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lfunc_lfunctions • Show schema
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{'Lhash': '409163952754087450970166570646', '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': '483.178', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '1194040334055755388012557888690', '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, 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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': 3, 'label': '2-483-161.17-c1-0-3', '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/178/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.24505594930966124, 0.16749270986217427, 0.0685248890674271, -0.05452380364011422, -0.2043026106202268, -0.3823268391333439, -0.5879746161935339, -0.8176741555068231, -1.0643293911471905, -1.3170268252372626, -1.5610761009323855, -1.7784417461422564, -1.9486132268652148, -2.0499320389359514, -2.0613497000380128, -1.964533463739048, -1.7461735929332753, -1.4002849927311978, -0.930246061123, -0.35028842416310124, 0.3138481804472894, 1.0253441951431799, 1.7379822848911952, 2.3991369632773494, 2.953977064456717, 3.350619212229376, 3.545803631616225, 3.510519993794968, 3.2349148046390415, 2.7317856253535298, 2.038028050667632, 1.213556506274071, 0.3374649515046136, -0.49849006025596027, -1.1986461122208427, -1.673642866326765, -1.8509970511815326, 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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': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32277344615339673292904880482', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44250121995398759366479715546', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04895300855962466319063105594', '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': '161.17', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/178/7'], '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': '2-483-161.17-c1-0-3', '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': '2-483-161.17-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': '0.32277344615339673292904880482', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '409163952754087450970166570646', 'Lhash_array': ['409163952754087450970166570646'], 'label': '2-483-161.17-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/178/7'}