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  • lfunc_lfunctions • Show schema
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12.464133927655567, 11.709740774332486, 10.710004660618372, 9.523585576535742, 8.213200372049434, 6.842229634792368, 5.470937625646849, 4.1546659487759365, 2.9420758507594145, 1.8735307721974537, 0.9802940659722124, 0.2842873764286314, -0.2047826828372902, -0.4899877627171669, -0.5863018864176764, -0.5186316420434762, -0.31564102468381655, -0.0036110663642833136, 0.39425249241977545], 'positive_zeros': ['0.64859685443543141162276940533841', '0.882199977243032778929710025783334', '0.932726770119098533681800958602997', '1.10305297478285514829812944435634', '1.46874180672732826845638630457449', '1.66057061958957648926926640924087', '1.71343423592962633141955333510517', '1.81964552155927779464209960617985', '2.22627011020930451794773391697638', '2.23576052236733492407079012231917', '2.24004368354240926938843715731673', '2.89009359418090848730770209898031', '2.93823951013180700871385913907567', '3.04625630065028179613573610341912', '3.09725519347025551541663215354639', '3.36435731162544093966857137854865', '3.59189917781294254172489595590820', '3.71971767275104789155218137542280', '3.72095512132286507300597668960336', '3.77030742875690921237359535823049', '4.33571019733651494623673640432181', '4.36656972394844686740856308358630', '4.36892577373737734072999174520412', '4.46833573210813958631462871175448', '4.83241165188445837318853061387925', '5.04064581241648262589470066282836', '5.05617677625977594549169227074503', '5.18343317752888293396534787999474', '5.45519646458287186993047335327880', '5.47702193755536052183395048525625', '5.57707791431417286126288211030387', '6.06521841688150259079659945990319', '6.08094901000050350774999152359614', '6.13457011955478612680161010365969', '6.25541909815546021008209861506835', '6.64121121842086762463026515303795', '6.66312812110099162460583336117647', '6.68481851290878416373411730447732', '6.83880392662720164780696900962071', '6.86451183725154980735736697003324', '7.18161263392669014029281464315262', '7.43954882266416155270524430340767', '7.50678870452413745689915333384432', '7.66715254149030029476512522729107', '7.80410151484902236201139234373993', '8.138525380168549397938070725807282', '8.189993162056730788438087356045442', '8.200662523559121529940470755861931', '8.296425200993044455660252146249778', '8.528787460004892007838794396527088'], 'prelabel': '10-5415e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.575636295790953, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e5-0', 'trace_hash': 1119279133142998562, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64859685443543141162276940534', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.882199977243032778929710025783', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '0.932726770119098533681800958603', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 151139450.83529282, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4655778439517634375, 'conductor_radical': 285, 'degree': 10, 'dirichlet_coefficients': [1, 1, 5, -1, 5, 5, 2, 0, 15, 5, 5, -5, 8, 2, 25, 0, 10, 15, 0, -5, 10, 5, -2, 0, 15, 8, 35, -2, 7, 25, 9, 0, 25, 10, 10, -15, -6, 0, 40, 0, -12, 10, -8, -5, 75, -2, 6, 0, -8, 15, 50, -8, -8, 35, 25, 0, 0, 7, 1, -25, 7, 9, 30, 3, 40, 25, 14, -10, -10, 10, 27, 0, 26, -6, 75, 0, 10, 40, -23, 0, 70, -12, -12, -10, 50, -8, 35, 0, 9, 75, 16, 2, 45, 6, 0, 0, -10, -8, 75, -15], 'euler11': [1, -5, 23, -72, 410, -1366, 4510, -8712, 30613, -73205, 161051], 'euler13': [1, -8, 66, -346, 1685, -6420, 21905, -58474, 145002, -228488, 371293], 'euler17': [1, -10, 50, -196, 1161, -5908, 19737, -56644, 245650, -835210, 1419857], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, -1, 2, -3, 5, -8, 10, -12, 16, -16, 32], 'euler23': [1, 2, 47, 160, 1270, 5628, 29210, 84640, 571849, 559682, 6436343], 'euler29': [1, -7, 83, -400, 3336, -14434, 96744, -336400, 2024287, -4950967, 20511149], 'euler3': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler31': [1, -9, 125, -894, 7009, -38247, 217279, -859134, 3723875, -8311689, 28629151], 'euler37': [1, 6, 98, 416, 5953, 23380, 220261, 569504, 4963994, 11244966, 69343957], 'euler41': [1, 12, 229, 1864, 19570, 112696, 802370, 3133384, 15782909, 33909132, 115856201], 'euler43': [1, 8, 216, 1306, 18575, 82860, 798725, 2414794, 17173512, 27350408, 147008443], 'euler47': [1, -6, 82, -410, 4225, -9896, 198575, -905690, 8513486, -29278086, 229345007], 'euler5': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler53': [1, 8, 170, 1086, 13589, 74500, 720217, 3050574, 25309090, 63123848, 418195493], 'euler59': [1, -1, 119, 96, 8426, 22834, 497134, 334176, 24440101, -12117361, 714924299], 'euler61': [1, -7, 132, -521, 9755, -35784, 595055, -1938641, 29961492, -96920887, 844596301], 'euler67': [1, -14, 168, -1112, 6163, -31692, 412921, 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-346, 1685, -6420, 21905, -58474, 145002, -228488, 371293], [1, -10, 50, -196, 1161, -5908, 19737, -56644, 245650, -835210, 1419857], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 47, 160, 1270, 5628, 29210, 84640, 571849, 559682, 6436343], [1, -7, 83, -400, 3336, -14434, 96744, -336400, 2024287, -4950967, 20511149], [1, -9, 125, -894, 7009, -38247, 217279, -859134, 3723875, -8311689, 28629151], [1, 6, 98, 416, 5953, 23380, 220261, 569504, 4963994, 11244966, 69343957], [1, 12, 229, 1864, 19570, 112696, 802370, 3133384, 15782909, 33909132, 115856201], [1, 8, 216, 1306, 18575, 82860, 798725, 2414794, 17173512, 27350408, 147008443], [1, -6, 82, -410, 4225, -9896, 198575, -905690, 8513486, -29278086, 229345007], [1, 8, 170, 1086, 13589, 74500, 720217, 3050574, 25309090, 63123848, 418195493], [1, -1, 119, 96, 8426, 22834, 497134, 334176, 24440101, -12117361, 714924299], [1, -7, 132, -521, 9755, -35784, 595055, -1938641, 29961492, -96920887, 844596301], [1, -14, 168, -1112, 6163, -31692, 412921, -4991768, 50528184, -282115694, 1350125107], [1, -27, 577, -8036, 95560, -862802, 6784760, -40509476, 206514647, -686115387, 1804229351], [1, -26, 426, -4848, 44229, -384492, 3228717, -25834992, 165721242, -738354266, 2073071593], [1, 23, 354, 2477, 11005, -4968, 869395, 15458957, 174535806, 895851863, 3077056399], [1, 12, 394, 3324, 61357, 384144, 5092631, 22899036, 225284078, 569499852, 3939040643], [1, -9, 313, -2328, 46270, -283038, 4118030, -18440088, 220655297, -564680169, 5584059449], [1, 10, 525, 3960, 105810, 580092, 10263570, 37259640, 479153325, 885292810, 8587340257]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5415/2/a/z'], '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': '10-5415e5-1.1-c1e5-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '10-5415e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.575636295790953, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 1119279133142998562, 'z1': {'__RealLiteral__': 0, 'data': '0.64859685443543141162276940534', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '822194191831216162102893451185,1118321330673460820836496831048,1182371649990413000185090127714,1398285765567020318707061852856,1861851432878191779408263837137', 'Lhash_array': ['822194191831216162102893451185', '1118321330673460820836496831048', '1182371649990413000185090127714', '1398285765567020318707061852856', '1861851432878191779408263837137'], 'factors': ['2-5415-1.1-c1-0-41', '2-5415-1.1-c1-0-86', '2-5415-1.1-c1-0-95', '2-5415-1.1-c1-0-124', '2-5415-1.1-c1-0-196'], 'label': '10-5415e5-1.1-c1e5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5415/2/a/z'}