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{'Lhash': '1619678316978249031107000993913,2153953680114227057720341084427,2287016610145819982195716305553,2338754708713271411480691639718,2643087801354222403703731302285,2771770014009296091463132489697', 'a10': 12, 'a2': -6, 'a3': -2, 'a4': 21, 'a5': -2, 'a6': 12, 'a7': 3, 'a8': -56, 'a9': -8, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 106342.34601317252, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 6, 15, 20, 15, 6, 1]], [431, [1, 6, 15, 20, 15, 6, 1]]], 'bad_primes': [2, 431], 'central_character': '862.1', 'coefficient_field': '1.1.1.1', 'conductor': 410245281783429184, 'conductor_radical': 862, 'degree': 12, 'euler_factors': [[1, 6, 15, 20, 15, 6, 1], [1, 2, 12, 17, 66, 73, 233, 219, 594, 459, 972, 486, 729], [1, 2, 12, 30, 120, 245, 661, 1225, 3000, 3750, 7500, 6250, 15625], [1, -3, 29, -49, 310, -273, 2182, -1911, 15190, -16807, 69629, -50421, 117649], [1, 6, 48, 227, 1124, 4111, 15599, 45221, 136004, 302137, 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2.623567162135243, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 251384150819480003, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27770090329830642501603474967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69916984989903885174403769138', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.80413799333512140313693570707', 'prec': 103}}
-
lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 106342.34601317252, 'bad_primes': [2, 431], 'central_character': '1.1', 'conductor': 410245281783429184, 'conductor_radical': 862, 'degree': 12, 'dirichlet_coefficients': [1, -6, -2, 21, -2, 12, 3, -56, -8, 12, -6, -42, -9, -18, 4, 126, -17, 48, 1, -42, -6, 36, -20, 112, -8, 54, 23, 63, 1, -24, 8, -252, 12, 102, -6, -168, -3, -6, 18, 112, -19, 36, -21, -126, 16, 120, -10, -252, -20, 48, 34, -189, -1, -138, 12, -168, -2, -6, 11, 84, -2, -48, -24, 462, 18, -72, 4, -357, 40, 36, -4, 448, -39, 18, 16, 21, -18, -108, -16, -252, 18, 114, -20, -126, 34, 126, -2, 336, -17, -96, -27, -420, -16, 60, -2, 504, -29, 120, 48, -168], 'euler11': [1, 6, 48, 227, 1124, 4111, 15599, 45221, 136004, 302137, 702768, 966306, 1771561], 'euler13': [1, 9, 69, 347, 1604, 6061, 22910, 78793, 271076, 762359, 1970709, 3341637, 4826809], 'euler17': [1, 17, 196, 1612, 10684, 57492, 259744, 977364, 3087676, 7919756, 16370116, 24137569, 24137569], 'euler19': [1, -1, 72, -92, 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2293450070, 10779215329], 'euler5': [1, 2, 12, 30, 120, 245, 661, 1225, 3000, 3750, 7500, 6250, 15625], 'euler53': [1, 1, 62, 602, 3056, 7280, 368223, 385840, 8584304, 89623954, 489209822, 418195493, 22164361129], 'euler59': [1, -11, 197, -1413, 16943, -104080, 1099549, -6140720, 58978583, -290200527, 2387120117, -7864167289, 42180533641], 'euler61': [1, 2, 223, -375, 18660, -107712, 1070434, -6570432, 69433860, -85117875, 3087622543, 1689192602, 51520374361], 'euler67': [1, -4, 271, -541, 34378, -41338, 2812384, -2769646, 154322842, -162712783, 5460953791, -5400500428, 90458382169], 'euler7': [1, -3, 29, -49, 310, -273, 2182, -1911, 15190, -16807, 69629, -50421, 117649], 'euler71': [1, 4, 291, 344, 35121, -29127, 2768778, -2068017, 177044961, 123121384, 7394799171, 7216917404, 128100283921], 'euler73': [1, 39, 800, 12316, 158260, 1697904, 15536962, 123946992, 843367540, 4791133372, 22718592800, 80849792127, 151334226289], 'euler79': [1, 16, 497, 5533, 96150, 803604, 9972182, 63484716, 600072150, 2727984787, 19358190257, 49232902384, 243087455521], 'euler83': [1, 20, 464, 5493, 76301, 673726, 7474786, 55919258, 525637589, 3140825991, 22020660944, 78780812860, 326940373369], 'euler89': [1, 17, 441, 5158, 75003, 691470, 7774914, 61540830, 594098763, 3636230102, 27669328281, 94929010633, 496981290961], 'euler97': [1, 29, 719, 12621, 187943, 2306480, 24765083, 223728560, 1768355687, 11518845933, 63652553039, 249032867453, 832972004929], 'euler_factors': [[1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0], [1, 2, 12, 17, 66, 73, 233, 219, 594, 459, 972, 486, 729], [1, 2, 12, 30, 120, 245, 661, 1225, 3000, 3750, 7500, 6250, 15625], [1, -3, 29, -49, 310, -273, 2182, -1911, 15190, -16807, 69629, -50421, 117649], [1, 6, 48, 227, 1124, 4111, 15599, 45221, 136004, 302137, 702768, 966306, 1771561], [1, 9, 69, 347, 1604, 6061, 22910, 78793, 271076, 762359, 1970709, 3341637, 4826809], [1, 17, 196, 1612, 10684, 57492, 259744, 977364, 3087676, 7919756, 16370116, 24137569, 24137569], [1, -1, 72, -92, 2710, -3364, 63083, -63916, 978310, -631028, 9383112, -2476099, 47045881], [1, 20, 244, 2156, 15310, 91015, 468821, 2093345, 8098990, 26232052, 68281204, 128726860, 148035889], [1, -1, 161, -121, 11109, -6338, 422299, -183802, 9342669, -2951069, 113872241, -20511149, 594823321], [1, -8, 137, -861, 8592, -43792, 330326, -1357552, 8256912, -25650051, 126522377, -229033208, 887503681], [1, 3, 142, 374, 10298, 22186, 466616, 820882, 14097962, 18944222, 266130862, 208031871, 2565726409], [1, 19, 330, 3913, 38572, 321343, 2191812, 13175063, 64839532, 269687873, 932501130, 2201267819, 4750104241], [1, 21, 368, 4390, 45032, 371896, 2674920, 15991528, 83264168, 349035730, 1258118768, 3087177303, 6321363049], [1, 10, 159, 459, 2364, -54006, -266724, -2538282, 5222076, 47654757, 775869279, 2293450070, 10779215329], [1, 1, 62, 602, 3056, 7280, 368223, 385840, 8584304, 89623954, 489209822, 418195493, 22164361129], [1, -11, 197, -1413, 16943, -104080, 1099549, -6140720, 58978583, -290200527, 2387120117, -7864167289, 42180533641], [1, 2, 223, -375, 18660, -107712, 1070434, -6570432, 69433860, -85117875, 3087622543, 1689192602, 51520374361], [1, -4, 271, -541, 34378, -41338, 2812384, -2769646, 154322842, -162712783, 5460953791, -5400500428, 90458382169], [1, 4, 291, 344, 35121, -29127, 2768778, -2068017, 177044961, 123121384, 7394799171, 7216917404, 128100283921], [1, 39, 800, 12316, 158260, 1697904, 15536962, 123946992, 843367540, 4791133372, 22718592800, 80849792127, 151334226289], [1, 16, 497, 5533, 96150, 803604, 9972182, 63484716, 600072150, 2727984787, 19358190257, 49232902384, 243087455521], [1, 20, 464, 5493, 76301, 673726, 7474786, 55919258, 525637589, 3140825991, 22020660944, 78780812860, 326940373369], [1, 17, 441, 5158, 75003, 691470, 7774914, 61540830, 594098763, 3636230102, 27669328281, 94929010633, 496981290961], [1, 29, 719, 12621, 187943, 2306480, 24765083, 223728560, 1768355687, 11518845933, 63652553039, 249032867453, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/862/2/a/i'], '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': '12-862e6-1.1-c1e6-0-0', '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': 6, 'prelabel': '12-862e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.623567162135243, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 251384150819480003, 'z1': {'__RealLiteral__': 0, 'data': '1.27770090329830642501603474967', 'prec': 103}}
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{'Lhash': '1619678316978249031107000993913,2153953680114227057720341084427,2287016610145819982195716305553,2338754708713271411480691639718,2643087801354222403703731302285,2771770014009296091463132489697', 'Lhash_array': ['1619678316978249031107000993913', '2153953680114227057720341084427', '2287016610145819982195716305553', '2338754708713271411480691639718', '2643087801354222403703731302285', '2771770014009296091463132489697'], 'label': '12-862e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/862/2/a/i'}