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  • lfunc_lfunctions • Show schema
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'10.74482382656222313337695963123763', '11.32754009764430338046869657439460', '11.70535350947778750669528392694629', '12.21420001837697700783114851421873', '12.50507141260342186601110567731130', '12.76463075947576565326796439298935', '13.05348638003073326427462600094585', '13.57297615398159351860169888367219', '13.66437127125386486412488800915355', '13.87631549844111119649760677640163', '14.45488707215421780811473907422939', '14.61041022410029421707455088785223', '15.19069639838994768343702892780935', '15.28091175938255730592532770559124', '15.34713987950776964078557677213593', '16.07019260069426336681165997261691', '16.46621334729973753839585077465655', '16.66509318585605293816148855240212', '16.68722904128151460029649069586649', '17.15676954044105743994314177257818', '17.32457896799792680685549169209191'], 'prelabel': '8-21e4-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8352275652007286, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e4-0', 'trace_hash': 821486867306386914, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.847065099873545780364881394854', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.91163078860558212956076279540', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.05949196601917328195645533906', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 128.68247042696558, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 194481, 'conductor_radical': 21, 'degree': 8, 'dirichlet_coefficients': [1, 3, 18, 4, 33, 54, -350, -183, 81, 99, 1137, 72, 1850, -1050, 594, 187, 324, 243, -2311, 132, -6300, 3411, -1596, -3294, 3472, 5550, -1458, -1400, -4434, 1782, -4294, -1116, 20466, 972, -11550, 324, 19109, -6933, 33300, -6039, -25716, -18900, -5542, 4548, 2673, -4788, 23160, 3366, 58261, 10416, 5832, 7400, 31653, -4374, 37521, 64050, -41598, -13302, -41097, 2376, -42052, -12882, -28350, 11441, 61050, 61398, -30763, 1296, -28728, -34650, 204192, -14823, 28577, 57327, 62496, -9244, -397950, 99900, 18464, 6171, -26244, -77148, 122358, -25200, 10692, -16626, -79812, -208071, -29322, 8019, -647500, -6384, -77292, 69480, -76263, -20088, -19582, 174783, 92097, 13888], 'euler11': [1, -1137, 647537, -367398810, 182185169004, -59169945749310, 16795442113857737, -4749531168625595187, 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'euler73': [1, -28577, -1819854179, 43141098817006, 960538312903836118, 89434586448341043910558, -7821052325964361718700065171, -254600666733610193310558140318489, 18469587772135192290560825407466407201], 'euler79': [1, -18464, -2991126965, 52106636539168, 585228301517857816, 160335059393214108536032, -28320815902809730695845874965, -537937921787321827472372187770336, 89648251976843595444986830377401534401], 'euler83': [1, -122358, 20921495609, -1532944268620866, 134295010901729690280, -6038329777551500731856838, 324618787567190409912351005441, -7478315013727673024406587136773106, 240747534123068430155382383568465195601], 'euler89': [1, 29322, -10522232110, 6271767496512, 93567411680290480719, 35021922550828908141888, -328101294692117128300597628110, 5105563582574121057864971772084378, 972299657790850297934682879408841327201], 'euler97': [1, 19582, 34364387569, 503680414299982, 442714185838663323268, 4325275098380673902975374, 2534112849934875128392934984881, 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1716155831334586342923895201], [1, 4434, 89165117, 277728746742, 2817559516755120, 5696535706008426558, 37512409679958718288517, 38261822906850349811167866, 176994576151109753197786640401], [1, 4294, -6712931, -137867178890, -714913793459948, -3947020282385822390, -5502108136150315437731, 100759834992981081383209594, 671790528819082282036142601601], [1, -19109, 180683803, -874851371876, 3899410282461118, -60665655912760353332, 868833311454825262399747, -6371824734291238703154012737, 23122483666661158726686253786801], [1, 25716, 622310408, 8855235758268, 117362097451813614, 1025933973912284819868, 8353060591745939208489608, 39990908268322388916411263316, 180167782956420929503029846064801], [1, 5542, 79907233, 1014866773738, 46784805537168040, 149193984259656669934, 1726913752682983480073017, 17607323967252270278329089394, 467056167777397914441056671494001], [1, -23160, -33691018, -2579713748640, 149370858967788675, -591644467739837040480, -1772118310941730425799882, 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10596610576391421032662867140133202401], [1, -28577, -1819854179, 43141098817006, 960538312903836118, 89434586448341043910558, -7821052325964361718700065171, -254600666733610193310558140318489, 18469587772135192290560825407466407201], [1, -18464, -2991126965, 52106636539168, 585228301517857816, 160335059393214108536032, -28320815902809730695845874965, -537937921787321827472372187770336, 89648251976843595444986830377401534401], [1, -122358, 20921495609, -1532944268620866, 134295010901729690280, -6038329777551500731856838, 324618787567190409912351005441, -7478315013727673024406587136773106, 240747534123068430155382383568465195601], [1, 29322, -10522232110, 6271767496512, 93567411680290480719, 35021922550828908141888, -328101294692117128300597628110, 5105563582574121057864971772084378, 972299657790850297934682879408841327201], [1, 19582, 34364387569, 503680414299982, 442714185838663323268, 4325275098380673902975374, 2534112849934875128392934984881, 12400324785676609757499429742840126, 5437943429267472574499737549036572950401]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/6/e/b'], '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': '8-21e4-1.1-c5e4-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [5, 5, 5, 5], 'order_of_vanishing': 0, 'prelabel': '8-21e4-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8352275652007286, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e4-0', 'trace_hash': 821486867306386914, 'z1': {'__RealLiteral__': 0, 'data': '0.847065099873545780364881394854', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1073782582287085393379894598584,2423279916590629700653101468929,4529343160658057278773999685059,4695332391707879906425245155924', 'Lhash_array': ['1073782582287085393379894598584', '2423279916590629700653101468929', '4529343160658057278773999685059', '4695332391707879906425245155924'], 'factors': ['2-21-7.2-c5-0-0', '2-21-7.4-c5-0-3', '2-21-7.2-c5-0-5', '2-21-7.4-c5-0-6'], 'label': '8-21e4-1.1-c5e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/6/e/b'}