Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 8.80707934379 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.018880438\) \(a_{4}=+0.500000000\) \(a_{5}=-1.814623902\)
\(a_{6}=-0.720457267\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.038117348\) \(a_{10}=-1.283132866\)
\(a_{11}=+1.552007177\) \(a_{12}=-0.509440219\) \(a_{13}=-1.300375147\) \(a_{14}=-0.267261242\) \(a_{15}=+1.848884797\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.315267673\) \(a_{18}=+0.026953035\) \(a_{19}=+1.202325477\) \(a_{20}=-0.907311951\)
\(a_{21}=+0.385100608\) \(a_{22}=+1.097434799\) \(a_{23}=+0.527998508\) \(a_{24}=-0.360228634\) \(a_{25}=+2.292859906\)
\(a_{26}=-0.919504084\) \(a_{27}=+0.980043418\) \(a_{28}=-0.188982237\) \(a_{29}=-0.213382679\) \(a_{30}=+1.307358977\)
\(a_{31}=+0.608269773\) \(a_{32}=+0.176776695\) \(a_{33}=-1.581309753\) \(a_{34}=-0.222927910\) \(a_{35}=+0.685863367\)
\(a_{36}=+0.019058674\) \(a_{37}=-0.721014791\) \(a_{38}=+0.850172498\) \(a_{39}=+1.324926799\) \(a_{40}=-0.641566433\)
\(a_{41}=-0.793964083\) \(a_{42}=+0.272307251\) \(a_{43}=+0.331898723\) \(a_{44}=+0.776003589\) \(a_{45}=-0.069168650\)
\(a_{46}=+0.373351325\) \(a_{47}=-0.801490290\) \(a_{48}=-0.254720110\) \(a_{49}=+0.142857143\) \(a_{50}=+1.621296787\)
\(a_{51}=+0.321220065\) \(a_{52}=-0.650187573\) \(a_{53}=-0.605989071\) \(a_{54}=+0.692995347\) \(a_{55}=-2.816309320\)
\(a_{56}=-0.133630621\) \(a_{57}=-1.225025909\) \(a_{58}=-0.150884340\) \(a_{59}=+0.964176853\) \(a_{60}=+0.924442398\)
\(a_{61}=+1.012376171\) \(a_{62}=+0.430111681\) \(a_{63}=-0.014407003\) \(a_{64}=+0.125000000\) \(a_{65}=+2.359691822\)
\(a_{66}=-1.118154850\) \(a_{67}=-0.678578128\) \(a_{68}=-0.157633837\) \(a_{69}=-0.537967351\) \(a_{70}=+0.484978638\)
\(a_{71}=+0.926350207\) \(a_{72}=+0.013476518\) \(a_{73}=-0.225505795\) \(a_{74}=-0.509834448\) \(a_{75}=-2.336150106\)
\(a_{76}=+0.601162739\) \(a_{77}=-0.586603575\) \(a_{78}=+0.936864724\) \(a_{79}=+0.339169109\) \(a_{80}=-0.453655975\)
\(a_{81}=-1.036664416\) \(a_{82}=-0.561417387\) \(a_{83}=+0.552472874\) \(a_{84}=+0.192550304\) \(a_{85}=+0.572092254\)
\(a_{86}=+0.234687838\) \(a_{87}=+0.217411439\) \(a_{88}=+0.548717400\) \(a_{89}=+1.127448543\) \(a_{90}=-0.048909622\)
\(a_{91}=+0.491495607\) \(a_{92}=+0.263999254\) \(a_{93}=-0.619754184\) \(a_{94}=-0.566739219\) \(a_{95}=-2.181768553\)
\(a_{96}=-0.180114317\) \(a_{97}=+0.719605492\) \(a_{98}=+0.101015254\) \(a_{99}=+0.059158375\) \(a_{100}=+1.146429953\)

Showing 100 of 192 available coefficients

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