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lfunc_lfunctions • Show schema
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{'Lhash': '1627551599381293736473954710214', 'a10': [101.3222304402216, -175.4952510586657], 'a2': [-4.590614487370919, -7.951177530088189], 'a3': [0.0, 0.0], 'a4': [-26.14748274331954, 45.28876860145989], 'a5': [11.035802583615514, 19.114570777121955], 'a6': [0.0, 0.0], 'a7': [126.88233933509011, 26.60586335481419], 'a8': [186.3327251673163, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-126.88233933509011, -26.60586335481419]]]], 'bad_primes': [3, 7], 'central_character': '63.46', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '1232447334769525112291222679856', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.590614487370919, 7.951177530088189], [-16.0, 27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-11.035802583615514, -19.114570777121955], [-1562.5, 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'8.332815347032031813548793087469591', '9.185959132174689573027062286562228', '10.53021928361379567888608450534737', '12.01063737435377176942895124473196', '13.67429754556134512360356435191621', '14.57689462076721489227273039848998'], 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.5859658738961209, 'root_number': '-0.26679866666539737 + 0.9637522873983575*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.292982936948', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28391182798183293440568151850', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.55324412657194406911919212732', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.96997733860352838886881321955', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/e/46/1'], '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': '2-63-7.4-c5-0-8', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.29298293694806044, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28391182798183293440568151850', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1627551599381293736473954710214', 'Lhash_array': ['1627551599381293736473954710214'], 'label': '2-63-7.4-c5-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/e/46/1'}