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lfunc_lfunctions • Show schema
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{'Lhash': '1194040334055755388012557888690', 'a10': [3.4346597689853375, -1.375030350253086], 'a2': [-1.8385405869691378, -0.1755593399356827], 'a3': [-0.690079011482112, 0.7237340381050702], 'a4': [1.3855530135687555, 0.26704345506570853], 'a5': [-1.780494976034193, 0.9179089572270491], 'a6': [1.3957965408441169, -1.209464587467972], 'a7': [-2.3381434697489216, -1.238178143431095], 'a8': [1.043668401632517, 0.30644869256194673], 'a9': [-0.0475819158237423, -0.998867339183008], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.690079011482112, -0.7237340381050702]]], [7, [[1.0, 0], [2.3381434697489216, 1.238178143431095]]], [23, [[1.0, 0], [-2.415940309876172, 4.142853173733704]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.19', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '409163952754087450970166570646', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8385405869691378, 0.1755593399356827], [1.9638573945254134, 0.37850248872082043]], [[1.0, 0], [0.690079011482112, -0.7237340381050702]], [[1.0, 0], [1.780494976034193, -0.9179089572270491], [2.900284547855991, -4.072879760251679]], [[1.0, 0], [2.3381434697489216, 1.238178143431095]], [[1.0, 0], [-0.5335137657035761, -5.587208930679063], [-10.801215669889773, 2.081763687964512]], [[1.0, 0], [3.847186991048607, 0.5531419822526233], [12.473408656988466, 3.662523238938586]], [[1.0, 0], [0.09748956205669342, -0.28167759087520045], [-13.362902610627387, -10.50870276575029]], [[1.0, 0], [0.8745698010986417, 2.5269034902670895], [-14.935008800112962, 11.7450207381915]], [[1.0, 0], [-2.415940309876172, 4.142853173733704]], [[1.0, 0], [-0.42009116901681964, -0.4848110532780404], [-4.127130309925269, 28.70482181454705]], [[1.0, 0], [-4.065673001733928, 0.9863215979942858], [27.553898908302628, -14.205022173549722]], [[1.0, 0], [-11.439305990089375, 0.5449213057137898], [36.83246113520413, -3.5170736022547584]], [[1.0, 0], [-2.9717043748372847, 4.624062266750812], [-17.03201553307734, -37.29491180953525]], [[1.0, 0], [3.5865218693751806, 12.21457176252827], [-36.17390191174079, 23.247555150590696]], [[1.0, 0], [5.76436391828118, 3.3280570599266053], [23.5, 40.703193977868615]], [[1.0, 0], [3.248472483551202, 4.130768792174352], [-12.495223581999642, 51.50601312114771]], [[1.0, 0], [0.26454809588318445, 0.6608091972111071], [-42.70030824819914, 40.71466167744461]], [[1.0, 0], [-9.284809143327994, 8.853047636399362], [2.9024968652482803, -60.93090769016349]], [[1.0, 0], [-8.3539931382231, -5.948851583624024], [21.91355354226725, 63.31505485388279]], [[1.0, 0], [-0.45711385017471784, -1.0009397123948593], [-46.49511211011524, 53.65821977915234]], [[1.0, 0], [-2.5694654969374784, 13.331652938907116], [-67.7708591101733, -27.13135926320391]], [[1.0, 0], [6.9011603699231365, -8.775539281990527], [-18.62495590524475, -76.7731138975598]], [[1.0, 0], [8.84293850682848, -5.6830115018378535], [34.479446079156574, -75.49945561442503]], [[1.0, 0], [-0.2972785860444827, 1.2253990217110629], [-79.10635493028819, -40.78216043373953]], [[1.0, 0], [2.1079054967655657, 1.3546686063298548], [40.295256261182985, 88.23430354938829]], [[1.0, 0], [6.058076907130634, -11.75102978639612], [-58.585747866691015, -82.2721711570839]], [[1.0, 0], [9.923003089838732, 13.93490803355678], [-33.68800022169443, 97.33508432761086]], [[1.0, 0], [-7.54815429244476, -7.916276390696707], [-5.091264993140426, 106.87880529258186]], [[1.0, 0], [0.7579241915441143, 0.2623201131344046], [85.67978732696383, 67.37932949804596]], [[1.0, 0], [5.739928009275103, -2.621337288903956], [73.99926293581721, -85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-483-161.19-c1-0-10', '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/483/2/bf/a/19/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.24505594930966124, 0.302862465284674, 0.34073241701492624, 0.3562906674426099, 0.3450937656124213, 0.3011897958151904, 0.21798574151688926, 0.08930146998451852, -0.08948026131203482, -0.32024036641847875, -0.6010041010903461, -0.9249731638262892, -1.2798282821406166, -1.647434322518548, -2.004076959454807, -2.321336676041664, -2.5676606830724897, -2.7106272763418957, -2.7198142384931745, -2.570090339905115, -2.245057008395761, -1.7402883584973792, -1.0659656645466546, -0.24849012772374104, 0.6693040794127356, 1.6296202540716593, 2.562987390494776, 3.3933047375345042, 4.044356518842341, 4.447281951777465, 4.548283489103929, 4.315713008237665, 3.745621611224695, 2.864916509589842, 1.7314486854126874, 0.4306521560404213, -0.9312537969906413, 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'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.3440368299132728, 'root_number': '0.4706018438745965 + 0.8823456831320873*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.172018414957', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.941931738793622525810298550011', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.90991552955182256877434804822', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41463315079376372120140019944', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.19', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/19/7'], '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': '2-483-161.19-c1-0-10', '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': '2-483-161.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.1720184149566364, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.941931738793622525810298550011', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1194040334055755388012557888690', 'Lhash_array': ['1194040334055755388012557888690'], 'label': '2-483-161.19-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/19/7'}