Properties

Level $65$
Weight $0$
Character 65.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 65 = 5 \cdot 13 \)
Weight: \( 0 \)
Character: 65.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.797411301766 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.673528000\) \(a_{3}=-1.009332135\) \(a_{4}=+1.800695968\) \(a_{5}=+0.447213596\)
\(a_{6}=-1.689145590\) \(a_{7}=-1.281183856\) \(a_{8}=+1.339987122\) \(a_{9}=+0.018751359\) \(a_{10}=+0.748424474\)
\(a_{11}=+0.964938790\) \(a_{12}=-1.817500306\) \(a_{13}=-0.277350098\) \(a_{14}=-2.144097057\) \(a_{15}=-0.451387053\)
\(a_{16}=+0.441810000\) \(a_{17}=+0.098242523\) \(a_{18}=+0.031380924\) \(a_{19}=+0.395403787\) \(a_{20}=+0.805295718\)
\(a_{21}=+1.293140037\) \(a_{22}=+1.614852084\) \(a_{23}=+0.736741245\) \(a_{24}=-1.352492062\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.464153155\) \(a_{27}=+0.990405786\) \(a_{28}=-2.307022604\) \(a_{29}=+0.720156105\) \(a_{30}=-0.755408872\)
\(a_{31}=-0.066024254\) \(a_{32}=-0.600605715\) \(a_{33}=-0.973943729\) \(a_{34}=+0.164411613\) \(a_{35}=-0.572962839\)
\(a_{36}=+0.033765496\) \(a_{37}=-1.067885066\) \(a_{38}=+0.661719309\) \(a_{39}=+0.279938367\) \(a_{40}=+0.599260459\)
\(a_{41}=+1.365703463\) \(a_{42}=+2.164106060\) \(a_{43}=-0.581348164\) \(a_{44}=+1.737561389\) \(a_{45}=+0.008385863\)
\(a_{46}=+1.232957102\) \(a_{47}=-1.270990542\) \(a_{48}=-0.445933031\) \(a_{49}=+0.641432073\) \(a_{50}=+0.334705600\)
\(a_{51}=-0.099159335\) \(a_{52}=-0.499423203\) \(a_{53}=-1.004376766\) \(a_{54}=+1.657471814\) \(a_{55}=+0.431533746\)
\(a_{56}=-1.716769868\) \(a_{57}=-0.399093749\) \(a_{58}=+1.205201406\) \(a_{59}=-1.476800754\) \(a_{60}=-0.812810847\)
\(a_{61}=-0.223390160\) \(a_{62}=-0.110493437\) \(a_{63}=-0.024023938\) \(a_{64}=-1.446940482\) \(a_{65}=-0.124034735\)
\(a_{66}=-1.629922102\) \(a_{67}=+1.256388662\) \(a_{68}=+0.176904915\) \(a_{69}=-0.743616614\) \(a_{70}=-0.958869354\)
\(a_{71}=-0.856037803\) \(a_{72}=+0.025126580\) \(a_{73}=+0.474788257\) \(a_{74}=-1.787135559\) \(a_{75}=-0.201866427\)
\(a_{76}=+0.712002005\) \(a_{77}=-1.236264000\) \(a_{78}=+0.468484695\) \(a_{79}=+0.924659486\) \(a_{80}=+0.197583439\)
\(a_{81}=-1.018399745\) \(a_{82}=+2.285542986\) \(a_{83}=+1.164581973\) \(a_{84}=+2.328552050\) \(a_{85}=+0.043935392\)
\(a_{86}=-0.972902431\) \(a_{87}=-0.726876699\) \(a_{88}=+1.293005552\) \(a_{89}=+1.832196017\) \(a_{90}=+0.014033976\)
\(a_{91}=+0.355336468\) \(a_{92}=+1.326646989\) \(a_{93}=+0.066640401\) \(a_{94}=-2.127038261\) \(a_{95}=+0.176829949\)
\(a_{96}=+0.606210649\) \(a_{97}=+0.202082220\) \(a_{98}=+1.073454535\) \(a_{99}=+0.018093914\) \(a_{100}=+0.360139194\)

Showing 100 of 630 available coefficients

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