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lfunc_lfunctions • Show schema
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{'Lhash': '2004265010753796382203028695842', 'a10': [1.9283941500475388, 1.131943462396612], 'a2': [0.28173255684142967, -0.9594929736144974], 'a3': [1.9597210854175349, 1.698107986922939], 'a4': [-0.8412535328311812, -0.5406408174555976], 'a5': [-0.5428003842074665, 2.1691859631908526], 'a6': [2.1814399139819627, -1.4019263067536483], 'a7': [-0.7486746209332377, 0.3419082430889544], 'a8': [-0.7557495743542583, 0.6548607339452851], 'a9': [0.529991482558749, 3.6861717289348155], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.28173255684142967, 0.9594929736144974]]], [5, [[1.0, 0], [0.5428003842074665, -2.1691859631908526]]], [23, [[1.0, 0], [4.762160899512085, 0.5672949560486567]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.179', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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[[1.0, 0], [11.800854478934772, -1.6967067246641814], [79.63791681000329, -23.383802217838664]], [[1.0, 0], [-3.587327720058241, 4.139996883260628], [-12.666020606322377, -88.094108327403]], [[1.0, 0], [-11.250808567866956, -1.6176220619519401], [93.07081844060625, 27.32805801361868]], [[1.0, 0], [-1.2482501121824687, -8.681770227612446], [-96.90879033506424, 28.4549882409844]], [[1.0, 0], [-0.7117080963384123, -2.4238551815138916], [-86.64911388161165, 55.68600419792655]], [[1.0, 0], [-10.63695909115474, 9.216977519744356], [15.22768769524151, -105.9108942812598]], [[1.0, 0], [0.0006315978847783323, -0.00040590331380909405], [45.28023641720562, -99.1498874936425]], [[1.0, 0], [-1.2820148373431863, 4.3661415716063665], [-95.06164920992347, -61.09241237248253]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-230-115.64-c1-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/179/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7320858826067935, 1.6878402911762163, 1.6522521122890383, 1.6193610937566996, 1.5815477179482818, 1.530343114766902, 1.4571946502376214, 1.354133944592096, 1.214362698021106, 1.0327915853841396, 0.8065530177005653, 0.535481910958022, 0.22253382423651508, -0.1259074927634106, -0.4998897742076619, -0.885975955059263, -1.2676007780889715, -1.6257333274980335, -1.9398554441014084, -2.189236731342119, -2.3544533092909368, -2.419062308535733, -2.3713107863737988, -2.205730330463935, -1.9244513456307177, -1.5380679050386945, -1.0658982985860477, -0.5355198726218786, 0.01849062156294986, 0.5566105001119924, 1.037136286999745, 1.4194920248663316, 1.6678301561702822, 1.7546067836349062, 1.6637703937716517, 1.393194402243658, 0.9560156753348249, 0.38061609348402653, -0.29090010728142707, 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'root_angle': -0.11882667901423716, 'root_number': '0.9311271089008094 - 0.36469481360449896*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0594133395071', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58108631068604077480066121710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49582183078577753797006774970', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69743645062703114462155879784', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.64', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/179/12'], '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': '2-230-115.64-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': '2-230-115.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.05941333950711858, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58108631068604077480066121710', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2004265010753796382203028695842', 'Lhash_array': ['2004265010753796382203028695842'], 'label': '2-230-115.64-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/179/12'}