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lfunc_lfunctions • Show schema
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{'Lhash': '836562584476251345317521788836', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.0, 0], 'a4': [0, 0], 'a5': [0, 0.5029007782382565], 'a6': [0, 0], 'a7': [0, 3.1024361145656276], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.70232898685172, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [3.605336892803884, 0.03931779987784422]]]], 'bad_primes': [2, 3, 11, 13], 'central_character': '1716.1585', 'coefficient_field': 'CDF', 'conductor': 1716, 'conductor_radical': 858, 'conjugate': '1985473936545363544779475312360', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -0.5029007782382565], [-5.0, 0]], [[1.0, 0], [0, -3.1024361145656276], [-7.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [3.605336892803884, 0.03931779987784422]], [[1.0, 0], [-5.579990488606711, 0], [17.0, 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'3.27047340398135411002805316986945', '3.95028650381403947074397030873788', '4.95204618347953313893739028902948', '5.82039080072202987438247083589434', '7.17751550624925629425550059752083', '7.38064425244623335254322493198350', '8.319003793558444289079572013582383', '9.108304427659445209722026839527361'], 'prelabel': '2-1716-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7016657043622563, 'root_angle': -0.4965288269387901, 'root_number': '0.01090479565369224014870297744947706658213245602253362207 - 0.9999405409481861861155287596696029298761516232767825451*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.24826441346939504', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65993151766396479440964575284', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98248346230115577873967770110', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27047340398135411002805316987', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.70232898685172, 'bad_primes': [2, 3, 11, 13], 'central_character': '13.12', 'conductor': 1716, 'conductor_radical': 858, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1716/2/e/b/1585/6'], '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': '2-1716-13.12-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1716-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7016657043622563, 'root_angle': -0.24826441346939504, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65993151766396479440964575284', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '836562584476251345317521788836', 'Lhash_array': ['836562584476251345317521788836'], 'label': '2-1716-13.12-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1716/2/e/b/1585/6'}