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lfunc_lfunctions • Show schema
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{'Lhash': '2607885436251208953698286637265', 'a10': [-0.20619352880957728, 2.226540866159221], 'a2': [-0.9369497249997617, -0.3494641795990983], 'a3': [1.266043100874984, 0.6913118354780443], 'a4': [0.7557495743542583, 0.6548607339452851], 'a5': [-0.5849033070213341, -2.1582141046326955], 'a6': [-0.9446300117701804, -1.090161147724609], 'a7': [1.3545930886919142, -1.809524520547863], 'a8': [-0.47924898672005684, -0.8776789895672557], 'a9': [-0.49696937296567034, -0.7732994387731433], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9369497249997617, 0.3494641795990983]]], [5, [[1.0, 0], [0.5849033070213341, 2.1582141046326955]]], [23, [[1.0, 0], [0.4308255803661971, -4.776441072524828]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.203', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '1575102619602936578717733345763', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9369497249997617, 0.3494641795990983]], [[1.0, 0], [-1.266043100874984, -0.6913118354780443], [1.6219224523667928, 2.5237605984935434]], [[1.0, 0], [0.5849033070213341, 2.1582141046326955]], [[1.0, 0], [-1.3545930886919142, 1.809524520547863], [-1.9721278978900079, -6.7164508153014815]], [[1.0, 0], [0.4753619395424913, 0.21709052375481072], [7.2034680733981356, 8.313245317896842]], [[1.0, 0], [-3.1124086673317697, 2.3299199442049834], [3.662523238938586, -12.473408656988466]], [[1.0, 0], [0.5784575923344573, -8.087893956887484], [-16.826964511975856, -2.4193522506458476]], [[1.0, 0], [-4.906588032391425, 5.662504445290715], [-2.7039819271924177, -18.80660739573772]], [[1.0, 0], [0.4308255803661971, -4.776441072524828]], [[1.0, 0], [-1.9373435289081509, 1.6787177238292967], [4.127130309925269, -28.70482181454705]], [[1.0, 0], [0.9109787748176111, 0.26748750279098527], [26.078859517766617, 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[-75.7999449155453, -22.256871990472945]], [[1.0, 0], [1.4666293433820392, -6.741986283089418], [-75.49945561442503, -34.479446079156574]], [[1.0, 0], [-9.076145325302537, 2.6649967212675354], [74.87156442197512, -48.11703275354819]], [[1.0, 0], [1.2205700590141269, 5.61087000785536], [-88.23430354938829, 40.295256261182985]], [[1.0, 0], [-1.8609904717851624, 1.195985955098406], [41.956916313190526, -91.87283153080635]], [[1.0, 0], [4.122740062605174, 11.05349387263319], [-77.84220615848861, 67.45065559636436]], [[1.0, 0], [6.561260647862726, 12.016051729426746], [-57.84856746774894, 90.01412801293638]], [[1.0, 0], [-5.717261215683543, -6.598071171856152], [-15.51231737178808, 107.89053716502167]], [[1.0, 0], [-17.363312384335714, -6.4761806910357835], [85.39970190203118, 73.99926293581721]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-230-115.88-c1-0-8', '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/l/a/203/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.132429493645503, 1.1913839831352382, 1.2552288819366761, 1.322622455759193, 1.3900705813984944, 1.4523202263158204, 1.5028573287812768, 1.534434650078219, 1.5396099925278393, 1.5113062867033522, 1.4434082726335369, 1.33139651933176, 1.1729992534306635, 0.9688225031135617, 0.7229026506738367, 0.44311432169326953, 0.1413618516451095, -0.16651453407864883, -0.4611753135997364, -0.7205982145399681, -0.9212829308578141, -1.0398158496446395, -1.0547251595562523, -0.9485135944120868, -0.7097157013816081, -0.3347939798303758, 0.17033122287662664, 0.7893246904537925, 1.4952386327914613, 2.251216861262091, 3.012176278591042, 3.727454021303468, 4.344307834542459, 4.812051968348121, 5.086512413930151, 5.134406211758984, 4.937202266774988, 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'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.2754620105098479, 'root_number': '0.6483436742762859 + 0.761347804899919*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.137731005255', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.05725886595382197113136654700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21111053515755037131443139486', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23070748482315376716246744596', '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': '115.88', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/l/a/203/4'], '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': '2-230-115.88-c1-0-8', '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': '2-230-115.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.13773100525492396, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.05725886595382197113136654700', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2607885436251208953698286637265', 'Lhash_array': ['2607885436251208953698286637265'], 'label': '2-230-115.88-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/l/a/203/4'}