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lfunc_lfunctions • Show schema
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{'Lhash': '1104137796218761449513837343702', 'a10': [0, 0], 'a2': [0, 0], 'a3': [103278.97497787137, 0], 'a4': [0, 0], 'a5': [0, -10429249.484478476], 'a6': [0, 0], 'a7': [0, 368005341.7488594], 'a8': [0, 0], 'a9': [7179762271.479782, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.12440483285178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.0', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '32.15', 'coefficient_field': 'CDF', 'conductor': 32, 'conductor_radical': 2, 'conjugate': '1827463798806391865923543681132', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-103278.97497787137, 0], [3486784401.0, 0]], [[1.0, 0], [0, 10429249.484478476], [-95367431640625.0, 0]], [[1.0, 0], [0, -368005341.7488594], [-79792266297612000, 0]], [[1.0, 0], [-33534132965.148388, 0], [672749994932560100000, 0]], [[1.0, 0], [0, -195314357916.5739], [-19004963774880800000000, 0]], [[1.0, 0], [159957932002.1221, 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'label': '2-2e5-8.3-c20-0-11', 'leading_term': '4.677469451320366577607052876112063554378338296866825399', 'load_key': 'CMFs-workshop', 'motivic_weight': 20, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [20], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/32/21/d/b/15/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [4.677469451320366, 4.47139866881778, 4.20634005476553, 3.8873886774681687, 3.5208450496396253, 3.1140621246460403, 2.6752661163132077, 2.213355686140246, 1.7376845946937836, 1.2578333392979415, 0.7833755870048805, 0.323645352695514, -0.11248913697228825, -0.5168391125187312, -0.8820909887112439, -1.2019791214414526, -1.471431142155911, -1.686682109495513, -1.8453545088953192, -1.9465020019316401, -1.9906157567871559, -1.9795931563048512, -1.9166696565833197, -1.806315532269122, -1.6541001700360776, -1.466527435289846, -1.250846416252603, 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'8.611424693508243213106895782918191', '9.968059868690914821964076607885856', '10.78429996279125513762035895800865', '12.80997908334721484523521016779196'], 'prelabel': '2-2e5-8.3-c20-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.006908727907248, 'root_angle': -0.19935169892324028, 'root_number': '0.81021245657970399819030875488791324907762609396094450757 - 0.58613631111123056185986045590548122842210388578690533805*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09967584946162014', 'prec': 67}, 'spectral_label': 'c20-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.871011141413865222808233250509', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.31038890964879586144933525988', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38615961108386387336805905649', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.12440483285178, 'bad_primes': [2], 'central_character': '8.3', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/32/21/d/b/15/17'], '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': '2-2e5-8.3-c20-0-11', 'motivic_weight': 20, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [20], 'order_of_vanishing': 0, 'prelabel': '2-2e5-8.3-c20-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.006908727907248, 'root_angle': -0.09967584946162014, 'self_dual': False, 'spectral_label': 'c20-0', 'z1': {'__RealLiteral__': 0, 'data': '0.871011141413865222808233250509', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1104137796218761449513837343702', 'Lhash_array': ['1104137796218761449513837343702'], 'label': '2-2e5-8.3-c20-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/21/d/b/15/17'}