Properties

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

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.29029769112 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.227079865\) \(a_{3}=+0.490256847\) \(a_{4}=-0.948434735\) \(a_{5}=-0.288707164\)
\(a_{6}=+0.111327459\) \(a_{7}=-1.291774611\) \(a_{8}=-0.442450297\) \(a_{9}=-0.759648224\) \(a_{10}=-0.065559584\)
\(a_{11}=+0.106056793\) \(a_{12}=-0.464976623\) \(a_{13}=+1.894169973\) \(a_{14}=-0.293336005\) \(a_{15}=-0.141540664\)
\(a_{16}=+0.847963181\) \(a_{17}=-1.377573747\) \(a_{18}=-0.172500816\) \(a_{19}=-0.525675762\) \(a_{20}=+0.273819902\)
\(a_{21}=-0.633301348\) \(a_{22}=+0.024083362\) \(a_{23}=+0.806902073\) \(a_{24}=-0.216914288\) \(a_{25}=-0.916648174\)
\(a_{26}=+0.430127862\) \(a_{27}=-0.862679590\) \(a_{28}=+1.225163911\) \(a_{29}=-1.071268438\) \(a_{30}=-0.032141035\)
\(a_{31}=-0.179605302\) \(a_{32}=+0.635005662\) \(a_{33}=+0.051995069\) \(a_{34}=-0.312819261\) \(a_{35}=+0.372944584\)
\(a_{36}=+0.720476762\) \(a_{37}=+0.206589587\) \(a_{38}=-0.119370381\) \(a_{39}=+0.928629799\) \(a_{40}=+0.127738570\)
\(a_{41}=+0.956067021\) \(a_{42}=-0.143809985\) \(a_{43}=-1.475283628\) \(a_{44}=-0.100587945\) \(a_{45}=+0.219315885\)
\(a_{46}=+0.183231214\) \(a_{47}=-0.047392117\) \(a_{48}=+0.415719754\) \(a_{49}=+0.668681647\) \(a_{50}=-0.208152340\)
\(a_{51}=-0.675364961\) \(a_{52}=-1.796496599\) \(a_{53}=-1.687772752\) \(a_{54}=-0.195897169\) \(a_{55}=-0.030619350\)
\(a_{56}=+0.571546071\) \(a_{57}=-0.257716141\) \(a_{58}=-0.243263503\) \(a_{59}=+0.767737556\) \(a_{60}=+0.134242088\)
\(a_{61}=+1.256600568\) \(a_{62}=-0.040784737\) \(a_{63}=+0.981294289\) \(a_{64}=-0.703766232\) \(a_{65}=-0.546860428\)
\(a_{66}=+0.011807039\) \(a_{67}=-0.764803866\) \(a_{68}=+1.306538769\) \(a_{69}=+0.395589274\) \(a_{70}=+0.084688267\)
\(a_{71}=-0.550567431\) \(a_{72}=+0.336106517\) \(a_{73}=+0.215511272\) \(a_{74}=+0.046912332\) \(a_{75}=-0.449393012\)
\(a_{76}=+0.498569186\) \(a_{77}=-0.137001495\) \(a_{78}=+0.210873071\) \(a_{79}=-0.122597411\) \(a_{80}=-0.244813051\)
\(a_{81}=+0.336713706\) \(a_{82}=+0.217103708\) \(a_{83}=+0.810842438\) \(a_{84}=+0.600644848\) \(a_{85}=+0.397715409\)
\(a_{86}=-0.335007112\) \(a_{87}=-0.525196616\) \(a_{88}=-0.046924795\) \(a_{89}=+0.698727941\) \(a_{90}=+0.049802115\)
\(a_{91}=-2.446840686\) \(a_{92}=-0.765293839\) \(a_{93}=-0.088052749\) \(a_{94}=-0.010761724\) \(a_{95}=+0.151766454\)
\(a_{96}=+0.311315893\) \(a_{97}=+0.102780866\) \(a_{98}=+0.151844007\) \(a_{99}=-0.080565876\) \(a_{100}=+0.869381019\)

Showing 100 of 1500 available coefficients

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