data: - - Lhash: '5709092708804284635613657015083' a10: - 1.0 - -2.0 a2: - -0.7071067811865476 - -0.7071067811865476 a3: - -0.2928932188134525 - -1.7071067811865475 a4: - 0.0 - 1.0 a5: - 0.7071067811865476 - 2.1213203435596424 a6: - -1.0 - 1.4142135623730951 a7: - -1.0 - 1.0 a8: - 0.7071067811865476 - -0.7071067811865476 a9: - -2.8284271247461903 - 1.0 accuracy: 100 algebraic: true analytic_conductor: 0.23955120606384128 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - - 1.0 - 0 - - 0.7071067811865476 - 0.7071067811865476 - - 3 - - - 1.0 - 0 - - 0.2928932188134525 - 1.7071067811865475 - - 5 - - - 1.0 - 0 - - -0.7071067811865476 - -2.1213203435596424 bad_primes: - 2 - 3 - 5 central_character: '30.23' coefficient_field: CDF conductor: 30 conductor_radical: 30 conjugate: '3408082167835782798416530038007' degree: 2 euler_factors: - - - 1.0 - 0 - - 0.7071067811865476 - 0.7071067811865476 - - - 1.0 - 0 - - 0.2928932188134525 - 1.7071067811865475 - - - 1.0 - 0 - - -0.7071067811865476 - -2.1213203435596424 - - - 1.0 - 0 - - 1.0 - -1.0 - - 0 - -7.0 - - - 1.0 - 0 - - 0 - 1.4142135623730951 - - -11.0 - 0 - - - 1.0 - 0 - - 0 - 0 - - 0 - 13.0 - - - 1.0 - 0 - - 1.4142135623730951 - 1.4142135623730951 - - 0 - 17.0 - - - 1.0 - 0 - - 0 - 4.0 - - -19.0 - 0 - - - 1.0 - 0 - - 2.8284271247461903 - -2.8284271247461903 - - 0 - -23.0 - - - 1.0 - 0 - - -7.0710678118654755 - 0 - - 29.0 - 0 - - - 1.0 - 0 - - 2.0 - 0 - - 31.0 - 0 - - - 1.0 - 0 - - -6.0 - 6.0 - - 0 - -37.0 - - - 1.0 - 0 - - 0 - 5.656854249492381 - - -41.0 - 0 - - - 1.0 - 0 - - -6.0 - -6.0 - - 0 - 43.0 - - - 1.0 - 0 - - 0 - 0 - - 0 - 47.0 - - - 1.0 - 0 - - -2.8284271247461903 - 2.8284271247461903 - - 0 - -53.0 - - - 1.0 - 0 - - 9.899494936611665 - 0 - - 59.0 - 0 - - - 1.0 - 0 - - 6.0 - 0 - - 61.0 - 0 - - - 1.0 - 0 - - 4.0 - -4.0 - - 0 - -67.0 - - - 1.0 - 0 - - 0 - -14.142135623730951 - - -71.0 - 0 - - - 1.0 - 0 - - 5.0 - 5.0 - - 0 - 73.0 - - - 1.0 - 0 - - 0 - 6.0 - - -79.0 - 0 - - - 1.0 - 0 - - -8.48528137423857 - 8.48528137423857 - - 0 - -83.0 - - - 1.0 - 0 - - 2.8284271247461903 - 0 - - 89.0 - 0 - - - 1.0 - 0 - - -3.0 - 3.0 - - 0 - -97.0 - - - 1.0 - 0 - - 0 - -9.899494936611665 - - -101.0 - 0 - - - 1.0 - 0 - - -1.0 - -1.0 - - 0 - 103.0 - - - 1.0 - 0 - - -2.8284271247461903 - -2.8284271247461903 - - 0 - 107.0 - - - 1.0 - 0 - - 0 - -10.0 - - -109.0 - 0 - - - 1.0 - 0 - - 9.899494936611665 - -9.899494936611665 - - 0 - -113.0 gamma_factors: - [] - - 0 group: GL2 id: 9589626 index: 1 label: 2-30-15.8-c1-0-1 load_key: CMFs-workshop motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 order_of_vanishing: 0 origin: ModularForm/GL2/Q/holomorphic/30/2/e/a/23/1 plot_delta: __RealLiteral__: 0 data: '0.17578125' prec: 34 plot_values: - 0.5495224093420378 - 0.5781704996161813 - 0.6284086162866335 - 0.7007470941672975 - 0.7949456302724278 - 0.9102999104024208 - 1.045710024283649 - 1.1995513888637919 - 1.3694418577385064 - 1.5519868514195927 - 1.742556156428646 - 1.9351284360914092 - 2.122232509465169 - 2.2950120680245565 - 2.4434379949535687 - 2.556687139275148 - 2.6236969635935545 - 2.6338915100072704 - 2.5780559081818883 - 2.4493151792568177 - 2.244150096457567 - 1.9633607931171053 - 1.6128707195098468 - 1.204252886955444 - 0.7548605769961412 - 0.28745886529602294 - -0.17071656110742464 - -0.5895002916669934 - -0.9379035383358519 - -1.186679861732859 - -1.311168474252257 - -1.2941626699033328 - -1.1284959173402294 - -0.8190097784421273 - -0.383576026464279 - 0.14710272392578363 - 0.7310913288145019 - 1.3182558028620055 - 1.8545955219104377 - 2.287549079625905 - 2.5717697935202173 - 2.674723847594145 - 2.5813847747251217 - 2.2973060694130507 - 1.8494643145471739 - 1.2844807254309478 - 0.6641361439410601 - 0.05846313652054699 - -0.46291644386890773 - -0.8401955704060572 - -1.0322707023632487 - -1.0237683816474383 - -0.8289674067266326 - -0.49168617545347404 - -0.08070655652400424 - 0.3190550828271629 - 0.6187260725734428 - 0.739460671744358 - 0.62620985026006 - 0.2590539994754552 - -0.33998895710978544 - -1.10626669540148 - -1.9386645272254797 - -2.712346529962789 - -3.296633930396173 - -3.5755706103250784 - -3.4680141557872117 - -2.94384930807034 - -2.0332475273191917 - -0.8267985118181892 - 0.5342813798453088 - 1.8770013751660686 - 3.0219847723764337 - 3.8115087176573907 - 4.135534305791667 - 3.9510767438321768 - 3.2911352035831563 - 2.2610445919594633 - 1.0222808451880045 - -0.23392613330064646 - -1.3187817709668317 - -2.07820201195917 - -2.4191601398213605 - -2.324959057935913 - -1.8562272817564758 - -1.1371377697801244 - -0.32930171160416616 - 0.4016038135247987 - 0.9197270911697953 - 1.146354853101808 - 1.0747010424111763 - 0.76872345941089 - 0.34590386736177264 - -0.052498570942319224 - -0.29723429822717334 - -0.3047382375849776 - -0.06064933507650405 - 0.37289197365682275 - 0.8687266533935767 - 1.2631762358030745 - 1.395621116129037 - 1.1501968104132019 - 0.4895726534708524 - -0.5279541005911187 - -1.7533465956444523 - -2.9740127894437647 - -3.9582062011422883 - -4.507048114114449 - -4.502106416124903 - -3.9367893098549613 - -2.923038656391165 - -1.6703344004345335 - -0.4406283142559924 - 0.5110637392302034 - 0.9966265243216402 - 0.9407297311782067 - 0.4007556735184874 - -0.445211175637279 - -1.3405982600012059 - -2.0133522387170713 - -2.2446601053589506 - -1.926209470102765 - -1.091024070378091 - 0.0909204216118401 - 1.3523715384946133 - 2.3947120811231657 - 2.963904151486431 - 2.9170618567094926 - 2.2620315020397115 - 1.1588681561773253 - -0.11819967940771359 - -1.24930012986112 - -1.9505584515773515 - -2.0475007695446603 - -1.5205585255598049 - -0.5100866047987919 - 0.7209830530179554 - 1.857225734892525 - 2.6147888743328127 - 2.8165472688315987 - 2.4376313078288803 - 1.608654577235854 - 0.57575357816088 - -0.37119486162380616 - -0.9816144609938147 - -1.1145685414493258 - -0.7759812272102286 - -0.1119369835843537 - 0.639766784747785 - 1.2250909746955314 - 1.453201398178565 - 1.2553817198668076 - 0.7049479189062697 - -0.008391696358373361 - -0.6420252833271551 - -0.9818324383354196 - -0.9152502154512164 - -0.4716438387341501 - 0.18461541474778567 - 0.8080690231482088 - 1.1573067462436692 - 1.0844087222710284 - 0.5988090984640957 - -0.117735164766833 - -0.7538701470992479 - -0.9596295810122645 - -0.4599369392414543 - 0.8441537243290606 - 2.8197272021537207 - 5.11284316401188 - 7.227444668281524 - 8.652757793865128 - 9.003573826082246 - 8.132134225241863 - 6.177260380751501 - 3.534209175377578 - 0.752275088908964 - -1.6108233019172942 - -3.135220804863819 - -3.642762696449559 - -3.22824788778588 - -2.210316935813099 - -1.0192219895337193 - -0.058224257941283754 - 0.41695315086227164 - 0.3629147443524821 - -0.06107821790992405 - -0.5709072190824458 - -0.8744607544741139 - -0.785736152086105 - -0.2959386664321989 - 0.42318881785877493 - 1.084458941017582 - 1.39497376751525 - 1.1705236905365268 - 0.412550487507426 - -0.6815026956621615 - -1.7799889461070542 - -2.5304166097929204 - -2.6845102461056207 - -2.189797937653763 - -1.2134735599353255 - -0.08793815677473904 - 0.804402994372577 - 1.1669214726624895 - 0.8963381498396846 - 0.12221754671724662 - -0.8377397347010721 - -1.5923719042107072 - -1.8214008196479445 - -1.3970826881970064 - -0.4376194722719025 - 0.7294004864223343 - 1.682674234785662 - 2.0614867685711142 - 1.7025620280540754 - 0.7080536433562432 - -0.5828293748830253 - -1.711151639622428 - -2.2637987091755933 - -2.0272217976617233 - -1.0717755671950582 - 0.2669995957450871 - 1.5065072334040934 - 2.1938263766860455 - 2.077065033534158 - 1.2072841100732241 - -0.06926919721174263 - -1.2293623770144781 - -1.7611819708197585 - -1.3555164158723048 - -0.02939492972359204 - 1.8650350886301676 - 3.752488181271861 - 5.0292594803096105 - 5.271661301835908 - 4.383305549336241 - 2.6280943955629743 - 0.5373038202744668 - -1.2749001192835678 - -2.319975021112966 - -2.3920713118856445 - -1.6184843204766035 - -0.3890751642648165 - 0.8041786591619797 - 1.5534534718940258 - 1.6754899278957853 - 1.2547869907881302 - 0.5782114523481345 - -0.006743982931168335 - -0.24807737927877513 - -0.09380041572690548 - 0.29786191421410396 - 0.6444868872823085 - 0.6820808748317989 - 0.2999452951577172 - -0.39396894302460334 positive_zeros: - '4.50368004225802633236355559239112' - '6.10595906160915434301636909296688' - '8.279743490344514498393476746398930' - '9.526070664807416336095550719717382' - '10.45471285693397489650266968308568' - '12.23668530395967147757095350018454' - '13.85289691093411225209009374022262' - '15.19197698537520675261550340977011' - '16.32141304116390009919213512708611' - '16.90375285714291204555643085105499' prelabel: 2-30-15.8-c1-0 primitive: true rational: false root_analytic_conductor: 0.4894396858284392 root_angle: 0.2697050848405203 root_number: 0.6620065617666444 + 0.7494980401428052*I self_dual: false sign_arg: __RealLiteral__: 0 data: '0.13485254242' prec: 44 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '4.50368004225802633236355559239' prec: 103 z2: __RealLiteral__: 0 data: '6.10595906160915434301636909297' prec: 103 z3: __RealLiteral__: 0 data: '8.279743490344514498393476746399' prec: 107 - - algebraic: true analytic_conductor: 0.23955120606384128 bad_primes: - 2 - 3 - 5 central_character: '15.8' conductor: 30 conductor_radical: 30 degree: 2 id: 9589626 index: 1 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/30/2/e/a/23/1 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: 2-30-15.8-c1-0-1 motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 order_of_vanishing: 0 prelabel: 2-30-15.8-c1-0 primitive: true rational: false root_analytic_conductor: 0.4894396858284392 root_angle: 0.13485254242026015 self_dual: false spectral_label: c1-0 z1: __RealLiteral__: 0 data: '4.50368004225802633236355559239' prec: 103 - - Lhash: '5709092708804284635613657015083' Lhash_array: - '5709092708804284635613657015083' id: 9955653 label: 2-30-15.8-c1-0-1 type: CMF url: ModularForm/GL2/Q/holomorphic/30/2/e/a/23/1 label_cols: - label - label - label labels: - 2-30-15.8-c1-0-1 - 2-30-15.8-c1-0-1 - 2-30-15.8-c1-0-1 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-16T13:18:29.778883'