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: \( 4.16786925047 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.585911413\) \(a_{3}=-1.430564032\) \(a_{4}=-0.656707816\) \(a_{5}=+0.946210435\)
\(a_{6}=-0.838183794\) \(a_{7}=+1.183277913\) \(a_{8}=-0.970684018\) \(a_{9}=+1.046513450\) \(a_{10}=+0.554395493\)
\(a_{11}=+0.002355296\) \(a_{12}=+0.939462581\) \(a_{13}=+1.606112983\) \(a_{14}=+0.693296035\) \(a_{15}=-1.353614615\)
\(a_{16}=+0.087972971\) \(a_{17}=-1.104776596\) \(a_{18}=+0.613164175\) \(a_{19}=+0.674190115\) \(a_{20}=-0.621383788\)
\(a_{21}=-1.692754823\) \(a_{22}=+0.001379995\) \(a_{23}=+1.484949844\) \(a_{24}=+1.388625643\) \(a_{25}=-0.104685814\)
\(a_{26}=+0.941039928\) \(a_{27}=-0.066540469\) \(a_{28}=-0.777067854\) \(a_{29}=+0.997965957\) \(a_{30}=-0.793098252\)
\(a_{31}=+0.179605302\) \(a_{32}=+1.022228385\) \(a_{33}=-0.003369402\) \(a_{34}=-0.647301217\) \(a_{35}=+1.119629908\)
\(a_{36}=-0.687253562\) \(a_{37}=+0.132686476\) \(a_{38}=+0.395015683\) \(a_{39}=-2.297647465\) \(a_{40}=-0.918471346\)
\(a_{41}=-1.333962245\) \(a_{42}=-0.991804371\) \(a_{43}=+1.133801502\) \(a_{44}=-0.001546741\) \(a_{45}=+0.990221947\)
\(a_{46}=+0.870049062\) \(a_{47}=+0.798246525\) \(a_{48}=-0.125850968\) \(a_{49}=+0.400146619\) \(a_{50}=-0.061336613\)
\(a_{51}=+1.580453663\) \(a_{52}=-1.054746948\) \(a_{53}=+0.070706007\) \(a_{54}=-0.038986821\) \(a_{55}=+0.002228605\)
\(a_{56}=-1.148588959\) \(a_{57}=-0.964472128\) \(a_{58}=+0.584719646\) \(a_{59}=-1.519812714\) \(a_{60}=+0.888929295\)
\(a_{61}=+0.975539964\) \(a_{62}=+0.105232796\) \(a_{63}=+1.238316255\) \(a_{64}=+0.510962311\) \(a_{65}=+1.519720864\)
\(a_{66}=-0.001974178\) \(a_{67}=-0.824908430\) \(a_{68}=+0.725515429\) \(a_{69}=-2.124315826\) \(a_{70}=+0.656003949\)
\(a_{71}=+0.696264884\) \(a_{72}=-1.015833896\) \(a_{73}=-1.017529305\) \(a_{74}=+0.077742536\) \(a_{75}=+0.149759789\)
\(a_{76}=-0.442745918\) \(a_{77}=+0.002786936\) \(a_{78}=-1.346217914\) \(a_{79}=+1.087870318\) \(a_{80}=+0.083241008\)
\(a_{81}=-0.951323003\) \(a_{82}=-0.781583729\) \(a_{83}=+0.297271404\) \(a_{84}=+1.111645315\) \(a_{85}=-1.045351142\)
\(a_{86}=+0.664307249\) \(a_{87}=-1.427654205\) \(a_{88}=-0.002286248\) \(a_{89}=-0.005690158\) \(a_{90}=+0.580182318\)
\(a_{91}=+1.900478018\) \(a_{92}=-0.975178147\) \(a_{93}=-0.256936870\) \(a_{94}=+0.467701722\) \(a_{95}=+0.637925700\)
\(a_{96}=-1.462363101\) \(a_{97}=+1.379074375\) \(a_{98}=+0.234450447\) \(a_{99}=+0.002464887\) \(a_{100}=+0.068748007\)

Showing 100 of 1500 available coefficients

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