Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.7063706851 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.617047334\) \(a_{3}=+0.577350269\) \(a_{4}=+1.614842079\) \(a_{5}=-0.523940118\)
\(a_{6}=+0.933602713\) \(a_{7}=-1.496002695\) \(a_{8}=+0.994228744\) \(a_{9}=+0.333333333\) \(a_{10}=-0.847235971\)
\(a_{11}=-0.133175958\) \(a_{12}=+0.932329509\) \(a_{13}=+1.318259251\) \(a_{14}=-2.419107169\) \(a_{15}=-0.302496968\)
\(a_{16}=-0.007127139\) \(a_{17}=-1.030476126\) \(a_{18}=+0.539015778\) \(a_{19}=-1.289711108\) \(a_{20}=-0.846080550\)
\(a_{21}=-0.863717559\) \(a_{22}=-0.215351828\) \(a_{23}=+0.695745837\) \(a_{24}=+0.574018233\) \(a_{25}=-0.725486752\)
\(a_{26}=+2.131687606\) \(a_{27}=+0.192450090\) \(a_{28}=-2.415808102\) \(a_{29}=-1.829913187\) \(a_{30}=-0.489151916\)
\(a_{31}=-0.714326522\) \(a_{32}=-1.005753666\) \(a_{33}=-0.076889175\) \(a_{34}=-1.666328671\) \(a_{35}=+0.783815829\)
\(a_{36}=+0.538280693\) \(a_{37}=-0.546580504\) \(a_{38}=-2.085523909\) \(a_{39}=+0.761097333\) \(a_{40}=-0.520916326\)
\(a_{41}=-0.558716830\) \(a_{42}=-1.396672175\) \(a_{43}=+1.382962070\) \(a_{44}=-0.215058141\) \(a_{45}=-0.174646706\)
\(a_{46}=+1.125053950\) \(a_{47}=+0.683650856\) \(a_{48}=-0.004114856\) \(a_{49}=+1.238024063\) \(a_{50}=-1.173146418\)
\(a_{51}=-0.594945669\) \(a_{52}=+2.128780509\) \(a_{53}=-0.564253176\) \(a_{54}=+0.311200904\) \(a_{55}=+0.069776227\)
\(a_{56}=-1.487368881\) \(a_{57}=-0.744615056\) \(a_{58}=-2.959056239\) \(a_{59}=+1.672641959\) \(a_{60}=-0.488484833\)
\(a_{61}=+0.636441403\) \(a_{62}=-1.155099797\) \(a_{63}=-0.498667565\) \(a_{64}=-1.619224144\) \(a_{65}=-0.690688908\)
\(a_{66}=-0.124333436\) \(a_{67}=-0.307479762\) \(a_{68}=-1.664056209\) \(a_{69}=+0.401689046\) \(a_{70}=+1.267467296\)
\(a_{71}=-1.121953602\) \(a_{72}=+0.331409581\) \(a_{73}=+0.295577140\) \(a_{74}=-0.883846546\) \(a_{75}=-0.418859972\)
\(a_{76}=-2.082679767\) \(a_{77}=+0.199231592\) \(a_{78}=+1.230730413\) \(a_{79}=+0.831963344\) \(a_{80}=+0.003734194\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.903471560\) \(a_{83}=-0.129177906\) \(a_{84}=-1.394767458\) \(a_{85}=+0.539907783\)
\(a_{86}=+2.236315128\) \(a_{87}=-1.056500871\) \(a_{88}=-0.132407366\) \(a_{89}=+0.251842699\) \(a_{90}=-0.282411990\)
\(a_{91}=-1.972119392\) \(a_{92}=+1.123519654\) \(a_{93}=-0.412416610\) \(a_{94}=+1.105495794\) \(a_{95}=+0.675731391\)
\(a_{96}=-0.580672150\) \(a_{97}=-0.685801668\) \(a_{98}=+2.001943511\) \(a_{99}=-0.044391986\) \(a_{100}=-1.171546535\)

Showing 100 of 1228 available coefficients

Rows: Cols: