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lfunc_lfunctions • Show schema
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{'Lhash': '639633684713032857718528163071,951807479983383517821371353501', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2530.668812404866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1, 0, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6300.1', 'coefficient_field': '1.1.1.1', 'conductor': 39690000, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1], [1], [1], [1, 0, 1], [1, 6, 31, 66, 121], [1, 0, -25, 0, 169], [1, 0, -25, 0, 289], [1, 4, 42, 76, 361], [1, 0, -10, 0, 529], [1, 18, 139, 522, 841], [1, -16, 126, -496, 961], [1, 0, 26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -82, 0, 1849], [1, 0, -85, 0, 2209], [1, 0, -106, 0, 2809], [1, -24, 262, -1416, 3481], [1, -16, 186, -976, 3721], [1, 0, -70, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 50, 0, 5329], [1, 10, 183, 790, 6241], [1, 0, -22, 0, 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0.17567020722749987, 0.5837093700369916, 1.1773431104624483, 1.9480493135778536, 2.8817047799985476], 'positive_zeros': ['0.50458200753257436089515812021030', '0.75084371025582199638616592370381', '1.94285307474004409515243035417549', '1.98701765255630521234778684789348', '2.52185719193018361747496175555507', '2.87705427227391922406622209807246', '3.61411530680295862166639123516590', '3.61465765061589448717294852684369', '4.35399722174269092243911263670588', '4.54744527736157926293075129106304', '5.16847347205826051430424425577539', '5.24942638568418603780842995719620', '5.86462622250061922150790372894153', '5.88427825224716048352033220052026', '6.49162882181503753863755006293886', '6.83022625351355182490901155849812', '7.36615797447158924154017608690377', '7.36861687619956048761521613228227', '7.995036569844709837871582790280345', '8.097536460848612501766689778865833'], 'prelabel': '4-6300e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.092654881876508, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1401146495982852387, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50458200753257436089515812021', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.75084371025582199638616592370', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.94285307474004409515243035418', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2530.668812404866, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 39690000, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, -25, 0, 169], 'euler17': [1, 0, -25, 0, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -10, 0, 529], 'euler29': [1, 18, 139, 522, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -16, 126, -496, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, -82, 0, 1849], 'euler47': [1, 0, -85, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 0, -70, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 50, 0, 5329], 'euler79': [1, 10, 183, 790, 6241], 'euler83': [1, 0, -22, 0, 6889], 'euler89': [1, -24, 322, -2136, 7921], 'euler97': [1, 0, 95, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, 6, 31, 66, 121], [1, 0, -25, 0, 169], [1, 0, -25, 0, 289], [1, 4, 42, 76, 361], [1, 0, -10, 0, 529], [1, 18, 139, 522, 841], [1, -16, 126, -496, 961], [1, 0, 26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -82, 0, 1849], [1, 0, -85, 0, 2209], [1, 0, -106, 0, 2809], [1, -24, 262, -1416, 3481], [1, -16, 186, -976, 3721], [1, 0, -70, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 50, 0, 5329], [1, 10, 183, 790, 6241], [1, 0, -22, 0, 6889], [1, -24, 322, -2136, 7921], [1, 0, 95, 0, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6300/2/k/c'], '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': '4-6300e2-1.1-c1e2-0-10', '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': '4-6300e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.092654881876508, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1401146495982852387, 'z1': {'__RealLiteral__': 0, 'data': '0.50458200753257436089515812021', 'prec': 103}}
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{'Lhash': '639633684713032857718528163071,951807479983383517821371353501', 'Lhash_array': ['639633684713032857718528163071', '951807479983383517821371353501'], 'label': '4-6300e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6300/2/k/c'}