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              lfunc_lfunctions •   Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '1828666233688654764', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 869.5708780117438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '108900.1', 'coefficient_field': '1.1.1.1', 'conductor': 108900, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 4, 7], [1], [1, -2, 13], [1, 0, 17], [1, 8, 19], [1, 0, 23], [1, 0, 29], [1, 4, 31], [1, -10, 37], [1, 0, 41], [1, -8, 43], [1, 0, 47], [1, 0, 53], [1, 0, 59], [1, 14, 61], [1, -16, 67], [1, 0, 71], [1, 10, 73], [1, -4, 79], [1, 0, 83], [1, 0, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 44, 'label': '2-330e2-1.1-c1-0-44', 'leading_term': '4.91104565087', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/108900/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.043098366965923, 1.07359384373289, -0.3291647697177155, -2.341398350442627, -3.139069803181884, -1.552030325280479, 1.334829039940996, 2.865102812937477, 1.69018760419079, -0.4373285576739222, -0.6858307116995065, 1.130284002457575, 2.21438532165861, 0.794847404976838, -1.112637349531009, -0.7181571301223454, 0.8747128669096711, -0.07531579933895521, -3.854217576192175, -5.879189145958241, -3.151517900661086, 1.029811423550137, 1.911937942421692, 0.2415786040516275, 0.05375588591061249, 1.366764044971827, 0.7269919299607819, -1.47438780523732, -0.8119336815997054, 2.909388873165243, 4.10927772784965, 0.7697392767183935, -1.658370225371292, 0.4638227036420109, 2.831676578444995, 1.360096678853035, -0.6366435501408221, 0.4535479264626114, 1.361004996583132, -1.115477356003784, -3.082074364709506, -1.076794330317724, 0.7817875394155469, -0.8296786108599719, -1.04999646465578, 3.597155055708732, 7.059565780163301, 4.217652355158317, 0.1811040356397569, 0.3344206859729535, 1.27790334558172, -0.1535907831206192, -0.281112507570263, 1.765696050642917, 0.5641210902426235, -3.557215046183437, -3.138968568586822, 1.737219036577014, 2.92068197091134, 0.07570212963186886, 0.4180624706860126, 3.350962826391334, 2.545033898187304, -0.1867260989703243, 0.360453785905714, 1.135468604148375, -1.202167374558473, -1.63764645947447, 1.443404824477042, 0.8002319576469105, -4.096448893011848, -4.284284624867177, 0.6439061036171476, 1.985690457571044, -0.2278355509174265, 0.4598034285844923, 1.945989344406495, 0.08879543437063658, -0.6053370703695029, 1.752926727812478, 0.7628481905701099, -2.868968090285715, -1.032189130449592, 3.673952073551908, 2.588583235348816, -0.7951386083673894, 0.3020141960715341, 1.03096436667406, -2.311898942449114, -3.10316556198769, -0.1195102701289492, -0.04334172895071642, -1.502205390136491, 0.08123546407798699, -0.3827907810713821, -4.797660448426265, -3.973111024966712, 2.556986867123104, 3.728371771576453, -0.3032330303819417, -0.3985366396866297, 1.579891831450712, 0.4257090310336575, -0.007259931585339492, 0.5042206217882355, -3.399869746815492, -6.599002302453698, -2.215479205236054, 1.91069408507418, -0.174918582313903, -0.2994387590622305, 3.272723158503889, 2.156354940946546, -1.339094581441768, -0.1311064826949898, 0.9915475549277122, -1.222812433552722, -0.7013152922083358, 0.8021233711073075, -2.491193297698388], 'positive_zeros': ['0.7065225390069753', '1.634396447817352', '2.438554103628295', '2.861586466503871', '3.587329830090276', '4.101726135921724', '4.493256542039794', '5.426653912218565', '6.048556599004429', '6.236771497520150', '6.829583165654961', '7.312400660459959', '8.049247260007441', '8.465271719509654', '9.132328307182646', '9.440918538813452', '9.913664625206546', '10.59587269012648', '10.90696462140835', '11.32802025182597', '12.27486492659095', '12.44215268627976', '12.97704343626131', '13.28894209251626', '13.78579561060997', '14.41046909651181', '15.00886250360780', '15.20680924387057', '15.97139739238938', '16.19637959219182', '16.64143115218783', '17.13620135811459', '17.54565273479094', '18.21526415003396', '18.71545530671257', '18.94386724026006', '19.50924976576841', '19.82396831953864'], 'prelabel': '2-330e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.48848721131255, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'N(U(1))', 'trace_hash': 1828666233688654764, 'z1': {'__RealLiteral__': 0, 'data': '0.7065225390069753', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.634396447817352', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.438554103628295', 'prec': 57}}
           
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              lfunc_search •   Show schema
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{'algebraic': True, 'analytic_conductor': 869.5708780117438, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 108900, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -14, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 0, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, 14, 61], 'euler67': [1, -16, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, -4, 79], 'euler83': [1, 0, 83], 'euler89': [1, 0, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, 0, 0], [1, -2, 13], [1, 0, 17], [1, 8, 19], [1, 0, 23], [1, 0, 29], [1, 4, 31], [1, -10, 37], [1, 0, 41], [1, -8, 43], [1, 0, 47], [1, 0, 53], [1, 0, 59], [1, 14, 61], [1, -16, 67], [1, 0, 71], [1, 10, 73], [1, -4, 79], [1, 0, 83], [1, 0, 89], [1, 14, 97]], 'index': 44, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/108900/j'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-330e2-1.1-c1-0-44', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-330e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.48848721131255, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1828666233688654764, 'z1': {'__RealLiteral__': 0, 'data': '0.7065225390069753', 'prec': 60}}
           
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              lfunc_instances •   Show schema
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{'Lhash': '1828666233688654764', 'Lhash_array': ['1828666233688654764'], 'factors': ['2-330e2-1.1-c1-0-44'], 'label': '2-330e2-1.1-c1-0-44', 'type': 'ECQ', 'url': 'EllipticCurve/Q/108900/j'}