Properties

Level $69$
Weight $0$
Character 69.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 69 = 3 \cdot 23 \)
Weight: \( 0 \)
Character: 69.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.59261226439 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.760833817\) \(a_{3}=+0.577350269\) \(a_{4}=-0.421131902\) \(a_{5}=-1.925926808\)
\(a_{6}=+0.439267609\) \(a_{7}=+0.010690947\) \(a_{8}=-1.081245210\) \(a_{9}=+0.333333333\) \(a_{10}=-1.465310245\)
\(a_{11}=+1.134686215\) \(a_{12}=-0.243140617\) \(a_{13}=-0.567202678\) \(a_{14}=+0.008134034\) \(a_{15}=-1.111934361\)
\(a_{16}=-0.401516018\) \(a_{17}=-0.350103474\) \(a_{18}=+0.253611272\) \(a_{19}=-1.502824670\) \(a_{20}=+0.811069221\)
\(a_{21}=+0.006172421\) \(a_{22}=+0.863307644\) \(a_{23}=+0.208514414\) \(a_{24}=-0.624257213\) \(a_{25}=+2.709194071\)
\(a_{26}=-0.431546979\) \(a_{27}=+0.192450090\) \(a_{28}=-0.004502299\) \(a_{29}=+0.238329411\) \(a_{30}=-0.845997265\)
\(a_{31}=-1.723870079\) \(a_{32}=+0.775758245\) \(a_{33}=+0.655111392\) \(a_{34}=-0.266370563\) \(a_{35}=-0.020589982\)
\(a_{36}=-0.140377301\) \(a_{37}=-0.764418059\) \(a_{38}=-1.143399830\) \(a_{39}=-0.327474619\) \(a_{40}=+2.082399137\)
\(a_{41}=+0.445026843\) \(a_{42}=+0.004696187\) \(a_{43}=+0.141519333\) \(a_{44}=-0.477852564\) \(a_{45}=-0.641975603\)
\(a_{46}=+0.158644818\) \(a_{47}=-0.525074539\) \(a_{48}=-0.231815381\) \(a_{49}=-0.999885704\) \(a_{50}=+2.061246467\)
\(a_{51}=-0.202132335\) \(a_{52}=+0.238867143\) \(a_{53}=-0.642134498\) \(a_{54}=+0.146422536\) \(a_{55}=-2.185322601\)
\(a_{56}=-0.011559536\) \(a_{57}=-0.867656228\) \(a_{58}=+0.181329076\) \(a_{59}=+0.637054994\) \(a_{60}=+0.468271033\)
\(a_{61}=-0.697741107\) \(a_{62}=-1.311578652\) \(a_{63}=+0.003563649\) \(a_{64}=+0.991739125\) \(a_{65}=+1.092390844\)
\(a_{66}=+0.498430901\) \(a_{67}=-0.302257308\) \(a_{68}=+0.147439742\) \(a_{69}=+0.120385853\) \(a_{70}=-0.015665555\)
\(a_{71}=+1.714480640\) \(a_{72}=-0.360415070\) \(a_{73}=+0.695671309\) \(a_{74}=-0.581595110\) \(a_{75}=+1.564153926\)
\(a_{76}=+0.632887412\) \(a_{77}=+0.012130871\) \(a_{78}=-0.249153764\) \(a_{79}=-1.563812548\) \(a_{80}=+0.773290464\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.338591472\) \(a_{83}=-0.229020349\) \(a_{84}=-0.002599404\) \(a_{85}=+0.674273667\)
\(a_{86}=+0.107672694\) \(a_{87}=+0.137599550\) \(a_{88}=-1.226874035\) \(a_{89}=-0.500637354\) \(a_{90}=-0.488436748\)
\(a_{91}=-0.006063934\) \(a_{92}=-0.087812072\) \(a_{93}=-0.995276854\) \(a_{94}=-0.399494466\) \(a_{95}=+2.894330320\)
\(a_{96}=+0.447884232\) \(a_{97}=+1.799224189\) \(a_{98}=-0.760746857\) \(a_{99}=+0.378228738\) \(a_{100}=-1.140928054\)

Showing 100 of 700 available coefficients

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