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lfunc_lfunctions • Show schema
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{'Lhash': '805364891326611730635380581274,1070676995381228022409903313120', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 931.3985971344308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 2, 1]], [7, [1]], [13, [1, -6, 13]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': '1.1.1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 2, 1], [1, 0, -6, 0, 25], [1], [1, 0, -22, 0, 121], [1, -6, 13], [1, -4, 38, -68, 289], [1, 0, -2, 0, 361], [1, -8, 62, -184, 529], [1, 20, 158, 580, 841], [1, 0, 38, 0, 961], [1, 0, -10, 0, 1369], [1, 0, 18, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 50, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -102, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -130, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 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0.15485666221585542, -0.05014911162741138], 'positive_zeros': ['0.63532087720513272905995758472017', '0.844615223775748613531646780089332', '1.79502897079381486437847821398573', '1.79593973989094017552982170992703', '3.01230306631566244689649768439480', '3.43753072507114542699678702953898', '3.48681924873775414111823132061511', '4.21043966905202273620386678417807', '4.57151468145937373871369189001601', '4.97300766978274485378060510492189', '5.34711438141615528898344326509830', '5.81251956109654462293586506546064', '6.06845525461585603333445897033324', '6.11725242134247229214825955898416', '6.99727455278791735341603897689212', '7.18606805449285450629387747141738', '7.43831754561200452866466859405782', '7.83144886322286838288380768686700', '8.508678442950309649005647619017282', '8.592443095006908719630686474791399'], 'prelabel': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 621500634916050395, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63532087720513272905995758472', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.844615223775748613531646780089', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.79502897079381486437847821399', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 931.3985971344308, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, -1, 0, 0, 0, 0, 3, 0, 0, 2, 6, 0, 0, 1, 4, 0, 0, 0, 0, 0, 8, 0, 6, 0, -4, 0, -20, 0, 0, 0, 0, 0, 0, -3, 0, 0, -12, 0, 0, 0, 8, 0, 0, 0, 0, -2, 0, 0, -8, -6, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, -4, -16, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -6], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, -6, 13, 0, 0], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, -2, 0, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 20, 158, 580, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, 38, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 50, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -102, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -130, 0, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, -150, 0, 6889], 'euler89': [1, 0, -142, 0, 7921], 'euler97': [1, 0, -50, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 2, 1, 0, 0], [1, 0, -6, 0, 25], [1, 0, 0, 0, 0], [1, 0, -22, 0, 121], [1, -6, 13, 0, 0], [1, -4, 38, -68, 289], [1, 0, -2, 0, 361], [1, -8, 62, -184, 529], [1, 20, 158, 580, 841], [1, 0, 38, 0, 961], [1, 0, -10, 0, 1369], [1, 0, 18, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 50, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -102, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -130, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -150, 0, 6889], [1, 0, -142, 0, 7921], [1, 0, -50, 0, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/c/d'], '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': '4-3822e2-1.1-c1e2-0-5', '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': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 621500634916050395, 'z1': {'__RealLiteral__': 0, 'data': '0.63532087720513272905995758472', 'prec': 103}}
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{'Lhash': '805364891326611730635380581274,1070676995381228022409903313120', 'Lhash_array': ['805364891326611730635380581274', '1070676995381228022409903313120'], 'label': '4-3822e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/c/d'}