Properties

Level $22$
Weight $0$
Character 22.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.07010414741 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.171148723\) \(a_{4}=+0.500000000\) \(a_{5}=-0.391975270\)
\(a_{6}=+0.121020423\) \(a_{7}=-0.863714357\) \(a_{8}=-0.353553391\) \(a_{9}=-0.970708114\) \(a_{10}=+0.277168371\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.085574362\) \(a_{13}=-0.136678489\) \(a_{14}=+0.610738279\) \(a_{15}=+0.067086067\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.265660576\) \(a_{18}=+0.686394290\) \(a_{19}=-0.829756943\) \(a_{20}=-0.195987635\)
\(a_{21}=+0.147823610\) \(a_{22}=-0.213200716\) \(a_{23}=-0.699222916\) \(a_{24}=+0.060510211\) \(a_{25}=-0.846355388\)
\(a_{26}=+0.096646287\) \(a_{27}=+0.337284178\) \(a_{28}=-0.431857179\) \(a_{29}=+1.889684265\) \(a_{30}=-0.047437013\)
\(a_{31}=-1.122738353\) \(a_{32}=-0.176776695\) \(a_{33}=-0.051603282\) \(a_{34}=-0.187850395\) \(a_{35}=+0.338554668\)
\(a_{36}=-0.485354057\) \(a_{37}=+0.472424993\) \(a_{38}=+0.586726761\) \(a_{39}=+0.023392349\) \(a_{40}=+0.138584186\)
\(a_{41}=+1.855094429\) \(a_{42}=-0.104527077\) \(a_{43}=-1.323447284\) \(a_{44}=+0.150755672\) \(a_{45}=+0.380493575\)
\(a_{46}=+0.494425265\) \(a_{47}=-1.189123607\) \(a_{48}=-0.042787181\) \(a_{49}=-0.253997509\) \(a_{50}=+0.598463634\)
\(a_{51}=-0.045467469\) \(a_{52}=-0.068339245\) \(a_{53}=-1.708214005\) \(a_{54}=-0.238495927\) \(a_{55}=-0.118184991\)
\(a_{56}=+0.305369139\) \(a_{57}=+0.142011838\) \(a_{58}=-1.336208558\) \(a_{59}=+0.174211452\) \(a_{60}=+0.033543039\)
\(a_{61}=-0.141463939\) \(a_{62}=+0.793895891\) \(a_{63}=+0.838414538\) \(a_{64}=+0.125000005\) \(a_{65}=+0.053574614\)
\(a_{66}=+0.036489019\) \(a_{67}=+0.185559451\) \(a_{68}=+0.132830233\) \(a_{69}=+0.119671179\) \(a_{70}=-0.239394268\)
\(a_{71}=+1.367520988\) \(a_{72}=+0.343197145\) \(a_{73}=+0.790404015\) \(a_{74}=-0.334054915\) \(a_{75}=+0.144852649\)
\(a_{76}=-0.414878469\) \(a_{77}=-0.260419675\) \(a_{78}=-0.016540879\) \(a_{79}=+0.252176771\) \(a_{80}=-0.097993814\)
\(a_{81}=+0.912982366\) \(a_{82}=-1.311749866\) \(a_{83}=-1.741057888\) \(a_{84}=+0.073911810\) \(a_{85}=-0.104132319\)
\(a_{86}=+0.935818502\) \(a_{87}=-0.323416988\) \(a_{88}=-0.106600815\) \(a_{89}=-1.618529402\) \(a_{90}=-0.269049669\)
\(a_{91}=+0.118050447\) \(a_{92}=-0.349611818\) \(a_{93}=+0.192152636\) \(a_{94}=+0.840839162\) \(a_{95}=+0.325241147\)
\(a_{96}=+0.030254688\) \(a_{97}=-0.510416412\) \(a_{98}=+0.179603906\) \(a_{99}=-0.292687385\) \(a_{100}=-0.423177665\)

Showing 100 of 1500 available coefficients

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