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lfunc_lfunctions • Show schema
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{'Lhash': '599499263118812009283337916705,1018736647331693315453065860649,1197066208819631019021173278663,1703829699809810678728911211183,1963386151116468187383068372146,1981578170697801753490351507392', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3196864.0641143927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -3, 6, -7, 6, -3, 1]], [19, [1, 0, 0, -133, 0, 0, 6859]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': '1.1.1.1', 'conductor': 12332795428864000000, 'conductor_radical': 190, 'degree': 12, 'euler_factors': [[1], [1, -1, -2, -5, 1, 12, 19, 36, 9, -135, -162, -243, 729], [1, -3, 6, -7, 6, -3, 1], [1, 4, 36, 122, 596, 1572, 5503, 11004, 29204, 41846, 86436, 67228, 117649], [1, -10, 95, -568, 3085, -12690, 47543, -139590, 373285, -756008, 1390895, -1610510, 1771561], [1, -15, 111, -680, 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-
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{'algebraic': True, 'analytic_conductor': 3196864.0641143927, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 12332795428864000000, 'conductor_radical': 190, 'degree': 12, 'dirichlet_coefficients': [1, 0, 1, 0, 3, 0, -4, 0, 3, 0, 10, 0, 15, 0, 3, 0, -1, 0, 0, 0, -4, 0, 4, 0, 3, 0, 10, 0, 2, 0, 2, 0, 10, 0, -12, 0, -4, 0, 15, 0, 2, 0, -1, 0, 9, 0, 6, 0, -20, 0, -1, 0, -11, 0, 30, 0, 0, 0, 6, 0, 9, 0, -12, 0, 45, 0, -20, 0, 4, 0, -29, 0, 22, 0, 3, 0, -40, 0, -24, 0, 20, 0, 6, 0, -3, 0, 2, 0, 14, 0, -60, 0, 2, 0, 0, 0, -7, 0, 30, 0], 'euler11': [1, -10, 95, -568, 3085, -12690, 47543, -139590, 373285, -756008, 1390895, -1610510, 1771561], 'euler13': [1, -15, 111, -680, 3789, -16785, 62646, -218205, 640341, -1493960, 3170271, -5569395, 4826809], 'euler17': [1, 1, -6, -47, -97, 240, 9433, 4080, -28033, -230911, -501126, 1419857, 24137569], 'euler19': [1, 0, 0, -133, 0, 0, 6859, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -4, -14, 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22164361129], 'euler59': [1, -6, -134, 298, 14916, -12556, -985377, -740804, 51922596, 61202942, -1623726374, -4289545794, 42180533641], 'euler61': [1, -9, -53, 892, 341, -26923, 157646, -1642303, 1268861, 202467052, -733829573, -7601366709, 51520374361], 'euler67': [1, 20, 91, 644, 19418, 116972, 70523, 7837124, 87167402, 193691372, 1833752011, 27002502140, 90458382169], 'euler7': [1, 4, 36, 122, 596, 1572, 5503, 11004, 29204, 41846, 86436, 67228, 117649], 'euler71': [1, 29, 392, 3851, 36757, 355872, 3184895, 25266912, 185292037, 1378315261, 9961378952, 52322651179, 128100283921], 'euler73': [1, -22, 148, -814, 16010, -143110, 774911, -10447030, 85317290, -316659838, 4202939668, -45607575046, 151334226289], 'euler79': [1, 24, 223, 1384, 11666, 62240, 107087, 4916960, 72807506, 682365976, 8685868063, 73849353576, 243087455521], 'euler83': [1, -6, 399, -2320, 73845, -362694, 7910351, -30103602, 508718205, -1326545840, 18935870079, -23634243858, 326940373369], 'euler89': [1, -14, -35, 1638, -1302, -97958, 1042389, -8718262, -10313142, 1154739222, -2195978435, -78176832286, 496981290961], 'euler97': [1, 7, -176, -899, 20141, 38638, -2016151, 3747886, 189506669, -820493027, -15581153456, 60111381799, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -2, -5, 1, 12, 19, 36, 9, -135, -162, -243, 729], [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], [1, 4, 36, 122, 596, 1572, 5503, 11004, 29204, 41846, 86436, 67228, 117649], [1, -10, 95, -568, 3085, -12690, 47543, -139590, 373285, -756008, 1390895, -1610510, 1771561], [1, -15, 111, -680, 3789, -16785, 62646, -218205, 640341, -1493960, 3170271, -5569395, 4826809], [1, 1, -6, -47, -97, 240, 9433, 4080, -28033, -230911, -501126, 1419857, 24137569], [1, 0, 0, -133, 0, 0, 6859, 0, 0, 0, 0, 0, 0], [1, -4, -14, 150, -330, -646, 13395, -14858, -174570, 1825050, -3917774, -25745372, 148035889], [1, -2, -78, 70, 4112, -1764, -135893, -51156, 3458192, 1707230, -55167918, -41022298, 594823321], [1, -2, 175, -284, 13073, -16886, 533807, -523466, 12563153, -8460644, 161616175, -57258302, 887503681], [1, 4, -12, -190, -844, 5556, 123235, 205572, -1155436, -9624070, -22489932, 277375828, 2565726409], [1, -2, -76, 94, 2866, -402, -115153, -16482, 4817746, 6478574, -214757836, -231712402, 4750104241], [1, 1, -84, 155, 3605, -8436, -152285, -362748, 6665645, 12323585, -287179284, 147008443, 6321363049], [1, -6, -98, 226, 8568, -6688, -450585, -314336, 18926712, 23463998, -478208738, -1376070042, 10779215329], [1, 11, 4, -423, -1917, -5488, -36627, -290864, -5384853, -62974971, 31561924, 4600150423, 22164361129], [1, -6, -134, 298, 14916, -12556, -985377, -740804, 51922596, 61202942, -1623726374, -4289545794, 42180533641], [1, -9, -53, 892, 341, -26923, 157646, -1642303, 1268861, 202467052, -733829573, -7601366709, 51520374361], [1, 20, 91, 644, 19418, 116972, 70523, 7837124, 87167402, 193691372, 1833752011, 27002502140, 90458382169], [1, 29, 392, 3851, 36757, 355872, 3184895, 25266912, 185292037, 1378315261, 9961378952, 52322651179, 128100283921], [1, -22, 148, -814, 16010, -143110, 774911, -10447030, 85317290, -316659838, 4202939668, -45607575046, 151334226289], [1, 24, 223, 1384, 11666, 62240, 107087, 4916960, 72807506, 682365976, 8685868063, 73849353576, 243087455521], [1, -6, 399, -2320, 73845, -362694, 7910351, -30103602, 508718205, -1326545840, 18935870079, -23634243858, 326940373369], [1, -14, -35, 1638, -1302, -97958, 1042389, -8718262, -10313142, 1154739222, -2195978435, -78176832286, 496981290961], [1, 7, -176, -899, 20141, 38638, -2016151, 3747886, 189506669, -820493027, -15581153456, 60111381799, 832972004929]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/j'], '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': '12-1520e6-1.1-c1e6-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-1520e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 21669977623785006, 'z1': {'__RealLiteral__': 0, 'data': '0.47292153138323557865301189351', 'prec': 103}}
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{'Lhash': '599499263118812009283337916705,1018736647331693315453065860649,1197066208819631019021173278663,1703829699809810678728911211183,1963386151116468187383068372146,1981578170697801753490351507392', 'Lhash_array': ['599499263118812009283337916705', '1018736647331693315453065860649', '1197066208819631019021173278663', '1703829699809810678728911211183', '1963386151116468187383068372146', '1981578170697801753490351507392'], 'label': '12-1520e6-1.1-c1e6-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/j'}