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lfunc_lfunctions • Show schema
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{'Lhash': '76318147663041177006671930068', 'a10': [-1.025806296635574, -1.7767486244968853], 'a2': [0.8660254037844386, 0.5], 'a3': [0.6628271480711836, -0.3826834323650898], 'a4': [0.5, 0.8660254037844386], 'a5': [-1.7767486244968853, -1.025806296635574], '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], [3.141267121810395, 1.0641620503631186]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.901', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '2885217012097335433624692647215', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.6628271480711836, 0.3826834323650898], [1.5, 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[29.5, -51.09549882328188]], [[1.0, 0], [5.667106170925683, -9.815715819930398], [-30.5, -52.827549630850754]], [[1.0, 0], [1.481229321192522, 2.565564441966208], [-33.5, 58.023702053557386]], [[1.0, 0], [2.134031517638854, 0], [71.0, 0]], [[1.0, 0], [5.41261751976796, 9.374928546175548], [-36.5, 63.21985447626402]], [[1.0, 0], [7.3484692283495345, 4.242640687119285], [39.5, 68.41600689897065]], [[1.0, 0], [12.315334296325464, 0], [83.0, 0]], [[1.0, 0], [-5.826837742047155, -3.364126338895196], [44.5, 77.07626093681505]], [[1.0, 0], [0, 9.238795325112868], [-97.0, 0]], [[1.0, 0], [-0.929830313258958, -1.6105133449822004], [-50.5, 87.4685657822283]], [[1.0, 0], [-5.811124242582109, -3.3550541457491403], [51.5, 89.20061658979718]], [[1.0, 0], [-12.776771049422225, -7.3766722047581395], [53.5, 92.66471820493493]], [[1.0, 0], [5.196152422706632, -3.0], [54.5, -94.39676901250381]], [[1.0, 0], [0.5973216737364816, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1078-77.54-c1-0-0', 'leading_term': '0.195382640664326825507430060197395782679128241587709799', '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/901/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.1953826406643268, 0.005226358844169241, -0.18510179145754974, -0.37625154930778765, -0.568743207692928, -0.7629052275060831, -0.9588225095394226, -1.156297226482843, -1.3548230942142447, -1.5535730931553091, -1.7514000225692343, -1.9468488973751163, -2.138180038051066, -2.3234016914478075, -2.5003110820338668, -2.666542869469352, -2.819624038612151, -2.9570342504192766, -3.076270630782252, -3.1749158743176524, -3.250708403519747, -3.3016131659166494, -3.325891489531457, -3.3221682662944296, -3.2894946091800374, -3.227404045220122, 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'6.02909893950951084359809923454395', '6.90237906144358141759177760931528', '7.81784616945729540244082621222990', '8.518253079738498566862800220721269', '9.846660722939183826134390438985795'], 'prelabel': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.9678050175530546, 'root_number': '-0.99488935320764381268444283228399063340287401525339660550 + 0.1009711586250061510342107449646930751867614338458152196*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4839025087765273', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.06020440305025750954643603355', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38506824352043387972113675950', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98355446919923031388627807095', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.54', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/14'], '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-c1-0-0', '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': 0.4839025087765273, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.06020440305025750954643603355', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '76318147663041177006671930068', 'Lhash_array': ['76318147663041177006671930068'], 'label': '2-1078-77.54-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/14'}