Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 13.3954804003 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.720014075\) \(a_{3}=+0.577350269\) \(a_{4}=-0.481579732\) \(a_{5}=+1.236902989\)
\(a_{6}=+0.415700320\) \(a_{7}=+0.522538840\) \(a_{8}=-1.066758260\) \(a_{9}=+0.333333334\) \(a_{10}=+0.890587561\)
\(a_{11}=+1.091562457\) \(a_{12}=-0.278040201\) \(a_{13}=+1.460650887\) \(a_{14}=+0.376235028\) \(a_{15}=+0.714127704\)
\(a_{16}=-0.286508347\) \(a_{17}=-0.113939219\) \(a_{18}=+0.240004692\) \(a_{19}=+0.688995405\) \(a_{20}=-0.595667410\)
\(a_{21}=+0.301687940\) \(a_{22}=+0.785940331\) \(a_{23}=-1.193890008\) \(a_{24}=-0.615893169\) \(a_{25}=+0.529929004\)
\(a_{26}=+1.051689153\) \(a_{27}=+0.192450090\) \(a_{28}=-0.251644115\) \(a_{29}=-1.012357245\) \(a_{30}=+0.514180968\)
\(a_{31}=-1.206412766\) \(a_{32}=+0.860473342\) \(a_{33}=+0.630213877\) \(a_{34}=-0.082063708\) \(a_{35}=+0.646329853\)
\(a_{36}=-0.160526577\) \(a_{37}=-1.585874836\) \(a_{38}=+0.496086389\) \(a_{39}=+0.843307148\) \(a_{40}=-1.319476481\)
\(a_{41}=+0.335011016\) \(a_{42}=+0.217219563\) \(a_{43}=+1.084328011\) \(a_{44}=-0.525674354\) \(a_{45}=+0.412300996\)
\(a_{46}=-0.859617610\) \(a_{47}=+0.467801778\) \(a_{48}=-0.165411563\) \(a_{49}=-0.726953162\) \(a_{50}=+0.381556342\)
\(a_{51}=-0.065803578\) \(a_{52}=-0.703419831\) \(a_{53}=+0.737663052\) \(a_{54}=+0.138566770\) \(a_{55}=+1.350156869\)
\(a_{56}=-0.557422613\) \(a_{57}=+0.397791680\) \(a_{58}=-0.728911503\) \(a_{59}=-0.512072431\) \(a_{60}=-0.343908686\)
\(a_{61}=-0.150701027\) \(a_{62}=-0.868634305\) \(a_{63}=+0.174179454\) \(a_{64}=+0.906054148\) \(a_{65}=+1.806683373\)
\(a_{66}=+0.453762862\) \(a_{67}=-1.501634463\) \(a_{68}=+0.054888119\) \(a_{69}=-0.689292718\) \(a_{70}=+0.465366592\)
\(a_{71}=+0.042484872\) \(a_{72}=-0.355586087\) \(a_{73}=+0.384803753\) \(a_{74}=-1.141852204\) \(a_{75}=+0.305954654\)
\(a_{76}=-0.331806221\) \(a_{77}=+0.570383778\) \(a_{78}=+0.607193014\) \(a_{79}=+0.369965498\) \(a_{80}=-0.354374225\)
\(a_{81}=+0.111111113\) \(a_{82}=+0.241212641\) \(a_{83}=-0.176941706\) \(a_{84}=-0.145286793\) \(a_{85}=-0.140976183\)
\(a_{86}=+0.780731428\) \(a_{87}=-0.584484749\) \(a_{88}=-1.164433272\) \(a_{89}=-0.699537610\) \(a_{90}=+0.296862558\)
\(a_{91}=+0.763246761\) \(a_{92}=+0.574953172\) \(a_{93}=-0.696522735\) \(a_{94}=+0.336823953\) \(a_{95}=+0.852220546\)
\(a_{96}=+0.496794363\) \(a_{97}=+0.011771242\) \(a_{98}=-0.523416411\) \(a_{99}=+0.363854480\) \(a_{100}=-0.255203080\)

Showing 100 of 5000 available coefficients

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