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{'Lhash': '1699921543091762535817463440515,2047906380266616509348097154768,2415367011977540904614481815108', 'a10': 0, 'a2': -1, 'a3': 9, 'a4': -14, 'a5': 0, 'a6': -9, 'a7': 16, 'a8': 18, 'a9': 54, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 115334.71800677532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -9, 27, -27]], [5, [1]], [11, [1, 33, 363, 1331]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'euler_factors': [[1, 1, 15, 11, 120, 64, 512], [1, -9, 27, -27], [1], [1, -16, 277, -5168, 95011, -1882384, 40353607], [1, 33, 363, 1331], [1, -42, 1363, -47132, 2994511, -202725978, 10604499373], [1, -34, 10079, -155020, 49518127, -820677346, 118587876497], [1, 280, 39201, 3743984, 268879659, 13172846680, 322687697779], [1, -112, 19477, -809120, 236976659, -16580019568, 1801152661463], [1, 290, 46667, 4894124, 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'8.664874130697926529337598270122721', '8.756886792663463848002055456392032', '8.975257984627867981597137714799178', '9.218593579642396503063982541067878', '9.348386146516061031470737342512102'], 'prelabel': '6-825e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.976860021151063, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3e3-0', 'trace_hash': 595753778559574558, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34100164728806702134706110119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61551328094500872726920373329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.90538860750957338173778733004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 115334.71800677532, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, -1, 9, -14, 0, -9, 16, 18, 54, 0, -33, -126, 42, -16, 0, 83, 34, -54, -280, 0, 144, 33, 112, 162, 0, -42, 270, -224, -290, 0, -392, -143, -297, -34, 0, -756, -570, 280, 378, 0, -662, -144, 68, 462, 0, -112, -264, 747, -21, 0, 306, -588, 94, -270, 0, 288, -2520, 290, -612, 0, -582, 392, 864, -68, 0, 297, -940, -476, 1008, 0, -1616, 972, -738, 570, 0, 3920, -528, -378, 124, 0, 1215, 662, 1232, -2016, 0, -68, -2610, -594, 838, 0, 672, -1568, -3528, 264, 0, -1287, 90, 21, -1782, 0], 'euler11': [1, 33, 363, 1331, 0, 0, 0], 'euler13': [1, -42, 1363, -47132, 2994511, -202725978, 10604499373], 'euler17': [1, -34, 10079, -155020, 49518127, -820677346, 118587876497], 'euler19': [1, 280, 39201, 3743984, 268879659, 13172846680, 322687697779], 'euler2': [1, 1, 15, 11, 120, 64, 512], 'euler23': [1, -112, 19477, -809120, 236976659, -16580019568, 1801152661463], 'euler29': [1, 290, 46667, 4894124, 1138161463, 172498763090, 14507145975869], 'euler3': [1, -9, 27, -27, 0, 0, 0], 'euler31': [1, 392, 121533, 23039344, 3620589603, 347901442952, 26439622160671], 'euler37': [1, 570, 212899, 56704796, 10783973047, 1462464053130, 129961739795077], 'euler41': [1, 662, 150855, 22689620, 10397077455, 3144569007542, 327381934393961], 'euler43': [1, -68, 11145, 9678104, 886105515, -429852687332, 502592611936843], 'euler47': [1, 264, 146893, 68940144, 15250871939, 2845712846856, 1119130473102767], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -94, 388819, -25584884, 57886206263, -2083449946126, 3299763591802133], 'euler59': [1, 612, 191353, 89255576, 39299887787, 25814486588292, 8662995818654939], 'euler61': [1, 582, 700987, 242850884, 159110730247, 29984857878102, 11694146092834141], 'euler67': [1, 940, 512801, 170936200, 154231567163, 85030879238860, 27206534396294947], 'euler7': [1, -16, 277, -5168, 95011, -1882384, 40353607], 'euler71': [1, 1616, 1744933, 1196967136, 624530714963, 207010058816336, 45848500718449031], 'euler73': [1, 738, 1335919, 586235356, 519695201623, 111684659001282, 58871586708267913], 'euler79': [1, -124, 1293245, -95402344, 637620221555, -30142844484604, 119851595982618319], 'euler83': [1, -1232, 2008521, -1393226768, 1148446197027, -402790539990608, 186940255267540403], 'euler89': [1, -838, 1110375, -349581812, 782779953375, -416470321825318, 350356403707485209], 'euler97': [1, -90, 441679, 759889556, 403108497967, -74967480443610, 760231058654565217], 'euler_factors': [[1, 1, 15, 11, 120, 64, 512], [1, -9, 27, -27, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -16, 277, -5168, 95011, -1882384, 40353607], [1, 33, 363, 1331, 0, 0, 0], [1, -42, 1363, -47132, 2994511, -202725978, 10604499373], [1, -34, 10079, -155020, 49518127, -820677346, 118587876497], [1, 280, 39201, 3743984, 268879659, 13172846680, 322687697779], [1, -112, 19477, -809120, 236976659, -16580019568, 1801152661463], [1, 290, 46667, 4894124, 1138161463, 172498763090, 14507145975869], [1, 392, 121533, 23039344, 3620589603, 347901442952, 26439622160671], [1, 570, 212899, 56704796, 10783973047, 1462464053130, 129961739795077], [1, 662, 150855, 22689620, 10397077455, 3144569007542, 327381934393961], [1, -68, 11145, 9678104, 886105515, -429852687332, 502592611936843], [1, 264, 146893, 68940144, 15250871939, 2845712846856, 1119130473102767], [1, -94, 388819, -25584884, 57886206263, -2083449946126, 3299763591802133], [1, 612, 191353, 89255576, 39299887787, 25814486588292, 8662995818654939], [1, 582, 700987, 242850884, 159110730247, 29984857878102, 11694146092834141], [1, 940, 512801, 170936200, 154231567163, 85030879238860, 27206534396294947], [1, 1616, 1744933, 1196967136, 624530714963, 207010058816336, 45848500718449031], [1, 738, 1335919, 586235356, 519695201623, 111684659001282, 58871586708267913], [1, -124, 1293245, -95402344, 637620221555, -30142844484604, 119851595982618319], [1, -1232, 2008521, -1393226768, 1148446197027, -402790539990608, 186940255267540403], [1, -838, 1110375, -349581812, 782779953375, -416470321825318, 350356403707485209], [1, -90, 441679, 759889556, 403108497967, -74967480443610, 760231058654565217]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/4/a/n'], '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': '6-825e3-1.1-c3e3-0-4', 'motivic_weight': 3, '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}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'prelabel': '6-825e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.976860021151063, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 595753778559574558, 'z1': {'__RealLiteral__': 0, 'data': '1.34100164728806702134706110119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1699921543091762535817463440515,2047906380266616509348097154768,2415367011977540904614481815108', 'Lhash_array': ['1699921543091762535817463440515', '2047906380266616509348097154768', '2415367011977540904614481815108'], 'label': '6-825e3-1.1-c3e3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/a/n'}