], [1, 3, 0, -177, 0, 2883, 29791], [1, 6, 75, 452, 2775, 8214, 50653], [1, 0, 99, 26, 4059, 0, 68921], [1, -9, 144, -763, 6192, -16641, 79507], [1, 12, 135, 922, 6345, 26508, 103823], [1, 0, 135, -16, 7155, 0, 148877], [1, 6, 165, 694, 9735, 20886, 205379], [1, 3, 162, 299, 9882, 11163, 226981], [1, 9, 120, 855, 8040, 40401, 300763], [1, 12, 165, 1022, 11715, 60492, 357911], [1, 21, 312, 2977, 22776, 111909, 389017], [1, 3, 144, 111, 11376, 18723, 493039], [1, 18, 309, 2820, 25647, 124002, 571787], [1, -30, 555, -6222, 49395, -237630, 704969], [1, 15, 282, 2321, 27354, 141135, 912673]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7605/2/a/bw'], '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': '6-7605e3-1.1-c1e3-0-13', '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': 3, 'prelabel': '6-7605e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.792703685960589, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 22621541632491578, 'z1': {'__RealLiteral__': 0, 'data': '1.14176125531208770803233411891', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1447354340613704658291815486193,1780147602687795901274429021840,2410402753340229037535942269347', 'Lhash_array': ['1447354340613704658291815486193', '1780147602687795901274429021840', '2410402753340229037535942269347'], 'label': '6-7605e3-1.1-c1e3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7605/2/a/bw'}