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lfunc_lfunctions • Show schema
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{'Lhash': '1116525427843175968639992304793', 'a10': [-0.7598422491582366, -2.037971065769296], 'a2': [0.9703264349216544, 0.06785183413858342], 'a3': [0.043500065178528585, 1.245678884275682], 'a4': [-1.0436066185713428, -0.14666934527495679], 'a5': [-0.9254207934752506, -2.035582559122483], 'a6': [-0.04231233388226799, 1.2116667100439178], 'a7': [1.7333638799645652, 3.0022743081033476], 'a8': [-2.9055675747618928, -0.6175974533912929], 'a9': [1.442868523719701, -0.10089519591735803], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.9254207934752506, 2.035582559122483]]], [19, [[1.0, 0], [0.007113642810990416, -4.35889313886977]]]], 'bad_primes': [5, 19], 'central_character': '475.111', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '2400731547792870377317808803916', 'degree': 2, 'euler_factors': [[[1.0, 0], 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5.510761425785899]], [[1.0, 0], [-4.220261404475244, 4.687075131660833], [-8.675862451215238, -82.54531731556669]], [[1.0, 0], [4.283220469764268, -1.2281937058925776], [75.47628055792191, -47.16281451675524]], [[1.0, 0], [-11.057279682737695, 6.909355189232478], [42.52200123854051, -87.1830224910192]], [[1.0, 0], [2.4024237073927135, 0.8744107195864044], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [-2.3899400789102514, -2.654297361329594], [-10.766431716568308, 102.43575522293216]], [[1.0, 0], [-7.5645092549588036, -13.102114363913643], [-53.5, 92.66471820493493]], [[1.0, 0], [-6.217632726420741, 6.004298129777613], [3.804045140572606, -108.93360014508143]], [[1.0, 0], [8.807665518469436, 6.399143571614432], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-475-475.111-c1-0-12', '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/475/2/bc/a/111/32', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6136778793760072, 1.4496996658060668, 1.2771764467397524, 1.0879114614591963, 0.873244591912656, 0.6257007811819488, 0.34036798923006417, 0.01592633236363528, -0.3446671225657446, -0.7338241487341786, -1.1393132813687348, -1.5446247385650669, -1.929750769221966, -2.272400305122133, -2.5496277039241257, -2.7398029722828907, -2.8247925691960205, -2.7921639639865723, -2.6371823907509864, -2.3643435175052625, -1.9881888749894323, -1.5331875170557991, -1.03253969233166, -0.5258639025837929, -0.05585995685794636, 0.3358154437332319, 0.6130849062108632, 0.749908612566143, 0.734106759804037, 0.5699840464042235, 0.2792659118291561, -0.09999273854296117, -0.516643480419458, -0.911669182580861, -1.2249495327029458, -1.4028472598703627, -1.4056871318532076, -1.2140967340701527, -0.8332111110695535, 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'root_angle': -0.46038822181556077, 'root_number': '0.12412312302812693 - 0.9922668241605906*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.230194110908', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.880783259710645293291318939021', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.01615311290981985187789939189', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84390982388628829007038924323', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '475.111', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/bc/a/111/32'], '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': '2-475-475.111-c1-0-12', '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': '2-475-475.111-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.23019411090778039, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.880783259710645293291318939021', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1116525427843175968639992304793', 'Lhash_array': ['1116525427843175968639992304793'], 'label': '2-475-475.111-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/bc/a/111/32'}