Properties

 Level $31$ Weight $0$ Character 31.1 Symmetry even Fricke sign $+1$

Related objects

The Maass form of level 31 with the smallest eigenvalue. This Maass form is even, and for all smaller prime levels the Maass form with the smallest eigenvalue is odd.

Maass form invariants

 Level: $$31$$ Weight: $$0$$ Character: 31.1 Symmetry: even Fricke sign: $+1$ Spectral parameter: $$0.78935617774$$

Maass form coefficients

$$a_{1}=+1.000000000$$ $$a_{2}=-1.374310443$$ $$a_{3}=-0.902704087$$ $$a_{4}=+0.888729194$$ $$a_{5}=-0.730042232$$
$$a_{6}=+1.240595654$$ $$a_{7}=+1.126296789$$ $$a_{8}=+0.152920630$$ $$a_{9}=-0.185125331$$ $$a_{10}=+1.003304663$$
$$a_{11}=-0.214467911$$ $$a_{12}=-0.802259476$$ $$a_{13}=-0.757205689$$ $$a_{14}=-1.547881439$$ $$a_{15}=+0.659012107$$
$$a_{16}=-1.098889613$$ $$a_{17}=+0.294474423$$ $$a_{18}=+0.254419676$$ $$a_{19}=+1.669683823$$ $$a_{20}=-0.648809845$$
$$a_{21}=-1.016712715$$ $$a_{22}=+0.294745490$$ $$a_{23}=-0.186602717$$ $$a_{24}=-0.138042078$$ $$a_{25}=-0.467038340$$
$$a_{26}=+1.040635685$$ $$a_{27}=+1.069817480$$ $$a_{28}=+1.000972838$$ $$a_{29}=+0.623885373$$ $$a_{30}=-0.905687220$$
$$a_{31}=-0.179605302$$ $$a_{32}=+1.357294842$$ $$a_{33}=+0.193601060$$ $$a_{34}=-0.404699275$$ $$a_{35}=-0.822244221$$
$$a_{36}=-0.164526286$$ $$a_{37}=-0.550425157$$ $$a_{38}=-2.294663915$$ $$a_{39}=+0.683532670$$ $$a_{40}=-0.111638518$$
$$a_{41}=+0.282161696$$ $$a_{42}=+1.397278901$$ $$a_{43}=-1.754380818$$ $$a_{44}=-0.190603894$$ $$a_{45}=+0.135149310$$
$$a_{46}=+0.256450063$$ $$a_{47}=+0.913504460$$ $$a_{48}=+0.991972145$$ $$a_{49}=+0.268544456$$ $$a_{50}=+0.641855668$$
$$a_{51}=-0.265823266$$ $$a_{52}=-0.672950802$$ $$a_{53}=-0.054369845$$ $$a_{54}=-1.470261335$$ $$a_{55}=+0.156570633$$
$$a_{56}=+0.172234015$$ $$a_{57}=-1.507230411$$ $$a_{58}=-0.857412183$$ $$a_{59}=+0.112243164$$ $$a_{60}=+0.585683299$$
$$a_{61}=+0.985441455$$ $$a_{62}=+0.246833442$$ $$a_{63}=-0.208506066$$ $$a_{64}=-0.766454862$$ $$a_{65}=+0.552792131$$
$$a_{66}=-0.266067959$$ $$a_{67}=+0.974063600$$ $$a_{68}=+0.261708017$$ $$a_{69}=+0.168447035$$ $$a_{70}=+1.130018820$$
$$a_{71}=-0.225908180$$ $$a_{72}=-0.028309482$$ $$a_{73}=-0.274541918$$ $$a_{74}=+0.756455042$$ $$a_{75}=+0.421597418$$
$$a_{76}=+1.483896759$$ $$a_{77}=-0.241554520$$ $$a_{78}=-0.939386087$$ $$a_{79}=+0.679788869$$ $$a_{80}=+0.802235826$$
$$a_{81}=-0.780603281$$ $$a_{82}=-0.387777765$$ $$a_{83}=-0.761608790$$ $$a_{84}=-0.903582272$$ $$a_{85}=-0.214978765$$
$$a_{86}=+2.411063880$$ $$a_{87}=-0.563183876$$ $$a_{88}=-0.032796568$$ $$a_{89}=-1.549844985$$ $$a_{90}=-0.185737108$$
$$a_{91}=-0.852838335$$ $$a_{92}=-0.165839282$$ $$a_{93}=+0.162130440$$ $$a_{94}=-1.255438719$$ $$a_{95}=-1.218939705$$
$$a_{96}=-1.225235601$$ $$a_{97}=+0.987747906$$ $$a_{98}=-0.369063451$$ $$a_{99}=+0.039703443$$ $$a_{100}=-0.415070607$$

Showing 100 of 546 available coefficients

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