Properties

Level $65$
Weight $0$
Character 65.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 65 = 5 \cdot 13 \)
Weight: \( 0 \)
Character: 65.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.85408138931 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.358211588\) \(a_{3}=-0.650946365\) \(a_{4}=+0.844738718\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.884122896\) \(a_{7}=-0.214950645\) \(a_{8}=+0.210877673\) \(a_{9}=-0.576268830\) \(a_{10}=+0.607410688\)
\(a_{11}=-0.995008999\) \(a_{12}=-0.549879597\) \(a_{13}=-0.277350098\) \(a_{14}=+0.291948456\) \(a_{15}=+0.291112064\)
\(a_{16}=-1.131155217\) \(a_{17}=+1.420314266\) \(a_{18}=+0.782695003\) \(a_{19}=+0.326719663\) \(a_{20}=-0.377778639\)
\(a_{21}=+0.139921341\) \(a_{22}=+1.351432752\) \(a_{23}=+0.474745466\) \(a_{24}=-0.137270055\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.376700117\) \(a_{27}=+1.026066465\) \(a_{28}=-0.181577132\) \(a_{29}=-1.222162344\) \(a_{30}=-0.395391779\)
\(a_{31}=-0.092338431\) \(a_{32}=+1.325470450\) \(a_{33}=+0.647697491\) \(a_{34}=-1.929087295\) \(a_{35}=+0.096128851\)
\(a_{36}=-0.486796593\) \(a_{37}=-0.535417897\) \(a_{38}=-0.443754433\) \(a_{39}=+0.180540038\) \(a_{40}=-0.094307362\)
\(a_{41}=+1.913912894\) \(a_{42}=-0.190042786\) \(a_{43}=-0.804434812\) \(a_{44}=-0.840522626\) \(a_{45}=+0.257715256\)
\(a_{46}=-0.644804793\) \(a_{47}=+0.675803334\) \(a_{48}=+0.736321376\) \(a_{49}=-0.953796220\) \(a_{50}=-0.271642318\)
\(a_{51}=-0.924548408\) \(a_{52}=-0.234288366\) \(a_{53}=+0.222615989\) \(a_{54}=-1.393615363\) \(a_{55}=+0.444981552\)
\(a_{56}=-0.045328292\) \(a_{57}=-0.212676977\) \(a_{58}=+1.659955057\) \(a_{59}=+1.218771693\) \(a_{60}=+0.245913632\)
\(a_{61}=+1.022140402\) \(a_{62}=+0.125415127\) \(a_{63}=+0.123869357\) \(a_{64}=-0.669114108\) \(a_{65}=+0.124034735\)
\(a_{66}=-0.879710237\) \(a_{67}=+0.078456267\) \(a_{68}=+1.199794452\) \(a_{69}=-0.309033835\) \(a_{70}=-0.130563319\)
\(a_{71}=+0.995283773\) \(a_{72}=-0.121522230\) \(a_{73}=+0.793286793\) \(a_{74}=+0.727210792\) \(a_{75}=-0.130189273\)
\(a_{76}=+0.275992749\) \(a_{77}=+0.213877826\) \(a_{78}=-0.245211572\) \(a_{79}=-1.896012031\) \(a_{80}=+0.505867991\)
\(a_{81}=-0.091645405\) \(a_{82}=-2.599498671\) \(a_{83}=-0.805626948\) \(a_{84}=+0.118196974\) \(a_{85}=-0.635183850\)
\(a_{86}=+1.092592683\) \(a_{87}=+0.795562135\) \(a_{88}=-0.209825182\) \(a_{89}=+0.200615940\) \(a_{90}=-0.350031847\)
\(a_{91}=+0.059616582\) \(a_{92}=+0.401035876\) \(a_{93}=+0.060107366\) \(a_{94}=-0.917883919\) \(a_{95}=-0.146113475\)
\(a_{96}=-0.862810171\) \(a_{97}=+0.945339358\) \(a_{98}=+1.295457079\) \(a_{99}=+0.573392672\) \(a_{100}=+0.168947744\)

Showing 100 of 630 available coefficients

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