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lfunc_lfunctions • Show schema
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{'Lhash': '2145977468247918524700319971949', 'a10': [-1.746979603717467, 3.025857433425196], 'a2': [-1.0799160148203788, -0.6234898018587335], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.2225209339563144, -0.38541756336001515], 'a5': [0.0, -2.801937735804838], 'a6': [1.0799160148203788, -0.6234898018587335], 'a7': [4.158600066598118, -2.400968867902419], 'a8': [0.0, 3.0489173395223053], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.316', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '987747788216253787403812894669', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0799160148203788, 0.6234898018587335], [1.0, 1.7320508075688772]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 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[29.5, -51.09549882328188]], [[1.0, 0], [-3.91454240558641, -6.780186334858557], [-30.5, 52.827549630850754]], [[1.0, 0], [-3.102194108684863, -1.7910526037276768], [33.5, 58.023702053557386]], [[1.0, 0], [7.654602380807059, -4.419386745098506], [35.5, -61.48780366869514]], [[1.0, 0], [0, -7.692021471630096], [-73.0, 0]], [[1.0, 0], [4.021770264154323, 0], [79.0, 0]], [[1.0, 0], [0, 0.6527928111319818], [-83.0, 0]], [[1.0, 0], [-5.452406692454437, -3.1479484716198862], [44.5, 77.07626093681505]], [[1.0, 0], [8.687498281813191, -5.015729471589257], [48.5, -84.00446416709055]], [[1.0, 0], [-6.943845414859658, 12.027093058441118], [-50.5, -87.4685657822283]], [[1.0, 0], [-17.403420301308575, 0], [103.0, 0]], [[1.0, 0], [5.276282612990715, -9.138789560792194], [-53.5, -92.66471820493493]], [[1.0, 0], [0, -1.0706876036766284], [-109.0, 0]], [[1.0, 0], [-8.265397480913554, -14.316088381694085], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-507-13.4-c1-0-15', '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/507/2/j/h/316/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8865332124975402, 1.008498794358341, 1.1285672557269766, 1.2443301386002272, 1.3502961043057848, 1.4380828694356889, 1.4970315350024566, 1.515124885566956, 1.4801293856885496, 1.3809104982543206, 1.208870583070071, 0.9594327866024834, 0.6334569792192848, 0.23843811640223672, -0.21068657053105855, -0.6913000771962208, -1.1735971151471851, -1.6219177308006882, -1.9969632947126241, -2.258839172112928, -2.370757117057224, -2.303115392178231, -2.037570547234314, -1.5706382289660166, -0.9163276629856536, -0.1073391894838093, 0.8055552072887988, 1.7561714136230877, 2.6676210797322373, 3.4588226920046456, 4.0523063695456285, 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'11.10947093088256157802709170566353'], 'prelabel': '2-507-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.6506552256252209, 'root_number': '-0.4558236307859736 + 0.890070119494578*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.325327612813', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69287772818594812639172215163', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14029745802830822169776279500', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65421019143111413033426139908', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.4', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/j/h/316/2'], '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': '2-507-13.4-c1-0-15', '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': '2-507-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.32532761281261047, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69287772818594812639172215163', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2145977468247918524700319971949', 'Lhash_array': ['2145977468247918524700319971949'], 'label': '2-507-13.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/j/h/316/2'}