Properties

Level $45$
Weight $0$
Character 45.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 45 = 3^{2} \cdot 5 \)
Weight: \( 0 \)
Character: 45.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.11891067053 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.357868384\) \(a_{3}=+0.000000000\) \(a_{4}=+0.843806549\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.746336362\) \(a_{8}=+0.212090149\) \(a_{9}=+0.000000000\) \(a_{10}=-0.607257202\)
\(a_{11}=-0.178980397\) \(a_{12}=+0.000000000\) \(a_{13}=-0.009669162\) \(a_{14}=-2.371294935\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.131797057\) \(a_{17}=+1.265271899\) \(a_{18}=+0.000000000\) \(a_{19}=+1.235126395\) \(a_{20}=+0.377361761\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.243031822\) \(a_{23}=-0.160540255\) \(a_{24}=+0.000000000\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.013129449\) \(a_{27}=+0.000000000\) \(a_{28}=+1.473570059\) \(a_{29}=+0.626366779\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.233291000\) \(a_{32}=+1.324741292\) \(a_{33}=+0.000000000\) \(a_{34}=-1.718072709\) \(a_{35}=+0.780985364\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.234314573\) \(a_{38}=-1.677139082\) \(a_{39}=+0.000000000\) \(a_{40}=+0.094849598\)
\(a_{41}=-0.908867833\) \(a_{42}=+0.000000000\) \(a_{43}=-0.274301491\) \(a_{44}=-0.151024831\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.217992536\) \(a_{47}=-0.930734101\) \(a_{48}=+0.000000000\) \(a_{49}=+2.049690691\) \(a_{50}=-0.271573677\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.008158902\) \(a_{53}=+0.467430404\) \(a_{54}=+0.000000000\) \(a_{55}=-0.080042467\)
\(a_{56}=+0.370380740\) \(a_{57}=+0.000000000\) \(a_{58}=-0.850523646\) \(a_{59}=-1.477917511\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.741384929\) \(a_{62}=+1.674646857\) \(a_{63}=+0.000000000\) \(a_{64}=-0.667027260\) \(a_{65}=-0.004324180\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.238348596\) \(a_{68}=+1.067644714\) \(a_{69}=+0.000000000\) \(a_{70}=-1.060475334\)
\(a_{71}=+0.829330127\) \(a_{72}=+0.000000000\) \(a_{73}=-0.861207160\) \(a_{74}=-0.318168351\) \(a_{75}=+0.000000000\)
\(a_{76}=+1.042207741\) \(a_{77}=-0.312559975\) \(a_{78}=+0.000000000\) \(a_{79}=-0.819001733\) \(a_{80}=-0.506155031\)
\(a_{81}=+0.000000000\) \(a_{82}=+1.234122895\) \(a_{83}=+1.305626787\) \(a_{84}=+0.000000000\) \(a_{85}=+0.565846795\)
\(a_{86}=+0.372465322\) \(a_{87}=+0.000000000\) \(a_{88}=-0.037959979\) \(a_{89}=-0.180244924\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.016885608\) \(a_{92}=-0.135464918\) \(a_{93}=+0.000000000\) \(a_{94}=+1.263814410\) \(a_{95}=+0.552365316\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.662626900\) \(a_{98}=-2.783210186\) \(a_{99}=+0.000000000\) \(a_{100}=+0.168761310\)

Showing 100 of 462 available coefficients

Rows: Cols: