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lfunc_lfunctions • Show schema
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{'Lhash': '2729483718431913706597712741202', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.1444032067896752, -1.98216449850447], 'a4': [0, 0], 'a5': [-0.17501729011261413, 0.3031388386780698], 'a6': [0, 0], 'a7': [-0.3039231177081617, -2.6282371922112646], 'a8': [0, 0], 'a9': [-1.1193173994209846, 1.938714605593012], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.166826152042992, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.3039231177081617, 2.6282371922112646]]], [41, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 41], 'central_character': '1148.821', 'coefficient_field': 'CDF', 'conductor': 1148, 'conductor_radical': 574, 'conjugate': '220810873919153045011030771156', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1444032067896752, 1.98216449850447], [-1.5, 2.598076211353316]], [[1.0, 0], [0.17501729011261413, -0.3031388386780698], [-2.5, -4.330127018922194]], [[1.0, 0], 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[-30.5, -52.827549630850754]], [[1.0, 0], [-1.5769836097236722, -2.7314157347447696], [-33.5, 58.023702053557386]], [[1.0, 0], [3.233259569162096, 0], [71.0, 0]], [[1.0, 0], [-0.29966554516178695, -0.5190359494980409], [-36.5, 63.21985447626402]], [[1.0, 0], [-0.42807486207897977, 0.7414474105638327], [-39.5, -68.41600689897065]], [[1.0, 0], [12.9143013661891, 0], [83.0, 0]], [[1.0, 0], [7.01464295437461, -12.149717993931878], [-44.5, -77.07626093681505]], [[1.0, 0], [3.407585395575944, 0], [97.0, 0]], [[1.0, 0], [-4.450089973964369, -7.707781933159149], [-50.5, 87.4685657822283]], [[1.0, 0], [-2.3261369760445065, 4.028987427873714], [-51.5, -89.20061658979718]], [[1.0, 0], [-2.6947804403791533, 4.667496637979527], [-53.5, -92.66471820493493]], [[1.0, 0], [3.6029450628114774, 6.240483905668919], [-54.5, 94.39676901250381]], [[1.0, 0], [4.458199965793335, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-1148-7.2-c1-0-25', 'leading_term': '0.3608726238617257281059133919433133856631701778256627387', '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/1148/2/i/d/821/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.36087262386172575, 0.4938518179022218, 0.6329913287654539, 0.7784837684754162, 0.9304353167525602, 1.0888077502642672, 1.2533659493204687, 1.4236332292855243, 1.5988561065709626, 1.7779794283759207, 1.959632254896981, 2.1421245121401062, 2.323454217591741, 2.5013249778459747, 2.6731734161181486, 2.836206162236849, 2.987445993640202, 3.1237866320568397, 3.2420555680755414, 3.33908410535787, 3.4117835951249407, 3.4572265812654708, 3.47273131088242, 3.4559477993897825, 3.4049433887850604, 3.3182855176116353, 3.1951192458769593, 3.03523696125679, 2.839137646338513, 2.6080731207000563, 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'9.814327078611391484069599731381456', '9.982239692366080793270199349520735'], 'prelabel': '2-1148-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0276766921259926, 'root_angle': -0.7234854552548663, 'root_number': '-0.6458226360269044629355352874941140948089176741527262710 - 0.7634874738954532983221953567777258185574540596022511541*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.36174272762743315', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15318299690821275192113157721', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30152281784824676285943903270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.60335375683832797618237715872', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.166826152042992, 'bad_primes': [2, 7, 41], 'central_character': '7.2', 'conductor': 1148, 'conductor_radical': 574, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1148/2/i/d/821/1'], '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': '2-1148-7.2-c1-0-25', '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': '2-1148-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0276766921259926, 'root_angle': -0.36174272762743315, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15318299690821275192113157721', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2729483718431913706597712741202', 'Lhash_array': ['2729483718431913706597712741202'], 'label': '2-1148-7.2-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1148/2/i/d/821/1'}