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  • lfunc_lfunctions • Show schema
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'10.11432296767543238494447938712658', '10.53892914289100836038892412714587', '10.64328891779203615123515754299733', '10.71061592417919901735505102266763', '11.26016897375270437546936502729001', '11.41486727848072677056344823432075', '11.44178199906520629197961186319161', '11.76470770780111847693815459397867'], 'prelabel': '8-272e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.006060349216105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e4-0', 'trace_hash': 512420806950753861, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74055304948636410348533807081', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.825916877904518928838301523312', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.33535045370642008471297947863', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 66334.56712215082, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 5473632256, 'conductor_radical': 34, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 140, 0, 0, 0, 112, 0, 112, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 520, 0, 0, 0, -952, 0, 842, 0, 0, 0, -576, 0, 0, 0, 0, 0, 1176, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -294, 0, 2856, 0, 0, 0, 0, 0, 1988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -1698, 0, 3550826, 0, -3008110578, 0, 3138428376721], 'euler13': [1, -140, 12904, -867860, 47200222, -1906688420, 62285143336, -1484629912220, 23298085122481], 'euler17': [1, -112, 6494, -550256, 24137569, 0, 0, 0, 0], 'euler19': [1, -112, 32140, -2392432, 347419414, -16409691088, 1512054615340, -36141022151248, 2213314919066161], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -20346, 0, 209323274, 0, -3011938197594, 0, 21914624432020321], 'euler29': [1, 0, -74036, 0, 2514340758, 0, -44038339393556, 0, 353814783205469041], 'euler3': [1, 0, -34, 0, 1450, 0, -24786, 0, 531441], 'euler31': [1, 0, -114890, 0, 5074759530, 0, -101965297910090, 0, 787662783788549761], 'euler37': [1, 0, -116372, 0, 7903483062, 0, -298578713668148, 0, 6582952005840035281], 'euler41': [1, 0, -158724, 0, 15178105958, 0, -753955545548484, 0, 22563490300366186081], 'euler43': [1, -520, 324124, -108039880, 39843213142, -8589926739160, 2048905476894076, -261348158207158360, 39959630797262576401], 'euler47': [1, 952, 742220, 344286040, 135078214438, 35744809530920, 8000549201490380, 1065412210393834184, 116191483108948578241], 'euler5': [1, 0, -20, 0, 12342, 0, -312500, 0, 244140625], 'euler53': [1, 576, 580268, 228982464, 130858420278, 34090222292928, 12861269503602572, 1900663828878028608, 491258904256726154641], 'euler59': [1, -1176, 1016732, -636066648, 338934405270, -130634732099592, 42886298329881212, -10187683082738208264, 1779197418239532716881], 'euler61': [1, 0, -425396, 0, 97219598358, 0, -21916561171671956, 0, 2654348974297586158321], 'euler67': [1, -240, 1157068, -209303280, 516001278294, -62950682402640, 104666499339520492, -6529568255110787280, 8182718904632857144561], 'euler7': [1, 0, -842, 0, 410922, 0, -99060458, 0, 13841287201], 'euler71': [1, 0, -1379018, 0, 731023514346, 0, -176652597332169578, 0, 16409682740640811134241], 'euler73': [1, 0, 55196, 0, 301853502630, 0, 8353043954247644, 0, 22902048046490258711521], 'euler79': [1, 0, -1282922, 0, 849811865706, 0, -311862244611912362, 0, 59091511031674153381441], 'euler83': [1, -2856, 5229500, -6188794920, 5530367595318, -3538672480922040, 1709734682533185500, -533901369044095390968, 106890007738661124410161], 'euler89': [1, -1988, 4272824, -4666557644, 5084490134926, -3289778475733036, 2123513587569143864, -696508530570480595492, 246990403565262140303521], 'euler97': [1, 0, -3375140, 0, 4511732954310, 0, -2811397132716065060, 0, 693842360995438000295041], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -34, 0, 1450, 0, -24786, 0, 531441], [1, 0, -20, 0, 12342, 0, -312500, 0, 244140625], [1, 0, -842, 0, 410922, 0, -99060458, 0, 13841287201], [1, 0, -1698, 0, 3550826, 0, -3008110578, 0, 3138428376721], [1, -140, 12904, -867860, 47200222, -1906688420, 62285143336, -1484629912220, 23298085122481], [1, -112, 6494, -550256, 24137569, 0, 0, 0, 0], [1, -112, 32140, -2392432, 347419414, -16409691088, 1512054615340, -36141022151248, 2213314919066161], [1, 0, -20346, 0, 209323274, 0, -3011938197594, 0, 21914624432020321], [1, 0, -74036, 0, 2514340758, 0, -44038339393556, 0, 353814783205469041], [1, 0, -114890, 0, 5074759530, 0, -101965297910090, 0, 787662783788549761], [1, 0, -116372, 0, 7903483062, 0, -298578713668148, 0, 6582952005840035281], [1, 0, -158724, 0, 15178105958, 0, -753955545548484, 0, 22563490300366186081], [1, -520, 324124, -108039880, 39843213142, -8589926739160, 2048905476894076, -261348158207158360, 39959630797262576401], [1, 952, 742220, 344286040, 135078214438, 35744809530920, 8000549201490380, 1065412210393834184, 116191483108948578241], [1, 576, 580268, 228982464, 130858420278, 34090222292928, 12861269503602572, 1900663828878028608, 491258904256726154641], [1, -1176, 1016732, -636066648, 338934405270, -130634732099592, 42886298329881212, -10187683082738208264, 1779197418239532716881], [1, 0, -425396, 0, 97219598358, 0, -21916561171671956, 0, 2654348974297586158321], [1, -240, 1157068, -209303280, 516001278294, -62950682402640, 104666499339520492, -6529568255110787280, 8182718904632857144561], [1, 0, -1379018, 0, 731023514346, 0, -176652597332169578, 0, 16409682740640811134241], [1, 0, 55196, 0, 301853502630, 0, 8353043954247644, 0, 22902048046490258711521], [1, 0, -1282922, 0, 849811865706, 0, -311862244611912362, 0, 59091511031674153381441], [1, -2856, 5229500, -6188794920, 5530367595318, -3538672480922040, 1709734682533185500, -533901369044095390968, 106890007738661124410161], [1, -1988, 4272824, -4666557644, 5084490134926, -3289778475733036, 2123513587569143864, -696508530570480595492, 246990403565262140303521], [1, 0, -3375140, 0, 4511732954310, 0, -2811397132716065060, 0, 693842360995438000295041]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/272/4/b/d'], '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': '8-272e4-1.1-c3e4-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '8-272e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.006060349216105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e4-0', 'trace_hash': 512420806950753861, 'z1': {'__RealLiteral__': 0, 'data': '0.74055304948636410348533807081', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '938762517682235126862482207107,1046974026014288677583404279958,1692757804155981879076226600319,2911390982431471344528160649329', 'Lhash_array': ['938762517682235126862482207107', '1046974026014288677583404279958', '1692757804155981879076226600319', '2911390982431471344528160649329'], 'factors': ['2-272-17.16-c3-0-7', '2-272-17.16-c3-0-9', '2-272-17.16-c3-0-15', '2-272-17.16-c3-0-22'], 'label': '8-272e4-1.1-c3e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/272/4/b/d'}