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lfunc_lfunctions • Show schema
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{'Lhash': '1144728068655272592712407077558', 'a10': [1.722859784356189, 2.9840806808220792], 'a2': [0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [3.445719568712378, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.667', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '1635237589857069957054895703335', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.445719568712378, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [-2.1213203435596424, -3.6742346141747673], [-6.5, 11.258330249197702]], [[1.0, 0], 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[-33.5, -58.023702053557386]], [[1.0, 0], [-9.872983346207416, 0], [71.0, 0]], [[1.0, 0], [2.211134680780002, 3.8297976094885544], [-36.5, 63.21985447626402]], [[1.0, 0], [-0.9364916731037084, -1.6220511586808073], [-39.5, 68.41600689897065]], [[1.0, 0], [1.3243992251527354, -2.2939267474693907], [-41.5, -71.88010851410841]], [[1.0, 0], [-3.5355339059327378, 6.123724356957945], [-44.5, -77.07626093681505]], [[1.0, 0], [7.508731581390944, -13.005504599366118], [-48.5, -84.00446416709055]], [[1.0, 0], [-13.345214505324044, 0], [101.0, 0]], [[1.0, 0], [-3.883383338237847, 0], [103.0, 0]], [[1.0, 0], [-0.12701665379258312, 0.21999929777614008], [-53.5, -92.66471820493493]], [[1.0, 0], [8.436491673103708, 14.612432215447386], [-54.5, 94.39676901250381]], [[1.0, 0], [-1.9364916731037085, -3.3541019662496847], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-2646-63.16-c1-0-19', 'leading_term': '2.841589952114817682749668511865952755480070709953074539', '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/2646/2/h/s/667/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.8415899521148176, 2.7462625007733408, 2.642451080964312, 2.530214409395819, 2.4095048319769186, 2.2802166890962474, 2.142238740124351, 1.9955076884757454, 1.8400600060358356, 1.6760795860645852, 1.5039391879454398, 1.324234108497769, 1.1378069700361797, 0.9457629214135717, 0.7494748906789975, 0.5505788077625023, 0.35095894353449775, 0.15272370276643032, -0.04182762186483884, -0.23024646695786122, -0.40998415873238203, -0.5784476243407967, -0.7330604935051157, -0.8713282601215893, -0.9909060079989881, -1.0896670509340107, -1.1657707031911688, -1.2177272908715324, -1.2444584462228272, 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'7.11360618532690189546354621250144', '8.000090139914153657571963281932813', '8.911977830421063614165636664673286'], 'prelabel': '2-2646-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.4541330183122005, 'root_number': '0.1435972366665227463185656888902738017825214497236716988 - 0.98963621276797397484532072972592334820511616241393350428*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22706650915610024', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.903031220471298887667788815760', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.00519502610533766731331240885', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83576080264526470913519780031', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/h/s/667/4'], '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': '2-2646-63.16-c1-0-19', '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': '2-2646-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.22706650915610024, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.903031220471298887667788815760', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1144728068655272592712407077558', 'Lhash_array': ['1144728068655272592712407077558'], 'label': '2-2646-63.16-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/h/s/667/4'}