Properties

Level $53$
Weight $0$
Character 53.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 53 \)
Weight: \( 0 \)
Character: 53.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.98721988657 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.456790277\) \(a_{3}=-1.613473249\) \(a_{4}=+1.122237911\) \(a_{5}=+0.043409085\)
\(a_{6}=-2.350492142\) \(a_{7}=-0.601928380\) \(a_{8}=+0.178075001\) \(a_{9}=+1.603295926\) \(a_{10}=+0.063237932\)
\(a_{11}=-0.515234049\) \(a_{12}=-1.810700849\) \(a_{13}=-0.765016731\) \(a_{14}=-0.876883412\) \(a_{15}=-0.070039397\)
\(a_{16}=-0.862819982\) \(a_{17}=-1.180356829\) \(a_{18}=+2.335665916\) \(a_{19}=+1.679853099\) \(a_{20}=+0.048715320\)
\(a_{21}=+0.971195340\) \(a_{22}=-0.750587952\) \(a_{23}=+0.129978957\) \(a_{24}=-0.287319250\) \(a_{25}=-0.998115651\)
\(a_{26}=-1.114468935\) \(a_{27}=-0.973401838\) \(a_{28}=-0.675506848\) \(a_{29}=-0.166591568\) \(a_{30}=-0.102032712\)
\(a_{31}=+0.982462564\) \(a_{32}=-1.435022761\) \(a_{33}=+0.831316355\) \(a_{34}=-1.719532352\) \(a_{35}=-0.026129160\)
\(a_{36}=+1.799279471\) \(a_{37}=-1.474255598\) \(a_{38}=+2.447193661\) \(a_{39}=+1.234334031\) \(a_{40}=+0.007730073\)
\(a_{41}=+1.744982883\) \(a_{42}=+1.414827928\) \(a_{43}=-0.613666641\) \(a_{44}=-0.578215183\) \(a_{45}=+0.069597608\)
\(a_{46}=+0.189352080\) \(a_{47}=-0.656278327\) \(a_{48}=+1.392136959\) \(a_{49}=-0.637682225\) \(a_{50}=-1.454045176\)
\(a_{51}=+1.904474168\) \(a_{52}=-0.858530778\) \(a_{53}=+0.137360564\) \(a_{54}=-1.418042333\) \(a_{55}=-0.022365838\)
\(a_{56}=-0.107188397\) \(a_{57}=-2.710398038\) \(a_{58}=-0.242688977\) \(a_{59}=+0.650164682\) \(a_{60}=-0.078600866\)
\(a_{61}=-1.841170319\) \(a_{62}=+1.431241911\) \(a_{63}=-0.965069320\) \(a_{64}=-1.227707224\) \(a_{65}=-0.033208676\)
\(a_{66}=+1.211053582\) \(a_{67}=+1.338933583\) \(a_{68}=-1.324641182\) \(a_{69}=-0.209717569\) \(a_{70}=-0.038064706\)
\(a_{71}=-0.466734871\) \(a_{72}=+0.285506923\) \(a_{73}=+0.843438941\) \(a_{74}=-2.147681221\) \(a_{75}=+1.610432903\)
\(a_{76}=+1.885194833\) \(a_{77}=+0.310133996\) \(a_{78}=+1.798165814\) \(a_{79}=-0.758808351\) \(a_{80}=-0.037454226\)
\(a_{81}=-0.032738100\) \(a_{82}=+2.542074097\) \(a_{83}=-1.489346524\) \(a_{84}=+1.089912230\) \(a_{85}=-0.051238209\)
\(a_{86}=-0.893983596\) \(a_{87}=+0.268791039\) \(a_{88}=-0.091750304\) \(a_{89}=-0.784164314\) \(a_{90}=+0.101389119\)
\(a_{91}=+0.460485282\) \(a_{92}=+0.145867313\) \(a_{93}=-1.585177066\) \(a_{94}=-0.956059885\) \(a_{95}=+0.072920885\)
\(a_{96}=+2.315370837\) \(a_{97}=+0.952547348\) \(a_{98}=-0.928969265\) \(a_{99}=-0.826072651\) \(a_{100}=-1.120123224\)

Showing 100 of 546 available coefficients

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