Properties

Level $691$
Weight $0$
Character 691.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 691 \)
Weight: \( 0 \)
Character: 691.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.3138699324 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.322487183\) \(a_{3}=-1.086464925\) \(a_{4}=+0.748972332\) \(a_{5}=+0.561538102\)
\(a_{6}=-1.436835903\) \(a_{7}=+0.192338183\) \(a_{8}=-0.331980843\) \(a_{9}=+0.180406017\) \(a_{10}=+0.742626897\)
\(a_{11}=-0.009030695\) \(a_{12}=-0.813732195\) \(a_{13}=-0.049925777\) \(a_{14}=+0.254364843\) \(a_{15}=-0.610091452\)
\(a_{16}=-1.188012801\) \(a_{17}=-0.769255518\) \(a_{18}=+0.238584630\) \(a_{19}=-0.000417747\) \(a_{20}=+0.420576528\)
\(a_{21}=-0.208968701\) \(a_{22}=-0.011943059\) \(a_{23}=-0.318804719\) \(a_{24}=+0.360685550\) \(a_{25}=-0.684674983\)
\(a_{26}=-0.066026162\) \(a_{27}=+0.890460137\) \(a_{28}=+0.144055967\) \(a_{29}=+1.207041051\) \(a_{30}=-0.806838029\)
\(a_{31}=-0.838475820\) \(a_{32}=-1.239150755\) \(a_{33}=+0.009811521\) \(a_{34}=-1.017330612\) \(a_{35}=+0.108005181\)
\(a_{36}=+0.135119113\) \(a_{37}=-0.581010985\) \(a_{38}=-0.000552495\) \(a_{39}=+0.054242666\) \(a_{40}=-0.186419897\)
\(a_{41}=-0.617068758\) \(a_{42}=-0.276358427\) \(a_{43}=+1.472917215\) \(a_{44}=-0.006763737\) \(a_{45}=+0.101304836\)
\(a_{46}=-0.421615229\) \(a_{47}=-1.711110069\) \(a_{48}=+1.290734201\) \(a_{49}=-0.963006022\) \(a_{50}=-0.905473935\)
\(a_{51}=+0.835769169\) \(a_{52}=-0.037393043\) \(a_{53}=-1.266315392\) \(a_{54}=+1.177622062\) \(a_{55}=-0.005071007\)
\(a_{56}=-0.063852649\) \(a_{57}=+0.000453874\) \(a_{58}=+1.596296355\) \(a_{59}=+1.899818267\) \(a_{60}=-0.456941638\)
\(a_{61}=+0.902473810\) \(a_{62}=-1.108873501\) \(a_{63}=+0.034698966\) \(a_{64}=-0.450748237\) \(a_{65}=-0.028035257\)
\(a_{66}=+0.012975657\) \(a_{67}=+1.123846687\) \(a_{68}=-0.576151104\) \(a_{69}=+0.346370109\) \(a_{70}=+0.142835540\)
\(a_{71}=+1.603288059\) \(a_{72}=-0.059891328\) \(a_{73}=+0.290623590\) \(a_{74}=-0.768379452\) \(a_{75}=+0.743875295\)
\(a_{76}=-0.000312893\) \(a_{77}=-0.001736966\) \(a_{78}=+0.071735136\) \(a_{79}=+0.429534519\) \(a_{80}=-0.667114433\)
\(a_{81}=-1.147859680\) \(a_{82}=-0.816065502\) \(a_{83}=-0.584082926\) \(a_{84}=-0.156511813\) \(a_{85}=-0.431966253\)
\(a_{86}=+1.947914152\) \(a_{87}=-1.311407749\) \(a_{88}=+0.002998033\) \(a_{89}=+1.282217383\) \(a_{90}=+0.133974346\)
\(a_{91}=-0.009602619\) \(a_{92}=-0.238775876\) \(a_{93}=+0.910974540\) \(a_{94}=-2.262921240\) \(a_{95}=-0.000234524\)
\(a_{96}=+1.346293831\) \(a_{97}=+1.335903467\) \(a_{98}=-1.273563078\) \(a_{99}=-0.001629204\) \(a_{100}=-0.512802623\)

Showing 100 of 1866 available coefficients

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