Formats: - HTML - YAML - JSON - 2026-07-17T14:20:46.497612
  • lfunc_lfunctions • Show schema
    {'Lhash': '2334892788039348300678448416247', 'a10': [-1.5, 0.8660254037844386], 'a2': [0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, -0.8660254037844386], 'a5': [-1.7320508075688772, 0], 'a6': [0, 0], 'a7': [2.0, -1.7320508075688772], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.0550355892132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.593', 'coefficient_field': 'CDF', 'conductor': 1134, 'conductor_radical': 42, 'conjugate': '754467251010928256001282062707', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.7320508075688772, 0], [5.0, 0]], [[1.0, 0], [-2.0, 1.7320508075688772]], [[1.0, 0], [0, 3.0], [-11.0, 0]], [[1.0, 0], [3.0, -1.7320508075688772], [6.5, -11.258330249197702]], [[1.0, 0], [1.7320508075688772, 3.0], [-8.5, 14.722431864335457]], [[1.0, 0], [-3.0, -1.7320508075688772], [9.5, 16.454482671904334]], [[1.0, 0], [0, 6.0], [-23.0, 0]], [[1.0, 0], [2.598076211353316, 1.5], [14.5, 25.11473670974872]], [[1.0, 0], [-1.5, -0.8660254037844386], [15.5, 26.846787517317598]], [[1.0, 0], [-1.0, 1.7320508075688772], [-18.5, -32.04293994002423]], [[1.0, 0], [3.4641016151377544, 6.0], [-20.5, 35.50704155516198]], [[1.0, 0], [-4.0, 6.928203230275509], [-21.5, -37.239092362730865]], [[1.0, 0], [-3.4641016151377544, -6.0], [-23.5, 40.703193977868615]], [[1.0, 0], [7.794228634059948, -4.5], [26.5, -45.89934640057525]], [[1.0, 0], [0.8660254037844386, -1.5], [-29.5, -51.09549882328188]], [[1.0, 0], [0, 0], [30.5, -52.827549630850754]], [[1.0, 0], [1.0, -1.7320508075688772], [-33.5, -58.023702053557386]], [[1.0, 0], [0, 12.0], [-71.0, 0]], [[1.0, 0], [-6.0, 3.4641016151377544], [36.5, -63.21985447626402]], [[1.0, 0], [-0.5, -0.8660254037844386], [-39.5, 68.41600689897065]], [[1.0, 0], [-4.330127018922194, 7.5], [-41.5, -71.88010851410841]], [[1.0, 0], [5.196152422706632, -9.0], [-44.5, -77.07626093681505]], [[1.0, 0], [-4.5, -2.598076211353316], [48.5, 84.00446416709055]], [[1.0, 0], [0, 0], [101.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-103.0, 0]], [[1.0, 0], [-2.598076211353316, -1.5], [53.5, 92.66471820493493]], [[1.0, 0], [-1.0, -1.7320508075688772], [-54.5, 94.39676901250381]], [[1.0, 0], [-10.392304845413264, 6.0], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-1134-63.47-c1-0-28', 'leading_term': '1.6989655843097424906480039646347722156611872518448220850', '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/1134/2/t/d/593/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.6989655843097424, 1.8568737643449043, 2.0128537770766712, 2.166916211269888, 2.318698899822031, 2.467429503314506, 2.611911594986475, 2.750533510181564, 2.8812978964979075, 3.0018691660543286, 3.1096358388162306, 3.201784909855491, 3.2753856853805363, 3.327480855426858, 3.3551828043530714, 3.3557732594764262, 3.326804342966222, 3.2661989497367214, 3.172348165130453, 3.044203204594555, 2.8813591447170652, 2.6841275568750196, 2.4535950808537543, 2.1916650090231626, 1.9010791084718017, 1.585417199140856, 1.2490724345664652, 0.8972007962875455, 0.5356440050705701, 0.17082585739108835, -0.1903771064913653, -0.5407887324914407, -0.8731073120192672, -1.1800967060047665, -1.454789715532789, -1.690698012789048, -1.882022206588492, -2.023855048810383, -2.112370431538459, -2.1449907147767, -2.120525089677538, -2.039272141958167, -1.90308054379442, -1.7153628672212882, -1.481058862140774, -1.2065461479877158, -0.8994980867610578, -0.5686905801667979, -0.22376159678538493, 0.1250706918152041, 0.4673232900170368, 0.79258756508187, 1.0908809607645216, 1.3529987262672385, 1.5708523431427277, 1.7377810184963776, 1.848822842055198, 1.900933009126828, 1.8931378998165966, 1.826615760246893, 1.7046972101725002, 1.5327817324136181, 1.3181695859487177, 1.0698121056326224, 0.797986966676128, 0.5139085456442135, 0.22928683743382097, -0.04414867653713344, -0.2951414297347728, -0.5133959757575141, -0.6900406657573808, -0.8180435142948561, -0.8925609880921255, -0.9112014547764258, -0.8741879838175686, -0.7844090196333021, -0.6473500199993789, -0.4709042996349126, -0.26506682809724275, -0.04152036038397259, 0.18687123621455173, 0.4066425284146199, 0.6043546275655651, 0.7672441200024016, 0.8838628017199225, 0.9446772741685437, 0.9425979947183772, 0.873409431726605, 0.7360765316931621, 0.5329076688427525, 0.2695604423982241, -0.0451161327088463, -0.3994016414965897, -0.779176926785051, -1.1685317529958281, -1.5504822790980912, -1.9077665115827929, -2.2236805958521497, -2.4829151558621687, -2.672349182728874, -2.7817593913289627, -2.8044055950300555, -2.737457464632877, -2.5822348921190783, -2.3442428093735628, -2.032991343589509, -1.6616031559912572, -1.246221165016455, -0.8052410057634093, -0.35840291119067214, 0.07421338286418361, 0.47324016046704853, 0.8210646247004659, 1.1028064238424458, 1.3071743878703352, 1.4271514894452852, 1.4604644717308193, 1.4098047374742577, 1.2827795303475689, 1.0915865714733575, 0.8524204281370673, 0.5846341847779073, 0.3096946065900351, 0.04998207903266696, -0.17250263593938914, -0.33745507731489377, -0.4275333590508357, -0.4295001294789869, -0.3351704241112296, -0.14210387966277888, 0.1460081161354634, 0.5192943395854627, 0.9620107133057892, 1.4531987131348214, 1.9676713286276446, 2.477283038059614, 2.9524223118758375, 3.3636500428036165, 3.6833960082309796, 3.887618810643603, 3.957333286497709, 3.8799134121180834, 3.650088244571876, 3.270563069861928, 2.7522170274654947, 2.113851086277514, 1.3814851643933295, 0.5872290327202213, -0.23222306850456598, -1.0374009513131068, -1.7880772825340998, -2.445388897939594, -2.9739437851586783, -3.343794385721444, -3.5321622845337486, -3.5248106501694663, -3.316978496851462, -2.913814090667465, -2.33027238602089, -1.5904717202791463, -0.7265363653297695, 0.2230179309199792, 1.215270451061138, 2.2051457336397537, 3.1478018148740676, 4.001020607545993, 4.727462349486109, 5.2966521692243935, 5.686581042114587, 5.884825042199717, 5.889114647693016, 5.7073183262353036, 5.3568397763578774, 4.863463885973066, 4.259720457048409, 3.5828648664302487, 2.872599114660773, 2.1686735185944643, 1.5085174375054042, 0.9250462291826452, 0.4447810460046035, 0.08639864391122663, -0.14019878025988824, -0.2342369288529215, -0.20382632633952566, -0.0651420232589198, 0.15891686842832758, 0.4404963617723282, 0.7488654446553201, 1.0526616896692065, 1.3221521365228377, 1.5313555312204201, 1.6598809573669673, 1.6943567481637287, 1.6293511635726534, 1.4677208800576338, 1.2203625880607787, 0.905384283618629, 0.5467533504336501, 0.17251544132986826, -0.18729112764661315, -0.5028784810093505, -0.7469506137294211, -0.8967828713308633, -0.9359893986209484, -0.8558493948179888, -0.6560933153008417, -0.3450878164990595, 0.06059933457407881, 0.5372289377155689, 1.055446289510326, 1.5822565833351707, 2.083281812785142, 2.5251396390731347, 2.8777744099653932, 3.116572440035333, 3.2241078014991684, 3.191390362494243, 3.018522932035115, 2.714716680502337, 2.297660486069268, 1.7922871397233708, 1.2290239400768712, 0.6416537827066713, 0.06494245032388181, -0.4677938859059364, -0.9270014556261537, -1.2889103813983744, -1.5371141795674392, -1.6635890516164344, -1.669076506003572, -1.5628008492720442, -1.3615437568680637, -1.0881476461394335, -0.7695641161948996, -0.43459979536081467, -0.11153663864161215, 0.17418503998693907, 0.4020358165572373, 0.5580515267114372, 0.6359367930412043, 0.6375241100198641, 0.5725452914488015, 0.4577267199763557, 0.31527448142639086, 0.17086580943709329, 0.051305246237376076, -0.017965948127258956, -0.01530296702239371, 0.07497056377790477, 0.2608388186227759, 0.5414730952423286, 0.906823789932232, 1.3379793950931698, 1.8082859930820159, 2.285158838882631, 2.7324596720976255], 'positive_zeros': ['1.84190563836673234661081376830162', '3.04005378728758285842249696310653', '4.17712071418802938193831533728074', '4.94885405164377825481164055834395', '5.67905567976881007511577342079009', '6.86400367928751011727549096352418', '7.70048193787092228798710869354590', '8.095787541454514379566294864143285', '9.232310835590818533224421187937713', '10.04817476103520631775692368603976'], 'prelabel': '2-1134-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.3510246345841381, 'root_number': '-0.59298146155838107131268591841634153036264338753136992902 + 0.8052161115179490941013076349425116740502897522357923283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3510246345841381', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84190563836673234661081376830', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04005378728758285842249696311', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17712071418802938193831533728', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 9.0550355892132, 'bad_primes': [2, 3, 7], 'central_character': '63.47', 'conductor': 1134, 'conductor_radical': 42, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/t/d/593/2'], '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': '2-1134-63.47-c1-0-28', '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': '2-1134-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.3510246345841381, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84190563836673234661081376830', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2334892788039348300678448416247', 'Lhash_array': ['2334892788039348300678448416247'], 'factors': ['2-1134-63.47-c1-0-28'], 'label': '2-1134-63.47-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/t/d/593/2'}