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  • lfunc_lfunctions • Show schema
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'1.46923222089454465193784103113622', '1.61655782865770239630900231395637', '1.62266904897607752513575859144614', '2.47879456273766357897552518536772', '2.69575563735575496139580642783811', '2.95700016599323887989685097185457', '3.13952738172133391689860311796606', '3.46626130918610480432785189004800', '3.70296973349955313367848209946995', '3.97429049954081141146203355571618', '4.10475765593241965676458394855703', '4.72256886851633731956872472458255', '4.80682614768122444897990905926706', '4.87914742664241811987270976645974', '5.41943662621103522210635532679324', '5.48816446748388282156307967317537', '5.62489608776219843822928289587556', '5.86800043356852777970644962711846', '6.05093445852663352246468487450650', '6.26323293432823735284398229035369', '6.43833051108593193571865909884212', '7.16179633061442411212625238381160', '7.32499937904793829968906574657771', '7.35176069053409261721157146275931', '7.37741550697353043970711722901801', '7.60452818112161174772924878471636', '7.60964463627892736061230460813722', '7.82031477277873499258537374448528', '8.323848127501314230610520633865567', '8.575023415752742458657592468568758', '8.670618637790239922654312583445329', '9.035041131724654924214461402758137', '9.165489438207780886426561409362279', '9.351299405560711021981839151178802', '9.387452417008642591538626392741170', '9.780379990646521993993058757303644', '9.898288000343592333480182066717884', '10.05537507804210476656021406734415'], 'prelabel': '8-1134e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 776482173991826165, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21845658474372100863496275516', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.20161706674668295012847074045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.46923222089454465193784103114', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 6722.9618416694475, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1653682833936, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -14, 0, 0, 2, 0, 0, -12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, -1, 0, 0, -28, 0, 0, 0, 0, 0, -42, 0, 0, 24, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, -14], 'euler11': [1, 0, -44, 0, 726, 0, -5324, 0, 14641], 'euler13': [1, 0, 26, 0, 507, 0, 4394, 0, 28561], 'euler17': [1, 0, -22, 0, 195, 0, -6358, 0, 83521], 'euler19': [1, -24, 278, -2064, 10683, -39216, 100358, -164616, 130321], 'euler2': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, -20, 0, 1158, 0, -10580, 0, 279841], 'euler29': [1, 0, -23, 0, -312, 0, -19343, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 12, 122, 888, 6003, 27528, 117242, 357492, 923521], 'euler37': [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], 'euler41': [1, 0, -70, 0, 3219, 0, -117670, 0, 2825761], 'euler43': [1, -16, 106, -1024, 9643, -44032, 195994, -1272112, 3418801], 'euler47': [1, 0, -82, 0, 4515, 0, -181138, 0, 4879681], 'euler5': [1, 0, 14, 0, 99, 0, 350, 0, 625], 'euler53': [1, 0, 97, 0, 6600, 0, 272473, 0, 7890481], 'euler59': [1, 0, 29, 0, -2640, 0, 100949, 0, 12117361], 'euler61': [1, 12, 182, 1608, 17163, 98088, 677222, 2723772, 13845841], 'euler67': [1, 28, 454, 5488, 51883, 367696, 2038006, 8421364, 20151121], 'euler7': [1, -2, 15, -14, 49, 0, 0, 0, 0], 'euler71': [1, 0, -212, 0, 21318, 0, -1068692, 0, 25411681], 'euler73': [1, 42, 881, 12306, 123444, 898338, 4694849, 16338714, 28398241], 'euler79': [1, 22, 205, 2662, 33364, 210298, 1279405, 10846858, 38950081], 'euler83': [1, 0, 134, 0, 11067, 0, 923126, 0, 47458321], 'euler89': [1, 0, -70, 0, -3021, 0, -554470, 0, 62742241], 'euler97': [1, -24, 434, -5808, 67779, -563376, 4083506, -21904152, 88529281], 'euler_factors': [[1, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 14, 0, 99, 0, 350, 0, 625], [1, -2, 15, -14, 49, 0, 0, 0, 0], [1, 0, -44, 0, 726, 0, -5324, 0, 14641], [1, 0, 26, 0, 507, 0, 4394, 0, 28561], [1, 0, -22, 0, 195, 0, -6358, 0, 83521], [1, -24, 278, -2064, 10683, -39216, 100358, -164616, 130321], [1, 0, -20, 0, 1158, 0, -10580, 0, 279841], [1, 0, -23, 0, -312, 0, -19343, 0, 707281], [1, 12, 122, 888, 6003, 27528, 117242, 357492, 923521], [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], [1, 0, -70, 0, 3219, 0, -117670, 0, 2825761], [1, -16, 106, -1024, 9643, -44032, 195994, -1272112, 3418801], [1, 0, -82, 0, 4515, 0, -181138, 0, 4879681], [1, 0, 97, 0, 6600, 0, 272473, 0, 7890481], [1, 0, 29, 0, -2640, 0, 100949, 0, 12117361], [1, 12, 182, 1608, 17163, 98088, 677222, 2723772, 13845841], [1, 28, 454, 5488, 51883, 367696, 2038006, 8421364, 20151121], [1, 0, -212, 0, 21318, 0, -1068692, 0, 25411681], [1, 42, 881, 12306, 123444, 898338, 4694849, 16338714, 28398241], [1, 22, 205, 2662, 33364, 210298, 1279405, 10846858, 38950081], [1, 0, 134, 0, 11067, 0, 923126, 0, 47458321], [1, 0, -70, 0, -3021, 0, -554470, 0, 62742241], [1, -24, 434, -5808, 67779, -563376, 4083506, -21904152, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/t/c'], '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': '8-1134e4-1.1-c1e4-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1134e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 776482173991826165, 'z1': {'__RealLiteral__': 0, 'data': '0.21845658474372100863496275516', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '276926620774186998417788987743,1523230595905917033711945528349,1862473106691624055190229309464,2056977393906294846259894214684', 'Lhash_array': ['276926620774186998417788987743', '1523230595905917033711945528349', '1862473106691624055190229309464', '2056977393906294846259894214684'], 'factors': ['2-1134-63.47-c1-0-2', '2-1134-63.47-c1-0-16', '2-1134-63.59-c1-0-24', '2-1134-63.59-c1-0-29'], 'label': '8-1134e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/t/c'}