Properties

Level $2$
Weight $0$
Character 2.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.3375089547 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.269130331\) \(a_{4}=+0.500000000\) \(a_{5}=+0.257308535\)
\(a_{6}=+0.190303882\) \(a_{7}=-0.307845636\) \(a_{8}=+0.353553391\) \(a_{9}=-0.927568865\) \(a_{10}=+0.181944610\)
\(a_{11}=-0.496835105\) \(a_{12}=+0.134565166\) \(a_{13}=-0.705553345\) \(a_{14}=-0.217679737\) \(a_{15}=+0.069249531\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.863190121\) \(a_{18}=-0.655890234\) \(a_{19}=-1.814172671\) \(a_{20}=+0.128654267\)
\(a_{21}=-0.082850598\) \(a_{22}=-0.351315472\) \(a_{23}=+0.156749539\) \(a_{24}=+0.095151941\) \(a_{25}=-0.933792318\)
\(a_{26}=-0.498901555\) \(a_{27}=-0.518767247\) \(a_{28}=-0.153922818\) \(a_{29}=+1.137319816\) \(a_{30}=+0.048966813\)
\(a_{31}=+0.894045848\) \(a_{32}=+0.176776695\) \(a_{33}=-0.133713397\) \(a_{34}=+0.610367588\) \(a_{35}=-0.079211310\)
\(a_{36}=-0.463784432\) \(a_{37}=-1.294030369\) \(a_{38}=-1.282813798\) \(a_{39}=-0.189885805\) \(a_{40}=+0.090972305\)
\(a_{41}=-1.332217543\) \(a_{42}=-0.058584220\) \(a_{43}=-1.868921335\) \(a_{44}=-0.248417553\) \(a_{45}=-0.238671386\)
\(a_{46}=+0.110838662\) \(a_{47}=-0.043976931\) \(a_{48}=+0.067282583\) \(a_{49}=-0.905231064\) \(a_{50}=-0.660290880\)
\(a_{51}=+0.232310643\) \(a_{52}=-0.352776672\) \(a_{53}=+1.084816724\) \(a_{54}=-0.366823838\) \(a_{55}=-0.127839913\)
\(a_{56}=-0.108839868\) \(a_{57}=-0.488248892\) \(a_{58}=+0.804206554\) \(a_{59}=-0.822119541\) \(a_{60}=+0.034624766\)
\(a_{61}=-0.170983679\) \(a_{62}=+0.632185882\) \(a_{63}=+0.285548027\) \(a_{64}=+0.125000000\) \(a_{65}=-0.181544897\)
\(a_{66}=-0.094549649\) \(a_{67}=-1.191149129\) \(a_{68}=+0.431595061\) \(a_{69}=+0.042186055\) \(a_{70}=-0.056010854\)
\(a_{71}=+1.117141886\) \(a_{72}=-0.327945117\) \(a_{73}=+0.891871996\) \(a_{74}=-0.915017649\) \(a_{75}=-0.251311836\)
\(a_{76}=-0.907086336\) \(a_{77}=+0.152948519\) \(a_{78}=-0.134269541\) \(a_{79}=+1.012699153\) \(a_{80}=+0.064327134\)
\(a_{81}=+0.787952864\) \(a_{82}=-0.942020059\) \(a_{83}=+0.233406071\) \(a_{84}=-0.041425299\) \(a_{85}=+0.222106185\)
\(a_{86}=-1.321526949\) \(a_{87}=+0.306087259\) \(a_{88}=-0.175657736\) \(a_{89}=+0.832681912\) \(a_{90}=-0.168766155\)
\(a_{91}=+0.217201518\) \(a_{92}=+0.078374770\) \(a_{93}=+0.240614855\) \(a_{94}=-0.031096386\) \(a_{95}=-0.466802112\)
\(a_{96}=+0.047575971\) \(a_{97}=+0.168065695\) \(a_{98}=-0.640095024\) \(a_{99}=+0.460848775\) \(a_{100}=-0.466896159\)

Showing 100 of 1228 available coefficients

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