-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1708170496637372736333149793226', 'a10': [1.9496858291468608, 3.3769549148794167], 'a2': [0.8660254037844386, 0.5], 'a3': [0.6628271480711836, -0.3826834323650898], 'a4': [0.5, 0.8660254037844386], 'a5': [3.3769549148794167, 1.9496858291468608], 'a6': [0.7653668647301796, 0], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [-1.2071067811865475, 2.0907702751760278], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-2.7588056345200664, 1.8409213646813747]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.901', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '2404311713080209264582941641506', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.6628271480711836, 0.3826834323650898], [1.5, -2.598076211353316]], [[1.0, 0], [-3.3769549148794167, -1.9496858291468608], [2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.7588056345200664, 1.8409213646813747]], [[1.0, 0], [-1.8190261538471002, 0], [13.0, 0]], [[1.0, 0], [3.038028810186926, 5.262020254101781], [-8.5, 14.722431864335457]], [[1.0, 0], [3.4147614618043445, -5.914540347573295], [-9.5, -16.454482671904334]], [[1.0, 0], [-2.1883361023790697, 3.7903093133577967], [-11.5, -19.91858428704209]], [[1.0, 0], [0, 9.361122065284126], [-29.0, 0]], [[1.0, 0], [6.827036058882001, -3.941591106362805], [15.5, -26.846787517317598]], [[1.0, 0], [-2.303888827883924, 3.9904525048852646], [-18.5, -32.04293994002423]], [[1.0, 0], [3.582346322731507, 0], [41.0, 0]], [[1.0, 0], [0, -3.258190826593298], [-43.0, 0]], [[1.0, 0], [-0.17654233411435438, -0.10192676412428735], [23.5, 40.703193977868615]], [[1.0, 0], [2.4922249302629935, 4.3166602031053065], [-26.5, 45.89934640057525]], [[1.0, 0], [4.501183445904788, -2.5987594741650164], [29.5, -51.09549882328188]], [[1.0, 0], [-4.491859399655057, 7.780128700658395], [-30.5, -52.827549630850754]], [[1.0, 0], [-4.01676322712526, -6.957237991355275], [-33.5, 58.023702053557386]], [[1.0, 0], [-8.86195357899671, 0], [71.0, 0]], [[1.0, 0], [-0.027852992481346622, -0.04824279812052629], [-36.5, 63.21985447626402]], [[1.0, 0], [7.3484692283495345, 4.242640687119285], [39.5, 68.41600689897065]], [[1.0, 0], [-10.46757523130289, 0], [83.0, 0]], [[1.0, 0], [1.4615996997890337, 0.8438549801206748], [44.5, 77.07626093681505]], [[1.0, 0], [0, 9.238795325112868], [-97.0, 0]], [[1.0, 0], [-2.6728332458079573, -4.629482981898616], [-50.5, 87.4685657822283]], [[1.0, 0], [-3.676390340122222, -2.1225649525157047], [51.5, 89.20061658979718]], [[1.0, 0], [6.268833817220742, 3.619312891877424], [53.5, 92.66471820493493]], [[1.0, 0], [5.196152422706632, -3.0], [54.5, -94.39676901250381]], [[1.0, 0], [-16.83996236085577, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-1078-77.54-c1-0-28', 'leading_term': '3.337561255016734213053406995436163100753287141834994002', '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/1078/2/i/d/901/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.3375612550167344, 3.2606458816272164, 3.1815418141047482, 3.0996002659782484, 3.013944039585111, 2.923533526857792, 2.827239615611051, 2.723919221625395, 2.6124895804861494, 2.4919981429247633, 2.3616857356287286, 2.2210414188576224, 2.0698480938992567, 1.908218350318475, 1.7366203062886885, 1.5558933248133633, 1.3672535344875636, 1.1722890933546402, 0.9729451467994502, 0.7714984720853852, 0.5705218887948366, 0.3728386525383754, 0.18146723825365066, -0.00044284649190720664, -0.16968330781563004, -0.3230661669043076, -0.4575082067963234, -0.5701189530234175, -0.6582900926816845, -0.719783985365515, -0.7528187154629126, -0.7561469922511702, -0.7291261345009344, -0.671776390648565, -0.5848249526019501, -0.4697332268134493, -0.32870523318882044, -0.16467541000948382, 0.018725393172377185, 0.21722636126083203, 0.4259955580487261, 0.6397404044756044, 0.8528282628140031, 1.0594248215962672, 1.2536472111125674, 1.4297280552785172, 1.5821860123800402, 1.705997804557299, 1.796766312753144, 1.8508790468281242, 1.8656512127240577, 1.8394477082866052, 1.7717786990740418, 1.663363960686991, 1.5161619225690852, 1.3333602991708886, 1.1193263284353507, 0.8795159266264736, 0.6203424760936498, 0.34900744452319954, 0.07329653994351386, -0.19865342044030673, -0.4586103664679435, -0.6985177628718205, -0.9107715124212231, -1.0884933994795578, -1.2257910535084386, -1.3179943192425458, -1.3618582088646634, -1.3557232969404196, -1.2996255016230733, -1.1953486601065566, -1.0464151201884186, -0.8580116841697499, -0.636850591383152, -0.39096773229278975, -0.12946285917632208, 0.13781090440986457, 0.40059855668237376, 0.6486238659531746, 0.8719855306120518, 1.061553859505958, 1.2093521666525062, 1.3089068595379392, 1.3555506319696193, 1.346664272446772, 1.2818443620870241, 1.1629865284167922, 0.9942768797549386, 0.7820876780718139, 0.5347770984045486, 0.26239692963037176, -0.02368386403388843, -0.311227850034414, -0.5876345705414887, -0.8404839918364869, -1.0580966622289925, -1.2300874889354474, -1.347889150468143, -1.405221254197609, -1.398482479474848, -1.3270451225246325, -1.1934346416752788, -1.0033809047233448, -0.7657327327032704, -0.4922328416894399, -0.19715619488913827, 0.10317915017266767, 0.39101364189037446, 0.6478396232471423, 0.8551608885521145, 0.9952887206772699, 1.052141774784296, 1.01201553601004, 0.8642868848954169, 0.6020206331335478, 0.22244775508893275, -0.27271062090132075, -0.8770937124837104, -1.5797394919363599, -2.365316699012397, -3.2145478570009924, -4.10481217502567, -5.0109088655519844, -5.905953605069407, -6.762374000481622, -7.55296434921833, -8.251956007339679, -8.836057554402238, -9.285418836920398, -9.584474965422418, -9.722630418241366, -9.694749453032763, -9.50142683045343, -9.149022106724752, -8.649451064663358, -8.019738772029454, -7.28134978127873, -6.459321592077198, -5.5812371647711245, -4.67608050431306, -3.7730256879018373, -2.9002138208869943, -2.083574007673827, -1.3457433661066895, -0.70513737093224, -0.17521549328889122, 0.2360215501433193, 0.526277246800251, 0.6989338596983862, 0.7627555843119846, 0.7313330907228933, 0.622295218541458, 0.4563255261151089, 0.25603166455631315, 0.04472358721475881, -0.15483804854853736, -0.3216596165878991, -0.43763563246915416, -0.4885146369403699, -0.4646585184176985, -0.3615540092581756, -0.18004749558157557, 0.07371157810442834, 0.3886182576420156, 0.7492347102139769, 1.136657212119578, 1.5295832824322806, 1.9055233858374587, 2.242093037050597, 2.5183158447675638, 2.715866390800008, 2.8201840157486235, 2.821394537978913, 2.7149864219337756, 2.5022004894844114, 2.1901073083080296, 1.7913631179951723, 1.3236526803040212, 0.8088448125793132, 0.27190261755820266, -0.26039536612056274, -0.7608555315890594, -1.2033157544826099, -1.5640590837779607, -1.8231161733254468, -1.9653830950802007, -1.981490409732409, -1.8683723543290514, -1.6295010717111627, -1.2747690956002258, -0.8200228156032011, -0.28626928560268566, 0.3014026148860849, 0.9151290903909826, 1.5257353348671143, 2.104275753624027, 2.623564731697564, 3.059611966181762, 3.3928811330880317, 3.6093001748131135, 3.700965285252475, 3.666497987796281, 3.511034576534801, 3.245848483707246, 2.8876276032146095, 2.4574489655334335, 1.9795111925313533, 1.479699749865029, 0.9840702373430025, 0.5173401403031486, 0.10147922906067447, -0.24551691585543767, -0.510596678576555, -0.6863074043586658, -0.7710967317746006, -0.7692431265284826, -0.6904214782547761, -0.5489324462719832, -0.36264546644871326, -0.1517236075464212, 0.0627873976676315, 0.26041457256832173, 0.42266287763285093, 0.5342781694396037, 0.5842846009877823, 0.566727245171222, 0.48106949004184196, 0.33221703206149455, 0.13016469733485037, -0.11071269712936234, -0.3726802850825573, -0.6359074105662298, -0.8798924508275666, -1.0849524440981426, -1.2336759133489772, -1.3122380852006772, -1.3114852491087126, -1.2277089247894943, -1.0630500174379232, -0.8254970667120387, -0.528469544835962, -0.19000521192791292, 0.16840204688789043, 0.5232425394341039, 0.8506171376044148, 1.127942546565119, 1.3356200944575338, 1.4585519934374933, 1.4873961387460297, 1.4194651405376146, 1.2591966412590145, 1.0181488091440538, 0.7145055681262799, 0.3721086800830472, 0.019066113923968408, -0.313983945480867], 'positive_zeros': ['1.34750892424918315901896969413849', '2.22081691602810806149870109497244', '3.53126465548856139943434727924338', '4.48152692002793566109467203545608', '5.38582026130882252810192337750946', '6.24930598313241621181390759401663', '6.82487096193128158766318682746606', '8.577602737644789961638704429479437', '9.094649997392289715888825769457809', '9.535260155882159332216369740182328'], 'prelabel': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.3234700527603254, 'root_number': '0.52659070375511231693127061816072257889632283249736824758 - 0.85011895092316083410679544797168388686387838710839399264*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1617350263801627', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34750892424918315901896969414', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22081691602810806149870109497', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53126465548856139943434727924', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.54', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/12'], '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': '2-1078-77.54-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': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.1617350263801627, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34750892424918315901896969414', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1708170496637372736333149793226', 'Lhash_array': ['1708170496637372736333149793226'], 'label': '2-1078-77.54-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/12'}