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lfunc_lfunctions • Show schema
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{'Lhash': '563037797309600147595157082418,1579196476052693979083523905786', 'a10': 0, 'a2': 0, 'a3': 90, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 3500, 'a8': 0, 'a9': 1539, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6117.851084464228, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -90, 6561]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -90, 6561], [1, 0, -730850, 0, 152587890625], [1, -3500, 14592102, -20176803500, 33232930569601], [1, 0, -380283362, 0, 45949729863572161], [1, 51460, 2293494342, 41977502902660, 665416609183179841], [1, 0, -8342551298, 0, 48661191875666868481], [1, -37876, 34325773926, -643269433740916, 288441413567621167681], [1, 0, 64711613182, 0, 6132610415680998648961], [1, 0, -788066452322, 0, 250246473680347348787521], [1, -702956, 1829318859366, -599544872115375596, 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'2.20009132927021261601765470668273', '3.24743228928982274160706143898490', '3.41550919490135299273803049759937', '4.68283541085945721547247226635199', '4.87415422025947824325835258399339', '5.17020925726390311216297228225692', '6.23492168679873949409838594242736', '6.92565056130325057527748665359058', '7.34540796917537938650444444446484', '7.966808776946808401961197392346518', '8.197969956219001378238944684681431', '8.821862544453052927987017647861264', '9.115432885666015484659206527134049', '9.900250127812971928510953078256164', '10.16087794975541997920810609143566', '10.78027315923164073354451235389446', '11.41374147273439395643806029110858'], 'prelabel': '4-192e2-1.1-c8e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.844020190599773, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c8e2-0', 'trace_hash': 1009878893583823022, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44415850645929573771848680659', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.24576636162076006430012520972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.11468252608290202986388957272', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 6117.851084464228, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 90, 0, 0, 0, 3500, 0, 1539, 0, 0, 0, -51460, 0, 0, 0, 0, 0, 37876, 0, 315000, 0, 0, 0, 730850, 0, -451980, 0, 0, 0, 702956, 0, 0, 0, 0, 0, -2670340, 0, -4631400, 0, 0, 0, -7052300, 0, 0, 0, 0, 0, -2342102, 0, 0, 0, 0, 0, 0, 0, 3408840, 0, 0, 0, -1507204, 0, 5386500, 0, 0, 0, 4537780, 0, 0, 0, 0, 0, 55345540, 0, 65776500, 0, 0, 0, 45961964, 0, -50775579, 0, 0, 0, 0, 0, 0, 0, 0, 0, -180110000, 0, 63266040, 0, 0, 0, 294542020, 0, 0, 0], 'euler11': [1, 0, -380283362, 0, 45949729863572161], 'euler13': [1, 51460, 2293494342, 41977502902660, 665416609183179841], 'euler17': [1, 0, -8342551298, 0, 48661191875666868481], 'euler19': [1, -37876, 34325773926, -643269433740916, 288441413567621167681], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 64711613182, 0, 6132610415680998648961], 'euler29': [1, 0, -788066452322, 0, 250246473680347348787521], 'euler3': [1, -90, 6561, 0, 0], 'euler31': [1, -702956, 1829318859366, -599544872115375596, 727423121747185263828481], 'euler37': [1, 2670340, 8807637836742, 9379514384983403140, 12337511914217166362274241], 'euler41': [1, 0, -12452468931842, 0, 63759030914653054346432641], 'euler43': [1, 7052300, 35810134377702, 82428694817725532300, 136614025729312093462315201], 'euler47': [1, 0, -30967680304898, 0, 566977372488557307219621121], 'euler5': [1, 0, -730850, 0, 152587890625], 'euler53': [1, 0, -80936075395298, 0, 3876269050118516845397872321], 'euler59': [1, 0, -105562517046242, 0, 21559177407076402401757871041], 'euler61': [1, 1507204, 383982541968966, 288942028978753912324, 36751693856637464631913392961], 'euler67': [1, -4537780, 817283216945382, -1842645785862974396980, 164890958756244164895763202881], 'euler7': [1, -3500, 14592102, -20176803500, 33232930569601], 'euler71': [1, 0, -1001758688017922, 0, 416997623116370028124580469121], 'euler73': [1, -55345540, 2378702383261062, -44633969274327535748740, 650377879817809571042122834561], 'euler79': [1, -45961964, 3562343153497446, -69729300505008200045804, 2301619141096101839813550846721], 'euler83': [1, 0, -2352070843223138, 0, 5072820298953863752478356399681], 'euler89': [1, 0, -2600204109557762, 0, 15496731425178936435099327730561], 'euler97': [1, -294542020, 37363617575174022, -2308453522503650734401220, 61425365346268570446197767595521], 'euler_factors': [[1, 0, 0, 0, 0], [1, -90, 6561, 0, 0], [1, 0, -730850, 0, 152587890625], [1, -3500, 14592102, -20176803500, 33232930569601], [1, 0, -380283362, 0, 45949729863572161], [1, 51460, 2293494342, 41977502902660, 665416609183179841], [1, 0, -8342551298, 0, 48661191875666868481], [1, -37876, 34325773926, -643269433740916, 288441413567621167681], [1, 0, 64711613182, 0, 6132610415680998648961], [1, 0, -788066452322, 0, 250246473680347348787521], [1, -702956, 1829318859366, -599544872115375596, 727423121747185263828481], [1, 2670340, 8807637836742, 9379514384983403140, 12337511914217166362274241], [1, 0, -12452468931842, 0, 63759030914653054346432641], [1, 7052300, 35810134377702, 82428694817725532300, 136614025729312093462315201], [1, 0, -30967680304898, 0, 566977372488557307219621121], [1, 0, -80936075395298, 0, 3876269050118516845397872321], [1, 0, -105562517046242, 0, 21559177407076402401757871041], [1, 1507204, 383982541968966, 288942028978753912324, 36751693856637464631913392961], [1, -4537780, 817283216945382, -1842645785862974396980, 164890958756244164895763202881], [1, 0, -1001758688017922, 0, 416997623116370028124580469121], [1, -55345540, 2378702383261062, -44633969274327535748740, 650377879817809571042122834561], [1, -45961964, 3562343153497446, -69729300505008200045804, 2301619141096101839813550846721], [1, 0, -2352070843223138, 0, 5072820298953863752478356399681], [1, 0, -2600204109557762, 0, 15496731425178936435099327730561], [1, -294542020, 37363617575174022, -2308453522503650734401220, 61425365346268570446197767595521]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/9/e/f'], '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': '4-192e2-1.1-c8e2-0-4', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8, 8], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c8e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.844020190599773, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c8e2-0', 'trace_hash': 1009878893583823022, 'z1': {'__RealLiteral__': 0, 'data': '0.44415850645929573771848680659', 'prec': 103}}
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{'Lhash': '563037797309600147595157082418,1579196476052693979083523905786', 'Lhash_array': ['563037797309600147595157082418', '1579196476052693979083523905786'], 'label': '4-192e2-1.1-c8e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/9/e/f'}